Abstract

Geometric variation is an inevitable element of any fabrication process. To secure the geometric quality of the assembled products, variation simulation is performed, approximating the statistical moments of the geometric variation, thereby controlling compliance with the set geometric requirements. Contact modeling involves describing the behavior of contacting bodies. In non-rigid variation simulation, contact modeling is used to avoid the virtual penetration of the components in the adjacent areas, enhancing the simulation accuracy. Variation simulation and contact modeling is based on the Method of Influence coefficients (MIC). Compared to the traditional MIC, the contact model imposes non-linear behavior on the deformation calculation. In this approach, the MIC matrix is utilized as the reduced stiffness matrix in the contact model. For frictionless contact models, numerical errors and convergence issues due to the deformation behavior of the interacting surfaces are still limiting the computational efficiency of solving this optimization problem. The optimization problem associated with a contact model is often large-scale, and in practice, fast and robust methods for achieving convergence are required. Previous implementations of contact modeling for non-rigid variation simulation have been prominently based on the Iterative or Penalty Methods, and Lagrangian Multipliers Method through Interior Point Solvers. In this paper, a quadratic programming approach has been introduced based on the Lagrangian multiplier method for robust contact modeling in non-rigid variation simulation, and the performance of the proposed approach has been compared to the previously applied Iterative and Interior Point Method. The methods have been compared on three industrial reference cases, and the convergence, and time-efficiency of each method are compared. The reference models have been chosen from different problem sizes, small, medium, and large-scale. The results show that robust optimization of the quadratic program associated with the contact model is highly dependent on the assemblies’ condition, composed of the reduced stiffness matrix condition. Furthermore, it has been shown that robust and efficient contact modeling in non-rigid variation simulation is achievable through the proposed quadratic programming method. Improvement in the convergence is achieved while maintaining the accuracy level to the predefined tolerance intervals.

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