はすば歯車の歯打ちにおける歯形誤差形状の影響と分数調波振動

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  • Influence of tooth profile errors and subharmonic resonance in helical gears rattle

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This paper deals with the gear rattle of helical gear system. Introducing the mesh stiffness and torque variation into the one pair of helical gear system, the effects of the shapes of the tooth profile errors on the rattle are studied, and the subharmonic vibrations generated in the system are also studied numerically. In the numerical analysis, shooting method with high accuracy is used. To obtain the high accurate periodic solutions, all cases of meshing are considered and the very short time integral step are adopted. As a result, the followings were made clear. (1) About the resonance amplitudes caused by tooth profile errors, those in the gears with middle concave tooth profile error are generally larger than those in the gears with middle convex tooth profile error. (2) About the resonance amplitude caused by the torque variation, there is little difference between the gears with the middle concave tooth profile error and those with the middle convex tooth profile error. (3) In the case without torque variation, there is a possibility that 1/2th-subharmonic vibration and 1/3th-subharmonic vibration occur because of tooth profile error. (4) When torque variation is increased, 1/3th-subharmonic vibration caused by tooth profile error degenerates. (5) In the near region where the 1/2th-subharmonic vibration generates, by the interaction of the vibrational force by the tooth profile error and the torque variation, many unstable branches are created, and chaos occurs.

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