The contributions of various non-linearities to an automotive drum brake’s transient response has been studied analytically. A discrete system model with friction, contact, and kinematic non-linearities is formulated such that each of the non-linearities could be linearized independently. The contact between the brake shoes and the brake drum is modeled using Hertzian contact theory, supported by kinematic relationships derived using vector geometry for a given design. Several variants of quasi-linear models are derived from the non-linear system by linearizing individual non-linearities. Transient responses of these models were obtained numerically during a typical braking event, consisting of the impacting phase and contact phase. The linearized and non-linear responses are compared based on the time-histories, spectra, and spectrograms. The self-energizing and de-energizing effects of the brake shoes on the dynamic behavior of the system were quantified. Finally, the trends from the developed non-linear model were qualitatively and quantitatively correlated with published data.

已经分析研究了各种非线性对汽车鼓式制动器瞬态响应的贡献。一个具有摩擦、接触和运动非线性的离散系统模型被公式化，这样每个非线性都可以独立地线性化。制动蹄和制动鼓之间的接触使用赫兹接触理论建模，并由使用给定设计的矢量几何导出的运动学关系支持。准线性模型的几种变体是通过线性化单个非线性从非线性系统导出的。这些模型的瞬态响应是在典型的制动事件期间以数值方式获得的，包括撞击阶段和接触阶段。基于时间历程、频谱和频谱图比较线性化和非线性响应。对制动蹄对系统动态行为的自激和断电影响进行了量化。最后，开发的非线性模型的趋势与已发布的数据在定性和定量上相关。