Key Engineering Materials Vol. 443 (2010) pp 274-278 Online available since 2010/Jun/02 at www.scientific.net © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.443.274
Finite Element Simulation of Chip Formation during High-Speed Peripheral Milling of Hardened Mold Steel 1,a Dewen Tang , Chengyong Wang1,b, Yingning Hu2,c and Yuexian Song1,d 1
Institute of Manufacturing Technology, Guangdong University of Technology, China 2 Guangxi university, Nanning, 530004, P. R .China a
[email protected],
[email protected],
[email protected],
[email protected] Keywords: High speed milling; finite element model; chip formation; cutting force
Abstract. The modeling and simulation of chip formation during high speed milling of hardened mold steel are systematically studied by the Finite Element Analysis (FEA). The modified Johnson-Cook’s constitutive equation for hardened mold steel is introduced. Comparing to the experimental results, the simulated results of cutting force, chip morphology, effective stress and cutting temperature in deformation zones of high speed peripheral milling indicate good consistence and the models established can be used to accurately predict the behavior of hardened mold steel. Introduction High-speed milling is a process of great interest in modern production engineering. In order to take advantage of its potential, knowledge of the material and structural behavior in combination with the technological conditions is essential. Thus, investigation based on the modeling and simulation of the process is very necessary. At first, many investigations were focused on the process of machining in nature [1, 2]. For the forming of complex-shaped items today, approaches based on numerical and in particular finite element simulation usually represent the state of the art [3-7]. To account for the effects of high strain-rates and temperature on the material behavior, most of approaches are based on thermo-visco-plastic material modeling. For example, the Johnson-Cook model is usually used in many investigations [6-8]. Hardened steel form segmented chips in high speed milling, where the deformation of the chip is inhomogeneous and the chip region of strong and weak deformation is in turn,, leading to a serrated chip. Generally, adiabatic shearing, caused by thermo-mechanical instability, is held responsible for this process: strong shear deformation leads to an increase of the temperature in front of the tool tip, thus weakening the material by thermal softening [9]. The deformation therefore concentrates in this region and causes the formation of narrow, heavily deformed shear bands. Because of the high speeds involved in the shearing, it is difficult to observe this process experimentally, and alternative explanations, based on damage models and crack formation processes, can be found in the literature as well [10]. Finite element simulations of the machining process allow studying chip formation and segmentation in detail. Such simulations have shown that it is indeed possible to form strongly segmented chips by the described process without the necessity of crack formation, although the usage of damage models can also produce chips that are in good agreement with experiment [7, 10]. In this paper, we study on the chip formation process in high cutting speed. It is clear from the mechanism described above that segmentation must become stronger with increasing cutting speed. It is, however, not clear whether the resulting stronger segmentation will also lead to a decrease in the cutting force. This may be expected as the cutting force drops during the shearing process. On the other hand, an increased heat in deformation zones will lead to a pre-heating of the material entering the shear zone, which will also lead to a softening of the material. In general, varying the cutting speed is a reasonable method to study the transition from continuous to segmented chips. Finite-element Simulation Model In this work, a peripheral milling process using helical flat end mills is usually regarded as a simplified 2-D cutting process, which has the characteristics of plane strain, shown in Fig.1 [10]. we use a two-dimensional fully thermo-mechanically coupled implicit finite element model of the cutting process. DEFORM-2DTM, a Lagrangian implicit code has been used for all simulations. finite element modeling of the orthogonal milling process was composed of the workpiece and the All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 121.8.210.55-08/10/10,08:58:51)
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tool. The workpiece was initially meshed with 800 isoparametric quadrilateral elements, depending on the chip configuration, shown in Fig.2. While the tool model is regarded as perfectly rigid, it is meshed and subdivided into 80 elements. A plane-strain coupled thermo-mechanical analysis was performed using an orthogonal assumption. More detailed information on the FEM model, including material model, simulation results and convergence in every simulation was tested by increasing mesh density, see Fig1.
Fig. 1 Simplified the process of peripheral milling
Fig. 2 2-D finite element model of cutting process
As predicted in high speed cutting, the initial mesh will be severely distorted. A very fine mesh has to be used in the shear zone in front of the tool tip, as high stress and temperature gradients are to be expected there. Arbitrary lagrangian eulerian (ALE) adaptive meshing was used during the simulation to maintain a high-quality mesh and prevent the analysis from terminating as a result of severe mesh distortion. To reduce simulation time, the adaptive meshing was applied to a local mesh domain, elements of potential chips. When elements within the domain fail, the nodes along the interface between the failed and unfailed elements will become non-adaptive since the failed elements are deleted [10]. At the same time, crack growth or damage model was assumed in the model discussed here, so that chip segmentation is caused by the described mechanism of adiabatic shearing. Cockroft and Latham’s criterion is used to predict the effect of tensile stress on the chip segmentation during orthogonal cutting [26]. Cockroft and Latham’s criterion is expressed as: f
0
1d C
Where
f
(1) is the effective strain, 1 is the maximum principal stress, and C is a material constant.
Cockroft and Latham’s criterion indicated when the integral of the largest tensile principal stress component over the plastic strain path in equation (1) occurs, and the fracture occurs or chip segmentation starts. When C is up to 0.22, the disabled elements will be removed from the calculation circle. The plastic material behavior is described by a modified J-C equation. The isothermal flow stress is given by k T T0 m n A B( ) （1 C ln ） 1 ( ) 0 0 Tmelt T0 when TTc
(3)
where is the flow stress, is the plastic strain, is the strain rate (s), 0 is the reference plastic strain rate (s-1), T (K) is the workpiece temperature, Tmelt is the melting temperature of the workpiece material and T0 (293K) is the room temperature. The material yield strength is defined as coefficient A (MPa), the hardening modulus is defined as coefficient B (MPa) and the strain rate sensitivity coefficient is defined as coefficient C. K is relate to workpiece material strain-rate effect coefficient after heat treatment The hardening coefficient and the thermal softening coefficient are defined separately as coefficient n and m. f rec and f def are the flow stresses just prior to and
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after recrystallization, respectively. Table 1 reports the material constants obtained by several researchers [12]. Table 1 The parameters of the the Johnson-Cook constitutive equation of SKD11 steel [12] A(MPa)
B(MPa)
n
C
M
K
2480
1440
0.45
0.012
1.1
-0.01
(
f
) r ec
1560.9765
(
f
) d ef
800.0941
Finite-element Simulation of Cutting Process Chip Formation. Chip flow was formed from the FEM simulations with a plane-strain simulation of the orthogonal cutting processes at cutting speeds 300m/min, . The simulations of the orthogonal cutting of hardened mold steel are conducted from the initial state to the steady state. The shapes of the segments are shown in Fig.3, and predicted the maximum cutting fracture value at chip-tool interface of primary cutting edge is 2.13.
Fig. 3 Comparison between predicted chip formations and experimental chip morphology As shown in Fig.3, the chip forms as the cutting edge rotates. Large strains and fracture coefficient due to friction induced deformation and thermal expansion at the tool rake face lead to a curling of the chip. Simultaneously, the chip segments are separated from each other at the free surface side of the workpiece, while connected with each other at the tool rake face side. The connecting portion of the chips is thicker and the segmentation is closer. The crack propagation resistance to the shear localized direction increases with the cutting speed. On the other hand, the crack that occurred inside the primary deformation zone is prone to developing in the free surface direction. And its lead to the chips separating from the shear zone and forming the serrated chip. This is followed by the formation of a new active shear band and the initiation of a ductile crack in the new primary shear zone, eventually leading to a second segment. As can be seen from the Fig. 3, the sequence of this process repeats itself indefinitely and results in the “shear localized chip morphology”, which is in good agreement with observation in table 2. Table 2 Comparison between simulation chip shape, cutting force and experimental data H L hc F x (N) F y (N) Experimental data Predicted Value Error %
428.07 388.61 10.1%
137.74 119.18 15.2%
34.4 33 4.1%
16 15 6.2%
18 14 22.2%
Effective Stress, Effective Strain and Temperature. Predicted effective stress, effective stain and temperature distributions at the peripheral milling in the workpiece material for the different cutting speed, are presented from Figs.4 (a-c). The maximum effective stresses, effective strains and maximum temperature in the workpiece material are 2136 MPa, 0.3 and 456℃ respectively. It is also found that the temperatures on the tool rake face are much higher than the temperatures in the shear zone. Predicted maximum material temperatures are located near to the tool tip but not on the
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tool tip. This proves that the chip–tool interface friction generates heat which leads to elevating temperatures on the rake face as the chip continues to slide on this surface. The maximum effective strain in the workpiece was located on the rake face and near the tool tip. (a)
(c)
(b)
Fig. 4 Predicted effective stress, effective strain and temperature in deformation zones Comparison of Predicted Cutting Forces with Experiment An experiment system was set up as illustrated in Fig.5. The cutting tests were conducted on a high speed machining center DMU-60T with a Heidenhain iTNC 530 numerical controller. The maximum machine spindle speed was 24000 rpm. A SKD11 mold steel (Pre-hardened 40 HRC) with a thickness of 20 mm was mounted on a three-component piezoelectric dynamometer (Kistler type 9625B), which was connected with charge amplifier (Kistler type 5001)) and a PC data acquisition system. The workpiece material used was hardened mold steel (62 HRC); its main chemical ingredients are: Cr - 12.0%, C - 1.5%, Mn - 0.5%, Mo - 1.0%, V - 0.2%. With six edges, rake 5° and flank 7° cutting tool, its material is TiSiN coated cemented carbide. In order to avoid run-out effects, only one cutting edge of the insert was used during machining. The other cutting edge was ground in each insert. Fresh inserts were used in each experiment and experiments were replicated at each cutting condition to reduce experimentation error and the effect of tool wear. The cutting Parameters are cutting speed 300 m/min, feed rate per tooth 0.1 mm/z, radial depth of cut 6 mm, axial depth of cut 0.2 mm and dry cutting. n Fz F y
Flat end mill
fz
Fx
Acceleration sensor Workpiece
Rd
(b) Cutting parameters (c) Dynamic signal analysis apparatus and data processing system
Dynamometer y x z y z In Charge amplifier x y z Out
F
Ad
x
A/D transducer Ch1
Ch2
Ch3
(a) Machine tool, cutting force measurement
Fig. 5 Schematic of high speed milling experiment The simulation was not run until the undeformation chip length corresponded to 60° of rotation angle. Thus, the predicted cutting force was compared with experimental force for the 6th of cutter rotation. The predicted cutting force that resulted from the primary cutting edge Fx (feed direction) and Fy (feed perpendicular to feed direction) were compared with the measured forces, as shown in the figure 6. Predicted cutting force is in good agreement with experimental data in table 2.
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Predicted Column 2Fx(FEM)
Column 4 Fx measured
Column 3Fy(FEM) Predicted
Column 5 Fy measured
Cutting Force,Fx(N)
600
400
200
45 60 30 Rotation Angle,(deg) Fig. 6 Comparison of predicted cutting force and experiment data 0
15
Conclusion A simplified panel strain model with the modified Johnson–Cook plasticity, damage models and adaptive meshing technique was used to simulate peripheral milling behavior of hardened mold steel. Chip formation, cutting force, the distribution of effective stress and temperature is simulated and investigated by the constructed model. The study showed the serrated chip is easily deformed at cutting speed 300 m/min. Workpiece material fracture values (the fracture occurs or chip segmentation starts values) is 2.13, and crack extends in the shear band direction. Predicted effective stress and cutting temperature at chip-tool interface of primary cutting edge in deformation zones is gradient distribution. At the same time, predicted cutting forces is consistent with experimental data. Simulation of chip flow has the potential to identify these cutting forces used in mechanistic modeling. Acknowledgements The authors gratefully acknowledge the foundation by the National Natural Science Foundation of China (NSFC) with the project number 50665001 and 2009AA044302. Reference [1] Y.N Hu, C.Y. Wang, H.W. Zhang, H.N. Liu: Journal of Mechanical Strength. Vol. 27(2005), p. 782 (in Chinese) [2] Y.N. Hu, C.Y. Wang, X.Q. Wu, Z. Qin, B.P. Zeng: Trans. of NUAA. Vol. 21(2004), p. 291 [3] M. Bäker, J. R O¨sier, C. Siemers: Comput Struct. Vol. 80(2002), p. 495 [4] M. Bäker: Tech. Mech. Vol. 23(2003), ,p. 1. [5] M. Bäker: J. Mater. Process. Technol. Vol. 176(2006), p. 117. [6] T. O¨ zel, T. Altan: J. Mach. Tools Manuf. Vol. 40(2000), p. 713 [7] T. O¨ zel, E. Zeren: J. Mater. Process. Technol. Vol. 153–154(2004), p. 1019. [8] C. Hortig, B. Svendsen: J. Mater. Process. Technol. Vol. 186(2007), p. 66 [9] M. Bäker, J. R¨osler, C. Siemers: Computational Materials Science. Vol. 26(2003), p. 175 [10] D.W.Tang, C.Y. Wang, Y.N.Hu, et al: Metall. Mater. Trans. B, (in proof)
Advances in Materials Processing IX doi:10.4028/www.scientific.net/KEM.443 Finite Element Simulation of Chip Formation during High-Speed Peripheral Milling of Hardened Mold Steel doi:10.4028/www.scientific.net/KEM.443.274 References [1] Y.N Hu, C.Y. Wang, H.W. Zhang, H.N. Liu: Journal of Mechanical Strength. Vol. 27(2005), p. 782 (in Chinese) [2] Y.N. Hu, C.Y. Wang, X.Q. Wu, Z. Qin, B.P. Zeng: Trans. of NUAA. Vol. 21(2004), p. 291 [3] M. Bäker, J. R O¨sier, C. Siemers: Comput Struct. Vol. 80(2002), p. 495 doi:10.1016/S0045-7949(02)00023-8 [4] M. Bäker: Tech. Mech. Vol. 23(2003), p. 1. [5] M. Bäker: J. Mater. Process. Technol. Vol. 176(2006), p. 117. doi:10.1016/j.jmatprotec.2006.02.019 [6] T. O¨ zel, T. Altan: J. Mach. Tools Manuf. Vol. 40(2000), p. 713 [7] T. O¨ zel, E. Zeren: J. Mater. Process. Technol. Vol. 153–154(2004), p. 1019. [8] C. Hortig, B. Svendsen: J. Mater. Process. Technol. Vol. 186(2007), p. 66 doi:10.1016/j.jmatprotec.2006.12.018 [9] M. Bäker, J. R¨osler, C. Siemers: Computational Materials Science. Vol. 26(2003), p. 175 doi:10.1016/S0927-0256(02)00396-8 [10] D.W.Tang, C.Y. Wang, Y.N.Hu, et al: Metall. Mater. Trans. B, (in proof)
