Aspects of the simulation of a cutting process with ABAQUS/Explicit including the interaction between the cutting process and the dynamic behavior of the machine tool 1
T. Schermann 1*, J. Marsolek 2**, C. Schmidt1, J. Fleischer 1 University Karlsruhe, Institute of Production Science, Kaiserstraße 12,76128 Karlsruhe, Germany 2 ABAQUS Deutschland GmbH, Theaterstr. 30-32, 52062 Aachen, Germany *
[email protected] **
[email protected]
Abstract In the field of simulation of metal cutting the coupling of the cutting process and the dynamic behaviour of the machine tool becomes more and more a great challenge nowadays. Interactions between the machine tool and the cutting process can e.g. lead to oscillations which influence the workpiece surface quality, tool wear and the stability of the cutting process. To investigate this effect a coupled simulation is needed. In order to ensure the coupling of cutting processes and machine tools it is necessary to identify the influences on both sides and to analyze their sensitivity. A lot of research activities were done in recent years in simulating both the cutting process and the machine tool behaviour and a lot of new research questions have resulted from that research. When simulating a cutting process with the finite element method it is necessary to analyze not only the influence of process parameters such as cutting speed, feed rate or tool geometry but also the influence of modelling parameters such as mesh fineness, material failure modelling, etc.. An approach for a 3D simulation of a turning process with the FEM-program ABAQUS/Explicit is shown. Results of parameter studies, which show the influences of different modelling parameters, are presented. To verify the simulation the results in terms of cutting forces and chip shape are compared with the results obtained from experiments. In addition a first approach for coupling a cutting process and a machine tool in an ABAQUS/Explicit simulation model is presented, which fulfills the requirement of an integrated and continuous simulation of these two components. 1 INTRODUCTION Productive and economical production processes are necessary for industrial growth and progress. By developing analytical and empirical models in the past a lot of research was done to make a statement of a manufacturing process both to reduce the time until process stability is reached and to determine further rationalization potentials and to use them in relevant optimisation attempts. The aim of cutting simulation is the discretization of cutting-technological processes with computers so that the base for an industrial application is reached. This enables a substitution of time and cost consuming cutting experiments [1]. A useful method to model cutting processes is the finite element method (FEM). By using FEM it is possible to simulate chip formation processes and thus a prediction about chip formation can be realised.
New developments are tending to consider the interaction between the cutting process and the machine tool. This interaction includes the reaction behaviour of the machine tool due to excitations from the machining process as well as the feedback on the process. The subsequently presented results were obtained within the project „SindBap“ funded by the German Federal Ministry of Education and Research (BMBF). The aim of this project is to perform sensitivity analyses. It is achieved by using the cutting simulation implying a preventive quality assurance. As a consequence potential problems can be predicted and avoided. It is important to drive forward the development and improvement of models and methods which accurately represent cutting processes and their interaction with the machine tool. Furthermore these models and methods should be user-friendly. In order to ensure a correlation between the process simulation and the experiment, se-
lected examples with the main focus on turning, milling and drilling are investigated in simulations and experiments in the project „SindBap“. This includes the determination of material specific parameters, the simulation of cutting forces as well as influence analyses with parameter variations. Finally, by considering the machine tool the basics for the aim of virtual production, namely the integrated and continuous simulation of process and machine tool, will be created [2].
Eulerian (ALE) process model outflow: eulian
tool workpiece surface: sliding with friction
worpiece surface: inflow: Eulerian sliding
outflow: Eulerian
μ
ALE-region: material flow through mesh
workpiece Mises stress in process zone [N/mm²]
A first approach for coupling a cutting process and a machine tool in ABAQUS/Explicit will be presented in this paper. Firstly the process model of a turning process will be introduced. Secondly different sensitivity analyses, which were performed at Institute of Production Science of University Karlsruhe, will be presented. Finally the machine model and a coupled model, which was setup at ABAQUS Deutschland GmbH and includes the process and the machine tool, will be presented. 2 PROCESS SIMULATION 2.1 Process Models ABAQUS/Explicit [3] offers two possible approaches to simulate metal cutting processes, the Eulerian (ALE) and the Lagrangian approach [4].
Figure 1: Eulerian (ALE) process model/example results Idealization of chip separation by element deletion plastic strain
material damage and element deletion => chip separation
Eulerian (ALE) approach The ALE method (Arbitrary LagrangianEulerian method) in ABAQUS/Explicit allows a material flow through the mesh (Figure 1). The material flow is independent from the movement of the mesh nodes inside the workpiece and tangential to the workpiece surface. Frictional contact shear stresses at the workpiece surface are transmitted to the flowing material. The mesh is smoothed in regular time intervals to maintain a good mesh quality and beneficial element aspect ratios, which govern the time step in an explicit analysis. Eulerian inlet and outlet boundary regions can be defined where material flows in and out of the control volume. Starting from an initial configuration after some simulation time a steady state configuration is reached. This way a cutting process model which is limited to the process zone can be defined. Eulerian (ALE) models are most suitable for detailed studies of local effects in the cutting process zone for continuous chip formation. Example results are presented in Figure 1.
chip
tool tip
workpiece
Reduction of yield stress σ and stiffness E of plastic material after damage initiation with damage variable D
σ ( D = 0)
σ y0
σ
undamaged
− Dσ
σ0
damaged:
σ = (1 − D )σ E
E
(1 − D) E
ε 0pl
ε ε fpl
Figure 2: Lagrangian process model with damage/element deletion Lagrangian approach According to the Lagrangian approach the movement of mesh nodes is connected to the material movement. A common way to idealize
the separation of the material flow at the tool tip, which leads to chip formation, is the deletion of elements according to appropriate failure criteria (Figure 2). ABAQUS/Explicit offers several failure models with and without damage initiation and damage evolution before element deletion. The failure/damage models have to be carefully calibrated. Lagrangian models with element deletion are most suitable for the simulation of complex 3D-cutting processes including non-continuous chip formation (e.g. segregated chips). Material behavior The specification of the material behaviour with the classic quasi-static behaviour of metallic material at tensile tests is not acceptable for cutting processes. By increasing the load speed or temperature the deformation behaviour of the material changes characteristically and shows a significant dependency on the plastic strain, the strain rate and the temperature induced by plastic deformation and friction. Such behaviour must be included in a suitable material model. In a Lagrangian process model a material model also has to include a failure behaviour, which is used to idealize material separation by element deletion at the tool tip. A possibility to specify the elasto-plastic deformation behaviour in ABAQUS is the tabular input of flow curves. Thereby the yield stress is specified dependent on the equivalent plastic strain, the strain rate and the temperature.
2.2
The constitutive material law chosen for the simulations presented in this paper considers plastic strains from 0 to 4, strain rates from 0.001 to 100,000 s-1 and temperatures from 293 K to 1473 K and is provided by [5]. Heat conduction ABAQUS offers different types of simulation procedures. For example fully-coupled thermalmechanical simulations (including heat flow and conduction) or pure adiabatic simulations (only including locally generated heat but no heat conduction) can be performed. Fully-coupled thermal-mechanical simulations are more computation time consuming than pure adiabatic simulations. Results of fully-coupled thermalmechanical simulations and pure adiabatic simulations of the investigated cutting processes were found to be very similar. This agrees well with the fact that heat flow is a very slow process compared to the deformation speed in the cutting zone. Therefore in a first
2.3
approach it is sufficient to consider a pure adiabatic simulation, neglecting heat conduction but taking into account local heat generation as a result of friction and plastic material deformation. Friction The contact and friction conditions at the tool/chip and the tool/workpiece interface determine the cutting forces, machining quality and tool wear, and therefore play an important role in metal cutting. Various approaches such as Coulomb’s assumption [6], Zorev’s slidingsticking model [7] and stress-based polynomial models of friction [8] are used to model friction in chip formation analysis. Often Coulomb’s friction law is used with a constant coefficient of friction. Normally the frictional coefficient µ is approximately defined according to the observed cutting force Fc, passive force Fp, and the rake angle α. For the simulations presented in this paper a constant Coulomb friction coefficient of µ=0,2 was used. The heat generated by friction was distributed evenly between the interacting surfaces.
2.4
Chip formation In order to model chip formation a fine mesh of at least 4 elements over the depth of cut has to be specified in the workpiece to adequately capture the bending stiffness of the chip with reduced integrated linear elements. In a Lagrangian-type model a minimum number of elements is also needed due to the fact that element deletion is used to realize the chip separation: The contribution of the deleted elements is missing in the bending stiffness of the chip.
2.5
The element deletion criterion used in the presented simulations is a simple shear failure criterion based on the value of the equivalent plastic strain at the element integration points: When the equivalent plastic strain at an integration point reaches a defined failure strain, material failure takes place. After material failure took place at all the integration points of an element, the element is removed from the mesh. Due to the fact that the failure criterion is used for all elements in the workpiece a definition of a separation path is not needed. Figure 3 shows a comparison of a chip formation in experiment and simulation.
tool
workpiece
workpiece
sumed that the friction is the same in all directions (isotropic friction) [3]. The setup of the 3D simulation model and the boundary conditions are shown in Figure 4. Figure 5 shows some results of a 3D turning process simulation. reference point
Source: WZL Aachen
x
Figure 3: Chip formation in experiment vs. simulation 3D turning process For the simulation of an outer longitudinal turning process with ABAQUS the workpiece is modelled as a pre-machined section of a spindle, whereas it is modelled as a straight workpiece to simplify matters. The 3D process simulation has the following configuration: It is modelled as a modular assembly with two parts, the tool and the workpiece. This enables a fast reconfiguration once the tool or workpiece geometry is changed.
y
vc
2.6
Tool (rigid body) y z workpiece (ideal-plastic)
Figure 4: Setup of the 3D simulation model in ABAQUS
The 3D turning process presented in this paper was simulated using a Lagrangian approach. To idealize the separation of the material flow at the tool tip, which leads to chip formation, elements were deleted according to a simple failure criterion without previous damage. Heat generation and friction was taken into account. If the stress distribution within the tool is not of interest a part can be modelled as a rigid body in order to save computation time. The rigid body motion is governed by a so called reference point, at which reaction force output is available. The tool geometry varies depending on the roughing or finishing geometry specified by the tool manufactures. For the simulations presented in this paper a simple cutting edge configuration of the tool has been chosen containing a flank angle of 5°, a rake angle of 6° and cutting edge radii of 8 µm, 35 µm and 60 µm. In order to model the small cutting edge radii a very fine mesh is defined in the cutting edge area. The workpiece is modelled as an elasto-plastic body. It is moving with the cutting speed vc in the x-direction, while the displacements in the other directions are fixed. The contact between workpiece and tool and the self-contact of the chip/workpiece is defined with the general contact algorithm in ABAQUS/Explicit. Coulomb friction is defined for contact between the two parts and for self-contact. Thereby it is as-
Figure 5: Results of a 3D turning process simulation in ABAQUS 3 PROCESS SENSITIVITY ANALYSES It is necessary to know all parameters that have an influence on the machining process in order to optimize the chip removal process. For example, the mechanical properties of the workpiece material have an important influence on the machinability and thus on the cutting parameters such as forces and temperature which directly affect tool wear. When using cooling lubricant or minimum quantity lubrication, friction and cooling conditions in the cutting area are changed. Third parameter within the tribological cutting system is the tool, which can be changed in terms of cutting material, cutting
In addition to the previously mentioned physical parameters several modelling parameters can significantly influence results of FEM simulations of cutting processes. Therefore parameter studies which study the influence of mesh fineness, mass scaling and the element failure criterion, which governs element deletion, were performed. Some of the results will be presented in the following. vc= 100 U/min; ap=0. 2mm; f= 0.1 mm
100
Coarse mesh Experiment Fine mesh
90 80 Forces [N]
70 60 50 40 30 20 10 0 rβ
10
35 Fc
60
10
35 Fp
60
10
35
60
Ff
Figure 6: Coarse mesh vs. fine mesh of the cutting edge of the tool Figure 6 shows the influence of different cutting edge radii on the cutting forces in simulation and experiment. In the simulations the different cutting edge radii were modelled with a fine and a coarse mesh. The differences of the results show that it is important to use an adequately fine mesh in the cutting edge area in order to correctly capture the cutting forces. Correspondingly the workpiece has to be meshed fine enough in the region of the developing chip.
scale the masses of elements with small edge lengths, which govern the critical maximum time step size which cannot be exceeded in an explicit dynamic analysis. The mass increase will directly lead to a larger maximum time step size and therefore to a speedup of the analysis. This correlation is shown in the following formulas (3.1) in which dt is the critical maximum time increment, cd the acoustic wave velocity in the material, L the characteristic element edge length, E the Young’s modulus of the material, δ the material density, m the mass and V the volume of a part.
dt =
L ; cd
E δ
cd =
δ=
;
m V
(3.1)
By presetting a minimum time increment for the analysis which is larger than the calculated critical time increment the mass of a part will increase in regions with small elements. If this mass increase is extensive, the inertia forces will increase, which leads to an unrealistic increase of the loading of the tool and the cutting force. Consequently it is necessary to make a sensitivity analysis in order to find out, how much mass scaling can be applied to shorten the computation time without significant falsification of the results. Figure 7 shows the dependency of the cutting forces on the mass scaling governed by the predetermined minimum time increment . It can be clearly seen that for the given example a prescribed minimum time step higher than 5e-8 s leads to an increased mass scaling and unrealistic high cutting forces. vc= 300 U/min; ap= 0.2 mm; f= 0.1 mm; rβ= 10 µm
820
200
1611
3299
4268
180 160 140 Fc [N]
geometry and coating technology. The influence of the machine stiffness and the dynamic behaviour given by the machine design should also not be neglected.
128
120 100
89
82
80 49
60 40 20 0 6,00E-07
Target time increment [s]
Ex pe rim en t
6. 0E -0 7
5. 3E -0 7
4. 0E -0 7
3. 0E -0 7
1,00E-07 4,00E-07 Target Time Increment [s]
1. 0E -0 7
5. 3E -0 8
1,00E-08
1. 0E -0 8
The computation time of a simulation depends very strongly on the mesh-fineness. An analysis of a model with a very fine mesh takes a longer computation time than one with a coarse mesh. Thereby the shortest edge of an element in the meshed part and the number of elements is determining the computation time. For representing a real chip formation process an adequate mesh fineness has to be ensured. In simulations of chip removal processes with small feed rates and small cutting depths the fine meshes with very small elements often cause long computation times. ABAQUS offers the possibility to reduce the computation time by using mass scaling. One approach is to
Mass scaling [%] start
0.002
0.547
1.935
17.394
30.924
54.817
69.585
end
0.018
0.556
1.994
32.091
59.932
101.72
122.51
Figure 7: Cutting forces vs. mass scaling/minimum time increment By using the mass scaling it is possible to simulate an outer longitudinal turning process on an standard computer (2,8 MHz; 4x 512 MB RAM)
for problems presented in this paper with a CPU time round about 4 hours. A further modeling aspect which should be carefully considered because it has a significant influence on the simulation results is the material failure criterion used for element deletion in front of the tool tip (see sections 2.1 and 2.5). Figure 8 shows the dependency of the simulated cutting- , passive- and feed rate forces on the shear failure criterion in ABAQUS: An increase of the chosen equivalent plastic failure strain leads to an increase of all force components until a certain failure strain is exceeded (approximately 2-5-3.0). At this stage element deletion only takes place directly in front of the tool tip. A possible reason why the tool forces stay approximately constant for failure strains in the range 3.0-3.5 is, that a further increase of the failure strain only leads to a small increase of energy dissipated by element straining but does not influence the cutting process configuration and the total process energy significantly.
Model description The original IDEAS model was translated into an ABAQUS analysis model. It consists of deformable solid parts, spring-type connector elements which e.g. represent the stiffness of bearings or connections and connected mass and intertia elements which represent the mass distribution of non meshed parts. Figure 9 shows the machine model. It includes one meshed spindle region.
4.1
worpiece holder tool
forces vs. equivalent plastic strain rate at failure rβ=10 mm; f=0.1 mm; vc=100; ap=0.2 mm 10 0
Fc
Forces [N]
machine
Fp Ff
80
spindle region
Figure 9: Machine model
60 40
Calibration and verification The machine model was recalibrated by comparison of the following ABAQUS/Standard simulation results with the experimentally measured machine behaviour (and IDEAS reference solution respectively): • Static stiffness measured at the workpiece position • Eigenfrequencies and eigenmode shapes. Figure 10 shows example eigenmode shapes including different workpiece holder movements. • Frequency-response characteristics for harmonic excitation at the workpiece position.
4.2
20 0 1. 0
1. 5
2.0
2.5
3 .0
3.5
Expe rime nt
equivalent plastic strain at failure εplf
Figure 8: Forces vs. equivalent plastic failure strain Other influence parameters for the simulation of chip removal processes were analysed and documented in different scientific papers [9, 10]. 4 MACHINE MODEL To take into account the interaction between machine and cutting process a model of the machine, which correctly represents its stiffness and dynamic behaviour is needed. The machine model used in the coupled simulations in this paper represents a multi-spindle machine manufactured by Alfred H. Schütte GmbH & Co KG, Germany. The FEM model was originally setup and calibrated at the Laboratory for Machine Tools and Production Engineering (WZL) of Aachen University of Technology (RWTH), Germany. More information about this type of FEM machine models is given in [11].
axial movement of workpiece holder
radial movement of workpiece holder
tangential movement of workpiece holder
Figure 10: Example eigenmode shapes
Figure 11 shows simulated frequency-response curves for an excitation at the workpiece position in global machine axis directions (undamped case). Test curves and data values cannot be published due to proprietary reasons. Axial excitation at workpiece
Radial excitation at workpiece
Tangential excitation at workpiece
Figure 11:Frequency-response characteristics for excitations at the workpiece (undamped simulation) 5 COUPLED SIMULATION Interactions between the machine tool and the cutting process have a significant effect on the dynamics of the process and the machine. Oscillations can influence the workpiece surface quality, tool wear and the stability of the cutting process. To investigate this effect a coupled simulation model of process and machine is needed. Several approaches for coupled simulations are investigated in the project "SindBap". Some approaches include a substitution of the process or the machine by simplified analogous or analytical models. Another approach is the inclusion of the cutting process model and the machine model in one ABAQUS analysis model. The current status of the latter approach will be described in the following. Coupled ABAQUS/Explicit model The coupled ABAQUS/Explicit model was built up by merging a cutting process model as described in section 2 (outer longitudinal turning)
5.1
and the machine model described in section 4. For this purpose the calibrated ABAQUS/Standard analysis model described in section 4.1 was already set up in such a way that it can easily be converted into an ABAQUS/Explicit Model: Element types and formulations which are available in both solvers were used. The fact, that the ABAQUS/Explicit solver is used for the whole coupled model eliminates the need for a special interface. In contrast to the simplified workpiece geometry, which was used for parametric studies described in section 3 (see also section 2.6), a complete cylindrical workpiece is modelled and attached to the workpiece holder of the machine model. The rotation of the workpiece holder is prescribed with a connector element. (ABAQUS connector elements can act like mechanisms including stiffness/damping, internal loads or prescribed relative motions. This way relative motion of machine parts can be prescribed during the simulation).To limit computation time only the process zone is meshed with a fine mesh, remaining regions of the workpiece are meshed coarsely or are defined as rigid. To demonstrate the feasibility of the chosen approach in a first step only 22.5° of the processed region of the workpiece are modelled in detail. In this first approach the tool is assumed to be rigid. It is connected to the tool holder region with kinematic coupling constraints. A connector element was placed in-between the coupling and the tool to allow the measurement of transmitted forces and moments. The simulation presented in the following starts with an initial rotational velocity of the workpiece. The actuation mechanism is idealized with a connector element, which allows the definition of a prescribed rotational relative velocity between two points. The tool is positioned right in front of the processed workpiece region. Results First exemplary results of the coupled simulation model are presented in figures 12, 13 and 14. Figure 12 shows a helically wound chip, which develops in the cutting process zone of the model. Figure 13 shows the process forces which are transmitted by the workpiece. The displacements of the workpiece (Figure 14) indicate starting oscillations, which might be caused by the sudden onset of the cutting process due to the chosen initial conditions. The calculation time needed to obtain the presented results was less than 24 hours (IBM power 4, single CPU run).
5.2
setting up a simulation model for a cutting process. In addition the feasibility of coupling a cutting process and a machine tool in an ABAQUS/Explicit simulation was demonstrated. Further coupled simulations will be performed to study the interaction between cutting process and machine tool with the goal to identify instable processes including chatter vibrations.
plastic strain
Figure 12: Chip in the process zone of the coupled ABAQUS model
cutting direction
other directions
Figure 13: Forces transmitted by the tool
Figure 14: Displacements of the workpiece 6 SUMMARY AND OUTLOOK An approach for a Lagrangian 3D simulation of a turning process with ABAQUS/Explicit was presented. Parameter studies showed up the influence of modelling parameters on the simulation results: Mesh fineness, failure criteria and mass scaling have to be carefully chosen when
7 REFERENCES [1] Söhner, J., Schmidt, J., 2001, Influence of Heat Treatment and Cutting Parameters on Chip Formation and Cutting Forces, International German and French Conference on High Speed Machining, Metz [2] Internet page of the project "SindBap" www.sindbap.de [3] ABAQUS Inc., 2004, ABAQUS Analysis User´s Manual, Version 6.5 [4] Schmidt, C., Marsolek, J., Fleischer, J., Schermann, T., 2005, Simulation von Zerspanungsprozessen mit ABAQUS, 15. Deutschsprachige ABAQUS-Benutzerkonferenz, Nürnberg [5] Treppmann, C., 2001, Fließverhalten metallischer Werkstoffe bei Hochgeschwindigkeitsbeanspruchung, PhDThesis, RWTH Aachen [6] Liu, C. R.; Guo, Y. B., 2000, Finite Element analysis of the effect of sequential cuts and tool-chip friction on residual stress in a machined layer, International Journal of Material Science 42, pp.1069-1086 [7] Shih, A. J., 1995, Finite element simulation of orthogonal metal cutting. Journal of Engineering for Industry 117, pp.84-93 [8] Yang, X.-P., Liu, C. R., 2002, A new stress-based model of friction behavior in machining and its significant impact on residual stresses computed by finite element method, International Journal of Mechanical Science 44, pp.703-723 [9] Piendl, S., Aurich, J.C., Steinicke, M., 2005, 3D Finite-Element Simulation of Chip Formation in Turning; 8th CIRP International Workshop on Modeling of Machining Operations, Chemnitz [10] Söhner J., 2003, Beitrag zur Simulation zerspanungstechnologischer Vorgänge mit Hilfe der Finiten Elementen Methode, PhD Thesis Universität Karlsruhe (TH) [11] Altintas, Y., Brecher, C., Weck, M., Witt, S., Annals of the CIRP, Key Note Paper of STC-M, 55/2, pp. 651-674, 2005.
