Conicity and cylindricity error evaluation using particle swarm optimization

The measurement data obtained from the Coordinate Measuring Machines (CMMs) have to be further processed and analyzed to evaluate the form errors of manufactured components. Particle swarm optimization (PSO), which is based on a metaphor of social interaction, searches a space by adjusting the trajectories of individual vectors, called “particles” as they are conceptualized as moving points in multidimensional space. Each particle represents a point in the d-dimensional search space and has a velocity to adjust its flying direction according to the particleʹs best position ever found and the best position of all particles. PSO is proposed to implement the minimum zone evaluation of conicity and cylindricity errors simultaneously. The method takes an ideal cone as a particle which is decided by vertex, central line and vertex angle of the cone. And the particle’ velocity is modified by constriction factor approach. Compared to other evolutionary computation such as traditional genetic algorithm (GA) and immune algorithm (IM), PSO is easier to implement and there are fewer parameters to adjust. Then, the minimum zone conicity method is formulated which unites conicity and cylindricity errors evaluation as one. Then, the objective function calculation approach of conicity is developed which conforms to the ISO/1101 standard. Finally, the experimental results evaluated by different methods confirm the effectiveness of PSO. Compared to conventional evaluation methods, it not only has the advantages of algorithm simplicity and good flexibility, but also improves conical and non-strict cylindrical parts error evaluation accuracy. And it is well suited for form error evaluation on CMMs.