1985Journal of the Japan Society of Precision EngineeringOpen access

Deflection and stiffness on line of action of internal spur gear with thin rim.

Takeshi Ishida, Teruaki HIDAKA, Nobuyuki SUGIMOTO

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Abstract

A deflection of an internal gear with thin rim is composed of both the deflection of tooth and that of rim. Therefore an equation of deflection of a tooth of the internal gear is obtained by replacing the tooth by a cantilever composed of two trapezoid and an equation of deflection of a rim of the internal gear is obtained by replacing the internal gear by an equivalent ring. Then using the equations mentioned above and an equation of deflection of an external gear, which is widely used, the stiffness of a pair of teeth between the internal gear and a planet gear is illustrated against the number of teeth of the internal gear and that of the planet gear, and also the stiffness of the rim is illustrated against the number of planet gears, the number of teeth of the internal gear and the rim thickness. Further a load sharing rate of the internal gear with thin rim is discussed.

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A deflection of an internal gear with thin rim is composed of both the deflection of tooth and that of rim. Therefore an equation of deflection of a tooth of the internal gear is obtained by replacing the tooth by a cantilever composed of two trapezoid and an equation of deflection of a rim of the internal gear is obtained by replacing the internal gear by an equivalent ring. Then using the equations mentioned above and an equation of deflection of an external gear, which is widely used, the stiffness of a pair of teeth between the internal gear and a planet gear is illustrated against the number of teeth of the internal gear and that of the planet gear, and also the stiffness of the rim is illustrated against the number of planet gears, the number of teeth of the internal gear and the rim thickness. Further a load sharing rate of the internal gear with thin rim is discussed.

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Available abstract

A deflection of an internal gear with thin rim is composed of both the deflection of tooth and that of rim. Therefore an equation of deflection of a tooth of the internal gear is obtained by replacing the tooth by a cantilever composed of two trapezoid and an equation of deflection of a rim of the internal gear is obtained by replacing the internal gear by an equivalent ring. Then using the equations mentioned above and an equation of deflection of an external gear, which is widely used, the stiffness of a pair of teeth between the internal gear and a planet gear is illustrated against the number of teeth of the internal gear and that of the planet gear, and also the stiffness of the rim is illustrated against the number of planet gears, the number of teeth of the internal gear and the rim thickness. Further a load sharing rate of the internal gear with thin rim is discussed.

Key concepts: Deflection (physics), Stiffness, Structural engineering, Internal forces, Spiral bevel gear, Cantilever, Non-circular gear, Spur gear

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