Integrated design-optimization method for high-performance and lightweight spiral bevel gears

Abstract

As a core component of high-power-density transmission systems, designing high-performance lightweight spiral bevel gears (SBGs) have become a key research focus. The SBG design comprises three essential phases: blank geometry, tooth surface geometry, and contact performance prediction. The lack of standardized frameworks makes the SBG design process heavily dependent on empirical expertise, limiting the full potential of SBG design. To address this limitation, an integrated design optimization method (IDOM) that integrates the blank geometry, tooth surface geometry, and contact performance was proposed. First, a general mathematical model for face-milled SBGs was established using tooth shrinkage principles and homogeneous coordinate transformations. Subsequently, a geometric optimization method for lightweight SBG blanks (GOMSB) was developed using genetic algorithms. Based on this, the spatial meshing theory and topological surface techniques were employed to construct a mathematical deviation model between the target and theoretical pinion tooth surfaces, leading to a high-performance geometric optimization method for SBG surfaces (GOMSS). An enhanced tooth contact analysis method integrating differential geometry and Hertz contact theory was proposed. This method quantifies time-varying loaded contact characteristics by combining elastic potential energy principles with meshing equilibrium conditions and establishing parametric criteria for iterative tooth surface modification. Finally, the IDOM was validated through SBG pair design case studies using numerical modeling, assembly, and meshing simulation analysis. Furthermore, the applicability of GOMSB and GOMSS as well as the key parameters influencing the fatigue strength and contact performance of SBG pairs and their operational laws were systematically analyzed, thereby establishing fundamental design principles for high-performance SBG development.