Hertz contact stiffness of inner gear and outer gear of Spur Planetary Gear

According to Hertz law, the elastic compression of two isotropic elastic bodies can be described by two projectile near the contact point. As shown in Fig. 1, the two gears can be assumed to be cylinders with radius R1 and R2 respectively under the action of positive pressure F.

The Hertz stiffness (KH) of the meshing pair of internal and external gears can be expressed as follows:


F — force;

E — elastic modulus;

L — tooth width;

V — Poisson’s ratio;

δ — deformation.

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