A non-contact high precision measuring method for the radial runout of cylindrical gear tooth profile

Abstract

Gear radial runout (eccentricity) is one of the common errors of gear, and it causes dynamic load, vibration, and noise seriously in a machine system. Therefore, the radial runout measurement is indispensable in gear manufacturing, running, and maintaining. With the advantages of low cost, high precision, and universal applicability, a non-contact measuring method for the radial runout of cylindrical gear tooth profile is proposed only using a single laser displacement sensor in this paper. A theoretical optimization model is established according to the measurement principle and the laser sensor characteristics, and the optimal installation position and angle of the laser sensor are presented for measurement arrangement. A mathematical model and algorithm for the circumferential measuring data of cylindrical gear tooth profile is deduced and proposed: a calculating initial value of radial runout (eccentric modulus and phase angle) is predicted by least square linear regression, and then the exact value of radial runout is determined by an iterative loop approximation with Jacobian gradient matrix. Numerical simulations of measuring process are carried out by setting different precision levels of system parameters to evaluate the method accuracy and applicability in the view of error distribution and sensitivity analysis. For a gear shaft with 11, 21 and 32 teeth gears, a specialized experiment is carried out to validate the correctness and reliability of the proposed measuring method by comparing with a conventional measuring method of the gear radial runout.