Evaluation of composite positional error based on superposition and containment model and geometrical approximation algorithm

Composite positional error is an important parameter in measuring parts with pattern of features. This paper, based on the method to define Spatial Straightness with mathematics according to ASME Y 14.5.1M standard, studied the evaluation of composite positional errors systematically. Firstly, the mathematical definitions of composite positional error in two most common types of pattern of features in engineering were researched. Then, an advanced mathematical model based on the superposition and containment method for the evaluation of composite positional error were proposed. In this model, another variable which represents the relative angle among holes was added into the optimization problem. To solve this model, an algorithm called geometrical approximation algorithm was also proposed. In this algorithm, the steepest descent direction was determined by the exact coordinates of the measured points which led to a better convergence and time efficiency than general algorithm for solving the proposed model. At last, two simulations showed that with the proposed model and algorithm, the accuracy was improved by about 8% and the efficiency was improved by about 50%. An application showed how this model and algorithm worked and due to their accuracy, less misrejection in product examination will be caused.