HPV Senior Project Report 2009

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Final report for the Human Powered Vehicle frame and drive train design. Senior Project for my time at Cal Poly.

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  • Excellent work, very informative. My only question as I design my own streamliner is the HeadTube Angle. This looks rather steep with a heavily negative rake/ front drop out, no? I understand there is excessive wheel flop on many longer wheelbase recumbents and the question of high speed stability if the rake is off.
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HPV Senior Project Report 2009

  1. 1. Human Powered Vehicle Frame and Drive Train Final Project Report Bicycle Technical Innovations Advisor: Brian P. Self, Ph.D. Mechanical Engineering Department California Polytechnic State University San Luis Obispo, California Aaron Williams williams@calpoly.edu Caleb Bartels caleb.bartels@gmail.com Sean McHugh seanmmchugh@yahoo.com
  2. 2. Statement of Disclaimer Since this project is a result of a class assignment, it has been graded and accepted as fulfillment of the course requirements. Acceptance does not imply technical accuracy or reliability. Any use of information in this report is done at the risk of the user. These risks may include catastrophic failure of the device or infringement of patent or copyright laws. California Polytechnic State University at San Luis Obispo and its staff cannot be held liable for any use or misuse of the project. Page | 1
  3. 3. Abstract Cal Poly’s Human Powered Vehicle Club challenged our team to design, build, and test a working recumbent frame and drive train to race in the annual ASME Human Powered Vehicle Challenge. By talking to Human Powered Vehicle club leadership and previous riders, a full list of engineering specifications was developed to focus the design process. Concepts were brainstormed, resulting in the most realistic and innovative ideas being selected. Among our concepts selected, we focused our project on creating a full carbon fiber-epoxy frame that could be removed from the vehicle fairing for test runs and training. Final designs were drafted using Computer Aided Design software to create engineering drawing schematics for manufacturing. Our team focused on composite manufacturing, outsourcing machining to technicians and other Human Powered Vehicle members. Our final product weighs less than 4 pounds, representing a 50% weight reduction from the last design. Further testing is needed to verify the performance of the bike once fully assembled. Page | 2
  4. 4. Table of Contents Statement of Disclaimer .......................................................................................................................... 1 Abstract .................................................................................................................................................. 2 Chapter 1: Introduction ........................................................................................................................ 8 1.1 Nomenclature ................................................................................................................................ 8 1.2 Background .................................................................................................................................... 8 1.3 The HPV Spectrum ......................................................................................................................... 9 1.4 Cal Poly HPV History ..................................................................................................................... 10 1.5 Objectives ...................................................................................................................................... 12 Chapter 2: Engineering Specifications ................................................................................................. 14 Chapter 3: Design Concept Development ............................................................................................ 15 3.1 Design Philosophy ........................................................................................................................ 15 3.2 Drive Train Concepts .................................................................................................................... 15 3.3 Frame Concepts ........................................................................................................................... 16 3.4 Seat Mount Concepts ................................................................................................................... 18 3.5 Final Concept ............................................................................................................................... 19 Chapter 4: Design Refinement ............................................................................................................ 21 4.1 Frame........................................................................................................................................... 21 4.2 Drive Train ................................................................................................................................... 24 4.3 Seat Mount ..................................................................................................................................... 24 Chapter 5: Final Design ....................................................................................................................... 26 5.1 Frame........................................................................................................................................... 26 5.2 Drive Train ................................................................................................................................... 27 5.3 Seat Mounts and Fairing Mounts .................................................................................................. 28 5.4 Integration with the Cal Poly Human Powered Vehicle Club ........................................................... 28 Chapter 6: Analysis ............................................................................................................................. 29 6.1 Frame........................................................................................................................................... 29 6.2 Drive Train .................................................................................................................................... 32 6.3 Seat Mount .................................................................................................................................. 34 Chapter 7: Manufacturing and Assembly .............................................................................................. 36 Chapter 8: Design Verification ............................................................................................................. 49 Chapter 9: Cost Analysis....................................................................................................................... 53 Chapter 10: Conclusions and Recommendations ................................................................................. 57 References ............................................................................................................................................ 59 Appendix A: Gantt Chart Project Plan Timeline ..................................................................................... 61 Appendix B: House of Quality ............................................................................................................... 62 Appendix C: Design Decision Matrices .................................................................................................. 64 Appendix D: Design Concepts ............................................................................................................... 65 Appendix E: Patterson Control Model Equations ................................................................................... 70 Appendix F: Patterson Control Model m File ......................................................................................... 71 Page | 3
  5. 5. Appendix G: Frame Hand Calculations .................................................................................................. 72 Appendix H: Matlab Code for Classical Lamination Theory .................................................................... 78 Appendix I: Gear Ratio Hand Calculations ............................................................................................. 80 Appendix J : Frame Load Calculations ................................................................................................... 81 Appendix K: Drive Train Hand Calculations............................................................................................ 83 Appendix L: Seat Mount Hand Calculations ........................................................................................... 86 Appendix M: Design Verification Plan and Test Report .......................................................................... 88 Appendix N: Bill of Materials Assembly ................................................................................................. 89 Appendix O: Cost Analysis and Material Allocation ............................................................................... 90 Appendix P: Vendor Component Data Sheets ....................................................................................... 91 Appendix Q: Full Assembly Drawing ...................................................................................................... 96 Appendix R: Schematic Drawings .......................................................................................................... 97 Appendix S: Routing Sheet For Front And Rear Idler Shafts ................................................................. 122 Page | 4
  6. 6. Table of Figures Figure 1.1 Bicycle terminology 8 Figure 1.2 Vehicles representing the two ends of the HPV spectrum 9 Figure 1.3 Matrix’ drive train 11 Figure 1.4 Athena drive train 12 Figure 3.1 Two-sided jackshaft drive train design 16 Figure 3.2 Single-sided serpentine drive train concept 16 Figure 3.3 Front partial frame with support tub 17 Figure 3.4 Virtual head tube steering design 17 Figure 3.5 Frame cross-sections for symmetric and asymmetric concepts 17 Figure 3.6 Initial soft tail concept 18 Figure 3.7 Adjustable sliding rails seat mount 18 Figure 3.8 Seat mount insert diagram. 19 Figure 3.9 2009 BTI Human Powered Vehicle initial concept 19 Figure 3.10 Seat Mount concept design 20 Figure 4.1 Simplified beam model sections 21 Figure 4.2 Original curved chain stay (top) vs. Final straight chain stay (bottom) 22 Figure 4.3 Rear dropout and bonding surface of frame 22 Figure 4.4 Head tube bulge 22 Figure 4.5 Original front end design with too little clearance over front wheel 23 Figure 4.6 New frame design over lighter old frame design 23 Figure 4.7 Dual cog lower shaft concept 24 Figure 4.8 Bearing and frame interface 24 Figure 4.9 Seat mount design prior to refinement 24 Figure 4.10 New seat mount design 25 Figure 5.1 Full assembly of the final frame and drive train 26 Figure 5.2 Render of frame and dropout inserts 26 Figure 5.3 Drive train locations along the frame 27 Figure 5.4 Jackshaft assembly 27 Figure 5.5 Inserts in the frame 28 Figure 5.6 Seat mount final design 28 Figure 6.1 Patterson Control Model output: control spring and sensitivity comparison 30 Figure 6.2 Geometry diagram for drive train force analysis 33 Figure 7.1 Molding plan for frame 36 Figure 7.2 MDF main frame and chain stays rough cut 37 Figure 7.3 Joined chain stay and main frame section for first MDF mold 37 Figure 7.4 Aaron setting up manual mill to cut head tube slot 37 Figure 7.5 Mill Cut outs on drive side to transition frame into chain stay section 38 Figure 7.6 MDF mold sprayed with Duratec surface primer and polished for fiberglass layup 38 Figure 7.7 Caleb and Sean applying mold release 38 Figure 7.8 Spraying gel coat of Duratec to begin fiberglass mold process 39 Figure 7.9 Laying down first fiberglass layers and spreading resin 39 Page | 5
  7. 7. Figure 7.10 Outside of fiberglass mold with stiffeners 39 Figure 7.11 Breaking the MDF out of the fiberglass mold 40 Figure 7.12 Aaron shaping the inner crotch piece with Bondo 40 Figure 7.13 Fiberglass crotch mold 40 Figure 7.14 Fiberglass mold, preparing to do first carbon layup 41 Figure 7.15 Laying out first layer of carbon fabric (Global 0-90) 41 Figure 7.16 Wetting fabric before laying it into mold 41 Figure 7.17 Laying the fabric into the fiberglass mold 42 Figure 7.18 Laying down peel ply and perforated plastic preparing for vacuum bag 42 Figure 7.19 Fixing bridging and holes in vacuum bag 42 Figure 7.20 Pulling the carbon part out of fiberglass mold 43 Figure 7.21 Imperfections in the outer part surface 43 Figure 7.22 Lexan clamped to the partially cured frame to fix surface imperfections 43 Figure 7.23 Seat Mount insert being machined in lathe 44 Figure 7.24 Cog spline in the CNC mill 44 Figure 7.25 Completed cog splines, jackshafts and bearing cups 44 Figure 7.26 Non-Drive side carbon mold before trimming 45 Figure 7.27 Setting up the mill to trim the parts down to width 45 Figure 7.28 Underlapping section of carbon tape before trimming 45 Figure 7.29 Cross section diagram of carbon molds, overlap and foam inserts 46 Figure 7.30 Acid etching seat mount inserts 46 Figure 7.31 Foam shaped to body and cutout for inserts, ready to bond molds together 46 Figure 7.32 Foam with polyurethane glue in frame while spreading epoxy on joggle 47 Figure 7.33 Caleb preparing to close the frame section 47 Figure 7.34 Frame finally joined together with foam, joggle, inserts 47 Page | 6
  8. 8. Table of Tables Table 2.1 Formal specification and compliance matrix 14 Table 6.1 Bicycle parameters based on Aaron's geometry 29 Table 6.2. Frame lay up schedule 31 Table 6.3 Chain tensions, shaft loads, and reaction forces 33 Table 6.4 Bearing loads in seat mount 35 Table 8.1 Estimated and actual frame weight 50 Table 9.1 Manufacturing labor costs 53 Table 9.2 Cost of material to be machined 54 Table 9.3 Cost of materials to build frame 54 Table 9.4 Cost of off the shelf bike parts 55 Table 9.5 Cost of all fasteners/bearings 55 Page | 7
  9. 9. Chapter 1: Introduction For our first project at Bicycle Technical Innovations, we have designed a new bike for Cal Poly’s 2009 Human Powered Vehicle team. Our bike will be used in the 2009 American Society of Mechanical Engineers Human Powered Vehicle competition, in Portland, Oregon. We have worked closely with the HPV club, their racers, and an Aerospace Engineering senior project group to determine the necessary engineering specifications and concepts for our new vehicle. The final bike will be a working prototype that is integrated with other components specified by the HPV team. Our goals, discussed in greater depth later in this report, are to design and build a new, lighter frame, more reliable drive train, and an easily adjustable seat mount. By completing these goals, we plan to deliver a high quality vehicle that performs exceptionally well at the ASME competition. 1.1 Nomenclature This document contains many terms that are very common in the cycling industry and the Human Powered Vehicle world. Figure 1.1 shows many of these terms to help clarify any parts or terms that may be discussed throughout this report. Figure 1.1 Bicycle terminology 1.2 Background Competition Details To begin our research, we considered the format of the competition and reviewed the body of rules relating to vehicle design and construction. The ASME judges have provided a detailed description of the competition formats and a list of rules [1]. The HPV Challenge involves three distinct areas of competition: a design category and two different races. Success in the competition will require excellent performance in all three areas. The first category of the competition, design, begins with the submission of a report several weeks before the actual event. Student teams must prepare and submit technical reports detailing the design and Page | 8
  10. 10. construction of their vehicles, with a presentation to the judges during the competition. Scoring in this event considers innovation, analysis, testing, safety, and utility. As our work is a significant portion of the vehicle, we will constantly consider the way our design will be judged. The two races take place over the weekend of the event. The second area of competition is called the sprint race. In this event riders are given a run-up of between 400 meters and 1 kilometer before a timed, flying 100m section. Points are awarded for both male and female categories. The female category also determines the starting positions for the third competition, an endurance race. This third area of competition is a relay race of 65 kilometers which includes sharp corners and some straight sections. The majority of the restrictions are in place to provide for fair and consistent competition and scoring. The rules also include some details to assure that all vehicles will be safe for both riders and spectators. The most specific and challenging rules describe the roll over protection system (RPS) testing regulations. These rules will have a significant impact on the design process; however, this portion of the design is the responsibility of the entire HPV team. 1.3 The HPV Spectrum The term human powered vehicle in general applies to any vehicle powered solely by human occupants; however, in the context of this report, we consider a narrower connotation. The term is used to represent the spectrum of wheeled ground vehicles powered largely by the legs and having at least a partial aerodynamic fairing. On the fast side of the spectrum, there are streamliners used for top speed competition on straight roads. The current top speed world record holder is shown in Figure 1.2a with the Varna Diablo 2. This bike can only be ridden on straight, closed roads or high speed automotive test tracks. It is optimized in every way for top speed - to the detriment of agility and practicality. In contrast, Figure 1.2b shows a recumbent tricycle from the utility class at an ASME race in 2005. This vehicle was meant to carry additional cargo and provide an agile platform for daily travels. There are of course many possible configurations between these two. (a) Varna Diablo II (b) Recumbent tricycle (UC Davis, Cat Trike) Figure 1.2 Vehicles representing the two ends of the HPV spectrum It appears that an ASME HPVC vehicle should combine some elements from both sides of the spectrum. The fast end offers high speeds which will benefit a vehicle in the sprint competition while the more practical end offers the cornering ability necessary for the endurance race. Please note that the foregoing Page | 9
  11. 11. project is not intended for competition in the utility class of the ASME HPVC and thus does not need to be street ready or able to carry any additional cargo. 1.4 Cal Poly HPV History In defining our design goals, we studied production vehicles, home built hobby vehicles, and other ASME vehicles. In particular, the Cal Poly team has a history of strong performances in the ASME event and a collection of various bicycle designs. We have presented only Cal Poly vehicles for consideration. There are two reasons for this: vehicles built solely for the ASME HPVC are most relevant, and we only have access to design details of Cal Poly vehicles. The Cal Poly HPV team is the oldest continually running HPV team for any event in the entire world; however, much of the information regarding earlier designs has been lost over the years. Information regarding the previous four generations has been compiled by members of the HPV team to follow the evolution through Princess, Secretariat, Matrix, and Athena. We have seen the vehicle frame built successfully with a structural fairing and partial frame; a full, detachable aluminum frame; and a full frame with redundant fairing structure. The drive trains of these vehicles have advanced from front wheel drive with internally geared hubs to a newer, more efficient system with multiple shafts and chains to allow rear wheel drive with a standard rear derailleur. A short description of these vehicles is provided below. Princess 2005 Princess was built with a structural fairing and partial aluminum frame. The vehicle is front wheel drive with an internally geared hub. She was very successful in ASME and was tough enough to endure several years of team training and abuse. A bulleted list of successful aspects and challenges follows. Successful Aspects Challenges Fairing is smaller because no frame or Feet strike fork due to wide rear hub in chain must pass behind rider front Simple drive train Chain frequently derails due to front wheel Fairly simple manufacturing tasks turning Geometry provides great handling Low efficiency due to geared hub Low torsional stiffness reduces handling quality and response Seat mechanism didn’t provide vertical adjustment Page | 10
  12. 12. Secretariat 2006 Secretariat was built with a non structural fairing and full aluminum frame. The vehicle is front wheel drive with a universal joint to move the final drive chain with front wheel. The front wheel has a standard gear cassette and derailleur for the final drive. She was unsuccessful in ASME and was accidentally broken shortly after the competition due to a poor weld. Secretariat is considered by some “a bike that could have been”. A bulleted list of successful aspects and challenges follows. Successful Aspects Challenges Lightest Cal Poly vehicle made, up to that Nearly impossible to ride due to a point – just over 50 pounds miscommunication of geometry (the fork Reduced derailments offset had to be reduced to accommodate Attempted to make a removable frame a design fault in the frame shape) Seat mechanism adjusted height and Drive train caused serious injuries to the length legs of all riders Feet strike fork due to wide rear hub in front Seat mechanism was slow to adjust due to binding in four parallel telescoping tubes Frame mounts broke and vehicle could not finish the endurance race Matrix 2007 Matrix was built with a structural fairing and partial composite frame. The vehicle is rear wheel drive with an internally geared hub. Matrix’ drive train lay out, shown in Figure 1.3, was so successful that it was used as a basis for the next generation as well. Matrix provided more rider safety than any previous Cal Poly vehicle at a competitive weight of about 60 pounds. He was very successful in ASME and still survives team training and abuse. In general, Matrix is a perfect starting point, but needs to lose Figure 1.3 Matrix’ drive train some weight. A bulleted list of successful aspects and challenges follows. Successful Aspects Challenges Unmatched safety and structure Low torsional stiffness reduces handling Upright rider position allowed improved quality and response visibility Low efficiency due to geared hub Simple, reliable drive train Fixed shaft locations for drive train made Geometry provides great handling gear changes difficult as chain tension was Ample clearance for feet, legs, and arms not adjustable – only a few combinations Multiple seats provided custom fit, would work as chain length must be without additional adjusting mechanism adjusted in half inch increments Very heavy drive train with nearly solid mild steel shafts and overbuilt composite bearing cups Page | 11
  13. 13. Athena 2008 Athena was built with a full length frame and light structural fairing. The vehicle is rear wheel drive with a rear derailleur and cassette. Additional research provided a much lighter post bonded drive mount which can be seen in Figure 1.4. She was somewhat successful in ASME though a drive train failure, shown in Figure 1.4b, caused a minor setback and was fixed in a machine shop at the university hosting the race. Athena was called by ASME judges, “the best looking bike ever seen at an ASME competition.” Athena also achieved a top speed of nearly 55 miles per hour in the World Human Powered Speed Championship in Battle Mountain, Nevada. She provided nearly as much rider protection as Matrix, and she was the lightest vehicle ever produced by Cal Poly. She is currently running and still survives team training. Overall, Athena is nearly perfect, aside from the drive train failure. A bulleted list of successful aspects and challenges follows. Successful Aspects Challenges Great safety and structure Fixed shaft locations for drive train made No derailment issues with drive train gear changes difficult as chain tension was Geometry provides great handling not adjustable – only a few combinations Ample clearance for feet, legs, and arms would work as chain length must be Multiple seats provided custom fit, adjusted in half inch increments without additional adjusting mechanism Long stem compromised handling quality Improved efficiency from larger rear wheel Frame and all components are bonded in and derailleur type final drive place, making repairs extremely difficult Extremely light weight drive train – a 70% Drive train failed by pedaling torque weight savings from Matrix (a) Athena drive shaft assembly (b) Shaft failure: Initiated by woodruff (retainer cap removed) torque keys Figure 1.4 Athena drive train 1.5 Objectives Our task, proposed by Cal Poly’s HPV team, is to deliver a new and innovative recumbent frame and drive train for the 2009 vehicle. Our team has collaborated with other design teams from the Human Powered Vehicle team to mesh our final design with the fairing, fork, and seat designs. Together all pieces should create a final product ready to be raced in competition. We intended to develop our design in parallel with the other components to accommodate integration. Page | 12
  14. 14. We sought to optimize the design while being somewhat conservative to create a high performance frame and more reliable drive train. Our objectives led us to develop quantitative specifications and a design philosophy described respectively in Chapter 2, Engineering Specifications and Chapter 3, Design Concept Development. Geometry and Handling The bicycle needs to handle several riders varying from 5’1” to 6’4”. This necessitates a certain amount of adjustability in the design. The layout is constrained primarily by the rider inside the vehicle, but must provide good handling qualities for all riders. We set out to improve upon the handling of the 2008 vehicle Athena, which was described as good but ready for improvement. Specifically, our goal was to increase the high speed stability of the vehicle while maintaining the current design’s low speed handling characteristics. We desired also to shorten the stem based on rider requests. The steering mechanism needs to fit inside the fairing and be located in a position so riders of varying heights can hold the mechanism and not obstruct vision. Drive Train Performance The Human Powered Vehicle Team President stressed the need for reliability in the new design due to drive train problems with the 2008 vehicle. We knew also that the weight of the overall drive train will impact the performance of the vehicle as a whole, so we set out to find a suitable compromise. Efficiency is also important, because power is very limited and efficiency losses are very significant. The team desires drive train efficiency similar to that of the 2008 vehicle. Safety Our goal here was to provide a vehicle that will not injure the rider during racing and training. There are two primary risks in this project, one is catastrophic frame failure and the other is bodily injury from the moving parts of the drive train. To provide the best in safety, we intended to be thoughtful and methodical in our design and analysis of all critical components. We also expected to create additional design features to assure rider safety. Manufacturing Our primary goals for manufacturing are to stay on budget and complete the project in the two quarter senior project schedule. We have allotted most of our budget toward materials as our labor is not factored into the costs. We plan to spend $7500 at most. We are using Microsoft Project Planner to make certain that we remain on track for our manufacturing time (See Appendix A for Gantt chart). ASME Competition The vehicle needs to adhere to the rules and categories judged in the ASME competition in order to win the competition. The entire vehicle must have a safe and attractive appearance. We will inspect the final design to ensure that it will be acceptable to the ASME judges. Additionally, the overall comfort and range of adjustability will increase the rated utility and marketability. Page | 13
  15. 15. Chapter 2: Engineering Specifications Given the wide scope of our project, it was determined that BTI should be responsible for creating the design specification documentation for much of the bike. We first contacted Robert Ehrmann, the current HPV President, to determine what areas needed to be addressed. We also considered input from the entire HPV team in group brainstorming sessions so that we would have a larger collection of ideas to work with. From those conversations and our own research of the ASME competition rules, we developed customer needs considering our main customers: the HPV President, the HPV team and riders, and the ASME judges. To organize the resulting information, we employed a quality function development tool, the house of quality. All pertinent needs are considered along with categories to quantify compliance with each need. We also researched some existing designs as benchmarks for our own new design. The combination of customer needs and benchmarks allowed us to turn a vague project definition into a concise set of engineering specifications. The house of quality, shown in Appendix B, was indispensable in the process of creating engineering specifications. We feel that communicating these goals in specific, quantifiable terms will allow us to develop a product that meets or exceeds all expectations. All current engineering specifications and tolerances are listed in Table 2.1. The requirements are organized to show which needs apply to the entire project and which are specific to the frame and drive train independently. Each specification is marked with an approximate level of risk associated with a lack of compliance. In this table, risk is rated L for low, M for medium, and H for high risk. We have marked each specification with the way in which it will be checked or considered. We will verify specifications by analysis (A), physical testing (T), comparison based upon similarity to other designs (S), or physical inspection (I). Table 2.1 Formal specification and compliance matrix Engineering Specifications Target Units Tolerance Risk Compliance Frame Frame weight 7 lb Max M A,T Torsional stiffness 0.04 Deg / ft-lb Max M A,T Hip angle 120 Degrees ±5 Deg L A,I Bottom bracket rise 8 in ±0.50 in M A,I Stem Length 10 in ±4 in L A,I Drive Train Drive train weight 6 lb Max M A,T Percent drive train covered 50 % Min M A,S,I Entire Project Budget 7500 $ Max L A Manufacturing 40 days ±5 days H S,I Total adjustability (seat to pedals) 8 in ±0.50 in H A,T,I Rider change time 25 sec Max L T,S Page | 14
  16. 16. Chapter 3: Design Concept Development As part of BTI’s design process, the project was divided into different design areas: frame, drive train and seat mounts. For each of these specific parts of the vehicle, we held a brainstorming session and came up with many different concepts. After exhausting ourselves of all possible design ideas for our vehicle, we formed a decision matrix for each area and analyzed our concepts based on our House of Quality chart, seen in Appendix B. All of the decision matrices can be found in Appendix C, and drawings of all our concepts are in Appendix D. 3.1 Design Philosophy We committed ourselves to innovating where significant improvement is possible; however, we chose not to stray too far from existing, successful technology. Throughout the design process we kept several things in mind to ensure we delivered the best possible product. We wanted the bike to have a low weight like Athena and a reliable drive train like Matrix. 3.2 Drive Train Concepts The Cal Poly Human Powered Vehicle team has been around for 31 years and they have tried many drive train configurations, which has provided a lot of valuable feedback. We examined many different ideas that have been used before, and tried to come up with new concepts as well. Using information from HPV team’s history, we were able to quickly identify areas of improvement for some of the more complex ideas. After we completed our decision matrix, we ended up with a drive train design different than anything the team has used in recent history. We knew early on that the form of the drive train would drive much of the design. For example, with a front wheel drive bike, there is no need for extra space under the rider and we would minimize the space needed for the frame in order to minimize the size of the fairing. It was known also that every drive train piece must be supported by a frame member, so the frame shape should be congruent with the drive train lay out. Front Wheel drive vs. Rear Wheel Drive Some members of the Human Powered Vehicle Team were excited about the potential of a front wheel drive design. This may end up making the bike slightly lighter, and would allow for a shorter wheelbase. A front wheel drive design however, requires some way to accommodate the wheel turning with steering, which will be inefficient when compared to a traditional chain driven system. One other major problem on the front wheel drive system is that there are simply too many parts that would need to fit in between the rider’s legs, compromising the ergonomics of the vehicle. Additionally, with so many parts connected to the front wheel and fork, steering the bike can become a major problem. These problems make a front wheel drive system much more difficult to produce, ride, and maintain than rear wheel drive. Page | 15
  17. 17. Jackshafts This is the same drive train design that both Matrix and Athena used the last two years, and in Matrix’s case, it proved to be a reliable drive system. This system involves routing the chain from the crank set to a cog on the right side of the frame that is attached to a cog on the left side of the frame via a jackshaft. A new chain is then routed below the rider’s seat where a jackshaft transfers power back to the right side of the frame. Another chain is Figure 3.1 Two-sided jackshaft drive train design connected to this jackshaft, and the cogs on the rear wheel. While this design has proved reliable in the past, we feel that it forces the frame to be too narrow in order to fit the drive train between the rider’s legs. Internally Geared Hub vs. Derailleur The internally geared hub could simplify our design, as all shifting is done within the hub and the chains will always stay in the same place. These hubs however are heavy, not nearly as efficient as a traditional derailleur, and do not allow for an easy change of gear ratios if that should be necessary on race day. A derailleur on the other hand, works with a traditional cassette that can be changed with ease to adjust gearing ratios. A derailleur and cassette is also much easier to maintain than the internally geared hub. Single Side Serpentine Chain This design keeps all drive train members on the right side instead of re-routing the chain to the left side of the bike. This allows an asymmetrical frame design, which is discussed further in the frame concepts section. When compared to the jackshaft system, we feel this design is obviously a better choice for the 2009 Human Powered Vehicle. Figure 3.2 Single-sided serpentine drive train concept 3.3 Frame Concepts During this portion of our design process, we were focusing on reviewing old concepts and thinking of ways that we could improve upon these previously tested designs. The main aspects that we were looking to improve upon were the weight of the frame and the torsional stiffness. We initially left out the comfort of the rider as an area to improve upon, but revisited this during our seat mount brainstorming session. Page | 16
  18. 18. Front Partial Frame After researching previous frames used, we considered the possibility of using a partial front frame and structural tub, similar to the frame used for Matrix in 2007. A partial frame would encompass the same function as a full frame in the front of the bike, but would not reach back to the rear wheel. This set up would allow more flexibility in rider geometry compared to a full frame, as Figure 3.3 Front partial frame with support tub more space would be available. The partial frame design would also allow for less constraint on our seat mechanism. The partial frame would have a lower stiffness, more weight due to the geometry, and negatively affect the handling of the vehicle. Because one of objectives is to increase the torsional stiffness of the bike, this concept is not a good choice. Virtual Head Tube Our motivation for examining this concept was to eliminate the need for a long stem. The long stem doesn’t fit well in the fairing and provides poor steering feedback. While this concept would provide a shorter stem length, it would also be more complex and much heavier. Additionally, the linkage to the head tube (See Figure 3.4) would have some play, which could harm the control feedback. After partially defining the geometry of our bike and measuring the riders we realized that the stem would be shorter than the Athena bike. With such a great reduction in stem length due to the change in rider position, we no longer had the need for the virtual head tube concept. Figure 3.4 Virtual head tube steering design Asymmetrical Frame The asymmetric frame cross-section was an interesting idea from our early brainstorming phases. This would only work if we used the single sided serpentine drive train design from above. While the total width of the frame and drive train needed to be tight enough to fit between the legs of a pedaling rider, a wider frame would allow for a greater strength to weight ratio. Using a Figure 3.5 Frame cross-sections for symmetric and asymmetric concepts Page | 17
  19. 19. single-sided drive train would allow us to expand the width of the non-drive side of the frame. This would allow a stronger, stiffer frame while leaving the overall width of the frame and drive train unchanged. However, an asymmetrical frame may be more difficult for our team to design and manufacture. Carbon Rear End One of our team’s least favorite frame features in Athena’s frame design was the integration of a carbon- fiber frame with a steel rear triangle to support the rear wheel. We instead considered a monocoque carbon-fiber frame. The composite material would reduce weight and likely improve the stiffness of the frame. A carbon rear triangle would also look safer and be more visually appealing, as material continuity would be kept throughout the frame. Fabrication of the split carbon rear end may be more difficult than simply bonding a rear triangle onto a front carbon frame. 3.4 Seat Mount Concepts This was one of the most interesting parts of the entire design process for our team. We had actually already decided on a frame design, but during the brainstorming session for the seat mounts, some very interesting ideas came out that would require a change in frame design. So we revisited the frame design brainstorm. As mentioned previously, we also took into account the comfort of the rider as an important factor in our decision. Soft Tail and Reverse Soft Tail This idea came up as one of the more interesting possibilities for mounting the seat to the frame, and eventually morphed into several other ideas to be discussed below. As seen in Figure 3.6, the soft tail incorporates a cantilever beam to support the seat. This design would possibly get in the way of some of the taller riders though, with the free hanging member needing to be too thick to comfortably fit between the rider’s legs. This problem appeared again when looking at the reverse soft tail design, which is a floating frame member extending up from Figure 3.6 Initial soft tail concept the chain stays, so we ultimately decided to eliminate this concept. Sliding Rail Inserts One of the many ways to actually mount the seat to the frame, and get the right amount of adjustability was to install an insert into the frame as seen in Figure 3.7. This would allow us to keep one seat in the vehicle at all times, and slide the seat forward and backward as needed. The sliding rail could also allow the seat to slide up. We would likely have to increase the frame size to support the proper adjustment motion. Figure 3.7 Adjustable sliding rails seat mount Page | 18
  20. 20. Multiple Seats and Mounting Points As we were discussing the ideas, and running through the decision matrix data, it became very clear that the best way to package such a wide range of adjustability while carrying the least amount of weight was to make a very simple mounting system and custom build seats to accommodate each rider. The logic behind this idea is simply to eliminate parts, and thus weight from the vehicle. One of the best aspects of this design is that each rider will have a seat that is custom made for them, which will increase their comfort. Additionally, the simplicity of picking up one seat and placing the new one down on the pegs then tightening a simple fastener will enable faster rider change times. Making the multiple seats will ultimately prove to be more expensive and time consuming, but with the HPV team has enough people to assist with this. Figure 3.8 Seat mount insert diagram. 3.5 Final Concept At the end of the concept design phase we selected ideas for frame, drive train, and seat mounts, which together make BTI’s 2009 Human Powered Vehicle concept shown in Figure 3.9. The vehicle has an asymmetric carbon-epoxy monocoque frame and integrated carbon rear end. This design allows the chain to fit under the chain stay and pass to the large cog in the middle of the bike. Not shown in this figure are the pegs that will be inserted into the frame to allow for the adjustment of the seat. Figure 3.9 2009 BTI Human Powered Vehicle initial concept The basic shape of the frame was designed to fit all of the geometric constraints. The frame section is small and close to the front wheel to allow clearance for shorter riders who must move forward to reach the pedals. The rear of the frame bends up before splitting into the curved chain stays to allow the chain to clear the side of the frame. The curvature will also provide added vertical compliance at the rear. This is only a rough layout of the frame, and the actual frame shape will be redesigned to meet structural requirements. Page | 19
  21. 21. Our seat mount design is a variation on the multiple seats and mounting points’ concept. The seat mount would use different combinations of four mounting inserts designs to accommodate the rider height. Two layouts were chosen for different sized riders. Since exchanging seats in races requires easy access to the mounting locations, the pegs have a conical shape to allow easier alignment with the seat inserts. The middle mounting mechanism differs from the front and rear cone peg designs. The middle has two mounting locations for stability. These mounting locations are shared by both seat mount sets. Having two mounting locations requires a thicker frame cross-section in the middle of the mount to give the inserts a surface to mount to. Our team considered widening the frame to allow for two mounting locations, but found a wider frame would infringe upon the drive train’s chain path from the rear cassette. Instead, we proposed a post-bonded mounting Figure 3.10 Seat Mount concept design beam on top of the frame. Page | 20
  22. 22. Chapter 4: Design Refinement This section details the refinement of our design from concept to final product. These changes are the result of additional concerns about manufacturing and performance. 4.1 Frame Beam Model In this estimation, the frame is modeled as a flat beam with varying cross sections and we focus only on the weight of the rider. To model the largest loads, we assumed a 3-g quasi-static impact load with a 200 lb rider. We considered the 600 lb load to be a point load in the center of the seat mount location, and found the reaction loads in the front and rear wheel locations from this. With these forces, we were able to make shear and moment diagrams, and using these, we found the largest moment at each section of the frame. Each section was assigned a representative section height based on the internal moments expected. The chain stays were modeled as a 2.25 in. tall, 1 inch thick section, the center of the frame was modeled as a 5 inch tall, 1.8 inch wide section, and the front portion of the frame as a 4 inch tall, 1.8 inch thick section. Figure 4.1 below shows how these sections were defined. Figure 4.1 Simplified beam model sections The section sizes and internal moments allowed us to make rough estimates for different parts of the carbon layup. This model only allows us to estimate the number of layers unidirectional fiber along the length of the frame, the 0° direction. We predict here that two layers will be sufficient for the entire frame. This of course is a very limited model, and we will not define a layup schedule until further analysis is completed. This model did not account for any torsion, lateral load, or drive train loads. This analysis was only used for rough sizing of cross section heights. Page | 21
  23. 23. Shape We initially intended to create very smooth, complex curves for the best in strength, stiffness, and appearance. As we moved out of the concept phase, we determined that our time line necessitated scaling back our efforts. The basic frame shape was still designed around the structural needs, but the detailed choices were simplified. This choice will allow us to complete the project in time to test the vehicle, which will be much more valuable than the meager gains from the more complex frame Figure 4.2 Original curved chain stay (top) shape. vs. Final straight chain stay (bottom) At this point, we decided that manufacturability was the most important factor in the details of the frame shape. Accordingly, we re-developed our manufacturing plan so that we would know how to build the frame. We chose to build a male plug out of flat sheets with filleted edges. The pieces could be cut with any 2-D shape. The manufactruing plan will be discussed in more detail in Chapter 7. The chain stays are a great example of this refinement. In Figure 4.2 an original curved shape is compared to the final straight shape. The final design also has a constant thickness instead of the gradual taper of the original shape. Figure 4.3 Rear dropout and bonding surface of frame Chain clearance also drove some of the shape changes. The chain must pass along the frame without obstruction. In particular, the right side of the bottom of the frame was kept narrow and flat. Also, the chain stays were designed with a high arching shape to allow the chain to pass underneath. The rear end of the frame was updated to allow for bonded aluminum drop outs. These require a straight or diverging opening at the ends of the chain stays so that part of the drop out can be inserted and bonded to the frame. We chose to extend a short straight section for this purpose. Figure 4.3 shows a rear drop out and the bonding area of the frame. The frame is reinforced with a steel head tube which we believe will simplify manufacturing and make the frame stiffer and safer. This Figure 4.4 Head tube bulge head tube requires a bulge on the right side. This shape was included to make the head tube fit in the narrow side of the frame. The left side of the frame does not need this shape, because it is wider than the head tube. We feel that the bulge perfectly highlights the asymmetry of the frame, which is perhaps the most interesting feature of the whole project. An image of the head tube’s interesting design is shown in Figure 4.4 for clarity. Page | 22
  24. 24. Another area of the frame that needed refinement was the clearance for the front fork. The frame was originally designed to incorporate the composite suspension fork developed as a previous senior project. While this was taken into account for designing the geometry of the bike and the handling, our initial CAD design did not leave enough space for the fork to be mounted. Figure 4.5 shows the spacing originally allotted for the fork, which would not have cleared the front tire. Another issue needing consideration was the travel of the fork, as we were designing for a suspension fork. To accommodate the fork and the possible travel due to suspension, the bottom side of the head tube needed to move up around two inches vertically. Moving the head tube up two inches was not as simple of a task as it seemed. Figure 4.6 compares the overall change in frame shape that was required. While the head tube needed to change Figure 4.5 Original front end design with too positions, the bottom bracket location could not change little clearance over front wheel positions, as the entire bike was designed around its fixed position. We also wanted to avoid changing height of the frame’s top due to spacing in the fairing. To accommodate these requirements, we went away from a “straight-line frame”. The frame was curved to match the arc of the front tire, improving spacing and aesthetics. We recognized the front of the original frame was thicker than necessary, allowing us to reduce the vertical thickness around the head tube. Locations of drive train and mounting points were inspected after the frame geometry was revised. Changing the frame geometry forced us to relocate the front idler, which interfered with the chain line. The front jackshaft location was repositioned for chain clearance in the front frame section. The last position moved was the location of the front seat mount. Forced to move due to available space after the geometry change, the seat mount repositioning does not affect the seat location for shorter riders. All of these movements can be compared in Figure 4.6. Figure 4.6 New frame design over lighter old frame design Page | 23
  25. 25. 4.2 Drive Train The drive train was changed significantly from the original single serpentine chain. The chain line required to pass through the rider’s leg is significantly different from the chain line required for the rear cassette. To accommodate both, we decided to use two chains. The lower idler was changed to a shaft with two cogs. The cogs are both mounted to an additional carrier that transfers torque between the two chains. The carrier and cogs use the standard Shimano free hub body splines. The lower shaft concept is shown in Figure 4.7. This part of the design is Figure 4.7 Dual cog lower shaft concept similar to the Athena drive train; however, the shaft does not transmit any torque. The frame was also modified to accommodate a change in shaft and bearing design. Originally, we were going to have a stationary shaft bonded into the frame and rotating cogs. This was turning out to be more complex than we had initially thought, so we decided to have a rotating shaft and fixed bearings. We returned to the Athena style drive train mounting. This was a very effective system last year and we feel no need to reinvent this part. The bearings are installed in an aluminum cup that is bonded to the frame. With this system, each material is appropriately used. The primary motivation for this change is the poor bearing strength of fiber reinforced plastic composites. The metallic cup supports Figure 4.8 Bearing and frame interface shear and bearing loads, while the adhesive and carbon support pure shear loads. The shaft, bearing and frame integration can be seen in Figure 4.8. 4.3 Seat Mount The seat mount design was initially developed into a set of two pegs for the front and rear mounting location and rectangular aluminum beam to support the middle mounts. Rectangular aluminum inserts would connect to the seats and be held in place by the detent pins. The seat designed for smaller riders would be held in place by another detent pin. The partially developed design can be seen in Figure 4.9. This design would require post bonding the additional pieces to the frame surface. We could not develop parts that we felt would work safely in this application. Figure 4.9 Seat mount design prior to refinement We ultimately realized that a more elegant solution was available and the entire mounting system was refined to create components that were structurally sound and simpler to construct. The second iteration of seat mount design borrows from both the drive train bonding and rear end inserts in Athena. The inserts have a hole for a detent pin, bonding flanges, and a core to join the two flanges. The flanges are used to transfer the seat load to the composite shell as a shear stress. The inserts will be hidden inside Page | 24
  26. 26. the frame, so they must be bonded in place when the two halves of the frame are joined. Figure 4.10 shows one mount of the new system. The frame will have three seat mounting inserts in approximately the same locations as the original mounting points. The team was satisfied with the overall concept of the second generation seat mounts, but worried about how the seat was held to the insert. We originally planned to hold the seats in place using the detent pins from our first seat mount design, coupled with aluminum plates attached to the seats and extra washers to accommodate any free space. While a decent design, the mounting would have to be manufactured perfectly to allow the detent pin securely clamp the seat plates. More likely than not, the seats would not have been stiffly secured, resulting in loose seats and reduced handling for the rider. We went through Figure 4.10 New seat mount design another redesign to develop our third and final seat mount design. To ensure a stiff connection between seat and frame, we replaced the detent pin with a bicycle quick release skewer. The skewer must be cut and threaded to appropriate length and will clamp the seat to the seat mount insert. The insert was slightly updated from the original design, with an increase in bonding area and geometry dimensioned to the quick release skewers. Each seat created by the HPV team will be attached to four aluminum plates, two on each side of the rider. These plates will transfer the loads to the detent pins. We have left the rest of the seat structure design to the HPV team, as the design and production is not included in the scope of our project. Page | 25
  27. 27. Chapter 5: Final Design With all of the design refinements that we made, we finally ended up with the product you see below in Figure 5.1. We embraced many of the ideas described in chapter 3.5 for our final concept. We still are using a full carbon frame, one sided drive train, and rear wheel drive. There are; however, some very important changes that did not carry over through our design refinement phase. A full set of assembly and schematic drawings can be found in Appendix R. Please note that all figures and drawings of the bike do not include the fork. This frame is designed to work with a fork created by a previous senior project team. Figure 5.1 Full assembly of the final frame and drive train 5.1 Frame Overall, the frame’s design did not change from our original concept. It only had some minor changes to its shape to help make it easier to manufacture. Several holes were cut out of the frame to allow for seat and faring mounts as well as bearings and shafts. The three holes in the bottom of the frame are there to allow us to securely mount the fairing to the frame. The fairing will be secured in a manner very similar to our final seat mount, with an insert in the frame. To ensure the frame stays secure however, they will not be detent pins, but rather threaded bolts. When the fairing is slid over the bolt, we will be able to secure it in place by tightening the nuts on the bolts attached to the frame. Figure 5.2 Render of frame and dropout inserts Page | 26
  28. 28. The dropouts on the final design pictured above and below in Figure 5.5 were modeled after those of a triathlon bicycle. They are rear entry horizontal dropouts which will allow faster wheel changes when the lower fairing is attached. 5.2 Drive Train Perhaps the biggest change that we made in our design was the switch to a 2-chain drive train. We are retaining the single sided idea that allows us to create an asymmetrical frame. The design had to be tweaked though to provide a more reliable drive train, and so we went with the 2- cog lower shaft described in the previous section. The new design will increase efficiency and reliability but it will also add a small amount of weight. The cog locations and all drive train components are seen in blue in Figure 5.3. Figure 5.3 Drive train locations along the frame The jack shafts, shown in Figure 5.4, are also crucial to the final design. Pictured in the assembly are the shaft, the spacer, the cog spline, and the retainer nut. The left side of the shaft has flat edges on it to allow for easy fastening of the retainer nut, which threads into the shaft, fastening the cog spline to the shaft. Each shaft will be placed inside of a bearing cup bonded to the outside surface of the frame. On the bottom of the frame are 3 small holes to allow for the fairing mount inserts. The front and middle inserts are simply going to bolt to the fairing, but the rear fairing mount also supports an idler pulley to direct the chain through the fairing. A custom shaft will be inserted to hold a small cog with enclosed bearings. Figure 5.4 Jackshaft assembly Page | 27
  29. 29. Figure 5.5 Inserts in the frame 5.3 Seat Mounts and Fairing Mounts The lower three red pieces shown in Figure 5.5 show the fairing mounts on the frame. In past years the fairing has been a part of the structural integrity of the bike, but our frame is stiff enough to handle these loads on its own. Thus the fairing no longer has to be a structural member of the bike. Nonetheless, the fairing still has to attach to the frame. This will be done by a channel molded into the fairing, and against the bottom of the frame, and will be secured by threading bolts through the fairing mount inserts shown above. The seats created by the HPV team attach to an aluminum insert bonded inside the frame by way of a detent pin. The seat is coupled with the pin through an aluminum sheet, supported by a carbon fiber seat mount to be designed by the HPV team. To ensure a stiff connection between seat and frame, we replaced our original detent pin design with a quick release skewer as seen in Figure 5.6. The skewer must be cut and threaded to appropriate length and will clamp the seat to the seat mount insert. The insert also has an increase in bonding area compared to the original design and geometry dimensioned to the quick release skewers. Figure 5.6 shows the basic setup for the seat mounting and aluminum plate. The stresses on this seat mount can be very high during cornering, and the analysis of this can be found in section 6.3. Figure 5.6 Seat mount final design 5.4 Integration with the Cal Poly Human Powered Vehicle Club As discussed in section 5.3, we have worked closely with the Human Powered Vehicle team to ensure that the seats, fairing, and bike will come together seamlessly. While we have made and designed many of the parts that will make this bike successful in competition, the team has been responsible for picking the proper stem, handlebar, shifters, derailleurs, brakes, and any other standard bicycle components used. These parts are very similar to parts used on older bikes, and have been proven to work very well during competition. Page | 28
  30. 30. Chapter 6: Analysis 6.1 Frame The frame has three basic requirements. It must provide: good handling, stiffness, and sufficient strength. In order to meet these goals, we used an existing mathematical model of bicycle controllability and classical lamination theory. 6.1.1 Handling and Controllability Analysis In recent years, the Cal Poly HPV designs have provided exceptional handling characteristics. Many of the team riders have provided feedback comparing some of these vehicles. We have also used the Patterson Control Model (PCM) to quantify the response of the various bikes. The qualitative rider input was used to interpret our results so that we could choose the best compromise of handling qualities. This model is based on several critical parameters that are shown in Table 6.1. The Patterson Control Model provides two very useful tools for analyzing the handling of a bicycle. The first is the control spring as a function of velocity, which indicates the force feedback felt through the handle bars. The positive values show a control reversal and tend to make a bike unstable and negative values tend to make a bike stable. In this case, the maximum value must be low and the transition to a negative control spring must happen at very low speeds so that the bike stabilizes itself quickly. The second tool is a graph of the control sensitivity as a function of velocity. Control sensitivity describes the roll response of the bike compared to the rider’s intention. The basic equations of this model are shown in Appendix E and the Mat lab code used is included as Appendix F. A full description of these tools is beyond the scope of this report, but more information is available from references 3 and 4. Table 6.1 Bicycle parameters based on Aaron's geometry Parameter Units 2009 BTI Athena Matrix Wheelbase A [m] 1.321 1.397 1.051 C.G. Position B [m] 0.838 0.874 0.531 C.G. Height h [m] 0.445 0.394 0.394 Head Tube Angle β [°] 12 12 12 Radius of Gyration Kx [m] 0.272 0.213 0.213 Control Radius Rh [m] 0.2 0.203 0.127 Front Wheel Radius R [m] 0.241 0.241 0.241 Offset e [m] -0.076 -0.076 -0.051 In particular, we chose to compare to Athena because the general configuration is the same as our design. We reduced the control sensitivity slightly while retaining a similar control spring response. Decreasing the control sensitivity will provide a ride that feels more stable and predictable and should ultimately lead to better performance. Testing by W.B. Patterson showed that a control sensitivity of about 14 made for a stable, comfortable ride. This line is shown on the graph for comparison. We have been careful to retain a fairly high amount of control sensitivity so that the bike will still feel responsive and quick. We believe that the HPV riders are exceptional bike handlers and will prefer higher control sensitivity. Page | 29
  31. 31. The handling changes were accomplished by moving the seat slightly up and back as well as making the seat back angle more upright. This change in seat location also allowed us to decrease the wheel base, and bring the front wheel closer to the rider, thus eliminating the need for a long stem. The seat angle change will increase the moment of inertia of the bike and rider and slow the roll response, which will contribute to a slightly more stable ride. Table 6.1 shows the critical parameters of the new geometry. Control spring and control sensitivity graphs for the current design as well as Matrix and Athena are shown in Figure 6.1. Figure 6.1 Patterson Control Model output: control spring and sensitivity comparison 6.1.2 Structural Analysis The structural analysis of the frame has been simplified considerably since the beginning of this project. Initial planning included a finite element analysis to predict frame stiffness and strength. This ended up being unpractical. The frame has been analyzed in pieces to determine a lay up schedule that will provide strength enough to survive regular use. Loading Conditions The critical frame loads are produced by rider weight, impact, braking, and pedaling/drive train forces. Impact and dynamic road loads are modeled here as a quasi-static loading equivalent to a 3G acceleration. This impact model has been the basis of the design of several previous Cal Poly HPVs and many other road going vehicles. Using static analysis and some simplifying assumptions, as shown in Appendix G, we were able to determine the loading conditions in the frame. The forces and moments are converted to line loads in the carbon skin as described in the next section. Strength Analysis and Lay Up Schedule Page | 30
  32. 32. The strength analysis uses classical lamination theory and the max strain failure criteria to predict the failure index of elements of the frame. The frame skin is considered in elements at critical locations and treated as a laminated plate with applied line loads. Additionally, bending moments in the frame section are resolved by a force couple due to uniform line loads in the top and bottom skins of each section. This method is conservative in general because it neglects the load carried by the sides of the frame. In this case; however, filleted corners and curves are not considered, so some caution must be used. This analysis is presented in Appendix G and uses the Matlab code provided in Appendix H. The composite analysis is based on the properties on AS4/3501-6 material. Previous testing of HPV team lay ups has shown properties comparable to this material. To account for potential damage, the maximum allowable strain has been reduced 20% as is standard practice. The reported maximum strain is based on tensile tests of small sample coupons and may not always represent an actual part, even if the part has not been damaged. It has been assumed that the structural foam core will provide adequate stability for the frame skin. Accordingly, no analysis has been performed to predict buckling or cross section changes. It is also particularly difficult to analyze the crotch piece of the frame, so additional material will be added to prevent failure. This area will be reinforced with Kevlar 49 for toughness. The final layup schedule for the frame will have a minimum safety factor of 1.7 not including the 20% reduction in allowable strain. This occurs in the rear end of the bike at the joint of the chain stays. The whole frame will have three layers of balanced fabric biased at 45 degrees to provide torsional stiffness. The whole frame will also have one layer of balanced fabric oriented at 0 and 90 degrees to provide balanced strength around the bonded components. In addition, the top and bottom on the frame sections will be capped with 2 layers of unidirectional tape oriented along the frame length. The layup schedule is shown below. Table 6.2 Frame lay up schedule Material Direction Layers Location Frame Sides Carbon fabric ±45° 3 Global Carbon fabric 0°,90° 1 Global Carbon uni 0° 1 Fillet, Insert Crotch Carbon fabric ±45° 3 Global Carbon fabric 0°,90° 1 Global Kevlar 29 ±45° 1 Inner Crotch Kevlar 49 uni 0° 1 Inner Crotch Carbon uni 0° 1 Fillet Bonded Drop Outs The drop outs will be loaded by both rider weight and chain tension. To be conservative, we chose to combine the two effects and determine a bond area that could support both forces together. Only the right side drop out will see this much stress, but both will be manufactured with the same bonding area. We also chose a degraded bond strength value of 1000 psi as we are working with average bond stress. Page | 31
  33. 33. In this combined loading case the right drop out must support 684 pounds from chain tension and 140 pounds from a 3g impact. The minimum required bond area is .82 inches 2 if the forces are added algebraically. The perimeter of each chain stay cross section is 3.4 inches, so the required length is then only .25 inches. There are a few problems with this estimate. The most concerning is that the carbon shell may fail due to edge effects if the drop outs are so short. The forces are not quite aligned and vector addition would provide a slightly smaller maximum force, but the larger algebraic sum is more conservative. In addition, both forces also produce a moment which will increase the stress and further complicate the stress distribution. Given the concerns with this analysis, we chose a length of 1 inch for the bond area, yielding an area of 3.4 inches2. According to the above estimation, this provides a safety factor of 4. This crude estimation is considered sufficient, because it is appropriately conservative and the weight of the drop outs is insignificant when compared to the frame. 6.2 Drive Train 6.2.1 Gear Ratio The drive train must provide sufficient gearing for high speed sprints and the endurance race at the ASME competition. The low speed gear ratio will be determined by experimentation when the bike is complete. The high speed gear ratio is estimated by simple calculations shown in Appendix I We chose to provide a speed of 45 miles per hour with a crank input of 100 rpm. We selected a 48 tooth chain ring and 16 tooth cog in the first position on Jack shaft 2 and then calculated that we will need a 21 tooth cog in the other position on jack shaft 2. 4.2.2 Loading Conditions The loading from the drive train impacted two design features: the layup schedule and sizing of the shafts and bearings needed. For a maximum loading case, we assumed a pedal input force of 500 pounds normal to the crank at top dead center. Last year the HPV team used the same approximation with a 250 pound pedal input. Considering the drive train failure in Athena, we chose to double the input force. The input force comes from a simulation for when a rider starts the bike. By nature, our muscles produce maximum force at low speeds. This will create forces within the drive train components along with forces and moments at each point of contact between the drive train and the frame. This provided loading conditions to be used for the drive train design and our original attempt at an FEA model, which later did not work out. Page | 32
  34. 34. Figure 6.2 Geometry diagram for drive train force analysis Using the geometry shown above in Figure 4.3, we were able to calculate the reaction forces for each shaft in the drive train based on the chain tension. The reactions for points 1, 2, and 3 are shown below in Table 6.3. These correspond to the bottom bracket, front jackshaft, and rear jackshaft respectively. Details regarding the geometry of Figure 6.2 can be found in Appendix J. Table 6.3 Chain tensions, shaft loads, and reaction forces based on 500lbf Pedaling Force Tension Vertical Shaft Loads Horizontal Shaft Location [lb] [lb] Loads [lb] 1 855 -219 -827 2 855 -391 227 3 684 735 -73 The reactionary loads on the drive and non drive side of the frame were calculated from the vertical loads, horizontal loads, and length of the shafts. This informed us where the critical sections were located and what was the minimum force needed to design our bearing cup mounts. The critical load takes place at location 3, on the drive side of the rear jackshaft. The skin of the frame experiences 1038 lb vertically and 411 lb horizontally. We designed around this loading case to ensure our drive train and frame would not fail. 6.2.2 Bonding Area The drive train shafts are bonded to the frame using round, tapered flanges. Adhesive bonding is a rapidly developing field, and exact stress analysis of a particular bond is very difficult. To avoid excessive analysis, we have used information from previous testing. The HPV performed careful testing of similar aluminum bonds last year. The test data was reported as maximum average stress at joint failure. The drive train cups will be similarly sized so an average shear stress approach is appropriate for design. Additionally, the bonded flanges are tapered to reduce stress concentrations and smooth the shear stress distribution. The analysis of a uniform stress distribution is used to determine the minimum outer diameter of the bonded flanges. The right side cups will see significantly higher loads, estimated up to 740 pounds. The Page | 33
  35. 35. right side cups must be at least 2.16 inches in diameter to provide a safety factor of three. The left side requires very little area. If sized by area alone, the left side may fail, as much of the bonded area could be affected by slight damage when cutting the hole in the frame. The minimum outer diameter is calculated as 1.67 inches. A minimum diameter of 2 inches is preferred to avoid edge effects. 6.2.3 Bearing Selection We chose to use the same bearing and shaft diameter in both shafts in order to simplify vehicle manufacture and service. All analysis was performed for the lower shaft, number 3 in Figure 6.3, which will be subjected to the highest loads. The maximum radial load on a bearing will be about 900 pounds. We chose a 20 millimeter shaft diameter as the largest that will fit within the spline of a standard cog. Additionally, our preferred supplier, McMaster-Carr, offers a thin section bearing in this size with sufficient load capacity. The bearing is specified in the bill of materials section, Appendix K. Shaft Sizing Shaft sizing is also quite simple in this project. The pedal input load of 500 pounds is significantly greater than expected in normal service, so the analysis is simplified greatly. We have ignored stress concentrations from threading and fatigue life. The bike is intended for a very short life cycle and thus it is safe to ignore these as long as reasonable safety factors are provided for strength. The shafts are checked for strength in two ways. The first check, which proved to be the most important, was maximum shear at the center line. The second check used the Von Mises yield criterion to determine if the extreme fibers would yield due to bending and shear stresses. Shaft sizing was constrained by bearing selection and the available die and tap sets at the Cal Poly Senior Project lab Machine Shop. We found all matched tap and die sets in sizes near the shaft diameter and analyzed each to determine the best choice. The best choice is 5/8-18 thread, which provides a minimum safety factor of 2.4 for shear failure. The calculations for shaft strength are shown in Appendix K. We ended up using standard threading because no large metric tools were available. This is a non issue, because we have made custom fasteners. 6.3 Seat Mount 6.3.1 Loads The seat mounts must support the weight of the rider and pedaling loads. The rider is also able to shift weight in the seat while adjusting position or leaning the bike in a turn. The seat mounting points were analyzed for the following three cases: 3g vertical impact, static rider weight with pedaling loads, and leaning rider weight. In the first case, the impact force was assumed to be distributed equally across all four holes of the seat mount. In the second case, the pedaling force is resolved by a point load from the rider’s back. The third case was modeled with the rider weight applied at the far right side of the seat. These cases are considered in detail in Appendix L. A summary of the maximum forces and corresponding locations is shown in Table 6.4. All seat mounts will be identical, so the critical case is used for design of all inserts. The critical loading case for the seat mounts is leaning or cornering according to this model. Page | 34
  36. 36. Table 6.4 Bearing loads in seat mount Maximum Force Loading Case Location Per Hole[lb] 3g Impact 150 all Leaning or Cornering 630 each side Max Pedal Force 460 rear 6.3.2 Sizing This section provides a description of the analyses made to size components and finalize the seat mount design. Bond Area As mentioned above, all inserts will be identical and all design is based on the highest load predicted. These inserts, like the drop outs will be bonded to the frame skin with round, tapered flanges. The bond is modeled as a simple lap shear joint with an even stress distribution. With a safety factor of 3 and maximum shear strength of 1500 psi, the outer diameter of the seat insert flange must be at least 1.3 inches, providing 1.26 in2 of bonding area. Bearing Surface The seat mount will have an aluminum plate as a bearing surface. This plate is intended only as a bearing surface and must be reinforced by additional structure. Accordingly, we have analyzed only bearing stress in the plates. The worst case load is 630 pounds per insert. These plates will be made of 7075 T6 aluminum sheet which has an approximate yield strength of 76 ksi [8]. The plate was sized by assuming uniform distribution of bearing stress and neglecting the clamping mechanism. Clamping force provides a more complex stress state and allows some load to be transmitted via friction and surface traction. According to this simplified analysis, shown in Appendix L, the plates must be 0.083 inches thick to provide a safety factor of 3. Page | 35
  37. 37. Chapter 7: Manufacturing and Assembly After completion of the final designs, we began the manufacturing of the frame and other parts necessary to build the vehicle. We will first discuss how we decided on certain manufacturing procedures, then describe each step in detail. 7.1 Manufacturing Philosophy The final frame design describes a single piece carbon skin, without reference to how it will be made. If this frame were going to production, we would consider building a 3 piece closed mold which would allow the frame to be made in one piece. Instead, we chose to lay up three separate pieces and join them together. We chose to design the molds in the manner shown in Figure 7.1 in order to make the seam go along the center of the frame rather than on either side. If the seam were on the side of the frame, it would interfere with the bonding area for drive train and seat inserts. . This seam location allows for proper bonding and will provide a better appearance. Figure 7.1 Molding plan for frame, including the three carbon fiber pieces to be bonded to a structural foam core For each jack shaft, fairing mount bolt, and seat mount pin in this design, we made an insert to go into the frame. To make each of these inserts, we started with a solid rod and cut the part on a lathe. Some parts needed to be milled and/or CNC machined. We utilized the CNC mill to cut a standard Shimano free hub splines onto our cog carriers in order to easily secure the cogs to each shaft. The retainer nut and the jackshafts need to be cut on a mill with a rotary table to create flat surfaces for wrenches. All parts were machined by either BTI, a member of the HPV team, or a student shop technician. When the frame lay ups and all drive train components were completed, we began assembling the bike. We first put all of the inserts into the frame, bonded the flanges to the outer surface of the frame, fit the bearings and cog splines to the shafts, and secured the cogs to their spline. An exploded view of the entire assembly can be found in Appendix N. Page | 36
  38. 38. 7.2 MDF Pattern Construction The molding process began with full size printed templates of the frame, and views of the chain stays normal to their surface. We traced these onto a ¾’x4’x8’ sheet of MDF (Medium Density Fiber) board and cut out these shapes using a Figure 7.2 MDF main frame and chain stays rough jigsaw. Because our total frame thickness is 1.5”, cut we needed to make our male plug thicker than this to allow for a flange when we lay the fiberglass molds down. So with 3 shapes for the frame and each chain stay cut out (Figure 7.2), we then glued them together to create a 2.25” thick frame, as seen in Figure 7.3. When the glue dried, we used a belt sander, an orbital sander, and a spindle sander to evenly shape the frame. Once the frame and chain stays had an even surface finish, it was time to attach the non-drive side chain stay to the frame. We decided to make this mold first so that we could re use the frame piece for the next mold. The non-drive side chain stay is longer, so when it came time to pull the MDF mold out of the fiberglass mold, we could simply cut the frame shorter to install the right side chain stay. To attach the left chain stay, we cut it as close Figure 7.3 Joined chain stay and main frame section for first MDF mold to the designed 8.4 degrees as possible using a Table saw, then glued it to the frame. Some shaping with Bondo was required once they were joined to get a smooth transition region. Before we could make our fiberglass mold, we had to consider how to create the head tube cut out for each side. To do this, we cut into the frame at 12 degrees using a mill to the depth of the head tube cutout. This process is seen in Figure 7.4. We then placed a rod cut to the head tube’s outer thickness in the cutout and filled the gaps with Bondo to smooth the region out. We also used a router to fillet both the frame and chain stays. Figure 7.4 Aaron setting up manual mill to cut Page | 37 head tube slot
  39. 39. Once the MDF model was complete, we sprayed the frame with several layers of Duratec surface primer. This primer allowed final, shaping, smoothing, and surface polishing. We polished the frame by wet sanding with increasing grades of sand paper. This process provides a smooth surface that is not possible with bare MDF. Once Figure 7.5 Mill Cut outs on drive side to transition the frame was sanded completely smooth, we were frame into chain stay section and allow for fairing ready to perform the non drive side fiberglass lay mount insert up on our backer board. When this was completed, we would pull the mold and create the drive side MDF mold. For the drive side chain stay, we need to make special considerations for the rear most fairing mount, and flatten the chain stay using the mill, as shown in Figure 7.5. This cut out from the mill needed a great deal of sanding and bondo in order to give the frame a reasonable shape. Once the shaping of the drive side MDF mold was completed, we once again sprayed Duratec and sanded to prepare for the fiberglass Layup process (Figure 7.6). The third and last mold is for the inside of the chain stays. For this mold, we built a frame or backer Figure 7.6 MDF mold sprayed with Duratec surface board to support the chain stays at the appropriate primer and polished for fiberglass layup angle. We cut the original chain stay patterns off of the frame pattern and attached them to the mold backer board. The crotch was then filled with Bondo and carefully shaped. This mold was also sprayed with Duratec surface primer and sanded. The shaping of the crotch can be seen in Figure 7.12 Figure 7.7 Caleb and Sean applying mold release Page | 38
  40. 40. 7.3 Fiberglass Mold Process Once each MDF mold was completed and sanded smooth, we could move onto the fiberglass mold process shown over the next several pages. Figure 7.8 Spraying gel coat of Duratec to begin fiberglass mold process The first step in this process is to spray the MDF mold with a mold release agent as seen in Figure 7.7. This allows the fiberglass resin to create a smooth outer surface without bonding to the MDF mold. We chose to do this with Frekote, which we will discuss more in section 7.4. When the mold release agent was absorbed into the surface of the MDF, we sprayed a thick layer of Duratec surface primer over the entire pattern (Figure 7.8). We chose this material because it is polyester based and can cure with the polyester resin for the rest of the mold. When the Duratec became tacky, we were able to lay down our first layer of Fiberglass, which was one continuous sheet. Figure 7.9 shows the team spreading polyester resin over a layer of fiberglass. Each layer was allowed to cure slightly before the next layer Figure 7.9 Laying down first fiberglass layers and was applied and this process was repeated 5 times spreading resin to create a stiff fiberglass mold. After letting the mold cure for 24 hours, we removed the MDF mold from the fiberglass. This was a very time consuming process because the MDF and the fiberglass molds were very stiff. We used wooden tongue depressor sticks as seen in Figure 7.11 to break the fiberglass free from the MDF to help pull the mold. Figure 7.10 Outside of fiberglass mold with Page | 39 stiffeners

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