Abstract Sommerfeld effect is a nonlinear phenomenon observed in rotating machinery driven by a non-ideal source. It is characterised by capture at resonance for a finite range of drive power followed by a sudden release. This paper investigates the dynamics of a direct current (DC) motor driven mechanism which excites the base of a vibrating structure. A slotted cam follower mechanism and a scotch yoke mechanism are chosen for the base excitations of a single degree of freedom oscillator. It is shown that the Sommerfeld effect leads to capture-and-escape (jump) through multiple resonance zones, and as a result, some intermediate speed ranges are missed. The critical power/voltage input to escape through all the resonances may exceed that required to escape the primary resonance. Moreover, while increased structural damping makes it easier to escape resonance capture, it reduces the system efficiency at super-critical operating speeds. These are important design considerations for sizing the motor drives of these mechanisms. Analytical predictions for jumps are obtained from a steady-state power balance whereas the transient analysis is performed with the help of Bond Graph (BG) models and MSC-ADAMS software. The transient responses from the numerical models are used to verify the analytical results.

中文翻译：

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电机驱动机构基础激励的单自由度系统中的索末菲效应

摘要 索末菲效应是在非理想源驱动的旋转机械中观察到的一种非线性现象。它的特点是在有限范围的驱动功率下共振捕获，然后突然释放。本文研究了激励振动结构底座的直流 (DC) 电机驱动机构的动力学。选择开槽凸轮从动机构和苏格兰轭机构作为单自由度振荡器的基础激励。结果表明，索末菲效应会导致通过多个共振区的捕获和逃逸（跳跃），因此会错过一些中间速度范围。通过所有谐振逃逸的临界功率/电压输入可能超过逃逸初级谐振所需的功率/电压输入。而且，虽然增加结构阻尼使其更容易摆脱共振捕获，但它会降低超临界运行速度下的系统效率。这些是确定这些机构的电机驱动器尺寸的重要设计考虑因素。跳跃的分析预测是从稳态功率平衡中获得的，而瞬态分析是在邦德图 (BG) 模型和 MSC-ADAMS 软件的帮助下进行的。数值模型的瞬态响应用于验证分析结果。跳跃的分析预测是从稳态功率平衡中获得的，而瞬态分析是在邦德图 (BG) 模型和 MSC-ADAMS 软件的帮助下进行的。数值模型的瞬态响应用于验证分析结果。跳跃的分析预测是从稳态功率平衡中获得的，而瞬态分析是在邦德图 (BG) 模型和 MSC-ADAMS 软件的帮助下进行的。数值模型的瞬态响应用于验证分析结果。