Compliance based mixed integer programming model and heuristic for support layout optimization

Machining-fixture supports are used to increase workpiece rigidity. A critical problem of machining fixture design is where to place a fixed number of supports in order to minimize the effect of workpiece deformation on machined feature geometric error during machining. In a previous effort, a linear Mixed Integer Programming (MIP) model was developed to solve this problem. This model is based upon a statically reduced FEA model of the workpiece, and is capable of solving the more general problem of locator button-support layout. A major disadvantage of this model is that its size is sensitive to the square of the number of machining response points considered. Since the difficulty of solving an MIP model increases with model size, this presents a severe limitation to the use of the MIP model in applications in which a large number of machining response points must be considered. This paper illustrates a technique that can be used to make the MIP model size strictly proportional to the number of machining response points. In addition, it presents a heuristic based on the MIP model, that can be used to solve support layout problems of any size.