Error evaluation of free-form surface based on distance function of measured point to surface

As free-form surface is widely used in engineering, it is urgently needed to develop advanced methodology of detecting and evaluating the profile error. To this end, the semantic of profile tolerance in ASME Y14.5.1M is reviewed and the mathematical definition of profile tolerance is discussed. Subsequently, a mathematical model for error evaluation is built. This mathematical model is augmented based on distance function by considering the second-order terms in the computation of the distance from point to surface. Then, a profile error evaluation algorithm, which combines Differential Evolution (DE) algorithm and Nelder–Mead (NM) algorithm, is developed to solve this model. The proposed model and optimization algorithm are validated with simulation results from a case study. Additionally, the model is superior to Least-squares (LS) model in simplicity, efficiency and robustness.