Simple Terramechanics Models and their Demonstration in the Next Generation NATO Reference Mobility Model

In 2014, a NATO Applied Vehicle Technology (AVT) Exploratory Team 148 (ET-148) was formed to explore the development of an improved Next-Generation NATO Reference Mobility Model (NG-NRMM)[1]. A development path forward was identified and initiated in a subsequent NATO research task group (AVT-248) to implement ET-148 recommendations. One key area for improvement was the vehicle-terrain interaction (Terramechanics) models defining important performance metrics for off-road performance in differing soils, and environmental conditions. The near term implementation focuses on existing “Simple” Terramechanics models as a practical improvement to the incumbent NRMM Cone Index (CI) empirically based method, without requiring the computational power of the large scale complex discrete element model (DEM) methods that are the targeted long term solution. Practical approaches and limitations to the implementation of these existing Simple Terramechanics models in 3D vehicle models are described along with parameter identification approaches and their limitations. INTRODUCTION The ultimate demonstration of a NG-NRMM simulation capability under the broad scope of it’s requirements, is depicted in Figure 1 wherein terrain mechanical properties are one of many overlaid geographically distributed features that affect vehicle mobility. Based on the terrain properties, mobility will be computed and expressed and displayed as a map of GO/NOGO capability and maximum Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Simple Terramechanics Models and their Demonstration in the Next Generation NATO Reference Mobility Model, McCullough, et al. UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited. #29303 Page 2 of 13 speeds attainable across a given region of interest. Soft soil effects are one of the primary attributes affecting vehicle mobility and are a foundational capability required in both the current NRMM and the NG-NRMM. The cone penetrometer and it’s CI metric holds a practical and intuitive appeal for linking terrain strength to vehicle performance. Unfortunately, a cone penetrometer is not a very close physical analog to vehicle running gear bearing and tractive load interactions with soil, and it is dimensionally insufficient to characterize the independent development of tractive and bearing loads as well as the properties and processes involved in the development of soil strength. The dual development path focusing on existing models under the title “Simple Terramechanics” and the longer term higher fidelity objective approach entitled “Complex Terramechanics” allows for theoretical and numerical approaches that are still under development and which overcome theoretical and practical limitations of existing Terramechanics models using fully 3D continuum failure and flow models Figure 1: Full Featured NG-NRMM Simulation Begins with GIS based data, predicts mobility and maps it back onto the terrain as an additional GIS parameters[2] Figure 2 depicts the spectrum of Terramechanics models beginning with the incumbent NRMM Cone Index (CI) empirically based method and ranges up to the Complex Terramechanics models, with Simple Terramechanics models providing a practical middle ground compromise solution between the limitations and challenges of those two extremes. Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Simple Terramechanics Models and their Demonstration in the Next Generation NATO Reference Mobility Model, McCullough, et al. UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited. #29303 Page 3 of 13 Figure 2: Replacing the Cone Index (CI) methods used in the current NRMM, simple Terramechanics models bring the full 3D mechanics of vehicles together with existing Terramechanics to provide a means for calculating critical mobility metrics on soft soil that are foundational components in the higher level mobility aggregated predictions of feasible trafficability (GO/NOGO regions) and maximum speed attainable. SIMPLE TERRAMECHANICS Pressure-sinkage testing using bearing stress platens, combined with grouser enhanced shear rings for tractive stress (both assumed to be geometric analogs of the vehicle running gear) are the most widely used improvement to the CI methods for characterizing soil strength [3,4]. Dimensionally, there are at least 5 independent parameters determined by the calibrating experiments. For bearing pressure, these are commonly represented as “p-z” equations where p is the bearing pressure under the platen that is pushed into the soil, z is the platen sinkage, and k and n are the best fit parameters in the equations that have taken several forms over the years. Originally Bernstein [3] proposed the following power law form of the plastic limit pressure: p = kzn Bekker added the effects of a primary running gear dimension, b, typically the width: where kc and kφ are intended to capture the cohesive and frictional soil strength effects. Wong [5] developed the experimental data reduction methodology for parameter identification and the elasto-plastic model of repetitive unload re-load cycles augmenting the Bekker model (see regime D in Figure 3). In combination, these are known as the Bekker-Wong model and must include the constants associated with the slope of the elastic unload/load in regime D. kunload = k0 + Aunload zunload where k0 and Aunload are developed from multiple repetitive load experiments. Later, Reece proposed the Bekker-Wong-Reece form pp = � kkcc bb + kkφφ� zznn Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Simple Terramechanics Models and their Demonstration in the Next Generation NATO Reference Mobility Model, McCullough, et al. UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited. #29303 Page 4 of 13 [6] of the plastic limiting bearing envelope: where the coefficients have slightly different units and meaning with the potential to account for geometric scale more effectively [6]. When combined with a shear response model developed from measurements using an annular ring shear device [7], they form the basis of most modern Simple Terramechanics models. Analytically, shear stress-shear displacement, “τ-j”, equations were proposed and demonstrated by Janosi and Hanamoto[7] in the following simplest form: τ = [c + p tan φ ](1 – e(-j/k)) Where τ is shear stress, j is shear slip, k is a exponential function constant, c is cohesion and φ is soil internal friction angle. They have been validated at the vehicle level for both tracked vehicles [5] and wheeled vehicles [ 7], and can take other more complex mathematical forms when necessary. For deformable soils, a common analytical construct of all Simple Terramechanics models must be some means of tracking permanent deformation and modifying the soil response due to the effects of compaction and flow as well as sheared soil layers (i.e., slip-sinkage). This typically requires a discretization of the soil substrate into cells for which the sinkage and shear states are numerically computed and tracked. This general construct has been described in [8] and [9] in the context of Vehicle Terrain Interface (VTI) real-time models for simulators, but is commonly known in recent engineering analysis implementations as a “height field” local terrain model [10], discussed later and shown in Figure 4. Figure 3: Data from [8] shows that the Bekker-Wong model includes procedures for parameter identification from test data and, most importantly, recognition of the elastic unload/reload portions of the response, D and D’[5,13] . Regime A is sinkage measurement error offset to the onset of actual soil loading; Regime B is the compacting of loose soil so the soil is strengthening and n>1; The transition to Regime C is an inflection point with changing exponent, toward n<1 in regime C, which is soil bearing failure controlled by the growth of shear slip line fields in the far field. Thus the model parameter identification is dependent upon peak pressure regime in the specific vehicle application for which it will be used. Regime A, sinkage measurement error Strengthening Regime B n>1 Failing regime C; n<1