# The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM

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2 The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM tools. The approach to this simulation is different for static, dynamic or thermal simulations. In the second stage the in-process behavior of a machine tool is simulated. A simulation in this stage can, for example, combine the process forces or the control loops with the mechanical behavior of a machine tool simulated in the first stage. Due to the increased complexity of a more detailed modeling approach, a better approximation to reality is not automatically achieved. This presentation will highlight several problems in the simulation of machine tools. 2

3 To calculate the static behavior of a machine tool, the stiffness matrix of the model needs to be set. The stiffness values of the connector elements in the machine tool like bearings and guides need to be defined, but these values are often not available or their calculation is not trivial. The stiffness of spindle bearings for example depends on several boundary conditions like preloads, turning speed and temperature. Furthermore the stiffness matrix of structural parts depends on the material coefficients like the E-module and the poison ratio. Especially the E-Module of cast varies widely. On account of these problems a lot of experience is required to define FEM meshes for complex structural parts. With the knowledge of the external forces that act on the structure one can simulate the static deformation and the stress. All dynamic problems cannot be calculated. 3

4 For the calculation of the dynamic behavior of a machine tool there is more information required than for a static simulation. The calculation of the undamped Eigen frequencies and the respective mode shapes gives a first impression of the dynamic behaviour of a machine tool. Apart from the stiffness matrix, as used in the static analysis, the mass allocation of the machine tool is needed to perform a modal analysis. The definition of the mass allocation of a structure is straight forward. On the one hand the material density can be measured or calculated easier than stiffness values, on the other hand the mass allocation is not as sensitive in regard to the mesh quality as the stiffness matrix as long as the geometry of the structure is correct. Consequently, incorrect calculation results are mostly caused by modelling faults in the stiffness matrix. Especially for complex mode shapes the calculation reacts more sensitive to an incorrect stiffness matrix than in a static analysis. Modal analyses give a first impression of the dynamic behavior of a machine tool through the calculation of its mode shapes and the corresponding Eigen frequencies. Modal analysis gives no information about the amplitude of the oscillation. Therefor it is not possible to calculate a frequency response function. 4

5 To build up a simulation model that can calculate most of the important dynamic effects, the damping matrix needs to be defined. With that information frequency response functions and the amplitude of an oscillation can be calculated. Damping is the dissipation of kinetic energy into other forms of energy. Up to now the physical relationships of damping effects are not fully understood. There is a lack of verified damping coefficients and suitable damping models to set up the damping matrix. The simulation of the dynamic behavior requires as of now a lot of experience and the results need to be treated very carefully. 5

6 To calculate the stationary temperature of machines in a thermally steady state two steps are required. The first step is the calculation of the temperature distribution for the whole part due to the heat flux. The knowledge of the temperatures of each node leads to a determination of the equivalent thermal forces which are used for the calculation of the static deformation in the second step. The temperature distribution results from the equilibrium of the incoming and the outgoing heat flux, i.e. the heat conduction in the part, the convection and the radiation to the environment. Once the model has been generated, the thermal loads in form of heat sources and heat sinks, the boundary conditions in form of prescribed temperatures at selected points and the heat transfer coefficients at the surfaces must be specified in order to calculate the thermal behaviour. The matrix [K 0 ] is the convection matrix and matrix [L] is the thermal conduction matrix. The vector {Q} describes the heat sources which affect the part. The quantity required in this equation is the temperature {T}. With the calculated temperatures at the element-nodes, the calculation of deformations can be performed. The calculation of thermoelastic deformations is transferred to a calculation of static de-formations. Therefore, equivalent forces are formulated which are based on the elongation of elements due to temperature changes. The equivalent thermal force is defined as a force which is applied to the element node and causes the same deformations as the temperature change. This definition is shown in the slide for a simple rod. 6

7 A typical example of an analysis of a thermal non-steady-state is shown in the illustration. Aim of the analysis was the determination of the thermal deformation of the spindle carrier of a lathe. The spindle carrier is heated by internal losses of the spindle drive, by friction losses in the bearings and losses due to the splashing of the lubricant (oil) in the gear. It is in direct contact with the atmosphere, so there is convection on all free surfaces with different values for the convection coefficients. The spindle carrier is mounted on the lathe, which can be abstracted as an infinite heat sink, thus the temperature at the joining nodes of the FE-mesh has been set to the environment temperature (21 C). The resulting temperature field is shown in the lower left-hand corner of the illustration as an isoline plot. From these temperature results, an equivalent thermal force field has been computed and applied to the FE-model. The result is shown in the lower right-hand corner. It can be seen that the maximum deformation is about 60 µm, which is far too much for a lathe capable of producing even medium-precision parts. As a solution for this problem, a cooling system could be installed to keep the temperature of the spindle carrier within a smaller range, thus minimising the thermal deformation. 7

8 To determinate the interaction of the machines control and its structural behavior there are different ways to combine the two models. One can either substitute one model in that way that it can be integrated into the other model, or one can do a co-simulation, where both simulations are running parallel and interact which each other. Whenever a FEM Simulation is used the kinematic systems need to be substituted into elastic elements like springs. This means that effects which are caused by the system s kinematic (direct measurement vs. indirect measurement of ball screw drives) cannot be calculated. Furthermore large displacements between the structural components cannot be taken into account. Through the use of the flexible multi body simulation these kinematic effects can be simulated. To simulate both the larger displacements and the displacement of the structure elements, a moving flexible multi body simulation model is necessary.

9 Analyzing the machine tool and the machining process individually is necessary in order to tackle the challenges that both have to offer. Nevertheless, to fully understand the manufacturing system, e.g. vibrations, deflections or thermal deformations, the interactions between the manufacturing process and the machine tool also have to be analyzed. In forming, turning and milling there are important effects that can only be explained through these interactions. To increase the productivity of a machine tool it is necessary to consider the dynamic behavior of the machine tool and the dynamic behavior of the machining process. Therefore theses process-machine-interactions have to be considered in a specialized simulation model. The results of such a simulation model are stability charts, which represent the maximum stable cutting depths. A higher limit of the stability curve results in a higher productivity. The process models have to be specialized on different process force dynamics. All in all for the design of a chatter free machine tool it is necessary to consider the process-machine-interactions and the resulting process stability in the design stage. 9

10 Problems and uncertainties in the simulation of the process-machineinteraction are given both in the FE-model and in the process model. On the side of the FE-model of a virtual machine tool the most important uncertainties are the missing damping parameters for the machine elements and the behavior of the control loops. On the side of the process model uncertainties are given in the cutting force model, the cutting force coefficients and in modeling the process kinematic. For detailed simulation results the precise tool geometry has to be known. 10

11 Spindle bearing systems are one of the most important machine components in machine tools. The basic FE-simulation of spindle bearing systems only contains the dynamic behavior of the structural components like spindle, bearings and additional masses. To enhance the simulation quality it is necessary to consider the speed and load dependent behavior of the bearing system. Therefore an integrated simulation system has been build up to join both simulation systems. 11

12 For the complete simulation of spindle bearing systems the spindle speed dependent behavior and the process behavior has to be considered. Therefore a model for the co-simulation of the dynamic behavior of the spindle bearing system and the milling process has to be build up and analyzed. 12

13 Due to the demand of a higher machine productivity, the machine tools are used with higher process parameters like spindle speed and feed rate. This leads also to an increase of the process forces and an increase of the load on the machine parts. Therefore the simulation of material contacts and the influence of work piece tolerances becomes more and more important. As an example the tool interfaces can be given. This machine part underlays the process forces, clamping forces and spindle speed. 13

14 The current research fields in the simulation of tool interfaces are the simulation of the static behavior, the optimization for high rotational speed and the revolver integration. The research goal is to develop an integrated simulation system for tool interfaces. 14

15 To shorten the set-up time of machine-tools, the software is tested on virtual machines. This is achieved through a coupled system of the controller simulation and the mechanical system. The long term aim is the development of controller software directly on virtual machines. 15

16 The handling of multi-physic FE-models of machine tools becomes more and more complex and expensive. The calculation of in-house FEM calculation of machine tools has to be done by technology leaders. In contrast to this small and midrange companies should outsource their FEM calculation of machine tools. 16

17 Due to the already existing possibilities for simulating machine tools an increasing demand for simulation input data is created. The accuracy of input data thereby decisively influences the reliability of forecasts, the benefits and therefore the reasonable cost of simulation projects. The effort to build up und use simulation models becomes uneconomic especially for small and medium-sized companies. On the other hand simulation results and protocols are requested in addition to the actual part from, for example, suppliers in the automotive industry as a proof of the completeness and correctness. Parallel to the trade in products a medium-term market for simulation services will come into existence. In the future the real product has to be delivered together with a virtual product. This new market offers the opportunity for additional unique characteristics of each market player. In addition, new opportunities arise through virtual products and the comparison of prices will be done much faster and objectively. 17

18 The increased complexity and velocity of the design process of machine systems, like machine tools or construction machines, generate on the one hand the demand for a integrated CAx software systems and on the other hand the need for a 1-for-all model. Future CAx software systems have to join both needs in one software system. 18

19 There are two ways of enhancing the FE-software with new features. New subsystems might get coupled to or integrated in the FE-software. 19

20 Manufacturing companies in high-wage countries are subject to an increasing and world-wide competition to use their production facilities very effectively and efficiently in order to compensate wage disadvantages. The choice of manufacturing strategy gets influenced by the contradiction between the number of units (economies-of-scale) and customer-specific products (economies-ofscope) affect. Many decisions in production technology are now made on the basis of long round-won experience. Both in the machining and manufacturing technology more and more simulation tools are used to optimize the efficiency of manufacturing processes at even shorter product cycles. Nowadays there are already a large number of simulation tools with varying precision available for individual aspects of the production technology. The main problem therefore lies in providing the right level of abstraction for each sub-problem and the integration of different models in a common virtual production system, so that the interactions can be simulated and analyzed in the right way. In the metal cutting process occurs, for example through the cutting process thermal and dynamic interactions between the machine tool, tool and work piece, which can be arbitrarily complex. Depending on the application, the virtual production system has to be expanded, so that all relevant special effects, such as regenerative chatter, can be modeled. When expanding a simulation model by more complex simulation models, such as the finite element simulation of the machining process, other aspects arise very quickly for this complex virtual system, which lead to unacceptable calculation times. 20

21 21

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