Geometrical variation and deviation in all manufacturing processes affect quality of the final product. Therefore geometry assurance is an important tool in the design phase of a new product. In the automotive and aviation industries where the use of composite parts is increasing drastically, new tools within variation simulations are needed.
Composite parts tend to deviate more from nominal specification compared to metal parts. Methods to simulate the manufacturing process of composites have been developed before. In this paper we present how to combine the process variation simulation of composites with traditional variation simulations.
The proposed method is demonstrated on a real complex subassembly, representing part of an aircraft wing-box. Since traditional variation simulation methods are not able to capture the spring-in and the special deviation behavior of composites, the proposed method adds a new feature and reliability to the geometry assurance process of composite assemblies.
We consider a stochastic mathematical program with equilibrium constraints (SMPEC), and show that under certain assumptions, global optima and stationary solutions are robust with respect to changes in the underlying probability distribution. In particular, the discretization scheme Sample Average Approximation, which is convergent for both global optima and stationary solutions, can be combined with the robustness result to motivate the use of SMPECs in practice.We also consider SMPECs with multiple objectives, and establish robustness of weakly Pareto optimal and stationary solutions.Two applications are presented, both principally and numerically, in order to exemplify the use of SMPECs: a classic traffic network design problem where travel costs are uncertain, and the optimization of a treatment plan in intensity modulated radiation therapy, where radiobiological parameters are uncertain.
Every series of manufactured products has geometric variation. Variation can lead to products that are difficult to assemble or products not fulfilling functional or aesthetic requirements. In this paper, we will consider the effects of welding in variation simulation. Earlier work that has been combining variation simulation with welding simulation has either applied distortion based on nominal welding conditions onto the variation simulation result, hence loosing combination effects, or has used transient thermo-elasto-plastic simulation, which can be very time consuming since the number of runs required for statistical accuracy can be high. Here, we will present a new method to include the effects of welding in variation simulation. It is based on a technique that uses a thermo-elastic model, which previously has been shown to give distortion prediction within reasonable accuracy. This technique is suited for variation simulations due to the relative short computation times compared to conventional transient thermo-elasto-plastic simulations of welding phenomena. In a case study, it is shown that the presented method is able to give good predictions of both welding distortion and variation of welding distortions compared to transient thermo-elasto-plastic simulations.
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