Coaxiality of Stepped Shaft Measurement Using the Structured Light Vision

Chunfeng Li,Jianwei Miao,Zhen Ren,Huiqi Sun,Xiping Xu,Sang-Bing Tsai

doi:10.1155/2021/5575152

Abstract

A method is proposed to measure the coaxiality of stepped shafts based on line structured light vision. In order to solve the repeated positioning error of the measured shaft, the light plane equation solution method is proposed using movement distance and initial light plane equation. In the coaxiality measurement model, the equation of the reference axis is obtained by the overall least square method through the center point coordinates of each intercept line on the reference axis. The coaxiality error of each shaft segment relative to the reference axis is solved based on the principle of minimum containment. In the experiment, the coaxiality measurement method is evaluated, and the factors that affect the measurement accuracy are analyzed.

Highlights

The laser is translated along a straight line multiple times, the intersection lines formed by the light planes and the measured stepped shaft are obtained by the camera, and the center of each intersection line is calculated by ellipse fitting. e reference axis equation is obtained by the global least square method. e distance from the center of each section to the reference axis is calculated, and the maximum distance corresponding to each shaft segment is regarded as the coaxiality of the shaft segment through the principle of least tolerance
E paper consists of the following parts: Section 2 proposes the calculation of the world coordinates of the stepped shaft surface contour points; Section 3 establishes the translational light plane calibration algorithm; Section 4 outlines the stepped shaft coaxiality measurement model; Section 5 reports the experimental results used to test the measuring; Section 6 provides the study’s conclusions
Solving the Camera Coordinates of Points on the Stepped Shaft Surface. e camera coordinate solution model for data points on the surface of the stepped shaft is shown in Figure 1. e Pi is any point on the measured shaft. e intersection P′ of the ray OCPi and the imaging plane is the

Summary

World Coordinate Calculation of Contour Points on Stepped Shaft Surface

Solving the Camera Coordinates of Points on the Stepped Shaft Surface. E camera coordinates of Pi can be calculated by equations (1) and (2), and xu and yu are the image coordinates of point Pi. 2.2. Solving World Coordinates of Points on Stepped Shaft Surface. E direction vector of the OWZW is the normal direction of the light plane (A1, A2, and A3), and the direction cosine of the OWZW in the camera coordinate system can be obtained by using the normal vector of the light plane. Where the direction vector of OCK is (1, 1, − ((A1XC + A2YC)/A3)), which is taken as the direction vector of OWXW in the camera coordinate system. E direction vector of OWYW which can be obtained through the direction vector of OWXW and OWZW is shown as.

Calibration Algorithm of the Translated Light Planes Equations

Experiments and Result Analysis