Compensation of Thermal Effects on Machine Tools using a FDEM Simulation Approach

The operating accuracy of metal cutting machine tools is finally based on the accuracy of the relative movement between the work-piece and tool. If this relative movement is, because of any disturbance, inaccurate, an error is directly reproduced on the work-pieces [1]. A lot of experimental work was done to quantify thermal induced errors based on work-pieces. The results are reported in literature and it can be seen that thermal effect in machining can contribute to up to 70% of the overall geometrical inaccuracies of work-pieces [2]. The Finite Difference Element Method (FDEM) is a very effective simulation approach which was especially developed to calculate the transient thermal behaviour of mechanical systems such as machine tools. The FDEM combines the advantages of Finite Difference Method (FDM) and Finite Element Method (FEM). The transient temperature distribution is calculated very efficiently using the FDM. The FDEM uses FEM to obtain thermally induced deformations [3] from a given temperature field. With the advantage, that for a compensation model of a machine tool only the displacements at the TCP (tool centre point) relative to the work-piece coordinate system are important, the linear system of equations of the FEM can be reduced to remaining six nodes to calculate the relative TCP-displacement in the relevant five degrees of freedom. Such a small system of linear equations allows the FDEM to be used for calculation of thermal compensation values in real time. A compensation model of a small three-axis milling machine is given as example, which shows the use of the FDEM for compensating thermally induced TCP-displacements caused by a moving linear axis. It is able to compute the temperature distribution and TCP-displacements in real time. The example compares the calculated TCP-displacements with measurements, thus verifying the quality of the compensation method before the model is installed on the machine tools numerical control.

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