This document summarizes a study that used finite element modeling to simulate the broaching process of Inconel718. The study compared simulation results to experimental data and found good agreement for cutting forces. Models for cutting forces as functions of cutting parameters were developed based on simulation results. Additionally, the effects of rake angle and rising per tooth on chip curling and gullet area ratios were examined. Increasing rake angle or decreasing rising per tooth decreased chip curling diameter. Simulated chip curling diameters and area ratios were larger than recommended design values, suggesting gullet dimensions could be increased to improve chip flow.

1. Finite Element Modeling of the Broaching Process of Inconel718
Y. L. Zhang a
, W.Y. Chenb
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
a
zhyinglin@me.buaa.edu.cn, b
wychen@buaa.edu.cn
Keywords: Finite element modeling, Inconel718, Cutting forces, Chip curling process,
Gullet-to-chip area ratio
Abstract. 2D finite element modeling of the broaching process of Inconel718 was conducted by
using the commercial software. Models between cutting forces and cutting parameters were
obtained. In addition, a general understanding of the effects of two machining variables rake angle
and rising per tooth on chip curling process and gullet-to-chip area ratio, was also obtained.
Introduction
Since finite element modeling (FEM) techniques were first applied to study metal cutting by
Klamecki (1973) [1]and Tay et al. (1974)[2], various researches on FEM simulations of machining
processes have been investigated. In recent years, many studies focused on the use of FEM
simulations to predict detailed information on cutting forces, temperature distribution, chip
formation, tool wear and residual stresses [3,4]. These predictions could help us optimize machining
parameters and tool design, improve productivity, reduce cost and obtain the desired surface
integrity [5].
Inconel718 superalloy is generally considered to be one of the most difficult-to-machine
materials [6]. When broaching Inconel718, high speed steel broaches suffer from sever tool wear
owing to large cutting force and high cutting temperature. Moreover, whether chips curl smoothly in
the tooth gullets greatly influences broach life and the workpiece surface quality. Gullet parameters
which influence heavily on the broaches’ strength are determined by chip volume and curling
pattern. Precise calculation of chip curling is therefore important for the broach tool design. In this
paper, 2D finite element modeling of the broaching operation of Inconel718 was conducted in order
to study machining forces and chip curling process under different cutting parameters.
Finite Element Simulations of Machining Forces
Experimental Design, Materials and Method. In order to assess the effectiveness of the FEM
simulations of machining forces, the results of two broaching simulations were compared with B. H.
Shi et al.’s orthogonal cutting experimental data [7]. Cutting parameters in the broaching simulation
and the corresponding orthogonal cutting test were basically the same, and the material hardness of
Inconel718 was 35HRC. Condition 1: cutting speed 11 m/min, rising per tooth (feed rate) 0.1mm,
width of tooth 2.5mm, rake angle 0°, dry cutting conditions. Condition 2: cutting speed 22 m/min,
rising per tooth (feed rate) 0.05mm, width of tooth 2.5mm, rake angle 0°, dry cutting conditions.
Machining forces at 1mm, 1.5mm, 2mm and 2.5mm length of cut were selected to calculated
average forces. As shown in Fig.1, the average cutting forces (Fx) predicted by the FEM
simulations showed good agreement with B. H. Shi et al.’s experimental data, with an error of
<12%. However, predicted perpendicular forces (Fy) were underestimated with big errors of
27% ~ 35%, which were possibly attributed to an inadequate friction model [8].
Materials Science Forum Vols. 697-698 (2012) pp 39-43
Online available since 2011/Sep/21 at www.scientific.net
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/MSF.697-698.39
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2. Fig.1 Experimental and simulation machining forces
In the FEM simulations of broaching Inconel718, workpiece and tool material were selected
from the standard material library of the software. The workpiece hardness was 44HRC, and the
tool material was M-grade high speed steel. The machine tool was perfectly rigid and no influence
of machine tool dynamics on machining was considered.
Combinations of cutting conditions were as follows: (1) Cutting speed 14m/min, rising per tooth
(RPT) 0.05mm, width of tooth 12mm, the following rake angles were used: 10°, 12°, 15°, 18°. (2)
For 15° rake angle, the three factors and three-level orthogonal design used were listed in Table 1.
The workpiece was 6mm in length and 0.35mm in height. And all these simulations were performed
at 3° relief angle, 0.015mm cutting edge radius and 3mm length of cut. Coolant options used were
as follows: (1) Coolant area option: Exclude tip vicinity; (2) Distance from cutting edge tip: 1mm;
(3) Heat transfer coefficient: 10000W·m-2
·K-1
; (4) Coolant temperature: 20℃.
Results and Discussion. Fig.2 shows that the variation of the machining forces and peak tool
temperature with time obtained from a typical simulation. In Fig.2 “Force-X” represents the main
cutting force, and “Force-Y” represents the force normal to the cutting speed. Fig.3 shows that
average machining forces decrease with rake angle increasing from 10° to 18°.
1817161514131211109
3000
2500
2000
1500
1000
rake angle (°)
Force(N)
Average cutting force (N)
Average perpendicular force (N)
2480.13
2571.25
2683.11
2761.40
1000.88
1078.95
1191.21
1291.36
Fig.2 Cutting forces and tool temperature Fig.3 Effect of rake angle on average cutting forces
40 Advances in Materials Manufacturing Science and Technology XIV

3. Simulation results of the three-level orthogonal tests were given in Table 1.
Table 1 Simulation results
Test
number
Cutting
speed
v [m/min]
Rising per
tooth
af [mm]
Width of
tooth
ae [mm]
Average
cutting force
Fx [N]
Average
perpendicular force
Fy[N]
1 6 0.02 4 392.571 238.648
2 6 0.05 8 1557.413 627.100
3 6 0.08 12 3660.783 1218.708
4 10 0.02 8 819.237 488.309
5 10 0.05 12 2451.268 1017.700
6 10 0.08 4 1273.953 431.397
7 14 0.02 12 1266.475 749.223
8 14 0.05 4 879.471 353.124
9 14 0.08 8 2626.593 924.694
According to orthogonal experiments, empirical models between cutting forces and machining
parameters could be represented by the expression:
F = CFvx
af
y
ae
z
. (1)
where CF, x, y and z are undetermined coefficients. The multiple linear regression models were
fitted based on the test results in Table 1 using the least squares approach by MinitabTM
. The
regression equations are:
Fx = 1958.63v0.104
af
0.811
ae
0.986
. (2)
Fy = 232.758v0.115
af
0.404
ae
0.984
. (3)
The squared multiple correlation R² of MinitabTM
output is respectively equal to 99.8%, 99.3%
and all of the variables are significant by the t tests. In analysis of variance table P-values both
equal to 0.000, showing the estimated regression models in a level of 0.05 are highly significant.
Finite Element Simulations of Chip Curling
Experimental Design and Method. In broaching, the chips are accommodated in the gullets. Due
to this reason, the tooth gullet must be designed to facilitate chips curling smoothly and freely,
sufficient chip space and the strength of broach tooth must be all ensured [9]. Fig.4 shows how a
chip fills the tooth gullet during a broaching operation, and D is the chip curling diameter.
Fig.4 Illustration of how a chip fills the tooth gullet during a broaching operation[10]
Because the chips did not usually curl tightly, the effective volume of tooth gullet should be
greater than the undeformed chip size. If the deformation of the chip width is negligible,
gullet-to-chip area ratio KGC can be expressed as [9]:
Materials Science Forum Vols. 697-698 41

4. KGC = AG/ AJ ≈ πh2
/4afL >1. (4)
Where AG = gullet area; AJ = uncut chip area; h= gullet depth; af = rising per tooth; L = broaching
length. Moreover, the ratio of deformed chip area to uncut chip area KCC can be expressed as:
KCC = πD2
/4afL. (5)
With the help of FEM simulations, directly measuring the diameter D and calculating the ratio
KCC, are undoubtedly useful to design gullet-to-chip area ratio KGC and gullet depth h. Therefore, in
this study chip natural curling process of broaching Inconel718 was simulated, i.e. in simulations
chip curled naturally and freely without the constraints of tooth gullet. The specific cutting variables
used in the investigation were as follows: (1) Cutting speed 14m/min, rising per tooth (RPT)
0.03mm, width of tooth 4mm, and rake angle 10°~18°; (2) Cutting speed 14m/min, rising per tooth
0.02~0.08mm, width of tooth 4mm, and rake angle 15°. The workpiece length was 28mm, length of
cut was 25mm, and other cutting conditions were the same as previously mentioned.
Results and Discussion. Fig.5 and Fig.6 show chip curls at different cutting conditions, and the
values of the diameter D and the ratio KCC are listed in Table 2. As rake angle increases, the
diameter D and the ratio KCC decrease. As rising per tooth increases, the diameter D and the ratio
KCC increase. These agree with the trends of the chip deformation in the actual machining process.
However, the values of KCC obtained from FEM simulations are all larger than the values of KGC
obtained from metal cutting tools design handbook. In design handbook, for superalloys the range
of the recommended values of KGC are 2.2~3.8[9]. Besides, the gullet depth is usually larger than
2mm [9], and close to or slightly smaller than the chip curling diameter obtained from simulations.
Table 2 The values of D and KCC
γ [°] D [mm] KCC af [mm] D [mm] KCC
10 2.30 5.5397 0.02 1.92 3.8604
12 2.24 5.2544 0.04 2.37 5.8820
15 2.15 4.8407 0.06 2.75 7.9194
18 2.05 4.4008 0.08 3.01 9.4877
Fig.5 Effect of rake angle on chip curls Fig.6 Effect of rising per tooth on chip curls
Conclusions
In this study finite element simulations of broaching Inconel718 were carried out, and then the
empirical formulas of cutting forces were established. The conclusions can be summarized as
follows. (1) With the decrease of rake angle or the increase of rising per tooth, the chip curling
diameter increases. (2) The chip curling diameters and the ratios of deformed chip area to uncut
42 Advances in Materials Manufacturing Science and Technology XIV

5. chip area, which was obtained from FEM simulations, are respectively larger than the gullet depth
and the gullet-to-chip area ratio, which was obtained from cutting tools design handbook.
Consequently, under the premise of ensuring the strength of broach tooth, appropriately increasing
the values of gullet-to-chip area ratio and gullet depth, may contribute to chips curling smoothly and
freely, and thus help to improve tool life and workpiece surface quality.
References
[1] B.E. Klamecki: Incipient Chip Formation in Metal Cutting—A Three Dimension Finite
Element Analysis (Ph.D. Dissertation, University of Illinois, 1973)
[2] A.O. Tay, M.G. Stevenson and G.D.V. Davis: Proceedings of the Institution of Mechanical
Engineers Vol. 188 (1974), p. 627
[3] S.L. Soo, D.K. Aspinwall and R.C. Dewes: Journal of Materials Processing Technology Vol.
150 (2004), p. 116
[4] B. Shi and H. Attia: Machining Science and Technology: An International Journal Vol. 14
(2010), p. 149
[5] B. Shi, H. Attia and N. Tounsi: Journal of Manufacturing Science and Engineering Vol. 132
(2010), p. 051008
[6] L.H. Li, H.J. Yang, W.Y. Chen and J. Zhu: Tool Engineering Vol. 44(2010), p. 3 (in Chinese)
[7] B. Shi, H. Attia and N. Tounsi: Journal of Manufacturing Science and Engineering Vol. 132
(2010), p. 051009
[8] B. Shi and H. Attia: Proceedings of the Institution of Mechanical Engineers, Part B, Journal of
Engineering Manufacture Vol. 224 (2010), p.1313
[9] Z.J. Yuan and H.M. Liu: Metal Cutting Tools Design Handbook (China Machine Press, China
2008) (in Chinese)
[10] George Schneider Jr.: Cutting Tool Applications (GMRS Associates, USA 2002)
Materials Science Forum Vols. 697-698 43

6. Advances in Materials Manufacturing Science and Technology XIV
10.4028/www.scientific.net/MSF.697-698
Finite Element Modeling of the Broaching Process of Inconel718
10.4028/www.scientific.net/MSF.697-698.39
DOI References
[5] B. Shi, H. Attia and N. Tounsi: Journal of Manufacturing Science and Engineering Vol. 132 (2010),
p.051008.
doi:10.1115/1.4002455
[7] B. Shi, H. Attia and N. Tounsi: Journal of Manufacturing Science and Engineering Vol. 132 (2010),
p.051009.
doi:10.1115/1.4002455