Modelling of Ultra-Precision Turning Processes in Consideration of Unbalances

In order to manufacture optical components or mechanical parts with high surface roughness requirements, diamond machining is used. To achieve the desired surface quality, the understanding of the surface generation process and its influencing parameters is important. Here, the crucial parameter is the residual unbalance of the main spindle. As the residual un-balance affects the process and vice versa, the investigation of the process-machine interaction is necessary. In this paper we present a model describing this interaction between dynamical unbalances that occur during the machining process and the engine-shaft structure at the example of an ultra-precision turning lathe. This model allows the determination of the achievable surface quality of a workpiece for a given balancing state. On the other hand we will present a mathematical method to solve the corresponding inverse problem of computing the necessary residual balancing state and balancing weights for a given desired or given measured surface quality.