Formational principle and accurate fitting methodology for a new tooth surface of the spiral bevel gear

Distinguished with some basic theory and approaches of traditional tooth surface design, the spiral bevel gear with new tooth surface, namely spherical involute tooth surface, is investigated. Firstly, it improved its formational principle based on the spherical involute theory. As a key part, the parametric equation of the generating line was made a detailed derivation. To this end, fast and accurate solutions of the boundary curves and the tooth profile curve family are accomplished, respectively. Then, taking advantages of modelling techniques of cubic non‐uniform rational B‐spline (NURBS) curve and surface in CAD/CAM, a reconstruction method for the spherical involute tooth surface was proposed to enhance the precision. At last, related optimisation schemes associated with constructed NURBS tooth surface are utilised to obtain the parameterisation of tooth surface data and higher‐accuracy fitting. Given numerical examples indicate that the accuracy of the tooth surface is obviously enhanced and is enough to provide gear finite element (FEM) analysis the data and the basic model in its digitised design and manufacturing.