Andreas Rademacher

Simulation based optimization of the NC-shape grinding process with toroid grinding wheels

For achieving high material removal rates while grinding free formed surfaces, shape grinding with toroid grinding wheels is favored. The material removal is carried out line by line. The contact area between grinding wheel and workpiece is therefore complex and varying. Without detailed knowledge about the contact area, which is influenced by many factors, the shape grinding process can only be performed sub-optimally. To improve this flexible production process and in order to ensure a suitable process strategy a simulation-tool is being developed. The simulation comprises a geometric-kinematic process simulation and a finite elements simulation. This paper presents basic parts of the investigation, modelling and simulation of the NC-shape grinding process with toroid grinding wheels.

Adaptive Optimal Control of the Obstacle Problem

This article is concerned with the derivation of a posteriori error estimates for optimization problems subject to an obstacle problem. To circumvent the nondifferentiability inherent to this type of problem, we introduce a sequence of penalized but differentiable problems. We show differentiability of the central path and derive separate a posteriori dual weighted residual estimates for the errors due to penalization, discretization, and iterative solution of the discrete problems. The effectivity of the derived estimates and of the adaptive algorithm is demonstrated on two numerical examples.

Angepasste Simulationstechnik zur Analyse NC-gesteuerter Formschleifprozesse

Kurzfassung Simulationen können als Hilfsmittel zur Optimierung von Fertigungsprozessen eingesetzt werden. Bei der Fertigung frei geformter Werkstücke durch Schleifen, unter Einsatz von Torusschleifscheiben, sind genaue Kenntnisse über den kontinuierlich variierenden Eingriff der Schleifscheibe in das Werkstück unentbehrlich. Die folgenden Ausführungen beschreiben die Vorgehensweise bei der Simulation des NC-Formschleifprozesses auf Basis einer geometrisch-kinematischen Simulation und einer Finite-Elemente-Simulation, deren Genauigkeit durch den Einsatz adaptiver Finite-Elemente-Methoden gesteigert wird.

Simulation of grinding processes using finite element analysis and geometric simulation of individual grains

The wear-resistance of sheet metal forming tools can be increased by thermally sprayed coatings. However, without further treatment, the high roughness of the coatings leads to poor qualities of the deep drawn sheet surfaces. In order to increase the surface quality of deep drawing tools, grinding on machining centers is a suitable solution. Due to the varying engagement situations of the grinding tools on free-formed surfaces, the process forces vary as well, resulting in inaccuracies of the ground surface shape. The grinding process can be optimized by means of a simulative prediction of the occurring forces. In this paper, a geometric-kinematic simulation coupled with a finite element analysis is presented. Considering the influence of individual grains, an additional approximation to the resulting topography of the ground surface is possible. By using constructive solid geometry and dexel modeling techniques, multiple grains can be simulated with the geometric-kinematic approach simultaneously. The process forces are predicted with the finite element method based on an elasto-plastic material model. Single grain engagement experiments were conducted to validate the simulation results.

Dual Weighted Residual Error Control for Frictional Contact Problems

Abstract In this paper goal-oriented error control based on the dual weighted residual error method (DWR) is applied to frictional contact problems. The derivation of DWR error controls is done for arbitrary discretization schemes via the introduction of some discrete Lagrange multipliers describing the residual of the discretization. The discrete Lagrange multipliers may be provided by a reconstruction in a post-processing step or by a discretization of a mixed formulation in which they are directly available. The error controls are defined for user-defined functionals (the quantities of interest) which measure the error of the displacement field as well as the normal and tangential contact forces. Numerical experiments confirm the applicability of the estimates within adaptive schemes.

NCP Function--Based Dual Weighted Residual Error Estimators for Signorini's Problem

In this paper, we consider goal-oriented adaptive finite element methods for Signorinis problem. The basis is a mixed formulation, which is reformulated as nonlinear variational equality using a nonlinear complementarity function. For a general discretization, we derive error identities w.r.t. a possible nonlinear quantity of interest in the displacement as well as in the contact forces, which are included as Lagrange multiplier, using the dual weighted residual method. Afterwards, a numerical approximation of the error identities is introduced. We exemplify the results for a low order mixed discretization of Signorinis problem. The theorectical findings and the numerical approximation scheme are finally substantiated by some numerical examples.

Experimental and Simulative Investigations of Tribology in Sheet-Bulk Metal Forming

Friction has a considerable influence in metal forming both in economic and technical terms. This is especially true for sheet-bulk metal forming (SBMF). The contact pressure that occurs here can be low making Coulomb’s friction law advisable, but also very high so that Tresca’s friction law is preferable. By means of an elasto-plastic half-space model rough surfaces have been investigated, which are deformed in such contact states. The elasto-plastic half-space model has been verified and calibrated experimentally. The result is the development of a constitutive friction law, which can reproduce the frictional interactions for both low and high contact pressures. In addition, the law gives conclusion regarding plastic smoothening of rough surfaces. The law is implemented in the framework of the Finite-Element-Method. However, compared to usual friction relations the tribological interplay presented here comes with the disadvantage of rising numerical effort. In order to minimise this drawback, a model adaptive finite-element-simulation is performed additionally. In this approach, contact regions are identified, where a conventional friction law is applicable, where the newly developed constitutive friction law should be used, or where frictional effects are negligible. The corresponding goal-oriented indicators are derived based on the “dual-weighted-residual” (DWR) method taking into account both the model and the discretisation error. This leads to an efficient simulation that applies the necessary friction law in dependence of contact complexity.

Modelling, Simulation and Compensation of Thermomechanically Induced Deviations in Deep-Hole Drilling with Minimum Quantity Lubrication

This chapter summarises interdisciplinary research work on deep-hole drilling of aluminium casting using twist drills and minimum quantity lubrication (MQL). The high thermal conductivity of the workpiece material, the low cooling performance of MQL and the long main time of the process lead to a significant thermal load onto the workpiece. The thermal distortion of the machined component causes a systematic deflection of the long drilling tool and thus a high straightness deviation of the produced bore. Based on extensive technological investigations with a focus on the heat input into the workpiece a reliable simulation-based prediction of the thermomechanical distortion and the resulting bore deviations is presented. Thereby a finite element (FE)-model of the workpiece was coupled with a simple analytic representation of the deep-hole drilling tool. Using the fictitious domain method, adaptive techniques, and massive parallelisation, the FE-simulation is most efficiently realised. In order to compensate the occurring deviations, a novel approach based on radial tool path adjustment was developed, which allows for the drilling direction to be controlled during the process. The sophisticated simulations enable the determination of the optimal NC-path for the deep-hole drilling tool, which is not possible based on experiments. The validation results show a great potential of the developed methods for the simulation-based minimisation of the thermomechanically induced straightness deviation in deep-hole drilling.

Adaptive optimal control of Signorini’s problem

In this article, we present a-posteriori error estimations in context of optimal control of contact problems; in particular of Signorini’s problem. Due to the contact side-condition, the solution operator of the underlying variational inequality is not differentiable, yet we want to apply Newton’s method. Therefore, the non-smooth problem is regularized by penalization and afterwards discretized by finite elements. We derive optimality systems for the regularized formulation in the continuous as well as in the discrete case. This is done explicitly for Signorini’s contact problem, which covers linear elasticity and linearized surface contact conditions. The latter creates the need for treating trace-operations carefully, especially in contrast to obstacle contact conditions, which exert in the domain. Based on the dual weighted residual method and these optimality systems, we deduce error representations for the regularization, discretization and numerical errors. Those representations are further developed into error estimators. The resulting error estimator for regularization error is defined only in the contact area. Therefore its computational cost is especially low for Signorini’s contact problem. Finally, we utilize the estimators in an adaptive refinement strategy balancing regularization and discretization errors. Numerical results substantiate the theoretical findings. We present different examples concerning Signorini’s problem in two and three dimensions.

Dual weighted residual error estimation for the finite cell method

The paper presents a goal-oriented error control based on the dual weighted residual method (DWR) for the finite cell method (FCM), which is characterized by an enclosing domain covering the domain of the problem. The error identity derived by the DWR method allows for a combined treatment of the discretization and quadrature error introduced by the FCM. We present an adaptive strategy with the aim to balance these two error contributions. Its performance is demonstrated for some two-dimensional examples.