Orthogonal Cutting Modelling

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MASTERS IN MECHANICAL ENGINEERING 
 
 
ADVANCED MANUFACTURING TECHNOLOGIES II 
2024/2025 
 
Orthogonal Cutting Modelling As a Tool For 
Machinability Assessment 
 
Students: 
Gonçalo Pinto Coelho Correia Duarte (202008108) 
José Gaspar Domingos (202104489) 
José Maria Pereira de Lemos Baptista Fernandes (202005372) 
Léonard Bergelin (202402944) 
Marco António Freitas dos Santos (202308637) 
 
 
 
 
 
 
 
 
 
 
 
 
Supervisor: 
Prof. Tiago Silva 
November 2024 
 
 Advanced Manufacturing Technologies II 
 
 
Summary 
The following is a report on the students’ numerical modelling of orthogonal cutting using 
DEFORM software. Three different materials will be simulated and the results obtained 
will be compared to the experimental results from orthogonal cutting in Module II as the 
materials used are the same. 
The tool wear values will also be analysed and compared to results in literature. The 
previous work also had experiments in turning. As such, this work will also study the 
predicting power when using an orthogonal cutting model as a basis for turning. 
 
 
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List of Tables 
Table 1: Chemical properties of St52 steel. [5] .............................................................. 9 
Table 2: Chemical properties of AISI 1025 steel. .......................................................... 9 
Table 3: Chemical properties of C26000 machining brass. [4] ...................................... 9 
Table 4: Chemical properties of Al 6061 T-6 and Al 6082 T-6.[6] .................................. 9 
Table 5: Results obtained in DEFORM, after analysis of data for St52 steel, AA6082 and 
a Brass alloy ....................................................................................................... 10 
Table 6: Comparison of DEFORM and Experimental Test Parameters: Material, Rake 
Angle, and Uncut Chip Thickness ....................................................................... 10 
Table 7: Wear rate distribution .................................................................................... 29 
 
 
 
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List of Figures 
Figure 1: Orthogonal cutting .......................................................................................... 7 
Figure 2: Shaping machine equipped with load-cell and DAQ system. .......................... 7 
Figure 3: Steel 5 degrees ............................................................................................ 12 
Figure 4: Steel 12 degrees .......................................................................................... 12 
Figure 5: Brass 5 degrees ........................................................................................... 12 
Figure 6: Brass 12 degrees ......................................................................................... 13 
Figure 7: Aluminium 5 degrees ................................................................................... 13 
Figure 8: Aluminium 12 degrees ................................................................................. 13 
Figure 9: Shear angle-Steel 5º .................................................................................... 14 
Figure 10: Shear angle-Steel 12º ................................................................................ 14 
Figure 11: Shear angle - Brass 5 º .............................................................................. 15 
Figure 12: Shear angle - Brass 12º ............................................................................. 15 
Figure 13: Shear angle - Aluminium 5º ........................................................................ 15 
Figure 14: Shear angle - Aluminium 12º ...................................................................... 16 
Figure 15: Specific cutting pressure for Steel .............................................................. 17 
Figure 16: Specific cutting pressure for Brass ............................................................. 20 
Figure 17: Specific cutting pressure for Aluminium ..................................................... 22 
Figure 18: Comparation of Specific cutting pressure from Lab and DEFORM ............. 24 
Figure 19: Comparation of uncut chip thickness from Lab and DEFORM.................... 24 
Figure 20: Comparation of friction from Lab and DEFORM ......................................... 24 
Figure 21: Comparation of Shear Strength from Lab and DEFORM ............................ 25 
Figure 22: Wear depth for 5° tool rank angle and steel as workpiece material ............ 27 
Figure 23: Wear rate for 5° tool rank angle and steel as workpiece material ............... 27 
Figure 24: Maximum wear depth for each simulation .................................................. 28 
Figure 25: Wear rate for each simulation .................................................................... 28 
Figure 26: Analysis of feed rate and cutting speeds - St52 steel ................................. 30 
Figure 27: Analysis of feed rate and cutting speeds - AA6082 .................................... 31 
Figure 28: Analysis of feed rate and cutting speeds - Brass alloy ............................... 31 
Figure 29: Results for 5° tool rank angle and aluminium as workpiece material .............. 
Figure 30: Results for 5° tool rank angle and brass as workpiece material...................... 
Figure 31: Results for 5° tool rank angle and steel as workpiece material ....................... 
Figure 32: Results for 12° tool rank angle and aluminium as workpiece material ............ 
Figure 33: Results for 12° tool rank angle and brass as workpiece material .................... 
Figure 34: Results for 12° tool rank angle and steel as workpiece material ..................... 
 
 
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Index 
 
Summary ...................................................................................................................... 2 
List of Tables ................................................................................................................ 3 
List of Figures ............................................................................................................... 4 
1. Orthogonal Cutting .................................................................................................... 6 
2. DEFORM results Analysis ......................................................................................... 9 
2.1 Forces, cutting speed and specific cutting pressure .......................................... 10 
2.2 Chip geometry ................................................................................................... 12 
2.3 Machinability ranking ......................................................................................... 14 
2.4 Shear angle....................................................................................................... 14 
3. Comparison with the experimental results ............................................................... 17 
3.1 Steel ................................................................................................................. 17 
3.2 Brass................................................................................................................. 20 
3.3 Aluminium ......................................................................................................... 22 
3.4 Summary .......................................................................................................... 24 
4. Studying tool wear .................................................................................................. 26 
5. Using orthogonal cutting model as a basis for turning predictions ........................... 30 
6. Conclusion ..............................................................................................................32 
7. Appendices ............................................................................................................. 33 
8. References ............................................................................................................. 35 
 
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1. Orthogonal Cutting 
Orthogonal cutting is a fundamental concept in material removal processes. It refers to 
a machining technique where the cutting tool interacts with the workpiece to remove 
chips. This theoretical model is widely used to study the basic mechanisms of cutting 
and to optimize process efficiency and quality. 
Orthogonal cutting is characterized by the following conditions: 
• The cutting edge of the tool is perpendicular to the feed direction. 
• The cutting motion and chip formation occur in a single plane. 
This model is primarily used for theoretical analysis as it simplifies the study of cutting 
mechanisms. Although it is an idealization, it provides a solid foundation for 
understanding more complex processes, such as oblique cutting. 
In orthogonal cutting, two main forces are considered: the cutting force that acts in the 
direction of the main cutting motion and is responsible for removing the material and the 
thrust force that acts perpendicular to the cutting force and pushes the chip against the 
tool. These forces are critical for calculating the required cutting power and assessing 
the performance of the process, including tool wear. 
Chip formation results from the plastic deformation of the material and can take different 
forms. The shape of the chips produced in this process says a lot about the workpiece 
and the cutting parameters. 
The geometry of the cutting tool is defined by several important angles: 
• Rake angle: Influences cutting efficiency and chip formation. 
• Shear angle: Determines the plane where the material is sheared. 
• Clearance angle: Prevents the tool from rubbing against the freshly 
machined surface, reducing friction and wear. 
Some important parameters in this procedure are: 
• Cutting Speed: Refers to the relative speed between the cutting tool and the 
workpiece. 
• Feed Rate: Represents the amount of material removed per unit of time. 
Higher feed rates enhance productivity but may compromise surface finish 
and dimensional accuracy. 
• Depth of Cut: Determines the thickness of the material layer to be removed 
in each pass. 
 
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Some advantages of this process are: simpler analysis of cutting forces and parameters, 
providing a theoretical basis for the development of optimized tools and processes, 
facilitating computational simulations of cutting operations. 
And it has disadvantages such as: it is a simplification since most practical cuts are 
oblique and does not account for dynamic effects such as vibrations or material 
inhomogeneities. 
So, orthogonal cutting plays a crucial role in understanding material removal processes. 
Despite its simplifications, it provides a robust theoretical framework essential for 
developing advanced production technologies. Understanding the principles of 
orthogonal cutting allows for process optimization, cost reduction, and improvement in 
the final quality of machined components. Figures 1 and 2 show diagrams of the 
orthogonal cutting. 
 
 
 Figure 1: Orthogonal cutting 
 
 
Figure 2: Shaping machine equipped with load-cell and DAQ system. 
As part of this work, we will model the orthogonal cutting process using computational 
methods with the DEFORM software. This approach allows us to simulate the material's 
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behaviour during the cutting process, considering parameters such as cutting force, chip 
formation, and tool wear. 
The DEFORM software allows the simulation of metal forming and cutting processes, 
analysing phenomena such as deformations, stresses, and the material's thermal 
behaviour. The use of DEFORM provides a detailed and accurate analysis of cutting 
conditions, enabling us to obtain computational results that can be directly compared 
with previously acquired practical results. This comparison is crucial for validating the 
theoretical model and identifying any deviations or necessary adjustments in the 
modelling process. 
Simulations will be conducted for three different workpiece materials: St52 steel, AA6082 
aluminium, and brass alloy, using tools with rake angles of 5° and 12°, respectively. 
 
 
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2. DEFORM results Analysis 
 
To use DEFORM, the tool that was used in the previous work was replicated. The tool is 
made from Tungsten Carbide (WC) with a 5-micron thick TiAlN coating which is less 
durable and resists lower temperatures than the one used in the laboratory – AlTiN.[7] 
The materials used for the simulation are as similar as possible to the ones used in the 
experimental process. 
The chemical composition of the St52 Steel used in the lab is displayed in Table 1. 
Table 1: Chemical properties of St52 steel. [5] 
C% Mn% Si% P% S% Cu% N% 
≤0,22 ≤1,60 ≤0,55 ≤0,030 ≤0,030 ≤0,55 ≤0,012 
 
The chemical composition of the AISI 1025 steel used for DEFORM is displayed in Table 
2. 
 
Table 2: Chemical properties of AISI 1025 steel. 
C% Mn% P% S% 
0,22-28 0.3-0.6 0 - 0,04 0 - 0,05 
 
 
The brass used in the lab is of an unknown alloy. The C26000 machining brass used for 
DEFORM is displayed in Table 3. 
Table 3: Chemical properties of C26000 machining brass. [4] 
Cu% Pb% Zn% Fe% 
68.50-71.50 0.07 Rem. 0.05 
 
Both Al 6061 T-6 used in the Lab and the Al 6082 T-6 used for DEFORM are displayed 
in Table 4. Something of note is that the 6082 alloy is characterized in Deform 3D for hot 
forming applications, which may not align perfectly with the machining temperatures 
experienced during orthogonal cutting. This discrepancy could lead to inaccuracies in 
the simulation results. 
Table 4: Chemical properties of Al 6061 T-6 and Al 6082 T-6.[6] 
Alloy Si% Fe% Cu% Mn% M%g Cr% Zn% Ti% Al% 
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Al 6061 T-6 
Lab 
0.56 0.3 0.31 0.052 0.9 0.06 0.024 0.018 Rem. 
Al 6082 T-6 
DEFORM 
1.3 0.5 0.1 1.2 1.2 0.15 0.20 0.20 Rem. 
 
2.1 Forces, cutting speed and specific cutting pressure 
For this procedure, the main objective was to compare the machinability of three metal 
alloys, namely St52 steel, AA6082 and a brass alloy, in an orthogonal cutting operation. 
Uncut chip thicknesses will be chosen as to match different experiments that were 
performed in the previous module. This will allow for both broad comparison with the 
previous data, as well as direct comparison within the same chip thickness. 
The following table presents the results obtained in DEFORM, after data analysis in 
Excel: 
 
Table 5: Results obtained in DEFORM, after analysis of data for St52 steel, AA6082 and a 
Brass alloy 
Test rake angle, 
degrees 
t0, mm tc, 
mm 
r Kc, MPa friction Shear 
Strength, MPa 
st5 5 0,340 0,682 0,498 2002,20 0,321 722,107 
lat5 5 0,347 0,909 0,382 1014,18 0,259 322,638 
al5 5 0,180 0,506 0,356 1231,49 0,289 368,716 
 
st12 12 0,32 1,09 0,29 1374,72 0,31 374,60 
lat12 12 0,20 0,74 0,27 1739,95 0,30 440,22 
al12 12 0,150 0,405 0,371 1061,35 0,329 345,797 
 
These results can, then, be added to the dataset created during the previous module. 
Notice how, for each DEFORM test, there is one experimental test with the same 
material, rake angle and uncut chip thickness: 
 
Table 6: Comparison of DEFORM and Experimental Test Parameters: Material, Rake Angle, 
and Uncut Chip Thickness 
Test 
rake 
angle, 
degrees 
t0, 
mm 
tc, 
mm 
r Kc, MPa friction 
Shear 
Strength, MPa 
steel_5_2 5 0,690 1,494 0,462 1924,95 0,476 616,338 
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steel_5_4 5 0,583 1,342 0,4351816,15 0,478 565,081 
steel_5_5 5 0,340 0,739 0,460 2002,2 0,535 619,381 
st5 5 0,340 0,682 0,498 2002,20 0,321 722,107 
steel_12_17 12 0,760 1,471 0,517 1821,04 0,539 651,472 
steel_12_21 12 0,610 1,471 0,415 1657,93 0,554 531,444 
steel_12_22 12 0,400 0,619 0,646 1383,27 0,528 522,225 
steel_12_23 12 0,320 0,442 0,725 1362,18 0,494 527,692 
st12 12 0,320 1,087 0,294 1374,71 0,309 374,598 
Test 
rake 
angle, 
degrees 
t0, 
mm 
tc, 
mm 
r Kc, MPa friction 
Shear 
Strength, MPa 
lat_5_7 5 0,347 1,494 0,232 521,280 0,212 113,138 
lat_5_8 5 0,460 1,342 0,343 476,276 0,253 140,697 
lat_5_9 5 0,825 0,739 1,116 498,813 0,218 205,605 
lat5 5 0,347 0,909 0,382 1014,18 0,259 322,638 
lat_12_15 12 0,693 1,471 0,471 452,938 0,181 186,438 
lat_12_20 12 0,510 1,471 0,347 402,996 0,098 135,290 
lat_12_25 12 0,200 0,619 0,323 565,093 0,247 169,829 
lat12 12 0,200 0,743 0,269 1739,94 0,296 440,218 
Test 
rake 
angle, 
degrees 
t0, 
mm 
tc, 
mm 
r Kc, MPa friction 
Shear 
Strength, MPa 
al_5_10 5 0,533 1,342 0,397 474,443 0,261 155,022 
al_5_11 5 0,650 1,494 0,435 446,906 0,260 154,665 
al_5_12 5 0,567 1,342 0,422 572,862 0,296 191,517 
al_5_13 5 0,180 0,739 0,243 702,177 0,396 151,829 
al5 5 0,180 0,506 0,356 1231,49 0,289 368,716 
al_12_14 12 0,713 1,471 0,485 465,066 0,378 176,454 
al_12_18 12 0,450 1,471 0,306 496,905 0,329 139,079 
al_12_19 12 0,380 0,619 0,614 496,202 0,360 209,889 
al_12_24 12 0,150 1,342 0,112 526,385 0,515 56,425 
al12 12 0,150 0,405 0,371 1061,35 0,329 345,797 
 
 
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2.2 Chip geometry 
 
Steel 5 degrees 
Uncut chip: 0.340 
Cut chip: 0.682301 
r: 0.4983 
 
Figure 3: Steel 5 degrees 
 
Steel 12 degrees 
Uncut chip: 0.320 
Cut chip: 1.08743 
r: 0.2943 
 
Figure 4: Steel 12 degrees 
 
Brass 5 degrees 
Uncut chip: 0.347 
Cut chip: 0.909071 
r = 0.3817 
 
Figure 5: Brass 5 degrees 
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Brass 12 degrees 
Uncut chip: 0.200 
Cut chip: 0.743317 
r = 0.2691 
 
Figure 6: Brass 12 degrees 
 
 
 
Aluminium 5 degrees 
Uncut chip: 0.180 
Cut chip: 0.50866 
r: 0.3539 
 
Figure 7: Aluminium 5 degrees 
 
Aluminium 12 degrees 
Uncut chip: 0.150 
Cut chip: 0.406426 
r: 0.3691 
 
Figure 8: Aluminium 12 degrees 
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2.3 Machinability ranking 
Based on the results for Kc, steel is, clearly, the hardest material to machine, due to its 
higher specific cutting pressure. Between Aluminium and brass, one could make a case 
for each of them, due to their similar values for specific cutting pressure. 
However, brass presented very high specific cutting pressure variability depending on 
rake angle. As such, Aluminium, as the material with least variation in Kc has a better 
case as the most easily machinable material of the three materials. 
Further, its shear strength was also the lowest in the group of materials. More tests, at 
different uncut chip thicknesses could change this ranking. 
 
Machinability from worst to best: 
Steel -> Brass -> Aluminium 
 
2.4 Shear angle 
 
 
Figure 9: Shear angle-Steel 5º 
Converges around 27.58 degrees 
 
 
Figure 10: Shear angle-Steel 12º 
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Converges around 28.76 degrees 
 
 
Figure 11: Shear angle - Brass 5 º 
Converges around 23.90 degrees 
 
 
 
Figure 12: Shear angle - Brass 12º 
Converges around 27.79 degrees 
 
 
Figure 13: Shear angle - Aluminium 5º 
Converges around 20.95 degrees 
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Figure 14: Shear angle - Aluminium 12º 
 
Converges around 22.95 degrees 
Merchant’s law always presented errors of, at least, 40%. 
 
It’s worth noting that shear angle can also be calculated using the chip compression ratio, 
obtained by measuring the uncut and cut chips, as well as the rake angle. This value 
was the same as the DEFORM outputs for all tests. 
 
 
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3. Comparison with the experimental results 
 
To properly understand the results obtained from DEFORM, these will be compared to 
the experimental results in the previous module: 
 
3.1 Steel 
 
 
 
Figure 15: Specific cutting pressure for Steel 
 
The DEFORM results for steel are almost completely identical to the experimental 
results. There was no size effect in the combined dataset, just as there was none in the 
previous results. The error between the results with the same chip thickness were of 
0.004% for the 5 degrees result and 0.87% for the 12 degrees result. 
 
 
Shear strength 
Lab 5 degrees average – 600.267 MPa 
DEFORM – 722.107 MPa 
Error: 20.298% 
 
Lab 12 degrees average – 558.208 MPa 
DEFORM – 374.598 MPa 
Error: -32.893% 
 
Shear strength presents some error compared to the experimental results with no trend 
being noticeable. Literature points to around 380 MPa for the shear strength of St52, 
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lower than the experimental results, but similar to the DEFORM result for the higher rake 
angle. 
 
 
Friction coefficient 
Lab 5 degrees average – 0.50 
DEFORM – 0.32 
Error: -36% 
 
Lab 12 degrees average – 0.53 
DEFORM – 0.31 
Error: -41.5% 
 
Friction was noticeably lower than observed in the laboratory. This might be due to the 
testing conditions being less than ideal. 
 
 
Chip deformation ratio, r 
Lab 5 degrees – 0.4598 
DEFORM – 0.4983 
Error: 8.37% 
 
Lab 12 degrees - 0.7245 
DEFORM - 0.2942 
Error: -59.39% 
 
This value was compared to the experiment with the same chip thickness. The DEFORM 
result for the higher rake angle led to much higher chip deformation than observed in the 
laboratory. 
 
 
Shear angle 
Lab 5 degrees - 25.51° 
DEFORM - 27.58° 
Error: 8.114% 
 
Lab 12 degrees – 34.84° 
DEFORM – 28.76° 
Error: -17.451% 
 
The shear angle was compared to the shear angle of the experiment performed with the 
same uncut chip thickness. 
 
 
Conclusions 
These results present the following conclusions: 
 
• The steel used for simulation is very similar to the one used in the experiment 
(St52 and AISI 2025 respectively); 
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• The results for specific cutting pressure are extraordinarily similar; 
 
• DEFORM obtained lower friction than the lab results. 
 
 
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3.2 Brass 
 
Figure 16: Specific cutting pressure for Brass 
 
Brass presented significant differences in Kc, compared to the previous experiments. 
Whereas the original results showed little to no size effect, the DEFORM results show 
the opposite, having a clear presence of size effect. 
 
 
Shear strength 
Lab 5 degrees average – 153.146 MPa 
DEFORM – 322.637 MPa 
Error: 110.67% 
 
Lab 12 degrees average – 163,852 MPa 
DEFORM – 440,218 MPa 
Error: 168.67% 
 
Shear strength presents a lot of error compared to the experimental results, showing 
higher values than before. This might indicate that the brass chosen for simulation is 
different from the one used in the laboratory experiments. 
 
 
Friction coefficient 
Lab 5 degrees average – 0.23 
DEFORM – 0.26 
Error: 13.04% 
 
Lab 12 degrees average – 0.18 
DEFORM – 0.30 
Error: 66.66% 
Friction was slightly higher than observed in the laboratory. 
 
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Chip deformation ratio, r 
Lab 5 degrees – 0.2320 
DEFORM – 0.3817 
Error: 64.53% 
 
Lab 12 degrees - 0.3231 
DEFORM - 0.2690 
Error: -16.74% 
 
This value was compared to the experiment with the same chip thickness. The DEFORM 
result for the higher rake angle led to much higher chip deformation than observed in the 
laboratory. This is also the case with the results for the steel 
 
 
Shear angle 
Lab 5 degrees – 13.27° 
DEFORM - 23.90° 
Error: 80.11% 
 
Lab 12 degrees – 18.71°DEFORM – 27.79 ° 
Error: 48.53% 
 
The shear angle was compared to the shear angle of the experiment performed with the 
same uncut chip thickness. The DEFORM results showed a much higher shear angle 
than the lab results. 
 
 
Conclusions 
These results present the following conclusions: 
 
• The brass used for simulation is, most likely, different from the one used in the 
laboratory experiments, due to the high variance in shear strength; 
 
• The results for specific cutting pressure show size effect, unlike before. 
 
 
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3.3 Aluminium 
 
Figure 17: Specific cutting pressure for Aluminium 
 
Aluminium presented significant differences in Kc, compared to the previous 
experiments. Whereas the original results showed little to no size effect, the DEFORM 
results show size effect very clearly, if added to the original dataset. Further, just as 
before, lower rake angles tend towards higher specific cutting pressures. 
 
 
Shear strength 
Lab 5 degrees average – 163.258 MPa 
DEFORM – 368.716 MPa 
Error: 125.85% 
 
Lab 12 degrees average – 145.462 MPa 
DEFORM – 345.797 MPa 
Error: 137.72% 
 
Shear strength presents a lot of error compared to the experimental results, showing 
higher values than before. This might indicate that the aluminium chosen for simulation 
has considerably higher shear strength than the one used in the lab. 
 
 
Friction coefficient 
Lab 5 degrees average – 0.303 
DEFORM – 0.289 
Error: -4.62% 
 
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Lab 12 degrees average – 0.396 
DEFORM – 0.329 
Error: -16.92% 
 
Friction was ever so slightly lower than observed in the laboratory. 
 
 
Chip deformation ratio, r 
Lab 5 degrees – 0.2435 
DEFORM – 0.3558 
Error: 46.11% 
 
Lab 12 degrees – 0.1118 
DEFORM – 0.3707 
Error: 231.57% 
 
This value was compared to the experiment with the same chip thickness. The DEFORM 
results show much less chip deformation than observed in the lab experiments, 
especially for the higher rake angle. This is the only material where this is the case. 
 
 
Shear angle 
Lab 5 degrees – 13.92° 
DEFORM – 20.95° 
Error: 50.50% 
 
Lab 12 degrees – 6.39° 
DEFORM – 22.95° 
Error: 259.15% 
 
The shear angle was compared to the shear angle of the experiment performed with the 
same uncut chip thickness. The DEFORM results showed a much higher shear angle 
than the lab results. 
 
 
Conclusions 
These results present the following conclusions: 
 
• The aluminium used in the laboratory experiments is different from the one 
used in DEFORM 
 
• The results for shear strength differ considerably from the expected results 
 
• More experiments could allow for a better evaluation of size effect 
 
 
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3.4 Summary 
 
 
Figure 18: Comparation of Specific cutting pressure from Lab and DEFORM 
 
Figure 19: Comparation of uncut chip thickness from Lab and DEFORM 
 
Figure 20: Comparation of friction from Lab and DEFORM 
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Figure 21: Comparation of Shear Strength from Lab and DEFORM 
 
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4. Studying tool wear 
In this section, we will study tool wear, a critical parameter in machining processes, as it 
directly impacts surface quality, dimensional accuracy of parts, and production costs. 
Tool wear results from complex mechanisms. Abrasion occurs due to the relative 
hardness between the tool and the workpiece, while adhesion stems from chemical 
interactions between their respective materials. Diffusion, facilitated by high 
temperatures, alters the properties of the surfaces in contact, and chemical dissolution 
becomes dominant under extreme thermal conditions. These mechanisms are 
influenced by various factors, such as cutting speed, temperature generated at the tool-
workpiece interface, normal stresses, and the relative sliding velocity. 
 
Numerical tests, particularly simulations based on the Finite Element Method, as 
conducted using the DEFORM software in our case, have become indispensable for 
predicting tool wear. These simulations help minimize the need for costly experimental 
tests. Additionally, they support the optimization of cutting parameters, thereby extending 
tool life and reducing costs associated with tool replacement. 
To model wear, several laws and models have been developed. Taylor's empirical model 
establishes a relationship between tool life and cutting parameters, such as speed and 
cutting depth. Usui's model, on the other hand, links the wear rate to state variables, 
such as normal stress, sliding velocity, and temperature at the interface. This relationship 
takes the following form: 
 
�̇� = 𝐴 × 𝜎 × 𝑉 × 𝑒(−𝐵/𝑇) 
 
where A and B are constants specific to the tool-workpiece pair. Rabinowicz's model 
focuses on abrasive wear and accounts for the relative hardness of the interacting 
materials. 
 
In our case, we began by performing a numerical orthogonal cutting test with the 
following parameters: 
- Tool rank angle: 5° 
- Workpiece material: Steel (AlSl 2025) 
Two results are particularly interesting to analyse in this context: wear depth (Fig.22) and 
wear rate (Fig.23). First, as shown in our analysis, we evaluated these parameters at 
nine different points on the tool surface. In the first graph (Fig.22) representing wear 
depth as a function of machining time, it is evident that the point experiencing the highest 
stress is point 7, which corresponds to the initial contact between the tool and the 
workpiece. This observation holds true across all simulations and aligns with findings in 
the literature, particularly the works of Ziqi Zhang et al. [1] and Amir Malakizadi et al. [2], 
which identify this region as having the highest pressure and temperature stresses. 
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Figure 22: Wear depth for 5° tool rank angle and steel as workpiece material 
 
Regarding the wear rate, the same analytical approach was applied: placing points on 
the tool surface to measure the wear rate values at these points as a function of 
machining time. Figure 23 shows the spatial distribution of the wear rate on the tool 
surface at a specific time. The resulting graph indicates a rapid initial increase in wear (a 
steep rise), often attributed to the initialization phase of the process, during which friction 
is intense before wear stabilizes. Indeed, after this initial phase, the wear rate tends to 
stabilize, particularly for nodes P3 through P9, indicating a more uniform wear regime. 
The wear rate converges to a value of approximately 0.88 mm/s. 
In contrast, zones P1 and P2 experience the least stress in this machining simulation, 
as evidenced by both figures. This explains why the wear rate in these zones does not 
exhibit the same profile as that of the other points. 
 
Figure 23: Wear rate for 5° tool rank angle and steel as workpiece material 
 
We can now compare these results with those obtained from the 5 other simulations 
involving different cutting parameters. 
 
After extracting the results of each simulation, we have drawn up the two histograms 
below: 
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Figure 24: Maximum wear depth for each simulation 
 
 
 
 
Figure 25: Wear rate for each simulation 
 
For the first histogram Fig.24, we can observe that the maximum wear depth is highest 
for steel across both tool rake angles. Conversely, the wear depth for brass is the lowest 
in both cases. Regarding the tool rake angle, the 5° angle consistently exhibits a much 
lower maximum wear depth across all workpiece materials. It is important to note that, in 
these two graphs, the result for steel with a 5° rake angle is significantly higher than 
expected and is likely an outlier, making itunreliable for this analysis. 
 
For the wear rate, we observe a similar trend : steel as the workpiece material results in 
a significantly higher tool wear rate compared to aluminum or brass. In this case, 
aluminum demonstrates the lowest tool wear rate among the workpiece materials. As 
with the previous analysis, the 5° rake angle shows a slightly lower tool wear rate 
compared to the 12° rake angle. 
All the graphs generated using the DEFORM software for each simulation can be found 
in Appendix 1. 
 
0
0,001
0,002
0,003
0,004
0,005
0,006
0,007
0,008
0,009
Aluminium Brass Steel Aluminium Brass Steel
5° 12°
Max wear depth (mm)
0
0,2
0,4
0,6
0,8
1
Aluminium Brass Steel Aluminium Brass Steel
5° 12°
Wear rate (mm/sec)
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 With regard to the distribution of the wear rate on the tool, we have drawn up the 
following table below: 
 
Table 7: Wear rate distribution 
 
From the table, we can observe that the wear distribution is uniform and spread over a 
larger area when using a tool rake angle of 5°, which is not necessarily the case when 
using a tool rake angle of 12°, except for brass, which exhibits a wide distribution across 
the entire tool edge for both angles. This distribution indicates that the wear rate for a 5° 
rake angle is spread across the entire cutting face, partially explaining why the wear rate 
is lower for a 5° tool rake angle compared to 12°. 
 
The area where tool wear is most pronounced corresponds to the interface zone between 
the tool and the chip. This area is damaged due to frictional forces generated by the 
contact between the tool and the chip, as well as the localized temperature, which can 
sometimes reach approximately 900°C, as demonstrated by Yung-Chang Yen et al. in 
their research [3]. 
 
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5. Using orthogonal cutting model as a basis for turning 
predictions 
Despite however accurate orthogonal cutting models are when used to predict experimental results 
for their own process, complications arise when using these for turning. 
First and foremost, the uncut chip thickness varies during turning due to using a circular tool with feed. 
This will significantly hamper the ability to compare results, as the feed is used as a reference for a 
turning operation is not quite the same as uncut chip thickness, not fully capturing the complexities of 
varying the uncut chip thickness. 
Furthermore, turning is a 3D process. While 2D processes can produce a rough estimate for the 
magnitude of the results, turning will introduce different forces. This phenomenon was analysed in the 
last report. However, due to its’ importance, this report will repeat said information. 
To properly understand the 3D effect of a cut, two ratios will be shown: Feed force by cutting force 
and perpendicular force by cutting force. While perpendicular force is also prevalent in orthogonal 
cutting, feed force is negligible due to the mere two-dimensionality of the cut. The higher the Ff/Fc 
ratio, the less reliable the orthogonal cutting results, as the 3D effect of the cut is more prevalent. This 
ratio will also be impacted by the radius of the piece. Orthogonal cutting and turning are much more 
similar when this radius is larger (should it be infinite, the results should be the same, as the piece 
would appear completely flat from the perspective of the tool). 
Each test also presents 3 different feeds, and 2 different cutting speeds, as to compare these values 
with different cutting parameters. All the data used comes from the turning experiments done during 
module II. 
St52 steel: 
 
Figure 26: Analysis of feed rate and cutting speeds - St52 steel 
In the case of steel, the Fp/Fc ratio remains relatively stable across feed rates and cutting speeds, 
showing a slight tendency to increase. This means that the penetration force Fp does not increase 
significantly compared to the cutting force Fc. The Ff/Fc ratio reduces with higher feed rates and is 
slightly lower for the lower cutting speed. 
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AA6082: 
 
Figure 27: Analysis of feed rate and cutting speeds - AA6082 
In the case of aluminium, the Fp/Fc ratio remains relatively stable with a slight increase for the lower 
cutting speed, showing a big tendency to increase, in the case with higher cutting speed, as the feed 
increases. The Ff/Fc ratio reduces with higher feed rates and is slightly lower for the lower cutting 
speed, like the steel. 
 
Brass alloy: 
 
Figure 28: Analysis of feed rate and cutting speeds - Brass alloy 
In the case of brass, the Fp/Fc ratio remains relatively stable with a slight decrease for the higher 
cutting speed and shows a big tendency to increase in the case of the higher cutting speed as the 
feed increases. The Ff/Fc ratio reduces from 0,05 to 0,1 feed values for both cutting speeds but then 
maintains a similar value for 0,2 of feed. 
In most results, a lower cutting speed showed less 3D effect of cut, while a higher feed tended to lower 
the relevance of cutting speed in this analysis. This indicates that lower cutting speeds and higher 
feeds increase the reliability of using orthogonal cutting modelling as a basis for turning. 
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6. Conclusion 
Almost all the DEFORM simulations (exception: Steel, rake angle 5) presented higher 
shear strengths than one would expect based on the experimental results. 
DEFORM also presented lower friction than observed, indicating that cutting conditions 
might not have been as good as they could be. 
As for machinability among materials, steel was, as before, the hardest to machine. 
Brass showed much more specific cutting pressure variability depending on rake angle 
than aluminum. As such, aluminum was considered the easiest to machine. 
The results for steel were the most similar to the experimental results obtained in the 
previous module. This indicates that DEFORM is very reliable for simulations using steel, 
as it is a very studied material, and that the steel chosen is similar to the one used in the 
experiment. 
Future works could see more simulations done for each material and rake angle, as well 
as more experiments. These could make the analysis more significant, as extra 
datapoints in the other uncut chip thicknesses used in the experiment could allow for 
better evaluation of size effect, as well as a better understanding of the reliability of 
DEFORM as an orthogonal cutting modelling tool for machinability analysis. 
Analysis of other, higher, chip thicknesses could also help evaluate whether DEFORM 
has difficulty in simulating low chip thicknesses, due to the relatively higher mesh size 
compared to the uncut chip thickness. 
 
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33 
 
7. Appendices 
Appendix 1: Graphs for tool wear 
 
 
 
 
 
 
 
Figure 29: Results for 5° tool rank angle and aluminium as workpiece material 
Figure 30: Results for 5° tool rank angle and brass as workpiece material 
Figure 31: Results for 5° tool rank angle and steel as workpiece material 
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Figure 32: Results for 12° tool rank angle and aluminium as workpiece material 
Figure 33: Results for 12° tool rank angle and brass as workpiece material 
Figure 34: Results for 12° tool rank angle and steel as workpiece material 
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35 
 
 
8. References 
[1] Ziqi Zhang, Zhanqiang Liu, Xiaoping Ren and Jinfu Zhao. Prediction of Tool Wear 
Rate and ToolWear during Dry Orthogonal Cutting of Inconel (2023) 
 
[2] Amir Malakizadi, HansGruber, IbrahimSadik, LarsNyborg. An FEM-based approach 
for tool wear estimation in machining (2016) 
 
[3] Yung-Chang Yen, Jörg Söhner, Blaine Lilly, Taylan Altan. Estimation of tool wearin 
orthogonal cuttingusing the finite element analysis. Journal of Materials Processing 
Technology (2004). 
 
[4] Concast Metal Products Co. C26000 Alloy—Cartridge Brass. Available: 
https://www.concast.com/c26000.php 
 
[5] Ramada Aços. ST-52 Structural Steel with Carbon. Available: 
https://www.ramada.pt/en/products/steels/structural-steels-with-carbon/st-52_.html 
 
[6] P.C. Arunakumara, H.N. Sagar, Bimal Gautam, Raji George, S. Rajeesh. "A review 
study on fatigue behavior of aluminum 6061 T-6 and 6082 T-6 alloys welded by MIG and 
FS welding methods," Materials Today: Proceedings, vol. 74, part 2, pp. 293–301, 2023. 
Available: https://doi.org/10.1016/j.matpr.2022.08.242. 
 
[7] Ruko GmbH Präzisionswerkzeuge. TiN, TiAlN, AlTiN – A Comparison of the Coatings. 
Available: https://ruko.de/en/knowledge/know-how/tin-tialn-altin-a-comparison-of-the-
coatings/ 
 
https://www.concast.com/c26000.php
https://www.ramada.pt/en/products/steels/structural-steels-with-carbon/st-52_.html
https://doi.org/10.1016/j.matpr.2022.08.242
https://ruko.de/en/knowledge/know-how/tin-tialn-altin-a-comparison-of-the-coatings/
https://ruko.de/en/knowledge/know-how/tin-tialn-altin-a-comparison-of-the-coatings/