# Milling process FEM simulation for identification of material parameters directly from experiments

Aurelien Maurel-Pantel, Michael Fontaine, Sébastien Thibaud, Jean-Claude

Gelin

► To cite this version:

Aurelien Maurel-Pantel, Michael Fontaine, Sébastien Thibaud, Jean-Claude Gelin. Milling process FEM simulation for identification of material parameters directly from experiments. NUMIFORM Conference, 2007, Porto, Portugal. 10.1063/1.2740820. [hal-00329585]

HAL Id: hal-00329585

https://hal.science/hal-00329585v1

Submitted on 17 Apr 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Milling Process FEM Simulation for Identification of Material Parameters Directly from Experiments

A. Maurel, M. Fontaine, S. Thibaud, G. Michel, J.C. Gelin

FEMTO-ST Institute / Applied Mechanics Laboratory, ENSMM, 26 rue de l'Epitaphe, 25000 Besançon, France

**Abstract.** An identification procedure for the determination of material parameters that are used for the FEM simulation of milling processes is proposed. This procedure is based on the coupling of a numerical identification procedure and FEM simulations of milling operations. The experimental data result directly from measurements performed during milling experiments. A special device has been instrumented and calibrated to perform force and torque measurements, directly during machining experiments in using a piezoelectric dynamometer and a high frequency charge amplifier. The forces and torques are stored and low pass filtered if necessary, and these data provide the main basis for the identification procedure which is based on coupling 3D FEM simulations of milling and optimization/identification algorithms. The identification approach is mainly based on the Surfaces Response Method in the material parameters space, coupled to a sensitivity analysis. A Moving Least Square Approximation method is used to accelerate the identification process. The material behaviour is described from Johnson-Cook law. A fracture model is also added to consider chip formation and separation. The FEM simulations of milling are performed using explicit ALE based FEM code. The inverse identification method is here applied on a 304L stainless steel and the first results are presented.

**Keywords:** FEM, Orthogonal cutting, Milling, 304L Material, Identification, Cutting forces measurements.

## INTRODUCTION

In the last ten years, High Speed Machining has become one of the most used processes in macro and micro manufacturing with applications in aeronautic, automotive or mechanical engineering industries. The understanding of the physical phenomena and the identification of material behaviour in machining are the main issue for the industrial process optimization. In fact the workpiece is machined under severe mechanical solicitations (very high strain rate, vibrations, failure) as well as thermal ones (thermal transfer, friction). Some analytical models were previously proposed by Merchant [1] which were developed by Oxley [2] and Molinari & Dudzinski [3], these last works were adapted to milling [4]. But also a complete semi-empirical approach was developed by Altintas [5]. More recently, calibrated FEM models appear and seem to progress in the way of the real machining process simulation, Pantalé [6]. Nevertheless, the high thermo-mechanical coupling and the nonlinear aspects involved in these models give only a partial interpretation of the process's phenomena. To improve predictive capacity of these models, one needs to characterize the material behaviour which is involved in the machining process.

Therefore it is emphasized in the present paper to proceed by an inverse method based on FEM models for the identification of material parameters from machining experiments.

Then this paper shows the developments carried out in our laboratory related to the identification methodologies [7][8][9], through three main tasks. The first one consists to develop a finite element model of machining process, then to set up experimental equipment allowing the measure of cutting forces during milling, and finally to lead on an identification procedure.

## NUMERICAL SIMULATION OF MACHINING

In order to perform numerical simulation of machining, a finite element model was implemented in LS-Dyna© FEM code. As machining is an high speed metal forming process characterized by large dynamic stresses and localized high strains, an explicit code solution scheme was adopted. LS-Dyna© FEM code has been chosen to build a Design of Experiment (DOE) empirical model of machining process in order to be able to identify and to understand process parameters. The final aim consists to obtain a reliable
simulation of milling that is one of the more complex cutting process.

## Numerical Simulation Of Orthogonal Cutting

At the beginning, orthogonal cutting process has been studied to compare results with bibliography data. In a first stage, a 2D orthogonal cutting model has been developed with LS-Dyna© FEM code. In this simulation, high speed cutting conditions and the material Ti-6Al-4V have been used to analyze the cutting parameters influence and compare the calculations with the analysis reported in Molinari et al. [11]. The model uses a linear plasticity material law with an element failure criterion based on a constraint critical value and an adaptative mesh routine which refines the mesh in function of the constraint value. The elements chosen are 2D elements with a plane strain formulation. The machined material is meshed with 20,000 elements and the tool is considered as a rigid body meshed with 10,000 elements.

The Figure 1 relates the simulation results that show the appearance of adiabatic shear banding in the chip formed by the machining process.

<figure><img src="image_2.png" /><figcaption>FIGURE 1. Adiabatic shear banding in simulation results of orthogonal cutting process.</figcaption></figure>

Then many parameters have been tested to understand their influence on the chip formation and on the simulation results.

<figure><img src="image_3.png" /><figcaption>FIGURE 2. Effects of friction coefficient in simulation results.</figcaption></figure>

Figure 2 reports an example of the friction coefficient effects. With a low coefficient, the chip motion is more fluid and the adiabatic shear banding appears hardly, whereas the inverse is obtained with an high coefficient.

Secondly, with these first results in 2D, a 3D orthogonal cutting model has been developed to improve the simulation and to correspond to results obtained by Pantalé [6]. In this simulation, a classical steel material have been chosen, and the cutting conditions have been defined with a cutting speed $V_c$ = 60 m/min. This model also uses a linear plasticity law with an element failure criterion based on a limiting plastic strain critical value. Furthermore the cutting tool is considered as a rigid body. The mesh is materialized with 49,000 solid elements, 40,000 solid cubic elements for the machined material and about 9,000 solid tetrahedral elements for the cutting tool.

The figure 3 relates the distribution of von Mises effective stress contours from simulation results. All this data in orthogonal cutting conditions has shown that LS-Dyna© is well adapted to create complex FEM numerical model as milling process.

<figure><img src="image_4.png" /><figcaption>FIGURE 3. Von Mises stress contours arising through FEM simulation of orthogonal cutting.</figcaption></figure>

## Numerical Simulation Of Milling

Accordingly with the experiments presented in the following part, a Ø 4 mm end mill and a 304L stainless steel rectangular specimen have been designed with SolidWorks©, and furthermore the same cutting conditions than in experiments have been used in the numerical FEM model. Figure 4 relates the first simulation results. The test specimen is meshed with 160,000 elements. The corresponding material behaviour has been firstly modelled using the classical Johnson and Cook constitutive model [10] whose the five parameters are A yield stress constant, B strain
hardening constant, n strain hardening exponent, C strain rate hardening constant, and m temperature dependent coefficient, the 304L stainless steel material parameters are provided by the CETIM foundation and related in Table 1.

<table><caption>TABLE 1. 304L stainless steel material parameters</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>A</td><td>253,32 Mpa</td></tr><tr><td>B</td><td>685,1 Mpa</td></tr><tr><td>n</td><td>0.3128</td></tr><tr><td>C</td><td>0.097</td></tr><tr><td>m</td><td>2.044</td></tr><tr><td>T<sub>seuil</sub></td><td>1698 °K</td></tr><tr><td>T<sub>f</sub></td><td>296 °K</td></tr></tbody></table>

$$ \sigma = [A + B(\varepsilon^p)^n] [1 + C \ln(\frac{\dot{\varepsilon}^p}{\dot{\varepsilon}_0})] [1 - (\frac{T - T_f}{T_{seuil} - T_f})^m] \quad (1) $$

The end mill is meshed with about 210,000 elements and considered as a rigid body. This model uses an element failure criterion based on a limiting plastic strain critical value.

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Von Mises stress contours obtained through simulation results of a milling process numerical model with LS-Dyna software.</figcaption></figure>

# EXPERIMENTAL INVESTIGATIONS

## Cutting Forces Measures During Milling

In the first step, a complete instrumentation including sensors and on line measuring system has been set up to obtain repetitive and reliable data. The sensor system is based on a Kistler® dynamometer using the piezoelectric accelerometers technology, in order to give, through direct measurement, the cutting forces during the machining process. Then the 9272A dynamometer has been preferred for its robustness and its wide range of use in force and frequency as related in Table 2. This device is based on four piezoelectric sensors, each of them delivering an electric signal function related to applied loads on each referenced axis.

<table><caption>TABLE 2. Kistler dynamometer's characteristics</caption><thead><tr><th>Natural Frequency(kHz)</th><th colspan="2">Measuring Range</th></tr></thead><tbody><tr><td>F<sub>n</sub> (x,y)</td><td>F<sub>x</sub>, F<sub>y</sub></td><td>-5...5 kN</td></tr><tr><td>F<sub>n</sub> (z)</td><td>F<sub>z</sub></td><td>-5...20 kN</td></tr><tr><td>F<sub>n</sub> (M<sub>z</sub>)</td><td>M<sub>z</sub></td><td>-200...200 N.m</td></tr></tbody></table>

The measuring channel has been completed by an high frequency Kistler charge amplifier and the TPCut© software is used for the treatment of the measured data. The software is also able to give the cutting areas in order to realize the tests in industrial conditions. The experiments were carried out on a KERN® micro milling machine as shown in Figure 5. The dynamometer was fixed on the table of the 3 axes CNC machine, and then it was linked to the charge amplifier which was connected to a PC through an input/output acquisition card. The equipments chosen for these milling experiments are as following.

<figure><img src="image_6.png" /><figcaption>FIGURE 5. Experimental data acquisition system used in milling experiments.</figcaption></figure>

The type of the selected milling tools are two teeth end mills to have a better description of the cyclical teeth motion and to avoid the perturbation on the
measured curves due to a poor balancing of end mills with three or four cutting edges. These tools are uncoated tungsten carbide mills with 30° nominal helix angle and 12° normal rake angle, and the tested diameters are in the range 2-6 mm. All the test specimens have been machined in the same 304L austenitic stainless steel bar and in the same dimensions: 80 mm x 40 mm x 10 mm.

All milling experiments have been carried out with a micro lubrication sprayed on the tooling area. The cutting velocities are defined between 50 and 400 m.min⁻¹ to reach a maximum spindle speeds corresponding to 40 000 rpm.

<figure><img src="image_7.png" /><figcaption>FIGURE 6. $F_x$ cutting forces measured curve with two tooth end mill O 4 mm, $I_c^* = 200$ m/min, $f_t = 0.01$ mm/tooth, $d_a = 0.5$ mm (sampling: 20000 Hz).</figcaption></figure>

Figure 6 relates a measured curve example: a force rise and instability at the input and the output of the test specimen must be noted. This effect is associated to a very fast shift of the tool engagement conditions and of the initial surface integrity of the test specimen

(hardening, residual stresses, and surface roughness). The central zone corresponds to the stabilized signal where sinusoidal like and repetitive curves are obtained.

Figure 7 relates a zoom of the cutting forces stabilized signal in milling for the same curve than in Figure 6, where the cutting conditions and machining parameters correspond to:

* 2 teeth end mill Ø 4 mm in slotting tests (full radial immersion);

* Spindle speed: $\Omega$ = 15920 rpm; Feed: ft = 0.01 mm/tooth; Cutting speed: Vc = 200 m/min; Axial depth of cut: da = 0.5 mm.

Under these conditions, the end mill perform one rotation in 3 ms. In sampling at a 20 000 Hz frequency, the curve is composed with sixty points by cutter rotation. Figure 7 shows that is possible to get a good and accurate variation of the milling forces on the 3 machine axes. The Figure 7 shows cyclic and sinusoidal curves, where each cycle corresponds to a milling cutter revolution and, each cycle peak corresponds to a tooth path. A discrepancy in the forces level appears between the two peaks, which is mainly due to the tool run-out (position and/or angle offset between the cutter axis and the spindle axis).

<figure><img src="image_8.png" /><figcaption>FIGURE 7. Cutting forces $F_x$, $F_y$, $F_z$ vs. end mill rotations.</figcaption></figure>
A signal spectral analysis was conducted on forces components in order to check the stability of measured data and to recover the equivalent forces for a rigid case after appropriate low filtering. These accurate and reliable measures allow the understanding of a part of the end mill behaviour during the milling process and then the setting up of the identification process.

## Mechanical Characterization Of The 304L Stainless Steel

In the same time, tensile tests have been performed in the laboratory on the 304L stainless steel provided by CETIM Research Center. These first experiments permit to identify the material parameters of the Johnson-Cook constitutive law (1). The final aim consists to compare the experimental characterization with the inverse identification method results presented in the next part, in order to validate the procedure. This model is based on tensile tests with low speed strain rate. The material parameters are identified by a genetic algorithm applied at the experiments results. The tensile tests have been realized with four test temperature 20°, 50°, 100°, 180°, and with the following range speed strain rate, 0.0001 %·s⁻¹ to 1 %·s⁻¹. The experimental results are related in Figure 8.

Then to improve this identified model, new tests in partnership with other laboratories of the PGV national project will be realized with high speed strain rate and a wide range of temperature. Soon, a generalized

Johnson-Cook constitutive law will be identified and a new model adapted to the high speed strain will be available to reach high speed milling cutting conditions.

## INVERSE IDENTIFICATION METHOD

The final aim of this work consists to lead an inverse identification procedure for the determination of 304L stainless steel parameters. The identification procedure methodology needs an objective function to minimize, a set of parameters to analyze, a finite element method solver and a procedure for updating the material parameters. For the milling experiments identification, the parameters system **p** (A, B, n, C, Tseul, m) has been chosen in the Johnson-Cook constitutive law (1). Then an objective function dependent of the measured experimental criteria (cutting forces) has been defined in (2).

$$ 
\begin{aligned}
R(\mathbf{p}) = & \frac{1}{2} \left( \sum_{i=1}^{N_p} \left[ F_x^{\text{exp}} - F_x^{\text{num}}(\mathbf{p}) \right]^2 + \dots \right. \\
& \left. \dots \sum \left[ F_y^{\text{exp}} - F_y^{\text{num}}(\mathbf{p}) \right]^2 + \dots \right. \\
& \left. \dots \sum \left[ F_z^{\text{exp}} - F_z^{\text{num}}(\mathbf{p}) \right]^2 \right)
\end{aligned}
\quad (2) $$

<figure><img src="image_9.png" /><figcaption>FIGURE 8. Tensile tests results</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>FIGURE 9. Diagram representing the inverse identification procedure.</figcaption></figure>

The previous function measures difference between the cutting forces curves obtained with the numerical simulation software and with the experimental device. Figure 9 schematically relates the identification loop, the procedure is based on a set of parameters obtain through simulation and then compared with experimental results.

After this estimate, whether the objective function is equal to zero and the optimized solution appeared, or the function is different to zero and the set of parameters has to be modified and the loop begin one more time. Several methods exist for the identification strategy, in this work the Moving Least Square Approximation (MLSA) method has been used.

## CONCLUSIONS

Milling experiments allowed us to analyze accurately the measured cutting forces curves and to obtain reliable and useful measured data for the identification procedure. Then, a first 3D simulation of milling process has been set up in the experiments conditions. The numerical model is based on a dynamic transient explicit scheme and on lagrangian formulation. At the end, this paper described the identification procedure which will be set up soon. Moreover, further developments are in progress and concern the numerical model improvements and the choice of a new material behaviour model more adapted to a high speed metal forming process in order to test the method in High Speed Milling conditions.

## ACKNOWLEDGMENTS

This work has been carried out with the financial support from the CETIM Foundation in the frame of PGV1 national project.

## REFERENCES

1. E. Merchant, *J. of Applied Mechanics*, **66**, 168-175(1944).

2. P.L.B. Oxley, *ASME*, 50-60(1963).

3. A. Molinari, D. Dudzinski, *C.R. Acad. Sciences Paris*, **315 (II)**, 399-405(1992).

4. M. Fontaine, A. Devillez, A. Moufki and D. Dudzinski, *Int. J. Machine Tools and Manufacture*, **46**, 367-380(2006).

5. Y. Altintas, *J. Machining Science and Technology*, **3-4**, 445-478(2000).

6. O. Pantalé, "Modélisation et simulation tridimensionnelle de la coupe des métaux", Ph.D. Thesis, Bordeaux I University, 1996.

7. J.C. Gelin, C. Labergere, *Int. J. Forming Processes*, **7**, 141-158(2004).

8. O. Ghouati, J.C. Gelin, *J. Material Processing Technology*, **80-81**, 560-564(1998).

9. O. Ghouati, J.C. Gelin, *Computational Materials Science*, **21**, 57-68(2001).

10. G.R. Johnson, W.H. Cook, *Proc. 7th Symp. On Ballistics*, Netherlands(1983).

11. A. Molinari, C. Musquar and G. Sutter, *Int J. Plasticity*, **18**, 443-459(2002).