**Clustering by optimal subsets to describe environment interdependencies**

J. Glänzel (a), R. Unger (b), S. Ihlenfeldt (a,c)

(a) Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz

(b) TU Chemnitz, Fakulty of Mathematics

(c) Institute of Machine Tools and Control Engineering, TU Dresden

*The paper copes with the problem of finding an optimal subset of interpolation points out of a given large set of computed values, arising from a finite element simulation. This simulation computes environment data, which are on their part input data for finite element simulations of machine tools.*

*For machine tool manufacturers it is still a seriously problem that the machine works imprecisely and produces scrap if environmental values like temperature changes. The change of the environment boundary conditions contribute to the phenomenon through sunlight or cold draught owing to open doors of the machine hall or factory. Resulting thermo-elastic effects on the tool *center* point are one of the major reasons for positioning errors in machine tools.*

*A genetic search algorithm for clustering relevant heat transfer coefficient values over the geometric surface through computational fluid dynamics (CFD) simulations will be described. These values are the input data for a developed thermo-elastic correction algorithm.*

**Using meta models for enclosures in machine tools**

F. Pavliček (a), D. P. Pamies (a), J. Mayr (b), S. Züst (a) , P. Blaser(a), P. Hernandez Becerro (b), K. Wegener (a,b)

(a) Institute of Machine Tools and Manufacturing, ETH Zurich

(b) Inspire AG, Zurich

*One of the crucial input parameters in *thermo-mechanical* simulation of machine tools is the surface heat transfer coefficient (h). The *h is* influenced among others by the nearby environment. The machine housing insulates the surface of the machine tool from the room environment. To precisely determine the h, the enclosure has to be taken into account. This paper presents how the enclosure can be considered in the thermo-mechanical simulation of machine tools by *meta models* facilitating an efficient calculation of the h in enclosures. The *meta models* are integrated *in* finite element simulations describing the boundary condition.*

**Model order reduction of thermal models of machine tools with varying boundary conditions**

P. Hernández-Becerro (a), J. Mayr (a), P. Blaser (b), F. Pavliček (b), K. Wegener (b)

(a) Inspire AG, Zurich

(b) Institute of Machine Tools and Manufacturing, ETH Zurich

*The numerical models describing the thermal *behavior* of machine tools lead to large systems of equations, which are computationally expensive. Efficient models by means of Model Order Reduction (MOR) aim at reducing the dimension of the system, enabling their use in applications requiring multiple evaluations, such as design optimization and compensation. The main contribution of this work is an efficient traceability of variable parameters defining the *behavior* of the system in the reduced models. This enables the model to represent sudden variations of boundary conditions, such as the application of a cooling fluid to the structure of the machine.*

**Effectiveness of modelling the thermal behaviour of the ball screw unit with moving heat sources taken into account**

J. Jedrzejewski, Z. Kowal, W. Kwasny, Z. Winiarski

Wroclaw University of Science and Technology

*This paper deals with the precise modelling of the thermal behaviour of the ball screw unit in the machine tool feed drive. The problem is discussed *for* the lathe centre. The serious consequences of thermal errors arising in the ball screw unit for the precision of positioning the lathe assemblies in controllable axes Z and X are highlighted. The factors, especially the ball screw preload and moving heat sources, having a bearing on the thermal errors are described. Using an FE model, integrating thermal and force deformations, the significant effect of moving heat sources is demonstrated and the thermal positioning error characteristic *along* the ball screw is determined.*