Takeshi Ishida

Analysis of bending stress of thin walled,intermediate gear. Influence of circular ring thickness on the stress.

博肉の遊星歯車の歯元応力を高弾性法で解析し,次のことを明らかにした.歯元すみ肉部での最大応力の発生位置は歯面荷重や軸すき間によって変化するが,曲げ強度に関しては最大の歯元引張応力と歯元圧縮応力を考慮すればよい.歯数18の遊星歯車では,円環部厚さが3m以上になると厚肉と考えてよい.博肉の遊星歯車では,ある軸すき間以上になると歯元の応力振幅が急増するが,このときの軸すき間は円環部が薄いほど小さくなる.

Calculation of the Torsional Rigidity of Strain-Wave Gearing by Finite Element Method.

The factors which determine the torsional rigidity of strain-wave gearing are not only due to torsion of a flexible spline (= FS) but also to flextural deformation of FS on the open side. As the deformation of FS occurs in three-dimensional situations and the amount of deformation is not proportional to the load, it is not easy to use the elastic theory in defining the torsional rigidity of the gearing. Thus, with the use of the three-dimensional finite element method, the torsional characteristics of the gearing were investigated. A solid element having eight nodes and six surfaces was used for modeling the FS. At the same time, the boundary conditions for calculations which took into consideration the region of contact with other structural parts were determined. Results of calculations under these boundary conditions agreed relatively well with the experimental values.

Deflection along line of action of idle gear with both thin rim and radial clearance between rim and gear shaft.

An idle gear with a thin rim is replaced by an equivalent ring whose bending stiffness is equal to that of the idle gear. Then the radial, tangential and angular displacements of the equivalent ring are analyzed theoretically considering the condition of contact between the idle gear and the gear shaft. Further, the displacements of the equivalent ring are translated to those along the line of action in order to obtain the deflection of the rim of the idle gear along the line of action. Consequently the deflection of the idle gear is obtained by adding the deflection to that of a tooth which is widely used. The deflection obtained theoretically agrees comparatively with that obtained by the finite element method.

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

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.