CED RClemson Engineering Design Applications and Research

Timothy Reeves: Presenter

Marisa Orr, Sherrill Biggers

Evaluation of the Holistic Method to Size a 3-D Wheel/Soil Model

2 of 202011.09.13

Tire Society11189 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

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3 of 202011.09.13

Tire Society11189 Holistic Method Overview

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4 of 202011.09.13

Tire Society11189 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

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5 of 202011.09.13

Tire Society11189 Example of Holistic Method

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Initialization 1st Expansion

2nd Expansion Reduction

6 of 202011.09.13

Tire Society11189 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

tcreeve@clemson.edu

7 of 202011.09.13

Tire Society11189 Simulation Details

Half of a symmetric system is modeled Simulation steps:

– Gravitational loading 9.81 m/s2 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

tcreeve@clemson.edu

8 of 202011.09.13

Tire Society11189 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

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9 of 202011.09.13

Tire Society11189 Key Dimensions

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10 of 202011.09.13

Tire Society11189 Visual Example (Reference Case)

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11 of 202011.09.13

Tire Society11189 Effect of Wheel Load

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60% Load

166% Load

12 of 202011.09.13

Tire Society11189 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

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13 of 202011.09.13

Tire Society11189 Effect of Wheel Size

Diameter and Width

Scaled proportionally

Equal Loads

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50% SizeCoarse Mesh

Fine Mesh

80% Size

50% Size

2x Size

14 of 202011.09.13

Tire Society11189 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

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15 of 202011.09.13

Tire Society11189 Effect of Wheel Proportion

Constant Diameter

Equal Loads

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166% width

60% width

33% width

16 of 202011.09.13

Tire Society11189 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)

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17 of 202011.09.13

Tire Society11189 Effect of Soil Type

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Sand

GRC-1

Clay

18 of 202011.09.13

Tire Society11189 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

tcreeve@clemson.edu

19 of 202011.09.13

Tire Society11189 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?

tcreeve@clemson.edu

20 of 202011.09.13

Tire Society11189

Thank You!

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