2020

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Browsing 2020 by Author "Adeel Qadir"

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    Fixture layout and clamping force optimization for sheet metals
    (UMT, Lahore, 2020) Adeel Qadir
    Elastic deformation produced during machining effects the dimensional and form errors of workpiece. For precision, accuracy, fine surface finish and minimized workpiece elastic deformation; the parameters like number and position of fixture elements and clamping forces are optimized. The work on rigid bodies is well established but the work on sheet metals is still under process by various researchers due to flexible nature of the sheet metals. The objective of this research work is to optimize the number and position of the clamps and also to optimize clamping forces to keep the maximum deformation of individual nodes up to 2 mm by minimizing the total deformation normal to the plane of workpiece. N-3-2-1 fixturing principle is used to place clamps on sheet metals. The value of N≥1. Fixturing principle provides constraints on 6 Degree of freedom of workpiece and stability to workpiece which increases the machining and assembly accuracy of workpiece. In this research, design elements are the clamps of primary plane whereas locators in secondary and tertiary planes are kept non design elements. To maximize the machining area, clamps are placed only at edges of workpiece. Selection of clamps depends totally on experience of designer. Automatic selection of number and position of clamps is new. In this research, a method is proposed to select number and position of clamps for sheet metals automatically. This work consists of two stages; stage 1 and stage 2. In stage 1; optimized number and position of clamps are calculated by Response Surface Methodology (RSM). It is done by considering initial number and position of clamps from already published work. In stage 2, clamping forces are calculated for optimum layouts obtained by RSM. Stage 1 involves a structural optimization technique; Response Surface Methodology. In RSM, a relationship between set design variables; number and position of clamps and an optimal response; deformation gives an approximation model using Minitab. The second order mathematical model is developed for workpiece elastic deformation. As the predictive model is being developed by response surface methodology, a huge reduction in computational complexity and time is achieved during the optimization of number and position of clamps. The necessary data for building the response models are generally collected by the design of experiments. In this work, the collection of experimental data adopts a standard RSM design, central composite design (CCD) and the approximation of response is proposed using the fitted second-order polynomial regression model known as quadratic model. Maximum deformation for each optimized layout was kept up to 2 mm. In 2nd stage, Clamping forces are calculated for optimum layouts obtained in stage 1. To calculate the minimum clamping forces to hold the workpiece, friction forces are considered due to clamps. A method; Balancing force moment is used for calculations of clamping forces. It states; Equilibrium occurs when the sum of all forces in the x, y and z direction is zero and the sum of moments at any point is zero. Coulomb static friction law is used to verify the calculated clamping forces required to hold the workpiece. The forces in each direction are multiplied by the static friction coefficient value. It gives the friction force values due to the clamps. For equilibrium condition, the amount of friction force should be greater than or equal to the machining force in that direction. Clamping forces are calculated for optimum layouts while keeping maximum deformation up to 2 mm. Two case studies are used; flat plate and spacer grid. Different loads at different positions are applied to check the effectiveness of proposed methods. After determining the geometric center, workpiece geometry is divided in to 4 hypothetical quadrants. Quadrants with minimal deformation are considered as non-design quadrants. Quadrants with maximum deformations are considered as design quadrants. Clamps are mounted in two different ways with in the proposed method. When clamps are mounted on long edge of workpiece, the condition is called 1 design edge. When clamps are mounted on both short and long edges of the workpiece, it is called 2 design edges. Both case studies are divided into subcases. For case study 1; subcase 1, subcase 2, subcase 3, subcase 4, subcase 5, subcase 6, subcase 7 and subcase 8 are considered. For all subcases, optimized number of clamps is 4, but for subcase 1; optimized number of clamps is 5 in number. For case study 2; subcase 9, subcase 10, subcase 11 and subcase 12 are used. For all subcases optimized number of clamps is 4. Experimental setup is also designed to check the effectiveness of proposed methods. Simulation results obtained for case study 1 only are verified. The final experimental results fully justify the computational results. Maximum deformation for all subcases is less than 10%. Several factors like analogue dial indicator, human errors are the reason of difference in values.