Abstract
In this paper, a mathematical model of meshing motion of three degree of freedom involute spherical gear pair is constructed. The mathematical model can realize continuous meshing transmission between gear pairs without transmission principle error. Based on the meshing principle and motion analysis of the gear, the tooth profile of the spherical gear is designed by combining the two tooth surfaces of the involute ring gear and the hemispherical bevel gear. According to the conjugate motion relationship of spherical gear pair, a mathematical model of arc tooth surface of hemispherical bevel gear is established, and the mathematical description of the tooth profile of spherical gear is completed by combining the equation of ring tooth surface. It provides the basis and Reference for the meshing design of ball gear.
Highlights
At present, the multi degree of freedom gear is only structural design, and there is no meshing analysis and mathematical description.The meshing motion of three degree of freedom involute spherical gear pair constructed in this paper is divided into the meshing motion of involute ring gear and the transmission between hemispherical bevel gear
The meshing motion between the involute ring tooth spherical gear is equivalent to the rolling between two spherical meridians, and the transmission between the hemispherical bevel gear is equivalent to the rolling between two spherical weft lines
This motion is the pitch motion of the spherical gear pair, which is realized by the meshing motion between the annular tooth surfaces; the main driving wheel 1 is turned clockwise around the z axis ∅, the driven wheel 2 rotates clockwise ∅ around the z axis, and the arrival position coincides with F x, y, z and F x, y, z respectively
Summary
The multi degree of freedom gear is only structural design, and there is no meshing analysis and mathematical description. The meshing motion between the involute ring tooth spherical gear is equivalent to the rolling between two spherical meridians, and the transmission between the hemispherical bevel gear is equivalent to the rolling between two spherical weft lines. The two kinds of tooth surfaces are combined to form the tooth profile of the spherical gear, so as to realize the transmission of three degrees of freedom motion. The mathematical models of the arc tooth surface of the hemispherical bevel gear and the ring tooth surface of the involute ring gear are established respectively. The data coordinates of the two Pitching motion kinds of tooth surfaces are obtained and imported into MATLAB software for rapid entity modeling
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