This paper proposed the simulation model of the servo system with three-stage reducer and presented the result of frequency analysis of the servo system considering backlash ratios and motor input voltage. By virtue of this work, we realized that if the motor input voltage of the system was large, the influence of each stage backlash ratio could be minimized or removed. Besides, we also found that if the motor input voltage was small, this created an optimal backlash ratio combination which could maximize the anti-resonance and resonance frequency of the servo system. This paper could be useful for determining each stage backlash ratio in designing a three-stage geared servo system with fast response.

This paper investigated the influence of the backlash ratio on frequency response characteristic in servo systems with twostage gear reducer, according to the change of magnitude of motor input voltage. The backlash ratio is defined as the ratio of the first gear stage backlash magnitude in relation to total backlash magnitude. This paper presents that the maximum anti-resonance and resonance frequency of the system can take place at the maximum backlash ratio if the motor input voltage of the system is large. On the other hand, if the motor input voltage is small, the maximum anti-resonance and resonance frequency of the system will occur at an arbitrary backlash ratio. In order to develop the geared servo system with fast response, it is effective to increase the maximum allowable motor input voltage and to reduce the magnitude of backlash on the second gear reduction stage.