はすば歯車系の振動解析 : 第1報, 起振力を考慮した多自由度シミュレーションの開発

A dynamic model of a helical gear pair has been developed taking the kinematic properties of the shafts and bearings as well as mesh excitation into account. The model can be used to describe transverse, rotational, tilting and axial vibration of gears, that is, the gears are assumed to be vibrating in six principal directions, three for translational motion and three for swing motion. To introduce mesh excitation into the equation of motion, the properties of the shafts and bearings are considered to be concentrated at the center of the gear bodies and are modeled in terms of a suspending spring and an additional mass besed on Rayleigh's principle. Then the tooth mesh stiffness was modeled in terms of two parallel springs which varies temporally with a certain phase relationship due to the helix angle. The differential equations are numerically solved using the Runge-Kutta-Gill method. The results are in good agreement with experimental results with respect to the major resonance frequencies and amplitudes.