Optimal design of fixture layouts for compliant sheet metal assemblies
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ORIGINAL ARTICLE
Optimal design of fixture layouts for compliant sheet metal assemblies Abolfazl Rezaei Aderiani1
1 · Rikard Soderberg 1 · Lars Lindkvist1 · Bjorn ¨ ¨ ¨ Lindau2 · Kristina Warmefjord
Received: 21 February 2020 / Accepted: 17 August 2020 / Published online: 5 September 2020 © The Author(s) 2020
Abstract A preeminent factor in the geometrical quality of a compliant sheet metal assembly is the fixture layout that is utilized to perform the assembly procedure. Despite the presence of a great number of studies about the optimization of assembly fixture layouts, there is not a comprehensive algorithm to optimize all design parameters of fixture layouts for compliant sheet metal assemblies. These parameters are the location and type of hole and slot in each part, the slot orientation, and the number and location of additional clamps. This paper presents a novel optimization method that optimizes all these parameters simultaneously to maximize the geometrical quality of the assemblies. To attain this goal, compliant variation simulations of the assemblies are utilized along with evolutionary optimization algorithms. The assembly springback and contacts between parts are considered in the simulations. After determining the optimal design parameters, the optimal positions of locators are fine-tuned in another stage of optimization. Besides, a top-down design procedure is proposed for applying this method to multi-station compliant assemblies. The presented method is applied to two industrial sample cases from the automotive industry. The results evidence a significant improvement of geometrical quality by utilizing the determined fixture layout from the presented method compared with the original fixture layouts of the sample cases. Keywords Fixture layout optimization · Sheet metal assembly · Compliant variation simulations Abbreviations and nomenclature BIW Body in white KPC Key product characteristic SSM State-space modeling MIC Method of influence coefficients FEM Finite element method GA Genetic algorithm RMS Root mean square P The number of parts in the assembly The number of areas in part p Qp The number of feasible areas for hole/slot in part Hp p αqp Indicator of being clamped or not in area q of part p β1p The area number of the hole location in part p
β2p θq N d
Abolfazl Rezaei Aderiani
1 Introduction
[email protected] 1
Department of Industrial and Materials Science, Chalmers University of Technology, Gothenburg, Sweden
2
Volvo Cars, Gothenburg, Sweden
d Q Fb Fa Da Db Ka Kb S W
The area number of the slot location in part p The in-plane locking direction of a slot Normal vector Vector of in-plane locking direction of a slot in slot’s local coordinate system Vector of in-plane locking direction of a slot in the global coordinate system Transformation matrix Clamping forces before welding Clamping forces after welding Deviations after releasing the clamps Deviations before clamping Stiffness matrix of assembly after welding Stiffness matrix of the assembly before welding Sensitivity
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