Measurement and prediction of backlash based on two-sided transmission error

Transmission error in gear system and backlash are important factors that affect the accuracy of precision transmission systems. The main sources of the complete cycle transmission errors and periodic backlash are eccentric errors due to imperfections in machining and assembling. Therefore, analyzing the transmission error in gear system and backlash under the effect of eccentricity error is necessary. Scholars from around the world have conducted extensive research on the transmission error of the gear system. They observed that the back-side contact of the gear tooth generally happens in high-speed light-load conditions, or when alternate load torque occurs or anti-backlash gear has been used. However, the existing literature does not evidently show the calculation method of the transmission error of the back-side tooth mesh. Therefore, analyzing the transmission error of the back-side tooth mesh is of great significance. The present work develops a calculation model of drive- and back-side (two-sided) transmission error of an involute gear pair with eccentricities to construct the equivalence of time-varying backlash calculation formula to demonstrate the continuous measurement of gear backlash based on two-sided transmission error that can also be realized in theory. The experimental transmission error and the corresponding hysteresis were acquired under various load torques and different initial conditions, such as initial position of the gear unit. The continuous backlash curve of the gear pair was obtained from the two-sided transmission curves, and the backlash of the whole cycle could be predicted. The result of the experiment shows that the continuous measurement curve agrees with the mechanical hysteresis method, and the prediction of backlash perfectly reflects the variation range and trend of backlash. Moreover, both the continuous measurement method of backlash and prediction of backlash demonstrate that the model is practicable and have higher efficiency, and the overall data retain instructional significance, reference value for nonlinear research, anti-backlash control, and gear accuracy of gear transmission.