Multi-speed transmissions can enhance the performance and reduce the overall cost of an electric vehicle, but they also introduce a challenge: avoiding gearshift jerk, which may sometimes prove to be impossible in the presence of motor and clutch saturation. In this article, we introduce three theorems that explicitly define the fundamental limitations to no-jerk gearshifts resulting from motor or actuator saturation. We compare gearshifts that consist of transferring transmission torque from one friction clutch to another, to the case in which one of the clutches is a one-way clutch. We show that systems with a one-way clutch are more prone to motor saturation, causing gearshift jerk to be more often inevitable. We also study the influence of planetary gearsets on the gearshift dynamical trajectories, and expose the impact on the no-jerk limitations. This work offers tools to compare transmission architectures during the conceptual design phase of a new electric vehicle.

多速变速器可以提高性能并降低电动汽车的总体成本，但同时也带来了挑战：避免换挡冲击，有时在电机和离合器饱和的情况下，这是不可能实现的。在本文中，我们介绍了三个定理，这些定理明确定义了由于电动机或执行器饱和而导致的急动换挡的基本限制。我们将换档包括将一个变速器的摩擦力矩从一个摩擦离合器传递到另一个离合器，并比较其中一个离合器是单向离合器的情况。我们显示，具有单向离合器的系统更容易出现电机饱和，从而导致换档跳动更为常见。我们还研究了行星齿轮组对变速动力学轨迹的影响，并揭露其对无拘无束限制的影响。这项工作提供了在新电动汽车的概念设计阶段比较变速箱架构的工具。