This document summarizes the design of a flexible wheel for lunar rovers. Requirements included withstanding lunar environmental conditions while providing traction, control and comfort. A terramechanics approach was used to model wheel performance. A mass-spring-damper dynamic model was developed. Multiple concept designs were generated and converged. A prototype was built and tested, showing vertical stiffness higher than required, comparable damping to tires, and lateral stiffness needing improvement. Drawbar pull predictions matched experimental results, validating the model. Further optimization of geometric parameters will improve performance.

1. 12/20/2013
DESIGN OF A HIGH TRACTION FLEXIBLE
WHEEL FOR THE NEXT GENERATION OF
MANNED LUNAR ROVERS
7th Americas regional conference of the ISTVS
Louis Corriveau
November 4th 2013
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PRESENTATION OVERVIEW
 Context & Objectives
 Requirements Definition
 Mission constraints
 Terramechanics approach
 Dynamic model
 Concept Generation
 Methodology
 Convergence
 Prototype
 Preliminary Results
 Vertical stiffness and damping
 Lateral Stiffness
Credit : Duncan Jones, 2009
 Traction and wheel dynamics
 Concluding Remarks
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CONTEXT & OBJECTIVES
 Sustainable human activity further than low Earth orbit
 Manned lunar missions lasting more than a few months
 Lunar vehicles used daily
 Safe, reliable and durable
 Fast, controllable and long range
 Design of a flexible wheel
 Maximize drawbar pull,
control and comfort
 Minimize energy requirements
Credit : NASA
 How to obtain a deformation of at least 10% of the wheel diameter,
while having enough damping to dissipate the energy of deformation?
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REQUIREMENTS DEFINITION
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MISSION CONSTRAINTS
 Performance requirements
 Speed of up to 20 km/h on a flat terrain
 Mass of 250 kg per wheel (410 N on the moon)
 Wheel mass up to 5 kg
 The moon
 Environment
 Resistant to space radiation (up to 10 Ge/nucleon)
 Resistant to temperature cycling (-233 C, +123 C)
 Terrain
 Drive up a 27 slope, which is the mean slope of a crater
 Avoid high sinkage which can lead to mission abortion
 Soil
 Generate traction on soil with similar trafficability parameters as on the moon
 Resistant to lunar dust infiltration and augmented wear
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TERRAMECHANICS APPROACH
Optimal values
D = 1.25 m
b = 0.25 m
Pg = 2.5 kpa
Kv = 4100 N/m
Lunar trafficability
parameters
Wong, 2010
Drawbar pull
Torque
Sinkage
NWVPM
Wheel diameter, width
and ground pressure
Vertical stiffness
New wheel
parameters
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DYNAMIC MODEL
 Mass-spring-damper model
 Mass is predefined from the mission requirements
 Spring stiffness is known from the terramechanics analysis
 Damper coefficient is unknown
X
m
 Load case
 Wheel maximum deformation of 15 cm
 Comfort
 Minimize the acceleration of the mass
 Control
K
C
 Minimize the force trying to lift
the vehicle off the ground
Damping coefficient
Optimal value : 2025 Ns/m
Limit value : 500 Ns/m
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CONCEPT GENERATION
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CONCEPT CONVERGENCE
 Materials
1
Requirements
2
3
4
 Spring
Concept
 Damper
 Fully metallic
 Cantilever Beams
 Active and passive
 Composites
 Cables
 Inertial
 Strips in bending
 Magnetic
 Piezoelectric
 Friction
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PROTOTYPE
 3D model
 Detailed design
 Mass estimation
 Titanium and aluminum construction
 Manufacturing drawings
 Finite element model of the spring part
 Equivalent beam model based on experimental tests
 Quickly determine a design point for the first prototype
 First prototype
 All stainless steel
 Find major design flaws
 Ascertain the hypothesis
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PRELIMINARY RESULTS
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MTS SHOCK DYNAMOMETER
 Most critical aspects of the design
 Vertical stiffness
 Vertical damping
 Wheel compression
 From 50 to 100 mm
 3 cycles at each frequency
 [0.05 0.1 0.5 1 2 3 4 5 6]Hz
 Force, displacement and velocity
were recorded
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VERTICAL STIFFNESS
1.6
 Almost constant over the
 Energy dissipated, i.e. hysteresis
 Stiffness 5 times higher
than the requirements
 FEM model is conservative
 Easier to reach a lower stiffness
than the opposite
 Mass will decrease along
with stiffness
0.05 Hz
0.1 Hz
0.5 Hz
1 Hz
2 Hz
3 Hz
4 Hz
5 Hz
6 Hz
1.4
1.2
Force [kN]
spectrum analyzed
 Gap between the compression
and rebound curves
1
0.8
0.6
0.4
0.2
0
0
10
20
30
Displacement [mm]
40
Average stiffness
Prototype : 20 000 N/m
Rubber tire : 60 000 N/m
Requirement : 4100 N/m 2 0 1 3 - 1 2 - 2 0
50
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VERTICAL DAMPING
 Log variation over the spectrum
 Used to characterize the
behavior of rubber tires
 Order of magnitude in line
with a rubber tire
 Damping coefficient is slightly less than
the requirement
 Need to identify the parameters
affecting the damping coefficient
10000
Damping Coefficient
[Ns/m]
analyzed
 Equivalent damping found using
the Gehman model
1000
100
10
1
0.01
0.1
1
Fréquence [Hz]
Equivalent damping
Prototype : 339 Ns/m
Rubber tire : 270 Ns/m
Requirements : 500-20000 1Ns/m
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MTS MULTIAXIAL LOAD FRAME
 Important aspect of the design
 Lateral stiffness
 Constant vertical load
 [230 430 630 830 1030 1530 2030]N
 Lateral deformation
 From 0 to 50 mm
 The forces and displacements
were recorded
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LATERAL STIFFNESS
 Why is lateral stiffness important?
 Keeps the vehicle parallel to the ground while traversing a slope
 Maintains control of the vehicle while turning and in emergency manoeuvers
 Skid steered vehicles
Lateral stiffness
[N/mm]
 Increases with vertical load
At a vertical load of 2000 N
Prototype : 15.5 N/mm
Rubber tire : 33 N/mm
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14
12
10
8
0
500
1000
1500
Vertical load [N]
2000
2500
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SINGLE-WHEEL TEST BENCH
 Verify the performance
 Drawbar pull
 Objectives
 Confirm the dynamic behavior
 Validate the terramechanics model
(performance predictions)
 Constant speeds
 Wheel speed
 Soil bin speed
 Fixed slip ratio of 30%
 Constant vertical load
 508 N
Drawbar Pull
Terramechanics : 324 N
Experiment : 319 N
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CONCLUDING REMARKS
 First prototype is encouraging
 Vertical stiffness is higher than the requirement
 Vertical damping is comparable to an ATV rubber tire, but is lower than requirement
 Lateral stiffness needs to be increased
 Terramechanics correlation with the experimental results is accurately validated
 Fractional factorial design
 Experimental model of the design
 Influence of chosen geometrical parameters
 Optimization theory to determine which combination of parameters give:
 Maximum drawbar pull
 Necessary admissible torque
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QUESTIONS
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