Timothy Reeves: Presenter Marisa Orr, Sherrill Biggers Evaluation of the Holistic Method to Size a 3-D Wheel/Soil Model

2 of Tire Society Preliminary Discussion Interaction between a deformable wheel and a soft terrain – Subject of research since the 1950’s – Analytical and empirical models attempted – Computational models applied, mostly 2-D – 3-D computational models applied, typically expensive Holistic Method to Size a 3-D wheel/soil model – Recently proposed by Orr et al. (2011) – Focuses on reducing computational requirements of soil – Involves simultaneous adjustment of soil dimensions – Requires fewer simulations than adjusting separately Evaluation of Holistic Method – Holistic Method was developed and proposed for a specific system – Current work seeks to determine its general applicability

3 of Tire Society Holistic Method Overview

4 of Tire Society Theory Step 1 (Initialization) provides a starting point Step 2 (Expansion) seeks to acquire a soil bed large enough that no significant soil displacement occurs near the boundaries – Significant displacement limit is a small value defined arbitrarily; in the current work, 0.1 mm – ‘Near’ is described by a distance called the characteristic length, defined arbitrarily; in the current work, ½ wheel diameter – Step 2 may be skipped or may need to be repeated several times, depending on the system and the initial size – Final iteration is assumed to represent an infinite soil bed Step 3 (Reduction) removes material such that the remaining soil just includes all significant displacement – Final size always at least one characteristic length smaller in every direction than the last iteration of Step 2

5 of Tire Society Example of Holistic Method Initialization 1 st Expansion 2 nd Expansion Reduction

6 of Tire Society Evaluation Technique The first priority of the Holistic Method is to provide a large enough soil bed to accurately model the system – The method is thus primarily evaluated based on its accuracy – The method is evaluated by the effect that changes in boundary conditions of the soil have on the motion of the wheel The final soil size is obtained through the Holistic Method The final size is simulated with two different sets of boundary conditions on the soil, pinned nodes and frictionless sliding nodes Wheel displacement values are used as metrics for comparison Reduction of soil size for computational efficiency is pursued within the requirement for accuracy – The method is informally evaluated for its effectiveness at size reduction by visual inspection – Cases of appropriate reduction will have significant displacement near all boundaries in the final size model

7 of Tire Society Simulation Details Half of a symmetric system is modeled Simulation steps: – Gravitational loading 9.81 m/s 2 introduced over 12 seconds (Wheel is held off the soil by an upward force) – Wheel coming to rest on soil surface Upward force supporting wheel is removed over 12 seconds – Rotation of rigid wheel Wheel angular velocity about its hub is introduced over 5 seconds and held constant for 10 more seconds Magnitude is determined by the equivalent linear velocity that would occur if the rigid wheel were rolling on a rigid surface without slip Same equivalent linear velocity for all cases; angular velocity varies by wheel diameter Each change is introduced into the system smoothly

8 of Tire Society Results: General System characteristics examined – Wheel load – Wheel size – Wheel proportion (diameter/width) – Soil type Effect of changes – Did Holistic Method provide appropriate soil size? Pinned node BC’s compared to sliding BC’s – How was final soil size affected? Soil dimensions compared to dimensions in reference case – How was wheel tractive performance affected? Wheel displacements compared to displacements in reference case

9 of Tire Society Key Dimensions

10 of Tire Society Visual Example (Reference Case)

11 of Tire Society Effect of Wheel Load 60% Load 166% Load

12 of Tire Society Wheel Load: Observations Wheels sink deeper with increasing load Wheels travel shorter distance with increasing load – Probably attributable to sinking – Note: All wheels in previous slide rotated through the same angle; no consideration given to effort required Wheels influence wider range of soil with increasing load

13 of Tire Society Effect of Wheel Size Diameter and Width Scaled proportionally Equal Loads 50% Size Coarse Mesh Fine Mesh 80% Size 50% Size 2x Size

14 of Tire Society Mesh Refinement In Case 3a, previous slide, agreement was not found between pinned and sliding BC’s – I.E. the Holistic Method did not generate appropriate soil size according to the established criteria Therefore Case 3b was simulated, having a finer mesh – (20mm) 3 elements vs. (28mm) 3 – This time the different BC’s produced consistent results Holistic Method failure to produce consistent results may indicate insufficient mesh – From the figure it is clear that the finer mesh provides a much smoother matching of the soil to the curved wheel surface

15 of Tire Society Effect of Wheel Proportion Constant Diameter Equal Loads 166% width 60% width 33% width

16 of Tire Society Wheel Proportion: Observations Narrower wheels sink deeper (same load) Narrower wheels do not travel as far – Again, kinematics only; effort not considered Narrower wheels displace adjacent soil higher – 2-D soil model increasingly inadequate as wheel becomes narrow Mesh refinement was not required in Case 8 – Deep sinking (comparable to Case 3, shown earlier) – Larger diameter than in Case 3: more soil elements along wheel contact surface resulting in smoother curve (i.e. mesh is adequate)

17 of Tire Society Effect of Soil Type Sand GRC-1 Clay

18 of Tire Society Soil Type: Observations Loose sand – Deeper soil bed required – Deeper sinking (Mesh adequate) Clay – Wider soil bed required – Sharp, distinct ridge formed beside wheel Reference case has greatest travel – GRC-1 is a sand but has unusually high strength due to irregular, interlocking grains

19 of Tire Society Conclusions and Future Work Holistic Method produced appropriate soil bed size for all cases except where mesh refinement was required – Need for mesh refinement may come about due to changes in loading conditions or wheel dimensions that result in extreme soil deformations Modification to Holistic Method was introduced – Pre-expansion-step reduction of soil length possible if the initial step reveals a much lower horizontal wheel travel than expected Future Research Question: – Can initialization and expansion steps of the Holistic Method be performed using a coarse mesh and then mesh refinement study done using reduced (final) soil size?

20 of Tire Society Thank You!