Sampling strategy and error estimation for evaluation of quadratic form error using Cartesian coordinate data

This study investigates the relationship between sampling strategy and error estimation, which is used to improve the measurement and evaluation of quadratic form error in Cartesian coordinates. This study is focused on the sampling strategy, the sampling error estimation, and the error evaluation model, and it is particularly useful when a special device measures the form characteristics of a workpiece. To obtain a reasonable sample size and an accurate error estimate for the geometric features of a quadratic form, Boltzmann curve is used to predict the reasonable sample size by fitting different evaluation results of form error. As a result, compared with earlier methods, the curve helps us to obtain a better accuracy, while the process only distinguishes a part of the form features on one or several workpieces from a mass production. In addition, a new error model based on the quadratic form is established by least squares method, which can be applied to measure and evaluate the roundness error and sphericity error. Two experiments are performed to verify the effectiveness of the new error model, and the results indicate that a systematic sampling strategy and error estimation can determine the reasonable sample size while maintaining high accuracy.