Aligning natural logarithmic spiral with gear drive: How bionic gear design and characteristics are affected by logarithmic spiral parameters

• An integral novel bionic gear design theory based on natural logarithmic spirals is proposed. • Evolution law of tooth profile generation, transmission performance of bionic gear are revealed. • Identifying the optimal parameter design range and addressing the critical challenge of selecting parameters of the proposed tooth design. • In terms of fatigue strength and bending strength, the designed bionic gear are better than the classical involute gear. Logarithmic spirals, common in biological and natural formations, have distinctive geometric and mechanical characteristics that provide substantial inspiration for engineering advancements. This research proposes a novel bionic gear design method that integrates the characteristics of logarithmic spirals into gear tooth profiles. The research seeks to investigate the modeling and generation methods of bionic gears derived from natural logarithmic spirals, as well as the mapping relationships between the spiral angle and the generated tooth profile shape, meshing characteristics, and mechanical properties, through a series of case analyses. Firstly, to address the theoretical issues in gear design, the properties of logarithmic spirals are investigated, and the design method and mathematical model of bionic gears with logarithmic spiral tooth profiles also are established. Secondly, to establish the feasible design range of spiral angle of key variables of logarithmic spiral, the evolution laws of the tooth profile shape, meshing characteristics, and mechanical properties with different spiral angles are revealed, ultimately establishing the feasible spiral angle range as 20°≤ β ≤25°. Finally, performance comparison tests between the fabricated bionic gears and standard involute gears validate the efficiency and feasibility of the proposed design method. Results indicate that, in contrast to involute gears, the novel bionic gear demonstrates better fatigue strength and load capacity.