Design and Analysis of Lunar Regolith Excavator

Design and Analysis of Lunar Regolith Excavator An Investigation By: Jonathan Bapst Bradley Cheetham Andrew Hatt Table of Contents Abstract 1.0 Int...
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Design and Analysis of Lunar Regolith Excavator

An Investigation By: Jonathan Bapst Bradley Cheetham Andrew Hatt

Table of Contents Abstract 1.0 Introduction................................................................................................................ 1 1.1 Scientific Implications................................................................................... 1 1.2 Educational Value.......................................................................................... 1 1.3 Economic Potential........................................................................................ 2 1.4 Process for Investigation................................................................................ 2 1.5 Specific Focus of Investigation...................................................................... 2 2.0 Background................................................................................................................ 3 2.1 Lunar Regolith............................................................................................... 3 2.2 Physical Properties Related to Excavating.................................................... 3 2.2.1 Excavation Models and Their Significance.................................... 4 2.2.2 Lunar Environment Effects on Excavation Forces......................... 8 2.2.3 Formulation and Conclusion of Results.......................................... 9 2.3 Elemental Composition and Applications..................................................... 9 2.3.1 Resources and Possible Uses.......................................................... 9 2.4 Summary........................................................................................................ 11 3.0 Tools and Methods Utilized....................................................................................... 12 3.1 Basic Conceptual Design and Optimization.................................................. 12 3.2 Engineering Equations and Calculations....................................................... 13 3.3 SolidWorks Design Solutions........................................................................ 15 3.4 COSMOS Products........................................................................................ 16 3.5 Summary........................................................................................................ 16 4.0 Design Process........................................................................................................... 17 4.1 Constraints on Design.................................................................................... 17 4.2 Initial Assumptions and Ideas........................................................................ 18 4.3 Excavation Vehicle........................................................................................ 18 4.3.1 Stationary Excavator with Angular Excavation Pattern................. 18 4.3.2 Mobile Rover with Mounted Excavation Mechanism.................... 20 4.3.3 Summary of Vehicle Analysis........................................................ 22 4.4 Excavation Mechanism.................................................................................. 22 4.4.1 Auger (“Snow-Blower”) Design..................................................... 23 4.4.2 Bucket Wheel.................................................................................. 25 4.4.3 Conventional Loader/Backhoe........................................................25 4.4.4 Summary of Excavation Mechanism.............................................. 27 4.5 Design of Bucket Wheel................................................................................ 27 4.5.1 Direct Deposit Design..................................................................... 28 4.5.2 Two Stage Bucket Wheel................................................................28 4.6 Power Usage.................................................................................................. 29 4.7 Summary........................................................................................................ 30 5.0 Final Design............................................................................................................... 31 5.1 Bucket Wheel................................................................................................. 31 5.1.1 Buckets............................................................................................ 31 5.1.2 Wheel Housing................................................................................33 5.1.3 Guide Plane..................................................................................... 34

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5.1.4 Guide Rail....................................................................................... 34 5.1.5 Shaft Housing................................................................................. 35 5.2 Forward Shaft.................................................................................................36 5.2.1 Forward Shaft Bearings.................................................................. 36 5.3 Excavating Arm............................................................................................. 37 5.4 Base................................................................................................................ 38 5.5 Crank Rocker................................................................................................. 38 5.6 Elevating Axle............................................................................................... 39 5.7 Regolith Transport Belt..................................................................................39 5.8 Material Selection.......................................................................................... 40 5.9 Proof of Concept Design................................................................................ 40 5.10 Summary of Design.................................................................................... 41 6.0 Report Summary........................................................................................................ 42 Appendix.......................................................................................................................... 43 I. Analysis of Parts............................................................................................ 43 a. Bucket Wheel Shaft........................................................................... 43 b. Excavation Arm................................................................................. 47 II. Calculations....................................................................................................50 III. Bucket wheel Design Progression................................................................. 53 IV. COSMOS Simulations of Loading................................................................ 54 V. Technical/Working Drawings........................................................................ 55 VI. Bibliography.................................................................................................. 59

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Abstract It has been nearly 40 years since man first walked on the moon and recently there has been renewed interest in returning. In order to sustain this exploration, in-situ resources must be utilized. The goal of this project was to design an excavator to mine lunar regolith. The following report will outline the various options that were investigated for this design as well as the final design which is capable of operating in the extreme lunar environment and mining large amounts of regolith.

1.0 Introduction Mining lunar regolith (equivalent to lunar dirt) has many significant implications. There are many resources that can be extracted from this material that are vital to space exploration and development.

It also can be used to provide radiation and micro-meteorite protection for

habitats.

1.1 Scientific Implications. Samples studied from the Apollo moon landings have provided very large amounts of data that has helped study the formation of both the earth and the moon. For scientific study, a lunar excavator would be capable of providing a large number of samples and thus allow this material to be studied by a larger group of scientists than currently have access to the limited number of Apollo samples. In addition to this scientific opportunity the lessons learned from a mission involving this excavator could also yield information about operating conditions on the moon and improve our understanding of the lunar environment. An understanding that could shape the design of future machines destined for operational life on the moon.

1.2 Educational Value The design of this excavator has provided an opportunity to learn many valuable things. The design process itself provided a multitude of challenges that were solved by implementing engineering reasoning and methods. The experience gained from such a group project will be of great value as this project continues and as others are undertaken in the future. The process of investigating a current challenge with a variety of solutions and unknown influences was an

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opportunity to think “outside of the box” and has lead to many possible continuations of this project.

1.3 Economic Potential A lunar excavator has the potential to be extremely valuable to any party interested in space exploration. This market is no longer only government organizations and as more commercial ventures begin to take shape in space the moon will become more like another continent and less like a different world. The first entity to successfully develop mining and processing facilities on the lunar surface will have the potential to utilize the lunar regolith to produce many resources that are vital in space and quite possibly here on earth as well.

1.4 Process for Investigation. Investigation Steps 1. Research physical properties of lunar regolith and the lunar environment 2. Define environmental and operational constraints on design 3. Develop and investigate designs for chosen application 4. Design and test chosen method 5. Integrate sub-systems and compile general design

1.5 Specific Focus of Investigation This research will focus on the actual excavating mechanism and its associated assembly to the point of depositing regolith onto whatever vehicle this is mounted on. Designing in this format allows the excavator design to be used in various applications and allows more focus on the challenge presented from excavating on the moon. A lunar rover or machine to mount this design on could have many other operational functions and thus needs to be designed with those in mind. Specifically this research focuses on: regolith properties, regolith excavation method, excavation arm assembly, and regolith transportation from extraction level to specified location.

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2.0 Background This section of the report will detail the background research done to develop an understanding of the problem. Specific areas of interest are behavioral properties of lunar regolith, elemental properties and possible uses for a lunar regolith miner, effects of the lunar environment, as well as the specific benefits such an excavator could provide.

2.1 Lunar Regolith Regolith is the Greek term for a layer of loose material covering rock. The moon is almost entirely covered by regolith with the only exceptions being very steep cliffs and deep impact craters. The lunar regolith is a result of 4.5 billion years of meteorite and micro-meteorite impacts. Because the moon does not have wind or water erosion, these impacts are the only major force to shape the landscape. In older regions of the moon the regolith can be 10-15 meters deep while in the younger areas this depth is closer to 4-5 meters deep. A significant problem is that small particles of regolith, on the order of microns in size, have very jagged edges and can stick to and wear parts during use. This structure is a result of the lack of weathering processes and frequent micro-meteorite impacts. This was a significant problem during Apollo missions and created many failures and safety hazards.(Heiken et al, 1991)

2.2 Physical Properties Related to Excavating One of the key problems in building an excavation unit is determining the force to fail lunar regolith or in other words the stress our excavator would be experiencing during excavation. Due to budgetary and logistical constraints actual testing was not feasible. In lieu of this we must look to previous documentation to identify the type of design factors we would have to consider in order to withstand excavation. Models for excavation (in general, not necessarily lunar regolith) have been used in the past and we initially looked over these to see if they were reliable and accurate. One major issue that needed investigation was the reduced gravity (1/6th) in the lunar environment. We must also consider these conditions and compare them to how an excavator on Earth would operate. All the results of our investigation would be combined to form an educated and reliable solution for excavation force.

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2.2.1 Excavation Models and their Significance To begin our research into excavation forces we focus on excavation models that are already introduced. In the documentation “Soil-tool interaction theories as they apply to a lunar soil simulant.” (Willman and Boles 1995) the examination/testing of current models is undergone and compared to that of a lunar simulant to prove whether the models are indeed a reliable resource in predicting excavation forces. Each individual model stated has their own set of characteristics, though most shared similar qualities. •

Hettiaratchi and Reece (1965) (Model 1) –

This first theory was based on the assumption that cutting soil is failing the soil in shear stress with the following force F,

The four K values in equation correlate to gravitational, cohesive, adhesive and surcharge components of the soil. Later, in Hettiaratchi and Reece (1967), another theory is created in respect to three dimensional soil failures, which seemed to be more useful for our purpose since a three dimensional/component

system

is

more

realistic

in

application.

Pf (force required for failure in the vertical regime), Ps (force of the sideways force), Ca (adhesional coefficient). •

Godwin and Spoor (1977) (Model 2)

Here we see another three dimensional model. This particular model was based on a soil wedge that is formed during all soil excavation, at any rake angle or width. This wedge is analyzed closely to create an accurate theorem for soil failure force, D. 4



McKyes and Ali (1977) (Model 3) –

This model was influenced heavily by Godwin (1974) and Godwin and Spoor (1977).

This equation (shown above) is used to find angle beta through the minimization of N. An iterative approach for solving the equation is stressed as noted in McKyes (1989). This beta (which minimizes N) is considered the critical angle or rake angle in which there is least resistance and the soil fails most easily. This angle and its importance is then adapted into Reece’s (1965) force equation thus bringing us to a total force required, P:

H being the horizontal component of this force •

Perumpral, Grisso, and Desai (Model 4) -

A three dimensional theory created to decrease the amount of mathematical complexity within soil failure models and theorems.

This equation is quite similar to the force equation (P) in Reece’s (1965). P symbolizes the forces in total exerted on the excavating tool. One notable difference is that this equation does not have an extra coefficient (q) for surcharge. Instead this surcharge effect is included within the Nvalues.

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Once P is calculated, the total draft force for the tool is then calculated based on angles made between the soil and the tool.

It may be noticed that the description of these models is somewhat brief. This is not a mishap but a result of the concluded evidence from Willman and Boles, 1995. The models, when in comparison to an actual regolith excavation experiment, produce unsatisfactory results. The reason for presenting actual formulas is to show the similarities between these models. The manner in which they were found and produced is not acceptable when applied to a lunar regolith simulant. The particular simulant (for lunar regolith) used in their comparison experiment was MSL-1 which seems to have drawbacks when compared to actual lunar regolith. Although NASA is in possession of actual lunar regolith, it does not allow its use for large-scale research or experimentation. The real regolith is viewed as a “valuable national resource”. This is understandable since this regolith was collected during Apollo missions.

The following is a comparison chart of MSL-1 simulant compared to the known data of lunar regolith:

The MLS-1, although looking like a reliable substitute, does not have the same interlocking particle attraction lunar regolith exhibits nor does it have as fine of particles as lunar regolith. The maximum density value (of 2.29 gm/cm^3) seen here for lunar regolith was taken from a 70 cm core sample during Apollo 17 (Willman and Boles 1995). The truth is that densities on the moon may vary in extremities when delving further below the lunar surface. Since the regolith 6

has been compacted and vibrated from meteor impacts for eons the compactness or density may very well be larger than our presumptions. Alas, these are our only real data figures for density so we will accept them for our design. An excavation experiment is undergone with the lunar stimulant (MLS-1) where a blade oscillating back and forth, powered by a winch, is forced through this simulant. A force transducer attached to the cable measures the forces in return from the blade failing the MLS-1 simulant. All four models are used with the supposed coefficients, it is tabulated versus the experiment and thus a comparison chart is created:

Depths = variable Width = 13 cm Angle to Horizontal = 60 degrees From the chart we can conclude that the predicted (3) and ŷ (4) (actual) are not even close. Although there are certain factors that can be modified (i.e. friction angle) there is no realistic explanation for this difference. Instead we see that the models are unable to correctly simulate this excavation force. There was some mention that the excavation models were for a more ductile type of substance (like common soil or dirt). The brittle regolith simulant reacted differently and therefore the models could not accurately predict the forces to fail the regolith. We had to search for more clues and the result of lower gravity levels. Another document we looked to is “Excavation forces in reduced gravity environment.” (Willman and Scott 1997),

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which practically follows up “Soil-tool interaction theories as they apply to a lunar soil simulant.” (Willman and Boles 1995) in search for a reliable force of lunar excavation.

2.2.2 Lunar Environment Effects on Excavation Forces “Excavation forces in reduced gravity environment.” (Willman and Scott 1997) focuses on the excavation forces of lunar regolith in a lunar environment (as compared to a terrestrial environment) where there will be about 1/6th of the gravitational forces as there are on Earth. This experiment is almost a direct response to what we’re looking for and may help clarify a reliable excavation force. The fact that certain excavation models seemed inaccurate when predicting excavation forces for lunar regolith was certainly a drawback. A different simulant (JSC-1) was used in this experiment but basically under the same preparations with a density of around 1.8 g/cm^3. Apparently the simulants are all rather similar but have minor variables in cohesion and internal friction angles. Using a KC-135 aircraft flying parabolas, the team was able to experience periods of time with 1/6th gravity conditions. During this time a similar experiment to that of (Willman and Boles 1995) was conducted to see how much force was required for a blade to fail in an amount of compacted regolith simulant. The following are average results based on the experiments:

Excavation Force @ 1g (Earth) ~ 95 N (@ depth x width == 8 x 5.75 cm, 90 degree orientation) Excavation Force @ 1/6g (Lunar) ~ 25 N (same dimensions)

These values will shape our own excavation forces in our design. Since they are much lower than previous MSL-1 simulant results (Willman and Boles 1995), a factor of error will be applied to our predictions. Also in that regard we understand that the purpose in this document (Willman and Scott 1997) was to find the actual force values involved with excavation. This correlates along the lines more closely to our own desires.

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2.2.3 Formulation and Conclusion of Results In 2.2.2 we see a more relevant source for regolith excavation. In both documents cited, we see two different simulants MSL-1 and JSC-1. Both have a similar density to that of lunar regolith (~2.29 g/cm^3) yet neither were exact. It is evident that certain properties aside from density affect the excavation force required. In our position we will assume that JSC-1 matches up more closely with actual lunar results thus leading us to an excavation force number. In regard to the models we viewed it’s unsure as to whether the properties of the lunar regolith simulant were the obtuse factor but it is definite to say they were inaccurate in predicting force results. In fact, for future models, it would be especially convenient to take into consideration lunar regolith and other lunar factors. It is destined to be a major issue and a reliable model would save much headache for those designing a lunar excavator.

Including a design factor of 2 for our force results we will use the following values in the design: F = 190 N (@ 1g) F = 50 N (@ 1/6th g)

2.3 Elemental Composition and Applications. The moon is rich in many resources that have the potential to benefit both space travelers and Earth. Resources for space travel that originate on the moon would be beneficial because the cost to launch from the lunar surface to orbit is much less than the cost to launch from Earth’s surface to orbit. The reduction of gravity as well as the lack of an atmosphere makes this possible. There is also a benefit to mining the moon for resources instead of mining earth. Open pit mining and other large mining procedures on earth scar the landscape and do permanent damage to the environment. There are also elements available on the moon that are unavailable on Earth due to weathering and our active atmosphere.

2.3.1 Resources and Possible Uses Lunar regolith is comprised of between 40-60% oxygen, mostly tied up in metallic oxides. These oxides could be refined and oxygen could be produced in large quantities. Work on this refining technology is currently being done by NASA and has shown positive progress. Such oxygen would be pivotal in permanent space settlements for life support. In addition to life

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support it has the possibility to be used as a propellant in rockets and could easily be sold to earth orbit as well as lunar orbit. This oxygen is tied to silicon, iron, and titanium. Thus removing the oxygen would leave refined iron, silicon, titanium, and other metals as bi-products. These biproducts have obvious value in building space structures as well as solar panels. Additional resources are present in the lunar regolith as a result of the implantation over 4.5 billion years of solar wind particulates. These particulates include hydrogen, helium, and their associated isotopes. Hydrogen can be removed from the regolith by heating the particles to an optimized level at which point the hydrogen gas would be released. This hydrogen could be combined with oxygen to produce water, or be used in combination with oxygen as propellant. The value of such resources, once recovered, would be unimaginable and could truly revolutionize the way space travel is approached. If hydrogen and oxygen were produced on the moon and sent to earth orbit to re-fuel space craft, a much larger mass could be launched to destinations including geosynchronous orbit, lunar orbit, or any other destination in the solar system. This paradigm shift would be made possible by a re-fueling station in low earth orbit. Such a station supplied from the moon could reduce costs and open frontiers to exploration in the very near future. Helium is another valuable solar wind volatile that could revolutionize the energy market of the world in the very near future. Helium-3 is an isotope of helium and when used in a fusion reaction, would produce absolutely no radioactive waste. This type of electricity generation is 100% clean and creates electricity directly, thus removing the losses associated with heating water and operating turbines. Helium-3 fusion is not yet possible on a commercial scale, but fusion technology is quickly developing and could become practical in the very near future. The case for lunar derived helium-3 fusion is made by Dr. Harrison Schmitt in his book titled “Return to the Moon”. Regolith itself can be very valuable in a lunar settlement. Fine grained regolith could be sintered into bricks, or piled onto habitats to provide very important radiation and micrometeorite protection.

Courser particles could be used as aggregate in lunar concrete or

compacted to create lunar roads. Such applications would be very beneficial considering the very high launch costs of comparable material for radiation shielding as well as road and structure construction.

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2.4 Summary In summary, regolith excavation forces are very difficult to predict because actual research is very difficult. Many models were found that have been tested and refined based on mining here on earth, but until there is a greater presence on the moon for testing and research, accurate models will be very difficult to develop. For this reason we modified experimental values derived with stimulant and added a design factor of safety to account for any deviations that could occur.

The physical properties of regolith are important when designing the

excavator, but the justification of mining the moon is also very relevant. Potential resources are very abundant on the moon, and as humans begin to develop technologies in space these resources will be very valuable. There is also potential need for these resources on earth, and it is very possible that in the future the moon will become a supplier of raw materials and energy for a continuously growing population on earth.

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3.0 Tools and methods utilized In the creation of our excavator a number of engineering methods and tools were applied to design considerations. Working through these various tools and methods we were able to analyze and acquire key information for our design. The limitations produced from each calculation helped us to converge on the final design. Initially, our method for creating the excavator consisted of nothing more than a pad of paper, pencil and three minds. With a relatively open ended design it can be quite difficult to understand what you need to consider all at once so we attacked individual pieces of the design and came up with a number of solutions, then analyzed each one until we had our final choice. The largest problem with this approach is the fact that convincing a person that one way is better or worse than another is extremely hard to do. The absence of mathematical backing or physical proof truly leads to speculation. This is where the various tools and methods were vital to design choices.

3.1 Basic Conceptual Design and Optimization In our basic conceptual design certain parameters were restricted by our given constraints.

We knew how much regolith would have to be mined in a given amount of time

and this gave us a basic mass flow equation. Once we all agreed on a bucket wheel type design we focused on the buckets themselves. With this mass flow equation we were able to decide how many buckets were needed and of what size. An excavation arm was decided on for a longer reach of our excavation tool. This arm was predicted to move in a biaxial manner. This way it could be raised up and down as well as side to side while excavating. Moving the regolith from the bucket wheel to the “container” was another problem for our design. We needed some sort of transport system. After some discussion including “throwing” of the regolith or “dumping” the regolith in large quantities we agreed on the idea of a conveyer belt. This belt would run the length of our excavation arm to our “container”. Now that we had a conveyer belt and an excavation tool attached to an arm we needed something to drive this but before that what power would be required to drive this? The answer came to regolith excavation forces, a fundamental piece to our design. After the consideration of some models, simulations, experiments and other research a force was decided on. Our

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excavation force was determined so now we could move onto a motor choice. The motor was practically a predetermined design with variable power output in regard to size. In order to move our excavation assembly back and forth we decided on the use of a crank-rocker. This choice came very easily since you could use a simple one speed motor and have a constant side-to-side movement during excavation. During the basic design segments optimization took place as well. Under certain constraints we were able to pretty much scale our pieces down in order to satisfy the requirements. Certain pieces like the bucket were optimized through minimization of friction. This kind of optimization helps us keep our excavation force as low as possible. Weight was minimized where possible based on stresses and failure theories.

3.2 Engineering Equations & Calculations Many equations and calculations were used to finalize design pieces and optimize them for the purpose of excavation. The entire calculation processes are located in Section I. Analysis located in the appendix. The first set of equations used was to find mass flow ( mA ) of the regolith based on our desired excavation rate. d

e

Mass rev f f f f f f f f f f f f f f f f f f f f f f f f f f m= f = V bucket x Ν buckets x Speed f x % filled = mA (kg/min) Time min A

These parameters setup our basic mass flow rate which controlled the rest of our design specifications. Once our bucket wheel size had been selected the number of buckets, their size, and angular velocity could calculated. To be conservative we assumed the buckets would be filled to only 60% of the total capacity.

Basic Equations served as basis for all parts: b

c

F = m Ba force

Τ = F Bd torque `

Power Equation used to select motor:

Η = Τ Bω power `

a

M = F Bd moment `

a

a

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For analytical calculations we used force based equations along with fatigue failure. Normal Stress (due to bending moment): 32M f f f f f f f f f f f f f f σb = f (for circular cross section) 3 πd

6M f f f f f f f f f f f σb = f (for rectangular cross section) 2 wh

Shear Stress (due to torsion) 16T f f f f f f f f f f f f τ= f (for circular cross section) 3 πd

Vf f f f (shear stress due to shear force) τ= f A

Maximum Stresses occur where maximum moments occur (or maximum torque).

For Dynamic loads and Fatigue Failure we use a conservative approach to predict life longevity. Amplitude and Midrange Stresses apply as: M L Lσ max @ σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M (amplitude) σa = K fL M L 2

M L Lσ max + σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M σm = K fL M L 2

M L Lτ max @ τ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M (amplitude) τa = K fL M L 2

M L Lτ max + τ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M τm = K f L M L 2

(midrange)

For pieces that do not exhibit a notch, K f = 1

(midrange)

The same rule applies to amplitude and midrange shear stress.

When a component is affected by both normal and shear stresses in the amplitude or midrange then we use von Mises formula to generalize our stresses into σ a . and σ m . . w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w b c 2 2 σ a . = rσ ax @ σ ax σ ay + σ ay + 3τ 2a

w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w bw c 2 2 2 σ m . = rσ mx @ σ mx σ my + σ my + 3τ m

The endurance strength ( S e ) is based on material properties and shape/size of component as well as the loads placed on the component. As followed:

S e = k a k b k c S e.

⎧0.504 S ut kpsi or MPa S ut ≤ 212 kpsi (1460MPa ) ⎪ where S = ⎨ ⎪⎩ 107 kpsi (740 MPa ) Sut > 212 kpsi (1460 MPa ) ' e

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ka = a S

b ut

⎧ 0.879d −0.107 0.11 ≤ d ≤ 2 in ⎪ − 0.157 2 < d ≤ 10 in ⎪ 0.91d kb = ⎨ − 0.107 2.79 ≤ d ≤ 51 mm ⎪1.24d − 0 . 157 ⎪⎩1.51d 51 < d ≤ 254 mm

⎧1 ⎪ k c = ⎨ 0.85 ⎪ 0.59 ⎩

bending axial pure torsion

Once S e is determined, further analysis can be completed. For our circumstance we wanted to use the most conservative failure theory. This led us to the Modified Goodman approach for fatigue failure. (Where S ut is ultimate strength and S y is yield strength) Modified Goodman (test for infinite life, true for n > 1)

σf 1f f f f σf f f f f f f f f f f f f f f f = m + a n S ut Se f

g f

g

Our test for first cycle failure: First Cycle Failure (if n > 1, does not fail at first cycle)

1f + Sf f f f Sf f f f f f f f f f f f f f f f f f f f f f af m = f n Sy 3.3 SolidWorks Design Solutions

SolidWorks is a brand of virtual prototyping tools used to three-dimensionally design products in a virtual environment. Vast applications include the modeling of individual components to the assembly and simulation of multi-stage machines. Use of such software benefits the design process in several ways. Three dimensional representation aids in the conveyance of conceptual proposals and provides intermediate stages of design to build on. In a team oriented environment, this is crucial to swift, unambiguous and widespread transference of ideas and design considerations. Furthermore, the use of virtual prototyping allows for simple, frequent changing of design parameters. Component dimensions, materials, and other parameters can be readily altered to fit new design constraints or incorporate new concepts. This enables deeper consideration of secondary models and testing of alternative design concepts without having to restructure the original design for each iteration. A secondary feature of the software is its ability to simulate motion of select design components. SolidWorks Design Solutions, 15

however, is limited in its ability to simulate mechanical behavior of design parts during said simulations. To compensate for this shortcoming, the design software is used in conjunction with simulation-oriented add-ons.

3.4 COSMOS Products

The COSMOS line of products are software packages developed to complement SolidWorks and provide the means of measuring and monitoring mechanical properties of virtual components. They compensate for the lack of experimental testing faculties in the standalone SolidWorks package. Two primary products were implemented during the design of the lunar excavation tool, COSMOSWorks and COSMOSMotion. COSMOSWorks is designed to provide measuring utilities to monitor component properties when exposed to static forces or environments. By specifying external forces, force-fields, or stresses acting on either the entire assembly or a particular component, the software takes into account material properties and is able to calculate strains, shear stresses, and other mechanical properties of a desired segment, part, or location. COSMOSMotion operates similarly to COSMOSWorks, except over a specified time domain. It allows component properties to be analyzed and monitored as they undergo changes over a period of time. Often times modeling through engineering equations is inadequate or unpredictable. As seen in chapter 2.2, attempts at modeling lunar excavation forces are inconsistent. Use of such programs allow for various models to be tested and their impacts on the overall design of the vehicle to be recorded quickly and with minimal effort. This made such applications critical tools in the timely and accurate design of the lunar excavation tool.

3.5 Summary

Clearly engineering equations, conceptual applications, and computer programs are vital in the design of an assembly. Without such tools every idea would need to be constructed and tested multiple times. The use of virtual prototyping software provides the opportunity to change and test designs quickly and without extensive costs.

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4.0 Design Process

The goal of designing a lunar excavator, something that NASA has even yet to completely develop, was a very steep challenge for a group of undergraduate engineering students. The following discussion of the design process that was undertaken is merely a summary of the conclusions reached after hours of design discussion and debate coupled with rough engineering analysis. Consideration was given to various models on several different levels. Specifically, design of the overall excavation vehicle was considered in light of larger implications of lunar excavation. Next, an investigation into an excavation mechanism to lift regolith off the lunar surface was performed, giving close consideration to design limitations. And finally, a conclusive conceptual design was chosen to be the subject of further analysis. Many of these possibilities could be a focus of specific study by themselves, however for the purposes of this design project, the focus was to narrow down the design options to find the “best” design for the given constraints; this chapter will detail this process.

4.1 Constraints on Design

Several restrictions were set on design parameters of the excavator to ensure its operation requirements and transportation specifications could be standardized for various deployment methods on the lunar surface. In accordance with the California Space Institute’s Lunar Regolith Excavation Challenge’s rulebook, a specified maximum weight and power usage was ascertained. The excavation tool itself was apportioned a total mass of 70kg. This allots a sufficient amount of mass to the vehicle on which the excavation tool is mounted, while keeping the overall mass of the vehicle at a minimum. This is vital to keeping mission costs down due to the large price of transporting mass from the Earth’s surface to the lunar environment. In addition, capping the apparatus’ mass defines a maximum stress the vehicle will need to endure in order to support the excavation mechanism. The power consumption of the excavation apparatus is limited to a maximum of 30 Watts of electrical power. This permits a standardized power source to be used in a variety of excavation scenarios. Under these restraints, the completed excavation apparatus is to be capable of excavating a minimum of 10kg of lunar regolith per minute. This allows for the excavator to reach an ambitious excavation rate while still accounting for loses endured during the excavation process. Finally, the excavation apparatus, when mounted on the excavator vehicle, should not inhibit the

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vehicle’s ability to maneuver, in both a forward and reverse fashion, or on to and off of a ramp. This constraint assures that it can efficiently be deployed and retrieved for mining excursions from a docking bay, or regolith deposit station, that is elevated above the lunar surface (if applicable).

4.2 Initial Assumptions and Ideas

Given these very limited constraints on the design, initially there were many design decisions to explore and discuss. Before any of these ideas could be further explored it was necessary to learn as much as possible about the environment of the moon and the physical properties of lunar regolith as mentioned previously. Many initial assumptions about how to excavate on the moon were debated and it was discovered that in order to create a design with such ambiguity and little to no prior designs to consider, any and all ideas were to be considered until they were proven to not be feasible.

4.3 Excavation Vehicle

The excavation vehicle’s method of maneuvering through the lunar environment greatly impacts the design of the excavation mechanism. The vehicle’s excavation path, direction, degrees of motion, and expected moments and reaction forces all have to be taken into account when considering the design of the excavation mechanism. Furthermore, after excavation the regolith must be either immediately processed on the vehicle, deposited in a collection compartment on the vehicle for storage, or dropped in a localized collection station to be retrieved at a later time. The transportation and associated losses must be considered when designing the excavation mechanism. For these reasons, an investigation into effective and efficient preliminary designs of excavation vehicles was performed, categorized into two major approaches.

4.3.1 Stationary Excavator with Angular Excavation Pattern

The first consideration involves a stationary module that is situated in a centralized location of the target regolith. Mounted on this base are two protruding arms that extend in opposite radial directions, each supporting an excavation mechanism. The arms are to be fastened to each other at a rotational axis projecting vertically out of the lunar surface and

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passing through the central stationary module. Driven by a motor located at said axis of rotation, the arms ideally move angularly in a “fan-like” manner at identical rates. This results in a circular area traversed by the arms with the stationary module located at the center. The advantage of such a design becomes apparent when the excavation tools are mounted on variable radius tracks (or threads) along the arms, allowing radial motion inward and outward from the center of rotation. By adding radial motion of the excavation mechanisms to the circular motion provided by the rotation of the arms, access to excavation of any and all points within the circular footprint is granted without having to move the stationary unit. Once mined, the regolith is transferred along the arm, by means of one of several possible transportation systems, back to the central module. These design principles are beneficial for several reasons.

Figure 4.3.1: Conceptual representation of stationary excavation vehicle.

As opposed to a fully mobile vehicle (as seen in 4.3.2), this design allows for certain components to remain static during excavation, reducing the need to transport such masses throughout the excavation field. Parts such as the motors that drive rotational velocities, processing facilities, crew quarters, regolith transportation systems, and the radial motion of the excavation mechanisms, as well as computerized hardware that monitors and controls the operation of the vehicle can be housed in the stationary unit. Additionally, the mined regolith, after being transported inward along the excavation arms, can be stored in the central unit until collected for use. This eliminates the need to compensate for increased power requirements caused by a need to carry an increasing mass of on-board regolith throughout the excavation field.

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Conversely, such an excavation vehicle presents dilemmas in means of regolith transportation, stable power consumption, and adaptation to the excavation environment. Methods of reliable regolith transportation between excavation mechanism and storage location operate optimally over a fixed distance. To integrate such concepts into a design with varying transportation lengths, adaptations such as overlapping belts, variable pitched conveyors, and variable length augers have been proposed. However, such alterations not only add possible failure points (by creating joints where airborne debris can settle as well as increasing dependency on coordination of mobile components), but create losses at points where regolith is transferred. The varying radius also requires the applied torque of the central motor to vary accordingly with the length of the moment arm between the rotational axis and the point of excavation. This results in a need for intricate power management, and at times, a possible need to detract from the excavation mechanisms’ power supply, as well as tolerance for increasing already high stresses in the arm mounts. The stationary approach yields little in terms of environmental adaptations when presented with possible obstacles in the lunar environment, requiring careful consideration of the surface surroundings and even subterranean complications that may be exposed by excavation when selecting a location. The design is also at risk of rapidly depleting local resources by continuously mining the same circular area. This leads to a desire for a possible degree of mobility of the central unit, allowing it to move between excavation areas when resources at one become scarce, as well as to and from a regolith “deposit station” (if called for). To optimize mining rates, the design demands a wide-faced excavation mechanism to upkeep regolith intake rates; compensating for the low circumferential speeds achieved. The mechanism must be able to tolerate horizontal forces and stresses generated by resistance of the lunar surface during radial motion

4.3.2 Mobile Rover with Mounted Excavation Mechanism

The second design consideration involves a self navigating, autonomous rover with a forward mounted excavation mechanism. The vehicle is situated on a series of treaded wheels, to allow traction and stability while navigating the lunar surface. The body of the vehicle is comprised of a solid base, the excavation mechanism, regolith transportation system, actuators, rockers, and motors for required motion of its components, and a regolith storage container or

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processing facility. The excavating component is mounted on the front of the vehicle, enabling use of the vehicle’s forward inertia to aid in excavation if needed. The storage container or initial processing facility is located on the aft of the vehicle, allowing the mined regolith and associated equipment to help counteract the large forward moment created by the weight of

the

front-mounted

excavation

mechanism. Unlike in the stationary design proposed in 4.3.1, this container is an intermediate location. The rover will venture on excavation “runs,” returning to empty its payload, when capacity is reached, at a centralized “deposit station” that may have several rovers operating out of it. The regolith transportation system acts as a means of carrying mined regolith from the excavation mechanism in the front of the vehicle to the temporary container in the rear.

Figure 4.3.2: Arial visualization of rover design.

The fixed transportation distance for the regolith eliminates complications seen by variable length systems. The freedom to tailor the vehicles base to complement the mounting of a range of excavation mechanisms allows for open-ended mechanism design and may eventually lead to the development of an interchangeable utility system, allowing the vehicle to fulfill a multitude of tasks on the lunar surface. The mobility associated with a rover type design inherently provides the tools to overcome various obstructions and terrain related challenges that may be encountered Associated with the design are high stresses required to support the excavation mechanism hanging out in front of the vehicle. This can also shift the center of weight forward,

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creating an overall forward moment on the vehicle. This problem can be overcome by calibrating the position of the wheel base, or positioning other components (motors, sensors, communication equipment, etc.) further towards the rear of the vehicle. The rover also requires temporary storage of the regolith during its excavation “runs.” Complications generated by the resulting fluctuation in mass during excavation need to be considered in the eventual design of the vehicle. The open-ended design of rover-type excavation vehicle permits a variety of possible excavation mechanisms. A mass efficient tool that keeps support stresses low, yet can take advantage of the vehicle’s low clearance and potentially broad face would be ideal. The excavation mechanism must also be able to readily realign itself to allow the vehicle to tackle obstructions or surface inclinations that may conflict with the position the mechanism takes while excavating.

4.3.3 Summary of Vehicle Analysis

The customizability of the rover’s design places fewer restrictions on the design of the excavation mechanism, allowing for greater optimization of the mechanism. Furthermore, the freedom to move about and avoid terrain obstacles that may prove fatal to the excavation vehicle makes the rover more suitable for lunar environment. The stationary design, although having a potentially higher excavation rate, has more possibilities for failure and a limited degree of autonomy. It also has greater risk of over-drawing its power supply, presenting unpredictability in behavior. For the specifications presented in 4.1, the rover design is more suitable for excavation in the lunar environment. For the purposes of this report, it will be assumed that such an approach is used.

4.4 Excavation Mechanism

Section 4.3 discussed the vehicle’s impact on the type of excavation mechanism used. In this chapter, methods of excavation will be presented, several iterations and conceptual approaches will be discussed in detail, highlighting reasons for each design as well as possible flaws, and the most suitable model selected. This is meant to only be a broad conceptual discussion, in depth analysis of the excavation mechanism will be presented in Section 5.

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Figure 4.4.1: Front view of the auger design’s excavation-compartment

4.4.1 Auger (“Snow-Blower”) Design

The first excavation method considered uses an auger-type device seen in many modern day snow blowers. The general principle is to use rotating helical blades whose axes lie perpendicular to the vehicles direction of motion. By positioning such blades so that the outer edges intercept the target material, the target substance can be “shoveled” in a direction parallel to the shaft, with a slight perpendicular component corresponding to the angle of the helix. With respect to lunar excavation, two such blades of opposite pitches are placed on the ends of a rotating shaft. Their angles are such that when spun, the regolith is accelerated inward towards the center of the shaft, and backwards towards the back of the excavation mechanism. In the central aft of the mechanism, the regolith is then funneled onto a transporting belt (or similar system) which transports the mined material to a storage compartment on the vehicle. To ensure efficiency, the auger will operate at fairly high rotational rates, raising concern for airborne grains causing losses and failure by settling in friction sensitive joints in the vehicle. To resolve this, the auger could be encased in a cylindrical compartment with a body long gap in the lower front to allow for regolith intake, and an outlet in the back where the regolith is deposited onto the transportation system. The primary grounds for regolith intake comes from forward motion of the vehicle compounded with the lower edge of the intake opening being angled to “scrape

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up” the regolith as it moves forward. A downside to this encasement is that the capability of mining forward into walls of regolith would be limited. The auger design allows for continuous mining of regolith, which is a very important plus. The excavation mechanism doesn’t require downtime or complex power management to reallot energy resources during intermediate mining stages. Additionally, the design integrates a method of controlling airborne particles - a problem which questions the use of other excavation methods. There is also a high potential for large flow rates using this design. However, the auger-approach follows similar principles to snow-blowers, and as such, is susceptible to the same flaws. Snow-blowers operate in conjunction with the cohesive nature of ice particles which can be at least 3 to 5 times more cohesive than lunar regolith (McClung), making it easier to accurately direct large flow volumes with minimal effort. Conversely, lunar regolith lacks such high inter-granular cohesion, yielding flows with greater unpredictability and a possible need for larger power consumption. This also adds to uncertainty as to how successfully regolith will enter the collection funnel at the rear of the mechanism, risking accumulation or jamming of the auger compartment by unexpectedly large rocks or meteor ejecta material. Finally, modern snow-blowers utilize a surface (sidewalk, street, etc.) to “scrape” snow off of and into the auger blades. Without the existence of such a surface on the lunar surface, the leading blade of the rear collection funnel has no planar guide and risks getting lodged deeper in the regolith than the miner can support and becoming stuck. The auger design is also heavily dependent on the size of the auger. As an initial excavation pass is completed the auger would compact any regolith not extracted and thus could create a more difficult secondary excavation pass. The design also lacks tolerance for lateral forces exerted by the regolith during pivoting or turning of the excavation vehicle. The entire front end of the excavator would have to be raised in order to move around the surface without mining. To fabricate an apparatus to elevate the entire auger during vehicle turns and maneuvers would require significant power and torque generation due to the heavy nature of the mechanism’s design. Such excessive forces and mobility restrictions were large factors in the decision to not pursue this design possibility further at this time.

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4.4.2 Bucket Wheel

The second design iteration is an excavation bucket wheel. In this design, a solid cylindrical drum, or wheel, is supported forward of the vehicle, with its central axis parallel to the front of the vehicle. The wheel is equipped with intermittent “scoops” or buckets that shovel regolith off the lunar surface as the wheel rotates about a central shaft. The regolith is then released from the bucket at a later point in rotation, primarily by means of gravity, and deposited either onto transporting machinery or directly into the vehicles collection compartment. The bucket wheel design has several advantages over other mechanism designs. Similar to the auger-approach presented in 4.1.1, the bucket wheel is a continuously mining mechanism. By avoiding downtime, excavation rates can be kept consistently high while power management is minimal and fairly direct. This can also be achieved through a multitude of customizable parameters. The indefinite nature of the bucket wheel allots for modifications of such factors as bucket size, shape and number of buckets, width of the wheel, and rate of rotation; allowing the design to be customized to specific restraints. Reliability and ruggedness are advantages of the bucket wheel design. The simplicity of the design leaves few aspects open for uncertainty. The system is also founded heavily on the consistency of gravitational forces, increasing reliability once operating. Consequently, this means initial uncertainty for conditions in the lunar environment. Gravitational forces on the moon are substantially different than those experienced on a terrestrial level. Without availability of experimental data, and the inability to accurately model excavation forces and regolith properties on the moon (see section 2.2), there’s a degree of uncertainty on the desired parameters for the bucket design. The bucket wheel approach also brings airborne particles into consideration. Any situation where regolith is freefalling allows for grains to get into the air, and potentially settle in undesired locations. This is critical to the designs dependency on gravity-accelerated falling regolith, as well as its need for several smoothly operating joints and rotational contact points.

4.4.3 Conventional Loader/Backhoe

The final excavation mechanism investigated is best categorized as a conventional loader. In this design, a large, multi-facetted, arm-like excavation mechanism is mounted on the top of the vehicle. With several joints and a pivoting mount providing multi-planar motion, a large

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bucket-like tool is fastened to the end of the arm. Operating similarly to today’s backhoe construction vehicles, the mechanism would rotate to target excavation point and dig up regolith into the bucket. It would then rotate to a regolith-depositing location and, either via inverting the bucket or opening a hatch on the bottom side, release the regolith to free-fall to the desired location.

Figure 4.4.3: Conventional Loader Design Approach

The conventional loader design has potential for large single loads. The design requires little motion of its vehicular component since the excavation mechanism can obtain regolith from a large area around its location. This enables more power to be routed to the excavation mechanism since very little is needed for the vehicles operation while excavating. The extra power is needed however, due to the large forces needed to support the arm. In addition to a large counter torque, extreme counter weights are required to balance the arm when excavating a significant distance from the wheel base of the vehicle. Due to the limitations on mass of the overall vehicle, the large weight itself becomes a problem for a rover type vehicle that ideally operates with a mass-efficient excavation mechanism. The conventional loader approach also impacts the excavation environment in large, rapid ways. Digging this way makes the excavation site prone to sudden alterations caused by tumbles, slides, and the possible exposure to larger rocks through the excavation of covering regolith. In a modern construction site, these factors are countered by human interaction and operation of the machinery. However,

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fulfilling the premise of full autonomy, the excavator must be able to react to such situations independently. Possible employment of various types of environmental spectral imaging and infrared recognition may help alleviate the problem. However, complexity behind such technologies increases chances for misdetection and eventual failure. Finally, in contrast to the other two proposed excavation mechanisms, the loader does not mine continuously, and its excavation rate is arbitrary due to the unpredictable volume of each load. This approach also requires simultaneous allotment of power to several components at varying rates, requiring intricate methods of power management.

4.4.4 Summary of Excavation Mechanism

All three proposed designs for the excavation mechanism are viable with respect to different criteria. However, as laid out in 4.1 and 4.3.3, mass and power efficiency, along with mobility are priorities. The conventional loader approach seems to fall short in these categories – being taxing mass-wise and complex with power allotment, it does possess a degree of mobility but not as versatile as the others. The auger design, although potentially power efficient, is heavy and possesses unpredictable flow rates for the same power input. Additionally, it may hinder vehicle mobility to a certain degree. The bucket wheel, although with its own flaws, was found to be the most suited for the mobile rover vehicle. Its customizable efficiency can make it both power-friendly and small-massed. It can maintain consistent flow rates while having minimal impact on the vehicles mobility. At this point, it is determined that a bucket wheel on a rovertype excavation vehicle is the most efficient approach to lunar regolith excavation. The following section, 4.5, will explore the design of the bucket wheel, discussing design features that optimize it for the lunar excavation environment

4.5 Design of Bucket Wheel

With the decision to use the bucket wheel as the excavation mechanism, a plethora of new design considerations emerge. The means of uprooting the regolith into the bucket is comfortably understood, yet the means by which it is moved from the bucket at the point of excavation to the rear of the vehicle still needs to be defined. This can be performed either directly or in a two step fashion. When considering a two stage approach the transition of regolith from the buckets to the associated transfer mechanism must also be investigated.

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4.5.1 Direct Deposit Design

In this design, regolith is deposited directly from the wheel’s buckets into the rear compartment of the vehicle. In this case, rather than a solid circular wheel, the bucket takes the form of a belt that transverses the length of the vehicle. Slanted, with respect to the vehicle base, the front will be low enough to mine regolith off the lunar surface through traditional “scraping” of its buckets; where as the back end will be raised above the rear chamber to allow “dumping” of the regolith through gravitational measures. By implementing a solid belt into the design, it allows the belt to act as a fail-safe to catch any falling regolith from the buckets. This design eliminates complicated regolith transfers inherent in a two step approach; the entire transfer of the mined material is performed by the bucket itself. It also permits the entire excavation tool to be driven by a single motor. However, this type of wheel requires significant rigidity and stress tolerance to show any form of feasibility. In addition, the direct deposit approach possesses poor mass efficiency, significantly increasing the overall weight of the excavator. Finally, the need to bear a loaded, full length belt increases the needed power draw of the system. These adverse impacts make the direct method unsuitable for the target design specifications.

4.5.2 Two Stage Bucket Wheel

A two stage approach to the bucket wheel entails excavation using the solid, circular wheel, followed by transference to a secondary mechanism which transports the regolith to the rear of the vehicle. Consideration was given to performing this using one of two methods. The first involves the transfer to occur behind the wheel, as the buckets pass the top of the wheel and begin their downward motion. The benefit of a backside-dumping bucket is that it avoids any necessary lateral motion of the regolith, limiting it to twodimensions. This creates a more consistent mining rate and minimal opportunity for losses

during

mining.

However,

complications arise when the transmission from

bucket

to

belt

is

taken

into

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consideration. To adequately “dump” regolith from the bucket, the target belt must be inclusive enough to cover the debris range of the bucket, while still be accommodating to allow buckets to pass through or by. A proposed solution is the shape the rear side of the buckets so they may be used to catch and redirect regolith. However, this compromises reliable mining rates and increases losses that the hind-side dumping approach was supposed to minimize. It is for these reasons, a second method was investigated. To resolve problems seen in the rear-dumping two-stage bucket wheel, a side depositing design was created. In this model, the wheel is mounted alongside the transporting belt. The wheel is modeled with an internal structure more suitable for the design. The buckets are open to drop regolith into the inner portion of the wheel, where it is then redirected laterally to the adjacent belt. This approach simplifies the transference problem and allows for multiple guides to be attached, encouraging regolith to navigate onto the belt. This yields a reliable flow rate, simple design, and efficient power usage with an optimal excavation method. This design is explored more deeply in Section 5.

4.6 Power Usage

In determining the power required for our excavator to run at optimal we look at the equation: P = T ×ω T is our torque value determined by the force of excavation per bucket

ω is the angular velocity required to satisfy our projected mass flow rate If we assume that at one single point in time we have 3 buckets excavating our total force is equivalent to about 570 Newtons on Earth and about 150 Newtons on the moon. The resultant powers required for these forces are 29.41 Watts and 15.12 Watts respectively. (Calculations included in appendix) For the application, we chose to drive our excavation assembly with an electric DC brushless motor. Unlike a regular DC electric motor, the brushless motor creates no internal friction which helps reduce power loss and fatigue. It will run off a basic DC power source, i.e. a rechargeable battery. We want to get a motor with a rating of around 65 W (~1/12 HP). The

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excess power is for running our excavation belt which carries regolith from our excavation bucket to the desired location on the excavator. Our motor specifications are based off of a Tecumseh electric motor with a power rating of 1/12 HP, revolutions up to 1500 RPM at 230 V and 1.3 A (Smith 2006). Based on the size aspects of the motor we are looking at a casing of roughly 3.5 in (8.89 cm) in height and width and 5 in (12.7 cm) in length that houses the motor. From the motor a gear train will transfer power throughout the excavation unit. This is the motor that we would use based on the atmospheric effects of the Earth. The lunar module may be somewhat smaller and less in power than our Earth unit but this would be the most conservative design.

4.7 Summary

As discussed, several properties of the excavation vehicle, mechanism, and method were taken into account when formulating a final approach to lunar excavation. Careful consideration was given to the suitability the various designs possessed for operation on the lunar surface and other limitations prescribed in 4.1.0. Conclusively, a rover mounted bucket wheel with a sidemounted transition point was deemed most suitable for the task at hand. This model exhibits suitable mass and power efficiency, while maintaining a sufficiently large and reliable regolith excavation rate. To further the investigation, detailed analysis on the selected excavation mechanism must now be performed.

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5.0 Final Design

This section will serve to detail the final proposed design for the lunar regolith miner. As mentioned in the previous section there were multiple design ideas but ultimately the following design was chosen.

5.1 Bucket Wheel.

The bucket wheel is the most important part of the design and as such took the longest time to complete. Many design iterations were investigated to arrive at this final design and snapshots of these can be found in the appendix section of the report. 1. Buckets 2. Wheel housing 3. Guide plane 4. Guide rail

5. Shaft housing

5.1.1 Buckets

The buckets are the digging mechanism. These parts have direct contact with the regolith and are used to loosen and scoop up the regolith so that it may be mined. The final design shown here was chosen because this curved bucket design maximizes the volume of each bucket while it minimizes sharp edges that would otherwise cause resistance during mining. This design also minimizes stress concentrations, an important consideration for such a part that will be subjected to many cycles of loading and unloading. The bucket wheel has 8 buckets all with the same dimensions. The ends of each bucket are angled to a point in an attempt to decrease resistance and increase force exerted by the bucket to the regolith. ( P = F / A ) These would serve to “cut” through the regolith as the bucket rotates. The sharp point will result in a more focused force,

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such an increased force will cause the regolith to shear easier than a broad front would and thus require less power to excavate. The sides of each bucket play very important roles. Primarily these sides serve to contain the regolith and maximize the volume of the buckets. This is vital in order to achieve the desired flow rate. Without such constraints regolith could easily fall to either side of the bucket as the load is lifted. Increased losses such as this would lower the efficiency of the excavator and require a faster angular velocity of the wheel and potentially require a much larger, heavier design with greater power requirements. These sides allow for an efficient excavation. In order to calculate the needed angular velocity, the assumption was that each bucket would be approximately 60% full. Optimally this would not occur because of the sides on the bucket; nonetheless this serves as a design factor to ensure that the required flow rate is matched. The sides of the bucket also serve an important secondary role of supporting and reenforcing the bucket. During excavation the forces from the mining will force the bucket back and away from the wheel. These sides would help to carry this load and prevent the buckets from deforming under such forces. As the excavating assembly sweeps side to side, the sides also serve to cut laterally into the regolith and thus were designed to take a variety of stresses. The buckets and sides, just as the rest of the bucket wheel, will be made from a titanium alloy (Ti-13 V-11 Cr-3 Al) which has superb strength and hardness. The alloy is solution hardened and aged. Because the buckets must be exceptionally strong they will be manufactured using a forging process. This process will align the grains along the curve of the buckets to provide maximum strength. While the buckets will be forged, the sides will be made of plate titanium. It is important to note that plate titanium and stock titanium do not have the same strengths, but given the application and the very large factors of safety built in, this difference can be considered negligible. These two parts are joined to the wheel by use of laser beam welding. This process will be used to limit the heat affected zones in the welds and insure that no significant material properties are changed during the weld process. This is especially important in this design because the walls are very thin and any loss of strength could cause deformation or failure of the bucket when the excavator is actively working. The other important joint that is sensitive to the heat affected zone is the joint between the bucket and the wheel. This joint must be extremely strong to withstand the stresses that excavating will cause, yet must not change the physical

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properties of the wheel or the bucket. These vital welds must be closely inspected after assembly using non-destructive testing to guarantee that each and every weld is perfect. A failed weld could easily cause the entire system to fail. This type of failure occurred last year at the Regolith Excavator Challenge to a bucket wheel design and resulted in the machine jamming itself and being forced to retire from the contest early.

5.1.2 Wheel Housing

The wheel housing is the part that holds the buckets and transfers power from a motor driven chain to the buckets. This part is the structure that holds the excavating system together and as such must be capable of withstanding many different forces. The buckets are the part that mines the regolith and as the wheel turns this regolith enters the wheel housing through square holes around the perimeter. As the wheel turns this material is pulled by gravity, which on the moon is approximately 1.635 m/s^2, down towards the middle of the wheel where it is transferred to a belt for transport up to the base of the excavator. The wheel will be subject to various loading due to excavating forces. These forces will be amplified by the stress concentrations caused by the square holes in the part. Every time a bucket engages in the regolith a load is applied to this part, thus fatigue failure is a very important consideration considering that every hour the wheel will be loaded and unloaded approximately 3300 times. This part will be manufactured from the same Ti-13 alloy that was used for the buckets. Due to the vital nature of this part such strength is considered necessary. This part will be custom machined to guarantee its structural integrity and dimensional accuracy. By machining the wheel out of one piece of material there are fewer possible joint failure points and there is less of a need for additional structural supports. As before, however, there is still a need for very careful inspection of this part to detect any defects that could initiate fatigue failure. Once assembled and launched there is no opportunity to fix or replace parts so they must all be made with the highest standards possible.

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5.1.3 Guide Plane

The guide plane is one of two parts that facilitates the transfer of regolith between the buckets and the belt. As regolith leaves the bucket and enters the wheel housing it comes in contact with the guide plane. This part is attached around the interior of the wheel housing and from this outer radius is angled such that it forces the regolith to move laterally as it falls and thus onto the belt that is in place along side the bucket wheel.

Without this part the regolith

would fall into the bucket wheel and could not be transferred to the belt. This design also minimized airborne regolith which could do significant damage to parts and must be minimized if the miner is to mine for long periods of time.

Although

disturbing some amounts of regolith is unavoidable, any design feature that can minimize this result is very beneficial. The guide plane will be fabricated out of titanium alloy sheet. This sheet will be laser beam welded to both the interior corner of the wheel housing as well as the shaft housing in the center of the wheel housing. This weld should be done well to insure that this interior cavity cannot be separated or penetrated. If this part were to separate from the wheel housing, the cavity could easily fill with regolith and thus increase the static weight of the bucket wheel as a whole.

5.1.4 Guide Rail

The guide rail is the second part that works to aid in the transfer of regolith from the buckets to the belt.

This part is

attached to the guide plane and is used to force the regolith to fall back towards the belt.

The angle of this guide rail is very

important in that it guides the regolith to where the belt is and prevents the regolith from falling out until it is over the belt. It works on both the forward and rear sides of the rotation. If for some reason the regolith were to get stuck or fall slower than anticipated, this guide rail would also work after the bucket has reached the apex of its revolution and is descending. The selection of this angle is very important to the design because if this

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guide rail is too steep the regolith could fall and miss the belt entirely where as if the angle were too flat, the regolith may not fall fast enough to reach the belt before the next bucket load is acquired. As it is designed the regolith should fall from the bucket to the belt in about .6 seconds under lunar conditions. The ideal time for this transfer to occur is when the bucket is passing through the highest 1/8th of each revolution which should take about 1.2 seconds. Thus this design should provide adequate time for the regolith to fall from the bucket to the belt even under lunar gravity conditions. This part will be manufactured from the same titanium plate as the guide plane. It will be slightly thicker than the guide plane, and will be laser beam welded in place. The reason it is slightly thicker than the guide plane is that in the event a larger than normal piece of regolith falls into the bucket wheel, this guide rail will be the part to engage and eject the obstruction. If it is desired to increase the radial size of the bucket wheel, this part could be changed to connect the outer wheel edge to the shaft housing similar to spokes on a bicycle wheel. This design is robust enough to not require this addition, but it could very well be implemented in future designs.

5.1.5 Shaft Housing

The shaft housing is the portion of this part that is connected to the shaft and thus the part that is the primary transfer of torque from the shaft to the bucket wheel. The design of this part allows for the shaft and the bucket wheel to be connected through the entire width of the bucket wheel.

The design includes a

woodruff key which would be supplemented by welding the shaft housing to the forward shaft. This weld would be done using a laser beam weld and would serve the purpose of ensuring a solid fit and fixing the location of the bucket wheel on the shaft, in addition to sealing the connection and preventing debris from entering the point of connection.

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5.2 Forward Shaft

The forward shaft is the part that the shaft housing of the bucket wheel sits on and is the location of power transfer from the chain to the bucket. Its primary function, like any shaft, is to transfer motion and power from the belt to the bucket.

As mentioned above, this part

will be secured to the shaft housing of the bucket wheel via a woodruff key and a circular weld. This part will be manufactured from ASTM A514 steel and turned to produce the required varying diameter. This turning will be done with great precision and small tolerances such that the part may be press fit into its associated ball bearings. The shaft will have a change in diameter and decrease at the ball bearing connection site into a shoulder. This shoulder will secure the shaft between the two excavating arms. Dimensions for the shaft can be found in the appendix as well as the calculations used to give this part an infinite life with a fatigue factor of safety of 1.44.

5.2.1 Forward Shaft Bearings

These ball bearings serve to allow rotational movement of the forward shaft with minimal interference. The shaft will be press fit into these bearings and the bearings themselves would be press fit into the excavating arm. These fits are of utmost importance and thus tolerances for the dimensions of the shaft and the bearings are very small. Due to the need for an unserviceable design “hybrid” ceramic ball bearings are used. These bearing use ceramic balls instead of steel balls which run at lower vibration levels with less heat build up. The ball bearings will also be sealed.

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Elevating axle location

Base axle location

Forward shaft location

5.3 Excavating Arm

The excavating arm is the part of the excavator that constrains and moves the bucket wheel. It has the very important function of securing the bucket wheel to the excavator and transferring forces between the platform and the bucket wheel.

Many designs for this portion were

investigated and along with these designs came a multitude of different operational constraints and ideas. This design was ultimately chosen because of its versatility and simplicity. As a functional note, the excavator will dig downward only initially and then it will, in most cases dig forward as it carves a path through the regolith. Thus the design must be capable of mining downward as well as forward.

This functioning of the excavator also requires that it be

controlled and powered both vertically and horizontally. This part again will be manufactured from titanium treated alloy. The part will be forged in order to obtain the maximum strength and grain orientation. After heat treating the required holes to house the shafts and connections will be laser cut into the piece. These parts will then be finished to meet the strict allowances required for the press fits of the bearings. The forward shaft, as described above, will be accompanied by a base axle as well as an elevating axle in the rear.

37

5.4 Base

The base of the excavating mechanism is the foundation for the excavation arm and the important point of connection between the excavating mechanism and the base of the excavator that it is attached to. The excavation arm is attached to the base by a base axle. This axle is pressure fit into to arms of the base and has two sealed “hybrid” ceramic ball bearings to allow the exaction arms to move in the vertical direction. This feature gives the excavating mechanism the flexibility to raise and lower to meet excavating or mobility needs. The base will rotate with the excavating arm and as such will house the motors to drive the system below it. The power requirements will be discussed in the appendix and will dictate the design of the excavator. This base axle also is the point of energy transfer from the motor below the base to the belt via a set of gears and ball bearings that will sit on this axle. The power will be transferred up from below the base with a simple chain. This chain will engage a gear train that will power the belt and subsequently power the bucket. Depending on the desired final location of the regolith, there would be a catch plate that would guide regolith from the end of the belt to its desired final location. The center of the base is extruded to allow clearance for the chain needed to drive the belt.

The removal of material also lowers the weight of the base which is an important

consideration in this design. Attached to the rear of the base would be a crank-rocker attachment that generates side to side motion of the bucket wheel and excavation arms.

5.5 Crank Rocker

Utilization of a crank rocker allows for a constant motor input for motion in variable directions. In order for the crank rocker to have the same speed in both directions, the input motor must be placed co-linear with both extreme points. These points can be moved around on the base and were not specifically included because their placement would be very much dependent on geometry of the entity onto which this excavator would be placed. The design would be based on 4-bar equations. The crank input would be ½ the linear distance between the

38

two desired extremes. Any final design must satisfy the Grashof criteria in order to operate and

thus:

S + L ≤ P +Q S = crank _ input L = dist . _ btwn _ input _ and _ center _ of _ bas P, Q = radius _ roc ker_ arm

The basic implementation however is that it attaches to the rear of the base and rotates the excavating mechanism to sweep back and forth and thus a larger area can be excavated as the machine moves forward.

5.6

Elevating Axle

The elevating axle is located on the back of the excavation arms and is comprised of an axle with an associated wire and pulley attachment. In order to raise the excavating mechanism this wire is attached to a motor under the base that can be used to pull in the wire, and thus raise the excavating assembly, or let out the wire and subsequently lower the excavating assembly. This design removes the need for a high torque actuator at the base axle location and also provides a mechanical advantage to lifting the front heavy bucket. Its location on the rear of the arm utilizes the base as a fulcrum and subsequently reduces the force required to lift the mechanism.

5.7 Regolith Transport Belt

The regolith transport belt is the part of the excavator that moves the regolith from the bucket wheel up the excavating arm and deposits it behind the base. The location of this deposition would be variable based on the design of the vehicle. The belt design incorporates both useful elements of a belt and a chain in one. The belt consists of jointed carbon fiber weave sections that are flat on the top, to carry regolith, and have chain like recessions on the underside so that the belt can transport regolith and power simultaneously. This design reduces the weight of the mechanism and simplifies both transfers. The stiffness of carbon fibers will be utilized to carry the regolith while its strength will be advantageous for transferring the torque from the motor at the base, to the bucket wheel during excavation. This aspect of the design would require prototype testing to validate the carbon fiber material’s appropriateness. The belt would also need to incorporate equally placed ridges to aid

39

in carrying the regolith, the placement of these ridges would best be decided after testing with regolith stimulant.

5.8 Material Selection

For this application titanium alloy was chosen for several reasons. First it has a very high strength to weight ratio which is vitally important. Weight is the most significant constraint on this design because the launch costs from earth to the moon during NASA’s Apollo program were approximately $60,000/kg. Although future missions could potentially lower this figure to around $20,000/kg there is still an advantage in using the lightest possible materials with the longest possible life and smallest possibility of mechanical failure.(Schmitt)

Due to these

considerations this expensive material is deemed justifiable to guarantee that the excavator performs as expected for as long as possible. Titanium also has many other valuable physical properties worth mentioning. Besides its great strength, it has a very thin conductive oxide surface film. This is important because some of the very small grains of lunar regolith become electro-statically charged by the solar wind during the lunar day. As a result these particles will be statically attracted to certain surfaces. One possible solution to this problem would be to run a very small current through the excavator and thus repel these very abrasive small particles from becoming lodged in moving parts. It is unknown whether this design consideration has been experimentally tested in the lunar environment so its effectiveness, at this point, is only in theory. A final benefit of using a titanium alloy is the hard smooth surface of the metal that limits adhesion of foreign materials.

5.9 Proof of Concept Design

If this model were built for a proof of concept design many of the materials and minor design considerations would be altered. Basic changes would include the excavation arm being constructed from wood and the bucket wheel being constructed from sheet metal. Basic welding would be used to join the pieces and the belt would most likely be made from simple cloth instead of carbon fiber. These design considerations will be explored in the coming semester as this overall design is constructed on a scaled level to experimentally examine the designs performance.

40

Excavation arm

Belt

Bucket wheel

5.10 Summary of Design

The design shown above has been developed to be robust and able to excavate in the extreme environment of the moon. It would operate on a moving platform that would receive the mined material as well as provide the required power to the system. The basic operation of this design begins with the bucket wheel that digs the regolith and collects this regolith in the buckets. The regolith then falls due to the acceleration of gravity. As it falls it is guided by both the guide plane and the guide rail. These two components guide the regolith towards the regolith return belt. Once the regolith falls to the belt, the belt carries this regolith up the excavation arm. The regolith is then deposited behind the base axle and depending on the desired location of the regolith could be directed via a chute or another belt system.

41

6.0 Report Summary

Lunar excavation will prove to be an intricate engineering challenge. Many complexities surrounding this undertaking stem from a lack of knowledge of the lunar environment and how mechanical systems translate from terrestrial applications to a lunar setting. Currently models for excavation forces and design appear to be inadequate for such analysis. Further research into this area is needed to better design future models of this excavator.

Due to changing

requirements of lunar missions, any model must be very robust and adaptable. This means early designs must abide by as many known lunar constraints as possible, as well as be accommodating towards possible alterations and modifications in the future. To fulfill the need for such a design, a bucket wheel excavation tool which could be mounted on various other mobile platforms has been proposed. The outlined design fulfills prescribed design constraints and follows suit with lunar considerations. The model is adjustable and provides opportunity for future development, while still following currently addressed lunar concerns and being a formidable approach in its current form. It is a thorough solution to the problem at hand, and will aid in the development of future lunar excavation.

42

Appendix: Section I

Analysis of Parts Here we analyze some critical parts in order to see if they last, under their respectable loads, for an infinite life. We will use a conservative approach to fatigue failure. The excavator arm be analyzed as if it were made from high strength steel alloy (ASTM A514). Of course the actual parts, if produced, would be made of finer materials with higher strengths. That is the case for the bucket wheel shaft. The steel is only used to add a higher factor of safety in our design. For steel: S y = 100 kpsi (690 MPa) S ut = 110 kpsi (760 MPa) a) Bucket Wheel Shaft

The bucket wheel axle is basically a steel shaft with two smaller ends where the shaft meets the joints in the arm. Ball bearings will be placed here. One forces taken into account is the weight of the regolith which is a normal force on the middle of the bar causing bending stress. A shear stress created from the torque exerted by the excavation bucket during excavation.

The torsion (conservative Earth value) is taken from our power section. T max = 280.9 N-m

43

The weight of the bucket wheel is roughly W BW = 20kg * 9.81 = 196.2 N With a full load of regolith our weight is W max = (30kg + 20kg) * 9.81 = 490.5 N Length of Shaft = Width = L = .22m The notch is located at 9.5 cm from the end of the shaft. The torque is dynamic from 0 – T max whereas our weight is dynamic from W BW – W max . Fully reversed bending stress takes place though so M max = - M min The corresponding shear and bending stress equations are utilized: 16 T 32 M f f f f f f f f f f f f f f f f f f f f f f f f f f τ= f and σ b = f (bending) 3 3 πd πd M max = W max * .095/2 = 490.5 * .0475m = 23.3 N-m M min = - M max = -23.3 N-m

With this we find: τ max = 1430.6/d^3 τ min = 0 σ max = 227.1/d^3 σ min = -227.1/d^3 Furthermore we focus on amplitude and midrange stresses where: M L Lσ max @ σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M σa = K fL M L 2 M L Lσ max + σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M σm = K fL M L 2

Following this formula we find: 1430.6 f f f f f f f f f f f f f f f f f f f f τa = τm = f 3 d 452.2 f f f f f f f f f f f f f f f f f f σa = σm = 0 3 d Using von Mises stress we can combine our different amplitude and midrange stresses into σ a . and σ m . : w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w b c 2 2 r σ a . = σ ax @ σ ax σ ay + σ ay + 3τ 2a w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w bw c 2 2 2 r σ m . = σ mx @ σ mx σ my + σ my + 3τ m

σ a . = 2518.8/d^3 σ m . = 2477.9/d^3

44

Using fatigue failure and iterations we are able to find possible diameter values for our shaft. D = 3.56 cm d = 2.67 cm Bucket Wheel Shaft Assume Kf = 2.0 Conservative Prediction (Relatively High Kf Value) Se' = .504Sut (for steel with Sut < 212 kpsi)

Se = ka*kb*kc*Se'

Se' = 383.04 Mpa

ka = 0.76

Sut = 760 Mpa

kc = 1

Sy = 690 Mpa

Sa = 2518.8/d^3 Sm = 2477.9/d^3 Mod. Goodman

1/n = (Sm/Sut)+(Sa/Se) First Cycle Failure 1/n = ((Sa + Sm)/Sy)

kb

diameter (mm)

Se

Sa

Sm

n

1.115E+00

2.700E+00

3.246E+08

1.280E+11

1.259E+11

1.786E-03

1.078E+00

3.700E+00

3.138E+08

4.973E+10

4.892E+10

4.488E-03

1.051E+00

4.700E+00

3.059E+08

2.426E+10

2.387E+10

9.032E-03

1.029E+00

5.700E+00

2.996E+08

1.360E+10

1.338E+10

1.587E-02

1.012E+00

6.700E+00

2.945E+08

8.375E+09

8.239E+09

2.546E-02

9.967E-01

7.700E+00

2.902E+08

5.517E+09

5.428E+09

3.823E-02

9.838E-01

8.700E+00

2.864E+08

3.825E+09

3.763E+09

5.462E-02

9.724E-01

9.700E+00

2.831E+08

2.760E+09

2.715E+09

7.506E-02

d(m) (=3/4D) 2.700E03 3.700E03 4.700E03 5.700E03 6.700E03 7.700E03 8.700E03 9.700E03

D (m) 3.600E03 4.933E03 6.267E03 7.600E03 8.933E03 1.027E02 1.160E02 1.293E02

First Cycle Failure (n) 2.718E-03 6.995E-03 1.434E-02 2.557E-02 4.153E-02 6.304E-02 9.093E-02 1.260E-01

45

9.622E-01

1.070E+01

2.801E+08

2.056E+09

2.023E+09

9.998E-02

9.531E-01

1.170E+01

2.774E+08

1.573E+09

1.547E+09

1.298E-01

9.447E-01

1.270E+01

2.750E+08

1.230E+09

1.210E+09

1.649E-01

9.371E-01

1.370E+01

2.728E+08

9.796E+08

9.637E+08

2.058E-01

9.301E-01

1.470E+01

2.708E+08

7.929E+08

7.801E+08

2.528E-01

9.236E-01

1.570E+01

2.689E+08

6.509E+08

6.403E+08

3.064E-01

9.175E-01

1.670E+01

2.671E+08

5.408E+08

5.320E+08

3.670E-01

9.118E-01

1.770E+01

2.654E+08

4.542E+08

4.469E+08

4.349E-01

9.064E-01

1.870E+01

2.639E+08

3.852E+08

3.789E+08

5.106E-01

9.014E-01

1.970E+01

2.624E+08

3.295E+08

3.241E+08

5.945E-01

8.966E-01

2.070E+01

2.610E+08

2.840E+08

2.794E+08

6.870E-01

8.921E-01

2.170E+01

2.597E+08

2.465E+08

2.425E+08

7.885E-01

8.878E-01

2.270E+01

2.585E+08

2.153E+08

2.118E+08

8.994E-01

8.837E-01

2.370E+01

2.573E+08

1.892E+08

1.861E+08

1.020E+00

8.798E-01

2.470E+01

2.561E+08

1.671E+08

1.644E+08

1.151E+00

8.761E-01

2.570E+01

2.550E+08

1.484E+08

1.460E+08

1.292E+00

8.725E-01

2.670E+01

2.540E+08

1.323E+08

1.302E+08

1.445E+00

8.691E-01

2.770E+01

2.530E+08

1.185E+08

1.166E+08

1.608E+00

8.658E-01

2.870E+01

2.520E+08

1.065E+08

1.048E+08

1.784E+00

8.627E-01

2.970E+01

2.511E+08

9.614E+07

9.458E+07

1.971E+00

8.596E-01

3.070E+01

2.502E+08

8.705E+07

8.564E+07

2.171E+00

8.567E-01

3.170E+01

2.494E+08

7.907E+07

7.779E+07

2.384E+00

8.538E-01

3.270E+01

2.486E+08

7.204E+07

7.087E+07

2.611E+00

8.511E-01

3.370E+01

2.478E+08

6.581E+07

6.474E+07

2.850E+00

8.484E-01

3.470E+01

2.470E+08

6.028E+07

5.931E+07

3.104E+00

8.458E-01

3.570E+01

2.462E+08

5.536E+07

5.446E+07

3.373E+00

8.433E-01

3.670E+01

2.455E+08

5.096E+07

5.013E+07

3.656E+00

1.070E02 1.170E02 1.270E02 1.370E02 1.470E02 1.570E02 1.670E02 1.770E02 1.870E02 1.970E02 2.070E02 2.170E02 2.270E02 2.370E02 2.470E02 2.570E02 2.670E02 2.770E02 2.870E02 2.970E02 3.070E02 3.170E02 3.270E02 3.370E02 3.470E02 3.570E02 3.670E02

1.427E02 1.560E02 1.693E02 1.827E02 1.960E02 2.093E02 2.227E02 2.360E02 2.493E02 2.627E02 2.760E02 2.893E02 3.027E02 3.160E02 3.293E02 3.427E02 3.560E02 3.693E02 3.827E02 3.960E02 4.093E02 4.227E02 4.360E02 4.493E02 4.627E02 4.760E02 4.893E02

1.692E-01 2.212E-01 2.829E-01 3.551E-01 4.386E-01 5.344E-01 6.432E-01 7.657E-01 9.030E-01 1.056E+00 1.225E+00 1.411E+00 1.615E+00 1.838E+00 2.081E+00 2.344E+00 2.628E+00 2.935E+00 3.264E+00 3.618E+00 3.996E+00 4.399E+00 4.828E+00 5.285E+00 5.770E+00 6.283E+00 6.826E+00

46

Fatigue Factor of Safety

Shaft diameter 16 14 12 10 8 6 4 2 0 0

10

20

30

40

50

60

70

diameter (mm)

Plot showing the relation between shaft diameter and factor of safety

b) Excavation Arm

The excavation arm actually consists of two arms which a conveyer belt will run in between. The two arms hold the bucket wheel shaft on both ends. It is supported by a pivot support and a counter force in the back, which can be variable to raise or lower the wheel but for our assessment we will consider a static situation.

47

We will assume there are no forces in the x-direction. The pivot does not support a moment and the bucket wheel load is dynamic. The bucket wheel load W BW is constant at least at 196.2 N and W max is 490.5 N. Using basic static equilibrium analysis we are able to find the force at each point. We find forces based on both of the bucket wheel loads. In order to find the maximum and minimum stresses in the bar we must draw the shear force and bending moment diagrams to find the max bending moments. We will do this for one load then use that information to find the other maximum bending moment. We focus on bending stress creating from the bending moment since it will yield a larger stress than shear stress due to shear force. Remember than there are 2 bars the entire stress will be divided by two to find stress in each bar. For the values h = .08m and w = .015m we use bending stress equations to find the maximum and minimum stress. 6f M f f f f f f f f f f σb = f 2 wh

σ max = 19.08 MPa

σ min = 7.634 MPa

*No notch sensitivity factor M L Lσ max @ σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M = 11.45 MPa σ a =L M L 2

M L Lσ max + σ M f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f M Lf min M = 13.36 MPa σ m =L M L 2

S e = k a k b k c S e.

⎧0.504 S ut kpsi or MPa S ut ≤ 212 kpsi (1460MPa ) ⎪ S =⎨ ⎪⎩ 107 kpsi (740 MPa ) Sut > 212 kpsi (1460 MPa ) ' e

S e . = .504 S ut = 383.04

d e = 0.808 hb

k a = a Sutb

⎧ 0.879d −0.107 0.11 ≤ d ≤ 2 in ⎪ − 0.157 2 < d ≤ 10 in ⎪ 0.91d kb = ⎨ − 0.107 2.79 ≤ d ≤ 51 mm ⎪1.24d ⎪⎩1.51d −0.157 51 < d ≤ 254 mm

⎧1 ⎪ k c = ⎨ 0.85 ⎪ 0.59 ⎩

bending axial pure torsion

S e = 252.68 MPa

Modified Goodman (test for infinite life, true for n > 1)

48

(From X.X : S ut = 760 MPa S y = 690 MPa ) 1f σf f f f σf f f f f f f f f f f f f f f f = m + a n S ut Se f

g f

g

n = 15.9

First Cycle Failure (if n > 1, does not fail at first cycle) 1f + Sf f f f Sf f f f f f f f f f f f f f f f f f f f f f af m = f n Sy

n = 27.8

49

Section II Calculations Mass budget

Part bucket wheel excator arm (x2) base front shaft base axle belt

Density 4500 4500 4500 7700 7700 unk

Approx volume 0.00412 0.00237 0.0031 0.0002 0.00014 unk

total

ρ = 1500kg / m 2 m& × 1 / ρ = V&

Mass 18.54

kg

21.33 13.95 1.54 1.078 5

kg kg kg kg kg

61.438

kg

m& = 10kg / min

V& = .00667m 3 / min

Buckets at 60% capacity

(.6 × Vol )×# _ buckets = m 3 / rev

(.6 × 2.04 E −4 ) × 8 = 9.792 E −4 m 3 / rev

chosen design flow rate calculations

ang. Vel. (rev/min) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

vol. flow rate (m^3/min) 0.000979 0.001958 0.002938 0.003917 0.004896 0.005875 0.006854 0.007834 0.008813 0.009792 0.010771 0.01175 0.01273 0.013709 0.014688 0.015667 0.016646

mass flow rate (kg/min) 1.4688 2.9376 4.4064 5.8752 7.344 8.8128 10.2816 11.7504 13.2192 14.688 16.1568 17.6256 19.0944 20.5632 22.032 23.5008 24.9696

50

18 19 20 21 22 23 24 25 26 27 28 29 30

0.017626 0.018605 0.019584 0.020563 0.021542 0.022522 0.023501 0.02448 0.025459 0.026438 0.027418 0.028397 0.029376

26.4384 27.9072 29.376 30.8448 32.3136 33.7824 35.2512 36.72 38.1888 39.6576 41.1264 42.5952 44.064

Mass flow rate

Mass flow rate 50 45 40 35 30 25 20 15 10 5 0 0

5

10

15

20

25

30

35

Angular velocity

Force and Power Calculations Force Total = F1 + F2 + F3 =

864.3

N

F1 (Weight of regolith in buckets) = Mass * Gravity = Mass (maximum) = 30 kg Mass (minimum) = 0 kg (EMPTY) Gravity = 9.81 m/s^2

294.3

N

51

F2 (Force of regolith excavation) F2 = 570 N *from scientific investigation F3 (Outside forces, possible frictions from bearings, etc) F3 = 0 N *Assuming zero presently T = F(total) * R = R= 0.325

280.8975 m

N*m

ω= 0.10472 rad/sec *Found from exterior analysis Power Calculation (for wheel) P =T*ω P= 29.41552 Watts

52

Section III - Bucket Wheel Design Progression

53

Section IV - COSMOS Simulations of Loading

Yield strength = 8.300e+008

54

Section V - Technical/Working Drawings (Not meant to be of production quality)

Bucket Wheel

55

Base

56

Excavating Arm

57

Front Shaft

58

Section VI – Bibliography Black, J.T. & Ronald A. Kohsher. “DeGarmo’s Materials & Processes in Manufacturing” 10th ed. John Wiley & Sons. MA. 2008. Boles, W. W.. and Scott, W. D. (1997). “Excavation forces in reduced gravity environment.” J. Aerospace Eng., ASCE, 10(2), 99-103. Godwin, R.J., and Spoor, G. (1977). “Soil failure with narrow tines.” J. Agric. Engrg. Res., 22(3), 213-228 Hettiaratchi, D. R. P.. and Reece, A. R. (1967). “Symmetrical three-dimensional soil failure.” J. Terramech., 4(3), 45-67. McClung, David. “Avalanche Handbook.” Mountaineers Books. Oct. 1993. McKyes, E., and Ali, O. S. (1977). “The cutting of soil by narrow blades.”J. Terramech., Vol. 14, 43-58. McKyles, E. (1989). “Agricultural engineering soil mechanics.” Elsevier, Amsterdam, The Nettherlands Reece, A.R. (1965). “The fundamental equation of earth-moving mechanics.” Proc., Symp. Automobile Div., Inst. Mech. Eng. On Earth-Moving Machinery, Session 1. Auburn Univ., Auburn, Ala. Schmitt, Harrison H. “Exploration, Enterprise, and Energy in the Human Settlement of Space, Return to the Moon.” Praxis Publishing, NYC. 2006. Shigley, Joseph E., Charles R. Mischke & Richard G. Budynas. “Mechanical Engineering Design” 7th ed. McGraw Hill. NYC 2004 Smith, A.O. Motors. (2006). www.aosmithmotors.com. Dec. 2007, Pg. 113. Willman, B. M., and Boles, W. W. (1995). “Soil-tool interaction theories as they apply to a lunar soil simulant.” J. Aerosp. Engrg., ASCE, 4(2), 77-87. http://www.californiaspaceinstitute.org

“California Space Institute”

http://www.key-to-metals.com/Article20.htm

http://www.cbrbearing.com/ceramic_hybrid_ball_bearings.htm

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