PDE-restringierte Optimierung in Anwendungen der spanenden Trockenbearbeitung

Abstract

Nowadays industrial manufacturing is highly widespread while the demand of high-precision manufacturing is increasing constantly. In such processes, it is common to apply coolants to reduce the thermal stress of workpieces and tools as well as to guarantee the functional performance of the final parts. Nonetheless, there are several reasons like cost reduction and ecological benefits for omitting coolants or to use minimum quantity lubrication (MQL). In order to satisfy the quality standards in dry machining, compensation strategies of shape deviations are necessary. Due to the increasing digitalization of process chains (Industry 4.0), modern sensors and the usage of high-performance computing, nonlinear optimization is more convenient than ever before. In this context, a prediction model is required by which the machining can be optimized. In this work a hybrid approach is used to model thermo-elastic effects as well as geometrical deviations caused by a change of the residual stress state. Physical correlations of the modeling which are not investigated yet can be synthesized by empirical regression with a wide variety of data. The first part of this elaboration is the determination of heat fluxes in milling and drilling which cana t be measured directly. One goal is to utilize nonlinear optimization to solve parameter identification problems. The second part is the minimization of shape deviations in dry milling processes by means of the hybrid model. To achieve this, different milling strategies are compared and machining parameters are optimized with nonlinear optimization techniques, while an efficient machining process is sought at the same time. The mathematical majority of this work covers the PDE-constrained optimization. Still a challenging topic in this field is the treatment of complex problems involving high computational costs. It is still advisable to increase the efficiency of the optimization methods whereby the accuracy of the underlying model can be improved. One promising approach is the Simultaneous Analysis and Design (SAND) where a discretized PDE act as constraints of the optimization. This approach gives importance to exploiting the system structure of the optimization problem. Another common method is the Nested Analysis and Design (NAND). Theoretical considerations suggest that the SAND approach favored in this work has computational benefits for treating nonlinear PDEs. Beside the successful application of the SAND approach in dry machining one goal is to provide evidence of its computational efficiency.