| The transmission error of harmonic gear is much smaller than ordinary gear dueto the specificity of its structure and transmission principle. But, as harmonic gear ismainly used in the field of some high precision. The influence of transmission erroron the system can’t be ignored. In view of the inevitability of transmission error. Wecan only take the compensating method to minimize the system transmission error. Sofar, study on system transmission error of the harmonic gear mainly focus on theanalysis of error sources, theoretic calculation of error amplitude, measurement oferror values and so on. But there is very little research on lessening transmission errorby controlling method. Therefore, this thesis intends to study the control andcompensation of transmission error of the harmonic gear drive system is necessary.This thesis begins with the analysis of harmonic gear drive system. After that, thedynamic model of the system is established, considering the meshing friction ofharmonic gear, torsional stiffness, backlash, transmission error，external disturbance,and other nonlinear factors. The PID controller for the closed-loop control system isemployed and the system transmission error of closed-loop control before and after isalso compared and analyzed. In order to study the compensation of transmission errorin harmonic gear drive system, the main works of this thesis are as follows:1) Torsional stiffness and backlash, which are the two main nonlinear factors ofharmonic gear drive system, are analyzed. A “hysteresis” model of stiffnesscharacteristics curve is developed and it can better reflect the changing rule of thetorsional stiffness. An improved model of backlash is proposed on the basis ofresearch of predecessors.2) A new dynamic model based on several typical dynamics model and theanalysis of the structure and principle of harmonic gear drive is established, considering multiple nonlinear factors.3) PID control for the closed-loop control system is employed to compensatetransmission error in harmonic gear drive system and the error of the system output isanalyzed. The experiment result indicates that the PID closed-loop control fortransmission error of the harmonic gear system has obvious compensation effect.4) The harmonic gear system is simplified to a linear second-order system andthe poles distribution of the system is changed by state feedback method. Resultshows that state feedback method improve the relative stability of the system.5) In order to make the simulation results of the transmission error is closer tothe actual system, transfer function of stepping motor is combined with the systemand its transmission error is compensated by the method of PID closed-loop control.By analyzing and comparing the transmission error of PID closed-loop controlbefore and after. The results show that PID closed-loop control for the transmissionerror compensation has obvious effect, no matter the harmonic gear system joiningtransfer function of the stepper motor or no. |
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