Digging and pushing lunar regolith: Classical soil mechanics and the forces needed for excavation and traction

There are many notional systems for excavating lunar regolith in NASA’s Exploration Vision. Quantitative system performance comparisons are scarce in the literature. This paper focuses on the required forces for excavation and traction as quantitative predictors of system feasibility. The rich history of terrestrial soil mechanics is adapted to extant lunar regolith parameters to calculate the forces. The soil mechanics literature often acknowledges the approximate results from the numerous excavation force models in use. An intent of this paper is to examine their variations in the lunar context. Six excavation models and one traction model are presented. The effects of soil properties are explored for each excavation model, for example, soil cohesion and friction, tool–soil adhesion, and soil density. Excavation operational parameters like digging depth, rake angle, gravity, and surcharge are examined. For the traction model, soil, operational, and machine design parameters are varied to probe choices. Mathematical anomalies are noted for several models. One conclusion is that the excavation models yield such disparate results that lunar-field testing is prudent. All the equations and graphs presented have been programmed for design use. Parameter ranges and units are included.     

Mechanics of cable shovel-formation interactions in surface mining excavations

The cable shovel excavator is used for primary production in many surface mining operations. A major problem in excavation is the variability of material diggability, resulting in varying mechanical energy input and stress loading of shovel dipper-and-tooth assembly across the working bench. This variability impacts the shovel dipper and tooth assembly in hard formations. In addition, the geometrical constraints within the working environment impose production limitations resulting in low production efficiency and high operating costs. A potential solution to the above problems is the deployment of an intelligent shovel excavation (ISE) technology, with real-time formation identification, recording and knowledge transmission capabilities. This paper advances the ISE technology by developing dynamic models of the cable shovel using the Newton-Euler techniques. The models include the main factors that influence shovel performance including the effect of both linear and angular motions of dipper handle and dipper. A path trajectory is modeled to demonstrate the dynamic velocity and acceleration profiles. Numerical examples show that the critical performance variables include geometrical and physical properties of the dipper and dipper handle, digging strategies and formation properties. The kinematic results show that the critical phase occurs between 1.5 and 2.0 s of a 3-s excavation cycle with occurrence of maximum kinematic effects. The dynamic results also show a similar trend with maximum dynamic effects between 1.5 and 2.0 s. The results also show that the maximum resistive force occurs at 1.625 s within the excavation cycle. At this point the maximum breakout force of the equipment is reached and any increase in the resistive load will require further fragmentation. The results provide appropriate information for excavation planning and execution. These models form the basis for developing dynamic shovel simulators for the ISE technology.     

Analysis of a resistance force for the locked-wheel of push-pull locomotion rovers using large subsidence

This paper provides a quantitative analysis of the resistance force of the locked-wheel for push-pull locomotion rovers using intentional sinkage. Our previous study has confirmed that push-pull locomotion using intentional subsidence at an initial position can contribute to improving the traveling performance. The key factor of this scheme is the resistance force of the locked-wheel. However, the resistance force at different sinkage conditions and wheel sizes (e.g., mass, width, and diameter) remains unclear, especially for the individual locked-wheel. The detailed investigation of this interaction can contribute to the accurate estimation of rover mobility. This paper, therefore, investigates the locked-wheel and soil interaction at different sinkage conditions experimentally, especially focusing on the intentional sinkage condition. Additionally, the resistance force is considered theoretically through the knowledge based on the soil flow patterns beneath the locked-wheel. The experimental results confirmed that the resistance force of the locked-wheel rose as the initial sinkage, wheel size, and weight increases. Furthermore, the theoretical calculation suggested the resistance force increased with a similar tendency of the experimental data.     

粘弹性岩体中支护圆形洞室施工过程的解析分析

地下洞室的开挖与支护是逐步的连续过程。对具有流变效应的粘弹性岩体,流变时效与施工效应发生耦合,变形与时间相关。针对深埋圆形洞室的施工,用半径时变函数模拟断面开挖过程。当岩体模拟为任一粘弹性材料时,将方程进行拉普拉斯变换求得位移通解,逆变换后代入边界条件确定待定函数,最终得到用洞周面力表达的围岩应力、位移统一解。区分开挖与支护时段,将半径时变函数、洞周面力不同表达式代入,利用支护后围岩与弹性支护接触条件建立关于支护力的Volterra积分方程。当岩石模拟为Boltzmann粘弹模型时,代入材料参数可求解积分方程得到支护力的确切表达,并进一步求得开挖过程及任意时刻支护后应力、位移分段解析表达式。表达式和算例分析表明:加支护后的径向位移增长呈指数形式变化且最终稳定于某一数值。最终洞型相同时,采用不同断面开挖速度且挖完立即支护时,开挖较快的情况位移变化较剧烈,而支护后最终稳定位移较小;但是,相应支护阶段产生的位移较大,支护力也较大。文中给出的方法可用于计算圆形洞室半径任意开挖并加支护后的应力、位移,适用于任一粘弹模型岩体的施工分析。     

Shape effects of wheel grousers on traction performance on sandy terrain

This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. Grouser wheels are locomotion gears that allow small and lightweight exploration rovers to traverse on the loose sand on extraterrestrial surfaces. Although various grouser shapes have been analyzed by some research groups, a more synthetic and direct comparison of possible grousers is required for practical applications. In this study, we developed a single wheel testbed and experimentally investigated the effects of four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) on the traction performance of linear movement on flat sand. The wheel slip, sinkage, traction and side force acting on the wheel axle, the wheel driving torque, and the efficiency of each wheel were examined. Thereafter, the effects on the lateral slope traversability of a small and lightweight four-wheeled rover with different grouser shapes were also examined. The traversability experiment demonstrated the vehicle mobility performance in order to contribute to the design optimization of rover systems. These experimental results and their comparisons suggested that, of the shapes studies herein, the slanted shape was the optimal grouser design for use in wheeled rovers on lunar and planetary soil.     

Analytical model of longitudinal tire traction in snow

An analytical model to estimate longitudinal traction of a tire in snow was developed and verified to have good predictability in comparison with measurements. Snow traction of a tire is composed of four kinds of forces in this model: braking force attributable to snow compression, shear force of snow in void (space between tread blocks), frictional force, and digging force (edge effect generated by sipes and blocks). The mechanical characteristics of snow were considered in the prediction of braking force and shear force, but were not considered in the prediction of other forces. The contribution of shear force of snow in void and the frictional force was large in static traction (traction just before a tire slips). On the other hand, the contributions of digging force and frictional force were large in situations involving high slip ratios.     

Prediction of tractive response for flexible wheels with application to planetary rovers

Planetary rovers are typically developed for high-risk missions. Locomotion requires traction to provide forward thrust on the ground. In soft soils, traction is limited by the mechanical properties of the soil, therefore lack of traction and wheel slippage cause difficulties during the operation of the rover. A possible solution to increase the traction force is to increase the size of the wheel-ground contact area. Flexible wheels provide this due to the deformation of the loaded wheel and hence this decreases the ground pressure on the soil surface. This study focuses on development of an analytical model which is an extension to the Bekker theory to predict the tractive performance for a metal flexible wheel by using the geometric model of the wheel in deformation. We demonstrate that the new analytical model closely matches experimental results. Hence this model can be used in the design of robust and optimal traction control algorithms for planetary rovers and for the design and the optimisation of flexible wheels.     

大跨度深埋黄土隧洞的开挖效应研究

本文研究了大跨度深埋黄土隧洞在其它条件不变的前提下, 全断面开挖时黄土的变形破坏规律和衬砌中内力的分布规律, 指出了它们存在本质区别的原因在于不同的开挖方式, 揭示了开挖的本质, 分析了内力合理分布的条件。     

On the treatment of soft soil parameter uncertainties in planetary rover mobility simulations

Nowadays soft soil–wheel contact models are widely used for predicting the mobility of rovers in off-road applications. However, most of the contact models used in computer simulations are based on semi-empirical laws for which soil parameters can be assessed only with large uncertainty. This lack of knowledge results in significant uncertainty on the rover position predictions. Applied to a planetary rover model, this paper illustrates probabilistic and non-probabilistic techniques for efficient treatment of soil parameter uncertainty for rover position predictions.     

SIMULATION OF THE INTERFACED STRUCTURAL COMPONENT BASED ON A MULTIPLE-TIME-SCALE ALGORITHM

A multiple-time-scale algorithm is developed to numerically simulate certain structural components in civil structures where local defects inevitably exist. Spatially, the size of local defects is relatively small compared to the structural scale. Different length scales should be adopted considering the efficiency and computational cost. In the principle of physics, different length scales are stipulated to correspond to different time scales. This concept lays the foundation of the framework for this multiple-time-scale algorithm. A multiple-time-scale algorithm, which involves different time steps for different regions, while enforcing the compatibility of displacement, force and stress fields across the interface, is proposed. Furthermore, a defected beam component is studied as a numerical sample. The structural component is divided into two regions： a coarse one and a fine one; a micro-defect exists in the fine region and the finite element sizes of the two regions are diametrically different. Correspondingly, two different time steps are adopted. With dynamic load applied to the beam, stress and displacement distribution of the defected beam is investigated from the global and local perspectives. The numerical sample reflects that the proposed algorithm is physically rational and computationally efficient in the potential damage simulation of civil structures.     

Predicting the performances of rigid rover wheels on extraterrestrial surfaces based on test results obtained on earth

With a growing number of nations interested in planetary exploration, research and development of extraterrestrial rovers have been intensified. The usual practice is to test the performances of rovers on soil simulants on earth, prior to their deployment to extraterrestrial bodies. It is noted that in the tests the soil simulant is subject to the earth gravity, while the terrain on the extraterrestrial surface is subject to a different gravity. Therefore, it is uncertain whether the rover/rover wheel would exhibit the same performance on the extraterrestrial surface as that obtained from tests conducted on earth. This paper describes a practical methodology that can be employed to predict the performances of rover wheels on extraterrestrial surfaces, based on test results obtained on earth. As rigid wheels are used in many extraterrestrial rovers, this study focuses on examining the effects of gravity on the sinkage and compaction resistance of rigid rover wheels. Predictions obtained using the methodology are shown to correlate reasonably well with test data.     

Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows

We present a pore network model to determine the permeability of shale gas matrix. Contrary to the conventional reservoirs, where permeability is only a function of topology and morphology of the pores, the permeability in shale depends on pressure as well. In addition to traditional viscous flow of Hagen–Poiseuille or Darcy type, we included slip flow and Knudsen diffusion in our network model to simulate gas flow in shale systems that contain pores on both micrometer and nanometer scales. This is the first network model in 3D that combines pores with nanometer and micrometer sizes with different flow physics mechanisms on both scales. Our results showed that estimated apparent permeability is significantly higher when the additional physical phenomena are considered, especially at lower pressures and in networks where nanopores dominate. We performed sensitivity analyses on three different network models with equal porosity; constant cross-section model (CCM), enlarged cross-section model (ECM) and shrunk length model (SLM). For the porous systems with variable pore sizes, the apparent permeability is highly dependent on the fraction of nanopores and the pores’ connectivity. The overall permeability in each model decreased as the fraction of nanopores increased.     

Systematic design and development of a flexible wheel for low mass lunar rover

Low mass compact rovers provide cost effective means to explore extra-terrestrial terrains. Use of flexible wheels in such applications where the wheel size is restricted, improves traction at reduced slip and sinkage. Design of a flexible wheel for a given mission is a challenging task requiring consideration of stiffness of rim and spokes, stress induced in the wheel, chassis movement during wheel rotation and the operating mode of the wheel. Also, accurate mathematical models are required to save design and development time and reduce the number of prototypes for selection. It is observed that most of the research papers deal with performance testing of flexible wheels and information on analytical formulation is scarce. Therefore, in the present work, a methodology has been formulated to systematically design a flexible wheel for a low mass lunar rover. The prototype performance is tested and compared with analytical estimates and reasons for difference are investigated. Paper contains details of design criteria, mathematical modelling, realisation of wheel prototype, test fixture and analysis test comparison. Authors believe that this work provides a useful aid to the designer to systematically design flexible wheels for low mass lunar rovers.     

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.

     

Development of a heavy demining machine

Heavy demining machines are intended for humanitarian demining of larger mine-suspected areas. Two combinations of tools were considered herein: a working tool with two-flails, and a design with one flail and one tiller, and analyze the function of these variants. Some time ago, it was unimaginable to combine a flail and tiller, mostly because power demands were too high. Nonetheless, by suitably allocating the power to the working tools a realistic option was designed, which should be feasible even for smaller sized machines. In order to destroy AP and AT mines, the primary role is given to a flail of high diameter, and a backup function to the tiller whose diameter is two times lower. The depth and rpm of the tiller may be controlled independently of the flail, which ensures that digging depth is good enough. With two independent and different tools the density of hammer strikes is immediately adaptable to the conditions of mine density at different depths. The required force of the hammer impulse is determined in order to be able to overcome the resistance from digging the soil resistance. Furthermore, the independence of tool adaptation together with remote control improves the speed of mine clearing. A high reliability of mine destruction is thereby ensured. The results of machine testing show high graded performance regarding mine-clearance quality.     

A comparative study on the control of friction-driven oscillations by time-delayed feedback

We perform a detailed study of two linear time-delayed feedback laws for control of friction-driven oscillations. Our comparative study also includes two different mathematical models for the nonlinear dependence of frictional forces on sliding speed. Linear analysis gives stability boundaries in the plane of control parameters. The equilibrium loses stability via a Hopf bifurcation. Dynamics near the bifurcation is studied using the method of multiple scales (MMS). The bifurcation is supercritical for one frictional force model and subcritical for the other, pointing to complications in the true nature of the bifurcation for friction-driven oscillations. The MMS results match very well with numerical solutions. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control effectiveness.     

气相爆轰波传播过程中的自点火效应

基于基元反应模型和单步反应模型,对直管道中H₂-air混合气体中爆轰波的传播过程进行了数值模拟,揭示了气相爆轰波传播过程中的自点火效应。利用数值模拟方法计算了不同爆轰模型的点火延迟时间,并得到了爆轰波三波点的传播过程以及所形成胞格结构的尺寸。结果表明,胞格宽度与点火延迟时间成正比;爆轰波诱导区内气体的点火延迟时间与三波点的运动周期基本一致。进一步对结果分析可知,爆轰波的自维持传播取决于点火延迟时间(表征化学反应的特征时间)和三波点的运动周期(表征流动的特征时间)的匹配;当二者相匹配时,经过前导激波压缩后形成的高温高压爆轰气体,在短时间内实现了自点火,同时释放出大量的能量推动了爆轰波的前进,即爆轰波的稳定自维持传播依靠其自点火机制。     

基于FLAC~(3D)的土钉内力分析

结合某基坑土钉支护实例,采用FLAC3D对土钉在开挖过程中的受力性能进行了模拟和分析。根据土钉支护结构的开挖、支护情况,研究了土钉的内力分布规律,得到了基坑在开挖过程中土钉的轴力、剪力变化规律。利用试验数据对模拟结果进行了验证,模拟结果与试测值基本吻合,研究成果近一步解释了钉土的相互作用机理。     

Analytical models and laboratory measurements of the soil-tool interaction force to push a narrow tool through JSC-1A lunar simulant and Ottawa sand at different cutting depths

Excavation equipment for developing NASA’s lunar outpost must be carefully designed to reduce launch cost, minimize operation cost, and enhance reliability. Excavation equipment requires knowledge of the stresses and strains in the equipment caused by the forces experienced during excavation. The types of excavation anticipated indicate that blade tools would move the most material. There are several analytical models available to predict forces from blade tools interacting with soil; however, it is not clear which if any, can predict lunar excavation forces precisely enough. Consequently, we measured the forces to push narrow (2.5-cm wide) square and round rods through a control material, Ottawa sand, and JSC-1A lunar mare regolith simulant at different cut depths in a controlled laboratory setting. The measurement results were compared with the forces predicted by eight analytical models. The Zeng, Luth and Wismer, and the Qinsen and Suren models fit the measurements best, considering that our study was limited to pushing stimulant and sand with small rods. The results show that depth of cut has a dramatic effect on the soil-tool interaction forces. Consequently, lunar missions should use a series of shallow cuts to reduce equipment size and power requirements.     

Computational nanoscale plasticity simulations using embedded atom potentials

In determining structure–property relations for plasticity at different size scales, it is desired to bridge concepts from the continuum to the atom. This raises many questions related to volume averaging, appropriate length scales of focus for an analysis, and postulates in continuum mechanics. In a preliminary effort to evaluate bridging size scales and continuum concepts with descritized phenomena, simple shear molecular dynamics simulations using the Embedded Atom Method (EAM) potentials were performed on single crystals. In order to help evaluate the continuum quantities related to the kinematic and thermodynamic force variables, finite element simulations (with different material models) and macroscale experiments were also performed. In this scoping study, various parametric effects on the stress state and kinematics have been quantified. The parameters included the following: crystal orientation (single slip, double slip, quadruple slip, octal slip), temperature (300 and 500 K), applied strain rate (10⁶–10¹² s⁻¹), specimen size (10 atoms to 2 μm), specimen aspect ratio size (1:8–8:1), deformation path (compression, tension, simple shear, and torsion), and material (nickel, aluminum, and copper). Although many conclusions can be drawn from this work, which has provided fodder for more studies, several major conclusions can be drawn.

• The yield stress is a function of a size scale parameter (volume-per-surface area) that was determined from atomistic simulations coupled with experiments. As the size decreases, the yield stress increases.

• Although the thermodynamic force (stress) varies at different size scales, the kinematics of deformation appears to be very similar based on atomistic simulations, finite element simulations, and physical experiments.

Atomistic simulations, that inherently include extreme strain rates and size scales, give results that agree with the phenomenological attributes of plasticity observed in macroscale experiments. These include strain rate dependence of the flow stress into a rate independent regime; approximate Schmid type behavior; size scale dependence on the flow stress, and kinematic behavior of large deformation plasticity.