Algorithm for extracting the normal cross-section parameters of multiple ball screw shaft ball tracks based on an optical micrometer measurement system

Abstract The accurate and efficient measurement of the normal cross-section parameters of multiple ball screw shaft spiral ball tracks are pivotal for ensuring quality control in ball track machining. Given the intricate nature of the ball screw shaft spiral ball track, balancing the accuracy and efficiency of the normal cross-section parameters measurement is a significant challenge. In this study, we present a method to calculate two core parameters, arc radius and contact angle. The method consists of four parts: the automatic axial cross-section separation method, the arc symmetric extraction method, the spiral transformation method, and the parameter algorithm based on the weighted least squares method. The experimental and simulation results validated the effectiveness of our method. Compared with the traditional axial measurement and transformation (AMT) method, our algorithm reduced the errors in arc radius and contact angle by up to 13.9 µm and 4.77°, respectively, and improved the accuracy by up to 78.34% and 85.04%. Compared with the traditional AMT methods and directly normal measurement method, the measurement time of our algorithm was reduced by up to 1565 s and 3475 s, respectively, and the efficiency was improved by up to 71.01% and 84.51%, respectively.