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2839 |
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Calculating Thermal Location and Component Errors on Machine Tools |
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Design of Precision Machines and Instruments |
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| Content |
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Introduction
The thermo-elastic deformations of machine tools caused by internal and external heat sources can contribute more than 50% to the overall geometrical inaccuracies of the work-piece [1]. Therefore thermal simulation and methods to compensate thermal errors on machine tools moved increasingly into the foreground of newer research activities. The given example illustrates the calculation of the “thermal location” and “thermal component errors” of a machine tool. These values modern machine tool controls can use to compensate thermal errors throughout the work space.
The effective simulation approach FDEM [2], is able to calculate the compensation values with the introduced method in real time.
Example
The example illustrates the proposed procedure for a three axis milling machine. The procedure includes:
• Building several local models representing the thermal 3D-behavior at chosen positions in the work space
• Reducing the linear system of equations using an alternative approach
• Calculating thermally induced TCP(tool centre point)-displacements at chosen positions
• Calculating “thermal location and component errors”
Bringmann [3] developed a method to identify all location and component errors for a machine tool using a “3D ball plate”. A modified form of this method is used to calculate the “thermal location and component errors” based on the calculated local TCP-displacements.
Because only the TCP-displacements are required for compensating machine tools, the simulation models are reduced to a few degrees of freedom only.
Compensation values have to be calculated often during operating a machine tool. Therefore it is not convenient to use approaches like substructure technique or elastic foundation, known from the finite element analysis. As only a few degrees of freedom are required here, an efficient alternative procedure for the reduction of reducing linear systems of equations helps to get easily a new effective solvable system of equations.
Considering the cinematic of the machine tool it is furthermore possible to calculate the thermally induced TCP-displacements in a “3D space lattice” with a further reduced number of models.
In the paper, the entire compensation approach is described and illustrated using an example. The system of equation reduction procedure is presented and discussed in detail.
References
[1] M.Weck, P.McKeown, R.Bonse, U.Herbst, Reduction and Compensation of Thermal Errors in Machine Tools, Annals of the CIRP, 44/2: 589-598, 1995,
[2] J.Mayr, S.Weikert, K.Wegener, Comparing the thermo-mechanical-behaviour of machine tool frame designs using a FDM-FEA simulation approach, Proc. ASPE Ann. Meeting, 17-20, 2007
[3] B.Bringmann, Improving Geometric Calibration Methods for Multi-Axis Machining Centers by Examining Error Interdependencies Effects, PhD-Thesis ETH, VDI Verlag, Düsseldorf, 2007 |
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