Fixtures are the work-holding devices, widely used in manufacturing, to completely immobilize the workpiece during machining. The position of fixture elements around the workpiece strongly influences the workpiece deformation which in-turn affects the machining accuracy. The workpiece deformation can be minimized by finding the appropriate position for the locators and clamps. Thus, it is necessary to model the complex behavioral relationship that exists in the fixtureworkpiece system. In this research paper, response surface methodology is used to model the relationship between position of locators and clamps and maximum deformation of the workpiece during end-milling, and then the developed model has been optimized by genetic algorithm and particle swarm optimization. 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 machining fixture layout. Also, it is evident that the approach which integrates response surface methodology and particle swam optimization produces better results.

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Machining fixtures play inevitable role in manufacturing to ensure the machining accuracy and workpiece quality. The layout of fixture elements, clamping forces, and machining forces significantly affect the workpiece elastic deformation during machining. The clamping and machining forces are necessary to immobilize and machine the workpiece, respectively. Finding the appropriate layout of fixture elements is the other possible way to reduce the workpiece deformation, which in turn improves the machining accuracy. The finite element method interfaced with evolutionary techniques is normally used for fixture layout optimization. In the finite element method, the workpiece is discretized into a number of small elements and fixture elements are placed only on the nodes. Hence, evolutionary techniques are capable of searching the optimal fixture layout from those discrete nodal points than from the entire area on the locating and clamping face. To overcome these limitations, in this research paper, response surface methodology is employed to establish a quadratic model between the position of fixture elements and maximum workpiece deformation. This enables the optimization techniques to search for the optimal solution in the continuous domain of the solution space. Then, the real-coded genetic algorithm based discrete optimization, continuous optimization based on binary-coded genetic algorithm and particle swarm optimization are employed to optimize the developed quadratic model and their performances are compared. The result clearly shows that the integration of finite element method, response surface methodology with particle swarm optimization is better than the integration with genetic algorithm to optimize the machining fixture layout and also reduces the computational complexity and time to a greater extent.

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Modern manufacturing industries are striving to improve the machining accuracy and productivity to reduce the rejection rate and unit cost of the machined parts. The properly designed fixture layout enables the designer to minimize the vibration so that the requisite machining accuracy can be achieved. During machining, especially in end milling, the intermittent engagement of multitooth cutter induces vibration on the workpiece. When the excitation frequency of multitooth cutter coincides with any one of the natural frequencies of the fixtured workpiece, it leads to the condition of resonance. The vibration increases under these circumstances, which degrades the machining accuracy and surface finish of the machined workpiece. Hence, the issues related to the design of fixture layout are to be addressed by recognizing the dynamic behavior of the fixture–workpiece system. In this research paper, finite element method is utilized to simulate the end milling operation and to determine the natural frequency of the workpiece. The main focus is to maximize the difference between natural frequency of the fixtured workpiece and excitation frequency of the cutter to minimize the vibration on the workpiece. Two different evolutionary techniques genetic algorithm and particle swarm optimization are employed to maximize the difference between these frequencies by optimizing the machining fixture layout. The performance of genetic algorithm and particle swarm optimization on the fixture layout optimization is compared. The comparison of results concludes that particle swarm optimization is the most appropriate approach than the genetic algorithm in achieving the better results.