Optimizing Cam Profiles Using the Particle Swarm Technique

Abstract

Cam-follower systems are ideally suited for many machine applications that require a specific and an accurate output motion. The required follower motion is achieved by carefully designing the shape or profile of the cam. Modern profiles are typically synthesized by piecing together a set of trigonometric and/or polynomial functions that satisfy the constraints. For most problems, there are many profile solutions that satisfy the constraints. In this paper, a relatively new optimization technique known as particle swarm optimization (PSO) is applied to the optimization of two different cam problems. The first example is a single-dwell cam in which the magnitude of the negative acceleration is minimized. The second example is a cam with a constant velocity segment in which the cycle time is optimized. The intent is to show the method in two different settings so that the reader can extend it to the optimization of any cam-follower problem. To illustrate the method, first the PSO method is applied to a mathematical function with two independent variables. Then, the method is used to find the cam profile that provides the minimum acceleration in a single-dwell cam using three independent variables. Finally, it is applied to obtain the minimum cycle time of a cam with a constant velocity segment using cubic interpolations and seven or more independent variables. The PSO method was very successful in all the optimization problems discussed in this paper. In the first cam problem, it significantly lowered the level of negative acceleration, while maintaining the positive acceleration at a constrained upper limit. The optimization procedure for the second cam problem found a very elegant five-segment solution. This solution results no matter how many initial segments or independent variables are chosen so long as there are at least five segments. Presented in this paper is the particle swarm optimizing technique that is applicable to many aspects of cam design. Two diverse examples were presented that illustrate how the PSO method can be used effectively in the optimization of cam-follower problems. In both illustrative examples, the PSO method proved to be robust, easy to implement, and suitable for minimizing a wide variety objective functions applicable to the design of cam-follower systems.