UNIVERSITY OF OKLAHOMA

GRADUATE COLLEGE

DESIGN AND ANALYSIS

OF

COMPLIANT WHEELS FOR A PLANETARY ROVER

A THESIS

SUBMITTED TO THE GRADUATE FACULTY

in partial fulfillment of the requirements for the

Degree of

MASTER OF SCIENCE

By

BRANDON MILLS Norman, Oklahoma 2007

c Copyright by BRANDON MILLS 2007 ! All Rights Reserved. Acknowledgements

I would like to my advisor, Dr. Miller, for his patience, insight, and guidance in the completion of this research. I also offer sincere appreciation to my other committee members, Dr. Baldwin and Dr. Chang. My thanks go to these three, not only for agreeing to serve on my committee, but for all that I learned in their classes as a student. I would also like to give thanks to the rest of the faculty and staff within the School of Aerospace and Mechanical Engineering. I could not have completed my projects and my classwork without these individuals. Thanks especially to machine shop director Billy Mays. I also thank my colleagues, Dan, Tim, and Matt, for their continual encourage- ment and advice. Sincere appreciation goes to Matt, who was always available to give assistance, and without whose help I would still be in the machine shop trying to learn how to use the machines. I have to thank my friends for ensuring that I didn’t miss out on “the college experience.” Finally, I would like to thank my parents, and the rest of my family, without whose love and endless support I would not be here today.

iv Contents

List Of Tables vii

List Of Figures viii

1 Introduction 1 1.1 Existing Rover and Wheel Designs ...... 1 1.1.1 Rovers on Other Planets ...... 1 1.1.2 Rover Prototypes ...... 11 1.2 Compliance ...... 18 1.3 Design Goals ...... 18 1.4 Problem Statement and Organization of Thesis ...... 20

2 Design Constraints 22 2.1 Fall Height ...... 22 2.2 Spaceworthiness ...... 24 2.3 Rolling Efficiency ...... 27

3 Flexure Wheel 31 3.1 Design ...... 31 3.2 Analysis ...... 33 3.3 Design Variations ...... 34

4 Tweel 37 4.1 Spring Rate ...... 38 4.2 Impact Force ...... 40

5 Tension-Spring Wheel 42 5.1 Design Considerations ...... 43 5.2 Computer Terrain Simulation ...... 50 5.3 Spun Wheel ...... 53 5.4 Metal Spinning ...... 55 5.5 Spun Wheel Design ...... 58 5.6 Wheel Fabrication ...... 60

v 6 Results and Conclusions 65 6.1 Flexure Wheel Results ...... 65 6.2 Accelerometer Testing ...... 67 6.3 Tweel Field Testing ...... 72 6.4 Tension-Spring Wheel Testing ...... 75 6.5 Tweel Design Changes ...... 79 6.6 Tension-Spring Wheel Design Changes ...... 81 6.7 Conclusions ...... 84

Reference List 86

Appendix A 90 Data Calculations ...... 90

Appendix B 91 Mechanical Drawings ...... 91

vi List Of Tables

2.1 Rolling resistance for various materials ...... 29

3.1 Flexure dimensions and mass for five wheel designs ...... 35 3.2 Forces, stresses, and displacements for falling flexure wheel ...... 36

5.1 Spring specifications and power losses ...... 48 5.2 Selected alloys and their elongations ...... 56

6.1 Voltages, currents, and power used by rigid wheel and spring wheel . 78 6.2 Theoretical and actual mass of tension-spring wheel components . . . 83 6.3 Pro/con table for Tweel and tension-spring wheel ...... 85 6.4 Comparison of three wheel types ...... 86

vii List Of Figures

1.1 Lunokhod ...... 3 1.2 Detail of Lunokhod’s wheels ...... 3 1.3 Lunar Roving Vehicle ...... 5 1.4 Detail of Lunar Roving Vehicle wheel ...... 5 1.5 Sojourner rover flown in Mars Pathfinder mission ...... 7 1.6 Sojourner wheels, prototype and final design ...... 9 1.7 Artist rendering of MER rover ...... 10 1.8 MER wheels ...... 11 1.9 Early wheel designs for University of Oklahoma rovers ...... 13 1.10 Carbon fiber wheel mounted on SR-II ...... 15 1.11 Carbon fiber wheel delaminating in extreme heat ...... 16 1.12 High-efficiency wheel ...... 17

2.1 Free-body diagram of wheel rolling across surface ...... 29

3.1 Five-spoke flexure wheel ...... 32 3.2 Von Mises stress in five-spoke flexure wheel under 650 N load . . . . . 34 3.3 Von Mises stress in eight-spoke flexure wheel under 800 N load . . . . 36

4.1 Michelin Tweel ...... 37 4.2 Tweel in materials testing machine ...... 40 4.3 Force vs. displacement for Tweel ...... 40

5.1 Cross-section of wheel with all springs in one plane ...... 44 5.2 Cross-section and free-body diagram of wheel ...... 44 5.3 Testing to find rolling friction of simple wheel model ...... 48 5.4 Simulated wheel rotation driving across terrain ...... 52 5.5 Original design for tension-spring wheel ...... 53 5.6 Diagram of lathe setup for spinning ...... 57 5.7 Spun wheel, exploded view ...... 58 5.8 Maximum deflection of tire section under loading ...... 59 5.9 Spinning setup used for first wheel ...... 61 5.10 Product of second attempt at spinning ...... 62 5.11 Rippled wheels from unsuccessful attempts at spinning ...... 64

viii 6.1 Acceleration during impact from a 5-cm fall with rigid wheel . . . . . 68 6.2 Acceleration during impact from a 5-cm fall with Tweels ...... 70 6.3 Acceleration during impact from a 5-cm fall with tension-spring wheels 71 6.4 Computer model of tweel and hub assembly, exploded view ...... 73 6.5 Field test of SR-II with Tweels ...... 74 6.6 Completed tension-spring wheel ...... 75 6.7 SR-II with tension-spring wheels ...... 76

ix Abstract

Robotic rovers are the foundation for the exploration of planetary bodies. These rovers must be designed to endure long durations in harsh environments. The wheels are a key system on planetary rovers. A rover wheel must meet many requirements: it must be compliant, in order to reduce the stress on the rover’s drivetrain components; it should be made of spaceworthy materials; it needs to provide high traction to traverse soil, sand, and rock; it must be robust; the wheel should have as little rolling friction as possible; and its mass should be minimal.

This thesis describes the design and analysis of non-pneumatic prototype wheels for a Mars rover, Solar Rover II (SR-II). Two possible final designs are presented: a

Tweel-style design, and a tension-spring wheel design. The Tweel uses thin rubber spokes to absorb energy, and increases the allowable fall height of the rover from 10 cm to 15 cm. The spring wheel design employs an arrangement tension springs to absorb impact forces. When mounted on SR-II, this design allows the rover to safely survive a fall from 18 cm. The total mass of the wheel is 657 g. The increase in

x power consumption for the rover is only about 1.5 W for various conditions, including straight-line traverses and skid-steering maneuvers.

xi Chapter 1

Introduction

Rovers are used to explore harsh space environments where it is too dangerous or too costly to send humans. Unmanned landers can be sent to very precise locations, but most missions can benefit collecting data from multiple sites. The additional freedom and mobility of a rover can be a great advantage.

1.1 Existing Rover and Wheel Designs

This section will highlight select rover designs and their mission accomplishments.

Technical specifications for the rovers will be presented, and any relevant informa- tion regarding mobility system, specifically, the rovers’ wheel designs, will also be introduced.

1.1.1 Rovers on Other Planets

The first rover to traverse an extraterrestrial body was Lunokhod 1. It landed on the moon on November 17, 1970, carried by the Luna 17 spacecraft. Built by the

Soviet Union, the rover consisted of a sealed tub-like body and eight, independently- powered wheels. The rover stood 1.35 m high, had a length of 2.30 m, a wheelbase of

1 1.70 m, and a track of 1.60 m. Its mass was a hefty 756 kg. Lunokhod 1 operated on the Moon for almost 11 lunar days1, in which it traveled 10.54 km, transmitted more than 20,000 television pictures, recorded over 200 panoramic photographs, and con- ducted more than 500 soil mechanics tests. The rover was equipped with cone-shaped antenna, a highly-directional helical antenna, one standard television camera, three panoramic television cameras, an x-ray spectrometer, an x-ray telescope, cosmic-ray detectors, and a soil testing apparatus. The rover was teleoperated by a team of five drivers [20, 23].

Lunokhod 2 followed in 1973, on the Luna 21 mission. This rover weighed 840 kg, 84 kg more than its predecessor. Lunokhod 2 was very similar to Lunokhod 1, and covered 37 km in four lunar days. It also took 86 panoramic images and 80,000 television images, and conducted mechanical tests of the lunar soil as Lunokhod 1 did.

The main tub-shaped compartment of the Lunokhod rovers was sealed with a convex lid, and pressurized with nitrogen to one atmosphere. The internal tem- perature of the nitrogen was kept between 0o and 40oC by the radioactive isotope

Polonium-210. All electronics were housed in this body, and this design allowed

1A lunar day is about equal to one month on Earth, or 29.5 Earth days

2 Figure 1.1: Lunokhod (image reproduced from NASA)

Soviet engineers to avoid having to design electronics which could withstand the extreme temperatures and low pressure of space. Solar arrays charged Lunokhod’s batteries during the lunar day, and the rovers would hibernate during the long, cold nights [17].

Figure 1.2: Detail of Lunokhod’s wheels (image reproduced from [17])

Each of the Lunokhod rovers’ wheels had its own suspension, motor, and brake, and any wheel could be disconnected from its motor in the case of a motor failure.

3 The rovers had two forward speeds, 0.9 - 1 km/h and 1.8 - 2 km/h. They used differential steering and could skid steer for zero-radius turning. Lunokhod could climb obstacles 40 cm in height and cross craters of width 60 cm. Each wheel on a Lunokhod rover consisted of a three titanium hoops, the largest of which was the centermost hoop, so that the tire would have a curved profile. Thin steel spokes connected these hoops to an aluminum hub. The hoops, or ribs, were covered with a lightweight steel mesh tire, and thin titanium grousers were riveted through the mesh to the ribs. These wheels had a diameter of 51 cm and a width of 20 cm.

Figure 1.2 shows a detailed view of the wheels [6, 32].

In 1971, the Apollo 15 mission landed on the moon. In this mission, and also in the Apollo 16 and 17 missions, a manned Lunar Roving Vehicle (LRV) was used to traverse and explore the surface of the moon. Although not an unmanned rover, the LRV made significant contributions to the achievements of the space program by allowing the crew to travel about four times the distance traveled on missions previous to the LRV.

Boeing was contracted to design and build the LRV, although the mobility system was actually designed, fabricated, and tested by General Motors. The final cost of the LRV was $38 million. Measuring 124 in (3.15 m) in length, the LRV was designed

4 Figure 1.3: Lunar Roving Vehicle (image reproduced from NASA) to be capable of climbing 12-in (30.5-cm) high obstacles and crossing craters up to

28 in (71 cm) in diameter. It could carry a payload of 455 kg on Earth, although its total mass was only around 200 kg. While driving on the moon, the astronauts were able to drive at an average speed of about 8 to 10 km/h, even over rough terrain and up slopes.

Figure 1.4: Detail of Lunar Roving Vehicle wheel (image reproduced from NASA)

5 The LRV had wheels made of zinc-coated piano wire woven into a torus shape with a spun aluminum hub. The tire section was 81.8 cm in diameter and had a width of 23 cm. The wire used was 0.083-cm-diameter stranded steel. Titanium grousers were riveted onto the exterior of the tires in a chevron pattern to keep the wheels from sinking into the soft lunar soil. These grousers covered 50% of the area of the tire. Inside the piano wire mesh was a titanium bump stop for support during high-impact loading, to prevent damage to the hub. Each wheel weighed 5.4 kg

[15, 16].

On December 4, 1996, the Mars Pathfinder was launched. The mission carried a variety of instruments, including a lander carrying Sojourner, a six-wheeled rover.

On July 4, 1997, the tetrahedral-shaped lander, cushioned by a surrounding layer of airbags, landed on Mars. After about fifteen bounces, it rolled to a stop. Shortly thereafter, the petals of the lander opened, and the following day, Sojourner crawled off the lander and became the first successful rover on Mars2 [25].

Sojourner was considered a microrover, being much smaller than most previous rover designs. It was only 63 cm in length, 48 cm wide, and 28 cm tall (without

2There were two Soviet rovers, Mars 2 and Mars 3, which reached the surface of Mars in Novem- ber and December 1971, but both rovers failed before being able to drive on Mars. The Mars 2 lander crashed on the surface, destroying its rover, and the Mars 3 lander failed after 15 seconds of operation, rendering it unable to deploy its rover.

6 antennae). The rover used a rocker-bogie suspension system, a system invented by

Donald Bickler, which has been proven capable of climbing obstacles up to 50% larger than the diameter of the wheels [4]. Sojourner had a ground clearance of 13 cm and could climb obstacles as high as 20 cm. The front and rear wheels were independently steerable, allowing the rover to turn in place without skid steering.

Sojourner’s maximum speed was only one cm/s. The mass of the rover was around

11 kg [28, 29].

Figure 1.5: Sojourner rover flown in Mars Pathfinder mission (image reproduced from NASA)

Sojourner was equipped with the following scientific instrumentation: an Alpha

Proton X-Ray Spectrometer, a black-and-white stereo camera, a color camera, a wheel abrasion experiment, and a material adherence experiment. The rover had a

7 laser-ranging hazard avoidance system. The rover was controlled by an operations team on Earth, who gave it waypoints. The rover then used its guidance system to navigate those waypoints and collect scientific data. The rover was intended to survive for seven sols, but it actually lasted 83 sols3. During this time, it traveled about 100 m, conducted 16 chemical analyses of rock and soil, and 550 camera images

[22].

The wheels for Sojourner were made of stainless steel. They were 13 cm in di- ameter. The contact surfaces of the wheels were covered with sharp grousers formed from 0.127-millimeter-thick stainless steel. These grousers had a height of 10 mm, and they significantly increased the wheels’ traction, particularly while climbing ob- stacles. Having a width of 79 mm, these wheels were designed to only have a ground pressure of 1.65 kPa. This low figure allows the wheels to perform well in very soft soil and sand [3]. Figure 1.6 shows a prototype wheel for Sojourner aside the style of wheel that was flown on the mission.

On January 4, 2004, Spirit landed on Mars, and 20 days later, Opportunity landed on the opposite side of Mars. Built by NASA, Spirit and Opportunity are twin rovers that have logged tens of kilometers exploring the surface of Mars. These

3“Sol” is the name given to a solar Martian day. A sol is equivalent to 24 hours, 39 minutes, and 35 seconds.

8 Figure 1.6: Sojourner wheels, prototype and final design (image reproduced from NASA) two rovers comprise the Mars Exploration Rover (MER) program. The scientific objective of the MER mission is to “search for and characterize a wide range of rocks and soils that hold clues to past water activity on Mars. The spacecraft are targeted to sites on opposite sides of Mars that appear to have been affected by liquid water in the past.” The mission was scheduled to last 90 sols, but both rovers have surpassed their expected operational lifetime, and the rovers are scheduled to continue exploring through September 2007 [18].

The MER rovers use a rocker-bogie suspension like that of Sojourner. The mass of each of the rovers is 185 kg. They are 1.6 m long, 2.3 m wide, and 1.5 m tall, making these rovers considerably larger than Sojourner, but still not nearly as heavy as the Lunokhod rovers. The rovers have a top speed of 5 cm/s, but when driving

9 Figure 1.7: Artist rendering of MER rover (image reproduced from NASA) through obstacles, Spirit and Opportunity stop every 10 seconds to analyze their surroundings, and only attain an average pace of 1 cm/s.

A panoramic camera, a navigation camera, and a thermal emission spectrometer are mounted on the rovers’ camera mast. There are a total of nine cameras on each rover. Scientific instrumentation carried on the rovers’ arm include a spectrometer, an alpha particle X-ray spectrometer, a microscopic imager, a rock abrasion tool, and magnets to collect ferrous minerals. The rovers are also designed to hold five wheels steady while one digs a trench to examine soil under the surface. For communications, each rover carries a high-gain and a low-gain antenna.

10 Figure 1.8: MER wheels (image reproduced from NASA)

The wheels on the MER rovers are 26 cm in diameter. Each wheel is CNC machined from a solid piece of aluminum to reduce the weight by eliminating fasten- ers and extra material where parts connect. The wheels feature spiral-shaped, thin spokes, or flexures. These flexures are designed to give the wheel some compliance.

As seen in Figure 1.8, the orange filling between the flexures is an open-celled foam called Solimide. This foam keeps soil, rocks, and debris out of the wheels, and has the flexibility needed to conform to any deflection of the wheel [19].

1.1.2 Rover Prototypes

Countless prototype rovers have been built to demonstrate and verify mobility concepts. Many of these rovers are predecessors to rovers that were flown in missions.

One such rover is NASA’s Field Integrated Design Operations Rover (FIDO). FIDO

11 is the concept rover that was built in preparation for the MER missions. FIDO incorporates most of the basic design features of its larger descendants, Spirit and

Opportunity, including a rocker-bogie suspension, a panoramic camera on a mast, a solar panel atop a rectangular body, a science arm, and stereo cameras. FIDO confirmed these concepts on several field tests in which it maintained average speeds between one and two meters per second [27, 31].

A similar rover was built by the Intelligent Robotics Laboratory at the University of Oklahoma. This rover, sometimes referred to as the OU FIDO rover, shared the six-wheeled rocker-bogie suspension design with NASA’s FIDO rover. This rover featured wheels which were made of a PVC tire and aluminum spokes, as seen in

Figure 1.9a. The tire was made by cutting a short length of 8-in (203 mm) diameter schedule-40 PVC pipe. This section of pipe was then mounted on a jig and fixtured in a 4-axis CNC mill, where a tread pattern was cut into its outer surface. There were six parabolic-shaped spokes connecting the wheel hub to an aluminum ring inside the PVC.

Another rover made at the Intelligent Robotics Laboratory is Solar Rover II (SR-

II). This rover was designed and fabricated by Matt Roman. The rover was developed as a concept to demonstrate the mobility of a solar-powered, four-wheeled design with

12 (a) OU FIDO wheel (b) First SR-II wheel

Figure 1.9: Early wheel designs for University of Oklahoma rovers a much simpler suspension than the rocker-bogie-style suspension. By reducing the mass of the rover’s mobility system, a larger portion of the rover’s allotted mass can be devoted to scientific instruments. Also, a simpler suspension should have a smaller probability of failure. Several versions of SR-II have been built, and these have endured multiple field tests and traversed tens of kilometers, and maintained average speeds of up to 15 cm/s [26].

Several sets of wheels have already been manufactured for SR-II. While none of these wheels have been designed with compliance in mind, these wheels have already demonstrated strength and high traction while keeping a low mass. The first wheels made for SR-II were made on an expeditious timeline so that SR-II would have some means of mobility; there were no off-the-shelf wheels that would fit on the rover.

Instead, a custom set of wheels was made based on a design that was used for the

13 FIDO-rover at the University of Oklahoma. Like the FIDO wheels, these first SR-II wheels were made of thin aluminum spokes attached to a plastic tire. The tire used was very similar to that of the OU FIDO rover, but the tread pattern was changed from a symmetric to a non-symmetric pattern for more efficient skid turning. Also, the spoke design was changed to a simpler, straight-spoke design, and the spokes were connected directly to the tire, eliminating the ring inside the tire, and reducing mass. Figure 1.9b shows this wheel, and the similarities and differences between it and the OU FIDO wheel, seen in Figure 1.9a, can be seen. There was very little analysis done on this set of wheels, and they were primarily for indoor use, so they were not heavily used.

The next generation of SR-II wheels was developed by Alois Winterholler. He experimented with wheels made from structures of hardfoam and honeycomb before deciding on a final design that uses carbon fiber. This final design incorporates three hollow carbon fiber spokes. The spokes were made by machining a six-piece aluminum mold and laying a carbon fiber cloth over the mold. The mold consisted of two parts to form the hollow inside of the spoke and four parts which surrounded the carbon fiber. By using both positive and negative mold features, the spokes were

14 given a smooth surface finish, making the wheel stronger, and the spokes could still be made as one piece each.

A liquid resin was then applied, and the fibers were allowed to cure for 24 hours.

After allowing the spokes to fully cure, they were epoxied to a central hub and an outer rim, both made from aluminum. This was done by assembling all of the components into an assembling device and applying epoxy to the contact surfaces.

The outer rim was epoxied to a separate strip of sheet aluminum with a tread pattern stamped into it. The final assembly has a mass of 411.5 g. This figure is significantly lighter than previous wheel designs.

Figure 1.10: Carbon fiber wheel, designed and built by Alois Winterholler, mounted on SR-II

15 The carbon fiber wheels were then subjected to various testing methods. A dy- namic test was performed to observe the wheels damping behavior by implementing strain gages and a conveyor-driven test bench. Static testing was done to failure of the wheel, and the maximum load that the wheel could withstand was determined to be between 1,800 N and 5,000 N, depending on the orientation of the wheel. Fi- nally, a field test was performed in the Anza Borrego desert near the Salton Sea in southern California. During this testing, the wheels met performance goals and demonstrated satisfactory strength, traction, and mobility through various types of rocky and sandy terrain. However, in the extreme heat of the desert, measured to be 113oF (45oC), the epoxy holding the wheel together failed, and the tread began to delaminate from the rest of the wheel. Temporary repairs were made with cable ties and rivets [33].

Figure 1.11: Carbon fiber wheel, with tread surface delaminating in extreme heat (image reproduced from [33])

16 The next wheels made for SR-II were created by various senior capstone classes at the University of Oklahoma. In the spring of 2005, three groups designed and manufactured prototype wheels. Each group had one primary design focus for their wheel. These objectives were high traction, compliance, and high efficiency. The final products for both the high traction and compliance projects were deemed unfavor- able for use on SR-II because the drawbacks outweighed the benefits of the wheels; specifically, the wheels were much heavier than the existing carbon fiber wheels. The third project, the high-efficiency wheel, proved itself adept at skid steering with min- imal energy while maintaining good tractive properties, and was used as the primary wheel during subsequent field testing.

Figure 1.12: High-efficiency wheel (image reproduced from [10])

This high-efficiency wheel was made entirely from 6061-T6 aluminum, with steel fasteners. The wheel weighs 609 g, but some of this mass could be removed by the

17 addition of lightening holes in the hub and the use of aluminum rivets in place of steel bolts and hex nuts. One of the primary features of this wheel is the incorporation of sloped surfaces on the tire. These sloped surfaces help to keep the wheel from scooping up rocks and soil while turning, particularly while turning in place [10].

1.2 Compliance

A compliant wheel, in the context of this thesis, refers to a wheel which will undergo elastic deformation to absorb and dissipate fall energy. In doing so, the wheel will protect the driveline of the rover from permanent damage sustained in a fall. Having compliant wheels on the rover will allow the rover to travel at higher driving speeds, and spend less time calculating the best route to avoid obstacles.

By increasing the speed of the rover, the range that it can travel in a given time is also increased, and the rover can complete more scientific objectives and collect data from a wider range of locations.

1.3 Design Goals

Compliant wheels are desirable for SR-II as a means of protecting the drivetrain components during impact loading. On Earth, pneumatic tires are frequently used

18 because the air in the tires helps to cushion the vehicle from shocks, rubber tires usually have good tractive properties, and the tire pressures can be adjusted to tune performance of the vehicle. However, because of the extreme temperatures and low pressures, pneumatic tires are not feasible for space missions. Therefore, some alternative wheel design must be developed.

It is unclear precisely how much compliance is needed from the wheels of SR-II.

The rover has adeptly proven itself capable of handling rugged terrain in multiple

field tests. These tests have been performed using various wheels, all of which have been rigid. During these tests, there have been instances in which the rover has fallen from small heights of a few centimeters, and no damage has been noted in the suspension tubes or in other parts of the drivetrain. However, adding compliant wheels will add an additional factor of safety to prevent failure of driveline parts, and protect the rover during falls from greater heights.

Increasing the amount of compliance in the wheel requires trade-offs in efficiency and stability. Therefore, the wheels should be designed to have a maximum amount of stiffness while still providing enough yield to prevent damage to the drivetrain.

The selected design must be robust enough to allow the rover to safely withstand

19 the loads generated from impact during these short falls. Furthermore, the design should be strong enough to withstand these loads over many cycles.

Due to the rover’s limited power budget, rolling efficiency of the wheels is a concern. It is expected that the wheels will be somewhat less efficient than rigid wheels, but a drastic loss of efficiency, more than 50%, is unacceptable.

Another objective in the design of the wheels is minimizing the mass. Due to the high cost of sending a payload into space, the mass must be kept as low as possible.

Current wheel designs for SR-II weigh around 450 g. The weight of a compliant wheel should be comparable, and if possible, less than this figure.

1.4 Problem Statement and Organization of Thesis

The goal of this thesis is to design, analyze, and test wheel concepts for SR-II that will absorb energy if the rover falls from a short ledge while driving. These concepts will be compared and contrasted to select the best design features for a compliant wheel. This wheel should demonstrate adequate compliance to protect the rover’s driveline components, and should also prove to be a feasible prototype for wheels for a Mars rover; that is, the wheels should be of a design that could be

20 made entirely spaceworthy and the design should minimize the tradeoffs in mass and rolling efficiency needed to obtain compliance.

The remainder of this thesis will introduce and analyze several concepts for a compliant rover wheel. Chapter Two will present the requirements and design con- siderations that must be taken into account in the design of a compliant wheel for a planetary rover. Next, several concepts will be analyzed in Chapters Three, Four, and Five. Finally, experimental results and conclusions will be presented in Chapter

Six.

21 Chapter 2

Design Constraints

This chapter introduces the requirements that a compliant wheel for a planetary rover must meet. These design constraints are explained and the analysis factors are presented.

2.1 Fall Height

SR-II was designed to safely withstand a fall from 10 cm. This calculation assumes that the combined deformation from the soil, the wheel, and the suspension tubes is

1 cm [26]. For rigid wheels, this assumption is generous, especially in the case where the impact occurs on solid rock. In such a fall, most of the forces of impact from landing would be absorbed by the suspension tubes.

This calculation is from the Work-Energy Principle, which is derived from the law of energy conservation. The Work-Energy Formula is given by Equation 2.1 [13].

1 1 F x = m v2 m v2 (2.1) avg · 2 · · − 2 · · 0

22 In this equation, Favg represents the average force exerted on a body, where the

body’s mass is given by m, and its initial and final velocities are denoted by v0 and v, respectively. The deceleration distance is given by x.

The velocity of a falling body under constant acceleration is given by Equation

2.2, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and

∆x is the distance traveled [13].

v2 = v2 + 2 a ∆x (2.2) 0 · ·

This will be solved for the rover falling from a short ledge. In this case, the initial velocity is zero, and g, the acceleration due to gravity, will be substituted for a, and

∆x will be replaced by h, the fall height. Solving for the final velocity yields:

v = 2 g h (2.3) · · !

Combining Equations 2.1 and 2.3, and setting v equal to zero,

2 g h m F = · · · (2.4) avg 2 x ·

Dividing this force by the number of wheels, 4, Equation 2.4 becomes:

23 g h m F = · · (2.5) avg 4 x ·

Applying the conditions g = 9.81 m/s2, h = 0.1 m, m = 30 kg, and x = 0.01 m, the resulting average deceleration force is 735N. Equation 2.5 assumes that the deceleration is constant, and that there is no rebound of the rover. This value will be used as a baseline for comparison.

It can be seen from Equation 2.5 that the deceleration force is inversely propor- tional to the deceleration distance. Therefore, to minimize the force on the rover after a short fall, the deceleration distance must be maximized.

It should also be noted that these calculations are for Earth-based testing, using the acceleration of gravity at Earth’s surface. The acceleration due to gravity on the surface of Mars is 3.69 m/s2. Thus, the final safety factor for a fall on Mars will be equal to the computed Earth-based safety factor multiplied by 2.66.

2.2 Spaceworthiness

Studies of spacecraft failure indicate that roughly one-fourth of all spacecraft fail- ures occur as a result of interaction with the space environment [30]. Because the

24 ultimate objective for SR-II is long-range traverse of the surface of Mars, all designs proposed herein should be considered spaceworthy, meaning that the materials and structures should be capable of withstanding the effects of the space environment without sustaining significant damage or undergoing any major changes in perfor- mance. This includes the ability to withstand very low atmospheric pressure, a zero-gravity environment, and temperature extremes.

In the near-vacuum of space, some materials will lose mass in a process known as vapor outgassing. During outgassing, some compounds in organic materials, particu- larly those with low molecular masses, can vaporize from the surface of the material.

These volatile compounds can then adhere to other surfaces, such as lenses and solar panels, resulting in interference in the performance of these instruments. NASA has precisely-defined standards to determine whether or not a material can be considered

’low-outgassing’ and therefore useable in aerospace applications. All of the materi- als selected for use in the wheel design should be low-outgassing materials, or have an equivalent low-outgassing material which may be substituted without significant changes in performance [24, 30].

The space environment is also a host to extreme temperatures. Because there is no atmosphere to regulate the temperature, spacecraft can reach extreme temperatures.

25 The sunlit side of a spacecraft can reach temperatures of 120oC, and the shaded side can drop well below 0oC. The actual temperature will depend on the distance from the sun, which emits solar flux of 1358 W/m2 at a distance of 1 AU, or the equivalent of a black body temperature of 6000 K with solar output of 3.8 1025 W. To put this × into perspective, Mercury, the closest planet to the Sun, which has no atmosphere, will have soil temperatures of 700 K (425oC) on the sunlight side, and temperatures as low as 90 K ( 185oC) on the shaded side. Due to conduction within the spacecraft, − temperatures on a small spacecraft will not reach the drastic extremes of Mercury, but the temperature limits will be much more radical than those experienced on

Earth [1, 11].

Once on Mars, temperatures will generally be much colder than those on Earth.

Martian surface temperatures range from as low as 140 K ( 133oC) at the poles to − almost 300 K (27oC) on the day side during summer. The average temperature on the surface of Mars is 55oC. The temperature range that a Mars rover is expected − to experience will depend on the location and season, but the rover and all of its components should be designed to safely operate in the full temperature range that

Mars offers [1].

26 2.3 Rolling Efficiency

Rolling friction is a force that acts opposite to the direction of vehicle travel.

Rolling friction has several causes: friction in the driveline of the vehicle, friction between the tire and the ground, and deformation of the tire while rolling. For SR-

II, driveline friction is caused by friction within the roller bearings, in the upper and lower gearboxes where the bevel gears mesh, and in the motors themselves. These friction sources have been minimized in both the design of SR-II and the use of lubricants.

Friction between the tire and the ground adds a very small contribution to the rolling friction. This component is a result of the molecular adhesion between the tire material and the ground surface. If the tire is metal, rather than rubber, this friction component is extremely minimal.

The deformation of the tire while rolling is the third source of rolling friction.

This factor is negligible for rigid wheels, like previous wheels for SR-II. However, compliant wheels will tend to deform while rolling. This deformation will result in the conversion of mechanical energy into other forms, mostly thermal energy, which will then be dissipated into the surroundings.

27 The rolling resistance of a wheel can be modeled by Equation 2.6. Here, µr is the rolling friction coefficient, W is the weight of the wheel, including any vehicle weight that the wheel bears, r is the wheel’s radius, and F is the rolling friction force [2, 7].

µ W F = r · (2.6) r

This frictional force incorporates the wheel’s radius because there is some defor- mation of the wheel and the surface as the wheel rolls1. In an idealized case, this radius could be ignored, but in actuality, there is some elastic deformation that oc- curs as the wheel flattens at the contact patch and the surface forms a slight trench.

The result is an uneven distribution of the normal forces on the wheel, rather than a simple normal vector at an infinetessimally small contact point. Figure 2.1 shows an exaggerated illustration of this deformation and the distribution of the normal forces. Because the surface material is pushed along with the wheel, a majority of the normal forces are at the front of the wheel, resulting in a net rearward normal force [8].

1Some sources indicate that the radius of the wheel is not a term in the equation for rolling resistance. In these cases, the friction coefficient given is unitless. However, it should be noted that for wheels having small radii, the radius must be considered in calculating the rolling resistance. Additionally, the values for µr are comparable between the two methods. For the purposes of this text, either equation could be used because a comparison between differing wheel materials is being analyzed.

28 No. of Flexure Suspension Wheel Force Stress Flexures Thickness (mm) Deflection (mm) Deflection (mm) (N) (MPa) 5 1.6 7.5 3.8 652 913 5 1.8 8.0 2.7 690 788 8 1.25 7.5 3.8 650 887 8 3 9.0 .27 796 149 8 3 9.3 .06 800 78

Design No. of Flexure Mass (g) No. Flexures Thickness (mm) 1 5 1.6 115 2 5 1.8 117 3 8 1.25 130 4 8 3 157 5 8 3 171 Figure 2.1: Ideal and realistic free-body diagram of wheel rolling across deformable surface (image reproduceDesignd from [8])Suspension Wheel Deflection Force Stress No. Deflection (mm) (mm) (N) (MPa) 1 7.5 3.8 652 913 The units of this frictio2n coefficien8.0t are the same2.7as the units690for the788 radius of 3 7.5 3.8 650 887 4 9.0 .27 796 149 the wheel. Typical values fo5 r µr are sho9.3wn in Table 2.1.06. 800 78

Material !r (m) Steel on Steel 0.0005 Wood on Steel 0.0012 Wood on Wood 0.0015 Iron on Iron 0.00051 Iron on Granite 0.0021 Iron on Wood 0.0056 Polymer on Steel 0.002 Hard Rubber on Steel 0.0077 Hard Rubber on Concrete 0.01 – 0.02 Rubber on Concrete 0.015 – 0.035

Table 2.1: Rolling resistance for various materials (reproduced from [2])

It can be seen that these values are very small for contact between two hard materials, such as steel on steel. For a hard rubber wheel on Martian rock, the value of F should be comparable to that of hard rubber on concrete, between 0.01 and

0.02. A metal wheel driving across smooth rock, however, will have a value around

0.0021. This coefficient is only one-tenth of the value for hard rubber on concrete.

29 Consequently, a hard rubber tire will experience about ten times as much rolling resistance as a metal tire. This added rolling resistance will require more power for a traverse of given length. The power needed to travel at a given velocity across level ground can be found by applying Equation 2.7, where P (t) is the power used, as a function of time, F (t) is the drag force, and v(t) is the velocity of the rover.

P (t) = F (t) v(t) (2.7) ·

Thus, it can be seen that the power required to overcome rolling friction is di- rectly proportional the friction force, for a given velocity. While a hard, metal wheel on a hard surface will use the least amount of power to overcome friction, rubber tire’s higher friction coefficients will enable it to have better traction, which is help- ful when climbing obstacles. A good wheel design would be a wheel that exhibits characteristics which show a balance between the tradeoffs of efficiency and traction.

30 Chapter 3

Flexure Wheel

The first compliant wheel design considered was a wheel with thin spiral-shaped spokes, or flexures. This flexure design was flown by NASA on the MER rovers.

Solid modeling software, Pro/Engineer, was used to create solid models, and finite element analysis, using Pro/Mechanica, was performed on these models to determine approximate quantities for amount of compliance gained and corresponding stresses.

This chapter will present this analysis and the resulting values.

3.1 Design

The first flexure design is shown in Figure 3.1. This design incorporates five spokes, aligned with the mounting bolt pattern on SR-II, for an even stress distribu- tion among the spokes. The width of the wheel was selected at 0.25 in (6.35 mm), so that the wheels could easily be machined from a sheet of 0.25 in aluminum. This wheel structure would need to be integrated and assembled with a tire section in order to be useful for SR-II, but for the purpose of this experiment, only the hub and spoke region will be analyzed, so the tire is not included for this analysis. The

31 thickness of each flexure is 1.6 mm, and the flexure angle, the angle swept by each

flexure, is approximately 90o. The outer diameter of this wheel is 6.5 in. (165 mm).

The mass of this wheel section is 115 g.

Figure 3.1: Five-spoke flexure wheel

Aluminum was chosen as the material for this design due to its high strength- to-weight ratio, relatively low cost, and ease of machining. Aluminum 6061-T6, a very machineable alloy, has a tensile yield strength of 276 MPa, and a density of 2.7 g/cc, whereas mild steel has a maximum tensile strength of 500 MPa, but a density of 7.9 g/cc. This 6061 alloy has only half the strength of mild steel but only about one-third the density, giving it a better strength-to-weight ratio. Other materials, such as titanium, could also be considered, but titanium is very expensive and quite difficult to machine. Because the flexure wheel needs to have high compliance, it is important that the material chosen will have high deflection under a given load.

Therefore, a material with a low modulus of elasticity is needed. Aluminum 6061

32 has a modulus of elasticity of 69 GPa, while mild steel has a modulus around 200

GPa [21].

3.2 Analysis

Finite element analysis was performed on the wheel to determine the displacement corresponding to a fall from 10 cm. The process for finding this displacement was as follows: first, a load of 735 N was applied to the hub in Pro/Mechanica. The bottom surface of the wheel was constrained against displacement. A design study was run to find the displacement of the center of the wheel under this loading. Then, this displacement was added to the deflection of the wheel hub resulting from bending of the suspension tubes of SR-II, and the total deflection was applied to Equation

2.5. A new value for the loading force was obtained from this equation, and the new force was inserted into the finite element study. Iterations were repeated until the force converged to within 5%.

Using this method, the amount of displacement that would occur upon landing on a hard surface after a fall from a height of 10 cm was found. This deflection was

3.75 mm for the wheel, and 7.5 mm for the rover’s suspension tubes. The associated load is 650 N. Next, the stresses in the wheel were found for this load. The maximum

33 Von Mises stresses were found to be 913 MPa, a value much higher than the yield strength of aluminum, which is between 40 MPa and 150 MPa, depending on the alloy [21]. These high stresses would cause failure of the wheel under these conditions, regardless of which aluminum alloy was chosen.

Figure 3.2: Von Mises stress in five-spoke flexure wheel under 650 N load

3.3 Design Variations

The wheel geometry was then changed to attain results having lower stresses.

First, the flexure thickness was increased to 1.8 mm. The analysis procedure was then repeated, but the maximum value of the stress was still 788 MPa, so the design was again changed. This time, eight flexures, each 1.25 mm thick, were used. Eight

flexures were chosen as a means of more evenly distributing the forces, and because the MER rovers have eight flexures per wheel. Force, displacement, and stress values

34 No. of Flexure Suspension Wheel Force Stress Flexures Thickness (mm) Deflection (mm) Deflection (mm) (N) (MPa) 5 1.6 7.5 3.8 652 913 were found for this5 design, but1.8 the stress 8.0va lues were still2.7 higher tha690n the788yield 8 1.25 7.5 3.8 650 887 8 3 9.0 .27 796 149 strength for alumin8 um. 3 9.3 .06 800 78

Design No. of Flexure Mass (g) No. Flexures Thickness (mm) 1 5 1.6 115 2 5 1.8 117 3 8 1.25 130 4 8 3 157 5 8 3 171

TableDesign3.1: FlexurSuspensione dimensions Wheeland Deflectionmass forForfivece wheStresels designs No. Deflection (mm) (mm) (N) (MPa) 1 7.5 3.8 652 913 2 8.0 2.7 690 788 3 7.5 3.8 650 887 In an attempt t4o drastically9.0 reduce the str.27ess in the 796wheels, 149another design change 5 9.3 .06 800 78

was made by increasingMaterialthe thic kness of Elongationthe flexures to 3.0 mm. The stress from this Aluminum 1100-H12 12% - 25% Aluminum 1100-O 35% - 45% trial was still too Ahigh,luminusom 30further03-H12 geome10%tric - 20%mo difications were made. The radii Aluminum 3003-O 30% - 40% Aluminum 6061-O 25% - 30% of the fillets betweenCothepper,flexures annealed and the6h0%ub and rim were increased to eliminate Gold 30% Steel, AISI 4130, annealed 28% Steel, AISI 1010 20% high stress concentratTitionaniump, oinannts,ealedand lightening30% holes were added in low-stress areas. Stainless steel, 303, annealed 50% Yellow Brass 65% This last design can be seen in Figure 3.3. The analysis procedure was repeated for this wheel. Flexure dimensions and mass for each design are presented in Table 3.1.

Here, and throughout the remainder of this thesis, the flexure wheel designs will be labeled by “Design Number,” referring to the specific iterations of the flexure design.

Stress and displacement results from all five wheel concepts are summarized in Table

3.2.

Results and conclusions from this study will be presented in Chapter Six.

35 Figure 3.3: Von Mises stress in eight-spoke flexure wheel under 800 N load

No. of Flexure Suspension Wheel Force Stress Flexures Thickness (mm) Deflection (mm) Deflection (mm) (N) (MPa) 5 1.6 7.5 3.8 652 913 5 1.8 8.0 2.7 690 788 8 1.25 7.5 3.8 650 887 8 3 9.0 .27 796 149 8 3 9.3 .06 800 78

Table 3.2: Forces,Designstr esses,No. of and displacFlexurementse for various flexure wheel designs in Mass (g) 10-cm fall No. Flexures Thickness (mm) 1 5 1.6 115 2 5 1.8 117 3 8 1.25 130 4 8 3 157 5 8 3 171

Design Suspension Wheel Deflection Force Stress No. Deflection (mm) (mm) (N) (MPa) 1 7.5 3.8 652 913 2 8.0 2.7 690 788 3 7.5 3.8 650 887 4 9.0 .27 796 149 36 5 9.3 .06 800 78

Material Elongation Aluminum 1100-H12 12% - 25% Aluminum 1100-O 35% - 45% Aluminum 3003-H12 10% - 20% Aluminum 3003-O 30% - 40% Aluminum 6061-O 25% - 30% Copper, annealed 60% Gold 30% Steel, AISI 4130, annealed 28% Steel, AISI 1010 20% Titanium, annealed 30% Stainless steel, 303, annealed 50% Yellow Brass 65%

Chapter 4

Tweel

The Michelin Tire Company developed a compliant wheel prototype called the

“Tweel.” The Tweel is available in a variety of sizes and stiffnesses. Full-size au- tomobile prototypes are currently being developed, and smaller, light-duty versions, intended for applications such as wheelchair casters, have already been produced.

Figure 4.1 shows one such light-duty Tweel.

Figure 4.1: Michelin Tweel

The Tweel is composed of thin steel coils molded into a rubber body. The rubber portion of the wheel comprises the spokes and the outer contact surface. In the center of the Tweel is a bearing, allowing it to mount as a non-drive wheel. If a downward-directed load is applied to the Tweel through the center, the spokes above the center become loaded in tension, and the spokes below the center are loaded in

37 compression. Spokes having a compression load will buckle, effectively transmitting no force. Spokes in tension pull on the outer band of the wheel, deforming it. The amount of deformation is proportional to the thickness of the rubber in the outer band and the quantity and size of the steel coils.

4.1 Spring Rate

Eight Tweels were obtained for testing. These Tweels had an outer diameter of

155 mm and a width of 55 mm. The mass of each Tweel was 480 g. To find out how the Tweels would affect the impact absorption ability of the rover, it is necessary to know the spring rate for each wheel.

The stiffness of the Tweels was measured by mounting a Tweel into a fixture on a Materials Testing Machine (MTS). However, a fixture had to be made to mount the Tweel into the machine.

The fixture consisted of two parts: a clevis and a base. The clevis was made from a section of 6-in x 6-in (152 mm) C-channel, with a thickness of 5/16-in (7.9 mm). A section of 5/16-in plate was welded to the top of the channel to increase its stiffness.

Holes were drilled through the web to accommodate a shaft passing through the axis of the Tweel. Another hole was drilled through the top of the channel to fit a bolt.

38 The jaws of the MTS would grip this bolt. The base was simply a flat plate with a bolt attached for the machine to clamp.

The fixture and Tweel were then mounted on the MTS machine, to apply an axial compression load. The machine was programmed so that the load would increase linearly at a rate of 120 kg per minute, and displacement and force would be logged.

Four trials were run. In between trials, the machine was reset, and the Tweel was arbitrarily rotated so that average measurements would be obtained, regardless of spoke alignment. A photograph of the setup can be seen in Figure 4.2.

A graph of force versus displacement can be seen in Figure 4.3. From the deflec- tion and force data obtained in these tests, the effective spring constant of the wheel through its center can be obtained. The spring constant, at any load within the

Tweels’ range, can be determined by finding the derivative of the trend line in Fig- ure 4.3. The spring rate for the Tweel is nonlinear, but within the domain that the wheels will be tested, from about 300 N to 800 N, the spring constant is essentially linear, with a value of 29 N/mm.

39 Figure 4.2: Tweel in materials testing machine

Figure 4.3: Force vs. displacement for Tweel

4.2 Impact Force

Much of the energy from a fall can be absorbed by the Tweels. The average forces of landing exerted on the suspension tubes can be found by applying the Work-

Energy Principle in conjunction with deflection data from the MTS testing. Unlike the calculations done with the flexure wheel, finite element analysis will not be used

40 for this calculation. This is because the Tweels undergo large deformations, and the

finite element analysis relies on small deformations. However, the same procedure, using multiple iterations, can be used, substituting the deflection obtained from the spring rate of the Tweels for the deflection that would be found from finite element analysis.

If the rover falls from 10 cm onto a hard surface, and is equipped with the Michelin

Tweels, the Tweels can absorb most of the forces of impact. The suspension tubes would only deflect 4.94 mm, and the Tweels would deform 12.21 mm. The average force experienced in this fall is only 430 N, and the resulting safety factor for failure in the suspension tubes is 1.88. This can be compared to suspension tube deflection of 9.19 mm and a resulting load of about 800 N if the rover falls onto solid rock with a completely rigid wheel. In this case, the safety factor is 1.01.

41 Chapter 5

Tension-Spring Wheel

A wheel having tension springs in place of spokes is another possible solution for a compliant wheel. This chapter will discuss the design, fabrication, and computer- simulated testing for such a wheel.

In this method, the tire section, the part of the wheel that contacts the ground, attaches to tension springs. The opposite ends of these springs are then connected to a central hub that bolts onto SR-II. One advantage of this approach is that the tire can be constructed of any material, given the material meets traction and space- worthiness criteria. The geometry of the tire section can also be designed to any specifications, as long as there remains an interface for the springs to connect.

Another advantage of this approach is modularity. Because the design has three independent components: the tire, the springs, and the hub, any component can be replaced with relative ease. This feature is useful for testing and for attempting to

find the set of components that optimize the performance of the wheel. Namely, the springs can be interchanged with springs having different spring constants in order to find the best stiffness of spring for overall performance.

42 Additionally, the Department of Aerospace and Mechanical Engineering machine shop at the University of Oklahoma has the machinery and tools to manufacture these wheels, so these wheels can be manufactured more easily and at a lower cost than, for example, an injection-molded wheel.

5.1 Design Considerations

In designing a tension-spring wheel, several factors must be considered. First, the number of springs must be selected. Too few springs will result in a wheel that is unstable. Another adverse effect of too few springs is that the tire will be subjected to more concentrated loading. While this is not a problem with a rigid tire, a less stiff tire will deform unfavorably. Too many springs, on the other hand, will result in a wheel that is excessively heavy. Based on these parameters, the minimal number of springs that gives the wheel stability should be selected. For initial calculations, a total of six springs was selected.

A second factor is the orientation of the springs. If all of the springs are mounted in one plane, the wheel will be unstable when a lateral load is placed on the wheel, as seen in Figure 5.1.

43 Figure 5.1: Cross-section of wheel with all springs in one plane

To counteract this type of deflection, the springs should be attached to the hub in pairs. The pairs can share a mounting hole on the hub or use mounting holes which are close in proximity, but the pairs should split as they approach the tire.

This stabilization force can be determined by drawing a free-body diagram of the tire, as seen in Figure 5.2.

Figure 5.2: Cross-section and free-body diagram of wheel with springs mounted in pairs for stability

From Figure 5.2, the stabilization force per spring is equal to F sin(θ), where F s · s is the tensile force in each spring as a result of stretching the spring when assembling

44 the wheel. It is apparent that as θ increases, the amount of lateral stability given to the wheel is also increased. Thus, wider the spacing of the springs at the tire gives the wheel more lateral stability.

A range for θ was chosen by selecting values that can easily be adapted into the geometry of existing designs. From this, θ should be around 20o. Knowing the basic geometry of the wheel, estimations for the stiffness of the spring can be made. The stiffness of springs needed to keep the maximum rotations of the hub relative to the tire within reasonable limits was found by calculating the change in length for each spring as the hub was subjected to these rotations. The stiffness of the entire wheel through the hub, the value that determines the amount of compliance during a fall, was found for these spring values, and the geometry and spring stiffness were adjusted until these values were all in the range needed. The final spring rate needed for all 12 springs was determined to be around 1.8 N/mm.

The tire section of the wheel will be built to the dimensions of the existing wheel, built by the senior capstone team. This tire demonstrated good performance during testing, so no changes need be made.

The final component of the design is the hub. This hub must incorporate the bolt pattern from SR-II’s lower gearboxes so that the wheels will fit the rover. It

45 also must have holes to accommodate the springs. The overall dimensions of the hub should allow the wheel to mount onto the rover without any interference problems between the suspension tubes of the rover and the tire. Finally, the hub should be as light as possible while maintaining robustness to prevent failure during impact loading.

An important design consideration for this style of wheel is the power lost due to friction. From Chapter Two, the three sources of friction were said to be driveline friciton, rolling friction, and friction due to deformation of the tire. Of these three, the wheel design affects the rolling friction and the deformation friction.

The rolling friction, from Table 2.1, was estimated to be 0.0021 for steel on rock.

Plugging in this value for µr, and 295 N, the expected weight of the rover, for W , and 0.1 m, the radius of the wheel, for r in Equation 2.6, the force opposing motion of the rover with steel wheels on smooth rock or concrete is 6.2 N. Then, using

Equation 2.7, the power required to overcome this force at a speed of 0.2 m/s should be around 1.2 W. This figure is very low compared to the 11.8 W that the rover uses for straight-line driving on concrete [26]. It is expected that the rolling resistance of steel on concrete is a very minimal contribution to the overall power usage. Most of

46 the power is lost to driveline friction, in the motor, gear meshes, and bearings, and power losses associated with driving on a wheel with protruding metal grousers.

The friction from tire deformation in a spring wheel is expected to provide a significant contribution to these power losses. As the tension-spring wheel turns, the weight of the rover will cause the springs to extend and contract. In doing so, some energy will be lost due to internal friction of the molecules in the spring. This energy will be dissipated, mostly as heat. To estimate the losses from spring deformation, simple wheel models were created for the rover. These wheels were designed with a hub to mount to SR-II, and an outer tire made from a ring of 0.25-in (6.35-mm) aluminum. Springs of various stiffnesses could be used to connect the tire to the hub. Then, to estimate the power lost in the springs, the wheels were attached to the rover, which was placed on a sloped table. The slope of the table was varied until the rover would roll down the table at a constant velocity. This was repeated for springs of three different spring rates, and for a completely rigid wheel. Figure

5.3 shows the rover with these wheel models mounted, on the test table.

The minimum table angle that would allow the rover to slowly roll at a constant speed was recorded. Next, a free-body diagram was used to calculate the force opposing the wheel’s motion for these slopes. For this testing, the rover had a mass

47 Figure 5.3: Testing to find rolling friction of simple wheel model of 16 kg, or a weight of 154 N. From the free-body diagram, this force is equal to

W sin(θ), where W is the weight of the rover, and θ is the slope of the table. ·

This force was calculated for each size of spring, and the power lost traveling at a velocity of 20 cm/s was also computed. The results from this testing, along with the specifications for each spring, are summarized in Table 5.1. It should be noted that data is unavailable for the first spring, Spring A, because its spring rate was too low, and the rover was unstable on wheels with these springs.

Wire Size O.D. Spring Rate Ground Power Force (N) (in) (mm) (in) (mm) (lb/in) (N/mm) Slope (°) (W) Spring A 0.02 0.508 0.312 7.9248 0.216 0.0378 n/a n/a n/a Spring B 0.032 0.8128 0.3125 7.9375 2.68 0.471 3.09 3.76 0.75 Spring C 0.041 1.0414 0.3125 7.9375 10.03 1.764 2.95 3.59 0.72 Rigid Wheel n/a n/a n/a n/a n/a n/a 2.78 3.39 0.68

Table 5.1: Spring specifications and power losses

From these results, the relation between the spring constant and the power can be derived. However, because the springs for the tension-spring wheel will not have the same orientation as the springs in the simple wheel models, a correlation between the

48 spring rate for each spring and the overall spring rate for the wheel must be found.

By measuring the deflection of the wheel hub in the simple wheel model under a given load, the overall spring constant for the wheel from the axis to the tire can be found. For simple wheel models with Spring B, the overall rate is 1.13 N/mm, and the rate for those with Spring C is 4.48 N/mm.

These calculations show that a compliant wheel having an overall spring rate of

1.13 N/mm will have a power loss of 0.75 W, and a wheel with spring rate 4.48 will have a power loss of 0.72 W. Adjusting these values to a fully loaded rover mass of 30 kg, the power losses are 1.44 W and 1.37 W, respectively. It should be noted that these wattages are for all four wheels combined. This data suggests that the power lost due to deformation of springs is not as great as expected. In fact, the power losses from spring deformation are about equal to those that were computed for rolling resistance, which was 1.2 W for four wheels. Because a trial was conducted with a rigid wheel, the calculations for rolling resistance can be verified with experimental data. The measured value, from Table 5.1, was only 0.68 W, and adjusting this value to that of a fully loaded rover, the power loss from rolling friction was about 1.30 W. This compares very well to the calculated value.

49 All of these calculations and experiments suggest that the friction losses due to a compliant wheel are minimal. This, of course, is only valid with wheels in the spring rate range of those tested and at speeds around 20 cm/s, but the power lost in the wheels represents only about one-tenth of the total power losses experienced during driving. During actual traverses across soil, most of the energy loss will occur as a result of soil deformation and wheel slippage obstacle climbing, both of which are caused by the rover doing work on the ground.

5.2 Computer Terrain Simulation

A program was written in MATLAB to simulate the forces and corresponding deflections and rotations of the wheel while driving on various terrain surfaces. In the program, the user must input a three-dimensional surface for the rover to drive across. The user must also choose a path across the surface. The program then computes the normal vectors to the surface along the path. Then, the program uses these normal vectors, transformed into the rover’s local coordinate system along the path, to find the corresponding wheel rotations about two axes. The program first displays lateral rotation. This refers to rotation of the tire about an axis that runs along the length of the rover, front to rear. This can be thought of as the same

50 rotation referred to as “camber” in motorsports. Next, the program displays axial rotation. Here, axial rotation refers to the rotation of the tire section relative to the hub about an axis parallel to the wheel’s axis. This rotation is essentially twisting of the tire that results from driving straight up or down a hill. To find these rotations, constants for the wheels’ rotational stiffness have been programmed into the code.

These constants were found by calculating the length that each spring will stretch for a given lateral rotation and for a given axial rotation. From this data, constants were derived.

Figure 5.4 shows the output of one such simulation. In the figure, the terrain surface can be seen. This surface is the “saddle” created by the equation z = x2 y2 − on the domain of -0.5 to 0.5 for both x- and y-limits. The selected path that the rover traversed in the simulation was the line y = 2x. This path is visible in the figure as a black line on the plot. The bottom left-hand graph shows the lateral rotation of the wheel. The bottom right-hand graph shows the axial rotation of the wheel.

The figure shows that along this path, the maximum axial rotation is 10o. ±

This axial rotation is acceptable and within reasonable limits. Motor torque will be effectively transmitted to the tire, propelling the rover forward.

51 Figure 5.4: Simulated wheel rotation driving across terrain

Figure 5.4 also shows that the maximum lateral rotation is 30o. The 30o of ± rotation is a higher value than the wheels are designed to accommodate. At around

10o of lateral rotation, the wheel hub will come into contact with the tire, limiting the rotation. This contact is thought to be undesirable, but physical testing will be necessary to verify the lateral stiffness of the wheels to see if contact occurs. In the case that there is contact, testing will be needed to find the consequences of this contact to see if it is harmful or helpful. It will likely cause a hard stop during a fall onto an uneven surface, which will reduce the amount of compliance that the wheel offers, and can possibly lead to excessive wear on the wheels and hubs, but too much rotation could also possibly damage the wheels.

52 5.3 Spun Wheel

Before the spring wheel was manufactured for testing, some design modifications were made. It was determined that a spun wheel would minimize weight. The initial spring wheel design included two bracing ribs that ran the circumference of the wheel.

These ribs would have holes in which springs would attach. Strips of aluminum sheet would be cut for the tire, and these strips would be wrapped around the ribs and bolted into place. Figure 6.6 shows the parts of this initial design.

Figure 5.5: Original design for tension-spring wheel

This design is advantageous because it is relatively simple to manufacture. How- ever, the design is somewhat heavy. The tire section of the wheel needs to be thin enough to easily wrap it around the ribs and securely fasten it in place. Because of

53 the thinness of the tire, the rib is required to be more robust, to handle forces from the springs and potential impact loads and point loads from sharp rocks. Also, it requires many fasteners to ensure rigid linkage between the tire and the rib. These factors add weight to the wheel. Another weakness of this design is that it is difficult to close the wheel out to prevent dust, dirt, and rocks from getting inside the wheel and to prevent the wheel from getting snagged on protruding rocks. For each dif- ferent sloped surface of the tire, a separate piece of aluminum must be used, adding gaps in the tire. It is also somewhat complicated to add “hubcap” sections to fully close out the section. Even if the wheel has “hubcaps” to make it a closed section, if it is made of separate sections, there is a possibility that the gaps between the sections could be points that can catch on rocks.

Switching to a spun wheel design holds many advantages. First, the weight of the wheel can be reduced. A wheel made according to the first method will weigh approximately 375 g, not counting the weight of the springs or fasteners. A spun wheel of comparable strength will weigh 300 g without springs and fasteners. The addition of springs and fasteners should bring the total mass of one wheel to about

375 g. The spun wheel utilizes slightly thinner walls for the tire, and one-piece construction for the different surfaces of the tire. This allows the tire to be much

54 more rigid, eliminating the need for a heavy circumferential rib to provide support for the tire. Instead, much smaller, lateral ribs are used. These ribs give mounting points for the springs and hold the halves of the tire together. Consequently, the number of fasteners can then be reduced, further improving on weight savings on the wheel. This construction method also makes it much easier to close the wheel out. The wheel can be easily designed and constructed so that there is an integrated

“hubcap” section to help keep the rover from getting hung up on rocks and other protruding obstacles, and to keep the wheels from filling with dirt and sand during skid steering maneuvers.

5.4 Metal Spinning

Metal spinning is a manufacturing process used to create round parts. In metal spinning, a thin disk of sheet metal is shaped around a mandrel while mounted on a lathe. The mandrel is fixed to the spindle of the lathe so that it spins, and the disk is clamped against the mandrel. Then, using a variety of tools, including blunt tools, spoon-shaped tools, and rollers, the disk can be pressed over the mandrel, and slowly formed to the mandrel over a series of passes.

55 Nearly any sheet metal can be spun, although metals with high elongations are easiest to form. Purer, softer aluminum alloys are preferred for their high elongaion.

Annealed aluminum is generally considered the easiest metal to spin due to its high elongation and ductility. Thus, Al 1100-O is a prime candidate for spinning, because

1100 is 99% pure aluminum, and the “O” denotes that the metal has been annealed.

1100-O has an elongation of 35% to 45%, the highest for any aluminum alloy. Copper and yellow brass are very elastic materials, making them a good choice for metal spinning, and materials as hard as stainless steel can also be spun, although they will require significantly more force than softer metals. Table 5.2 shows the elongations for various alloys.

Material Elongation Aluminum 3003-H12 10% - 20% Aluminum 1100-H12 12% - 25% Steel, AISI 1010 20% Aluminum 6061-O 25% - 30% Steel, AISI 4130, annealed 28% Gold 30% Titanium, annealed 30% Aluminum 3003-O 30% - 40% Aluminum 1100-O 35% - 45% Stainless steel, 303, annealed 50% Copper, annealed 60% Yellow Brass 65%

Table 5.2: Selected alloys and their elongations (data from [21])

To form the metal, a variety of special tools have been developed. These tools typically have a long handle - around three feet in length - to provide ample leverage

56 Figure 5.6: Diagram of lathe setup for spinning (image reproduced from [12]) for forming and shaping the metal. The tool point can be a variety of shapes, including round and oblong balls, hooks, and dull blade shapes. Rollers are also used, particularly when the spinning is done on a CNC machine. To apply pressure on the part, the tool rests on the lathe’s tool post, and an operator uses the long handle of the tool as a lever. The lathe’s tool post is typically fitted with a tool holder used for holding a boring bar, but instead of a boring bar, a rod of the same diameter is mounted into the tool holder. This rod will have one or more holes drilled about halfway through it, and a smaller rod, having the same diameter as the holes, will fit snugly into the holes. The intersection of these two rods is where the tool rests, allowing the tool post to be used as a fulcrum for apply force to the part. The handle of the tool can be placed in the underarm of the operator, with the operator

57 firmly gripping the handle in both hands. In this manner, a maximum amount of force can be applied without straining the operator. The part is clamped to the mandrel by pressing a live center in the tailstock of the lathe against the part. A side and top view schematic of this setup are shown in Figure 5.6 [12].

5.5 Spun Wheel Design

Figure 5.7: Spun wheel, exploded view

The wheel design selected for spinning is shown in Figure 5.7. The wheel’s outer shell is made of Al 3003 having a thickness of 0.025 in (0.635 mm). This tire section was designed to be as thin as possible to reduce the mass of the wheel. To ensure that the aluminum was not too thin, a brief analysis was done in Pro/Mechanica.

58 To simplify this analysis, only one-sixth of the wheel was modeled, and point loads were placed on the tire where the ribs and springs would attach. These loads were assigned a value of 100 N each. This loading is based on the calculated force from stretching the springs to connect them to the wheel and the additional loading of an impact. Next, a finite element analysis design study was run to check the maximum deformation as a result of the spring loads. It was found in this study that the maximum deflection of the section was only 0.997 mm. This small deformation is acceptable.

Figure 5.8: Maximum deflection of tire section under loading

This tire section features a flat middle section and a section on either side with a 20o slope. This sloped section is for efficient turning, and allows the rover to drive on a narrower tire over smooth terrain, while keeping a wide tire for obstacle maneuvering. As shown in the figure, the tire is made of two halves. The outer half is slightly larger than the inner half, and the two halves should be manufactured

59 so that they snugly fit together. The outer half is fully closed to prevent rocks and debris from entering the wheel and to minimize the likelihood of the wheel catching on a protruding rock. The inner half includes a 76-mm hole to allow the hub to fit through with room for movement resulting from the compliance of the wheel. The hole will allow the wheel to rotate to a maximum angle of 10o relative to the hub.

To fix the halves together, small bracing ribs are used. These ribs not only connect the halves, they add rigidity and dent-resistance to the tire sections. The ribs are to be made of Al 6061. This alloy was chosen for its lightness and machinability.

In each rib is a small hole for affixing a spring. The wheel uses 12 of these springs, which all connect to the central hub, also made from Al 6061. The hub features a bolt pattern to allow it to mount to the lower gearbox of SR-II.

5.6 Wheel Fabrication

After completing the design phase for the tension-spring wheel, it was determined that a set of these wheels should be manufactured for testing. The spun design was selected to be made and analyzed.

To make this spun wheel, a mandrel had to be first made. This mandrel was made from mild steel, turned on a CNC lathe. Dimensions for the mandrel are shown in

60 Appendix B. A hole was drilled in the back of the mandrel and this hole was tapped to accommodate a 1” - 8 threaded rod. Next, the chuck was removed from a manual lathe so that the mandrel could be attached to the spindle of the lathe. The mandrel was fitted snugly onto the spindle, the threaded rod was passed through the spindle and screwed into the mandrel, and a washer and nut were tightened onto the opposite end of the rod to secure the mandrel. Then, the aforementioned metal spinning setup was used to prepare to spin a wheel.

Figure 5.9: Spinning setup used for first wheel

A sheet of 0.063-in (1.6-mm) aluminum was cut into a disk having a diameter of 13 in (330 mm). This disk was mounted into the fixture for spinning. Stick wax was applied to the surface of the part for lubrication, and the lathe was started at a speed of 285 rpm. Using a blunt steel rod as the forming tool, a first attempt at

61 spinning a wheel was made. The metal conformed to the first bend in the mandrel, but would not bend around the second radius. An increasing amount of force was used to try to create a plastic deformation of the aluminum, but the forces were too great and the center of the disk sheared where the live center of the lathe pinned the disk against the mandrel.

Figure 5.10: Product of second attempt at spinning

A second attempt was made, but to ensure adequate softness of the metal, this aluminum disk was annealed with an acetylene torch. The metal was heated with an acetylene-rich flame until a thin black carbon coating covered the surface, and then a hotter, neutral flame was used to burn the carbon off. After several minutes of heating, the carbon disappeared from the surface, indicating that the aluminum had reached its annealing temperature of 343oC [9]. If the flame was held in one spot too long, the aluminum would get much hotter than the temperature needed to anneal, and begin to melt, indicating that the temperature exceeded 643oC, the

62 solidus temperature of Al 1100 [14]. The metal was then allowed to cool for about

15 minutes.

The spinning process was repeated with this disk, at speeds of 285 and 395 rpm.

Unfortunately, it still took a great amount of force to get the disk to bend, and the disk began to ripple at the second radius. The resulting product can be seen in Figure 5.10. It can be seen that the aluminum began to take the shape of the mandrel, and formed onto the first section of the mandrel, but at the second radius of the mandrel, the wheel began to wobble and ripple. These ripples could not be removed from the material by further spinning.

In an attempt to determine the source of error in the spinning process, a pro- fessional metal spinning company was consulted. Several suggestions were made to improve the process. First, stamped 1100-O aluminum disks should ordered from a vendor and used to minimize wobbling of the part due to instability resulting from an imperfect circle. Next, a tool having a wheel was recommended to ease the forming process. Also, the mandrel should be checked for runout, and any runout should be eliminated [5].

Following these recommendations, stamped disks were ordered in several sizes, the mandrel was trued to eliminate some slight runout that had been noticed earlier,

63 and a roller tool was made. After making these corrections, further attempts were made at spinning. Various speeds, including 285, 395, 510, 710, and 1010 rpm were used while spinning, and various techniques of applying force with varying tool angles were applied. Again, however, all of the results were rippled wheels, as seen in

Figure 5.11. Although each attempt produced a wheel having more of a bend than the previous, the material beyond the second radius continued to wrinkle each time.

It was then decided that the wheels would be best made by a professional metal spinning company.

Figure 5.11: Rippled wheels from unsuccessful attempts at spinning

64 Chapter 6

Results and Conclusions

This chapter will present results from each concept. Physical testing will be presented and discussed, and the different concepts will be compared.

6.1 Flexure Wheel Results

In the design study presented in Chapter Two, several variations of a flexure wheel were analyzed for amount of compliance and Von Mises stress. As seen in

Table 3.2, the maximum stresses in all of the wheel designs were higher than the yield strength for aluminum, so all of the wheel designs would fail in a 10-cm fall.

The first two wheels, the five-spoke wheels, had the highest amount of compliance, but also the highest stresses. The first eight-spoke wheel had comparable compliance to the previous designs, and slightly lower stresses. Finally, the last two models, the eight-spoke wheels having 3-mm thick flexures, had the lowest amounts of compliance and also the lowest stresses. Of these two, the latter had design features which were intended to lower the stress concentrations, but these changes made the wheel very stiff. It can be seen from the table that the wheel would only have 0.06 mm

65 of deflection in a fall, whereas the suspension of the rover would give 9.3 mm of deflection, meaning that less than one percent of the cushioning from a fall will be absorbed by the wheels, and the remaining ninety-nine percent is absorbed by SR-II’s drivetrain.

As the design was refined to reduce stress within the wheel, the mass of the

flexure wheel continued to increase. The mass of the last iteration of the design was 171 g, and the wheel was still not within the limits of the yield strength for aluminum. While weight savings could be made by removing material from the center of the wheel and by making the outer band thinner, these wheel designs were still relatively heavy.

Because the final iterations of the flexure wheel deigns had such low compliance and high mass, the other concepts discussed in this thesis appear to be advantageous over the flexure method. Further investigation of the flexure wheel could be done, performing analysis of various materials, and performing topographical optimization to produce a design that meets the compliance and mass goals for the wheel, and is robust enough to maintain a high safety factor.

66 6.2 Accelerometer Testing

To verify the calculations for average forces exerted with each wheel concept, drop testing was performed with an accelerometer. A Freescale Low-G Micromachined Ac- celerometer, part number MMA1220, was obtained for measurements. This device can measure unidirectional acceleration up to 15 g’s (150 m/s2). The accelerometer was surface-mounted onto a small circuit board as per the data sheet’s instructions, and the leads were connected to a National Instruments DAQ box. National Instru- ments’ LabVIEW software was used to measure and log acceleration data from the accelerometer.

For baseline comparisons, average deceleration values with rigid wheels were first found. Rigid wheels were mounted on SR-II, and steel weights were added to the body and fastened with tape to get the total rover mass to a payload of 22.2 kg.

This smaller mass was used, rather than the original 30 kg, because the safety factor for a 10-cm fall on Earth was only slightly over 1.0, and it was deemed that the risk of damaging the suspension tubes was too high with a full 30-kg payload. The accelerometer was firmly mounted inside the body of the rover. Then, the rover was carefully raised to a height of 5 cm and dropped onto a hard cement floor. Again, a

67 lessened value, 5 cm rather than 10 cm, was used to protect the rover and to keep the accelerometer within its limits. The output of the accelerometer was recorded over ten trials.

Figure 6.1: Acceleration during impact from a 5-cm fall with rigid wheels

Figure 6.1 shows a plot of the deceleration of the rover with respect to time. The data shows a typical result from the ten trials. It can be seen that the deceleration is three sharp spikes, the first with a maximum value of 8.3 g’s, the second with a value of about 12.6 g’s and the last with a value of around 13.6 g’s. The zero-g period during the fall should also be noted. The first spike is almost entirely positive, and the two rebound spikes have large negative g values. Finally, oscillations can be noted at the end of the trial. These oscillations have a frequency of about 12.5 Hz.

68 The data obtained from this drop testing can be compared to predicted values from previous calculations. First, the deceleration distance must be estimated. Be- cause the rover is falling onto cement and has rigid wheels, a distance of only 2 mm will be assumed. Changing the rover’s mass from 30 kg to 22.2 kg, the fall height from 0.1 m to 0.05 m, and the deceleration distance to 2 mm, the expected force of impact, from Equation 2.5, is 1360 N. From the data obtained during the drop test, the first spike, the acceleration from initial impact, had a value of about 8.3 g’s, or about 81 m/s2. From Newton’s first law, F = m a, so the maximum value · of this force is equal to 1800 N. This is roughly comparable to the predicted 1360 N, although there is a major source of error in estimation of the deceleration distance for a rigid wheel. However, the second and third bounces have larger acceleration values than the first. The maximum forces in these two bounces are 2700 N and

3000 N. These forces are significantly higher than the estimation.

With the Tweels mounted on SR-II, this testing was repeated. Again, ten trials were used to obtain normalized results. Figure 6.2 shows a typical graph of a data set from the testing. The results from this look similar to those of the rigid wheel, only with shorter, slightly wider peaks, and more oscillation. The wider peaks indicate that the loading occurred over a greater time span, and consequently, the maximum

69 Figure 6.2: Acceleration during impact from a 5-cm fall with Tweels value of the deceleration is less than that of a rigid wheel. With the Tweels mounted on SR-II, the maximum acceleration was about 8.8 g’s. In most of the Tweel trials, the first spike was the largest, but the precise reason why this is reversed from the rigid wheel testing is not known.

Repeating the calculations from the rigid wheel drop, the maximum acceleration with the Tweel is 87 m/s2, and the maximum force is 1900 N. Again, the experimental data shows higher forces than the preliminary calculations. From Chapter Four, the expected force for a 22.2 kg rover falling from 5 cm is only 280 N. This error of over

500% is most likely caused by the rover’s unsteady deceleration. The Work-Energy

Principle assumes that the force of the ground acts on the rover with a constant force

70 over the distance interval in which it acts. In reality, the force is very unsteady, and it can be seen from Figure 6.2 that the deceleration is not constant.

Finally, this testing was repeated with the tension-spring wheels mounted on the rover. The aforementioned procedure was repeated. A plot of the deceleration of the rover during the same 5-cm fall is shown in Figure 6.3. In these tests, the first peak was generally close to 7.4 g’s, and the second spike was about 6.5 g’s. The mass oscillated for the next few seconds. It can be seen that the oscillations occur for a longer duration than with rigid wheels, and that the time span over which the deceleration occurred was again lengthened for this wheel design.

Figure 6.3: Acceleration during impact from a 5-cm fall with tension-spring wheels

The maximum acceleration value for the tension spring wheel was 73 m/s2, and the corresponding force is 1600 N. This force is less that than of the Tweels, and a

71 drastically less than that of the rigid wheels. In fact, the force is reduced by almost half for the tension-spring wheels versus the rigid wheels. The tension-spring wheels significantly reduce the forces and stresses on the rover during a fall from a given height.

Based on this testing, the forces and stresses associated with a fall on the rigid wheels should be approximately equal to those from 1.8 times that height on spring wheels. Therefore, if the rover could survive a fall from 10 cm with rigid wheels, it should be able to withstand a fall from 18 cm with tension-spring wheels, using the same factor of safety.

Although the forces experienced in the fall for all wheel designs are greater than those that were predicted, general trends can be observed from the different types of wheel. With a rigid wheel, the forces during a fall have a maximum of about 13 g’s, or 130 m/s2. However, the Tweels reduce this figure to about 9 g’s, or 87 m/s2.

Lastly, the spring wheel design kept the force under 7.5 g’s, or 73 m/s2.

6.3 Tweel Field Testing

Four hubs were made as an interface between the Tweel and SR-II. These were needed due to the fact that the Tweels obtained for research were not designed to be

72 drive wheels, and had bearings in the center for free rotation. The hubs provided a means of eliminating the free rotation about the wheels’ axes. The hubs consisted of thin aluminum disks drilled with a hole pattern to mate with the rover, and spring pins protruding from one side to fit into a corresponding hole pattern drilled into the

Tweels. A single 5/16-in bolt in the center of the wheel held the hub onto the Tweel.

Figure 6.4 shows the hub assembly. The Tweels were then fitted onto the rover for testing.

Figure 6.4: Computer model of tweel and hub assembly, exploded view

A field test took place in the Anza Borrego desert in California. After completing the primary objective of the field test, a long distance traverse, several miscellaneous experiments were carried out. At this time, the Tweels were tested for shock absorp- tion, traction, and terrain-climbing ability.

During the test, it was observed that the Tweels underwent noticeable deflection when the rover drove off short ledges. This indicated that some of the fall energy

73 was being diverted from the suspension tubes to the Tweels. The Tweels appeared to adequately provide cushioning during short falls.

However, as tested, the Tweels had no grousers or other features on their tread surface. In fact, the Tweels had a very thin layer of mold-release wax on their outer surface. For these reasons, the Tweels had poor traction on the sandy soil. While driving on slopes, sand would stick to the wheels, and the rover would then slowly slide downhill.

Figure 6.5: Field test of SR-II with Tweels

Additionally, the Tweels were smaller than other, custom-built wheels for SR-II.

Consequently, the rover had lower ground clearance than with larger wheels, and the rover’s lower gearboxes, located interior to each wheel, would contact obstacles during rock-climbing maneuvers. On one occasion, this contact caused the rover to

74 become stuck on a rock while traversing the natural landscape of the desert. Figure

6.5 shows the left front rover wheel driving over a large, highly sloped rock, with the lower gearbox for that wheel becoming stuck on the rock.

6.4 Tension-Spring Wheel Testing

A set of tension-spring wheels was mounted on SR-II and testing was performed.

The wheels were tested without grousers or tread. General observations were made about the wheels’ performance, and experiments were conducted to estimate the power lost compared to that of other wheels.

Figure 6.6: Completed tension-spring wheel

A set of four wheels was mounted on SR-II, and the rover was placed on the ground. The ground surface chosen was thinly-carpeted concrete. The stance of the wheels was level, as expected, and no anomalies were noted, so the rover was given the command to drive forward. The rover drove smoothly, and the wheels remained

75 stable. Then, the rover was put into a skid steering turn about its center. Under these lateral forces, the wheels began to show lateral rotation. The protruding bolt heads on the surface of the tire would catch on the carpet and the rotation would continue until the tire came into contact with the hub, at which point the bolt would become freed from the carpet and the wheel would bounce back to a neutral position.

Figure 6.7: SR-II with tension-spring wheels

There was some concern about this rotation, as mentioned in the discussion of the computer terrain simulation. The tire essentially has six degrees of limited freedom.

Springs limit the maximum deflections of all six degrees, and the translational degrees are not expected to cause any problems, but the implications of having three degrees of rotational freedom will not be revealed until field testing can be performed. These three degrees of rotational freedom, as briefly mentioned in Chapter Five, are lateral

76 rotation, axial rotation, and rotation about a vertical axis. The rotation about the vertical axis is not thought to be of concern because it should be extremely limited during normal driving. The axial rotation is also very limited. However, the lateral rotation, which causes the tire to contact the hub, requires further investigation.

To compare the power consumption of the rover using these wheels to rigid wheels, another test was performed. An ammeter was connected to SR-II’s electronics, and the voltage of the battery was also measured. Because only one instrument was available for both measurements, the voltage was recorded before and after the test, and the average was used for calculations. No data acquisition was performed for this test, rather, a rough estimate of the average value displayed on the ammeter was observed. Due to the manner in which these experiments were performed, the uncertainty for the following calculations is estimated at 50%. To obtain more accu- rate results, the current and voltage need to be measured simultaneously, and data acquisition should be used to log data for analysis.

With the rigid OU-FIDO wheels on SR-II, motor current for straight-line driving and skid steering, both at 50% motor speed, were observed. The current drawn by the motor was within the range of 0.10 A to 0.17 A for straight-line driving and 0.92

A to 1.15 A for skid turning.

77 This procedure was repeated with the tension-spring wheels on the rover. The voltage during this test was close to that of the previous test, but the currents were somewhat higher. Table 6.2 summarizes this data, and includes calculations for power usage. Again, it should be noted that these are only rough estimations, and the power calculation has significant error because the current and voltage were not measured simultaneously, but the procedure was the same for all tests, so compar- isons between different wheels can be made.

Rigid Wheel Spring Wheel Straight Skid Turn Straight Skid Turn Starting Voltage (V) 13.62 13.62 13.59 13.64 End Voltage (V) 13.58 13.49 13.58 13.57 Average Voltage (V) 13.60 13.56 13.59 13.61 Current Range (A) 0.10 - 0.17 0.92 - 1.15 0.29 - 0.36 0.90 - 1.37 Average Current (A) 0.16 1.00 0.30 1.05 Average Power (W) 2.18 13.56 4.08 14.29

Table 6.1: Voltages, currents,Theoreticaland power Actualused by rigid wheel and spring wheel Component Mass (g) Mass (g) Outer Tire Half 129 277 Inner Tire Half 123 254 Hub 47 52 It can be seMusicen fro Wirem SpringsTable (x12)6.2 that66 the powe66r used for straight-line driving almost #4-40 bolts (x24) 8 8 Total 373 657 doubles for the spring wheels. This increase is more than was predicted in Chapter

Five, but the amount of power used for straight-line driving across a cement surface is small compared to the power used for skid-steering, and should also be small compared to the power consumed crossing sandy soil, climbing a hill, or traversing obstacles. An additional factor in the increase in power for the spring wheels is the

78 protruding bolts on the tire surface. The OU-FIDO wheel, from Figure 1.9b has a much smoother surface.

During skid steering, the power increase for the spring wheel was about 5%. This was expected, because during the skid steering, the lateral deflection of the wheel was high enough to cause the tire to contact the hub.

6.5 Tweel Design Changes

If further investigation were done using Tweels, several modifications would be necessary. First, the Tweel needed grousers for additional traction. All other wheels built for SR-II have had grousers: the OU-FIDO wheel had tread that was cut into the tire by using a four-axis milling machine; the carbon-fiber spoke wheel made by Alois Winterholler had grousers stamped into the tire; the senior capstone wheel had grousers which were bolted into the tire. Grousers could be added to the Tweel by several means. The grousers could be cut into the Tweel on a mill, like those cut into the plastic wheel. However, cutting into the outer band of the Tweel will change its compliance characteristics, making the Tweel less rigid. Also, the depth that the grousers can be cut is limited by the depth of the steel coils inside the Tweel.

Damaging these coils would render the Tweel useless. Another means of attaching

79 grousers is by adding material to the Tweel. This could be accomplished by using fasteners or epoxy to fix plastic, metal, or rubber grousers to the outer surface of the

Tweel. However, attempting to affix separate parts to the Tweel is not as reliable as manufacturing the Tweel as one piece, and during long-distance driving across rough, rocky terrain in extreme temperatures, the grousers are likely to come unattached.

The most secure method of integrating grousers into the Tweel is by redesigning the

Tweel and making a new injection mold. In this manner, any type of grouser pattern could be added, and the grousers would be a permanent feature on the Tweel.

A second modification that should be incorporated into future investigation of the

Tweels is an increase in size. As previously mentioned, the diameter of the model of Tweel that was tested was 155 mm. Other wheels made specifically for SR-II have diameters closer to 200 mm, and these wheels have performed well for obstacle climbing during field testing. The most practical means of increasing the size of the

Tweel is to redesign the Tweel and create new molds. In doing so, other dimensional changes can be incorporated, such as increasing the width, if necessary, and adding sloped sections to the outer surface.

An added benefit of redesigning the Tweel is that the amount of compliance can be easily adjusted. The spring rate of the Tweel is a function of the number and

80 size of the steel coils inside the outer band, and the thickness and width of the band itself. These band dimensions can be easily adjusted if a new mold is being created, as well as the number and size of steel coils within the band.

By manufacturing a new Tweel made to custom specifications, all parameters of the Tweel can be modified as needed. The overall dimensions, traction features, and amount of compliance can be altered to fit performance needs, and new wheels can be made by machining a new mold, making the spring-steel coils, and injection-molding a Tweel.

6.6 Tension-Spring Wheel Design Changes

The tension-spring wheel had the highest amount of compliance, and overall performed very well. There is, however, room for improvement. Several design changes for future versions of the spring wheel are proposed here.

Like the Tweels, the spring wheels need the addition of grousers for traction.

These grousers can easily be incorporated into the existing structure by utilizing the hole pattern that the ribs use. In the same manner that grousers were attached to the high-efficiency wheel built by the senior capstone team, thin strips of aluminum can be bolted to the surface of the tire for modular grousers.

81 A second design modification should be a different means of mounting the wheels to SR-II. The current design requires that 12 bolts be removed per wheel in order to separate the halves. This is necessary to access the five bolts that affix each wheel to the rover. This makes changing the wheels very time consuming. One possible solution to this problem is a removable section in the outside half of the wheel to access the bolts. This has the drawbacks of added weight (in the form of fasteners for the section) and a wheel that is more difficult to seal to keep soil out.

Another concept, one which requires more significant alterations, is changing the mounting style of the wheels to a single threaded nut that holds the wheel onto the lower gearbox. This concept will require aligning pins to prevent free rotation of the wheel, and a means of locking the nut into place to keep it from backing out during driving.

In addition, the tension-spring wheel is somewhat heavy. The final design, as tested, is 657 g. The theoretical mass of the wheel, calculated by computing the volumes of each part in Pro/Engineer and multiplying by the density of each material, was around 375 g. Most of the mass discrepancy comes from the tire halves. It was found that the thickness of the inner and outer tire halves were 0.040 in (1.02 mm) and 0.037 in (0.94 mm), respectively. The dimensions on the drawings sent

82 to the metal spinning company were .025 in (.64 mm) for both parts. Because the outsourced parts were not made to specifications, the wheels are overweight by about

280 g each. If the wheels were made again, the thickness of the wheels should be Rigid Wheel Spring Wheel Straight Skid Turn Straight Skid Turn Starting Voltage (V) 13.62 13.62 13.59 13.64 made somewhere in the middleEndof Voltagethis (V)range.13.58Some addit13.49 ional 13.58weight could13.57 also be Average Voltage (V) 13.60 13.56 13.59 13.61 Current Range (A) 0.10 - 0.17 0.92 - 1.15 0.29 - 0.36 0.90 - 1.37 Average Current (A) 0.16 1.00 0.30 1.05 saved by using aluminum rivAverageets to Poweraffi (W)x the c2.18omponen13.56ts instead4.08of steel 14.29bolts.

Theoretical Actual Component Mass (g) Mass (g) Outer Tire Half 129 277 Inner Tire Half 123 254 Hub 47 52 Music Wire Springs (x12) 66 66 #4-40 bolts (x24) 8 8 Total 373 657

Table 6.2: Theoretical and actual mass of tension-spring wheel components

Lastly, the wheels might need to have more lateral stiffness. As stated earlier, it is still uncertain whether or not the current amount of lateral stability is sufficient, but should it be determined that more stiffness is needed, the spring arrangement can be changed to provide this. Possible means of increasing the lateral stability are increasing the separation of the springs at the tire, separating the connection points for the springs at the hub, or adding extra springs to increase stiffness. Merely using more springs or stiffer springs is also a possible solution, but one of the previous methods is preferred in order to keep the other parameters of the wheel at current

83 levels. If more stiffness is not needed, a bump stop should be added to the hub to prevent the tire and hub from contacting each other.

6.7 Conclusions

There are many possible solutions to reduce the stress on the driveline components of a rover during a fall. NASA has successfully implemented a flexure wheel on the

MER rovers. However, analysis of the flexure wheel designs presented in this thesis shows that this design does not give as much compliance as other designs, and the stresses within the wheel are relatively high during falls.

The Tweel approach, a rubber-based wheel with spokes that only transmit a force when loaded in tension, is a possible solution, but an injection molding process must be developed for this wheel. In the case of rover wheels, when a very limited quantity of parts is needed, the high startup costs and development time associated with injection molding are a major disadvantage. However, the Tweels are a viable solution to add compliance to a rover, and if a spaceworthy polymer with similar properties to those of the Tweel can be chosen, an adaptation of the Tweel could be made to meet the exact requirements for a compliant wheel.

84 A wheel that uses springs to attach the tire to the hub is another possible solution.

This method has the advantage of modularity and relative ease to produce, although if a spun design is selected, the manufacturing process becomes significantly more difficult and costly. A tension-spring wheel demonstrates compliance and drastically reduces the forces of impact on the rover.

Table 6.3: Pro/con table for Tweel and tension-spring wheel

Table 6.3 summarizes the benefits and drawbacks of the Tweel and the tension- spring wheel. While either approach will lead to a viable solution, the tension-spring wheel has more pros and less cons than the Tweel, and seems to be a better solution at present. The Tweel, if redesigned and remolded from a spaceworthy polymer,

85 could prove to be the best solution, because of its potential for high traction, with the proper grousers, and the fact that it does not twist about the x- or z- axes like the spring wheel does.

Rigid Wheel Tweel Spring Wheel Max. Acceleration (g's) 13 8.8 7.4 Power Consumption lowest medium highest Mass (g) 412 480 657

Table 6.4: Comparison of three wheel types

A summary of the data for compliance, power usage, and mass among a rigid wheel, the Tweel, and the tension-spring wheel is given in Table 6.4. The maximum deceleration recorded in the 5-cm fall is given in the first row of the table. Qualitative power consumption for each wheel is also presented, rather than quantitative values, because testing methods gave high uncertainty. The final row of the table gives the mass of each wheel. It should again be noted that the tension-spring wheel’s mass was drastically higher than expected because the parts were not made to specifications.

However, the spring wheel, as tested, meets the requirements for a compliant wheel for SR-II.

86 Bibliography

[1] Bill Arnett. The nine planets solar system tour, August 25 2006. URL http: //www.nineplanets.org.

[2] Roy Beardmore. Coefficients of friction, 1999. URL http://www.roymech.co. uk/Useful_Tables/Tribology/co_of_frict.htm.

[3] Donald Bickler. Roving over mars. Mechanical Engineering, April 1998. URL http://www.memagazine.org/backissues/membersonly/april98/ features/mars/mars.html.

[4] Donald B. Bickler. The new family of jpl planetary surface vehicles. In D. Moura, editor, Missions, Technologies and Design of Planetary Mobile Vehicles, pages 301–306, Toulouse, France, September 1992. CNES, Cepadues-Editions Pub- lisher.

[5] Wayne J. Boeckman, November 2006. Personal conversation.

[6] A. Bogatchev, V. Gromov, V. Gorbunov, V. Koutcherenko, M. Malenkov, S. Ma- trossov, and V. Petriga. Wheel propulsive devices for mobile robots: Designs and characteristics. Technical report, Russian Mobile Vehicle Engineering Institute.

[7] Frank Philip Bowden and David Taylor. Friction: An Introduction to Tribology. Anchor Press/Double Day, Garden City, NY, 1973.

[8] Dan Boye. Rolling friction, 1998. URL http://webphysics.davidson.edu/ faculty/dmb/PY430/Friction/rolling.html.

[9] William D. Callister, Jr. Materials Science and Engineering: An Introduction. John Wiley and Sons, Inc., fifth edition, 2000.

[10] Peter Duggan, Jonas Houchin, Oren Lever, James Miller, and Orin Miller. AME 4553: Solar rover 2 (SR2) efficient wheel. Final report, The University of Okla- homa, 2005.

[11] Alex Ellery. An Introduction to Space Robotics. Praxis Publishing, 2000.

[12] Peter R. Fletter. Metal spinning tutorial, November 1995. URL http://www. stanford.edu/group/prl/documents/pdf/spinning.pdf.

87 [13] Douglas C. Giancoli. Physics for Scientists and Engineers. Prentice Hall, third edition, 2000.

[14] John M. Holt, Harold Mindlin, and C. Y. Ho. Structural Alloys Handbook. CINDAS/Purdue University, West Lafayette, IN, 1996.

[15] Lunar Roving Vehicle. A brief history of the lunar roving vehicle. NASA Mar- shall Space Flight Center, April 2002.

[16] Lunar Roving Vehicle. Lunar rover, 2007. URL http://en.wikipedia.org/w/ index.php?title=Lunar_rover&oldid=103483206.

[17] Lunokhod. Lunokhod, 2007. URL http://en.wikipedia.org/w/index.php? title=Lunokhod_1&oldid=99471843.

[18] Mars Exploration Rover. Mars exploration rover mission: Overview, 2006. URL http://marsrovers.nasa.gov/overview/.

[19] Mars Exploration Rover. Mars exploration rover mission: Features, 2005. URL http://mars.jpl.nasa.gov/mer/spotlight/wheels01.html.

[20] Harold Masursky, G. W. Colton, and Farouk El-Baz, editors. Apollo Over the Moon: A View from Orbit. National Aeronautics and Space Administration, Scientific and Technical Information Office, 1978.

[21] Material Properties. Matweb - the online materials information resource, 2006. URL http://www.matweb.com/.

[22] Andrew Mishkin. Sojourner: An insider’s view of the Mars Pathfinder Mission. Berkley books, 2003.

[23] NASA National Space Science Data Center. Luna 17/lunokhod, 2005. URL http://nssdc.gsfc.nasa.gov/database/MasterCatalog?sc=1970-095A.

[24] Outgassing. Outgassing data for selecting spacecraft materials system, 2006. URL http://outgassing.nasa.gov/.

[25] V. G. Perminov. The difficult road to mars: A brief history of mars exploration in the soviet union. Monographs in Aerospace History, (15), July 1999.

[26] Matthew J. Roman. Design and analysis of a four wheeled planetary rover. Master’s thesis, The University of Oklahoma, 2005.

88 [27] P. S. Schenker, E. T. Baumgartner, P. G. Backes, H. Aghazarian, L.I. Dorsky, J. S. Norris, T. L. Huntsberger, Y. Cheng, A. Trebi-Ollennu, M. S. Garret, B. A. Kennedy, A. J. Ganino, R. E. Arvidson, and S. W. Squyres. FIDO: A field integrated design and operations rover for mars surface exploration. In Proceedings in i-SAIRAS, Montreal Canada, June 2001.

[28] Sojourner. Description of the rover sojourner, 1996. URL http://mpfwww.jpl. nasa.gov/rover/descrip.html.

[29] Sojourner. Mars pathfinder rover, 2005. URL http://nssdc.gsfc.nasa.gov/ database/MasterCatalog?sc=MESURPR.

[30] Alan C. Tribble. The Space Environment: Implications for Spacecraft Design. Princeton University Press, 2003.

[31] Edward Tunstel, Terry Huntsberger, Hrand Aghazarian, Paul Backes, Eric Baumgartner, Yang Cheng, Michael Garrett, Brett Kennedy, Chris Leger, Lee Magnone, Jeffrey Norris, Mark Powell, Ashitey Trebi-Ollennu, and Paul Schenker. FIDO rover field trials as rehearsal for the NASA 2003 mars ex- ploration rovers mission. In Ninth International Symposium on Robotics with Applications. World Automation Congress, June 2002.

[32] Mark Wade. Lunokhod, 2007. URL http://www.astronautix.com/craft/ lunokhod.htm.

[33] Alois Winterholler. Development, design and verification of different wheel con- cepts for NASA’s field integrated design and operations rover. Master’s thesis, Fachhochschule Augsburg, Hochschule fur¨ Technik Wirtschaft Gestaltung, Uni- versity of Applied Sciences, November 2002.

89 Appendix A Data Calculations

90 Appendix B Mechanical Drawings

91 92