Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear

Abstract

In order to realize planar deformation of the tooth ring in radial direction which leads to planar line contact engagement between tooth profiles， according to the geometric equation of the cylindrical shell theory， the connection condition between the bell shaped shell and the tooth ring is proposed. A parametric bell shaped flexspline shell contact model is established. The geometric condition of the bell shaped curve which realizes planar deformation of the tooth ring is solved iteratively，that is，the relationship between the ratio of the radius of the tooth ring to the radius of the bell shaped curve and the central angle of the circular bell shaped curve. The result is fitted with a five-order spline curve expression. The connection condition between the bell shaped shell and the cup bottom is solved and according to the theory of circular thin plate，the calculation method of the deformation and stress of the cup bottom is proposed. The research found that the stress of the bell shaped flexspline cup bottom increases exponentially with the increase of the shaft radius when the shaft radius greater than 0.65 times of the cup bottom radius. However，the geometric conditions of the bell-shaped curve for the planar deformation of the tooth ring are independent of the shaft radius.

Keywords

• Taper deformation