Vibration in the direction of the w

Vibration in the direction of the worm screw axis We consider the vibration that acts on the axis of the worm screw Sy , as shown in Fig. 3a. The weight of the worm wheel, the worm screw, and the exciting force are MW , MS , and f sin ωt , respectively. Theoretically, the x and z components of the force are also generated by the contact force of the gear teeth. However, they are smaller than y components of the force, because the lead angle of the worm gear is small. To simplify the analysis, we considered only the spring stiffness ky1 and ky2 . If the worm wheel and the worm screw are in contact in the static friction condition, they vibrate as a single body by the shaft of the worm wheel, bending by the motion shown in Fig. 2a. Therefore, the equation of the motion can be written as shown in Eq. (5), and the displacement y can be calculated.