Cliff Jumping Bike Final Report ME 4182 Capstone Design
Transcription
Cliff Jumping Bike Final Report ME 4182 Capstone Design
Cliff Jumping Bike Final Report ME 4182 Capstone Design Fall 2008 Team Unit 91 Jon Gutierrez, Chris Sauer, Simon Radomski, Chat Huynh, Jeff Burton and Robert Platt TABLE OF CONTENTS I. EXECUTIVE SUMMARY .................................................................................................... 1 II. INTRODUCTION .................................................................................................................. 1 III. DESIGN PROCESS ............................................................................................................... 2 A. DESIGN CONCEPTS ........................................................................................................ 2 B. PRODUCT AND PATENT SEARCH ............................................................................... 4 C. SELECTION ANALYSIS .................................................................................................. 8 IV. SYSTEM DESCRIPTION.................................................................................................... 11 V. ENGINEERING ANALYSIS............................................................................................... 14 VI. PROTOTYPE RESULTS AND ANALYSIS....................................................................... 16 VII. FUTURE IMPROVEMENTS .............................................................................................. 18 VIII. CONCLUSION..................................................................................................................... 18 IX. Bibliography ......................................................................................................................... 19 APPENDIX A. FINITE ELEMENT ANALYSIS (FEA) ...................................................... 20 APPENDIX B. BILL OF MATERIALS AND PART DRAWINGS .................................... 25 I. EXECUTIVE SUMMARY The design presented in this report represents an extreme incarnation of a downhill bike. Current downhill bikes have a maximum rear suspension travel of 7 – 12 inches. The goal of this project is to increase overall energy dissipation through a novel suspension geometry that allows extreme rear wheel travel, thus resulting in the overall ride-ability and safety of a downhill bike. The rider needs a bike that can descend a mountain with maximum speed and safety. The suspension of the downhill bike allows the rider to overcome obstacles, jump off of cliffs and cope with extreme conditions. Extreme rear wheel travel will be defined as a suspension design that provides a reaction force to the rear wheel while the wheel travels from the un-loaded position to the fully loaded position. The travel distance chosen to define extreme travel is 14 inches as this allows the bottom bracket to still be low enough for the rider to pedal the bike while in a seated position. The characteristics of a successful design are high safety and force dissipation, good ride characteristics, and marketability. These characteristics are further broken down into design goals. Each of the candidate designs were ranked based on there ability to fulfill the design goals and the design with the highest overall score was selected. The selected design was dubbed the Parallel Linkage design. The Parallel linkage design provided the full 14 inches of rear wheel travel providing for additional safety and force dissipation while jumping or falling from a cliff. It incorporates two shocks set in a parallel arrangement in order to provide a sufficiently high spring force to prevent bottoming out of the shocks. The path that the rear wheel followed while compressing was a rearward arc. This type of path prevents the suspension from binding while negotiating rocks and other obstacles. Finally the design was aesthetically pleasing providing a cool look that should be marketable to downhill bike enthusiasts. II. INTRODUCTION The design presented in this report represents an extreme example of a downhill bike. The goal was to increase energy dissipation through rear wheel travel. Current downhill bikes have a maximum rear suspension travel of 7 – 12 inches. For this project, rear wheel vertical travel was chosen to increase to 14 inches to decrease the acceleration felt by the rider when 1 landing from obstacles. 14 inches of rear wheel travel was the limit as the height of the bottom bracket is limited by human constraints and limits wheel travel. III. DESIGN PROCESS A. DESIGN CONCEPTS The two highest scoring design concepts were the Parallel Linkage design and the Progressive Suspension Design. The strengths of the Parallel Linkage design, shown in Figure 1 and Figure 2 are that the rear wheel creates a rearward arc as it travels from the un-compressed to the compressed state. During the design selection phase of the project the parallel linkage concept did not specify dual shocks. As design discussions progressed it became clear that in order to provide sufficient reaction force to the rear wheel over the entire 14 inches of travel dual parallel shocks would be needed. Dual parallel shocks were added to the Parallel Linkage design and the final conceptual design is shown in Figure 3. Seat Handlebar Linkages Shock Pivots Un-compressed State Wheels Figure 1 Parallel Linkages Conceptual Design Showing Un-Compressed State 2 Shock Compressed State Pivots Linkages Wheels Figure 2 Parallel Linkages Conceptual Design Showing Compressed State Dual Shocks Figure 3 Parallel Linkages Final Conceptual Design Incorporating Dual Shocks The second highest ranking design was the progressive suspension concept. The Progressive Suspension concept was a long travel suspension that uses two springs to create a progressive spring rate. The advantage of this design the dual shocks are arranged in series. This would allow tuning one shock to handle regular riding while the other shock is only used in extreme conditions like landing a jump, resulting in a progressive suspension rate. The uncompressed image of the design is shown in Figure 4 and the compressed design in shown in Figure 5. 3 Figure 4 Progressive Suspension Conceptual Design Showing Un-Compressed State Figure 5 Progressive Suspension Conceptual Design Showing Compressed State B. PRODUCT AND PATENT SEARCH A patent search was conducted in order to make sure that the team’s ideas did not infringe on current patents. The patent search also gave the team new ideas on how to approach the design problem. Patents usually state what is good about the patented innovation and why it is better than current designs, so valuable information can be found from a patent document. The team learned about problems caused by chain extension, energy losses due to suspension bobbing, and other ride issues by examining the many bicycle patents already issued. One of the most important patents found was patent# 7296815, “Bicycle Suspension Apparatus and Related Method.” This patent was the basis for the Ellsworth Dare production bike which was used as the team’s baseline. The patent explains that the chain torque line is positioned between the upper and lower rocker arm lines and the three lines coincide at the 4 instant center. Figure 6 shows the rear suspension geometry claimed in the patent. The chain torque line is the line created by the upper section of the chain from the rear to the front chainring. The line extends infinitely in both directions. The upper and lower swing arms also have infinite lines that go through each arms pivot points. The point where these three lines meet is the instant center. The chain torque has the least effect on suspension movement when it is positioned between the two swing arm lines. A minimal amount of suspension movement caused by chain torque is desirable, so that pedaling the bike does not cause suspension bobbing or increased difficultly getting the suspension to compress. Suspension bobbing is what happens when the suspension compresses from the force of pedaling. Bobbing converts pedaling energy from a horizontal movement to a vertical movement wasting the rider’s energy in the dampener. Figure 7 shows the Ellsworth Dare, which has been in production for a number of years, proving that the design is successful in the market place. Figure 6 Rear Suspension Drawing from Patent# 7296815 Figure 7 Ellsworth Dare Production Bicycle 5 Patent# 6843494, “Rear Suspension System for Two-Wheeled Vehicles, Particularly Bicycles,” was also very informative. This patent was the basis for the Rocky Mountain Bicycles ETSX 50 production bicycle, shown in Figure 8. Figure 8 Rocky Mountain Bicycles ETSX 50 Production Bicycle Patent# 6843494 claims that the rear suspension geometry has a minimal amount of chain extension and a nearly vertical wheel path. Figure 9 shows a drawing of the rear suspension from the patent. Chain extension is the elongation of the chain length from the bottom bracket (point 23) to the rear axle (point 36), caused by the wheel path as the suspension compresses. Chain extension puts a force on the chain making pedaling more difficult; therefore a minimal amount of chain extension is desirable. The wheel path is the line that the rear axle traces as the suspension compresses. A near vertical or slightly rearward path is most desirable. If the path moves forward then the suspension will have a harder time going over bumps. As the wheel moves up to go over a bump, it will also move slightly forward, creating a binding force on the suspension. The binding force will stop the suspension from compressing, transferring the force created by the bump straight to the rider and forcing the rider and entire bicycle to move up. This unsettles the rider and can cause a crash. Designing a vertical or rearward wheel path gets rid of the binding force and alleviates the problem. 6 Figure 9 Rear Suspension Geometry Drawing from Patent# 6843494 Patent# 7395892, Cycle Suspension Assembly, was an example of a creative solution to the long travel problem facing our team. Figure 10 shows one of the patent drawings. The suspension uses two shocks connected in series in order to give the bike a maximum amount of travel and to reduce the probability of bottoming out. Bottoming out is what happens when the shocks get completely compressed and the remaining force gets violently transferred directly to the rigid frame and rider. Bottoming out usually causes bodily injuries and breaks the bicycle. The two shock system shown in Figure 10 is an intelligent design, because two different spring rates can be employed in order to minimize the risk of bottoming out. Figure 10 Rear Suspension Geometry Drawing from Patent# 7395892 Shock 28 can be made much stiffer than shock 22, so the initial impact force can be taken up by shock 22. If more force still needs to be dissipated, such as when the bicycle is taken over a large jump, then shock 28 will begin to compress as well. This design is also good, because the weaker 7 shock makes riding over small bumps more comfortable, while not causing too much energy robbing suspension bobbing that most bicycles with very large suspension travel have a problem with. The problem with this design is that it will not be laterally stiff, because link 26 will have all of the lateral loads going through it. Link 26 will be loaded in torsion and in compression so it will be very difficult to make it strong and stiff enough not to fail. The patent search introduced the team to a number of design problems that would be necessary to consider in order to create a bicycle that would accomplish the goals that where set. Although the design that was ultimately chosen does not solve all of the suspension bobbing or chain extension problems introduced by the patents, it did get influenced by these problems. Compromises between suspension travel distance, suspension travel path, chain extension, chain torque location, and other geometric issues where made in order to create the best design. C. SELECTION ANALYSIS Several conceptual designs were developed and compared to a representative baseline design. The two highest ranking conceptual designs were discussed in the Design Concept section. The baseline design was selected from patents discussed in the Product and Patent Search section. The bike selected as the baseline bike was the Ellsworth Dare. The Ellsworth Dare’s key features are a nearly vertical wheel path and a specially developed four bar linkage. It is claimed that the specially developed four bar linkage limits chain extension which reduces pedal feedback. In order to rank the designs the design selection matrix Figure 11 (A) was developed. The design selection matrix groups the design goals into three major categories: safety / force dissipation, ride characteristics, and marketability. The most important design goals are included in the safety / force dissipation category, with the ride-ability being the next most important. The best ranked proposed designs were the parallel linkages design and the progressive suspension design. Both the parallel linkages and the progressive suspension designs were superior or equal to the baseline in most ways. Specifically, they were much better in terms of suspension travel, traveling the desired 14”, and force to rider while the anti-bob characteristics, weight and number of parts were less desirable. However, the travel and force transmission dominated the other considerations with their ranking weights because the ability to minimize shock to the rider is more important for a downhill bike with the laid out objectives. 8 The parallel linkage design also had other good features, such as a very short chain extension length and lateral stiffness matching that of the baseline. Also, due to adding a second shock absorber, the chances of a shock failure on the parallel linkage is very low. Shock failure is very dangerous and expensive to the rider, so avoiding this is a key design feature. Finally, like the baseline, the parallel linkage design did not require custom shocks, allowing it to be made with pre-existing shock models that have been proven in the field. These benefits made the parallel linkage design the best option. One notable characteristic of the design selection matrix is that a progressive mechanical advantage was considered to be a positive feature. It was also assumed that the parallel linkages design would provide this feature. However, as the project progressed it was found that a constant mechanical advantage would provide the best compromise between the maximum force transmitted to rider from a fall and ride-ability. Also, as it turned out, the parallel linkage design naturally provided a constant mechanical advantage. All in all, considering the knowledge gained by working on the project, the parallel linkage design is still the superior design. 9 Design Selection Safety / Force Suspension Travel Dissipation Low max force to rider during landing Progressive Mechanical Advantage Should not destroy shock Lateral Stiffness Ride Characteristics Rear wheel should travel rearward or vertical Chain Extension Anti-bob characteristics (instantaneous centers coincide) Marketability Standard Shock Minimum number of parts Minimize Weight Aesthetics Baseline: Parallel Progressive Top Tube Parallel Series Double Ranking Weight Ellsworth Dare Linkages Suspension Shock Double Shock Shock 15 0.16 2 5 5 5 5 5 15 0.16 2 5 4 4 4 4 13 0.14 4 4 4 3 1 3 11 9 7 0.12 0.10 0.08 2 5 4 5 5 4 2 4 4 1 2 2 4 2 2 2 4 6 5 0.06 0.05 4 3 5 2 4 2 5 2 5 2 2 2 5 3 4 4 3.18 5 2 3 4 4.46 1.00 5 2 3 4 3.78 0.85 5 2 4 2 3.23 0.72 1 3 3 3 3.12 0.70 1 4 4 3 2.94 0.66 5 0.05 3 0.03 2 0.02 2 0.02 Weighted Score Normalized Score (A) (B) (C) (D) Figure 11 (A) Design Selection Matrix (B) Baseline Ellsworth Dare (C) Parallel Linkages (D) Progressive Suspension 10 IV. SYSTEM DESCRIPTION The complete downhill bike is made up of seven different parts. These are; the steering and front suspension, braking system, power train, wheels, shocks, frame, and back suspension. The design focused on creating the right suspension and frame and finding a way to integrate the other systems around it. For most of the other systems, such as the wheels and power train, available parts from the mountain bike industry were used. Our efforts were focused on creating a system that would support customization and easy replacement and maintenance with standard industry parts. For the steering and front suspension, a front fork from an existing mountain bike was used. The fork chosen for the prototype was a 2002 Marzocchi Jr. T. It was chosen for it’s larger than usual travel, 7 inches, but any standard mountain bike fork will fit on the bike frame. The goal for the steering and front suspension was to maximize the travel and impact absorption using standard industry parts. The braking system for the bike is also interchangeable with industry parts. The system employed in the downhill bike uses brakes on the front and rear wheels. These are hydraulic disk brakes that work very well and slow the bike down smoothly and completely. For the prototype only an 8 inch diameter disc with a hydraulic caliper was used. It worked well with the prototype and had no issues stopping the bike. Attaching the brakes and the links to the brakes on the rear suspension would involve unnecessary cluttering and complication to building the prototype. The power train used on the bike is a standard pedal and chain setup. The frame was built to accommodate standard bottom brackets from the mountain bike industry. The bottom arm on the rear suspension was specially designed to not interrupt the chain at any degree of suspension travel. The design of the bike allows for a standard derailleur and gearshifts. The design permits the use of standard mountain bike wheels as long as the front wheel is equipped with a disk for the disk brakes. For the prototype, big wide wheels were used with dirt tires mounted on them. However, the bike will support any standard mountain bike wheel. The shocks used on the prototype are two custom built shocks with 637.5 lb/inch springs. However, the design allows for standard downhill mountain bike shocks to be used. The spring constant needed will depend on the weight of the rider, but something close to 637.5 lb/inch is recommended for a 180 lb rider. 11 The frame and the back suspension were designed to work together. The frame was purposefully built to accommodate the rear suspension geometry, two large shocks, and the requirements for extreme mountain biking. The bottom bracket on the frame is higher off the ground that in most bikes to allow the full compression of the back geometry without having the gears on the bottom bracket hit the ground. The bottom bracket and the head tube, where the front fork connects, are made of thicker steel tubing than the rest of the frame to allow for threading for the connecting parts. The seat tube was redesigned to incorporate a wider tube around because of the high stresses from where the shocks connect and also where the upper arm of the suspension pivots. The back suspension is made up of eleven moving parts. The geometry of the suspension attached to the back wheel forms a four bar linkage. The upper arm is attached to the seat tube with a bolt that allows it to rotate. When the bike lands a jump or goes over an obstacle, the rear wheel pushes the end of the upper arm upwards, making the other side of the arm pull downwards as it rotates about the pin on the seat tube. The other end of the upper arm is attached to a link called the arm link, which pulls on the shock connect. The shock connect is attached to the shock link, a member attached to the top tube on the frame which allows the shock connect to rotate about the bolt on the top tube. Then the bike is compressed, the wheel pushes the upper arm making it rotate and pull on the arm link, which in turn pulls on the shock connect compressing the shocks along the path dictated by the shock link and opposing the force that made the wheel move in the first place. The members of the suspension are free to rotate at all the points at which they are attached by a bolt, as seen in Figure 12. The shock link was designed and placed purposefully to force the shock connect into its optimal path. This specific suspension geometry provides a linear mechanical advantage of 5.8 as seen in Figure 13. A list of parts and the method of fabrication is provided in Table 1, milled parts are 1045 Cold Drawn steel and tube parts are ASTM A513 Type 5 tubes with 1/8” max wall thickness. 12 Figure 12 Rotation Points as Defined by Bolts Figure 13 Comparison of average Mechanical Advantage for several test cases. The final design utilized the original position resulting in an average Mechanical Advantage of 5.8. Table 1 Part Fabrication Methods Description Part Type Thumbnail Quantity Description Part Type Thumbnail Quantity Bottom Bracket Tube 1 Top Tube Tube 1 Arm Link Milled 2 Top Tube Link Milled 2 Lower Arm Milled 1 Seat Tube Tube 1 Axel Mount Milled 2 Shock Connect Milled 1 Upper Arm Milled 2 Bottom Tube 1 13 Tube V. ENGINEERING ANALYSIS The forces on the bike were found using the conservation of energy. The weight of the bike was found to be 70 pounds and the average weight of the rider assumed to be 180 lbs. The forces found using the conservation of energy are an average force over the distance the rider takes to stop traveling vertically. The bike was designed with 14 inches of travel and the rider was assumed to give 16 inches of travel using their arms and legs adding to a combined stopping distance of 30 inches. Using the springs specified for the bike, the average force found combined between the front and rear wheels was 546.5 lbs with the rider landing horizontal on the ground with the front and rear tire landing at the same time. This applies a peak of 1093 lbs when the front and rear suspensions are fully compressed. The rider will land standing on the pedals. The pedals are located at 27.6 inches rear from the center of the front wheel. The bike has a total wheelbase of 46.1 inches. 59.4% of the force from landing is translated to the rear wheel. This force is 649.8 lbs at maximum compression. Figure 14 shows the max forces on the bike when fully compressed. Figure 14 Forces on compressed bike frame A safety factor of 2.5 was chosen for the frame of the bike. This allows the bike to withstand fatigue loads and the impact force from landing while not making the bike so heavy that it cannot be ridden. A FEA analysis was performed to find the strength of the members. The yellow arrows are the forces derived from Figure 14 and the red arrows are the constraints. The factors of safety found for each part is shown in Table 2. The fatigue life was calculated and is shown in Table 3. The material chosen for the milled parts of the bike is 1045 steel with a yield strength of 14 85 ksi. The steel tubing for the frame is ASTM A513 Type 5 with a yield strength of 70 ksi. The FEA images are shown in Attachments 1-10 in the Appendix A. Table 2 Safety factor of parts Part Top Tube Top Tube Link Shock Connect Arm Link Lower Arm Axle Mount Upper Arm Seat Tube Bottom Bracket Bottom Tube Part Type Tube Milled Milled Milled Milled Milled Milled Tube Tube Tube Material Yield Strength (ksi) 70 85 85 85 85 85 85 70 70 70 Max Stress (ksi) 28 32 34 20 34 8.8 32 26 14 20 Factor of Safety 2.5 2.7 2.5 4.3 2.5 9.7 2.7 2.7 5.0 3.5 Table 3 Fatigue life of parts Part Top Tube Top Tube Link Shock Connect Arm Link Lower Arm Axle Mount Upper Arm Seat Tube Life Cycles 1.9E+08 1.9E+08 9.3E+07 4.7E+10 5.9E+06 5.6E+14 1.9E+08 3.3E+06 Bolt sizes and safety factors were chosen from the forces they would be experiencing. The bolt sizes and safety factors are shown in Figure 15. The lowest factor of safety for the bushings was 10.3. 15 Figure 15 Bolt sizes and safety factors VI. PROTOTYPE RESULTS AND ANALYSIS A prototype was built in order to prove the design concept. The prototype is shown in Figure 16. The prototype was simplified in terms of structure geometry, joints, and materials, but it still proved the concepts of the design. It was simplified due to a lack of funding and time to build. The prototype tests were carried out at only 25 % of the design potential. However, the linkage design did work according to design. Figure 16 Picture of Prototype Cliff Jumping Bike 16 The materials used for the prototype were 6061 Aluminum and 1018 Cold Drawn Steel. The designed material was 1045 Cold Drawn Steel. The arm link, shock link, and axle mount were made out of aluminum, because it is much easier and faster to machine than steel. The geometry of the upper arm and the lower arm was simplified due to limited equipment capability and lack of time to manufacture. The upper arm was split into 4 unique parts that were welded together instead of one solid cast part. The bend in the upper arm was not manufactured according to the design. The bend was replaced by a round spacer, which still worked but lacked aesthetic quality. The lower arm geometry was also modified in the prototype. It also made out of 4 unique parts. The round tube used was thinner, because it was the only tube the team had left over from building the bike frame. The rectangular tube used was of a smaller cross section due to lack of funding. The shock connect geometry was also simplified. Everything else was made to the designed geometry. The bike failed at the lower arm round tube. The collapse of this tube was not due to the bottoming out of the suspension; rather it resulted from the large force translated from the upper arm through the axle mount while the shocks were being compressed. It was fixed by pressing a steel rod inside the tube. This was not anticipated while doing analysis, because the axle mount rotation was not taken in consideration and the round tube used in the prototype was thinner than the designed tube. The back wheel was off balanced due to manufacturing error, which made it much harder to ride. The initial designed shock spring rate was only 371 lbs/in, which bottomed out over a 3 ft jump and sagged quite a bit when a 200 lbs person sat on the bike. The redesigned shock spring rate was twice as big and resulted in only 30 % sag, which is the desired amount. The test runs were carried out at a max height of 3 ft. The prototype could have survived twice as high of a jump, but there were no places on campus where such a test could be carried out. The prototype was also tested on rocky roads and down long sets of stairs where the suspension was subjected to large vibrations. This test would have destroyed a regular bike that has little to no suspension travel. The prototype sustained no damages after many jumps and long runs down stairs. Throughout the tests, the large shocks did not bottom out. The final prototype weighted 58 lbs. Due to the modifications in geometry and materials, the prototype was a lot weaker than the design; therefore higher jumps could not be achieved. However, the designed concept was proved after many jumps and runs down stairs with out damage. 17 VII. FUTURE IMPROVEMENTS The goal of future improvements will be to lighten the bike and refine the ride characteristics. Also complex parts like the upper arm could be re-designed for ease of manufacturing. Lateral stability of the rear wheel can be improved by revising the suspension arm arrangement. Like most other high end downhill bikes, this bike is not intended to be mass produced. This bike is intended to be hand fabricated. As such, high complexity is acceptable. However upon addition design review further simplification for manufacturing purposes should be possible. Finally, before this product can be sold to the consumer market, extensive product and safety testing would be required. VIII. CONCLUSION The design succeeded in meeting the major design goal of creating a downhill bike that can overcome obstacles and survive impacts from falling or jumping off cliffs. The prototype provided solid proof of concept. While the prototype was not capable of jumping from extreme heights due to its simplified fabrication, we are confident that a bike built to the design specifications would have no rival in today’s market. 18 IX. Bibliography CATIA Version 5.17, Dassault Systems 1994 – 2005 DwLink Suspension System, Accessed September 15, 2008. http://dw-link.com/reasons.html Free Patents Online, Accessed September 10, 2008. http://www.freepatentsonline.com Path Analysis, Kenneth M. Sasaki, Peter Ejvinsson. Accessed September 9, 2008. http://www.mundobiker.es/content/category/3/67/185/. SolidWorks Education Edition, Dassault Systems Academic year 2007-2008 / 2007 SP3.1 19 APPENDIX A. FINITE ELEMENT ANALYSIS (FEA) Attachment 1 FEA of upper arm Attachment 2 FEA of arm link 20 Attachment 3 FEA of axle mount Attachment 4 FEA of bottom bracket 21 Attachment 5 FEA of bottom tube Attachment 6 FEA of lower arm 22 Attachment 7 FEA of seat tube Attachment 8 FEA shock connect 23 Attachment 9 FEA of shock link Attachment 10 FEA of top tube 24 APPENDIX B. BILL OF MATERIALS AND PART DRAWINGS 25 26 27 28 29 Bottom Bracket 30 Arm Link 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50