Parameter Identification for Finite Element Based Models in Dry Machining Applications

Abstract

Dry machining is a challenging topic in industrial manufacturing: The absence of coolants results in ecological and economical benefits, but also in a significant increase of the occurring thermal stress. This leads to geometrical deviations of the machined workpiece impairing the functional performance of the final part. The increased thermal stress is especially important in high-precision manufacturing and requires careful process planning. To determine process parameters in order to minimize geometrical errors, optimal control is an appropriate tool. A precise partial differential equation model representing the material behavior is required. The partial differential equation contains unknown physical quantities, such as heat fluxes, which cannot be measured directly. One common method to derive these quantities is solving an inverse problem by parameter identification, i.e. determining the model parameters, such that the model matches the measurements best. We will present a simultaneous analysis and design approach which states a numerical finite element discretization of the model as constraints of the resulting nonlinear optimization problem (NLP). The proposed method takes advantage of both, direct consideration of state constraints, like temperature boundaries, and lower computational costs compared to the nested analysis and design approach. The additional implementation costs can be significantly reduced by using an external finite element library for assembling the optimization constraints and its derivatives. This approach for determining physical parameters of milling experiments is user-independent and works fully automated. It is the first step for an optimal control of dry machining processes. We will give a description of this method as well as numerical identification results of real heat flux densities by the sparse NLP solver WORHP.