This study presents model and analysis of a robust one-dimensional stick–slip transportation of an object, on dry contact with an oscillating platform suspended by nonlinear leaf spring. The oscillating platform is designed and modeled such that the elastic spring constant is direction dependent. A recursive analytical solution algorithm is proposed to solve nonlinear system dynamics. The system and the input force parameters are both investigated with goal to optimize the average velocity of the object. Both experimental and analytical results showed that the stick–slip motion is highly nonlinear and sensitive to the system and input force parameters. Moreover, the simulations showed that it is feasible to design a platform with robust sets of parameters (natural frequencies) and further use the input force parameters (amplitude and driving frequency) to tune for desired average velocity, under given dry friction conditions.

这项研究提出了一种模型，该模型对与非线性弹簧悬吊的振动平台进行干式接触时，物体的一维粘滑滑动进行了稳健的分析。对振动平台进行设计和建模，以使弹性弹簧常数与方向有关。提出了一种求解非线性系统动力学的递归解析解算法。目的是研究系统和输入力参数，以优化物体的平均速度。实验和分析结果均表明，粘滑运动是高度非线性的，并且对系统和输入力参数敏感。而且，