Frame Design Independent Research – Honors Thesis

Joshua M. Willard Bachelor of Science in Mechanical Engineering Magna Cum Laude Spring 2016 Bicycle Frame Design Independent Research Study – Executive Summary Joshua M. Willard 4/24/16 Presentation Date – 4/26/16

Project Description: This project explored unique bicycle concepts and spawned an exciting new manufacturing technique. Through additive manufacturing this original fabrication technique provides the ability to yield a repeatable, quality product. The design concepts and techniques from this project may soon be provided to consumers through boutique bicycle manufacturers. Project Objective: The objective of this project was to follow Shigley’s design process to design and manufacture a bicycle frame while exploring novel concepts. The bicycle geometry was developed to be rider specific while maintaining industry fit standards. Without access to traditional fixtures and tooling an additional constraint is placed on the novel concepts; a small bicycle company must have the ability to produce the concept in house. Project Results: The project unveils the novel concept of producing 3D printed jigs for aiding in the construction of a bicycle frame. These jigs allowed for quick frame assembly while ensuring the design specifications and geometry were met. The unique bicycle frame features a removable rear triangle giving the ability to change the bicycle’s geometry. Changing the geometry allows the user to optimize the bike’s characteristics for different riding conditions while maintaining the same basic platform. The result is a comfortable bike on the road, beach, or mountain.

3D printed jigs set the frame angles for repeatability and precision.

The removable rear triangle gives the ability to change bicycle’s geometry with ease.

Lessons Learned: Design for manufacturability in unique bicycle frames requires an iterative process. Manufacturing techniques developed in this study through rapid prototyping produce a fast and repeatable product. Finite element analysis methods for complex assemblies are not explicit and should be taken with caution before proceeding.

Project Partners: Michael W. Griffis – Project Advisor, Nancy J. Ruzycki – Honors’ Committee Member, Curtis R. Taylor – Honors’ Committee Member Table of Contents 1. ABSTRACT ...... 5 2. NEED ...... 5 Design Considerations: ...... 5 3. SPECS ...... 5 PERFORMANCE SPECS: ...... 5 4. SYNTHESIS ...... 6 4.1 CONCEPT INTRODUCTION ...... 6 4.1.1 GENERAL BICYCLE OVERVIEW ...... 6 4.1.2 FIRST DESIGN CONCEPT ...... 7 4.1.3 SECOND DESIGN CONCEPT ...... 8 4.2 SYNTHESIZED CONCEPT ...... 8 4.2.2 CONCEPT COMPONENTS ...... 9 5. MATERIAL SELECTION PROCESS ...... 11 5.1 TRANSLATION OVERVIEW ...... 11 5.2 TRANSLATION EXPLAINED ...... 12 5.3 MATERIAL EQUATIONS ...... 13 5.3.1 MATERIAL STRENGTH AND ...... 13 5.3.2 MATERIAL STRENGTH AND RELATIVE COST...... 14 5.4 MATERIAL SELECTION – ASHBY...... 15 5.5 MATERIAL SELECTION REFINEMENT ...... 19 5.6 ENVIRONMENTAL IMPACT OF MATERIAL ...... 19 5.7 OTHER CONCERNS ...... 19 5.8 MATERIAL SELECTION CONCLUSION ...... 20 6. ANALYSIS AND OPTIMIZATION ...... 20 6.1 INTRODUCTION ...... 20 6.2 FREE BODY DIAGRAMS ...... 21 6.3 CRITICAL LOCATIONS ...... 22 6.4 SOLIDWORKS VERIFICATION ...... 24 6.4.1 SOLIDWORKS SET UP ...... 24 6.4.2 SOLIDWORKS SIMULATION RESULTS ...... 26 6.5 ANALYSIS CONCLUSION ...... 28 7. PROTOTYPE CONSTRUCTION ...... 28 8. INTELLECTUAL PROPERTY ...... 33 8.1 CLAIM FOR NOVEL FEATURES ...... 33 8.2 CLAIM FOR NOVEL MANUFACTURING METHOD ...... 33 9. EVALUATION...... 33 9.1 Pros and Cons ...... 33 10. LESSONS LEARNED...... 34 11. APPENDIX ...... 35

1. ABSTRACT Modern bicycle frames have followed a basic, double triangle format over the past century. Novel concepts have been introduced into bicycle components, but the frame has generally gone unchanged. The objective of this project is to explore and encompass innovative ideas, through synthesis and iteration, while using a rigorous design process. Concepts are realized and then iterated upon while searching for a final synthesized model. Using industry standards, solid modeling, and simulation techniques, a final concept is developed. Manufacturing techniques are explored as the concept evolves during prototyping and this phase of the project unveils a new manufacturing method to decrease time and increase productivity. Rapid prototyping is found to be exceptional in bicycle frame construction. As a result, boutique bicycle manufacturers will soon have the opportunity to produce a novel concept using the exclusive methods developed in this project. 2. NEED There is a need to safely support a rider of 180 lbs. while minimizing cost and weight. Design Considerations: 1. Product Safety 2. Load Rating (rider weight) 3. Novel Manufacturing Methods 4. Novel Design 5. Overall Weight 6. Overall Size 7. Overall Worst Case Scenario (Intended and Unintended) 8. Overall Factor of Safety 9. Ease of Use 10. Material Choice 11. Material Geometry 12. Geometry / Size 13. Wheel / Tire Capacity 14. Manufacturing Method 15. Manufacturing Cost 16. Manufacturing Time 17. Environmental Impact 3. SPECS PERFORMANCE SPECS: 1. Capacity: 180lbf 2. Nominal Worst Case: Standing Pedal (30% weight handlebar end , 70% weight one pedal) 3. Factor of Safety: 2.0 Minimum

4. SYNTHESIS Novel concepts were developed following Shigley’s design process. With this, two innovative models were developed and then synthesized together on further iterations. The combination of the two main ideas allowed for the empowerment of each concept, thus making the entire concept reinforced. The design introduces a set of novel ideas to immediately decrease manufacturing time, increase productivity, and allow for multiple applications. 4.1 CONCEPT INTRODUCTION 4.1.1 GENERAL BICYCLE OVERVIEW Bicycle frames have generally remained consistent for over 100 years. Innovations have been made to components of the bicycle, but the double triangle design is considered the industry standard. Almost every bicycle produced in the world today has a double triangle design and follow a basic set of rules and nomenclature. Figure 1 is shown below establishing the nomenclature of bicycle frame geometry.

Head Tube Top Tube Seat Tube

Seat Stays Down Tube Main Triangle

Rear Triangle Rear Dropouts

Bottom Bracket Chain Stays

Figure 1. Nomenclature of a standard bicycle is shown in the figure above. Note: main triangle and front triangle are often interchangeable.

Seat Tube Angle

Head Tube Angle

Figure 2. The head tube angle and seat tube angle of a bicycle are shown.

4.1.2 FIRST DESIGN CONCEPT The first concept that was developed through this project gave the combination of bicycle speed, rollover capability, and agility. Traditionally, are designed and built with to have a specific goal in mind. Rider comfort, bicycle speed, agility, and rollover capability are usually the main goals for a bicycle (“The War on Wheel Sizes”). Mountain bikes currently have three main diameter wheel sizes. These wheel sizes along with the geometry of the bike will characterize how the bicycle handles. Industry standards rate the following wheel sized bikes in Table 1 below (“The War on Wheel Sizes”).

Table 1. Bicycle standards for different wheel sizes. Speed, agility, and rollover are considered in a qualitative assessment of their performance. (“The War on Wheel Sizes”). Bicycle Standards Wheel Size Speed Agility Rollover 26" 3 1 3 27.5" 2 2 2 29" 1 3 1

The first concept combines the idea of having a fast bicycle, lower center of gravity, great agility, and retaining some roll over. A fast 29-inch will never steer at the ability of a 26 or 27.5-inch mountain bike with similar geometry. The increase in wheelbase does not allow the rider to quickly weave through trees at the same rate as the smaller wheel platforms. The other downside to the larger wheel size is the gyroscopic effect of the larger front wheel (“The War on Wheel Sizes”). This gyroscopic effect requires more input force while steering and some users have noted the front wheel fighting the steering input. The concept attempts to combine the pros of the smaller wheel sizes while retaining the benefits of the larger wheel size. A mismatched wheel set on the bicycle. Bicycle geometry is designed to run a 27.5-inch wheel in the front and a 29-inch wheel in the rear. The difference in height is accommodated by pulling the rear wheel in close to the and raising the wheel causing the rear to sag. Short chain stays bring the rider’s weight more directly over the rear wheel which causes the rear of the bike to become twitchier (“The War on Wheel Sizes”). With the rear of the bike having a twitchy nature and the front of the bike using a slightly smaller wheel, the geometry and components of the bike will produce a better handling, but equally fast bicycle (“The War on Wheel Sizes”). 4.1.3 SECOND DESIGN CONCEPT The second design concept comes in the form of a multiple use concept. Nearly every bicycle frame has the front and rear triangle as one assembly. Traveling with such a large item can be difficult and many enthusiasts desire to travel to new biking locations. Unfortunately, renting a bicycle causes the enthusiast to be unfamiliar with not only the terrain and topography, but also the bicycle. This can cause a dangerous combination when riding a new bicycle through a completely new area. Many cyclists would prefer to travel with their bike to get the full experience of a new track, trail, or road. Reducing the size of a bicycle is not possible, but allowing the front and rear to separate at a bolted joint could be a reasonable concept. For this concept, the chain stays, seat stays, and rear dropouts will be produced as a separate entity than the main triangle. With a removable rear triangle, the bicycle can pack into a smaller box or bag to travel on an airplane, bus, or backpack. 4.2 SYNTHESIZED CONCEPT The synthesized model combined the two concepts into one. The removable rear triangle allows for the bike to be packed into a smaller box. The mismatched wheels give the bicycle better handling characteristics and a faster ride. Combining these concepts into one is where the ownership of intellectual property is pursued. The concept: a bicycle with adjustable geometry and variable wheel sizes to give the rider an almost endless set of configurations. The configurations will permit the owner of the bicycle to choose what wheel configuration and rear triangle configuration would work best for the terrain, topography, and style of riding. 4.2.2 CONCEPT COMPONENTS

Standard Main Triangle

Rear Triangle Detachment Points

Sized for 27.5” Front Wheel

Low Bottom Bracket Height

Figure 3. The realized concept. This concept is sized for 27.5” wheels while providing a low bottom bracket height while allowing for the rear geometry to change.

Rear Triangle Detachment Points

Figure 4. Isometric view of the rear triangle detachment points.

Sliding Dropouts Give Detachment Points Chain Tensioning

Figure 5. The rear triangle is shown in the figure. Sliding dropouts and the detachment points are critical in this design. Detachment Point Reinforcement

Rectangular Bar Stock Increases Moment of Inertia Without Large Weight Increase, I = bh3

Figure 6. The shortened chain stays require more strength. Creating a larger moment of inertia about the bolted region decreases the effective stress within the beam. At the upper detachment point is reinforcement to increase the factor of safety.

The synthesized concept gives the best of both concepts allowing for the next part of the design process. 5. MATERIAL SELECTION PROCESS 5.1 TRANSLATION OVERVIEW a) Identify a model – Bicycle frames are in the form of columns for the head tube and seat tube, but the frame also acts in the form of beams for the top tube, down tube, chain stays, and seat stays. b) Identify function – The bicycle frame will be examined as a set of beams. c) Identify constraints – Minimum factor of safety, η = 2.0, beam length of L, and corrosion resistance d) Identify objective – Maximum strength per unit mass and maximum strength per unit cost. e) Identify free variables – diameter, d, material choice - Strength, σf, density, ρ, and cost, CV,R.

5.2 TRANSLATION EXPLAINED Designing and manufacturing a bicycle frame has many constraints which add to the overall cost. These costs do not always stack at a linear rate, but at an exponential rate depending on the material choice. For example, in the manufacturing of fiber reinforced polymers, there will always be the concern of quality as the part becomes more complex. The fiber to volume ratio may become skewed in some areas of complex parts creating defects; a defect in a bicycle frame is a safety issue. With this, increased construction costs of the frame will ultimately be reflected in the final price of the bicycle. The general consumer of a bicycle frame will have two main concerns when conducting a comparison. The main concern of the bike will be the price and the second will be the weight of the frame. For safety reasons, the weight and strength will go hand in hand while other factors of the bike are predetermined constraints at this moment. The geometry will be a uniform cross section for the tubing shown in Figure 1 above. The main triangle consists of the seat tube, top tube, down tube, bottom bracket shell, and head tube. The fork of the bicycle fits through the main triangle’s head tube with a press fit bearing where the and handlebars are attached. At the bottom of the fork there are dropouts for the front wheel to be attached. The pedals attach through the bottom bracket shell which contains a bearing; the bearing is dependent on the designer’s preference as it can be threaded or press fit. The rear triangle consists of the seat stays and chain stays. The rear triangle is supported through the bottom bracket shell, seat tube, and the rear dropouts where the rear wheel is bolted into place. The geometry of a bicycle frame act mainly in the form of beams, but in some instances the tubing may be treated as a column. Most cases, the frame’s tubing will be acting as beams and for the simplicity of this analysis they will be treated as such. The triangles will be combined at preset angles and the material selected must follow a general set of guidelines to ensure the durability of the frame. Material stiffness is important in frames. The frame must be stiff enough to prevent significant flexing. The flexing can cause energy to be lost through the frame instead of sending the energy through the pedals to the rear wheel. The frame also must have the stiffness to prevent parts from making contact under heavy loading. In some instances, there have been bicycle frames that twist under hard pedaling conditions. This hard pedaling condition caused enough twist to cause the rear triangle to make contact with the pedals. In the event of an unfortunately, but likely accident, the frame must be able to withstand permanent deformation and fracture. A requirement that comes from this condition is that the material must have a high level of strength. Bicycle crashes are inevitable however minor the collision; the frame must be prepared to withstand any impact. Taking strength into consideration also begs the requirement for an excellent fatigue endurance limit. Cyclic stresses will cause some materials to weaken significantly over time and this should be a consideration. 5.3 MATERIAL EQUATIONS The industry standard for frame designers is to use computer aided design software. While this may be an industry standard engineers and designers should consider the physics and important mechanical properties of the bicycle frame. Taking these properties and constraints into consideration give a material selection process that is not subjective to what designer might prefer, but what is best for the goal. As previously stated in the part of the research paper, “Materials Selection of Alloys for Use in Bicycle Frames,” ‘Equations the designer should keep in mind while selecting materials for this job are plentiful, but they are required to make sure the frame is built well enough for the consumer (“Frame Design”).’ 5.3.1 MATERIAL STRENGTH AND DENSITY The frame will be treated as solid beams for simplicity of equations and walking through the material selection process. With this, the equations are simplified enough to walk through and not become too complicated. The beams will be loaded as cantilever beams. The end will be fixed and the free end is loaded at a length, L. With this, the bending stress of a cantilever beam loaded at the end is 푃퐿 (1) 휎 = 푏 푍 Where P is the load at the end of the beam, L is the length of the beam from the fixed end to the free end, and Z is the section modulus. Relating the bending stress to the factor of safety we can rewrite the material strength and simplify the equation

휎푓 휂 = 휎푏 휎푓 = 휂휎푏 (2)

And then combining (1) and (2) 푃퐿 (3) 휎 = 휂 푓 푍 The section modulus of a solid circular beam follows the equation 휋 푍 = 푑3 (4) 32 Therefore, the strength of the material depends on combining (3) and (4) 푃퐿 1 휎 = 32 휂 ( ) 푓 휋 푑3 Rewriting to get the diameter as the free variable 푃퐿 1 푑3 = 32 휂 ( ) (5) 휋 휎푓 For the first objective, we must minimize the mass, so we must relate the material strength to material mass using the equation 푚 = 휌퐴퐿 (6) And the cross-sectional area of a solid circular beam follows the equation

휋 퐴 = 푑2 (7) 4 And combining (6) and (7) 휋 푚 = 휌 퐿 ( 푑2) (8) 4 Inserting (5) into the mass equation (8) 2 휋 푃퐿 1 3 푚 = 휌 퐿 (32 휂 ( )) 4 휋 휎푓 Separating the equation into a functional part, geometric part, and material part

4 1 2 5 휌 3 3 3 3 푚 = (2 휋 휂 푃 ) (퐿 ) ( 2) 휎푓3 The material index, M1 is defined as such 2 휎푓3 푀 = 1 휌 When maximizing M1, the mass is minimized.

5.3.2 MATERIAL STRENGTH AND RELATIVE COST Now, moving forward to material cost and building on equations from the previous section. The material cost equation is dependent on the volume of the material and the cost per unit volume shown in the equation

퐶 = 퐶푚 휌퐴퐿 (9) With this (9), and using (5) 2 휋 푃퐿 1 3 퐶 = 퐶푣,푆푇 퐶푣,푅 퐿 (32 휂 ( )) 4 휋 휎푓 Separating into a function, geometric, and material part

4 1 2 5 퐶푣,푅 3 3 3 3 퐶 = (퐶푣,푆푇 2 휋 휂 푃 ) (퐿 ) ( 2 ) 휎푓3 And defining the material index, M2 2 휎푓3 푀2 = 퐶푣,푅 When M2 is maximized, the cost is minimized. 5.4 MATERIAL SELECTION – ASHBY

Direction of increasing M1

Figure 7. Strength – Density Ashby Chart. The direction of the material index, M1, is shown above where it is increasing moving up and to the left.

Using Figure 7, all ceramics and elastomers will be ignored. In the case of a bicycle frame, and especially a beam, the main concern is tensile failure and yield strength in tension. One can notice using Figure 7, Carbon Fiber Reinforced Polymer (CFRP) lies on the line for the absolute minimum mass and most strength, alloys, parallel to the grain, and aluminum are on the second line, and the third line has Steel. The following table shows the ranking and approximate material index value for these materials.

Table 2. Material Ranking for Ashby Selection – Strength v. Density Material σ ρ M1 1 CFRP 1000 1.5 66.7 2 Titanium 1000 4.5 22.2 2 Aluminum 400 2.5 21.7 2 Wood || 60 0.7 21.9 3 Carbon Steel 800 8 10.77

Direction of increasing M2

Figure 8. Strength – Relative Cost Ashby Chart. The direction of the material index, M2, is shown above where it is increasing moving up and to the left.

Using Figure 8, all ceramics and elastomers will be ignored for the same reasons stated above under the first material index. Inspecting the figure, it can be noticed that wood parallel to the grain and carbon steel lie on the same line. For this purpose, carbon will be considered for the increasing strength with minimal relative cost. Aluminum alloys lie on the second line, CFRP on the third line, and titanium alloys on the fourth line. The following table shows an approximation of material index values for the strength – relative cost chart.

Table 3. Material Ranking for Ashby Selection – Strength v. Relative Cost Material σ Cr M2 3 CFRP 1000 100 1 4 Titanium 1000 300 0.333 2 Aluminum 400 2 27.1 1 Wood || 60 0.15 102.2 1 Carbon Steel 800 1 86.2

Direction of increasing M3

Figure 9. Fracture Toughness – Strength Ashby Chart. The direction of the material index, M3, is shown above where it is increasing moving up and to the left. Materials will yield before fracture as the material index increases.

Using Figure 9, all ceramics and elastomers will be ignored for the same reasons stated above under the first material index. The fracture toughness is important to consider as the bicycle will go through a cyclic life and it is important for the frame to experience yield before fracture, not a fracture before yield. With this, the first line contains aluminum, the second line contains wood parallel to the grain, the third line has carbon steel, fourth line has titanium, and the last line has CFRP. The following table shows the results of the material index.

Table 4. Material Ranking for Ashby Selection – Fracture Limit v. Yield Strength Material K σ M3 5 CFRP 15 1000 0.015 4 Titanium 30 1000 0.030 1 Aluminum 30 35 0.857 2 Wood || 8 45 0.178 3 Carbon Steel 60 1000 0.060

Unfortunately, the Ashby charts do not consider the entire costs of a project. Material cost is important, but the manufacturing cost can outweigh the material cost at times. With this, the following qualitative assessment is used to assist in the material selection process. CFRP for bicycle frames can be expensive when producing a low volume of frames per mold. In this case, the time and manufacturing cost will become too large and is assigned a value of 5 for the M5 column. CFRP can have a high risk of defects if not manufactured properly. The matrix ratio of resin to fabric can cause issues as well as complex geometrics where the matrix ratio becomes skewed, thus CFRP is assigned a value of 4 for risk in column M4. Titanium requires a special chamber to extract air gasses out of the environment and shielding gas to be pumped in place of air. Titanium is more difficult to weld and requires a more skilled welder than for aluminum and carbon steels. With this, the risk and overall manufacturing cost have been assigned values of 3 and 4 respectively. Aluminum does not produce a very large risk when and manufacturing, but does have an added cost as it does require to be heat treated before and after welding. With this, aluminum is assigned a value of 2 for M4 and 3 for M5. Wood parallel to the grain is a great material for bicycle frames. At a low production rate, the wood parallel to the grain will become difficult to produce without risk. Wood parallel to the grain requires a perfect treatment process to be considered an engineering material. As outlined in more detail, wood does not fit the bill with the risks associated with treatment processes and is assigned a value of 5 for M4 and 2 for M5. Lastly, carbon steel does not have a large risk associated with manufacturing. It does not require heat treatment processes if welded using GTAW methods and the time to manufacture is lowered as it does not require these heat treatments. Therefore, carbon steel is assigned values of 1 for both M4 and M5. The results of these qualitative assessments are shown in Table 5 below.

Table 5. Material Ranking for Manufacturing Defect Risk and Manufacturing Cost / Time. Material Min. Risk (M4) Cost / Time (M5) CFRP 4 5 Titanium 3 4 Aluminum 2 3 Wood || 5 2 Carbon Steel 1 1

Moving forward in material selection, the composite rankings for each material are determined and carbon steel is shown as the winner in the table below.

Table 6. Composite Material Selection Ranking Material M1 M2 M3 M4 M5 Composite Average Composite Rank CFRP 1 3 5 4 5 3.6 5 Titanium 2 4 4 3 4 3.4 4 Aluminum 2 2 1 2 3 2 2 Wood || 2 1 2 5 2 2.4 3 Carbon Steel 3 1 3 1 1 1.8 1

5.5 MATERIAL SELECTION REFINEMENT Carbon steel is chosen using standard material selection methods. Material selection software will refine the solution to provide options for the best material. Different grades of carbon steel are considered for this, but after research 4130 is chosen as the best material. It retains the basic structure of steel, but with and it becomes a strong that is easily weldable. 5.6 ENVIRONMENTAL IMPACT OF MATERIAL In summer 2014, part of the research paper “Materials Selection of Steel Alloys for Use in Bicycle Frames” by Joshua M. Willard (6-7), Steel is formed from the naturally occurring element iron. While carbon is a naturally occurring element, carbon fiber composite materials are not naturally occurring and are not recyclable. One property of steel is it can be recycled and smelted once again to create another object later in its life. Sustainability has been rising in the steel industry since the 1990’s. The industry has been working very hard in reducing CO2 emissions from their factories and they have reduced their emissions by 33 percent since 1990 (“Goal: Steel, Our Most Sustainable Material.”). The energy required to manufacture and produce steel has also been reduced by a grand total of 28 percent (“Goal: Steel, Our Most Sustainable Material.”). These reductions in emissions and energy use will continue as the industry pushes toward sustainability. Some may be concerned with welding steel, but most alloys of steel are safe to weld with the exception of those with high zinc content. The fumes of welding are inevitable but can be run through a filter to alleviate environmental concerns from the fumes. For bicycle frames, wood would have the least environmental impact, but unfortunately does not meet the criteria for this project. Thus, steel is the best option to deliver the most suitable frame, but can still be made with limited environmental impact. 5.7 OTHER CONCERNS (GTAW) produces the best penetration in thin materials. This is because the heat and filler rod is controlled precisely with a foot pedal and both hands. Other welding methods do not acquire the same depth of penetration in a material without much more heat. The reason for GTAW having the best control for heat is because it uses a separate electrode instead of letting the filler material carry the arc. In GMAW, , the welding wire carries the arc and it also is the electrode. It is difficult to produce the heat penetration desired for a safe and reliable weld unless the material is thick. In the case of a bicycle frame, the material is thin and GTAW reduces the need for heat treatment after welding. Filler rod material and thickness is another important concern in material selection. With 4130 selected, a neutral rod is chosen. The ER70S-2 fill rod at 0.035 inches provides the best weld for 4130. The strength of the fill rod is comparable to 4130 and it obtains the remaining properties of 4130 when welded. As for thickness, the fill rod should always be equal to or less than the thickness of the material. With this, the best penetration is gained and the weld becomes just as strong as the material that is welded. 5.8 MATERIAL SELECTION CONCLUSION In summer 2014, part of the research paper “Materials Selection of Steel Alloys for Use in Bicycle Frames” by Joshua M. Willard (6), Steel alloys such as 4130 (Chromium Molybdenum) or Reynolds 531 ( Molybdenum) have very high strength, stiffness, corrosion resistance, resistance to elongation, and are not too expensive. Added manufacturing costs are taken into consideration with this choice of steel alloys too. Steel is easy to weld or even braze where titanium and aluminum are not as easy to weld (“AISI 4130 Alloy Steel (UNS G41300)”, 2012). This ease of welding is complemented by the ease of handling. Steel doesn’t require special tooling to drill, make cuts, or even make notches. Thus, the manufacturing cost for this metal in comparison to aluminum or titanium is fractional. All these costs add up and with a reduced material cost and manufacturing cost, the bicycle frames can be produced at a lower rate than if another material was used. In summer 2014, part of the research paper “Materials Selection of Steel Alloys for Use in Bicycle Frames” by Joshua M. Willard (11), The 4130 steel alloy meets all the requirements for a consumer bicycle frame. The minimum desired performance for this frame is for the frame to be lightweight, reasonably priced, and reliable. Meeting these requirements requires specific properties. These properties to meet the performance requirements include stiffness, strength, ductility, toughness, resistance to corrosion, and to have reasonable density. Achieving the necessary stiffness, corrosion resistance, and density is through the structure. The structure of 4130 steel gives the stiffness and corrosion since they are molecular properties. The density of steel is approximately the same regardless of how it is processed. Lastly, the method in which the 4130 steel is processed determines the last of the desired properties. Using an annealing processing technique allows the material to have strength and ductility which gives the material a great toughness. Other processing techniques would not allow the material to have a reasonable strength while retaining ductility. With this, the annealing technique was best suited for the bicycle frame. 6. ANALYSIS AND OPTIMIZATION 6.1 INTRODUCTION The objective of the following analysis is to determine the effect of nominal and worst case loading scenarios on the design. The specifications designate the frame must have a factor of safety, η > 2.0. This means the frame must be able to withstand a minimum rider weight of 180lbf while retaining the factor of safety mentioned above. Nominal loading conditions are described in the performance specifications from section 3. The following analyses will include a beam analysis while considering the factor of safety and material choice designated. Free body Diagrams will be provided for the novel frame design where critical locations will be shown and examined in further detail. Lastly, using finite element analysis, these critical locations as well as the entire frame will be undergo a rigorous static failure analysis while being compared to the results of the theoretical analysis. 6.2 FREE BODY DIAGRAMS

V30%

Mf

MB

RB

MA T70%

RA V70%

Figure 10. The main triangle is subjected to the loading conditions shown in the free body diagram. The

MBF

RBF

RAF RRW

MAF

Figure 11. The rear triangle is subjected to the loading conditions shown in the free body diagram.

6.3 CRITICAL LOCATIONS An atypical design with a removable rear triangle increases the amount of critical locations. Typically, in a bicycle frame the critical locations would be in the rear triangle where the chassis twists. In this case, the bolted connections will pose the largest threat to the design and those connection points will be examined in more detail.

Figure 12. The main triangle has the critical locations at the attachment points for the rear triangle.

Figure 13. The rear triangle’s attachment point is where the critical location should be examined.

6.4 SOLIDWORKS VERIFICATION 6.4.1 SOLIDWORKS SET UP

In SolidWorks, there is the ability to analyze structural members as beams. This is an important feature of SolidWorks. By simplifying the model, the geometry of a bicycle can be optimized through the beam analysis. The beam analysis will be used since the model and material were chosen using beam analysis. The setup for the boundary conditions are shown in Figure 15. The rider’s weight accounts for 30% of the load on the handlebar and 70% of the load on the bottom bracket. This scenario is for when the rider is standing and pedaling under heavy load and is considered an ideal worst case situation. 30% Rider Weight

Gravity

70% Rider Weight

Fixed Supports

Figure 14. A false set of handlebars, stem, and fork are created for the simulation. The loading and boundary conditions are shown for this case.

Figure 15. The bolted joint in SolidWorks.

6.4.2 SOLIDWORKS SIMULATION RESULTS

Figure 16. Using a false set of handlebars, fork and stem. The results are shown for the simulation under axial loading and bending.

Figure 17. The displacement results are shown for the simulation the loading conditions described in the set up.

Figure 18. The von Mises stress results are shown for the simulation the loading conditions described in the set up. The von Mises stress criterion does calculate the stress in the beams.

2.21 minimum in frame

Figure 19. Factor of Safety (FOS) results are shown for the simulation the loading conditions described in the set up. SolidWorks uses the von Mises stress criterion and compares to the material selected in this project, 4130 steel.

6.5 ANALYSIS CONCLUSION The analysis results through SolidWorks do not provide an ideal result. Ideally the results would include all parts of the assembly into one plot. Separated plots need to be cross examined to ensure no failure in the critical part locations. A cross examination using ANSYS or similar finite element analysis software would be the ideal situation. Otherwise, the model should be analyzed with the same method and remove beam analysis from the equation all together. Fortunately, SolidWorks does produce a plot for the von Mises criterion in an overall consideration of beams and trusses. The minimum factor of safety in the frame was found to be 2.21 which is above the minimum for this design. The analysis is concluded and the project moves forward to prototyping as a result. 7. PROTOTYPE CONSTRUCTION The construction of the prototype proved to go as planned. The Jiggernaut by Mixed Media Engineering lived up to the Kickstarter project’s deliverables. The Jiggernaut was easily assembled in 30 minutes to provide a backbone and jig to the bicycle construction process. The Jiggernaut retails for $349 USD and fits a wide variety of frame styles for the novice or experienced frame builder. Comparable systems start around $1500 USD and easily surpass $4000 USD for a frame jig.

Figure 20. The Jiggernaut comes as a ready to build kit. The image also shows the build kit offered by Mixed Media Engineering. Image from MixedMediaEng.com

The JD2 tube notcher provides an excellent piece of equipment for any frame builder. The Notchmaster gives a range of 0-50° and a tubing range of 0.75 to 3 inches. The tubing clamp is biaxial which allows the clamp to be move around tubing bends and other profiles. The best feature of the tube notcher is the ability to offset the notches. This feature shines in cases where tubing centerlines do not cross at the notch.

Figure 21. JD2 Tubing Notcher, “Notchmaster” with a Lenox 48mm Bi-Metal hole saw.

Figure 22. JD2 Tubing Notcher, “Notchmaster” with a Lenox 48mm Bi-Metal hole saw. Cutting the second part of the top tube after measuring a one degree cut.

Once the frame tubes were coped properly using the JD2 tubing notcher they were ready to be placed into the Jiggernaut. Unfortunately, the Jiggernaut creates some difficulty while setting the frame angles. Luckily with the new innovation developed in this project the frame was set up with ease. Only use two of the three 3D printed connections gave a semi rigid connection. The semi rigid connection ensured the angles and lengths were in spec before clamping the tubes to the Jiggernaut frame jig.

Figure 23. The 3D printed frame jigs. Printed at the University of Florida in the MAE Department’s Rapid Prototyping Lab located in MAE-B.

Figure 24. The tubing is shown as it is being assembled after coping. The tubing angles are held with the 3D printed jigs. The tube clamps are used to hold the tube in place of the universal tube holder.

Figure 25. Another image showing the tubing is shown as it is being assembled after coping.

Figure 26. The 3D printed jigs show the frame held in the exact position in which the tubes were intended.

Once the frame was locked into the Jiggernaut it was ready to be tack welded together. It is important to tack weld using a cross pattern within a plane going through the centerline. By using a cross pattern, the tubing will not be pulled to one side as the material expands and contracts. This is a common welding practice to ensure the bodies do not twist during the welding process. The figures below show the TIG weld through a shaded lens.

Figure 27. Looking through the welding hood showing the frame being tack welded together.

Figure 28. Flowing argon over the weld after tacking to prevent oxidation while cooling. 8. INTELLECTUAL PROPERTY The project developed novel design concepts as well as manufacturing methods. With this, the project owner claims the intellectual property of such features and is prepared to move forward in defense. 8.1 CLAIM FOR NOVEL FEATURES The following novel features will be claimed when filing for a patent. A double diamond bicycle frame, including: a) Removable rear triangle giving adjustability to frame geometry b) Modified geometry to allow multiple combinations of wheel sizes 8.2 CLAIM FOR NOVEL MANUFACTURING METHOD The following novel manufacturing method will be claimed when filing for a patent. Bicycle frame manufacturing aided through: a) 3D printed jigs to hold tubing in specified angles creating repeatability and precision 9. EVALUATION The prototype developed using the Shigley’s design process passes the analysis as shown above. Based on the results, the prototype meets the need which were proposed at the front end of the report. The bicycle frame achieves a factor of safety minimum of 2.21 when using 4130 as the material for the tubing. This design prototype with the novel design features and manufacturing methods proves to be successful. 9.1 Pros and Cons Pros  Will safely support a rider in a normal worst case loading situation  Novel design features o Increased handling without sacrificing speed o Comfortable riding platform that can be used for mountain, road, or beach biking  Unique manufacturing method o Reduced manufacturing cost o Increased repeatability o Increased precision

Cons  Analysis method needs refinement  Manufacturing method needs to include all aspects of frame design o Not only front triangle, but rear triangle and dropouts

10. LESSONS LEARNED Bicycle frame design is not as clear as many would expect. The geometry plays a larger role in handling than many would expect. Simply moving a tube such as the downtube slightly will change the results of the simulation significantly. Joints between beams should align on centerlines of other beams when considering the use of beams as the analysis method. Bolted joints are not used in the beam analysis which gives uncertainty to the results obtained this project. Justifying the results from the analysis will require the model to be examined outside of the beam analysis entirely. Using ANSYS comparatively will help in aiding in this justification, but for this prototype, the results are reasonable. The manufacturing methods established through prototyping of this bicycle frame were extremely helpful. Setting frame angles on the Jiggernaut can be difficult and tube copes are not exact. The front triangle was assembled quickly with the assistance of the 3D printed parts. The rear triangle was not assembled as it proved to be difficult without 3D printed parts. The complexity of a removable rear triangle would require 3D printed jigs for a repeatable and precise product. Moving forward, the design will be iterated once again while incorporating a more rigorous analysis method. 3D printed jigs will be used to for the front and rear triangles to ensure the precision and repeatability of the design. These results are to be expected when prototyping a design; iteration is a common result to provide an honest, repeatable, safe product.

11. APPENDIX

Ashby, Mike. "Material Selection Guidelines." Composites Manufacturing Materials, Product, and Process Engineering (2001): n. pag. Cambridge University. Granta, 3 Sept. 2009. Web. 10 Jan. 2016. Budynas, Richard G., J. Keith. Nisbett, and Joseph Edward. Shigley. Shigley's Mechanical Engineering Design. New York: McGraw-Hill, 2011. Print. Digital image. Mixed Media Engineering. 24 Apr. 2016. Web. 24 Apr. 2016. Felton, Vernon. "War of the Wheel Sizes." Bike Mag. N.p., 3 Mar. 2012. Web. 10 Jan. 2016. Willard, Joshua. EMA 3010 Summer 2014, “Materials Selection of Steel Alloys for Use in Bicycle Frames”