Investigation into the Effects of Tool Geometry and Metal Working Fluids on Tool 
Forces and Tool Surfaces during Orthogonal Tube Turning of Aluminum 6061 Alloy 
 
by 
 
Prajwal Swamy Sripathi 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
 Auburn University 
 in partial fulfillment of the 
 requirements for the Degree of 
 Master of Science 
 
 
Auburn, Alabama 
December 18, 2009 
 
 
 
 
Keywords: metal cutting, metal working fluids, cutting parameters 
 
 
Copyright 2009 by Prajwal Sripathi 
 
 
Approved by 
 
Lewis N Payton, Chair, Associate Research Professor of Mechanical Engineering 
J T Black, Professor Emeritus of Industrial and Systems Engineering 
Robert L Jackson, Associate Professor of Mechanical Engineering 
 ii
Abstract 
 
 
Orthogonal Metal Cutting has evolved as a significant way of analyzing the 
mechanics involved in the art of metal cutting.  An orthogonal tube turning apparatus was 
constructed and validated.    The instrument was used to investigate the effects of back 
rake angle, uncut chip thickness and cutting environments on the tool forces generated 
during tube turning.    Surface roughness was used to parameterize tool surface finish for 
cutting each factor level combination of the experiment.  This work empirically 
documents the variation of tool forces and tool surface roughness under the influence of 
various cutting parameters. Force ratios and shear plane angles are calculated using the 
classical metal cutting equations, analyzing the behavioral patterns and interdependence 
of cutting forces, tool surface roughness and shear angle.  
 
 
 
 
 
 
 
 
 
 
 iii
Acknowledgements 
 
 
It is with profound gratitude that I would like to thank my advisor Dr. Lewis N 
Payton for his incredible support and guidance. I am highly indebted to him for his 
continuous encouragement, advice and suggestions involving my academic course work 
and research. His support also includes funding for this research. 
I would like to convey my heartfelt thanks to Dr. J T Black for supporting me 
with my academics and research throughout my schooling at Auburn University. His 
constant encouragement, motivation and counseling have been major factors responsible 
for the successful completion of my work. 
I would also like to thank Dr. Robert L Jackson for his advice and encouragement 
with my research work. Thanks to XYRIS4000CL Taicaan and John McBride at the 
University of Southampton for lending the Taicaan confocal Laser Proflometer used to 
make the measurements. 
Special thanks to Namo Pankaj Vijayakumar for his invaluable assistance and 
patience in helping me carry out my experiments. I would also like to thank my 
colleagues Sakthivael Kandaswaamy, Suresh Muthusamy, Alan Dunlavy, John David 
Jenkins and Eileen Vega Ortiz for their support, advice, guidance and suggestions with 
my work.  
Finally, words alone cannot express the thanks I owe to my parents Mr. Sripathi N 
G and Mrs. Sujatha H and to my sister Pruthvi Sripathi for their invaluable support and 
guidance, special thanks to them for being a never ending source of inspiration in my life. 
 iv
Table of Contents 
 
Abstract??????????????????????????????? ...ii 
Acknowledgements??????????????????????????....iii 
List of Figures??????????????????????????..............v 
List of Tables?????????????????????????????viii 
Nomenclature?????????????????????????????...x 
1. Introduction???????????????????????????..1 
2. Scope and Objectives???????????????????????...5 
3. Literature Review?????????????????????.................6 
4. Description of Equipment?????????????????????..18 
5. Construction of the Orthogonal Tube Turning Apparatus?????????.25 
6. Instrument validation and Sample size determination??????????...38 
7. Statistical Design of Experiment (DOE)????????????................44 
8. Results and Discussion??????????????????..................50 
9. Conclusion???????????????????????????.79 
10. Scope for future work??????????????????....................81 
References??????????????????????????????..83 
Appendices??????????????????????????????.86 
 
 
 
 v
List of Figures 
 
Figure 1: Oblique Machining ???????????????????????..2 
Figure 2: Orthogonal Tube Turning?????????????????????.3 
Figure 3: Orthogonal Metal Cutting Model??????.???????????....3 
Figure 4: Orthogonal Tube Turning????????????????????.....7 
Figure 5: Merchant Circle diagram illustrating the Orthogonal Force System????...8 
Figure 6: Summary of papers by keywords for this literature review????????.8 
Figure 7: HAAS Two axis Lathe?????????????????????...19 
Figure 8: KISTLER 3 Component Dynamometer??????????????.....21 
Figure 9: KISTLER Charge Amplifiers (Model 5004)????????????......21 
Figure 10: National Instruments USB 6008?????????????????...22 
Figure 11: Vortec Cold Air Gun?????????????????????....22 
Figure 12: Kool Mist Spray Coolant Generator????????????????.23 
Figure 13: TaiCaan Xyris series Surface profiler with a LT-8010 Sensor head, 
                  LT-V201 Camera unit and a LT-8105 Controller unit?...??????.....23 
Figure 14: Overall Network schematic of the Experimental set up?...??????....24
Figure 15: Geometry of Orthogonal Tube Turning??????????????...25 
Figure 16: Dynamometer and Tool holder mounting assembly??????????26 
Figure 17: Top block of the Tool holder???????????????????27 
Figure 18: Bottom block of the Tool holder?????????????????..28
 vi
Figure 19: Charge amplifiers and USB DAQ system module connected to the LAB  
                  VIEW 8.2 system Software???????????????????..29 
Figure 20: Block diagram of the program in LAB VIEW 8.2 Software??????....30 
Figure 21: Dry Machining????????????????????????.31 
Figure 22: Turning at Cold Compressed Air Environment???????????...32 
Figure 23: Turning at Nitrogen gas Environment???????????????..33 
Figure 24: Turning at Spray Coolant Environment?.......................................................34 
Figure 25: Area being scanned on top face of a ? x ? x 5 inch tool????????35 
Figure 26: Laser Beam Path???????????????????????..35  
Figure 27: Enlarged camera view of the cutting edge?????????????...37 
Figure 28: Power Curve to achieve 95% statistical Power????????????43 
Figure 29: Machining a 30 degree tool on a HARIG 618 Automatic Surface Grinder?.48 
Figure 30: Selected Rake Angles machined on a Square Section HSS Tool?????.48 
Figure 31: Variation of Tool Forces with time????????????????..50 
Figure 32: Main Effects Plot for Thrust Force response?????????????54 
Figure 33: Interaction Plot for Thrust Force response?????????????...54 
Figure 34: Main Effects Plot for Cutting Force response????????????..56 
Figure 35: Interaction Plot for Cutting Force response?????????????.56 
Figure 36: Main Effects Plot for Friction Force response????????????.58 
Figure 37: Interaction Plot for Friction Force response?????????????.58 
Figure 38: Main Effects Plot for Normal Force response????????????..60 
Figure 39: Interaction Plot for Normal Force response?????????????.60 
Figure 40: Main Effects Plot for F/N Ratio response........................................................62
 vii
Figure 41: Interaction Plot for F/N Ratio response???????????????62 
Figure 42: Main Effects Plot for Shear Force along Shear Plane?????????..64 
Figure 43: Interaction Plot for Shear Force along Shear Plane??????????.64 
Figure 44: Main Effects Plot for Normal Force along Shear Plane????????...66 
Figure 45: Interaction Plot for Normal Force along Shear Plane?????????..66 
Figure 46: Main Effects Plot for Fs/Fn Ratio response?????????????.68 
Figure 47: Interaction Plot for Fs/Fn Ratio response??????????????.68 
Figure 48: Main Effects Plot for Shear Plane Angle??????????????.70 
Figure 49: Interaction Plot for Shear Plane Angle???????????????.70 
Figure 50: Main Effects Plot for Friction Angle????????????????72 
Figure 51: Interaction Plot for Friction Angle????????????????...72 
Figure 52: Main Effects Plot for Shear Stress????????????????...74 
Figure 53: Interaction Plot for Shear Stress?????????????????...74 
Figure 54: Main Effects Plot for Tool Surface Roughness?????????..??..76 
Figure 55: Interaction Plot for Tool Surface Roughness????????????...76 
Figure 56: Variation of Tool Surface Roughness with Normal Force???????...78 
 
 
 
 
 
 
 viii
List of Tables 
 
 
Table 1: Summary of variation of response with input parameters???????.......17 
Table 2: Thrust force data for Repeatability Analysis?????????????...39 
Table 3: Cutting force data for Repeatability Analysis?????????????.39 
Table 4: Repeatability Analysis??????????????????????.40 
Table 5: Thrust force data for Sensitivity test?????????????????41 
Table 6: Cutting force data for Sensitivity test????????????????..41 
Table 7: Sensitivity test Analysis?????????????????????...42 
Table 8: Input parameters for Tube Turning Experiments???????????....44 
Table 9: Evaluation of hardness of Aluminum 6061?????????????.....46 
Table 10: Factor Level combination of Principal Experiment??????????...49 
Table 11: Thrust force and Cutting force raw data?????????????........51 
Table 12: Calculated results from the force response and chip thickness data????..52 
Table 13: Force Ratios Calculation data???????????????????53 
Table 14: Surface Roughness, Shear Angle and Shear Stress Calculation data???....53 
Table 15: ANOVA Table for Thrust Force response??????????????55 
Table 16: ANOVA Table for Cutting Force response?????????????...57 
Table 17: ANOVA Table for Friction Force response?????????????..59 
Table 18: ANOVA Table for Normal Force response?????????????...61 
Table 19: ANOVA Table for F/N Ratio???????????????????63 
Table 20: ANOVA Table for Shear Force along Shear Plane??????????...65
 ix
Table 21: ANOVA Table for Normal Force along Shear Plane??????????67 
Table 22: ANOVA Table for Fs/Fn Ratio??????????????????.69 
Table 23: ANOVA Table for Friction Angle?????????????????.71 
Table 24: ANOVA Table for Friction Angle?????????????????.73 
Table 25: ANOVA Table for Shear Stress??????????????????75 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x
Nomenclature 
 
F
c         
Cutting Force; Force component acting in direction of motion of tool. 
F
t          
Thrust Force; Force component acting in direction nomal to shear plane. 
F        Frictional Force upon Chip 
N       Normal Force upon Chip 
?        Friction Co efficient 
F
s          
Shear Force on the Plane 
F
n          
Normal Force on the Plane 
t         Uncut Chip Thickness (also referred to as Feed Rate) 
t
c   
Cut Chip Thickness 
t/t
c         
Chip Thickness Ratio 
A
s          
Area of the Shear Plane 
?
s           
Shear Stress on the Shear Plane 
?         Rake Angle 
?         Friction Angle 
?       Shear Plane Angle 
?        Shear Front Angle 
V        Cutting Velocity 
Vc      Chip Velocity 
Vs       Shear Velocity 
HPs     Specific Horse Power 
CHAPTER 1 
INTRODUCTION 
 
The process of material removal is one of the most extensively used mechanical 
processes in the industry. The material removal is by a cutting edge in oblique machining 
processes such as drilling, milling, turning, shaping where in most of these cases the 
cutting edge is not perpendicular to the cutting motion. In order to simplify the 
mathematical models, a two force component process called orthogonal machining has 
been developed and used extensively by metal cutting researchers.  M.E.Merchant [1] in 
1944 defined the orthogonal tube turning process as characterized by following 
assumptions, 
? The plane of the cutting tool is parallel to the plane of the material being cut. 
? The cutting velocity vector and the cutting edge are perpendicular, with the width 
of the cutting tool more than the width of the work piece. 
? The plane of the cutting edge is perpendicular to the direction of motion, 
generating a plane surface as the work moves beyond the tool with a constant 
depth of cut. 
? The cutting edge is perfectly sharp and has no contact on the clearance face. 
? There is relative motion between work and tool with continuous chip formation 
with no built up edge formation. 
? The shear and normal stress along the shear plane and the tool are uniform. 
 1
Researchers use orthogonal machining for research purposes since it is easy to model and 
obtain the required forces. Orthogonal machining is usually performed [2] on 
        1.   Metal plates at low speed 
2. Tube turning at moderate speed 
3. Plate turning at high speed 
Figure 1 shows the motion of the tool and the force system involved in the 
oblique machining. It can be modified to form a tube turning orthogonal system as in 
Figure 2 for the ease of understanding, modeling and analyzing the force components.  
 
Figure 1: Oblique Machining [2] 
F
c
 = Cutting Force; F
t
 = Thrust Force; F
r
 = Radial Force; V = Velocity of Cut;  
t = Uncut Chip Thickness; t
c
 = Cut Chip Thickness; V
c
 = Cut Chip Velocity. 
 
The process chip formation is influenced by various parameters including 
workpiece material, cutting tool material, feed rate, cutting speed, tool rake angle, depth 
 2
of cut and cutting environment. Extensive research has been carried out in order to 
understand the effects of these parameters on the cutting forces and tool wear.  
 
Figure 2: Orthogonal Tube Turning (Top View) 
 
Orthogonal tube turning experiments have also been carried out to measure the 
variables such as chip geometry, chip thickness, cutting forces, cutting temperatures from 
which one can calculate shear plane angle, strain and strain rate.  
 
 
Figure 3: Orthogonal Metal Cutting Model 
 3
 4
Historically, numerous models have been proposed for the parametric evaluation 
of the mechanisms of chip formation detailed in Figure. 2 including the force system 
involved in cutting process, the shear plane angle, ? and the tool wear. None of the 
models successfully explains the variation of tool forces and tool wear mechanism under 
the influence of different cutting parameters. The following work will address the 
construction and validation of an orthogonal tube turning set up on a 2 axis HAAS TL 42 
lathe at Auburn University in order to  explore the effects of cutting parameters like rake 
angle ?, feed rate and cutting environment on the tool forces,surface roughness and shear 
angle.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CHAPTER 2 
SCOPE AND OBJECTIVES 
 
The main aim of the experiment was to develop a better understanding of the 
force system involved in the Orthogonal Tube Turning process, which seems to be the 
least well studied of the orthogonal turning experimental setups.  The variation of these 
forces under different cutting environments and the progressive tool surface roughness 
were studied to develop an alternative yet efficient cooling system at the tool chip 
interface where almost all the energy produced by the plastic deformation of the material 
is converted into heat. The objectives of the experiment included: 
1) A comprehensive review of the available orthogonal turning processes to include:  
a. Previous force measurements. 
b. Previous tool surface measurements.         
2) Construct an experimental set up capable of accomplishing following goals: 
a. Measure the cutting forces generated during tube turning. 
b. Measure the tool surface roughness under different cutting conditions. 
c. Calculate the chip thickness ratio and onset of shear plane angle.  
d. Validate statistical repeatability and statistical sensitivity of the 
experiments. 
e. Achieve a statistical sampling power of 95% with 5 replications. 
3) Develop a better understanding of the orthogonal tube turning process. 
4) Design an experiment using ANOVA with the orthogonal tube turning equipment. 
5) Compare resulting data to previous model.
 5
CHAPTER 3 
LITERATURE REVIEW 
  
Overview 
The principle of orthogonal machining is to observe variations in the metal cutting 
process for different parameters during the using a 2 dimensional geometry rather than 
the regular 3 dimensional geometry called oblique machining used in manufacturing 
environments.  Orthogonal machining geometries can be attained utilizing a mill, a 
shaper or a lathe. In the lathe orthogonal machining can be done on a tube at normal 
speeds and on a disc at very high speeds with the tool feed in the direction of facing.   
The tool in both cases is wider than the piece being machined. 
  The tube to be machined is fastened firmly within the chuck. The tool is mounted 
on a dynamometer which is used for tube machining to measure the forces involved in 
the machining. The tool feeds perpendicular to the tube wall to generate a cutting force 
and a normal (or thrust) force. The tool?s direction of motion eliminates the radial force 
or brings it down to near zero. The tube can be created from a solid through a grooving 
operation in order to increase the rigidity.   This allows the use of a tailstock to support 
the center of the workpiece. This set-up is commonly done with high tensile strength 
materials such as steel, sacrificing long duration runs.   Figure 3 shows a schematic of 
orthogonal tube turning on a lathe [2]. The jaws may be insulated to protect the work.
 6
 
 
 
 
 
 
 
Figure 4: Orthogonal Tube Turning [2] 
 
 
Dr. M.E. Merchant?s [1] classic force diagram for orthogonal machining is depicted 
in Figure 4.   In Figure 4, the cutting force F
c
 is the force generated by the motion of the work 
piece with respect to the tool and thrust force F
t
 is the force generated perpendicular to the 
point of contact of the tool and work piece. Fc and Ft form the resultant force R. These forces 
are measured with the dynamometer. The resultant force can be resolved into two 
components; the shearing force along the onset of shear plane, F
s
, and a force normal to the 
onset of shear plane, F
n
. The resultant force can also be resolved into F, the force parallel to 
the rake face and N, a force normal to the tool face. The onset of shear plane angle is 
represented as ? and the friction angle as ? [3].   The cutting force and the thrust force are 
easily captured by the dynamometer setup shown in Figure 3.    
Figure 5 summarizes the papers reviewed chronologically within this chapter by 
broad subject area for the reader.   This should facilitate area reviews by future researchers as 
well. The papers reviewed within this work helped frame and support the objectives of this 
thesis.   A detailed discussion of the many orthogonal machining models is precluded here 
but available through other sources [3, 22]. 
 7
Figure 5: Merchant Circle diagram illustrating the Orthogonal Force System 
 
 
Figure 6:  Summary of papers by keywords for this literature review 
 8
Chronological Review of Papers 
The forces involved in machining processes are affected by parameters like feed, 
cutting speed, tool rake angle, depth of cut and cutting environment.  An instrument 
designed to collect Orthogonal Tube Turning data must yield results that are consistent 
with the published literature observations as the experimentalist varies the cutting 
parameters (feed, tool rake, etc) and environment (dry, wet, etc). 
Lee and Shaffer [4] in 1951 developed a slip line theory in which the chip 
formation is considered where the forces exerted by the tool are transmitted to the shear 
plane and in two dimensions; shear plane is the cut along which the tangential velocity is 
discontinuous. By applying this theory a plastic zone is assumed to exist within the chip 
bounded by shear plane, tool face and an imaginary boundary across which no stress is 
transmitted. This state can be represented on a Mohr?s circle where the circle passes 
through the origin and the radius of the circle is equal to the shear strength since it 
assumes that the shear stress and normal stress are zero along the imaginary boundary. 
The angle between the slip line and the tool face depends on the friction on the tool face. 
It is assumed that sticking happens when the friction angle is larger than 45
o
.  
Rowe and Smart [5] in 1963 conducted experiments to show the importance of 
oxygen in dry machining environment. To examine this, machining was carried out in a 
vacuum chamber and was compared against oxygen environment. They used an 18
o
 rake, 
6
o
 clearance high speed steel tool and a depth of cut 0.003 inch/rev on 0.15% carbon 
steel. Experiments revealed that the pure oxygen provides lower cutting forces when 
compared to a vacuum chamber or a normal atmosphere. It is also explained that a jet of 
 9
oxygen directed at the cutting tool edge decreases the cutting force as against the 
atmospheric air.  
Kovacevic, Cherukathota and Mazurkiewicz [6] in 1994 evaluated the 
effectiveness of high pressure water jet assisted cooling system in terms of cutting force, 
surface finish and tool wear during milling a stainless steel tubing. Water jets were 
delivered at high pressure through a nozzle onto a tool chip interface through the tool 
rake face. The tool forces tend to decrease drastically with the increase in water pressure. 
A smooth tool chip contact surface was achieved with the help of water jet cooling 
because of the absence of high shearing forces as compared to flood coolant. The 
reduction in tool wear was observed due to the reduced tool chip interface resulting from 
the fragmentation of the chip by the impinging jet. 
Klocke and Eisenblatter [7] in 1997 presented the dry machining techniques for 
cast iron, steel, super alloys and titanium. The work presented a deterministic way of 
using the cutting parameters to reduce heat generated at the tool chip interface by 
reducing the friction. The control of chip formation was found to be of prime importance 
as it has significant effects on machining temperature.  
Huang and Chen [8] in 1999 found that the temperature and force involved in 
machining increased with the increase in depth of cut and contact length of the tool/chip 
interface. They also found that the change in force due to the change in contact length of 
the tool chip interface is accompanied by the change in shear angle to match the change 
in resultant force. It is further explained that the shear angle becomes small as the 
deformation of the chip reduces thus reducing the cutting forces.  
 10
Sreejith and Ngoi [9] in 1999 presented the significance of dry machining in the 
near future and the cutting tool requirements for the same. It is stated that the cutting 
fluids has been greatly reduced due to the increase in use of mist coolant lubrication 
which is found to cause serious respiratory effects on the operator. This study insists on 
the use of cemented carbide, ultra-hard tool materials such as diamond and cubic boron 
nitride which produces better machined surfaces with remarkable increase in tool life due 
to the extremely high ?hot? hardness of the tool materials. 
Marghitu, Bogdan and Nicolae [10] in 2000 proposed a non-linear dynamics 
approach for the analysis of cutting and thrust force data obtained during orthogonal 
turning processes. They conducted turning operations on various materials like 
aluminum, ductile cast iron and grey cast iron.  After applying several non-linear 
dynamic tools to determine the type of time evolution in terms of periodicity or non-
periodicity of the forces, it was concluded that the orthogonal turning of aluminum work 
pieces is more stable than ductile cast iron and grey cast iron and produces a stable force 
response.  
Grzesik [11] in 2000 investigated the influence of thin hard coatings on frictional 
behavior during the orthogonal turning process. During the experiment he was able to 
observe a visual difference at the tool chip contact area for different friction forces and 
was more pronounced in TiC/TiN coatings. The reduction in the friction forces suggested 
that the energy required in overcoming friction and shearing is less, where as the 
tangential force decreased intensively with increase in cutting speed. The reduction of 
friction force is probably due to an intensive thermal softening in the shearing zone. The 
reduction of contact area at higher speeds can intensify the thermal softening of the 
 11
material. Two mechanisms that influence he contact stress were clarified in this research. 
One is reduction of the contact area and the other is intense thermal softening of the work 
at the interface. He also concluded that the interplay between mechanical stress at rake 
and thermal energy between the chip and tool is a key factor influencing the surface 
temperature of the tool.  
Vieira, Machado and Ezugwu [12] in 2001 studied the cooling ability of different 
cutting fluids in comparison with dry machining. During the machining of AISI 8640 
steel bars using carbide inserts an increase in the tool life was achieved under dry 
machining conditions as compared to other synthetic coolant environments. This was 
explained by the fact that dry machining generated higher cutting temperature leading to 
decrease in shear strength of the work material thus reducing the power consumption and 
eventually causing a reduction in tool wear. However their recorded surface roughness 
values under various cutting environments showed a random behavior with time. 
Paul and Chattopadhyay [13] in 2001 investigated the beneficial effects of 
cryogenic cooling over dry and wet machining. They used liquid nitrogen jets on the tool 
wear surface and they found the forces involved in machining were less and the surface 
finish was better as against dry machining. 
Diniz and Micaroni [14] in 2002 conducted experiments to remove the use of 
cutting fluid from a finish turning process without harming the tool life by increasing the 
feed and tool nose radius and decreasing the cutting speed. In turning a 1045 steel using 
carbide inserts under large feeds, tool life for dry cutting gets closer to that of wet turning 
where in synthetic oil with 6% concentration in water was used. With the increase in 
feed, heat generated at the tool chip interface increased, but the surface area on the tool to 
 12
dissipate this heat also increased. This also resulted in decrease in specific cutting force. 
It is further concluded that with the increase in tool nose radius, the surface area 
dissipating the heat increases making the cooling of cutting zone not so necessary. 
Cakir et al [15] in 2004 investigated the effects of cutting fluids to provide 
quantitative results about the cutting force, thrust force and the surface roughness. A 5% 
emulsion type cutting fluid was used as liquid coolant and compressed oxygen, nitrogen 
and carbon dioxide gas stored in cylinders at their normal temperatures were used. They 
used tubes ending with nozzles and fitted with suitable pressure regulators to direct the 
gases and the coolant at the cutting edge of the tool.    The response curve of the mean 
cutting force and the thrust force showed that all gaseous and flood coolant is different 
from the dry cutting and also increases with increase in feed. Later Cakir analyzed the 
response of the shear plane angle under varying depth of cut. This showed an appreciable 
increase in the shear angle in the gaseous and flood coolant environment leading to 
smaller shear area and reduced cutting forces as compared to dry cutting environment. 
Although the effect of feed was obvious on the surface roughness of the machined parts 
the investigation concluded that the dry machining produced the highest value of 
roughness then wet machining.  
Saoubi and Chandrashekaran [16] in 2004 investigated the effect of tool micro-
geometry and temperature on coated tools. During their investigation they found that 
machining parameters chosen has an effect on temperature. An increase in cutting speed 
or feed resulted in the increase in the temperature. It was noted that the maximum 
temperature moved closer to the tip of the tool as cutting speed increased and away as the 
feed increased. The material hardness as well had an effect on the temperature. This may 
 13
be explained by the fact that harder the materials, smaller will be the plastic deformation 
zone and the size of tool chip contact length.   
Saglam, Yaldiz and Unsacar [17] in 2005 investigated the effect of tool geometry 
on the cutting forces and tool temperature. During machining large amount of energy is 
converted into heat energy considerably on the shear plane, rake face and clearance face. 
In orthogonal machining, the cutting is assumed to be uniform along the cutting edge; 
hence it is a two dimensional plane strain deformation. The cutting forces are exerted 
only in the direction of velocity and uncut chip. Rake angle determines the tool/chip 
contact area. They found that with the increase in the rake angle from 0
o
 up to 20
o
 has a 
positive effect on the tool by increasing the shear plane angle causing the reduction in the 
force system. But increasing beyond a point affects the tool?s performance and 
accelerates tool wear. Smaller positive rake angles leaves a better finish but excessive 
positive angle weakens the tool causing tool breakage. The optimal rake angle was 
obtained as 12
o
. 
Kalyankumar and Choudhury [18] in 2007 investigated the effects of cryogenic 
cooling on tool wear and high frequency dynamic cutting forces generated during high 
speed machining of stainless steel. They observed from their experiments that the cutting 
force decreased with increase in cutting speed since the co-efficient of friction at the tool 
chip interface decreases and the shear plane angle increases, decreasing the area of 
shearing. They also found that the increase in feed and depth of cut increased the cutting 
force. Due to the increase in depth of cut and feed, the material removal rate also 
increases eventually the rate of plastic deformation and hence the cutting force increases. 
With the increase in cutting speed, higher cutting temperature and shortened contact area 
 14
were observed. As a result the temperature concentration moved towards the tip of the 
tool resulting in the reduction of tool strength and increased tool wear. They concluded 
that the cutting force and tool wear was considerably less using the cryogenic 
environment compared to a dry environment as well as tool wear. 
Pujana, Azarolla and Villar [19] in 2008 developed an in-process high speed 
photography for orthogonal turning to measure strain and strain rates. The work piece 
was micro-scale grid printed by the process of photochemical milling. They calculated 
the strain and strain rate manually based on the grid pattern. It was observed that the 
strain decreased with an increase in cutting speed and shear angle. They also noted that 
the chip topology for the working conditions they chose were not uniform. The chip 
formation of 42CrMo4 they observed was defined as a random process between serrated, 
transitional and continuous chip.  
Stanford, Lister and Kibble [20] in 2008 studied the effects of cutting forces and 
tool wear under different cutting conditions. The behavior of the responses were derived 
by using a 4% dilution semi synthetic flood coolant, compressed air (20% oxygen at 0.27 
MPa), Nitrogen gas (6% oxygen at 0.27 MPa) and liquid nitrogen and eventually 
compared against dry cutting. Plain carbon steel with UTS of 217 MPa was machined on 
a CNC turning center with a constant depth of cut of 1.2 mm and a feed rate of 
0.1inch/rev under different cutting environments. Results show that the cutting force and 
the thrust force decreases with the use of flood coolant and liquid nitrogen as compared 
to the other gaseous environments and dry machining. Also the use of flood coolants 
showed a significant increase in the shear plane angle as compared to dry and gaseous 
environment cutting. It was observed that compressed air and nitrogen environment 
 15
produced significantly thicker chips which can be confirmed by smaller shear angle and 
longer shear plane. Stanford et al further discusses the behavior of the crater wear and 
flank wear and concludes that although all the environments show significant wear, the 
dry cutting environment produces the highest level of wear. According to their 
experiments the best performing environment with considerably less wear is produced 
when flood coolant is used and lowest density of work piece adherence at the crater face 
and the flank edge is achieved. It is also explained that the use of nitrogen environment 
would assist in the reduction of notch wear reducing oxidation and providing better finish 
of the machined component.  
One of the early advantages which drove metal cutting research was an interest in 
the power required by a machine to remove a certain ?swept volume?.   Using the classic 
Merchant force diagram for example, total energy per unit time can be calculated by the 
product of primary cutting force, F
c
, and the velocity of the cut, V. Due to the fact that 
many parameters can be varied during the cutting process that affects the total energy 
consumed, this energy is normalized by dividing it by the rate at which the material is 
removed. The material removal rate for a tube is the product of area being cut and the 
velocity perpendicular to the area at which the material is removed. Considering the 
thickness of uncut chip, t and the width of the tube wall, the energy per unit time or 
specific energy, u, is calculated by, 
wt
F
Vwt
VF
u
cc
...
.
==  
Specific energy can be partitioned into 4 components (a) Shear energy per unit volume, 
(b) Friction energy per unit volume, (c) Kinetic energy per unit volume and (d) Surface 
energy per unit volume. Specific energies can be used to calculate the power/volume/time 
 16
 17
(specific horsepower) and are available for most engineering material. They are a 
measure of the difficulty involved in machining a particular material and are sometimes 
used to model a given material?s machinability. 
Summary 
The parametric effects upon measured results discussed within this literature 
review are summarized in Table 1.   Any newly constructed instrument must yield results 
consistent with these historical results. 
 
Parameter Change Cutting Force Thrust Force Chip Thickness Wear Shear Angle 
Feed, t Increase Increase Increase Increase Increase Increase 
Rake Angle 
(0-20) 
Increase Decrease Decrease Decrease Decrease Increase 
Negative Rake 
Angle (< 0) 
Increase Increase Increase Increase Increase Decrease 
Cutting Speed, v Increase Decrease Decrease Decrease Increase Decrease 
Width of Cut, w Increase Increase Increase Increase Increase Decrease 
Compressed Air On Increase Increase Increase Decrease Increase 
Metal Working 
Fluid 
On Decrease Decrease Decrease Decrease Increase 
Contact Length Increase Increase Increase Increase Increase Increase 
 
Table 1: Summary of Variation of Response with Input Parameters. 
. 
 
 
 
CHAPTER 4 
DESCRIPTION OF EQUIPMENT 
This chapter documents the materials, equipment and software used to conduct 
the experimental research. Below is the list of the machine tools and instruments used to 
construct an orthogonal tube turning setup, the materials used in the experiments and 
further to carryout the data analysis.  
? HAAS Two Axis Lathe (Model TL-2) 
? KISTLER Three Component Dynamometer (Type 9257A) 
? KISTLER Charge Amplifier (Model 5004) 
? NATIONAL INSTRUMENTS DAQ device (NI USB-6008, with Digital I/O 
channels and a 32-bit counter) 
? LABVIEW 8.2 Data Acquisition Software 
? HSS Stick Tools (?? x ?? x 5?), ground to appropriate angles 
? Aluminum 6061 Alloy Tubing (3? OD with wall thickness 1/8?) 
? Nitrogen Cylinder supplied by Air Gas with Pressure Regulator 
? VORTEC Cold Air Gun 
? Commercial Spray Coolant Generator 
? TaiCaan XYRIS series Surface Profiler with a LT-8010 Sensor head, LT-V201 
Camera Unit and a LT-8105 Controller unit 
? HARIG 618 AUTOMATIC Surface Grinder
 18
 
 
Figure 7: HAAS Two Axis Lathe 
The final experimental setup consists of a HAAS two axis lathe with a 
conventional tool post being replaced by a custom tool post to hold the HSS tool in a way 
that the force in the radial direction is reduced to zero. A three component KISTLER 
dynamometer is mounted on a steel plate which in turn is mounted onto the lathe bed in 
position of the conventional tool post. A custom made Aluminum tool post is fastened 
onto the Dynamometer so that the complete load on the tool holder will be transmitted to 
the dynamometer. An aluminum 6061 alloy tube is held firmly in the chuck for 
machining.  
 
 19
Control Validation of the Two Axis HAAS Lathe 
The HAAS (Model TL-2) lathe features an option where the spindle rotations are 
input in revolutions per minute and feed is input in inches per revolution. Validation of 
feed in a lathe is of prime importance yet difficult with feed being in inches per 
revolution; hence to make it easier, the spindle speed was multiplied with feed to convert 
feed in terms of inches per minute. 
A feed rate of 0.001 inches per revolution was chosen with a rpm of 100. The feed 
in terms of inches per minute is 0.1 inch/minute. To validate the X-Axis, the lathe was 
run and the time taken for the tool post to travel 0.1 inches were recorded with the help of 
a stop watch. The lathe took 60, 60 and 61 seconds on the first, second and third trial 
respectively. For Z-Axis, same steps were followed and the time taken for carriage to 
move 0.1 inches were recorded. The lathe took 62, 60 and 61 seconds respectively. 
Considering the fact that the stopwatch is being operated by a human, human error has to 
be taken into account during switching on and off the stopwatch and hence conclude that 
the lathe is validated for the expected feed rate. The lathe has an inbuilt feature to adjust 
the RPM according to the work piece radius in order to maintain the specified SFM. 
 
 
 
 
 
 
 
 
 20
 
 
Figure 8: KISTLER 9257A 3 Component Dynamometer 
 
A calibrated 3 axis dynamometer collected the force data exterted on the tool in cutting, 
normal and radial directions. 
 
 
Figure 9: KISTLER Charge Amplifiers (Model 5004) 
 
Dual mode charge amplifiers were used to amplify the piezo electic output of the 
dynamometer. 
 21
 
 
 
Figure 10: National Instruments USB 6008 
 
The output signal from the amplifiers is converted to digital voltage signals using a NI 
USB 6008 module and LabVIEW 8.2 software. 
 
 
Figure 11: Vortec Cold Air Gun 
 
A cold air gun usually used for spot cooling when machining plastics is used to achieve 
cold compressed air environment in this experiment. 
 22
 
 
Figure 12: Kool Mist Spray Coolant Generator 
 
A spray coolant generator capable of producing a mist environment with the mixture of 
compressed air and water soluble synthetic coolant is used.   Manufacturers 
recommended settings were used through out.    
 
 
Figure 13: TaiCaan XYRIS Series Surface Profiler with a LT-8010 Sensor head, LT-
V201 Camera Unit and a LT-8105 Controller unit. 
Unit was graciously loaded to Auburn University by XYRIS4000CL Taicaan and John 
McBride at the University of Southampton.   This Confocal Laser Profilometer was used 
for measuring the surface roughness of the tool 
 23
 
 
Figure 14: Overall Network Schematic of the Experimental Set up 
 
 
The forces exerted on the tool are effectively delivered to the dynamometer which sends 
the piezo-electric signals to the charge amplifiers. The charge amplifiers amplify the 
signals and are traferred to a digital input/output DAQ system. The DAQ system converts 
the voltage signals to the force signals with the aid of labview computer software which 
displays the variation of forces with time. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 24
CHAPTER 5 
CONSTRUCTION OF THE ORTHOGONAL TUBE TURNING APPARATUS 
 
The Auburn University instrument was designed with an objective to study the 
response of the tool force system, tool surface roughness and the shear angle behavior 
under the influence of various cutting parameters and environments during the orthogonal 
tube turning process on a HAAS two axis CNC lathe modified to carry out orthogonal 
tube turning.  The basic geometry of the tube turning is as shown in Figure 19. 
 
 
 
Figure 15: Geometry of Orthogonal Tube Turning 
 
 
 
 25
The KISTLER 3 component dynamometer is mounted on a steel plate and in turn 
is bolted down onto the lathe in the position of the tool post. A custom made tool holder 
machined using an aluminum alloy with a slot exactly sufficient to seat a ? inch tool is 
mounted onto the dynamometer in way that the total base area of the tool post is seated 
completely on the dynamometer surface to achieve total load transfer from the tool to the 
dynamometer. The tool holder consists of top and bottom blocks with bolts to clamp 
down the tool. The bottom block is bolted down to the dynamometer where as the top 
block is adjustable using four 2 ? inch long, ? - 20 bolts at each edge to facilitate the 
tool change as shown in Figure 21. 
 
 
Figure 16: Dynamometer and Tool Holder Mounting Assembly 
 26
 
 
 
Figure 17: Top block of the Tool Holder. 
 
 
 
 27
 
 
Figure 18: Bottom block of the Tool Holder. 
The x, y and z output from the dynamometer which is in the form of an electric 
charge were connected to KISTLER 5004 charge amplifiers for signal amplification. The 
sensitivity and the linearity of the charge amplifiers are adjusted according to the 
manufacturer?s calibration certificate (Appendix A). The amplifiers convert the electric 
charge from the piezoelectric transducer into a higher voltage, more sensible output.  The 
 28
output voltages from the charge amplifiers are then connected to the National Instruments 
(NI) USB - 6008 which has 12 digital input/output (DIO) channels and a 32-bit counters 
with a full speed USB interface.  
 
 
Figure 19: Charge Amplifiers and USB DAQ system module connected to the 
LABVIEW 8.2 system software 
 
 29
The software interface for NI USB ? 6008 is LABVIEW which reads out the 
force signals. The outputs of the Kistler Amplifiers are converted into cutting and normal 
force data by the software.  The block diagram of the Lab View program used to convert 
the electrical signals to the force data is shown in Figure 24.  
 
Figure 20: Block Diagram of the program in LABVIEW 8.2 Software 
The DAQ assistant receives the signals from the amplifiers which are sent to the filtering 
block. These filtered signals are recorded in a measurement file and a waveform chart is 
displayed. 
 
 30
 
Figure 21: Dry Machining 
Enviromental Controls 
As mentioned in the literature review, it is desirable for a number of reasons to 
study the environmental effects upon the cutting process.   Four different environments 
have been prepared initially for experiments at Auburn University using dry (or hard) 
turning with no applied gases or coolants, cold compressed air, gaseous nitrogen and 
commercially available water based spray coolants.  
The dry machining is done at the atmospheric temperature without the aid of any 
apparatus to dissipate the heat generated at the tool chip interface. The tool mounted on 
the tool holder plunges into the material in the direction of the axis of the spindle 
rotation. A canned cycle for constant feed was used and the total material to be cut was 
calculated so that the tool cuts exactly for 60 seconds under all different feeds.   This is 
the basic setup described by Figures (19) and (25). 
 31
 
Figure 22: Turning at Cold Compressed Air Environment with Vortex Air Gun 
To achieve a cold compressed air environment a Vortex air gun with a nozzle is 
used to direct the cold air generated by the air gun to the tool chip interface.   The Vortex 
air gun is designed to keep plastics cold and hard during machining so that they do not 
melt into the harder, hot tool.  The inlet of the air gun is connected to a compressed air 
main bus through a pressure regulator. The compressed air enters the cylindrical 
generator which is proportionately larger than the hot tube where it causes the air to 
rotate. This rotating air is forced down on the inner walls of the hot tube at speeds 
reaching 1,000,000 rpm. At the end of the hot tube, a small portion of this air exits 
through a needle valve as hot air exhaust. The remaining air is forced back through the 
center of the incoming air stream at a slower speed. The heat in the slow moving air is 
transferred to the fast moving incoming air. This super cooled air flows through the 
center of the generator and exits through the cold air exhaust port. The nozzle connected 
to the exhaust port directs the cold air over the cutting zone. The pressure of the 
compressed air before it enters the cold air gun is maintained at 75 psi.   Temperatures 
down to -70 degrees Fahreinheit are routinely achieved at the outlet to the nozzle. 
 32
 
 
Figure 23: Turning at Nitrogen Gas Environment 
 
A Nitrogen cylinder with a suitable pressure regulator was used to generate a 
continuous directed flow of nitrogen gas at high pressure over the cutting zone at the tool 
chip interface. The outlet from the pressure regulator was connected to a suitable nozzle 
and clamped to a magnetic stand which can be seated on the lathe bed conveniently to 
adjust the direction of the gas flow. The pressure at the regulator was maintained at 75 psi 
and the outlet nozzle used for the nitrogen is same as the one used to direct cold 
compressed air at the cutting zone. 
 
 33
 
Figure 24: Turning at Spray Coolant Environment 
 
A commericially available, popular cool mist environment was obtained using a 
spray coolant generator which basically consists of a steel tank with a siphon line 
immersed in the tank. The outlet of the siphon is connected to the valve fitted with an 
inlet and an outlet port. The inlet line is connected to the compressed air line fitted with a 
suitable pressure regulator maintained at 75 psi. The tank is filled with 1:40 ratio 
commericially available synthetic coolant and water. The compressed air entering the 
valve creates the suction in the siphon and a mist of spray coolant and compressed air is 
sprayed over the cutting zone. The coolant tank as supplied by the manufacturer has two 
outlet ports for the spray coolant and both the outlets are connected to separate nozzle 
and directed at the tool chip interface from either sides as shown in Figure 29.    These 
are the manufacturer?s recommended ?ideal? settings.   All components in the system 
were ?new? out of the box and undamaged. 
 34
The continuous chips obtained during all different runs under various 
environments and various cutting parameters are collected and stored for analysis 
purposes as will be described later. 
Tool Surface Roughness Measurements:  
The average surface roughness of a tool face can be mapped using a confocal 
laser profilometer. A tool to be scanned was placed under the scanner so that the laser 
beam is projected above the surface of the tool and travels 3 mm in the x-direction so as 
to just stop at the edge of the tool and jump to the next line for scanning. Adjusting the 
area of the surface to be profiled is aided by a camera to position and preview the area to 
be scanned. The tool path of the laser over the profiled surface is as shown in figure 26.  
 
Figure 25: Area being scanned on top face of a ? x ? x 5 inch tool 
 
Figure 26: Laser Beam Path 
 35
The TAICAAN software used was programmed to scan 101 points in x direction 
(3 mm) and 101 points in y direction (3 mm) resulting in 10201 data points for each tool 
profiled. The number of points to be scanned can be varied depending upon the accuracy 
of the roughness value needed. The resolution of the instrument is evaluated as 0.1 ?m 
according to manufacturer specifications.  
The readout represents the height of the surface being profiled (in mm) from the 
tip of the laser probe. This profile data was used to calculate the root mean square 
deviation of the profile from the mean line. Suppose z
1
, z
2
, z
3
... z
n
 represents the height 
variation of the surface from the laser tip, Root mean square deviation is defined as,  
n
zzzz
R
n
q
22
3
2
2
2
1
...........++
=
 
The ?R
q
? value calculated as above is a direct measure of the surface roughness. 
The same tool after being used for 300 seconds on a tube turning setup was used to map 
the profile again. The used tool is placed below the laser beam. With the aid of the 
camera unit, the position of the tool is adjusted to scan the same 3mm x 3mm area 
scanned for the unused tool. This was achieved through carefully positioning the tool by 
observing the light spot at the edge of the tool as shown in figure below. Before scanning 
the tool, the laser path is previewed using the camera multiple times to make sure the 
laser beam travel path is not crossing the edge of the tool and is over the light spot where 
tool wear is expected  to be remarkable. 
 
 36
 
 
Figure 27: Enlarged camera view of the cutting edge. 
 
This way the tool is profiled and subsequently the root mean square deviation is 
calculated. After obtaining the average surface roughness for new tool ((R
q
)
new
) and for 
the used tool ((R
q
)used) the effective surface roughness of the tool face is calculated as 
the difference in the surface roughness values of used and new tool. 
?R
q
 = (R
q
)
new
 ? (R
q
)
used
 
 37
CHAPTER 6 
INSTRUMENT VALIDATION AND SAMPLE SIZE DETERMINATION 
 
Having constructed the Orthogonal Tube Turning (OTT) instrument, it is 
necessary to validate the instrument for repeatability, sensitivity and standard deviation in 
order to design and determine the statistical power of the response data.    The instrument 
repeatability requires one set of tests to establish that for a given set of conditions, the 
same result is returned.   A second series of tests to validate that the instrument is capable 
of measuring an actual change is then required in order to prove the instrument is not 
always returning the same (potentially false) result.    Finally, in order to determine the 
confidence one can place in the results at a given factor level combination of 
experimentation, one must establish the standard deviation of the instrument. 
Repeatability Test 
For the purpose of instrument repeatability, three data sets were considered each 
with five runs carried out on different days over a period of time at dry environment with 
a 0
o
 rake angle tool and a constant feed of 0.001 inch. The standard spindle rpm was used 
and the force data was saved in a MS Excel file for analysis. The dynamometer records a 
response reading for every 0.01 seconds, so for 60 seconds of cut a total of 6000 readings 
are recorded. The initial 10 seconds are disregarded during which the tool is deflected 
during the onset of the force occurs and response curve stabilizes. Table 3 and Table 4 
 38
shows the average and the standard deviation values of the thrust force and the cutting 
force data under each run. 
Thrust Force Data 
Data Set 1 Data Set 2 Data Set 3 
Run 
No. 
Mean 
Std 
Deviation 
Mean 
Std 
Deviation 
Mean 
Std 
Deviation 
Run 1 178.7172 6.6239 185.3432 3.1193 175.1395 3.5045 
Run 2 175.5777 7.9548 177.0952 7.7615 17.6127 3.3581 
Run 3 175.7445 6.5045 178.2868 2.1636 173.0687 6.6251 
Run 4 173.5154 4.3147 176.9404 2.1055 177.4118 3.0499 
Run 5 178.1167 1.8644 174.6758 1.7307 177.2100 1.7704 
 
Table 2: Thrust Force Data for Instrument Validation 
Cutting Force Data 
Data Set 1 Data Set 2 Data Set 3 
Run 
No. 
Mean 
Std 
Deviation 
Mean 
Std 
Deviation 
Mean 
Std 
Deviation 
Run 1 172.4828 6.9405 179.2302 4.0760 168.4391 3.0778 
Run 2 171.1007 7.5971 172.5878 7.3604 166.7893 3.3153 
Run 3 174.1149 6.3800 176.8490 2.3010 178.2868 6.2337 
Run 4 170.2533 4.4802 173.8834 2.1370 168.8458 3.0956 
Run 5 175.4985 1.9894 171.2168 1.8795 169.6373 1.9405 
 
Table 3: Cutting Force Data for Instrument Validation 
 39
The mean and standard deviation values of the cutting force and thrust force is 
used to conduct a 2 sample t-test using the MINITAB 15 statistical software to determine 
the repeatability of the instrument. The test was conducted with a null hypothesis that the 
two means were equal. The t-test was conducted for force values between two data sets 
with different combination available between the three data sets for an average time 
interval of 50 seconds. The comparison between different data set combinations and their 
respective p-values are given in Table 5. The p-values of the t-tests under all different 
combinations conclude that the cutting force and thrust force responses are equal at 95% 
confidence interval and hence the data sets are repeatable since all tests were conducted 
under the same cutting conditions. 
P ? Value 
95% Confidence 
Interval 
Data Set 
Combination 
Thrust Cutting Thrust Cutting 
Remarks 
Data 1 vs. Data2 0.337 0.281 Equal Equal Repeatable 
Data 1 vs. Data3 0.615 0.354 Equal Equal Repeatable 
Data 2 vs. Data3 0.219 0.124 Equal Equal Repeatable 
 
Table 4: Repeatability Test Analysis 
Sensitivity Test 
The experiment was conducted at the same dry environment using a 0
o
 rake tool 
under two different feeds of 0.001 and 0.002 inches in order to force variation in the 
response.  Three different data sets were collected with each data set comprising of five 
replicates.  The mean of the thrust and cutting force data for an average cutting time of 50 
seconds is recorded and is shown in Table 6 and Table 7.  
 
 40
Thrust Force Data (N) 
Data Set 1 Data Set 2 Data Set 3 
Run No. 0.001? 
D1F1 
0.002? 
D1F2 
0.001? 
D2F1 
0.002? 
D2F2 
0.001? 
D3F1 
0.002? 
D3F2 
Run 1 178.7172 248.7989 185.3432 241.3228 175.1395 240.6577 
Run 2 175.5777 240.2342 177.0952 240.373 170.6697 239.6734 
Run 3 175.7445 236.3356 178.2868 233.2487 173.0687 240.4760 
Run 4 173.5154 239.5938 176.9404 240.9454 172.2748 235.7926 
Run 5 178.1167 240.2020 174.6758 237.1459 173.2100 237.4057 
Table 5: Thrust Force Data for Sensitivity Test 
 
Cutting Force Data (N) 
Data Set 1 Data Set 2 Data Set 3 
Run No. 0.001? 
D1F1 
0.002? 
D1F2 
0.001? 
D2F1 
0.002? 
D2F2 
0.001? 
D3F1 
0.002? 
D3F2 
Run 1 172.4828 268.7188 179.2302 265.6712 168.4391 259.0863 
Run 2 171.1007 265.9970 172.5878 266.5099 166.7893 266.4834 
Run 3 174.1149 266.5493 176.8490 264.6484 178.2868 270.369 
Run 4 170.2533 265.4674 173.8834 266.5676 168.8458 262.2706 
Run 5 175.4985 268.2023 171.2168 260.7075 169.6373 265.3257 
Table 6: Cutting Force Data for Sensitivity Test 
 
MINITAB was again utilized to compare paring of data.  The t-tests conducted on 
the data sets under various combinations show that the change in feed has an influence 
over the cutting and thrust force response and the two means of the data sets are not equal 
thereby rejecting the null hypothesis. The P-values are calculated and is presented in the 
Table 8. This shows that the instrument is capable of detecting a change in the cutting 
parameter and hence was determined to be sensitive to change in variables.  
 41
P - Value 95 % Confidence Interval Data Set 
Combination Thrust Cutting Thrust Cutting 
Remarks 
D1F1 vs. D1F2 0.000 0.000 Not Equal Not Equal Sensitive 
D1F1 vs. D2F2 0.000 0.000 Not Equal Not Equal Sensitive 
D1F1 vs. D3F2 0.000 0.000 Not Equal Not Equal Sensitive 
D2F1 vs. D1F2 0.000 0.000 Not Equal Not Equal Sensitive 
D2F1 vs. D2F2 0.000 0.000 Not Equal Not Equal Sensitive 
D2F1 vs. D3F2 0.000 0.000 Not Equal Not Equal Sensitive 
D3F1 vs. D1F2 0.000 0.000 Not Equal Not Equal Sensitive 
D3F1 vs. D2F2 0.000 0.000 Not Equal Not Equal Sensitive 
D3F1 vs. D3F2 0.000 0.000 Not Equal Not Equal Sensitive 
 
Table 7: Sensitivity Test Analysis 
Standard Deviation of the Instrument 
The standard deviation of the instrument is given by the sum of the sensitivity of 
the dynamometer and the sensitivity of the NI USB 6008. The sensitivity of the 
dynamometer is estimated to be +/- 10 N by the manufacturer (KISTLER) and the 
sensitivity of the USB module is +/- 1 N (National Instruments).  So the standard 
deviation of the instrument can be determined as 11 N under normal atmospheric 
conditions. The standard deviation values of the thrust force and cutting force presented 
in Table 3 and Table 4 is compared with the standard deviation of the instrument and was 
found to be less than 11 N which is a good measure for the accuracy and sensitivty of the 
experimental set up. 
Determination of Sample Size 
The sample size necessary to obtain reportable results is of prime importance 
during the planning stage of the experiments. Sample size is dictated by how accurate 
 42
you must be, or how large a margin of error you can tolerate. The larger your sample size, 
the more sure you can be that their averages truly reflect the population. Power analysis 
can either be done before or after the data is collected. A power analysis was conducted 
prior to the research study to determine an appropriate sample size to achieve adequate 
power.  
Statistical power is the capability of the analysis to detect a difference which 
actually exists between two sets of data or the ability that the test will reject a false null 
hypothesis to avoid Type II error. A Type II error is the error of not rejecting a null 
hypothesis when it is not true and increases with decreases with increase in power. 
Using the previously collected data from the repeatability and sensitivity analysis, 
the minimum number of replicates necessary to achieve a statistical power of 95% was 
calculated using the MINITAB software. The output of the software is shown in Figure 
30 and is evaluated that a sample size of 5 yields in achieving 95% statistical power 
which is more than our target power. 
5.02.50.0-2.5-5.0
1.0
0.8
0.6
0.4
0.2
0.0
Difference
Po
we
r
Alpha 0.05
StDev 2.10486
Alternative Not =
A ssumptions
5
Size
Sample
Power Curve for 1-Sample t Test
 
Figure 28: Power Curve to achieve 95% Statistical Power
 43
CHAPTER 7 
STATISICAL DESIGN OF EXPERIMENT (DOE) 
The orthogonal tube turning experiment was mainly designed to study the 
variation of tool forces, tool surface roughness and shear angle with varying input 
parameters. The input parameters were decided based upon the literature, trial runs and 
experience. The different parameters involved in the experiments are presented in Table 9 
and are further discussed in this chapter. 
 
Parameter Value 
Spindle RPM, N
s
 640 rpm 
Tool Material HSS T-56 
Sample Material Aluminum ? 6061 (54.5 HRB) 
Width of Cut (tube wall), w 0.125 inches 
Environment 
Dry, Cold Compressed Air, Nitrogen 
and Spray Coolant. 
Tool Rake Angle, ?  -10
o
, 0
o
, 15
o
 30
o
 
Uncut Chip Thickness, t
1
 0.001, 0.002, 0.003, 0.004,0.005 inches 
Total Time for each Run 60 seconds 
Cutting Speed, v 500 SFPM 
 
Table 9: Input Parameters for Tube Turning Experiment 
 
 44
The spindle RPM was calculated based on a cutting speed of 500 sfpm 
considering the hardness and the geometrical dimensions of the alloy and was determined 
to be 640 RPM according to the Metals Handbook [21].  RPM calculations are shown in 
Appendix B. 
The properties of Aluminum 6061-T6 are well documented and considering the 
ease of availability and cost, this alloy was selected for all the experimental purposes. 
The tube used in this set up was a 3 inch diameter 6061 alloy with a wall thickness of 
0.125 inch.  Usually the tubes were machined to be a maximum of 9 inches long to avoid 
the deflection of the work from the chuck.   It was decided to use hollow tubes with no 
supporting tailstock in order to permit long periods of heavy chip cutting. 
The effects of atmospheric temperature and humidity are neglected while 
measuring the responses or while calculating the results, although it should be noted that 
the lab temperarture and humidity are well controlled by the environmental system.  A 
piece of HSS tool stock with ? inch x ? inch x 5 inches is used for all the cutting 
operations on the lathe.  The work piece was machined along the circumference of the 
tube using the HSS tool.   Precise rake angles are ground into the tools as discussed later. 
The hardness of Aluminum 6061 was measured using a Rockwell Hardness 
Tester HR 150A. The indentation for plastic deformation was by 1/16? ball and a HRB 
scale was used. The standard and the sample were tested alternately to find the deviation 
from the exact value and the data is presented in Table 2. The average hardness of the 
sample is determined to be 54.5 HRB, as would normally be expected of a T6 tempered 
piece of aviation grade general purpose aluminum (AL 6061).   All aluminum was 
obtained from the same manufacturer and the same production batch. 
 45
Standard = 91.0 B Scale 
Major Load = 100 Kg, Minor Load = 10 Kg 
Indenter = 1/16 inch ball 
Standard = 90.5 Standard = 91.0 
Specimen 1 Trial 1 = 54.5 Specimen 2 Trial 2 = 54.5 
Standard = 90.5 Standard = 91.0 
Specimen 1 Trial 2 = 54.5 Specimen 3 Trial 1 = 54.0 
Standard = 91.0 Standard = 91.5 
Specimen 2 Trial 1 = 55.0 Specimen 3 Trial 2 = 54.5 
 Standard = 91.5 
 
Table 9: Evaluation of Hardness of Aluminum 6061 
In order to compare the behavior of the responses under various environments, 
four different cutting environments were chosen. Dry machining with out the aid of any 
kind of cooling mechanism, Cold compressed air environment obtained by a vortex air 
gun to direct a continuous supply of cold air at the tool chip interface, Nitrogen 
environment with the aid of the gas cylinder fitted with a suitable pressure regulator and 
lastly Cool Mist Environment using a spray coolant generator fitted with a splitter and 
directed onto the tool chip interface. An argon environment was disregarded after the trial 
runs since no significant changes in the responses were observed. 
Historically, the variation of the tool forces and the tool wear is largely attributed 
to the tool rake angle. In order to investigate the influence of the tool geometry, four 
different rake angles were selected and the tools were machined to -10
o
, 0
o
, 15
o
 and 30
o
 
so as to obtain data over a wide range of varying rake angles. The 0
o
 tool is commonly 
used in industries because of their superior tool life and rigidity [22]. The selected rake 
angles are machined onto the HSS tools using a surface grinder.   The normal range of 
tool rake angles (-5 to 15 degrees) is well represented by the 0 and 15 degree tools.   The 
 46
-10 and +30 degree tools represent an extreme outer range and are not commonly used 
values except within academia. 
Traditionally, the selection of feed is also of prime importance as this decides the 
variation of tool forces significantly and also determines the chip thickness ratio.  During 
the trial runs the possible optimum feeds were determined to be 0.001, 0.002, 0.003, 
0.004 and 0.005 inches/revolution. Any feed after 0.005 inch/rev led to an increase in the 
disfiguration of the chip and a feed of 0.008 inch/rev resulted in smoke which could have 
burnt the tool or would have caused severe damage to the machine tool if carried out.    
Traditionally, lathe operators consider a 0.005 inch/rev cut as a ?heavy? roughing cut.    
A finishing cut of 0.0005/rev to 0.0010/rev is quite common in industry because of the 
superior finish produced. 
The HSS tools are machined using a HARIG 618 Automatic surface grinder as in 
Figure 19 to the required rake angles. An angular milling machine vice which can be 
swiveled to 45 degrees in both the directions was used. The angular vise is held on the 
magnetic bed of the grinding machine. The tool is held in the vice and is swiveled to the 
required angle. A dial gauge is run over the surface of the vice to make sure that the vice 
is gripped parallel to the machine reference. The tool is then machined with a slow feed 
rate and depth of cut to achieve high quality surface and reduce surface roughness. The 
vice is swiveled to prepare multiple -10
o
, 0
o
, 15
o
 and 30
o
 tools. During the trial runs it 
was also established that up to a certain limit the length of the tool protruding out of the 
tool holder does not make any significant difference with the responses measured (i.e., 
the tool is stiff).  The clearance angle of all the tools was measured to be 15
o
.  
 47
 
Figure 29: Machining a 30 degree tool on a HARIG 618 Automatic Surface Grinder 
 
Figure 30: Selected Rake Angles machined on a square section HSS tool 
 
The Aluminum tubing measuring 72 inches as obtained by the supplier is cut into 
tubes of 9 inch length on a Horizontal band saw and the faces are sanded on a vertical 
belt sander to make them flat and burrs if any are removed using a deburring tool. A 
small experiment was conducted during the trial runs to determine if there is any 
 48
 49
significant change in the force response based on the length of the tube protruding outside 
the chuck. It is concluded that the length of this protrusion has very negligible effect on 
the forces and hence can be disregarded. 
The experiments are designed at various factor level combinations as shown in 
Table 10. Each factor level combination comprises of 5 replicates leading to 100 runs 
under each environment which amounts to 400 runs over a range of four different 
environments, four different rake angle and five different feeds. 
The cutting force and thrust force responses at all possible factor level 
combination is recorded. Each factor level combination uses a new tool machined to 
required rake angle. So assuming that the material is being cut for a total of 60 seconds 
under each cut, every tool was used for 300 seconds to obtain 5 replicates. The used tool 
was then stored for surface roughness analysis using the confocal laser profilometer. The 
aluminum chips obtained under each run was labeled accordingly and stored for chip 
thickness measurement to aid in shear angle calculations. 
Design of Experiment 
Environment Rake Angle Feed (inches) 
Dry -10
o
 0.001 
Cold Compressed Air 0
o
 0.002 
Nitrogen 15
o
 0.003 
Spray Coolant 30
o
 0.004 
 0.005 
 
Table 10: Factor Level Combinations of the Principal Experiment.
 
 
CHAPTER 8 
RESULTS AND DISCUSSION 
 
The designed experiment as discussed in Chapter 7 consists of large number of 
runs at various factor level combinations. Four different cutting environments, four 
different rake angles and five different feeds were used resulting in 80 different factor 
level combinations each with five replicates amounting to 400 total runs. The cutting 
force and thrust force data are initially saved as MS excel files for ease of calculations. A 
typical graph of variation of cutting tool forces with time is as shown below. 
-50
0
50
100
150
200
250
300
0 2 4 5 7 9 1
1
1
2
1
4
1
6
1
8
1
9
2
1
2
3
2
5
2
7
2
8
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2
3
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3
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4
4
4
6
4
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0
5
1
5
3
5
5
5
7
5
8
Time (seconds)
For
c
e
 (
N
)
Radial Force, Fr Thrust Force. Ft Cutting Force, Fc
 
Figure 31: Variation of Tool forces with time. 
 
 
 50
Further the used tools are measured for surface roughness estimation using a laser 
confocal profilometer and the data is saved in .txt format. The uncut chip thickness is 
measured at 5 different locations along the continuous chip and is saved for shear angle 
calculations. The observed experimental data are tabulated to facilitate further 
calculations as in Table 11.  
Run  Rake Angle Feed Run Thrust Force, Ft (N) Cutting Force, Fc (N)
1 -10 0.001 Run 1 177.7517 175.9930 
2 -10 0.002 Run 1 251.7904 263.4748 
3 -10 0.003 Run 1 310.3103 335.1369 
4 -10 0.004 Run 1 356.3264 412.3702 
5 -10 0.005 Run 1 407.1834 474.6960 
 
Table 11: Example Thrust Force and Cutting Force Raw Data (Appendix C) 
 
Based on the observed cutting force and thrust force data, the friction force (F), normal 
force (N), shearing force along the shear plane (Fs) and a force normal to the shear plane 
(F
n
) is calculated and the corresponding force ratios are derived. 
 51
 
The cutting forces, shear angle, friction angle and shear stress calculations are 
based on the classical equations presented in Table 12 as first developed by Merchant (1). 
Data Symbol Units Equations 
Chip Thickness Ratio r
c
 none 
2
1
t
t
r
c
=  
Friction Force F N 
?? cos.sin.
tc
FFF +=  
Normal Force N N 
?? sin.cos.
tc
FFN ?=  
Friction Co-efficient ? none 
N
F
=?  
Shear Force on Shear 
Plane, Merchant 
(F
s
) M N 
?? sin.cos.)(
tcs
FFMF ?=  
Normal Force on 
Shear Plane, Merchant  
(F
n
) M N 
?? cos.sin.)(
tcn
FFMF ?=  
Area of Shear Plane A
s
 inch
2
 
?sin
.
1
wt
A
s
=  
Shear Stress on Shear 
Plane 
?
s
 MPa 
s
s
s
A
F
=?  
Shear Plane Angle ? degree ?
?
?
?
?
?
?
=
?
?
?
sin1
cos
arctan
r
r
 
Friction Angle ? degree 
?
?
?
?
?
?
=
N
F
arctan?  
 
Table 12: Equations used to calculate results from the Force Response and Chip 
Thickness Data (also discussed in Appendix D)
 52
 
Table 13 and Table 14 show examples of the various forces, force ratios and shear 
stress calculations. The complete set of experimental force calculations, surface 
roughness, shear angle and shear stress calculations are presented in Appendix D and 
Appendix E. All calculations are the factor level average of the 5 replicates meaning that 
the average of each of the run is averaged to obtain the following data. 
 
Run 
No. 
Friction 
Force (F) 
Normal 
Force (N) 
F/N 
Ratio 
Fs 
(Merchant) 
Fn 
(Merchant) 
Fs/Fn 
(Merchant) 
1 144.4904 204.1855 0.7076 154.0374 -155.9893 -0.9875
2 184.1773 177.2929 1.0388 177.2929 -184.1773 -0.9626
3 177.9254 180.9517 0.9833 180.9517 -177.9254 -1.0170
4 189.0791 181.1614 1.0437 181.1614 -189.0791 -0.9581
5 194.3560 185.0437 1.0503 185.0437 -194.3560 -0.9521
 
Table 13: Example of Force Ratio Calculations from Appendix (E) 
 
 
Run 
No. 
Roughness 
(microns) 
t/tc Phi (degrees) Beta (degrees) As (in2) 
?s (Mpa) 
1 35.2848498 
2 46.09109792
3 44.5168538 
4 46.22510005
5 
154.942318 0.121892 6.704454207
46.40603269
0.001070683 254.3531778
6 33.70095615
7 43.80856404
8 44.03211179
9 43.9692226 
10 
161.1517652 0.162259 8.83393002
43.64414797
0.001627911 248.960118
 
Table 14: Example of Surface Roughness, Shear Angle and Shear Stress Calculation Data 
from Appendix F
 53
Variation of Thrust Force (F
t
) with Environment, Rake angle and Feed 
Statistical analysis of the thrust force (F
t
) was conducted using the GLM (general 
linear module) of MINITAB 15.   The main effects plot indicates that environment has a 
relatively less effect on this result.   The thrust force decreases greatly with increasingly 
positive rake angles.  The thrust force increases sharply as the depth of cut or feed is 
increased.
 
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Environment
Me
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Rake Angle
Feed
Main Effects Plot for Thrust Force Avg
Data Means
 
Figure 32: Main Effect Plot for Thrust Force response (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
400
200
0
400
200
0
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Thrust Force Avg
Data Means
 
 
Figure 33: Interaction Plot for Thrust Force response (Minitab 15) 
 
 54
General Linear Model: Thrust Force versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels     Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Thrust Force Avg, using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS   Adj MS         F      P 
Environment                    3    38078    38078    12693    559.98  0.000 
Rake Angle                     3  3693229  3693229  1231076  54313.14  0.000 
Feed                           4  1439297  1439297   359824  15874.88  0.000 
Environment*Rake Angle         9    34456    34456     3828    168.91  0.000 
Environment*Feed              12    40228    40228     3352    147.90  0.000 
Rake Angle*Feed               12   175989   175989    14666    647.03  0.000 
Environment*Rake Angle*Feed   36   153141   153141     4254    187.68  0.000 
Error                        320     7253     7253       23 
Total                        399  5581673 
 
 
S = 4.76091   R-Sq = 99.87%   R-Sq(adj) = 99.84% 
 
 
Table 15: ANOVA Table for Thrust Force response (Minitab 15) 
 
The Analysis of Variance (ANOVA) of the thrust force response indicates that the Rake 
Angle has by far the dominant effect on this force with an F-statistic of 54,313.   The feed 
factor is second in significance with an F-statistic of 15,874.   The interaction of the rake 
angle and feed outperforms the environment in terms of the F-statisic.   
 This result can be interpreted as follows. A sharper tool plunges into the work and 
can form a chip piece with considerably less force required than a blunt tool. The thrust 
force increases with the increase in feed. Turning using a sharper tool is more likely to 
reduce the thrust force than just decreasing the feed. The main effects of environment 
achieve significance but are less than the effect of rake angle and feed on the thrust force.  
It can also be observed from the main effect plot that the drop in thrust force is more 
rapid from 0
o
 to 15
o
 as compared to other trends.  
 
 
 55
Variation of Cutting Force (F
c
) with Environment, Rake angle and Feed 
Statistical analysis of the Cutting force (F
c
) was conducted using the GLM (general linear 
module) of MINITAB 15.   The main effects plot indicates that environment has a 
relatively less effect on Cutting force but decreases considerably with increasing positive 
rake angles.  The cutting force greatly increases as the depth of cut or feed is increased. 
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Environment
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Rake Angle
Feed
Main Effects Plot for Cutting Force Avg
Data Means
 
 
Figure 34: Main Effect Plot for Cutting Force response (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
500
300
100
500
300
100
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Cutting Force Avg
Data Means
 
 
Figure 35: Interaction Plot for Cutting Force response (Minitab 15) 
 
 
 56
General Linear Model: Cutting Force versus Environment, Rake Angle, Feed  
 
Factor       Type       Levels       Values 
Environment  fixed       4        Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4        -10, 0, 15, 30 
Feed         fixed       5        0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Cutting Force Avg, using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS   Adj MS         F      P 
Environment                    3    38297    38297    12766    662.04  0.000 
Rake Angle                     3   970355   970355   323452  16774.39  0.000 
Feed                           4  4097534  4097534  1024384  53125.13  0.000 
Environment*Rake Angle         9    27001    27001     3000    155.59  0.000 
Environment*Feed              12    17951    17951     1496     77.58  0.000 
Rake Angle*Feed               12    36005    36005     3000    155.60  0.000 
Environment*Rake Angle*Feed   36    35516    35516      987     51.16  0.000 
Error                        320     6170     6170       19 
Total                        399  5228829 
 
 
S = 4.39118   R-Sq = 99.88%   R-Sq(adj) = 99.85% 
 
 
Table 16: ANOVA Table for Cutting Force response (Minitab 15) 
 
 
The Analysis of Variance (ANOVA) of the cutting force response indicates that 
the significant main effect of feed on this force with an F-statistic of 53125. The rake 
angle is the next most significant factor with an F-statistic of 16774. The effect of 
environment outperforms the interaction of feed and rake angle in terms of the F-statistic 
The cutting force is the force in the direction of the work motion against the tool. 
The increase in feed demands more energy for the plastic deformation of the material 
thus consuming more power leading to larger cutting force responses. The simple effect 
also shows the decrease in cutting force with decrease in feed. Turning at a lower feed is 
more likely to reduce the cutting force than just using a sharper tool. The main effects of 
environment achieve significance but are less than the individual effect of rake angle and 
feed on the cutting force. It is also to be noted that the increase in cutting force is close to 
linear with the increase in feed. 
 
 57
Variation of Friction Force (F) with Environment, Rake angle and Feed 
Statistical analysis of the Friction force (F) was conducted using the GLM (general linear 
module) of MINITAB 15. The main effects plot indicates that cold compressed air 
environment showed a reduction in the friction force as compared to other environments. 
Friction force decreases greatly with increasing positive rake angles.  The friction force 
greatly increases as the depth of cut or feed is increased. 
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Feed
Main Effects Plot for Friction Force
Data Means
 
 
Figure 36: Main Effect Plot of Friction Force data (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
450
300
150
450
300
150
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Friction Force
Data Means
 
 
Figure 37: Interaction Plot for Friction Force data (Minitab 15) 
 58
 
 
General Linear Model: Friction Force versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels      Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Friction Force, using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS  Adj MS       F      P 
Environment                    3    38329    38329   12776   11.99  0.000 
Rake Angle                     3  2807437  2807437  935812  878.55  0.000 
Feed                           4  1547405  1547405  386851  363.18  0.000 
Environment*Rake Angle         9    35399    35399    3933    3.69  0.000 
Environment*Feed              12    41267    41267    3439    3.23  0.000 
Rake Angle*Feed               12   118045   118045    9837    9.24  0.000 
Environment*Rake Angle*Feed   36   154762   154762    4299    4.04  0.000 
Error                        320   340856   340856    1065 
Total                        399  5083501 
 
 
S = 32.6370   R-Sq = 93.29%   R-Sq(adj) = 91.64% 
 
 
Table 17: ANOVA Table for Friction Force (Minitab 15) 
 
 
The calculated friction force response was subjected to Analysis of Variance 
(ANOVA) and the result shows a significant main effect of rake angle upon the force 
response with an F-statistic of 878. The feed factor is second in significance with an F-
statistic of 363. The environment has very little effect on the friction force response when 
compared to rake angle and feed in terms of F-statistic. 
 The pattern of the findings during the analysis of the friction force is same as the 
ones observed for thrust force response. A rapid decrease in friction force values occur 
for a rake angle between 0
o
 to 15
o
. The friction force is considerably less when cutting 
using a sharper tool. Also the increase in feed causes an increase in friction force due to 
the increase in energy consumed to cause the plastic deformation of the work piece. 
 
 
 59
Variation of Normal Force (N) with Environment, Rake angle and Feed 
Statistical analysis of the Normal force (N) was conducted using the GLM (general linear 
module) of MINITAB 15. The main effects plot indicates that the Environment has very 
little effect on the normal force response as compared to the other parameters. A 
considerable decrease in normal force is observed with the increasing positive rake 
angles.  The Normal force greatly increases as the depth of cut or feed is increased. 
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Main Effects Plot for Normal Force
Data Means
 
 
Figure 38: Main Effect Plot of Normal Force response (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
500
300
100
500
300
100
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Normal Force
Data Means
 
 
Figure 39: Interaction Plot for Normal Force response (Minitab 15) 
 60
General Linear Model: Normal Force versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels      Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Normal Force, using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS  Adj MS        F      P 
Environment                    3    36553    36553   12184    20.68  0.000 
Rake Angle                     3  1354337  1354337  451446   766.05  0.000 
Feed                           4  3967380  3967380  991845  1683.05  0.000 
Environment*Rake Angle         9    26064    26064    2896     4.91  0.000 
Environment*Feed              12    17871    17871    1489     2.53  0.003 
Rake Angle*Feed               12    56526    56526    4711     7.99  0.000 
Environment*Rake Angle*Feed   36    29600    29600     822     1.40  0.072 
Error                        320   188580   188580     589 
Total                        399  5676911 
 
 
S = 24.2758   R-Sq = 96.68%   R-Sq(adj) = 95.86% 
 
Table 18: ANOVA Table for Normal Force response (Minitab 15) 
 
The calculated normal force response was subjected to Analysis of Variance and 
the result shows that feed has by far the dominant effect on this force with an F-statistic 
of 1683. The tool rake angle is second in significance with an F-statistic of 766. 
Environment does have very little effect on the normal force response but is negligible 
when compared to individual effects of rake angle and feed. 
 The pattern of the findings during the analysis of the normal force is same as the 
ones observed for cutting force response. The increase in feed causes an increase in 
normal force due to the increase in energy consumed to cause the plastic deformation of 
the work piece. It is also to be noted that the combined effect of environment, rake angle 
and feed fails to achieve significance on the normal force response with an F-statistic of 
1.40 and p > 0.001. The main effect curve for increase in normal force with increase in 
feed is close to linear however rake angle too has a considerable effect resulting in 
reduced normal force when using a sharper tool. 
 61
Variation of F/N Ratio with Environment, Rake angle and Feed 
Statistical analysis of the F/N Ratio was conducted using the GLM (general linear 
module) of MINITAB 15. The main effects plot indicates that the Environment has 
almost constant effect on this force ratio. F/N ratio is found to abruptly decrease with the 
increasing rake angle.  An appreciable decrease in F/N ratio is observed with the increase 
in depth of cut or feed. 
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Feed
Main Effects Plot for F/N Ratio
Data Means
 
Figure 40: Main Effect Plot of F/N Ratio (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
1.00
0.75
0.50
1.00
0.75
0.50
Environment
Rake Angle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for F/N Ratio
Data Means
 
Figure 41: Interaction Plot for F/N Ratio (Minitab 15) 
 62
General Linear Model: F/N Ratio versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels      Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for F/N Ratio, using Adjusted SS for Tests 
 
Source                        DF    Seq SS    Adj SS   Adj MS      F      P 
Environment                    3   0.10326   0.10326  0.03442   0.71  0.546 
Rake Angle                     3   8.31765   8.31765  2.77255  57.31  0.000 
Feed                           4   0.62511   0.62511  0.15628   3.23  0.013 
Environment*Rake Angle         9   0.28728   0.28728  0.03192   0.66  0.745 
Environment*Feed              12   0.27026   0.27026  0.02252   0.47  0.934 
Rake Angle*Feed               12   0.37164   0.37164  0.03097   0.64  0.807 
Environment*Rake Angle*Feed   36   1.01625   1.01625  0.02823   0.58  0.974 
Error                        320  15.48097  15.48097  0.04838 
Total                        399  26.47244 
 
 
S = 0.219950   R-Sq = 41.52%   R-Sq(adj) = 27.08% 
 
Table 19: ANOVA Table for F/N Ratio (Minitab 15) 
 
 
 
Analysis of Variance (ANOVA) of F/N Ratio indicates that the rake angle has by 
far the dominant effect on this force ratio with an F-statistic of 57. The environment and 
feed fail to attain significance on F/N ratio with their p values being greater than 0.001.d  
Also the effect of the interaction between environment, rake angle and feed has no 
significance on the F/N ratio. The interaction plot obtained shows that with a 30
o
 rake 
angle tool a much lower F/N ratio is obtained than compared to a 0
o
, 15
o
 or a -10
o
 tool. 
Also a drastic decrease in F/N ratio is observed between rake angles of 0
o
 to 15
o
. 
 
 
 
 
 
 
 
 
 
 63
Variation of Shear Force along Shear Plane (F
s
) with Environment, Rake and Feed 
Statistical analysis of the Shear force along the shear plane (F
s
) was conducted 
using the GLM (general linear module) of MINITAB 15. The main effects plot indicates 
that the effect of environment on the shear force is nearly a constant. Shear force 
decreases appreciably with increasing positive rake angles.  The Shear force greatly 
increases as the depth of cut or feed is increased. 
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Main Effects Plot for Fs (Merchant)
Data Means
 
 
Figure 42: Main Effect Plot of Shear Force along Shear Plane (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
500
300
100
500
300
100
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Fs (Merchant)
Data Means
 
 
Figure 43: Interaction Plot for Shear Force along Shear Plane (Minitab 15) 
 
 64
General Linear Model: Fs (Merchant) versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels     Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Fs (Merchant), using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS  Adj MS        F      P 
Environment                    3    36379    36379   12126    21.64  0.000 
Rake Angle                     3   878195   878195  292732   522.42  0.000 
Feed                           4  3785829  3785829  946457  1689.08  0.000 
Environment*Rake Angle         9    26975    26975    2997     5.35  0.000 
Environment*Feed              12    16441    16441    1370     2.45  0.005 
Rake Angle*Feed               12    30081    30081    2507     4.47  0.000 
Environment*Rake Angle*Feed   36    29863    29863     830     1.48  0.042 
Error                        320   179308   179308     560 
Total                        399  4983070 
 
 
S = 23.6715   R-Sq = 96.40%   R-Sq(adj) = 95.51% 
 
 
Table 20: ANOVA Table for Shear Force along Shear Plane (Minitab 15) 
 
 
Analysis of Variance (ANOVA) of the shear force response indicates that feed 
has a significant main effect of feed upon the force response with an F-statistic of 1689. 
The tool rake angle is the next most dominant factor with an F-statistic of 522. 
Turning at a lower speed is more likely to decrease the shear force than using a 
sharper tool. Also the effect of interaction between environment, rake angle and feed 
failed to achieve significance with F-statistic being 1.48 and a p value > 0.001. Negligible 
drop in shear force is observed between -10
o
 and 0
o
 rake angle where as a drop in nearly 
100 N is observed between a 0
o
 and a 30
o
 tool. Environment does have an effect on the 
shear force but the effect is negligible when compared to individual effects of tool rake 
angle and feed. 
 
 
 
 
 65
Variation of Normal Force along Shear Plane (F
n
) with Environment, Rake an Feed 
Statistical analysis of the Normal force along the shear plane (F
n
) was conducted using 
the GLM (general linear module) of MINITAB 15. The main effects plot indicates that 
the Environment has very little effect on the normal force response. A considerable 
decrease in normal force is observed with the increasing positive rake angles.  The 
normal force along shear plane increases considerably as the depth of cut or feed is 
increased. 
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300
250
200
150
100
Environment
Me
a
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Rake Angle
Feed
Main Effects Plot for Fn (Merchant)
Data Means
 
 
Figure 44: Main Effect Plot of Normal Force along Shear Plane (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
0.8
0.6
0.4
0.8
0.6
0.4
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Friction Co-efficient
Data Means
 
 
 
Figure 45: Interaction Plot for Normal Force along Shear Plane (Minitab 15) 
 66
General Linear Model: Fn (Merchant) versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels      Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen, Cool Mist 
Rake Angle   fixed       4      -10, 0, 15, 30 
Feed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Fn (Merchant), using Adjusted SS for Tests 
 
Source                        DF   Seq SS   Adj SS   Adj MS        F      P 
Environment                    3    39001    39001    13000    18.28  0.000 
Rake Angle                     3  3683843  3683843  1227948  1726.71  0.000 
Feed                           4  1684883  1684883   421221   592.31  0.000 
Environment*Rake Angle         9    34355    34355     3817     5.37  0.000 
Environment*Feed              12    42449    42449     3537     4.97  0.000 
Rake Angle*Feed               12   176403   176403    14700    20.67  0.000 
Environment*Rake Angle*Feed   36   155940   155940     4332     6.09  0.000 
Error                        320   227568   227568      711 
Total                        399  6044442 
 
 
S = 26.6674   R-Sq = 96.24%   R-Sq(adj) = 95.31% 
 
 
Table 21: ANOVA Table for Normal Force along Shear Plane (Minitab 15) 
 
 
 
Analysis of Variance of the Normal force along the shear plane indicates that the 
rake angle has a significant effect on this force with an F-statistic of 1689. The rake angle 
factor is second in significance with an F-statistic of 592. Environment has an effect on 
the normal force along the shear plane but is negligible compared to individual effects of 
rake angle and feed. 
Turning using a sharper tool is more likely to reduce the nomal force than just 
decreasing the feed although a considerable decrease in force is observed with the 
decrease in feed. Also the effect of cutting environment is prominent for the normal force 
on the shear plane and is found be the same for nitrogen and spray coolant environment. 
 
 
 
 
 
 67
Variation of Fs/Fn Ratio with Environment, Rake and Feed 
Statistical analysis of the F
s
/F
n
 Ratio was conducted using the GLM (general linear 
module) of MINITAB 15. The main effects plot indicates that the Environment has 
varying effect on this force ratio. F
s
/F
n
 ratio is found to increase with the increasing rake 
angle.  A fairly constant response is obtained due to the increase in the feed. 
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1.5
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Environment
Me
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Rake Angle
Feed
Main Effects Plot for Fs/Fn (Merchant)
Data Means
 
 
Figure 46: Main Effect Plot for Fs/Fn Ratio (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
0.4
0.2
0.0
0.4
0.2
0.0
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Fs/Fn (Payton)
Data Means
 
 
Figure 47: Interaction Plot for Fs/Fn Ratio (Minitab 15) 
 
 68
 
General Linear Model: Fs/Fn (Merchant) versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels      Values 
Environment  fixed       4      Dry, Cold Compressed Air, Nitrogen
ake Angle   fixed       4      -10, 0, 15, 30 
, Cool Mist 
ed         fixed       5      0.001, 0.002, 0.003, 0.004, 0.005 
  2.85  0.000 
 42.2117   0.1319 
tal                        399  208.4623 
= 0.363196   R-Sq = 79.75%   R-Sq(adj) = 74.75% 
 
Table 22: ANOVA Table for Fs/Fn Ratio (Minitab 15) 
Analysis of Variance (ANOVA) of F
s
/F
n
 Ratio indicates that the rake angle has by 
far the dominant effect on this force ratio with an F-statistic of 350. The environment and 
feed fail to attain significance on F
s
/F
n
 ratio with their p values being greater than 0.001.  
Also the effect of the interaction between environment, rake angle and feed has no 
significance on the F
s
/F
n
 ratio. The interaction plot obtained shows that with a 30  rake 
angle tool a much lower F
s
/F
n
 ratio is obtained than compared to a 0
o
, 15
o
 or a -10
o
 tool. 
Also a drastic decrease in F
s
/F
n
 ratio is observed between rake angles of 0
o
 to 15
o
. 
 
 
 
 
R
Fe
 
 
Analysis of Variance for Fs/Fn (Merchant), using Adjusted SS for Tests 
 
Source                        DF    Seq SS    Adj SS   Adj MS       F      P 
Environment                    3    1.6244    1.6244   0.5415    4.10  0.007 
Rake Angle                     3  138.7786  138.7786  46.2595  350.69  0.000 
Feed                           4    2.6490    2.6490   0.6623    5.02  0.001 
Environment*Rake Angle         9    3.0344    3.0344   0.3372    2.56  0.008 
Environment*Feed              12    4.1636    4.1636   0.3470    2.63  0.002 
   1.56  0.103 Rake Angle*Feed               12    2.4645    2.4645   0.2054 
  13.5361   0.3760  Environment*Rake Angle*Feed   36   13.5361 
Error                        320   42.2117  
To
 
 
S  
 
 
 
o
 
 
 69
Variation of Shear Plane Angle (?) with Environment, Rake and Feed 
Statistical analysis of the Shear angle (?) was conducted using the GLM (general 
linear module) of MINITAB 15. The main effects plot indicate that environment and feed 
has very little effect on the shear angle. Shear angle increases greatly with increasing rake 
angles. Also an increase in feed results in considerable rise in the shear plane angle value. 
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Environment
Me
a
n
Rake Angle
Feed
Main Effects Plot for Shear Angle (phi)
Data Means
 
 
Figure 48: Main Effect Plot for Shear Plane Angle (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
15
10
5
15
10
5
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Shear Angle (phi)
Data Means
 
 
Figure 49: Interaction Plot for Shear Plane Angle (Minitab 15) 
 
 
 70
General Linear Model: Phi (degrees) versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels  Values 
vironment  fixed       4  Dry, Cold Compressed Air, NitrogenEn , Cool Mist 
ke Angle   fixed       4  -10, 0, 15, 30 
   35.51  0.000 
 126.512    3.514    21.38  0.000 
ror                        320    52.588    52.588    0.164 
= 0.405384  
Table 23: ANOVA Table for Shear angle (?) (Minitab 15) 
 
und to 
have ap
gle tool is found to produce higher 
shear angle than compared to a -10
o
, 0
o
 or a 15
o
 tool. 
Ra
Feed         fixed       5  0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Phi (degrees), using Adjusted SS for Tests 
 
Source                        DF    Seq SS    Adj SS   Adj MS        F      P 
Environment                    3    42.746    42.746   14.249    86.70  0.000 
Rake Angle                     3  1921.459  1921.459  640.486  3897.42  0.000 
Feed                           4   766.450   766.450  191.612  1165.98  0.000 
Environment*Rake Angle         9   132.056   132.056   14.673    89.29  0.000 
  17.82  0.000 Environment*Feed              12    35.141    35.141    2.928  
  70.031    5.836 Rake Angle*Feed               12    70.031  
nvironment*Rake Angle*Feed   36   126.512  E
Er
Total                        399  3146.982 
 
 
S  R-Sq = 98.33%   R-Sq(adj) = 97.92% 
 
 
 
Analysis of Variance (ANOVA) of Shear angle indicates that the rake angle has 
by far the dominant effect on this force ratio with an F-statistic of 3,897. The feed factor 
is second in significance with an F-statistic of 1,165. The individual effect of 
environment and the interaction effect of environment and rake angle are also fo
preciable effect on the shear angle with their significant F-statistic values. 
The shear plane angle is found to be lowest when machining under a nitrogen 
atmosphere when compared to other environments and is as shown in the main effects 
plot in figure 48. It can also be observed that the shear plane angle increases with 
increase in both rake angle and feed. A 30
o
 rake an
 
 
 71
Variation of Friction Angle (?) with Environment, Rake and Feed 
Statistical analysis of the Friction angle (?) was conducted using the GLM 
(general linear module) of MINITAB 15. The main effects plot indicates that the effect of 
environment and feed on the friction angle is nearly a constant. Friction angle decreases 
appreciably with increasing positive rake angles.   
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Environment
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Rake Angle
Feed
Main Effects Plot for Friction Angle (beta)
Data Means
 
 
Figure 50: Main Effect Plot for Friction Angle (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
40
32
24
40
32
24
Environment
Rake Angle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Friction Angle (beta)
Data Means
 
 
Figure 51: Interaction Plot for Friction Angle (Minitab 15) 
 72
General Linear Model: Friction Angle versus Environment, Rake Angle, Feed  
 
Factor       Type      Levels    Values 
nvironment  fixed       4     Dry, Cold Compressed Air, Nitrogen,E  Cool Mist 
ke Angle   fixed       4     -10, 0, 15, 30 
 0.55  0.878 
 1423.97    39.55   0.67  0.930 
ror                        320  18979.97  18979.97    59.31 
 = 7.70145   R-Sq = 49.40%   R-Sq(adj) = 36.91% 
 
Table 24: ANOVA Table for Friction Angle (Minitab 15) 
 to attain significance on friction angle (?) with their p values being greater 
than 0.0
ident from the above 
xsperiment that the friction angle is soley dependent on rake angle. 
Ra
Feed         fixed       5     0.001, 0.002, 0.003, 0.004, 0.005 
 
 
Analysis of Variance for Friction Angle (beta), using Adjusted SS for Tests 
 
Source                        DF    Seq SS    Adj SS   Adj MS      F      P 
Environment                    3    173.48    173.48    57.83   0.97  0.405 
Rake Angle                     3  14983.93  14983.93  4994.64  84.21  0.000 
Feed                           4    759.27    759.27   189.82   3.20  0.013 
Environment*Rake Angle         9    410.15    410.15    45.57   0.77  0.646 
  0.54  0.888 Environment*Feed              12    383.82    383.82    31.98 
   394.25    32.85  Rake Angle*Feed               12    394.25 
nvironment*Rake Angle*Feed   36   1423.97  E
Er
Total                        399  37508.82 
 
 
S
 
 
 
Analysis of Variance (ANOVA) of Friction angle indicates that the rake angle has 
by far the dominant effect on this force ratio with an F-statistic of 84. The environment 
and feed fail
01.  
The interaction plot obtained shows that with a 30
o
 rake angle tool a much lower 
friction angle is obtained than compared to a 0
o
, 15
o
 or a -10
o
 tool. Also a drastic decrease 
in friction angle is observed between rake angles of 0
o
 to 15
o
.It is ev
e
 
 
 
 
 
 
 
 
 73
 
Variation of Shear Stress (?
s
) with Environment, Rake and Feed 
Statistical analysis of the Shear Stress (?
s
) was conducted using the GLM (general linear 
module) of MINITAB 15. The main effects plot indicates that machining under nitrogen 
environment results in reduced shear stress as compared to other environments. The 
effect of rake angle factor is variable on the shear stress however a decrease in feed 
causes a significant decrease in the shear stress. 
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3
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260
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230
Environment
Me
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Rake Angle
Feed
Main Effects Plot for Shear Stress, Ts (Merchant)
Data Means
 
 
Figure 52: Main Effect Plot for Shear Stress (Minitab 15) 
 
30150-10 0.0050.0040.0030.0020.001
270
245
220
270
245
220
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Shear Stress, Ts (Merchant)
Data Means
 
 
Figure 53: Interaction Plot for Shear Stress (Minitab 15) 
 74
 
 
ironment, Rake Angle, Feed  General Linear Model: Shear Stress versus Env
 
actor       Type     Levels    Values F
Environment  fixed       4    Dry, Cold Compressed Air, Nitrogen, Cool Mist 
 3.59  0.000 
 11712.5    976.0   3.11  0.000 
vironment*Rake Angle*Feed   36   52191.2   52191.2   1449.8   4.61  0.000 
.9    314.2 
S = 17.7257   R
 
 
Analysis of Variance (ANOVA) of the shear stress response indicates that feed 
has a significant main effect upon the response with an F-statistic of 48. The tool rake 
angle is the next m
The interaction between the environment, rake angle and feed is found to have 
increase in feed due to the decrease in shear force and increase in shear area leading to 
increase in shear plane angle [23]. 
 
 
 
Rake Angle   fixed       4    -10, 0, 15, 30 
eed         fixed       5    0.001, 0.002, 0.003, 0.004, 0.005 F
 
 
Analysis of Variance for Shear Stress, Ts(MPa), using Adjusted SS for Tests 
 
Source                        DF    Seq SS    Adj SS   Adj MS      F      P 
Environment                    3    6467.6    6467.6   2155.9   6.86  0.000 
Rake Angle                     3   34665.2   34665.2  11555.1  36.78  0.000 
Feed                           4   61430.8   61430.8  15357.7  48.88  0.000 
  9.90  0.000 Environment*Rake Angle         9   27982.0   27982.0   3109.1 
  13519.3   1126.6  Environment*Feed              12   13519.3 
ake Angle*Feed               12   11712.5  R
En
Error                        320  100543.9  100543
otal                        399  308512.5 T
 
 
-Sq = 67.41%   R-Sq(adj) = 59.36% 
Table 25: ANOVA Table for Shear Stress (Minitab 15) 
 
ost dominant factor with an F-statistic of 36. 
prominence over the shear stress. Also the shear stress is found to decrease with the 
 
 
 
 75
Variation of Tool Surface Roughness with Environment, Rake and Feed 
The visual observations, study and literature, all states that the variation of environment, 
rake angle and feed will have an influence on the tool surface. It can be observed from 
the main effects plot that the tool wear is found to be the least under nitrogen 
environment than compared to dry, cold compressed air or spray coolant environment. 
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80
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40
3
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120
100
80
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40
Environment
Me
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Rake Angle
Feed
Main Effects Plot for Surface Roughness (microns)
Data Means
 
 
Figure 54: Main Effect Plot for Tool Surface Roughness (Minitab 15) 
 
 
30150-10 0.0050.0040.0030.0020.001
150
100
50
150
100
50
Environment
Rake A ngle
Feed
Dry
Cold Compressed Air
Nitrogen
Cool Mist
Environment
-10
0
15
30
Angle
Rake
Interaction Plot for Surface Roughness (microns)
Data Means
 
 
Figure 55: Interaction Plot for Tool Surface Roughness (Minitab 15) 
 76
The dry cutting environment produced an average surface roughness of 102 
microns, with cold compressed air environment producing a surface roughness of 75 
microns. The spray coolant environment resulted in a tool surface roughness of 70 
ic
 in feed and is highest for a 0.005 inch feed. Also it is to be noted that the tool 
 Appendix G provides detailed examples of each calculated value which was 
discussed in the chapter. 
m rons as against nitrogen environment resulting in an average tool surface 
roughness of 55 microns.  
  Tool surface roughness is also found to be higher for the -10
o
 and 30
o
 tool when 
compared to a 0
o
 or a 15
o
 tool which showed significantly less surface roughness 
under all environments. Increase in tool surface roughness is observed with the 
increase
surface roughness is found to increase with the increase in thrust force and cutting 
force.   
 
 
 
 
 
 
 
 
 
 
 77
 
 
Variation of Tool Surface Roughness with Normal Force 
10
20
30
40
50
60
70
100 200 300 400 500
Normal Force (N)
T
o
o
l
 S
u
rface Ro
ug
hn
ess (
m
i
c
ron
s
)
0 degree, Dry 15 degree, Dry 0 degree, Compressed Air 15 degree, Compressed Air
0 degree, Nitrogen 15 degree, Nitrogen 0 degree, Cool Mist 15 degree, Cool Mist
Dry,?0
Dry,?15
Comp?Air,?15 Comp?Air,?0
Cool?Mist,?15
Cool?Mist,?0
Nitrogen,?0
Nitrogen,?15
Figure 56: Variation of Tool surface roughness with Normal Force 
 
ear angle and reduction 
 
 
 
The plot of variation of Tool surface roughness with normal force as shown in Figure 56 
for a 0
o
 and a 15
o
 tool under all cutting environment shows that tool surface roughness 
increases with the increase in normal force. It is also to be noted that a 15
o
 tool has 
always generated less force compared to a 0
o
 tool under all four cutting environments. 
The tool surface roughness in the case of Nitrogen environment is less than the cool mist 
environment for both 0
o
 and 15
o
 tool rake angles. It is evident that nitrogen environment 
showed reduced tool surface roughness due to the decrease in sh
 78
 79
in tool chip contact length. During the experiments it was also observed that the gases 
applications generally proved better results than dry machining.  
CHAPTER 9 
CONCLUSIONS 
nd observations the 
following conclusions are made about the variation of tool forces, tool surface roughness 
and the behavior of the shear angle with the change in input parameters. 
1. The cutting force and the thrust force increases significantly with increase in feed. 
This can be explained by the fact that a feed rate increase will increase the amount 
increased tool forces.  
2. The cutting force and thrust force decreases marginally with the increase in rake 
angle from -10
o
 to 0
o
 but decreases rapidly with the increase in rake angle from 0
o
 
to 30
o
. This can be explained by the fact that the tool chip contact area decreases 
with the increase in rake angle leading to the decrease in tool forces.  
3.  Reduced cutting force and thrust force are achieved using cold compressed air 
environment as compared to dry environment. The nitrogen environment produced 
a marginal decrease in forces as compared to spray coolant environment. It can be 
concluded that a tube turning set up with a nitrogen environment is the best 
environment for prolonging tool life at 500 sfpm during Orthogonal Tube Turning 
     of AL 6061-T6.
 
Based on a through analysis of the experimental results a
of energy required to cause the plastic deformation of the material, resulting in 
 80
4. Onset of Shear angle is found to be influenced by all the factor levels and is found 
to be the least at nitrogen environment. An increase in onset of shear angle is 
observed with an increase in rake angle and feed. 
5. Tool surface roughness increases with the increase in feed from 0.001 inch to 0.005 
inch.The surface roughness is also found to be significantly less when using a 0
o 
or 
a15
o
 rake angle tool when compared to a -10
o
 or a 30
0
 tool. 
6. Environment is found to have a significant effect on the tool surface roughness. 
The surface roughness in the nitrogen environment is found to be significantly less 
than all the other machining environments. The dry cutting environment produced 
an average surface roughness of 102 microns, with cold compressed air 
environment producing a surface roughness of 75 microns. The spray coolant 
environment resulted in a tool surface roughness of 70 micros as against nitrogen 
environment resulting in a average tool roughness of 55 microns.  
 
 
 
 
 
 
 81
CHAPTER 10 
SCOPE FOR FUTURE WORK 
A recent CIRP working paper reports the survey by a leading tool manufacturer 
indicating the following factors  
? A correct cutting tool is selected less than 50% of the time. 
? A tool is used at the rated cutting speed only 58% of the time. 
  Viktor P Astakhov [24] states that today?s Industry is completely dependent on 
empirical data provided by cutting tool and machine tool manufacturers as well as data 
provided through handbooks and workshops by Professional Engineering Associations. 
There is a lack of agreement in the data as it does not originate from the same source and 
there is no unified Metal Cutting Theory. Non availability of reliable tool life and optimum 
cutting parameters data for various tool and work material combinations leads to the 
reduced life of cutting tool and machine tools, so it is of prime importance to develop a 
realistic theory that governs the mechanism of metal cutting more deterministically and 
more accurately. 
 
1. Additional models, other than the 1945 Merchant Model, can be compared to the data 
obtained in this thesis.
 
 
? Only 38% of tools are used up to their full life capability 
 82
2. Cryogenic nitrogen is being investigated routinely as a cutting enviorment.   It was not 
done during this experiment due to time and cost constraints.  The forces, shear angle 
and tool surface roughness data under the various environments carried out can be 
compared with the cryogenic environment to more accurately determine the variation 
of responses with environment.  
plete insight of the behavior of the cutting forces, onset of shear plane angle, 
friction angle, shear stress and tool surface roughness with the variation in the feed, 
rake angle, cutting speed and environment is yet to be established by providing 
correction factors to the classical equations if necessary. 
4. A simulation of the orthogonal tube turning can be carried out using an analysis 
package like ANSYS or NASTRAN to develop an optimum cutting condition in terms 
of tool forces and tool surface roughness. 
 
 
 
 
3. The com
 
 83
REFERENCES 
 
Journal of Applied 
Physics, Vol. 16, pp 267-275, 1945. 
2. Paul Degarmo, E., Black, J.T., Kosher, R A., ?Materials and Processes in 
Manufacturing,? 10
th
 Edition, Prentice Hall, Inc. 
3. Payton, L.N., ?A Correction to the 20
th
 Century Orthogonal Metal Cutting 
Proceedings of the 2009 Industrial Engineering Research Conference.
4. Lee, E.H., Shaffer, B.W., ?The Theory of Plasticity Applied to a Problem of 
Machining,? Journal of Applied Mechanics
5. Rowe, G.W., SMART, E.F., ?The Importance of Oxygen in Dry Machining of 
Metal on a Lathe,? British Journal of Applied Physics, Vol.14, 1963. 
rkiewicz, M., ?High Pressure Water jet 
Cooling/Lubrication to Improve Machining Efficiency in Milling,? Journal of 
Machine Tools Manufacturing
7. Klocke, F., Eisenblatter, G., ?Keynote Papers,? RWTH Aachen, Germany. 
8. Huang, L.H., Chen J.C., Chang, T., ?Effect of Tool/Chip Contact Length on 
Orthogonal Tube Turning Performance,? Journal of Industrial Technology, 
Vol.15, No. 2, February 1999 to April 1999. 
goi, B.K.A., ?Dry machining: machining of the Future,? Journal 
of Materials Processing Technology, Vol. 101, 2000, pp 287-291
1. Merchant, M.E., ?Mechanics of the Metal Cutting process,? 
Models,?  
, Trans. ASME, Vol.73, 1951. 
6. Kovacevic, R., Cherukuthota, C., Mazu
, Vol.35, No. 10, 1995, pp 1459 ? 1473. 
9. Sreejith, P.S., N
 84
 
10. Margitu, D.B., Ciocirlan, B.O., Craciunoiu, N., ?Non-linear Dynamics in 
Orthogonal Turning Process,? Department of Mechanical Engineering, Auburn 
University, 202, Ross Hall, Auburn, AL 36849, 2000. 
11. Grzesik, W., ?The Influence of Thin Hard Coatings on Frictional Behavior in the 
 of Cutting Fluids 
A.B., ?Beneficial effects of Cryogenic 
Machine Tools and 
 in Turning,? Journal of Materials Processing Technology, Vol.153-
rasekaran, H., ?Investigation of the Effects of Tool Micro-
Tool and 
Orthogonal Cutting Process? Technical University of Opole, Department of 
Manufacturing Engineering and Automation, Opole, Poland, 2000. 
12. Vieira, J.M., Machado, A.R., Ezugwu, E.O., ?Performance
during Face Milling of Steels,? Journal of Materials Processing Technology, 
Vol.116, 2001, pp 244-251. 
13. Paul, S., Dhar, N.R., Chattopadhyay, 
Cooling over Dry and Wet Machining on Tool Wear and Surface Finish in 
Turning AISI 1060 Steel,? Journal of Materials Processing Technology, 2007. 
14. Diniz, A.E., Micaroni, R., ?Cutting Conditions for Finish Turning Process Aiming 
the use of Dry Cutting,? International Journal of 
Manufacture, Vol.42, 2002, pp 899-904. 
15. Cakir, O., Kiyak, M., Altan, E., ?Comparison of Gases Applications to Wet and 
Dry Cuttings
154, 2004, pp 35-41. 
16. M?Saoubi, R., Chand
geometry and Coating on Tool Temperature during Orthogonal Turning of 
Quenched and Tempered Steel,? International Journal of Machine 
Manufacture, Vol.44, No.2, pp213-224, 2004. 
 85
 
17. Salgam, H., Yaldiz, S., Unsarcar, F., ?The Effect of Tool Geometry and Cutting 
Speed on Main Cutting Force and Tool Tip Temperature,? Mechanical 
Engineering department, Technical Science College, Selcuk University, Konya, 
Turkey, 2005. 
18. Kalyankumar, K.V.B.S., Choudry, S.K., ?Investigation of Tool Wear and Cutting 
Force in Cryogenic Machining using Design of Experiments,? Journal of 
Materials Processing Technology, Vol.203, 2007, pp 95-101. 
19. Pujana, J., Azarolla, P.J., Villar, J.A., ?In-process High Speed Photography 
Applied to Orthogonal Turning,? Journal of Materials Processing 
Technology,Vol.202, 2008, pp 475-485. 
20. Stanford, M., Lister, P.M., Morgan, C., Kibble, K.A., ?Investigation into the use 
of Gaseous and Liquid Nitrogen as a Cutting Fluid when Turning BS 970-80A15 
(En32b) Plain Carbon Steel using WC-Co uncoated tooling,? Journal of Materials 
Processing Technology, Vol.209, Issue 2, 2009, pp 961-97 
21. William H Cubberly., ?Metals Handbook by American Society for Metals, ASM 
Handbook Committee, ASM International, Bruce P Bardes Edition: 9, 
illustrated?. 
22. Payton, L.N., ?Orthogonal Machining of Copper using a Virtual Quick Stop 
Device?, June 2000. 
23. Kobayashi, S., Thomsen, E.G., ?Role of Friction in Metal Cutting,? Journal of 
Engineering for Industry, Transactions of the ASME, 1960, pp324-332. 
24. Astakhov, V.P., ?Metal Cutting Mechanics,? Boca Raton: CRC Press, c1999.  
 86
APPENDIX A 
The calibration certificate for the Kistler 9257 A dynamometer is given below. 
 
 
 
 87
APPENDIX B 
 
The spindle speed was calculated considering the material hardness and the 
geometrical dimensions of the alloy as shown below. 
: 61 
Har e .5 HRB 
Dia
Wall thickness: 0.125 inches 
Con d  a feed of 02 .00 e ?M ry?s 
Handbook? 27 ition, pp 1038 for an Alumi 061 i ne SS 
tool the speed is 500 feet/minute
 
Volum pt by the to  1 re o x ?
                                                                                        = 0.7855 feet. 
                                        Cutting Speed 
RPM =              
                      Volume Swept by the tool in 1 revo
                      
Alloy Aluminum 60  
dn ss: 54
meter: 3 inches 
si ering 0.0 inch/rev to 0 5 inch/r v from achine
th
 Ed num 6  alloy be ng machi d by a H
. 
e Swe ol in voluti n = 2  x 1.5 = 9.426 inches 
lution 
 
rev
feet
ute
feet
78.0 55
min
 = 636.5372 RPM 
The spindle speed was approximated as 640 RPM for the ease of calculations. 
500
=
 88
 89
AP
The below table gives the Thrust rce,  an i ss
the 80 different factor level comb tion
Run N onment ? F
PENDIX C 
 
Fo  Cutting Force d Cut Ch p thickne  data for all 
ina s. 
o. Envir eed Run Ft Fc tc 
1 Dry -10 0.001 Run 1 177.7517 175.993 0.0079 
2 Dry -10 0.001 Run 2 184.1773 177.2929 0.00833 
3 Dry -10 0.001 Run 3 177.9254 180.9517 0.00834 
4 Dry -1 10 0.001 Run 4 89.0791 181.1614 0.00808 
5 Dry -10 0.001 Run 5 194.356 185.0437 0.00837 
6 Dry -10 0.002 Run 1 2 251.7904 63.4748 0.01248 
7 Dry -10 0.002 Run 2 257.8228 268.7747 0.01263 
8 Dry -10 0.002 Run 3 258.6709 267.5613 0.01207 
9 Dry -10 0.002 Run 4 2 262.6206 72.2441 0.01229 
10 Dry -10 0.002 Run 5 264.2924 277.1065 0.01216 
11 Dry -10 0.003 Run 1 310.3103 335.1369 0.0177 
12 Dry -10 0.003 Run 2 327.1769 341.8487 0.01766 
13 Dry -10 0.003 Run 3 304.3356 340.2505 0.01742 
14 Dry -10 0.003 Run 4 313.9446 347.0742 0.0176 
15 Dry -10 0.003 Run 5 301.7063 335.4178 0.01719 
16 Dry -10 0.004 Run 1 356.3264 412.3702 0.02054 
17 Dry -10 0.004 Run 2 350.0089 402.2674 0.02122 
18 Dry -10 0.004 Run 3 370.2052 419.0703 0.02041 
19 Dry -10 0.004 Run 4 364.9769 409.6705 0.02143 
20 Dry -10 0.004 Run 5 375.6279 424.4903 0.02065 
21 Dry -10 0.005 Run 1 407.1834 474.696 0.02355 
22 Dry -10 0.005 Run 2 410.9808 475.7449 0.02417 
23 Dry -10 0.005 Run 3 404.456 467.8064 0.02412 
24 Dry -10 0.005 Run 4 415.8704 479.9004 0.02454 
25 Dry -10 0.005 Run 5 416.2005 483.9898 0.02425 
26 Dry 0 0.001 Run 1 178.7172 172.4828 0.00647 
27 Dry 0 0.001 Run 2 175.5777 171.1007 0.00624 
28 Dry 0 0.001 Run 3 175.7445 174.1149 0.0063 
29 Dry 0 0.001 Run 4 173.5154 170.2533 0.00651 
30 Dry 0 0.001 Run 5 170.9717 172.3044 0.00647 
31 Dry 0 0.002 Run 1 223.7989 255.7188 0.01126 
32 Dry 0 0.002 Run 2 2 2518.0048 0.2855 0.01114 
 90
Run No. E ?nvironment  Feed Run Ft Fc tc 
33 Dry 0 0.002 Run 3 219.3895 254.1104 0.01158 
34 Dry 0 0.002 Run 4 226.1762 264.9091 0.01145 
35 Dry 0 0.002 Run 5 2 020.2374 255.4329 .01138 
36 Dry 0 0.003 Run 1 293.5401 323.8849 0.01375 
37 Dry 0 0.003 Run 2 304.5111 329.6172 0.0141 
38 Dry 0 0.003 Run 3 297.467 329.553 0.01405 
39 Dry 0 0.003 Run 4 292.9392 325.1263 0.01384 
40 Dry 0 0.003 Run 5 292.05 323.1182 0.01385 
41 Dry 0 0.004 Run 1 360.526 414.8286 0.01746 
42 Dry 0 0.004 Run 2 3 3963.5965 9.0163 0.01774 
43 Dry 0 0.004 Run 3 377.5881 399.5048 0.01746 
44 Dry 0 0.004 Run 4 361.6405 411.0423 0.01735 
45 Dry 0 0.004 Run 5 373.5652 403.9943 0.0179 
46 Dry 0 0.005 Run 1 319.7004 460.565 0.02348 
47 Dry 0 0.005 Run 2 327.1955 450.0505 0.02348 
48 Dry 0 0.005 Run 3 3 027.1843 459.6015 .02314 
49 Dry 0 0.005 Run 4 329.8673 448.3882 0.02324 
50 Dry 0 0.005 Run 5 323.936 458.4112 0.02357 
51 Dry 15 0.001 Run 1 58.8858 127.9112 0.00547 
52 Dry 15 0.001 Run 2 65.4667 120.879 0.00556 
53 Dry 15 0.001 Run 3 69.0838 114.2018 0.00562 
54 Dry 15 0.001 Run 4 66.4581 122.6205 0.00522 
55 Dry 15 0.001 Run 5 66.4237 120.155 0.00527 
56 Dry 15 0.002 Run 1 107.4316 201.9459 0.01054 
57 Dry 15 0.002 Run 2 113.0798 200.5681 0.0106 
58 Dry 15 0.002 Run 3 114.3104 199.1714 0.01055 
59 Dry 15 0.002 Run 4 118.0056 204.2604 0.01019 
60 Dry 15 0.002 Run 5 118.1204 201.6331 0.01074 
61 Dry 15 0.003 Run 1 131.4321 261.1614 0.01455 
62 Dry 15 0.003 Run 2 142.362 262.1011 0.01446 
63 Dry 15 0.003 Run 3 153.4347 268.9463 0.01457 
64 Dry 15 0.003 Run 4 148.8125 262.3391 0.01459 
65 Dry 15 0.003 Run 5 151.5232 265.1171 0.01466 
66 Dry 15 0.004 Run 1 199.523 355.5064 0.01961 
67 Dry 15 0.004 Run 2 201.9163 354.7528 0.01952 
68 Dry 15 0.004 Run 3 207.3945 347.9605 0.0196 
69 Dry 15 0.004 Run 4 201.1935 339.4066 0.0194 
70 Dry 15 0.004 Run 5 212.3329 348.3219 0.0195 
71 Dry 15 0.005 Run 1 214.2508 410.0906 0.02203 
72 Dry 15 0.005 Run 2 224.6541 411.051 0.02271 
73 Dry 15 0.005 Run 3 227.3489 405.2153 0.02242 
74 Dry 15 0.005 Run 4 223.9582 407.5608 0.02251 
75 Dry 15 0.005 Run 5 233.539 412.6333 0.02249 
76 Dry 30 0.001 Run 1 63.2424 116.0273 0.00565 
77 Dry 30 0.001 Run 2 63.6391 116.4696 0.00554 
78 Dry 30 0.001 Run 3 63.6573 117.28 0.00562 
79 Dry 30 0.001 Run 4 64.9941 118.6791 0.00552 
Run No. F Run Ft Fc tc Environment ? eed 
80 30 0. R 1 0Dry  001 un 5 62.9518 15.4918 .00545 
81 30 0. R 18 0Dry  002 un 1 81.252 8.0265 .00951 
82 30 0. R 17Dry  002 un 2 81.1605 6.7414 0.0096 
83 30 0. R 1 0Dry  002 un 3 88.0791 78.6659 .00958 
84 30 0. R 1 0Dry  002 un 4 90.344 81.2736 .00927 
85 30 0. R 0Dry  002 un 5 91.9134 182.55 .00933 
86 30 0. R 2 0Dry  003 un 1 92.8429 36.4955 .01134 
87 30 0. R 2 0Dry  003 un 2 99.4893 39.5004 .01155 
88 30 0. R 2 0Dry  003 un 3 98.1772 38.2484 .01113 
89 30 0. R 9 0Dry  003 un 4 8.0449 242.13 .01143 
90 30 0. R 1 2 0Dry  003 un 5 00.0638 39.2623 .01156 
91 30 0. R 1 31Dry  004 un 1 36.5777 6.4789 0.0115 
92 30 0. R 1 3 0Dry  004 un 2 40.2462 23.6529 .01152 
93 30 0. R 1 3 0Dry  004 un 3 43.6655 15.2217 .01569 
94 30 0. R 1 3 0Dry  004 un 4 41.0172 22.3968 .01583 
95 30 0. R 3Dry  004 un 5 141.963 16.2296 0.0156 
96 30 0. R 3 0Dry  005 un 1 90.2882 33.6152 .01761 
97 30 0. R 3 0Dry  005 un 2 93.9447 33.7997 .01768 
98 30 0. R 3 0.Dry  005 un 3 91.8477 39.6543 01733 
99 30 0. R 1 3 0Dry  005 un 4 01.1709 35.6297 .01756 
100 30 0. R 34 0Dry  005 un 5 99.2913 3.7709 .01766 
101 -10 0. R 1 1 0Compressed Air  001 un 1 97.7884 82.1416 .00933 
102 -10 0. R 2 18 0Compressed Air  001 un 2 01.2496 5.7809 .00958 
103 -10 0. R 1 1 0Compressed Air  001 un 3 99.8761 84.3276 .00919 
104 -1 0. R 19 1 0Compressed Air 0 001 un 4 9.5928 86.4235 .00951 
105 -1 0. R 20 1 0Compressed Air 0 001 un 5 0.8335 87.2002 .00975 
106 -1 0. R 25 2 0Compressed Air 0 002 un 1 6.1353 62.1515 .01296 
107 -1 0. R 25 2 0.Compressed Air 0 002 un 2 9.7657 60.5958 01365 
108 -1 0. R 261 2 0Compressed Air 0 002 un 3 .4814 64.5966 .01346 
109 -1 0. R 2 27 0Compressed Air 0 002 un 4 68.5294 1.2766 .01356 
110 -1 0. R 2 2 0Compressed Air 0 002 un 5 69.8701 74.0365 .01359 
111 -1 0. R 29 3Compressed Air 0 003 un 1 3.3559 24.7656 0.0165 
112 -1 0. R 2 3Compressed Air 0 003 un 2 96.6442 24.1789 0.0164 
113 -1 0. R 3 3 0Compressed Air 0 003 un 3 02.8356 29.6997 .01657 
114 -1 0. R 2 3 0.Compressed Air 0 003 un 4 99.3754 31.8196 01632 
115 -1 0. R 3 0Compressed Air 0 003 un 5 10.1497 340.834 .01661 
116 -1 0. R 33 3 0Compressed Air 0 004 un 1 9.8878 95.3502 .01964 
117 -1 0. R 3 3 0.Compressed Air 0 004 un 2 47.7198 97.9039 01972 
118 -1 0. R 3 4 0Compressed Air 0 004 un 3 54.7987 05.5534 .01951 
119 -1 0. R 3 4 0Compressed Air 0 004 un 4 58.8273 05.5811 .01965 
120 -1 0. R 3 4 0Compressed Air 0 004 un 5 59.2857 10.5226 .01973 
121 -1 0. R 40 4 0Compressed Air 0 005 un 1 2.3728 59.5607 .02311 
122 -1 0. R 4 0Compressed Air 0 005 un 2 396.068 66.8819 .02345 
123 -1 0. R 4 4 0Compressed Air 0 005 un 3 07.5286 74.8292 .02309 
124 -1 0. R 4 4Compressed Air 0 005 un 4 02.6982 77.0524 0.0237 
125 -1 0. R 3 0Compressed Air 0 005 un 5 99.2012 472.631 .02363 
126 0. R 1 1 0Compressed Air 0 001 un 1 62.9359 65.2332 .00768 
 91
 92
Run No. Environment ? Feed Run Ft Fc tc 
127 Compressed Air 0 0.001 Run 2 162.1041 165.1499 0.00737 
128 Compressed Air 0 0.001 Run 3 162.9914 165.581 0.00727 
129 Compressed Air 0 0.001 Run 4 165.6891 166.338 0.00737 
130 Compressed Air 0 0.001 Run 5 1 166.8184 68.7141 0.00771 
131 Compressed Air 0 0.002 Run 1 2 2619.5647 1.0481 0.01325 
132 Compressed Air 0 0.002 Run 2 21 23.2506 54.2292 0.01335 
133 Compressed Air 0 0.002 Run 3 21 25.2732 54.5406 0.01311 
134 Compressed Air 0 0.002 Run 4 220.1807 259.7471 0.01298 
135 Compressed Air 0 0.002 Run 5 213.1102 256.4842 0.01278 
136 Compressed Air 0 0.003 Run 1 306.661 331.6338 0.01537 
137 Compressed Air 0 0.003 Run 2 304.5306 333.9596 0.01518 
138 Compressed Air 0 0.003 Run 3 298.4483 337.417 0.01564 
139 Compressed Air 0 0.003 Run 4 309.4737 345.7519 0.01527 
140 Compressed Air 0 0.003 Run 5 3 302.9238 42.2661 0.01543 
141 Compressed Air 0 0.004 Run 1 371.3089 412.5695 0.02037 
142 Compressed Air 0 0.004 Run 2 3 079.8773 415.9003 .02058 
143 Compressed Air 0 0.004 Run 3 378.5803 417.6269 0.01986 
144 Compressed Air 0 0.004 Run 4 374.1755 407.4259 0.02045 
145 Compressed Air 0 0.004 Run 5 377.5255 403.7149 0.0196 
146 Compressed Air 0 0.005 Run 1 3 422.9589 63.6449 0.02241 
147 Compressed Air 0 0.005 Run 2 328.9528 459.787 0.02253 
148 Compressed Air 0 0.005 Run 3 337.3287 459.4949 0.02239 
149 Compressed Air 0 0.005 Run 4 328.9954 454.964 0.02239 
150 Compressed Air 0 0.005 Run 5 337.7602 463.6962 0.02234 
151 Compressed Air 15 0.001 Run 1 61.5124 113.1831 0.00548 
152 Compressed Air 15 0.001 Run 2 63.2416 114.0435 0.00556 
153 Compressed Air 15 0.001 Run 3 64.4127 116.2906 0.00542 
154 Compressed Air 15 0.001 Run 4 65.1112 117.1496 0.0053 
155 Compressed Air 015 0.001 Run 5 66.058 117.3281 .00537 
156 Compressed Air 1015 0.002 Run 1 5.2246 197.447 0.00976 
157 Compressed Air 15 0.002 Run 2 104.2617 190.4033 0.01001 
158 Compressed Air 15 0.002 Run 3 112.199 195.5409 0.00965 
159 Compressed Air 15 0.002 Run 4 114.3065 199.6868 0.00969 
160 Compressed Air 1115 0.002 Run 5 9.2931 200.8401 0.00975 
161 Compressed Air 15 0.003 Run 1 134.4895 254.2782 0.0138 
162 Compressed Air 15 0.003 Run 2 143.1355 265.2779 0.01368 
163 Compressed Air 215 0.003 Run 3 142.515 65.0369 0.01354 
164 Compressed Air 215 0.003 Run 4 144.0262 65.7019 0.0135 
165 Compressed Air 15 0.003 Run 5 145.1991 268.8831 0.01379 
166 Compressed Air 15 0.004 Run 1 167.0502 323.9666 0.01654 
167 Compressed Air 15 0.004 Run 2 163.5994 323.5697 0.01638 
168 Compressed Air 15 0.004 Run 3 165.446 323.5697 0.01631 
169 Compressed Air 015 0.004 Run 4 172.0612 329.7176 .01671 
170 Compressed Air 15 0.004 Run 5 167.4072 326.1765 0.01645 
171 Compressed Air 15 0.005 Run 1 159.3689 363.3295 0.01976 
172 Compressed Air 15 0.005 Run 2 167.9498 372.6552 0.01953 
173 Compressed Air 15 0.005 Run 3 169.5887 372.6489 0.01964 
 93
Run No. Environment ? Feed Run Ft Fc tc 
174 Compressed Air 15 0.005 Run 4 167.1795 376.4682 0.01979 
175 Compressed Air 15 0.005 Run 5 170.1 375.4764 0.01981 
176 Compressed Air 30 0.001 Run 1 29.9759 89.3659 0.00359 
177 Compressed Air 30 0.001 Run 2 33.7425 91.2695 0.00387 
178 Compressed Air 30 0.001 Run 3 32.2379 95.873 0.00374 
179 Compressed Air 30 0.001 Run 4 35.996 95.9412 0.00373 
180 Compressed Air 30 0.001 Run 5 38.689 94.1467 0.00381 
181 Compressed Air 30 0.002 Run 1 44.4358 149.7706 0.00755 
182 Compressed Air 30 0.002 Run 2 47.7565 152.4468 0.00754 
183 Compressed Air 30 0.002 Run 3 50.2597 155.6077 0.00705 
184 Compressed Air 30 0.002 Run 4 50.2975 155.8898 0.00742 
185 Compressed Air 30 0.002 Run 5 51.8714 156.5935 0.00704 
186 Compressed Air 30 0.003 Run 1 63.5885 215.6585 0.00967 
187 Compressed Air 30 0.003 Run 2 61.2472 210.745 0.00965 
188 Compressed Air 30 20.003 Run 3 64.6666 11.8868 0.00977 
189 Compressed Air 30 0.003 Run 4 69.2517 216.0162 0.0097 
190 Compressed Air 30 0.003 Run 5 70.628 217.1014 0.00964 
191 Compressed Air 30 0.004 Run 1 92.6672 285.7289 0.01352 
192 Compressed Air 30 0.004 Run 2 88.1638 279.4771 0.01333 
193 Compressed Air 30 0.004 Run 3 86.1354 277.423 0.01349 
194 Compressed Air 30 0.004 Run 4 86.2464 281.964 0.01342 
195 Compressed Air 30 0.004 Run 5 91.2761 287.9853 0.01348 
196 Compressed Air 30 0.005 Run 1 109.3864 328.9997 0.01762 
197 Compressed Air 30 320.005 Run 2 107.6019 5.5716 0.01754 
198 Compressed Air 30 00.005 Run 3 108.0435 331.8501 .01757 
199 Compressed Air 30 0.005 Run 4 112.4562 336.0007 0.01767 
200 Compressed Air 30 0.005 Run 5 102.807 322.619 0.01777 
201 Nitrogen -10 0.001 Run 1 206.6564 195.5815 0.00968 
202 Nitrogen -10 0.001 Run 2 207.1426 192.6893 0.0095 
203 Nitrogen -10 0.001 Run 3 202.68 194.1392 0.00924 
204 Nitrogen -10 0.001 Run 4 217.7624 200.6148 0.00938 
205 Nitrogen -10 0.001 Run 5 214.5732 198.1373 0.00967 
206 Nitrogen -10 0.002 Run 1 287.6712 281.1819 0.01354 
207 Nitrogen -10 0.002 Run 2 287.13 282.1961 0.01346 
208 Nitrogen -10 0.002 Run 3 292.2072 285.1416 0.01364 
209 Nitrogen -10 0.002 Run 4 284.7899 279.5205 0.01352 
210 Nitrogen -10 0.002 Run 5 289.2702 279.558 0.01318 
211 Nitrogen -10 0.003 Run 1 383.9224 395.708 0.01845 
212 Nitrogen -10 0.003 Run 2 373.3497 398.0761 0.01843 
213 Nitrogen -10 0.003 Run 3 382.5961 385.8474 0.01838 
214 Nitrogen -10 0.003 Run 4 382.5391 391.1423 0.01855 
215 Nitrogen -10 0.003 Run 5 379.7901 396.6776 0.01825 
216 Nitrogen -10 0.004 Run 1 368.9621 439.3335 0.0205 
217 Nitrogen -10 0.004 Run 2 373.8964 424.6515 0.02083 
218 Nitrogen -10 0.004 Run 3 381.3443 437.8459 0.02043 
219 Nitrogen -10 0.004 Run 4 390.1037 439.4337 0.02089 
220 Nitrogen -10 0.004 Run 5 377.0451 433.2095 0.02045 
Run No. Environment ? Feed Run Ft Fc tc 
221 Nitrogen -10 0.005 Run 1 395.6619 495.5847 0.02189 
222 Nitrogen -10 0.005 Run 2 373.1608 478.6916 0.02219 
223 Nitrogen -10 0.005 Run 3 378.8455 472.3057 0.02183 
224 Nitrogen -10 0.005 Run 4 382.9149 474.1717 0.02223 
225 Nitrogen -10 0.005 Run 5 392.4226 487.8136 0.02217 
226 Nitrogen 0 0.001 Run 1 164.5504 184.5599 0.00813 
227 Nitrogen 0 0.001 Run 2 163.1026 182.9984 0.00817 
228 Nitrogen 0 0.001 Run 3 159.9201 178.6047 0.00812 
229 Nitrogen 0 0.001 Run 4 1 161.9422 82.6511 0.00825 
230 Nitrogen 0 0.001 Run 5 16 13.0827 81.1829 0.00806 
231 Nitrogen 0 0.002 Run 1 2 233.1829 71.1694 0.01107 
232 Nitrogen 0 0.002 Run 2 2 234.9983 66.0591 0.01385 
233 Nitrogen 0 0.002 Run 3 242 2.5081 75.9159 0.01366 
234 Nitrogen 0 0.002 Run 4 236.4188 270.1852 0.01361 
235 Nitrogen 0 0.002 Run 5 237.9905 274.003 0.01357 
236 Nitrogen 0 0.003 Run 1 279.5769 346.4283 0.01688 
237 Nitrogen 0 0.003 Run 2 279.0627 343.8411 0.01675 
238 Nitrogen 0 0.003 Run 3 281.6154 342.3731 0.01656 
239 Nitrogen 0 0.003 Run 4 275.8128 342.3738 0.01689 
240 Nitrogen 0 0.003 Run 5 279.2154 342.2708 0.01653 
241 Nitrogen 0 0.004 Run 1 334.6459 425.5195 0.01958 
242 Nitrogen 0 0.004 Run 2 331.8301 416.7075 0.01971 
243 Nitrogen 0 0.004 Run 3 335.0354 424.1981 0.01964 
244 Nitrogen 0 0.004 Run 4 328.8234 420.35 0.01964 
245 Nitrogen 0 0.004 Run 5 326.9944 424.9836 0.0197 
246 Nitrogen 0 0.005 Run 1 430.5991 484.6631 0.02352 
247 Nitrogen 0 0.005 Run 2 4 027.0402 488.0082 .02404 
248 Nitrogen 0 0.005 Run 3 417.6366 483.0138 0.02342 
249 Nitrogen 0 0.005 Run 4 424.0487 490.4496 0.02468 
250 Nitrogen 0 0.005 Run 5 417.0269 487.2506 0.02383 
251 Nitrogen 15 0.001 Run 1 78.6877 132.4233 0.00646 
252 Nitrogen 15 0.001 Run 2 77.7225 130.8423 0.00596 
253 Nitrogen 15 0.001 Run 3 78.8442 129.2723 0.00632 
254 Nitrogen 15 0.001 Run 4 76.9546 133.4419 0.00612 
255 Nitrogen 15 0.001 Run 5 77.8638 129.4782 0.00641 
256 Nitrogen 15 0.002 Run 1 150.1096 221.7002 0.01123 
257 Nitrogen 15 0.002 Run 2 152.0043 220.2428 0.01148 
258 Nitrogen 15 0.002 Run 3 156.324 228.9791 0.01119 
259 Nitrogen 15 0.002 Run 4 149.3831 219.0391 0.01152 
260 Nitrogen 15 0.002 Run 5 149.2316 219.1011 0.01164 
261 Nitrogen 15 0.003 Run 1 167.8966 291.6661 0.01467 
262 Nitrogen 15 0.003 Run 2 163.8237 284.3597 0.01483 
263 Nitrogen 15 0.003 Run 3 166.1155 286.7002 0.01511 
264 Nitrogen 15 0.003 Run 4 169.8913 290.2186 0.01501 
265 Nitrogen 15 0.003 Run 5 170.3016 295.5275 0.01529 
266 Nitrogen 15 0.004 Run 1 241.7012 380.6288 0.02117 
267 Nitrogen 15 0.004 Run 2 243.4664 381.1891 0.02134 
 94
Run No. Environment ? Feed Run Ft Fc tc 
268 Nitrogen 15 0.004 Run 3 236.7358 376.3736 0.02151 
269 Nitrogen 15 0.004 Run 4 240.0703 388.8308 0.02168 
270 Nitrogen 15 0.004 Run 5 247.0985 389.9095 0.02121 
271 Nitrogen 15 0.005 Run 1 223.7015 430.0145 0.02171 
272 Nitrogen 15 0.005 Run 2 222.2084 427.8287 0.02216 
273 Nitrogen 15 0.005 Run 3 229.9665 428.6029 0.02209 
274 Nitrogen 15 0.005 Run 4 230.929 429.1843 0.02194 
275 Nitrogen 15 0.005 Run 5 233.4081 433.5332 0.02206 
276 Nitrogen 30 0.001 Run 1 34.2568 91.7117 0.00406 
277 Nitrogen 30 0.001 Run 2 34.379 93.6644 0.00414 
278 Nitrogen 30 0.001 Run 3 36.4733 95.4205 0.00396 
279 Nitrogen 30 00.001 Run 4 37.0401 96.0515 .00403 
280 Nitrogen 30 0.001 Run 5 31.39 92.8399 0.00367 
281 Nitrogen 30 0.002 Run 1 57.6798 158.8456 0.00755 
282 Nitrogen 30 0.002 Run 2 58.8684 169.1589 0.00755 
283 Nitrogen 30 10.002 Run 3 64.8787 66.0229 0.00761 
284 Nitrogen 30 00.002 Run 4 64.8416 167.4373 .00754 
285 Nitrogen 30 00.002 Run 5 54.8339 171.6381 .00753 
286 Nitrogen 30 0.003 Run 1 70.0972 213.5992 0.01228 
287 Nitrogen 30 0.003 Run 2 74.4158 219.5313 0.01212 
288 Nitrogen 30 20.003 Run 3 76.2422 18.8497 0.01257 
289 Nitrogen 30 0.003 Run 4 74.3471 217.4577 0.01227 
290 Nitrogen 30 20.003 Run 5 83.6924 24.6447 0.01268 
291 Nitrogen 30 0.004 Run 1 76.5872 261.6407 0.01532 
292 Nitrogen 30 0.004 Run 2 76.7912 262.8484 0.01655 
293 Nitrogen 30 0.004 Run 3 82.3925 270.9511 0.01568 
294 Nitrogen 30 0.004 Run 4 85.1815 271.8372 0.0167 
295 Nitrogen 30 0.004 Run 5 83.8936 269.3505 0.01676 
296 Nitrogen 30 0.005 Run 1 195.738 376.7756 0.01659 
297 Nitrogen 30 00.005 Run 2 191.2584 369.0897 .01658 
298 Nitrogen 30 0.005 Run 3 198.9184 369.0897 0.01651 
299 Nitrogen 30 0.005 Run 4 197.3296 364.3208 0.01687 
300 Nitrogen 30 30.005 Run 5 186.2928 69.2408 0.01652 
301 Cool Mist -1 10 0.001 Run 1 95.7094 196.7856 0.00929 
302 Cool Mist -10 0.001 Run 2 196.3354 192.175 0.00955 
303 Cool Mist -1 20 0.001 Run 3 204.0934 01.2071 0.00931 
304 Cool Mist -10 0.001 Run 4 201.2784 193.76 0.00956 
305 Cool Mist -10 0.001 Run 5 208.4875 202.2933 0.00952 
306 Cool Mist -10 0.002 Run 1 2 297.3487 90.4151 0.01465 
307 Cool Mist -10 0.002 Run 2 300.1617 291.3465 0.01463 
308 Cool Mist -10 0.002 Run 3 28 289.5194 6.3318 0.01472 
309 Cool Mist -10 0.002 Run 4 289.8274 286.5597 0.01462 
310 Cool Mist -10 0.002 Run 5 2 29387.2581 .0959 0.01475 
311 Cool Mist -10 0.003 Run 1 3 359.714 75.0335 0.01655 
312 Cool Mist -10 0.003 Run 2 359.7902 373.8692 0.01676 
313 Cool Mist -10 0.003 Run 3 349.0415 367.1384 0.01673 
314 Cool Mist -10 0.003 Run 4 356.6663 364.5413 0.01685 
 95
Run No. Environment ? Feed Run Ft Fc tc 
315 Cool Mist -10 0.003 Run 5 349.8105 362.813 0.01679 
316 Cool Mist -10 0.004 Run 1 375.2386 428.8634 0.0223 
317 Cool Mist -10 0.004 Run 2 386.0774 429.459 0.02259 
318 Cool Mist -10 0.004 Run 3 373.0587 428.976 0.02229 
319 Cool Mist -10 0.004 Run 4 374.3297 435.5474 0.02246 
320 Cool Mist -10 0.004 Run 5 376.0092 429.0622 0.02241 
321 Cool Mist -10 0.005 Run 1 483.7339 534.68 0.02549 
322 Cool Mist -10 0.005 Run 2 490.7619 544.2519 0.02545 
323 Cool Mist -10 0.005 Run 3 491.3546 544.1311 0.02561 
324 Cool Mist -10 0.005 Run 4 491.4266 546.3741 0.02552 
325 Cool Mist -10 0.005 Run 5 491.3052 547.4965 0.02548 
326 Cool Mist 0 0.001 Run 1 152.4772 175.133 0.0075 
327 Cool Mist 0 0.001 Run 2 152.2068 180.9133 0.00764 
328 Cool Mist 0 0.001 Run 3 156.0352 179.9308 0.00743 
329 Cool Mist 0 0.001 Run 4 158.5667 179.1254 0.00756 
330 Cool Mist 0 0.001 Run 5 156.9991 176.181 0.00763 
331 Cool Mist 0 0.002 Run 1 247.4289 279.3266 0.0135 
332 Cool Mist 0 0.002 Run 2 243.5632 275.3585 0.0136 
333 Cool Mist 0 0.002 Run 3 246.5875 278.1679 0.01361 
334 Cool Mist 0 0.002 Run 4 2 0.52.9061 282.2953 01338 
335 Cool Mist 0 0.002 Run 5 252.7687 284.098 0.01361 
336 Cool Mist 0 0.003 Run 1 307.5088 364.4924 0.01765 
337 Cool Mist 0 0.003 Run 2 3 0.04.3039 358.126 01779 
338 Cool Mist 0 0.003 Run 3 299.7853 355.6117 0.01761 
339 Cool Mist 0 0.003 Run 4 298.1503 356.1509 0.01764 
340 Cool Mist 0 0.003 Run 5 306.4602 362.9809 0.01773 
341 Cool Mist 0 0.004 Run 1 335.8497 421.2274 0.0214 
342 Cool Mist 0 0.004 Run 2 335.8612 418.2116 0.02153 
343 Cool Mist 0 0.004 Run 3 334.4233 418.9726 0.02152 
344 Cool Mist 0 0.004 Run 4 338.8065 422.3275 0.0217 
345 Cool Mist 0 0.004 Run 5 338.8065 422.8405 0.02106 
346 Cool Mist 0 0.005 Run 1 462.9319 556.5036 0.02455 
347 Cool Mist 0 0.005 Run 2 463.8574 554.134 0.02461 
348 Cool Mist 0 0.005 Run 3 461.594 546.7876 0.02471 
349 Cool Mist 0 0.005 Run 4 456.2306 559.0695 0.02474 
350 Cool Mist 0 0.005 Run 5 454.8527 541.429 0.02464 
351 Cool Mist 15 0.001 Run 1 61.4443 117.727 0.00528 
352 Cool Mist 15 0.001 Run 2 61.1567 117.5025 0.00547 
353 Cool Mist 15 0.001 Run 3 62.3705 120.783 0.00518 
354 Cool Mist 15 0.001 Run 4 63.5301 120.5455 0.00548 
355 Cool Mist 15 0.001 Run 5 64.199 121.12 0.00558 
356 Cool Mist 15 0.002 Run 1 85.1025 187.8264 0.00956 
357 Cool Mist 15 0.002 Run 2 86.1069 189.8 0.00932 
358 Cool Mist 15 0.002 Run 3 86.883 189.432 0.00938 
359 Cool Mist 15 0.002 Run 4 82.936 185.5118 0.00963 
360 Cool Mist 15 0.002 Run 5 82.9105 185.8108 0.00946 
361 Cool Mist 15 0.003 Run 1 153.7815 277.4535 0.01353 
 96
Run No. Environment ? Feed Run Ft Fc tc 
362 Cool Mist 15 0.003 Run 2 151.4303 274.1256 0.01328 
363 Cool Mist 15 0.003 Run 3 156.5936 276.4732 0.0136 
364 Cool Mist 15 0.003 Run 4 157.1355 277.2494 0.01309 
365 Cool Mist 15 0.003 Run 5 159.999 279.3632 0.01303 
366 Cool Mist 15  187.335 341.0167 0.01809 0.004 Run 1
367 Cool Mist 15  181.2863 342.5107 0.01822 0.004 Run 2
368 Cool Mist 15 0.00  Run 3 188.967 347.3744 0.01788 4
369 Cool Mist 15 0.00  Run 4 181.3638 342.7891 0.01809 4
370 Cool Mist 15 0.004 Run 5 186.9441 347.3383 0.01775 
371 Cool Mist 15 0.005 Run 1 202.7457 419.7883 0.0236 
372 Cool Mist 15 0.005 Run 2 209.5801 414.2354 0.02362 
373 Cool Mist 15 0.005 Run 3 209.4235 415.6389 0.02341 
374 Cool Mist 15 0.005 Run 4 211.2018 416.244 0.02326 
375 Cool Mist 15 0.005 Run 5 212.4995 423.9621 0.02362 
376 Cool Mist 30 0.001 Run 1 51.8232 111.6602 0.00384 
377 Cool Mist 30 0.001 Run 2 50.7544 109.552 0.00388 
378 Cool Mist 30 0.001 Run 3 51.1189 112.6215 0.00383 
379 Cool Mist 4 30 0.001 Run 49.955 108.7509 0.00388 
380 Cool Mist 5 30 0.001 Run 50.6559 110.5263 0.00382 
381 Cool Mist 30 0.002 Run 1 55.3825 166.1258 0.007 
382 C 0.002 Run 2 57.7285 169.ool Mist 30 0374 0.00692 
383 Cool 0.002 Run 3 45.0762 158. Mist 30 2031 0.00705 
384 Cool Mist 30 0.002 Run 4 47.4462 161.4845 0.007 
385 Cool 0. Mist 30 002 Run 5 46.0538 157.6917 0.00701 
386 C 0.ool Mist 30 003 Run 1 60.3193 218.0873 0.01036 
387 Cool Mist 30 0.003 Run 2 63.5088 220.3345 0.01041 
388 Cool Mist 30 0.00 3 Run 3 66.2184 223.8298 0.01045 
389 Cool Mist 30 0.003 Run 4 67.4257 224.4799 0.01022 
390 Cool Mist 30 0.003 Run 5 69.5599 224.3973 0.01055 
391 Coo 30 l Mist 0.004 Run 1 189.3965 327.3907 0.01382 
392 Coo 30 l Mist 0.004 Run 2 183.8052 324.5705 0.01378 
393 Cool Mist 30 0.004 Run 3 187.4379 329.6599 0.01391 
394 Cool Mist 30 0.004 Run 4 193.1028 328.3061 0.01384 
395 Cool Mist 30 0.004 Run 5 187.2169 329.0382 0.01342 
396 Cool Mist 30 0.005 Run 1 103.1147 345.305 0.01649 
397 Cool Mist 30 0.00 6.5 Run 2 101.9503 34 1842 0.01632 
398 Cool Mist 30 0.0 305 Run 3 94.5451 33 .1663 0.01572 
399 Cool Mist 30 0.005 Run 4 95.4506 334.7357 0.01666 
400 Cool Mist 30 0.005 R 01un 5 97.1873 341. 94 0.01643 
 
  
 
 
 97
APPENDIX D 
 
The classical metal cutting equations generally used in the study of the mechanics are as 
hip Thickness ratio,
given below. 
C
c
c
t
t
r =                                                               
Onset of Shear Plane Angle,
?
?
?
?
?
?
??
?
=
?
?
?
?
sin1
cos
tan
1
c
c
r
r
    
riction Force, ?? cossin ?+?=
tc
FFFF                                                 
mal Force, ?? sincos ?+?=
tc
FFN  Nor
,
N
F
=?Friction Co-efficient                          
t Force,
22
tc
FFR +=Resultan           
riction Angle,
?
?
?
?
?
?
=
?
N
F
1
tan?  F
?? sincos ???=
tcs
FFF  Shear Force along the onset of Shear Plane,
?? cossin ???=
tcn
FFF  Normal Force along the onset of Shear Plane,
Shear Area, 
?sin
wt
A
s
?
=  
Shear Stress, 
s
s
s
A
F
=? = 
wt
F
s
?
? ?sin
 
 98
 
000,33
VF
HP
c
?
=  Horse Power,
wt
DD
MRR ??
?
=
4
)(
2
1
2
?
 Material removal Rate, 
MRR
HP
HP
s
=  Specific Horse Power, 
n
zzzz
Rq
2222
...........++
=
Root Mean Square Deviation, 
n321
 
 
?R
q 
= (R
q
) 
ne
 (R
 
 
 
 
 
 
 
 
 
 
 
 
 
w
 ?
q used
)  
 
 99
 100
 
 
 
PPEN  
The Force Ratios d fr assic l C u ng  data 
obtained fr  the ents are tablulated below. 
Run F/N F
A DIX E
 
 calculate om the cl al Meta utting eq ations usi the raw
om  experim
 No. F N Ratio Fs  Fn  s/Fn  
1 0144.4904 204.1855 0.7076 154.0374 197.0830 .7816 
2 0184.1773 177.2929 1.0388 177.2929 184.1773 .9626 
3 1177.9254 180.9517 0.9833 180.9517 177.9254 .0170 
4 0189.0791 181.1614 1.0437 181.1614 189.0791 .9581 
5 1 1 0194.356 85.0437 1.0503 85.0437 194.3560 .9521 
6 0202.2132 303.195 0.6669 221.6816 289.2657 .7664 
7 0 1257.8228 268.7747 .9593 268.7747 257.8228 .0425 
8 2 1258.6709 267.5613 0.9668 67.5613 258.6709 .0344 
9 1262.6206 272.2441 0.9647 272.2441 262.6206 .0366 
10 1264.2924 277.1065 0.9538 277.1065 264.2924 .0485 
11 0247.4001 383.9302 0.6444 280.5633 360.4074 .7785 
12 1327.1769 341.8487 0.9571 341.8487 327.1769 .0448 
13 1304.3356 340.2505 0.8944 340.2505 304.3356 .1180 
14 34 1313.9446 347.0742 0.9045 7.0742 313.9446 .1055 
15 1301.7063 335.4178 0.8995 335.4178 301.7063 .1117 
16 0279.3057 467.9808 0.5968 341.5569 424.6841 .8043 
17 1350.0089 402.2674 0.8701 402.2674 350.0089 .1493 
18 1370.2052 419.0703 0.8834 419.0703 370.2052 .1320 
19 0 4 1364.9769 409.6705 .8909 09.6705 364.9769 .1225 
20 1375.6279 424.4903 0.8849 424.4903 375.6279 .1301 
21 0 0318.5673 538.191 .5919 387.0387 491.2592 .7879 
22 1410.9808 475.7449 0.8639 475.7449 410.9808 .1576 
23 1404.456 467.8064 0.8646 467.8064 404.4560 .1566 
24 1415.8704 479.9004 0.8666 479.9004 415.8704 .1540 
25 4 4 1416.2005 83.9898 0.8599 83.9898 416.2005 .1629 
26 0178.7172 172.4828 1.0361 142.8156 203.2089 .7028 
27 0175.5777 171.1007 1.0262 171.1007 175.5777 .9745 
28 1 0175.7445 174.1149 .0094 174.1149 175.7445 .9907 
29 1 0173.5154 70.2533 1.0192 170.2533 173.5154 .9812 
30 1170.9717 172.3044 0.9923 172.3044 170.9717 .0078 
31 25 2 2 0.223.7989 5.7188 0.8752 13.049 64.7417 8047 
32 2 1.1218.0048 250.2855 0.871 250.2855 18.0048 481 
R  un No. F N F/N Ratio Fs  Fn  Fs/Fn 
3 2   3 19.3895 254.1104 0.8634 254.1104 219.3895 1.1583
3  4 226.1762 264.9091 0.8538 264.9091 226.1762 1.1713
3 2   5 20.2374 255.4329 0.8622 255.4329 220.2374 1.1598
3 2 0   6 93.5401 323.8849 .9063 254.7618 355.1952 0.7172
37 30   4.5111 329.6172 0.9238 329.6172 304.5111 1.0824
3 3   8 297.467 29.553 0.9026 329.553 297.4670 1.1079
3  9 292.9392 325.1263 0.901 325.1263 292.9392 1.1099
4   0 292.05 323.1182 0.9038 323.1182 292.0500 1.1064
4   1 360.526 414.8286 0.8691 324.5147 443.5673 0.7316
4 3 39 3   2 63.5965 9.0163 0.9112 99.0163 363.5965 1.0974
4  3 377.5881 399.5048 0.9451 399.5048 377.5881 1.0580
4  4 361.6405 411.0423 0.8798 411.0423 361.6405 1.1366
4  5 373.5652 403.9943 0.9247 403.9943 373.5652 1.0815
4  6 319.7004 460.565 0.6941 383.5295 408.9421 0.9379
4  7 327.1955 450.0505 0.727 450.0505 327.1955 1.3755
4 3  8 27.1843 459.6015 0.7119 459.6015 327.1843 1.4047
4 0  9 329.8673 448.3882 .7357 448.3882 329.8673 1.3593
5   0 323.936 458.4112 0.7066 458.4112 323.9360 1.4151
5  1 89.9852 108.312 0.8308 114.9185 81.3790 1.4121
5  2 65.4667 120.879 0.5416 120.879 65.4667 1.8464
53 69.0838 114.2018 0.6049 114.2018 69.0838 1.6531 
54 66.4581 122.6205 0.542 122.6205 66.4581 1.8451 
55 66.4237 120.155 0.5528 120.155 66.4237 1.8089 
56 156.0384 167.2594 0.9329 177.9194 143.7650 1.2376 
57 113.0798 200.5681 0.5638 200.5681 113.0798 1.7737 
58 114.3104 199.1714 0.5739 199.1714 114.3104 1.7424 
59 118.0056 204.2604 0  .5777 204.2604 118.0056 1.7309
60 118.1204 201.6331 0.5858 201.6331 118.1204 1.7070 
61 194.5472 218.2454 0.8914 228.55 182.3310 1.2535 
62 142.362 262.1011 0.5432 262.1011 142.3620 1.8411 
63 153.4347 268.9463 0.5705 268.9463 153.4347 1.7528 
64 148.8125 262.3391 0.5673 262.3391 148.8125 1.7629 
65 151.5232 265.1171 0.5715 265.1171 151.5232 1.7497 
66 284.7362 291.7525 0.976 307.181 268.0188 1.1461 
67 201.9163 354.7528 0.5692 354.7528 201.9163 1.7569 
68 207.3945 3 0  47.9605 .596 347.9605 207.3945 1.6778
69 201.1935 339.4066 0.5928 339.4066 201.1935 1.6870 
70 212.3329 348.3219 0.6096 348.3219 212.3329 1.6405 
71 313.0896 340.6649 0.9191 352.0655 300.2126 1.1727 
72 224.6541 411.051 0.5465 411.051 224.6541 1.8297 
73 227.3489 405.2153 0.5611 405.2153 227.3489 1.7823 
74 2  23.9582 407.5608 0.5495 407.5608 223.9582 1.8198
75 233.539 412.6333 0.566 412.6333 233.5390 1.7669 
76 112.7831 68.8614 1.6378 103.6847 81.9232 1.2656 
77 63.6391 116.4696 0.5464 116.4696 63.6391 1.8302 
78 63.6573 117.28 0.5428 117.28 -63.6573 4 -1.842
79 64.9941 118.6791 0.5476 118.6791 -64.9941 6 -1.82
 101
Run No. F N F/N Ratio Fs  Fn  Fs/Fn  
80 62.9518 115.4918 0.5451 115.4918 62.9518 1.8346 
81 164.3796 1 122.2097 1.3451 67.9031 117.3218 1.4311 
82 81.1605 1 176.7414 0.4592 76.7414 81.1605 2.1777 
83 88.0791 178.6659 0.493 178.6659 88.0791 2.0285 
84 90.344 181.2736 0.4984 181.2736 90.3440 2.0065 
85 91.9134 182.55 0.5035 182.55 91.9134 1.9861 
86 198.6521 158.3897 1.2542 205.1901 149.8231 1.3695 
87 99.4893 239.5004 0.4154 239.5004 99.4893 2.4073 
88 98.1772 238.2484 0.4121 238.2484 98.1772 2.4267 
89 98.0449 242.13 0.4049 242.13 98.0449 2.4696 
90 100.0638 239.2623 0.4182 239.2623 100.0638 2.3911 
91 276.5192 2 205.7899 1.3437 66.3191 218.8299 1.2170 
92 140.2462 323.6529 0.4333 323.6529 140.2462 2.3077 
93 143.6655 315.2217 0.4558 315.2217 143.6655 2.1941 
94 141.0172 322.3968 0.4374 322.3968 141.0172 2.2862 
95 141.963 316.2296 0.4489 316.2296 141.9630 2.2275 
96 244.9995 243.7751 1.005 295.7011 178.9187 1.6527 
97 93.9447 333.7997 0.2814 333.7997 93.9447 3.5531 
98 91.8477 339.6543 0.2704 339.6543 91.8477 3.6980 
99 101.1709 335.6297 0.3014 335.6297 101.1709 3.3175 
100 99.2913 3 343.7709 0.2888 43.7709 99.2913 3.4622 
101 163.155 213.7201 0.7634 161.1101 215.2657 0.7484 
102 201.2496 1 185.7809 1.0833 85.7809 201.2496 0.9231 
103 199.8761 184.3276 1.0844 184.3276 199.8761 0.9222 
104 1 1 199.5928 86.4235 1.0706 86.4235 199.5928 0.9340 
105 200.8335 187.2002 1.0728 187.2002 200.8335 0.9321 
106 206.7219 302.6463 0.683 223.3055 290.6258 0.7684 
107 259.7657 260.5958 0.9968 260.5958 259.7657 1.0032 
108 26 01.4814 264.5966 .9882 264.5966 261.4814 1.0119 
109 268.5294 271.2766 0.9899 271.2766 268.5294 1.0102 
110 269.8701 274.0365 0.9848 274.0365 269.8701 1.0154 
111 232.5042 370.7724 0.6271 269.7435 344.6286 0.7827 
112 296.6442 324.1789 0.9151 324.1789 296.6442 1.0928 
113 302.8356 329.6997 0.9185 329.6997 302.8356 1.0887 
114 299.3754 331.8196 0.9022 331.8196 299.3754 1.1084 
115 310.1497 340.834 0.91 340.834 310.1497 1.0989 
116 266.0723 448.3648 0.5934 323.5304 408.8442 0.7913 
117 347.7198 397.9039 0.8739 397.9039 347.7198 1.1443 
118 354.7987 405.5534 0.8749 405.5534 354.7987 1.1431 
119 358.8273 405.5811 0.8847 405.5811 358.8273 1.1303 
120 359.2857 410.5226 0.8752 410.5226 359.2857 1.1426 
121 316.458 522.4502 0.6057 370.3565 485.7324 0.7625 
122 396.068 466.8819 0.8483 466.8819 396.0680 1.1788 
123 407.5286 474.8292 0.8583 474.8292 407.5286 1.1651 
124 402.6982 477.0524 0.8441 477.0524 402.6982 1.1846 
125 399.2012 472.631 0.8446 472.631 399.2012 1.1839 
126 162.9359 165.2332 0.9861 142.1853 183.3943 0.7753 
 102
Run No. F N F/N Ratio Fs  Fn  Fs/Fn  
127 162.1041 165.1499 0.9816 165.1499 162.1041 1.0188 
128 162 0.9914 165.581 .9844 165.581 162.9914 1.0159 
129 1 065.6891 166.338 .9961 166.338 165.6891 1.0039 
130 1 1 166.8184 68.7141 0.9888 68.7141 166.8184 1.0114 
131 2 26 219.5647 1.0481 0.8411 24.903 256.4632 0.8769 
132 21 2 23.2506 54.2292 0.8388 54.2292 213.2506 1.1922 
133 21 2 25.2732 54.5406 0.8457 54.5406 215.2732 1.1824 
134 220.1807 259.7471 0.8477 259.7471 220.1807 1.1797 
135 213.1102 256.4842 0.8309 256.4842 213.1102 1.2035 
136 306.661 331.6338 0.9247 266.7801 364.4864 0.7319 
137 304.5306 333.9596 0.9119 333.9596 304.5306 1.0966 
138 298.4483 337.417 0.8845 337.417 298.4483 1.1306 
139 309.4737 345.7519 0.8951 345.7519 309.4737 1.1172 
140 3 3 302.9238 42.2661 0.8851 42.2661 302.9238 1.1299 
141 371.3089 412.5695 0.9 332.4675 444.4651 0.7480 
142 379.8773 415.9003 0.9134 415.9003 379.8773 1.0948 
143 378.5803 417.6269 0.9065 417.6269 378.5803 1.1031 
144 374.1755 407.4259 0.9184 407.4259 374.1755 1.0889 
145 377.5255 403.7149 0.9351 403.7149 377.5255 1.0694 
146 3 4 322.9589 63.6449 0.6966 82.1987 416.1649 0.9184 
147 328.9528 459.787 0.7154 459.787 328.9528 1.3977 
148 337.3287 459.4949 0.7341 459.4949 337.3287 1.3622 
149 328.9954 454.964 0.7231 454.964 328.9954 1.3829 
150 337.7602 463.6962 0.7284 463.6962 337.7602 1.3729 
151 88.7104 93.4059 0.9497 99.9529 81.2626 1.2300 
152 63.2416 114.0435 0.5545 114.0435 63.2416 1.8033 
153 64.4127 1 116.2906 0.5539 16.2906 64.4127 1.8054 
154 65.1112 117.1496 0.5558 117.1496 65.1112 1.7992 
155 66.058 117.3281 0.563 117.3281 66.0580 1.7761 
156 15 02.7422 163.485 .9343 171.7785 143.3516 1.1983 
157 104.2617 190.4033 0.5476 190.4033 104.2617 1.8262 
158 112.199 195.5409 0.5738 195.5409 112.1990 1.7428 
159 114.3065 199.6868 0.5724 199.6868 114.3065 1.7469 
160 119.2931 200.8401 0.594 200.8401 119.2931 1.6836 
161 195.7189 210.8054 0.9284 218.5745 187.0027 1.1688 
162 143.1355 265.2779 0.5396 265.2779 143.1355 1.8533 
163 142.515 2 265.0369 0.5377 65.0369 142.5150 1.8597 
164 144.0262 265.7019 0.5421 265.7019 144.0262 1.8448 
165 145.1991 268.8831 0.54 268.8831 145.1991 1.8518 
166 245.2068 269.6919 0.9092 273.7338 240.6864 1.1373 
167 163.5994 323.5697 0.5056 323.5697 163.5994 1.9778 
168 165.446 323.5697 0.5113 323.5697 165.4460 1.9557 
169 172.0612 329.7176 0.5218 329.7176 172.0612 1.9163 
170 167.4072 326.1765 0.5132 326.1765 167.4072 1.9484 
171 247.9751 309.7016 0.8007 311.0038 246.3400 1.2625 
172 167.9498 372.6552 0.4507 372.6552 167.9498 2.2188 
173 169.5887 372.6489 0.4551 372.6489 169.5887 2.1974 
 103
Run No.  F FF N F/N Ratio Fs  n  s/Fn  
174 167.1795 376.4682 0 3 1 2.4441 76.4682 67.1795 .2519 
175 170.1 375.4764 0.453 3 1 275.4764 70.1000 .2074 
176 70.6428 62.4051 1.132 78.6263 51.9876 1.5124 
177 33.7425 91.2695 0 2.3697 91.2695 33.7425 .7049 
178 32.2379 95.873 0 2.3363 95.873 32.2379 .9739 
179 35.996 95.9412 0 2.3752 95.9412 35.9960 .6653 
180 38.689 94.1467 0 2.4109 94.1467 38.6890 .4334 
181 113.3678 107.4873 1 1 1.0547 32.6994 82.4417 .6096 
182 47.7565 152.4468 0 1 3.3133 52.4468 47.7565 .1922 
183 50.2597 155.6077 0.323 1 355.6077 50.2597 .0961 
184 50.2975 155.8898 0 1 3.3226 55.8898 50.2975 .0994 
185 51.8714 156.5935 0 1 3.3312 56.5935 51.8714 .0189 
186 162.8985 154.9715 1 1 1 1.0512 86.3179 25.8480 .4805 
187 61.2472 2 0 310.745 .2906 210.745 61.2472 .4409 
188 64.6666 211.8868 0 2 3.3052 11.8868 64.6666 .2766 
189 69.2517 216.0162 0 2 3.3206 16.0162 69.2517 .1193 
190 70.628 217.1014 0 2 3.3253 17.1014 70.6280 .0739 
191 223.1166 201.1148 1 2 1 1.1094 46.6438 71.4498 .4386 
192 88.1638 279.4771 0 2 3.3155 79.4771 88.1638 .1700 
193 86.1354 277.423 0 3.3105 277.423 86.1354 .2208 
194 86.2464 281.964 0 3.3059 281.964 86.2464 .2693 
195 91.2761 287.9853 0 2 3.3169 87.9853 91.2761 .1551 
196 259.2312 23 286. 1 10.2289 1.126 2171 95.6679 .4628 
197 107.6019 325.5716 0 3 1 3.3305 25.5716 07.6019 .0257 
198 108.0435 331.8501 0 3 1 3.3256 31.8501 08.0435 .0714 
199 112.4562 336.0007 0 3 1 2.3347 36.0007 12.4562 .9878 
200 102.807 322.619 0 1 3.3187 322.619 02.8070 .1381 
201 169.5545 228.4957 0.742 1 2 073.6316 25.4131 .7703 
202 207.1426 192.6893 1.075 1 2 092.6893 07.1426 .9302 
203 202.68 194.1392 1.044 1 2 094.1392 02.6800 .9579 
204 2 1. 2 2 017.7624 200.6148 0855 00.6148 17.7624 .9213 
205 2 1 2 014.5732 198.1373 1.083 98.1373 14.5732 .9234 
206 2 0 2 3 034.4741 326.8637 .7173 37.7651 24.4777 .7328 
207 287.13 282.1961 1 2 2 0.0175 82.1961 87.1300 .9828 
208 2 1 2 2 092.2072 285.1416 .0248 85.1416 92.2072 .9758 
209 284.7899 279.5205 1 2 2 0.0189 79.5205 84.7899 .9815 
210 2 1 2 089.2702 279.558 .0347 279.558 89.2702 .9664 
211 309.3758 456.3637 0. 3 4 06779 31.7829 40.3423 .7535 
212 373.3497 398.0761 0 3 3 1.9379 98.0761 73.3497 .0662 
213 382.5961 3 0 3 3 185.8474 .9916 85.8474 82.5961 .0085 
214 382.5391 391.1423 0.978 3 3 191.1423 82.5391 .0225 
215 379.7901 396.6776 0 3 3 1.9574 96.6776 79.7901 .0445 
216 287.0673 496.7286 0 3 4 0.5779 64.9637 42.6607 .8245 
217 373.8964 424.6515 0 4 3 1.8805 24.6515 73.8964 .1357 
218 381.3443 437.8459 0.871 4 3 137.8459 81.3443 .1482 
219 390.1037 439.4337 0.8877 4 3 139.4337 90.1037 .1265 
220 377.0451 433.2095 8704 433.2095 377.0451 1.1490 0.
 104
Run No. F N F/N Ratio Fs  Fn  Fs/Fn  
221 303.5935 556.7616 0.5453 401.4681 490.8930 0.8178 
222 373.1608 478.6916 0.7795 478.6916 373.1608 1.2828 
223 378.8455 472.3057 0.8021 472.3057 378.8455 1.2467 
224 382.9149 474.1717 0.8075 474.1717 382.9149 1.2383 
225 392.4226 487.8136 0.8045 487.8136 392.4226 1.2431 
226 164.5504 184.5599 0.8916 163.1351 185.8121 0.8780 
227 163.1026 182.9984 0.8913 182.9984 163.1026 1.1220 
228 159.9201 178.6047 0.8954 178.6047 159.9201 1.1168 
229 1 1 161.9422 82.6511 0.8866 82.6511 161.9422 1.1279 
230 16 1 0 13.0827 81.1829 .9001 81.1829 163.0827 1.1110 
231 2 2 233.1829 71.1694 0.8599 33.0307 271.3002 0.8589 
232 2 2 234.9983 66.0591 0.8833 66.0591 234.9983 1.1322 
233 242 2 2.5081 75.9159 0.8789 75.9159 242.5081 1.1378 
234 236.4188 270.1852 0.875 270.1852 236.4188 1.1428 
235 2 037.9905 274.003 .8686 274.003 237.9905 1.1513 
236 279.5769 346.4283 0.807 291.6152 336.3575 0.8670 
237 279.0627 343.8411 0.8116 343.8411 279.0627 1.2321 
238 281.6154 342.3731 0.8225 342.3731 281.6154 1.2157 
239 275.8128 342.3738 0.8056 342.3738 275.8128 1.2413 
240 2 079.2154 342.2708 .8158 342.2708 279.2154 1.2258 
241 334.6459 425.5195 0.7864 350.2322 412.7858 0.8485 
242 331.8301 416.7075 0.7963 416.7075 331.8301 1.2558 
243 335.0354 424.1981 0.7898 424.1981 335.0354 1.2661 
244 328.8234 420.35 0.7823 420.35 328.8234 1.2783 
245 326.9944 424.9836 0.7694 424.9836 326.9944 1.2997 
246 430.5991 484.6631 0.8885 386.2096 520.7264 0.7417 
247 427.0402 488.0082 0.8751 488.0082 427.0402 1.1428 
248 417.6366 483.0138 0.8646 483.0138 417.6366 1.1565 
249 424.0487 490.4496 0.8646 490.4496 424.0487 1.1566 
250 417.0269 487.2506 0.8559 487.2506 417.0269 1.1684 
251 110.2801 107.5452 1.0254 118.2208 98.7498 1.1972 
252 77.7225 130.8423 0.594 130.8423 77.7225 1.6835 
253 78.8442 129.2723 0.6099 129.2723 78.8442 1.6396 
254 76.9546 133.4419 0.5767 133.4419 76.9546 1.7340 
255 77.8638 1 129.4782 0.6014 29.4782 77.8638 1.6629 
256 202.375 175.2947 1.1545 192.0853 186.5131 1.0299 
257 152.0043 22 220.2428 0.6902 0.2428 152.0043 1.4489 
258 156.324 228.9791 0.6827 228.9791 156.3240 1.4648 
259 149.3831 219.0391 0.682 219.0391 149.3831 1.4663 
260 149.2316 219.1011 0.6811 219.1011 149.2316 1.4682 
261 237.6644 238.273 0.9974 252.2228 222.8049 1.1320 
262 163.8237 284.3597 0.5761 284.3597 163.8237 1.7358 
263 166.1155 286.7002 0.5794 286.7002 166.1155 1.7259 
264 169.8913 290.2186 0.5854 290.2186 169.8913 1.7083 
265 170.3016 295.5275 0.5763 295.5275 170.3016 1.7353 
266 331.9794 305.1023 0881 328.8548 308.4677 1.0661 1.
267 243.4664 381.1891 0.6387 381.1891 243.4664 1.5657 
 
 105
R F    un No.  N F/N Ratio Fs  Fn Fs/Fn
268 236.7358 376.3736 0.629 376.3736 236.7358 1.5898 
269 240.0703 388.8308 0.6174 388.8308 240.0703 1.6197 
270 247.0985 389.9095 0.6337 389.9095 247.0985 1.5780 
271 327.375 357.4639 0.9158 367.9325 315.5638 1.1660 
272 222.2084 427.8287 0.5194 427.8287 222.2084 1.9253 
273 229.9665 428.6029 0.5365 428.6029 229.9665 1.8638 
274 230.929 429.1843 0.5381 429.1843 230.9290 1.8585 
275 233.4081 433.5332 0.5384 433.5332 233.4081 1.8574 
276 75.5231 62.2963 1.2123 80.6946 55.4341 1.4557 
277 34.379 93.6644 0.367 93.6644 34.3790 2.7245 
278 36.4733 95.4205 0.3822 95.4205 36.4733 2.6162 
279 37.0401 96.0515 0.3856 96.0515 37.0401 2.5932 
280 31.39 92.8399 0.3381 92.8399 31.3900 2.9576 
281 129.375 108.7244 1.1899 138.8432 96.3403 1.4412 
282 58.8684 169.1589 0.348 169.1589 58.8684 2.8735 
283 64.8787 166.0229 0.3908 166.0229 64.8787 2.5590 
284 64.8416 167.4373 0.3873 167.4373 64.8416 2.5823 
285 54.8339 171.6381 0.3195 171.6381 54.8339 3.1301 
286 167.5055 149.9337 1.1172 191.4866 117.7756 1.6259 
287 74.4158 219.5313 0.339 219.5313 74.4158 2.9501 
288 76.2422 218.8497 0.3484 218.8497 76.2422 2.8705 
289 74.3471 217.4577 0.3419 217.4577 74.3471 2.9249 
290 83.6924 224.6447 0.3726 224.6447 83.6924 2.6842 
291 197.1468 188.2939 1.047 236.0396 136.4065 1.7304 
292 76.7912 262.8484 0.2922 262.8484 76.7912 3.4229 
293 82.3925 270.9511 0.3041 270.9511 82.3925 3.2885 
294 85.1815 271.8372 0.3134 271.8372 85.1815 3.1913 
295 83.8936 269.3505 0.3115 269.3505 83.8936 3.2106 
296 357.9019 228.4282 1.5668 302.7941 297.6389 1.0173 
297 191.2584 369.0897 0.5182 369.0897 191.2584 1.9298 
298 198.9184 369.0897 0.5389 369.0897 198.9184 1.8555 
299 197.3296 364.3208 0.5416 364.3208 197.3296 1.8463 
300 186.2928 369.2408 0.5045 369.2408 186.2928 1.9820 
301 158.5647 227.7806 0.6961 175.8309 214.7329 0.8188 
302 196.3354 192.175 1.0216 192.175 196.3354 0.9788 
303 204.0934 201.2071 1.0143 201.2071 204.0934 0.9859 
304 201.2784 193.76 1.0388 193.76 201.2784 0.9626 
305 208.4875 202.2933 1.0306 202.2933 208.4875 0.9703 
306 242.4013 337.6371 0.7179 249.2924 332.5815 0.7496 
307 300.1617 291.3465 1.0303 291.3465 300.1617 0.9706 
308 289.5194 286.3318 1.0111 286.3318 289.5194 0.9890 
309 289.8274 286.5597 1.0114 286.5597 289.8274 0.9887 
310 287.2581 293.0959 0.9801 293.0959 287.2581 1.0203 
311 289.1253 431.7996 0.6696 308.9547 417.8412 0.7394 
312 359.7902 373.8692 0.9623 373.8692 359.7902 1.0391 
 
 
 106
Run No. F N F/N Ratio Fs  Fn  Fs/Fn  
313 349.0415 367.1384 0.9507 367.1384 349.0415 1.0518 
314 356.6663 364.5413 0.9784 364.5413 356.6663 1.0221 
315 349.8105 362.813 0.9642 362.813 349.8105 1.0372 
316 295.0665 487.5075 0.6053 359.6964 441.9800 0.8138 
317 386.0774 429.459 0.899 429.459 386.0774 1.1124 
318 373.0587 428.976 0.8696 428.976 373.0587 1.1499 
319 374.3297 435.5474 0.8594 435.5474 374.3297 1.1635 
320 376.0092 429.0622 0.8764 429.0622 376.0092 1.1411 
321 383.5387 610.5565 0.6282 436.8354 573.6341 0.7615 
322 490.7619 544.2519 0.9017 544.2519 490.7619 1.1090 
323 491.3546 544.1311 0.903 544.1311 491.3546 1.1074 
324 491.4266 546.3741 0.8994 546.3741 491.4266 1.1118 
325 491.3052 547.4965 0.8974 547.4965 491.3052 1.1144 
326 152.4772 175.133 0.8706 153.6019 174.1474 0.8820 
327 152.2068 180.9133 0.8413 180.9133 152.2068 1.1886 
328 156.0352 179.9308 0.8672 179.9308 156.0352 1.1531 
329 158.5667 179.1254 0.8852 179.1254 158.5667 1.1297 
330 156.9991 176.181 0.8911 176.181 156.9991 1.1222 
331 247.4289 279.3266 0.8858 240.1728 285.5896 0.8410 
332 243.5632 275.3585 0.8845 275.3585 243.5632 1.1305 
333 246.5875 2 278.1679 0.8865 78.1679 246.5875 1.1281 
334 2 2 252.9061 82.2953 0.8959 82.2953 252.9061 1.1162 
335 252.7687 284.098 0.8897 284.098 252.7687 1.1239 
336 307.5088 364.4924 0.8437 307.9256 364.1404 0.8456 
337 304.3039 358.126 0.8497 358.126 304.3039 1.1769 
338 299.7853 355.6117 0.843 355.6117 299.7853 1.1862 
339 298.1503 356.1509 0.8371 356.1509 298.1503 1.1945 
340 306.4602 362.9809 0.8443 362.9809 306.4602 1.1844 
341 335.8497 421.2274 0.7973 352.4936 407.4012 0.8652 
342 335.8612 418.2116 0.8031 418.2116 335.8612 1.2452 
343 3 034.4233 418.9726 .7982 418.9726 334.4233 1.2528 
344 338.8065 422.3275 0.8022 422.3275 338.8065 1.2465 
345 338.8065 422.8405 0.8013 422.8405 338.8065 1.2480 
346 462.9319 556.5036 0.8319 453.3699 564.3208 0.8034 
347 463.8574 554.134 0.8371 554.134 463.8574 1.1946 
348 461.594 546.7876 0.8442 546.7876 461.5940 1.1846 
349 456.2306 559.0695 0.8161 559.0695 456.2306 1.2254 
350 454.8527 541.429 0.8401 541.429 454.8527 1.1903 
351 89.8206 97.8126 0.9183 104.3512 82.1333 1.2705 
352 61.1567 117.5025 0.5205 117.5025 61.1567 1.9213 
353 62.3705 120.783 0.5164 120.783 62.3705 1.9365 
354 63.5301 120.5455 0.527 120.5455 63.5301 1.8975 
355 64.199 121.12 0.53 121.12 64.1990 1.8866 
356 130.8158 159.4002 0.8207 165.649 122.8072 1.3489 
357 86.1069 189.8 0.4537 189.8 86.1069 2.2042 
358 86.883 189.432 0.4587 189.432 86.8830 2.1803 
 
 107
 108
Run No. F N F/N Ratio Fs  Fn  Fs/Fn  
359 82.936 185.5118 0.4471 185.5118 82.9360 2.2368
360 82.9105 185.8108 0.4462 185.8108 82.9105 2.2411
361 220.3518 228.197 235.667 212.3447 1.10989 0.9656 
362 151.4303 274.125 274.1256 151.4303 1.81026 0.5524 
363 156.5936 276.4732 5664 276.4732 156.5936 1.76550.
364 157.1355 277.2494 5668 277.2494 157.1355 1.76440.
365 159.999 279.3632 0.5727 279.3632 159.9990 1.7460
366 269.2133 280.911 0.9584 290.9219 258.3626 1.1260
367 181.2863 342.5107 0.5293 342.5107 181.2863 1.8893
368 188.967 347.3744 0.544 347.3744 188.9670 1.8383
369 181.3638 342.7891 0.5291 342.7891 181.3638 1.8901
370 186.9441 347.3383 0.5382 347.3383 186.9441 1.8580
371 304.4865 353.0099 0.8625 367.1155 287.3226 1.2777
372 209.5801 414.2354 0.5059 414.2354 209.5801 1.9765
3 389 4 9. .973 209.4235 415.6 0.5039 15.6389 20 4235 1 847
374 211.2018 416.244 0.5074 1.2018 1.9708416.244 21
375 21 95 42 1 2.2.49 3.962 0.5012 423.9621 21 4995 1.9951
376 10 03 9 0.71 70.78 1.4227 95.1356 78.1208 1.2178
377 50.7544 109.552 0.4633 4 2.1585109.552 50.754
378 51.1189 112.6215 0.4539 9 2.2031112.6215 51.118
379 49.955 108.7509 0.4594 0 2.1770108.7509 49.955
38 9 3 0 .10 50.655 110.526 0.4583 110.5263 5 .6559 2 819
381 131.0256 116.1779 1.1278 1 4 1.452344.2305 99.310
382 57.7285 169.0374 0.3415 5 2.9281169.0374 57.728
383 45.0762 158.2031 0.2849 2 3.5097158.2031 45.076
384 47 62 5 .44 161.484 0.2938 161.4845 47.4462 3.4035
385 8 7 6 .4 46.053 157.691 0.292 157.6917 4 .0538 3 241
386 161.2817 158.7095 1.0162 1 9.0273 1.616892.4396 11
387 63.5088 220.3345 0.2882 8 3.4694220.3345 63.508
388 66.2184 223.8298 0.2958 4 3.3802223.8298 66.218
389 7 9 7.4 .3 67.425 224.479 0.3004 224.4799 6 257 3 293
390 69.5599 224.3973 0.31 9 3.2260224.3973 69.559
391 327.7175 188.8304 1.7355 4.2228 0.9499260.4949 27
392 183.8052 324.5705 0.5663 3 3.8052 1.765824.5705 18
393 187.4379 329.6599 0.5686 7.329.6599 18 4379 1.7588
394 28 1 3 .7 193.10 328.306 0.5882 328.3061 19 .1028 1 002
395 187.2169 329.0382 0.569 7.2169 1.7575329.0382 18
396 261.9524 247.4856 1.0585 1.6161 1.4815298.6957 20
397 101.9503 346.1842 0.2945 1.9503 3.3956346.1842 10
398 51 3 4 .5 94.54 333.166 0.2838 333.1663 9 .5451 3 239
399 95.4506 334.7357 0.2852 6 3.5069334.7357 95.450
400 97.1873 341.0194 0.285 3 3.5089341.0194 97.187
 
P  
 
The effective tool surface roughness calculated  obtained from the 
profilome , the Chip thickness ratio, Shear Plane Angle, Shear Front angle, Friction 
angle, Shear Area and Shear Stress calculated from th etal Cutting equations 
using the  d ed xp re ta o
Run No. oughness(?m) t/tc ? (degrees) A
s 
(inch
2
) 
?
s 
(MPa) 
A PENDIX F
using data
ter
e classical M
 raw ata obtain from the e eriments a blulated bel w. 
R ? (degrees) 
35.2848498 1 
46.09109792 2 
44.5168538 3 
46.22510005 4 
5 
1 0  54.942318 .121892 6.704454207 
46.40603269 
0.0010707 254.35318
33.70095615 6 
7 43.80856404 
44.03211179 8 
43.9692226 9 
10 
1 0  61.1517652 .162259 8.83393002 
43.64414797 
0.0016279 248.96012
32.79725047 11 
43.74369905 12 
41.81090436 13 
42.13079373 14 
15 
1  69.620113 0.171292 9.303365676 
41.9711911 
0.0023197 219.85956
30.83008201 16 
41.02620866 17 
18 41.45726363 
41.69795712 19 
20 
1  64.004236 0.191847 10.36155416 
41.50534539 
0.00278 222.69739
30.6222396 21 
40.82268516 22 
23 40.84603361 
24 40.91143225 
25 
172.25711 0.207245 11.14494369 
40.69343989 
0.0032335 219.97836 
46.01699116 26 
45.73987577 27 
45.26687443 28 
45.54367647 29 
30 
5 8
44.77756185 
 7.234495 0.156299 .883390955 0.0008095 318.0925
 109
 
Run No. Roughness(?m) t/tc ? (degrees) ? (degrees) A
s 
(inch
2
) ?s )(MPa
31 41.19162882 
32 41.05666261 
33 40.8061092 
34 40.49030077 
35 
53.159259 0.176025 9.98323796 0.0014421 266.08323
40.76831763 
36 42.18632849 
37 42.73275743 
38 42.07060344 
39 42.01889115 
40 
58.699539 0.215548 12.16389917 
4
0.0017797 272.10987
2.10881411 
41 40.99378438 
42 42.34078987 
43 43.38448966 
44 41.34174946 
45 
65.485074 0.227505 12.816942 0.0022539 266.56076
42.75892418 
46 34.76638147 
47 36.01788354 
48 35.44656672 
49 36.34093095 
50 
84.619697 0.21384 1 0 22.07032234 
35.24691529 
.0029888 2 8.18156
51 39.71967382 
52 28.4394782 
53 31.17087907 
54 28.45687613 
55 
35.1411615 0 1 0 7.18423 0.58436298 
28.93456114 
.0006805 2 0.02966
56 43.01217718 
57 29.41419657 
58 29.85279808 
59 30.01594471 
60 
37.817199 0.190042 10.92721737 
30.36256106 
0 3.0013188 2 1.19109
61 41.71428606 
62 28.50889896 
63 29.70489255 
64 29.5641814 
65 
43.691054 0.205959 11.86763239 
29.74939623 
0 1.0018235 2 8.80615
66 44.30271024 
67 29.64743485 
68 30.79616222 
69 30.65862121 
70 
53.175756 0.204855 11.80234505 
31.36598967 
0 1.0024446 2 5.28004
71 42.58470373 
72 28.65818527 
73 29.29491121 
74 28.78917684 
75 
54.113999 0.222896 12.8701278 
29.50865716 
0 1.0028059 2 9.69272
 110
 
Run Roughness(?m) t/tc ? (degrees) A
s 
(inch
2
) ?s (MPa)  No. ? (degrees) 
76 58.5932362 
77 28.65223424 
78 28.49222898 
79 28.70710918 
80 
116.491447 0.179986 9.719680126 
 
0.0007404 239.32775 
28.59372273
81 53.3706542 
24.66481459 82 
26.24246689 83 
26.4909587 84 
137.235826 0.211461 11.57316922 
 
0.0012461 220.69079 
26.7251257185 
51.43387331 86 
22.55817056 87 
22.39552793 88 
89 22.04434714 
142.468258 0.263112 14.70181433 0.0014776 244.27549 
22.6955593 90 
53.34280063 91 
23.42818756 92 
24.50160964 93 
23.62469373 94 
135.535181 0.285144 16.06656599 
 
0.0018067 264.90069 
24.1764476995 
45.14351729 96 
15.71874978 97 
15.13175104 98 
16.77470165 99 
149.38949 0.284608 16.03318923 
 
0.0022629 225.83987 
16.11029953100 
37.35830095 101 
47.28875955 102 
47.31746222 103 
46.95394022 104 
118.496228 0.105574 5.829622051 
 
0.0012307 227.92588 
47.01222052105 
34.33494855 106 
44.90859972 107 
44.66072384 108 
44.70841079 109 
133.933197 0.148765 8.127782915 
 
0.0017683 226.82207 
44.56111497110 
32.09103038 111 
42.46048613 112 
42.56808022 113 
42.05751601 114 
110.688898 0.182039 9.858404852 
 
0.0021902 225.93223 
42.30134468115 
30.68608481 116 
41.14952263 117 
41.18108185 118 
41.49995673 119 
120 
126.345719 0.203562 10.95831878 
41.19212386 
0.0026303 229.01087 
 111
 
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
121 3  1.20408077
122 40.30880414 
123 40.63829025 
124 40.16899295 
125 
113.423296 0.213712 11.47147953 0.0031426 223.10984 
40.18564309 
126 44.59891579 
127 44.46675534 
128 44.54844023 
129 44.88802365 
130 
19.352671 0.13369 7.614711942 0.0009433 265.52076 
44.6762923 
131 40.06682403 
132 39.99034048 
133 40.22227919 
134 40.28705667 
135 
24.915753 0.152742 8.684335384 0.0016557 234.01789 
39.72285881 
136 42.7594888 
137 42.3610167 
138 41.49304171 
139 41.83091193 
140 
33.139799 0.195084 11.03883918 0.0019585 257.40035 
41.51054659 
141 41.98693244 
142 42.40812283 
143 42.19242117 
144 42.56402744 
145 
38.858533 0.198295 11.21595131 0.0025706 238.43237 
43.08000153 
146 34.85972652 
147 35.5816763 
148 36.28348575 
149 35.87159574 
150 
49.853782 0.223095 12.57643961 0.0028704 239.77567 
36.06990863 
151 43.5230622 
152 29.01007802 
153 28.98179965 
154 29.06511571 
155 
32.636596 0.184298 10.58836712 0.0006803 257.36627 
29.3803564 
156 43.05430474 
157 28.70438441 
158 29.8466818 
159 29.7880701 
160 
30.554164 0.204666 11.79118859 0.0012234 242.80984 
30.70906352 
161 42.87467325 
162 28.34988487 
163 28.26770075 
164 28.46032117 
165 
37.8082255 0.219587 12.67416333 0.0017092 232.79172 
28.36941354 
 
 112
 113
 
Run Roughness(?m) t/tc (degrees) As  Ts No. (degrees) 
166 42.27745102 
167 26.82152185 
168 27.08133603 
169 27.55754097 
170 
42.3096365 0.242748 14.04679692 0.00206 237.27695 
27.16876053 
171 38.68392024 
172 24.26033583 
173 24.46979594 
174 23.94473221 
175 
46.1084783 0.25373 14.69812596 0.0024633 227.56587 
24.37169004 
176 48.54295922 
177 20.28945305 
178 18.58555156 
179 20.56549311 
180 
121.240644 0.266809 14.92963965 0.0004852 291.26065 
22.33990008 
181 46.52520894 
182 17.39404798 
183 17.89991409 
184 17.88218123 
185 
125.14415 0.273224 15.32609707 0.0009459 246.87197 
18.32739056 
186 46.42855131 
187 16.2050536 
188 16.97187965 
189 17.77510871 
190 
118.718115 0.309725 17.60841967 0.0012396 260.5954 
18.0208893 
191 47.96885199 
192 17.50838508 
193 17.24873959 
194 17.00767905 
195 
117.246707 0.297442 16.83552537 0.0017264 246.6355 
17.58585984 
196 48.39102061 
197 18.28880409 
198 18.03417339 
199 18.50489775 
200 
1  013.104302 .283543 15.96683921 
17.67519805 
0.0022721 218.61285 
201 36.5771382 
202 47.0702517 
203 46.23299541 
204 47.34701011 
205 
52.118844 0.10533 5.81644704 
47.28055825 
0.0012334 241.07724 
206 35.65358416 
207 45.49652487 
208 45.70115128 
209 45.53499919 
210 
57.687602 0.1485 8.113851469 
45.97817584 
0.0017713 238.75172 
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
211 34.13393102 
212 43.16413518 
213 44.75758184 
214 44.36290735 
215 
93.959022 0.162937 8.869287411 
43.75406285 
0.0024322 242.61655 
216 30.02429158 
217 41.36321563 
218 41.05441531 
219 41.59680663 
220 
110.938971 0.193986 10.47090273 
41.03477238 
0.0027512 236.63271 
221 2  8.60295374
222 37.93795612 
223 38.73377128 
224 38.92242908 
225 
131.161133 0.226634 12.11963791 
38.81500604 
0.0029768 241.0205 
226 41.71964144 
227 41.70994256 
228 41.84081167 
229 41.56085238 
230 
19.937807 0.12276 6.99859315 0.0010259 268.50532 
41.99037291 
231 40.69276358 
232 41.45274501 
233 41.31289647 
234 41.18673587 
235 
17.636055 0.152068 8.646617757 0.0016629 245.92637 
40.97656697 
236 38.90445738 
237 39.06291105 
238 39.43864681 
239 38.85456006 
240 
27.020858 0.179404 10.17091464 0.0021236 242.68349 
39.20664911 
241 38.18295517 
242 38.53080781 
243 3  8.30199033
244 38.03468489 
245 
14.950266 0.203521 11.50377489 0.0025071 251.80642 
37.57570096 
246 41.61950008 
247 41.18812113 
248 40.84824563 
249 40.84709285 
250 
23.386262 0.209223 11.81710815 0.0030519 237.1712 
40.55947967 
251 45.71933637 
252 30.71101543 
253 31.37932982 
254 29.9715998 
255 
20.5794515 0.159898 9.152670309 
31.02125831 
0.0007858 252.96485 
 
 114
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
256 49.10129007 
257 34.61215505 
258 34.32134804 
259 34.29370822 
260 
23.3734121 0.175254 10.05549407 
34.25910613 
0.0014318 233.70773 
261 44.92673638 
262 29.9468613 
263 30.0882126 
264 30.34431365 
265 
20.6853593 0.20024 11.52953691 
29.95326133 
0.0018762 232.81205 
266 47.41575244 
267 32.5664694 
268 32.16954441 
269 31.69183965 
270 
20.7577006 0.187073 10.75205775 
32.36378236 
0.0026801 215.73722 
271 42.48428541 
272 27.44675008 
273 28.21574245 
274 28.28313444 
275 
20.8684733 0.227355 13.13433213 
28.29738964 
0.0027505 235.23231 
276 50.48199183 
277 20.15539787 
278 20.91871662 
279 21.08799022 
280 
71.088548 0.251762 14.00557088 
18.68083078 
0.0005165 275.29501 
281 49.95691006 
282 19.18822072 
283 21.3446422 
284 21.16935148 
285 
79.01599 0.26469 14.79902697 
17.71731102 
0.0009787 257.53574 
286 48.16836424 
287 18.72541568 
288 19.20715874 
289 18.87515773 
290 
97.07791 0.242248 13.42561044 
20.4331013 
0.0016151 205.75187 
291 46.31575535 
292 16.28572723 
293 16.9137869 
294 17.39863067 
295 
106.87934 0.246883 13.70771943 
17.30005457 
0.00211 192.6175 
296 57.45224505 
297 27.39271565 
298 28.32214753 
299 28.44161136 
300 
107.649215 0.300951 17.05583469 
26.77228235 
0.0021309 258.15728 
 
 115
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
301 34.84289847 
302 45.61353377 
303 45.40801828 
304 46.09032587 
305 
121.806137 0.105865 5.845269409 
45.86390265 
0.0012274 243.7968 
306 35.67586264 
307 45.85381127 
308 45.31715513 
309 45.32482235 
310 
115.622348 0.136295 7.470094597 
44.4236793 
0.0019229 226.76377 
311 33.80555492 
312 43.90062299 
313 43.55252096 
314 44.37440158 
315 
129.862754 0.179254 9.714966585 
43.95469948 
0.0022223 247.93154 
316 31.18464826 
317 41.95508114 
318 41.01183172 
319 40.67729674 
320 
108.54511 0.178492 9.675640327 
41.22974519 
0.0029749 217.02949 
321 32.13616906 
322 42.04155916 
323 42.08228092 
324 41.96924183 
325 
103.904811 0.196002 10.57373429 
41.90375002 
0.003406 238.38043 
326 41.04402325 
327 40.07472539 
328 40.93168557 
329 41.51613203 
330 
15.744253 0.132415 7.542953922 
41.70499515 
0.0009522 283.14689 
331 41.53468336 
332 41.49376414 
333 4  1.55602605
334 41.85690719 
335 
21.373276 0.14771 8.402429902 
41.66024506 
0.0017109 246.44243 
336 40.15309215 
337 40.35494988 
338 40.13132544 
339 39.9342506 
340 
37.702539 0.169645 9  .628268605
40.17398099 
0.0022421 240.69029 
341 38.56577913 
342 38.76756981 
343 38.59681483 
344 38.7378555 
345 
27.113344 0.18655 10.56705068 
38.70391014 
0.0027265 231.36113 
 
 116
 117
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
346 39.75564374 
347 39.93220429 
348 40.17080691 
349 39.21628381 
350 
21.472416 0.20284 11.46629484 
40.03350653 
0.003144 261.76429 
351 42.56104242 
352 27.49569151 
353 27.31114832 
354 27.79020572 
355 
23.5926107 0.185254 10.64474123 
27.92556918 
0.0006767 267.67096 
356 39.37486468 
357 24.40244384 
358 24.63857018 
359 24.0877774 
360 
30.7779982 0.211193 12.17726827 
24.04687895 
0.0011852 239.64441 
361 43.99786953 
362 28.91679199 
363 29.52708703 
364 29.54308487 
365 
29.6081105 0.225462 13.02215933 
29.80095548 
0.0016642 250.13986 
366 43.78186721 
367 27.89166617 
368 28.5455959 
369 27.88254479 
370 
30.247557 0.222148 12.82583963 
28.28998527 
0.0022524 229.97571 
371 40.77920915 
372 26.83687613 
373 26.74167247 
374 26.90319282 
375 
37.3319742 0.212748 12.26926654 
26.62107593 
0.0029411 214.72721 
376 54.89672427 
377 24.85781941 
378 24.4132774 
379 24.67182121 
380 
80.090936 0.25974 14.49449315 
24.6226962 
0.0004994 333.06602 
381 48.43719405 
382 18.85569715 
383 15.90364506 
384 16.37345565 
385 
81.766506 0.285878 16.1122984 
16.2804337 
0.0009008 272.08272 
386 45.46054437 
387 16.07899756 
388 16.48045914 
389 16.71838305 
390 
97.385863 0.288517 16.27697499 
17.22267609 
0.0013379 251.50532 
 
Run No. Roughness(?m) t/tc (degrees) (degrees) As  Ts 
391 60.04950995 
392 29.52299472 
393 29.62167771 
394 30.46315721 
395 
127.930611 0.290824 16.42113251 
29.63910855 
0.0017687 275.53886 
396 46.62663458 
397 16.40955704 
398 15.84274896 
399 15.91561355 
97.068583 0.306297 17.392 5545 0.0020909 245.1935 
400 
15.90704706 
2
 118
APPENDIX F 
 
The Flow stress and Specific Horse power calculations are as shown below. 
 
ut, V = 500 SFM 
idth of cut, w = 0.125 inch 
Uncut chip thickness, t = 0.001 inch 
 
ake Angle, ? = 0
o 
utting Force, Fc = 172.4828 N = 38.7756 lbs 
Thrust Force, Ft = 178.7172 N = 40.1772 lbs 
 
Flow Stress,
Velocity of C
W
R
Shear Angle, ? = 8.8834
o
 
C
 
wt
FF
ct
.
)(sin)sin().cos(.(
2
???
?
?
=  = 41641.8558 psi 
 
pindle Horse Power, HP = 
000,33
.VF
c
S = 0.58750909 
aterial Removal Rate, MRR =
 
 Nt
DD
..
4
).(
2
1
2
??
M  = 0.7226 inch
3
/min. 
pecific Horse Power = HP
s
 = 
 
MRR
SpindleHP
= 0.8130488 hp/inch
3
/min. S
 
 
 119
Rake Angle, ? = 15
o 
Shear Angle, ? = 10.5844
o
 
Cutting Force, Fc = 122.6205 N = 27.5661 lbs 
Thrust Force, Ft = 66.4581 N = 14.9403 lbs 
 
wt
FF
ct
.
)
Flow Stress, 
(?
? =
sin)sin().cos(.(
2
?? ?
 = 14140.1440 psi 
ower, HP = 
 
000,33
.VF
c
Spindle Horse P = 0.41766818 
 
Nt
DD
.
).(
2
1
2
??
.
4
 = 0.72266 inch
3
/min. Material Removal Rate, MRR = 
 
Specific Horse Power = HP
s
 = 
MRR
SpindleHP
= 0.577959 hp/inch
3
/min. 
 
 
 
 
 
 
 
 
 
 
 
 
 120
APPENDIX G 
Sample Calculations: 
lations are provided using the data in Run 1 (or page 88) to illustrate 
the exact method for data reproduction. 
Friction Force
These sample calcu
, ?? cossin ?+?=
tc
FFF    
                        )10cos(7517.177)10sin(993.175 ??+??=F = 144.4904 N                             
eNormal Forc ?=
c
FN, ?? sincos ??
t
F  
)10sin(7517.177)10cos(993.175 ?????=N                       = 204.1855 N 
Shear Force along the onset of Shear Plane, ?? sincos ???=
tcs
FFF  
)7.6sin(7517.177)7.6cos(993.175 ???=
s
F                       = 154.0374 N 
Normal Force along the onset of Shear Plane, ?? cossin ?+?=
tcn
FFF  
)7.6cos(7517.177)7.6sin(993.175 ?+?=
n
F                        = 197.0830 N 
Onset of Shear Plane Angle,
?
?
?
?
?
?
??
?
=
?
?
?
?
sin1
cos
tan
1
c
c
r
r
    
                                             
?
?
?
?
?
?
???
??
=
?
)10sin(12189.01
)10cos(12189.0
tan
1
? = 6.704454
o
 
 
Friction Angle,
?
?
?
?
?
?
=
?
N
F
1
tan?  
 
?
?
?
?
?
?
=
?
1855.204
4904.144
tan
1
? = 35.284849
o
                         
 121
 122
Shear Area, 
?sin
wt
A
s
?
=  ; 
)704454.6sin(
125.0001.0 ?
=
s
A = 0.0010707 inch
2
 
Shear Stress, 
s
s
s
A
F
=? = 
wt
F
s
?
? ?sin
;   
                     
0010107.0
0374.154
=
s
? = 152406.6489 N/inch
2
 =    254.35318 MPa