Simulation and compensation of thermal errors of machine tools

The following thesis deals with the simulation and compensation of thermal errors on machine tools using the finite element method (FEM). Whilst FEM has become increasingly important in analyzing the static behavior, its usage for thermal problems has so far been limited. This is because the thermal error on machine tools depends on a wide variety of effects, leading to a complexity that is hard to comprehend in its entirety. The first problem is that machine tools consist of a large variety of components that influence the thermal behavior and as such it is necessary to understand the physics of every component. A variety of models are created for these components. These models are founded on known parameters and render further measurements for parameter identification unnecessary. This is of utmost importance during the design phase, where no prototype exists that can be used for measuring. Still it is desirable to perform reliable simulations in order to determine the quality of the design. Common components are rolling bodies that are used in bearing, guideways and ball screws. Appropriate models are shown that consider the load and velocity of the rolling bodies in order to determine their friction loss and heat conductance. Feed drives and auxiliary components can also be found on every machine tool and hence models are derived that can be used to study their effect. Even if the physics for these components are known it still is a difficult task to implement these in a FEM software. Some tasks that are connected to this are the implementation of the equations for the models in the FEM software, the knowledge of the loads and velocities and how to consider the positioning of the axes. A simulation software, called Virtual Machine Prototype (VMP) was developed in order to remedy the aforementioned problems. It is specifically design to simulate machine tools and to assist designers in creating more accurate and better machine tools. VMP consists of a multibody dynamics and thermomechanical FE code. Multibody dynamics are included to derive the loads on the components based on the NC path. The thermomechanical FE code automatically updates the model of the machine tool according to its current state and position. The next step is to ensure that the simulation of the thermal problem can be performed in a matter of minutes. This is contrary to the common knowledge that the simulation of thermal problems can take many hours and even days. Whilst many researchers try to reduce the thermal system of equations, it will be shown that this is not necessary. By analyzing the physics behind thermal problems it is possible to write the problem in such a way that the solution takes little time. Together with a reduction of the mechanical system of equations it is even possible to use FEM for the compensation of thermal errors on a machine tool. VMP will be connected to the CNC of a machine tool in order to compensate the thermal error in the whole working