Froude scaling for rovers on small body surfaces 

摘要

<p><strong>Abstract</strong></p><p><span>We study rover-regolith interactions in low-gravity environments by conducting soft-sphere discrete element method (SSDEM) simulations with a simplified rover wheel and a bed of spherical particles. The simulations reveal that rover performance scales according to the Froude number, or a dimensionless parameter which accounts for the size of the wheel, the rotational velocity of the wheel, and gravity. This relationship provides valuable insight into how to operate rovers and analyze wheel-regolith interactions during future rover missions.</span></p><p><strong>Introduction</strong></p><p>Wheeled-rovers are useful tools for identifying the surface material properties of planetary surfaces [1-3]. The sinkage and traction of a rover can be used to assess the bearing strength of a material, and the tracks left behind by a rover’s wheels can provide information regarding the density, the friction angle, and the cohesion of the regolith [3]. To maximize the scientific return from a rover mission, however, the vehicle must first be able to drive on a granular terrain in a reduced-gravity environment. Parabolic flight experiments and numerical simulations have shown that, as gravity decreases, wheel slip increases and rover traction decreases [4-6]. At the same time, wheel sinkage remains comparable for different gravity levels, at least for certain types of materials [4]. While a few models have been proposed to help explain these findings [7,8], an explicit scaling relationship between rover performance and gravity has yet to be established.</p><p>In this work, we analyze rover-regolith interactions on Earth versus a small moon, Phobos. Based on the findings of [8] and [9], we hypothesize that rolling behavior scales with gravity according to the dimensionless Froude number, Fr = Lω^2/g, where L is a characteristic length (e.g., the radius of a rover wheel), ω is the rotational velocity of the wheel, and g is gravity.</p><p><strong>Simulations</strong></p><p>We conducted SSDEM simulations using a simplified rover wheel and the MULTICORE module of the open-source code CHRONO [10, 11]. The rover wheel is 214 mm in diameter and 53 mm in width and has 9 thin grousers that are equally spaced around a cylindrical hub. The wheel rotates at a constant speed through a bed of spherical grains and can translate freely in the horizontal and vertical directions. The grains are 6 +/- 0.5 mm in diameter and are contained within a 800x250x150 mm box. Simulations were performed using different material cases (e.g., glass beads, rough glass beads, and rough glass beads with cohesion), two gravity levels (g = 9.81 and 0.006 m/s<sup>2</sup>), and several wheel speeds (ω = 0.065-2.65 rad/s). Fig. 1 provides a snapshot of a typical simulation. We evaluate driving performance by comparing the travel distance of the wheel Δx as a function of its angular displacement Δθ. We also compare the static and dynamic sinkage of the wheel for the different simulation cases.</p><p> </p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.56c98b7f948267478582561/sdaolpUECMynit/2202CSPE&app=m&a=0&c=d7ee57bf8d9c41de975b217dd53b81b7&ct=x&pn=gnp.elif&d=1" alt="" width="589" height="217"></p><p>Fig. 1: Snapshots from a simulation where gravity is 9.81 m/s<sup>2