On the design of power gear trains: Insight regarding number of stages and their respective ratios

This paper presents a formulation for selecting the stage ratios and number of stages in a multistage transmission with a given desired total transmission ratio in a manner that maximizes efficiency, maximizes acceleration, or minimizes the mass of the transmission. The formulation is used to highlight several implications for gear train design, including the fact that minimizing rotational inertia and mass are competing objectives with respect to optimal selection of stage ratios, and that both rotational inertia and mass can often be minimized by increasing the total number of stages beyond a minimum realizable number. Additionally, a multistage transmission will generally provide maximum acceleration when the stage ratios increase monotonically from the motor to the load. The transmission will have minimum mass when the stage ratios decrease monotonically. The transmission will also provide maximum efficiency when the corresponding stages employ constant stage ratios. This paper aims to use this optimization formulation to elucidate tradeoffs between various common objectives in gear train design (efficiency, acceleration, and mass).

本文针对给定期望总传动比（total transmission ratio）的多级变速器（multistage transmission），提出一种级比（stage ratios）与级数选取方法，可在该约束下实现效率最大化、加速度最大化，或使变速器质量最小化。该优化公式可用于阐明齿轮传动系统设计（gear train design）中的多项关键结论：其一，转动惯量（rotational inertia）最小化目标与质量最小化目标在最优级比选取中存在竞争关系；其二，通过将总级数增加至超过最小可实现级数，通常可同时实现转动惯量与质量的最小化。此外，多级变速器通常可在级比从电机端向负载端单调递增时获得最大加速度；当级比单调递减时，变速器质量达到最小值；而当各级采用恒定级比时，变速器可实现最高效率。本文旨在通过该优化公式，阐明齿轮传动系统设计中效率、加速度与质量等各类常见优化目标之间的权衡关系。