Mixed-Dimensional Finite Element Modelling of Passive Thermal Error Compensation Systems in Machine Tools

Due to the high relevance of thermally induced errors in machine tools, numerous thermal error compensation methods are discussed in literature. While most of the approaches demand significant cooling, measurement or simulation effort, design-related strategies contribute to the reduction of thermal errors by convenient heat distribution within the machine tool. This is achieved by reducing the sensitivity of the machine structure to thermal loads as, for example, realized through thermal-symmetric design. By providing more design-related strategies, the compensation efforts during machine operation may be reduced. A currently investigated approach is the integration of passive thermal error compensation systems that inherently enhance the heat transfer and storage capabilities of the machine structure. As demonstrated in recent studies, latent heat storage systems can reduce temperature fluctuations close to machine-internal heat sources of high temporal variability. This approach is based on the high effective heat capacity of phase change materials during the phase transition. Another approach is to add heat pipe heat sink assemblies to passively increase the convective heat dissipation. Both phase change materials and heat pipes are characterized by nonlinear thermal properties that require a thorough understanding of the underlying heat transfer and storage mechanisms. At the same time, efficient modelling techniques are needed to provide convenient design tools that are compatible with common machine tool models. This work illustrates the application of mixed-dimensional finite element models to describe the effect of latent heat storage systems and heat pipe assemblies integrated into machine tool structures. It is demonstrated how thermal resistance networks composed of point and line elements can be implemented within three-dimensional finite element models to represent heat pipe assemblies. Furthermore, the use of volume-shell elements is proposed as an efficient way to model latent heat storage systems. Both approaches are evaluated using different numerical scenarios and validated by comparing the simulation results to experimental data. The results imply that the mixed-dimensional finite element modelling provides high accuracy at considerably lowered modelling and simulation effort compared to three-dimensional modelling. The proposed method hence allows for an increased efficiency during the design phase of the corresponding compensation components.