Optimization of number and position of the clamps in sheet metals fixture
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Date
2018
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UMT Lahore
Abstract
The accuracy of manufacturing process is highly dependent on how well a workpiece is constrained in the fixture. A well constrained workpiece show minimum deformation during manufacturing process or application of load and workpiece will have high stiffness. Workpiece can be constrained by proper positioning of fixture elements. Most of research in fixture layout optimization is done on rigid bodies and some work has been done on sheet metals to find the optimum position of the fixture elements. But, the selection of number of clamps entirely depends on the expertise and knowledge of designer. Therefore, the research work to select automatically the initial numbers of clamps and their positions is fairly new. In this research; a methodology is devised to select the number of clamps automatically and then finding the optimum position of clamps even if the designer lacks in expertise to do so. The objective function of this research is to minimize total deformation normal to the plane of workpiece while keeping maximum deformation of individual nodes upto 2 mm. The proposed method consists of two stages; in first stage, the initial number of clamps is calculated. In second stage, initial number of clamps and their positions are optimized using genetic algorithm. The first stage involves two different methodologies namely maximum deformation method and means method. The edges of the workpiece are design edges because clamps are placed on the edges only. In maximum deformation method workpiece is divided into four quadrants and the node with maximum deformation in each quadrant is selected. Clamps are added at the edge near to the maximum deformation nodes in each quadrant and adding clamps on the edge near to maximum deformation nodes is continued until deformation becomes lower than 2 mm. In means method, procedure is the same as in maximum deformation method, but average deformation is measured in each quadrant instead of maximum deformation. Then a node is selected from each quadrant whose value is closer to the value of average deformation of respective quadrant. Then clamps are placed on the edge near to the average deformation values nodes till the value of maximum deformation becomes less than 2 mm. In second stage only one method is devised. In second stage, genetic algorithm is implemented on layouts. Genetic algorithm is used to optimize number and position of clamps therefore first genetic algorithm is used to optimize the number of clamps then it is used to optimize the position of clamps. Number and position of clamps are not optimized simultaneously because the computational load is significant. When the number of clamps are optimized only population is generated and processes like crossover and mutation are not implemented because of significant number of clamps. More clamps produce lengthy chromosomes which are cumbersome to handle and when crossover Is performed the resulting computations takes significant time to complete when number of candidates in population are also significant. Once the clamps are reduced to minimal numbers then second population is generated and crossover, mutation are implemented to diversify population for optimizing the position of remaining clamps. Different kinds of case studies are solved with the proposed methods in different scenarios to check the effectiveness of the proposed method. An experiment is also performed in which the proposed method is implemented on case study 1. This was done to compare the computational results with experimental results and verify the effectiveness of the methodology. The final results of the experiment fully justify the proposed method.