This thesis analyzes how the input voltage of the motor and the magnitude of the total backlash of a servo system with a gear reducer affect the bandwidth of the servo system. For this purpose, I have investigated the change in the frequency response characteristics depending on various motor input voltages and the magnitude of the total backlash. The bandwidth of the system is defined as the anti-resonance frequency, which appears in the frequency response characteristic. In particular, it is shown that when the motor input voltage is infinite, the servo system has a bandwidth of the system that does not have any backlash, and the amount of system’s bandwidth reduction due to the backlash changes greatly with motor input voltage. Through this work, it has become possible to determine the necessary maximum input voltage of the motor and the maximum permissible magnitude of total backlash to satisfy the desired bandwidth for a servo system with a gear reducer.
And, this thesis also investigates the change in frequency response characteristics of a servo system with a two-stage gear reducer in relation to the change in a backlash ratio or the backlash magnitude of each stage under the condition that the total backlash magnitude of the servo system is known. The backlash ratio is defined as the ratio of the first gear stage backlash magnitude to the total backlash magnitude. It is found that although the total backlash magnitude is constant, the frequency response characteristic of the servo system is greatly changed according to the magnitude of the backlash ratio or the backlash of each stage. It is also found that there is an optimal backlash combination to maximize the bandwidth of the servo system, when the permissible total backlash magnitude is determined. I conclude that, if the intention is to expand the bandwidth, the determination of the magnitude of backlash at each stage would be an effective and efficient means of accomplishing this.
A unique technique to estimate the magnitude or backlash ratio of each stage backlash in a system with a two-stage gear reducer is proposed. The concept to estimate the magnitude or backlash ratio of each stage backlash is based on the change of frequency response characteristic, in particular, the change of anti-resonance frequency and resonance frequency, due to the change of each stage backlash magnitude, even though the total backlash magnitude of a system with a two-stage gear reducer is constant. The validity of the technique is verified in a gimbal system and satisfactory results are obtained. It is thought that the diagnosis and maintenance of the manufacturing machines and systems with two-stage gear reducers will become more efficient and economical by virtue of proposed technique.
