General scaling relations for locomotion in granular media.
General scaling relations for locomotion in granular media.
复制标题
粒状介质中运动的一般比例关系。
作者：
J. Slonaker;D. C. Motley;Qiong Zhang;Stephen Townsend;C. Senatore;K. Iagnemma;K. Kamrin
受流体系统动力学相似性的启发，我们推导了颗粒材料运动的一般无量纲形式，并在实验和离散元法（DEM）模拟中得到了验证。该表格说明了如何缩放尺寸、质量和驱动参数，以便在相同的颗粒介质中关联不同移动设备的动态行为。尺度化可以通过假设侵入力来自于阻力理论，或者假设颗粒材料的行为是一个连续体，遵循摩擦屈服准则来推导。用不同形状和尺寸的车轮对在普通砂床上的许多驾驶条件下进行了实验验证。我们讨论了为什么这两个模型提供了如此强大的一套标度定律，即使它们忽略了颗粒流变性的一些复杂性。考虑到潜在的行星外应用，无量纲形式还意味着一种基于不同环境重力测试来预测车轮在一种环境重力下性能的方法。我们使用DEM模拟证实了这一点，该模拟表明，即使在缩放测试之间重力不同的情况下，也满足了一系列驾驶模式的缩放关系。
Inspired by dynamic similarity in fluid systems, we have derived a general dimensionless form for locomotion in granular materials, which is validated in experiments and discrete element method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from resistive force theory or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extraplanetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.