Computer Aided Design

Final Project

By:

Michael Alva

Charly Bertran

Pavel Bobreshov

William Kalbacker

May 25th, 2018

Introduction and Problem Statement

Cycling is a popular sport and pastime practiced internationally by millions of people. People ride bikes for competition, commuting, and exercise. Within the sport are several widely known disciplines such as mountain bike riding, road cycling, and track. Due to the nature and speed of cycling, safety is a paramount issue, and should be ever-present on the minds of those who ride. Mountain biking, with its rough terrain and technical courses, is of particular concern to bike and equipment manufacturers. Every part and component of a bicycle must be designed to withstand punishing and repetitive stresses at a minimum weight. The weight to strength ratio is the biggest challenge for engineers in the design of bike frames and components. If a critical component fails at the wrong time, the rider’s life may be put at risk. This important nature of crucial bicycle parts makes them an interesting and meaningful area of study and evaluation.

In addition to being subject to certain safety standards, handlebars are one of the most important components when it comes to the comfort and handling of a bicycle. Experienced riders have strong preferences about the stiffness and size of their bars. For those who are competitive in bicycle racing, a high stiffness to weight ratio is the ultimate goal. This allows for maximum power transfer to the wheels while keeping the bike lightweight. Therefore the ability to finely control handlebar stiffness is an important design consideration. For this project we analyze the stress, displacement, and design of a set of titanium mountain bike handlebars under static loading. We assume a scenario in which an existing handlebar requires a redesign per the request of a cyclist who desires a stiffer response to riding conditions. The handlebar in question is an integrated bar and stem combination, meaning that a single component connects the rider’s hands to the steering tube. Further, since bicycle handlebars are required by law to meet a minimum safety standard under the consumer product safety commission1, we take the initiative to ensure the final design meets these standards. Specific safety standards vary by region and industry, however for this study we will follow the procedure from the German Institute for Standardization, which sets detailed prescriptive standards for stress testing bicycle handlebars. The purpose of the analysis will be to accurately model the handlebars in question and to verify that they meet the safety standards set forth in the German Institute for Standardization document. Verification will be accomplished through Finite Element Methods using SolidWorks Simulation.

Experimental data will also be captured for comparison to the FEM simulation in order to validate the SolidWorks model. Strain gauges will be mounted to the handlebars to measure the strain associated with a perpendicular force applied to the bar ends. These strain values can then be used to derive both the stress and displacement during loading. Using the results of the FEM simulation and our experimental data, we should be able to satisfactorily determine if the model is valid. The validated model will then be subjected to the industry safety standards above. Finally, if required, any design modifications will be considered to improve the performance, ergonomics, or production costs of the part.

1 https://www.ecfr.gov/cgi-bin/text-

idx?SID=9aecc8b1f5aa1aee327f8e78f16cf513&mc=true&node=se16.2.1512_16&rgn=div8

Experimental Procedure

For this study, acquiring experimental data is an important part of establishing a valid SolidWorks model. The empirical data was recorded in a laboratory setting using a series of strain gauges and a displacement indicator on the bars loaded with hanging weights. To prepare for the experiment, strain gauges needed to be affixed to the main axis of the handlebars. This was accomplished by securely gluing the gauges to the bars. We selected a section of the handlebars close to the stem that we thought would give reliable strain values. When installing strain gauges, keeping the gauge perfectly aligned with the strain axis is critically important for accurate measurements. The alignment with the main handlebar longitudinal axis was eyeballed to the best of our ability. Lead wires were then fluxed and soldered to the strain gauges to allow for data capture. Figure 1 shows the results of this process:

Figure 1

The lead wires would be attached to a Tektronix oscilloscope which would interpret and record the signal from the gauges. To securely fix the handlebars to the work service, the bars were clamped to a custom mount that was screwed into the tabletop. This prevented bars from moving on their own and ensured that the displacement was a result of material bending. To measure displacement, a mechanical indicator was magnetically clamped to the work surface and calibrated to measure downward deflection resulting from the load. The indicator setup is shown in the Figure 2 below:

Figure 2

Finally, a C-clamp was loaded with 20lbs of free weights and hung from a selected location on the handlebars. This location was chosen based on the prescriptive requirements in the safety standard. The full experimental setup is shown in Figure 3:

Figure 3

The oscilloscope captured the strain data for a duration of around 30 seconds. For a control and baseline, the strain of the unloaded bar was also measured. The oscilloscope results could then be exported and analyzed in Matlab to determine the final strain experienced by the bars. The results of the strain and displacement are displayed below:

ε - X (με) d - Y (mm)

EXPERIMENTAL DATA 350 0.68

Table 1

Solid Modeling With the experiment complete, we had the benchmark data needed before starting the process of modeling the part in SolidWorks. The handlebars presented a challenge to model due to the curvature and smooth welds of the components. First, the overall shape was sketched, measurements of key tube diameters were taken with a caliper, and tube angles were determined by importing sketch pictures into SolidWorks.

Figure 4

Figure 5

Importing pictures formed the basis of sketches that were used to extrude and loft specific parts.

Figure 6

Figure 7

Reference planes marked the various point where the widths of angles and diameters changed.

Figure 8

Using the reference planes as landmarks, the tube lengths could be extruded since their diameter was measured with a caliper.

Figure 9

The remaining portions of the handlebars, where the tube diameter change, were modeled using the loft feature. The loft was bridged over a section of known length, connecting the thinner diameter outer tube section with the thicker center section that connects to the stem.

Figure 10

The final solid body was the stem that connects the clam to the handlebars. This could be extruded from a sketch of the diameter of the stem on the surface of the bars through to the clamp.

Figure 11

The tube bodies of the handlebars remained solid at this point. Using an extrude cut and an lofted cut, the center of each tube was bored to create a tube of constant thickness, which was given to us by the manufacturer.

Figure 12

One difficulty faced in the modeling process was accurately adding the fillets at the intersection point between the stem and the handlebars. We measured the radius of the fillet on the handlebars using a drill-bit with known diameter:

Figure 13

Despite knowing the radius, SolidWorks did not apply the fillet properly across both bodies. We realized the difficulty lied in how the two components were mated. When the stem tube was extruded to meet the handlebars,

the two bodies were not automatically bonded to create a single part. This prevented SolidWorks from applying the fillet. This problem was solved once we combined both bodies into a single part.

We chose to simplify the model by excluding the bolt holes in the stem clamp. Although we initially modeled this feature, we decided that leaving in the holes would introduce unnecessarily complex stress distributions. Thus the bolt holes were removed and replaced with a smooth cylindrical stem clamp that would provide a consistent point of fixture.

We knew before starting the modeling process that the handlebars had a large length-to-thickness ratio, which dictates the best type of meshing and surface geometry to use in SolidWorks. This drove our decision to try three different model iterations in an attempt to find the most efficient geometry and mesh combination for our finite element analysis. Theoretically the shell mesh method is the most efficient when working with thin parts. To assess this, we made the decision to test three different combinations of body geometries. We broke the part into three main components: the handlebars, stem body, and stem clamp. For the first of the three models, all of these components would be made using traditional solid body construction in SolidWorks; that is they would have a three dimensional shape with a finite tube thickness. This concept is illustrated using a cross-section image below:

Figure 14

The second iteration kept the stem clamp as a solid model, but changed both the stem body and handlebar to a surface feature geometry with an infinitely thin, two dimensional tube shape. This feature allows SolidWorks to mesh and solve thin-walled bodies in a much more computationally efficient manner by avoiding three dimensional elements in the thin bodies.

Figure 15

The final iteration transformed all three components into surface bodies so that the entire model had infinitely thin tube walls.

Figure 16

We would test both a shell and solid mesh for each model (except the third iteration which can only have shell mesh elements). It became clear during early simulations that the shell mesh models were easier to work with and calculated solutions faster. Towards the end of the mesh testing, we decided to use the solid body with a solid mesh to the surface body composed of shell mesh elements to see how the results would compare. During the initial test simulations, we found a stress concentration started appearing on the interior side of the handlebar tubing. Although we created fillets at the contact point between the stem and handlebars, the interior intersection between the parts had not been filleted. Thus a sharp corner at this area became problematic. We corrected this by performing an extrude cut using the interior cross section of the stem body as the reference plane. The cut was extruded forward through the intersection point between the bars and stem to remove this material. Although the real handlebars have this connecting material at the intersection, removing it from the model eliminated a stress concentration.

Figure 17

Finite Element Method

The first goal of the finite element study was to validate the model. Without a valid model, the results of any comparison to safety standards are meaningless. Therefore the first step is to compare the results of the experimental data to the results of a simulation set up with identical loading and boundary conditions. Selecting the boundary conditions for the simulation was straightforward and would be natural to anyone who is familiar with the feel of bicycle handlebars. There is a single point of fixture on the handlebars that secure the bars to the rest of the bicycle. This is the cylindrical stem clamp mentioned above. We simplified this geometry a bit in our model to avoid any unintended complications. The only other boundary condition is the 25lb load applied perpendicular to the main axis of the handlebars. This load is 230mm laterally offset from the centerline of the stem. This location was selected in accordance with the safety standards and is approximately where the rider would likely place their hands. The finite element analysis was repeated for both a solid and shell mesh.

Figure 18

The handlebars we selected are made from a specific titanium alloy not found in the default material library within SolidWorks. The material, named Ti3AL2.5V, is a titanium alloy containing aluminum and vanadium in a 3% and 2.5% ratio respectively. These two elements add needed stiffness to the titanium. The material properties of this alloy are listed in the table below and were created as a custom material in the SolidWorks library for these studies:

Property Value Units

Elastic Modulus 100 GPa

Poisson's Ratio 0.3

Shear Modulus 44 GPa

Mass Density 4480 kg/m^3

Tensile Strength 620 MPa

Compr Strength N/A MPa

Yield Strength 500 MPa

Table 2

In order to ensure consistent results in all future studies with this model, we needed to determine an appropriate mesh size. An appropriate mesh size is defined as the maximum element size below which stress and displacement results do not significantly vary (e.g., mesh independent). This is important because it allows us to have confidence in the results of the study without needlessly expending unnecessary time and computational resources. Determining the appropriate mesh size is accomplished through a convergence study in which the mesh is continually refined until a maximum von Mises stress has reached a stable value. We use von MIses stress as the failure criteria in this study because titanium is a ductile material. Once this is complete, we select the largest mesh element size that resulted in our stabilized stress value and use this size for future studies. The convergence study was performed for both the solid mesh and shell mesh described above. The results of those studies are outlined below and show the value of the converged strain versus the degrees of freedom.

Shell Mesh:

Max von

Mises Stress Displacement X-Strain

Max Element

Size (mm)

Min Element

Size (mm) Elements Nodes Total DOF

Solver

Time

Mesh 1 170 3.738 2.7 7 2.3 8k 4k 49k 2s

Mesh 2 175 3.785 2.702 4 1.33 22k 11k 124k 4s

Mesh 3 181 3.801 2.706 2.5 0.83 56k 38k 325k 11s

Mesh 4 182 3.804 2.704 1.5 0.5 172k 85k 981k 23s

Mesh 5 179 3.804 2.714 0.8 0.26 598k 299k 3,400k 1m

Mesh 6 178 3.8 2.7 0.6 0.2 983k 491k 5,618k 2m

Mesh 7 177 3.804 2.772 0.4 0.13 2,415k 1,207k 13,725k 9m

Table 3

Figure 19

Solid Mesh:

Max von

Mises Stress Displacement X-Strain

Max Element

Size (mm)

Min Element

Size (mm) Elements Nodes

Total DOF

Solver Time

(s)

Mesh 1 152.9 2.825 0.5708 6 1.2 29k 14k 86k 4

Mesh 2 165.181 2.904 0.5909 2.5 0.5 112k 56k 330k 5

Mesh 3 161.595 2.903 0.5913 3 0.6 129k 66k 382k 11

Mesh 4 168.851 2.914 0.5943 2 0.4 265k 140k 780k 29

Mesh 5 174.7 2.918 0.5952 1.2 0.24 918k 525k 1,446k 2m Table 4

Figure 20

We also found an appropriate mesh size from the convergence study (max element size 2mm, minimum element size 0.4mm). A sample mesh with a refinement around the intersection between the bars and stem is displayed below.

Figure 21

We can use the converged strains and displacements of the simulations to compare to our collected experimental data to conclude if the models are valid. We focused on using the strain and displacement of the simulation to compare to the experimental data. The convergence results we saw for the strain in both the solid and shell models are contrasted with the experimental results in the table below:

ε - X (με) d - Y (mm)

SHELL MESH 277 0.87

SOLID MESH 334 0.60

EXPERIMENT 350 0.68

Table 5

These values show considerable agreement. The strain and displacement values for the shell and solid mesh differ, likely due to the way that SolidWorks calculates the strain matrix for shell and three dimensional mesh elements. The solid mesh shows precision with experimental result, with a difference of less than 5%. The shell mesh displays less agreement at a 20% difference from the experiment. However this does not signify that the shell mesh is invalid. Systematic error may be responsible for the discrepancy between the experimental and simulated results, as there are several variables involved with properly placing and soldering strain gauges. The gauges are highly sensitive so even a slight misalignment with the intended axis would lead to error. With this in mind, we felt the strain for both the solid and shell mesh was within our range of comfort to consider the model validated. The results of the model validation left us with comfort in the validity of the model as well as knowledge about the mesh sizing to take into the second phase of the FEM analysis. The second phase of the FEM study is to investigate how the model will respond to the loading set forth in the safety standards. An underlying assumption made during all of these studies is that the material is responding to the loading within its linear elastic region. This assumption theoretically simplifies the analysis as we can take the results from the previous convergence study and linearly scale up the loading. This increased loading should lead to linearly increased stress with equal validity to the initial loading. Applying this to our model, we should find that the stress state of the handlebars displays a maximum value of 1400 MPa at the weld point between the bars and the stem. Not taking this assumption for granted however, we conducted additional simulations for the 1000N load under the same boundary conditions to establish if the handlebars adequately meet the safety standards. The standards stipulate that the bars should not display any plastic deformation, cracks, or fractures, and should be displaced a maximum of 15mm. For thoroughness we ran multiple study iterations for both the shell and solid mesh models at various element sizes. The results of the 1000N load for the shell mesh are shown below:

Study Max von

Mises Stress (MPa)

Max Displacement at Bar End (mm)

Max Element size

(mm)

Min Element size (mm)

Total Nodes

Total elements

Total DOF

Time (s)

Mesh 2 1564.8 34.25 2 0.67 85k 42k 475k 16

Mesh 1 1639 34.21 3 1 94k 47k 552k 16

Mesh 3 1617 34.22 1.5 0.5 178k 89k 1,018k 31

Mesh 4 1640.8 34.23 1 0.33 354k 177k 1,986k 61

Mesh 5 1647.8 34.21 0.7 0.23 782k 390k 4,474k 2:15

Mesh 6 1637.968 34.23 0.5 0.166 1,396k 698k 7,841k 5:28

Mesh 7 1660.991 34.21 0.4 0.13 2,492k 1,245k 14,192k 10:46

Table 6

Figure 22

Figure 23

The results for the solid mesh:

Study Max Stress (Von Mises)

MPa

Max Displacement at Bar End (mm)

Max Element size

(mm)

Min Element

size (mm)

Local Element Size

(mm)

Total Nodes

Total elements

Total DOF

Time (s)

Mesh 1 1432 26.08 3 1 127k 64k 375k 12

Mesh 2 1461.7 26.1 3 0.6 131k 67k 389k 14

Mesh 4 1512 20.2 2 0.66 265k 139k 777k 28

Mesh 3 1649.1 26.2 3 0.6 0.5 318k 159k 949k 35

Mesh 5 1641.7 26.23 2 0.4 0.5 450k 236k 1,333k 47

Mesh 6 1534.9 20.2 1.5 0.5 575k 311k 1,702 58

Mesh 7 1608.9 26.25 1 0.33 1,599k 970k 4,730 2:46

Mesh 8 1641.2 26.25 0.7 0.23 2,795k 4,433k 13,192k 2:15

Table 7

Figure 24

Figure 25

Both the shell mesh and the solid mesh show agreement in the max von Mises stress with convergence at around 1650 MPa. However both studies showed disagreement in the maximum handlebar displacement with shell and solid mesh converging to roughly 34 mm and 26 mm respectively. As was mentioned regarding the differing strain results between solid and shell meshing strategies, the notable displacement difference seen here could be a result of how SolidWorks calculates displacements based on the differing element geometries. One possible explanation for our disagreement is that shell elements have only a single element through its thickness, hence, the final displacement may be calculated differently from that of a solid mesh. Despite these differences, we felt confident in these results based on our previous validation of the model and decided to proceed with both meshing strategies.

Results of FEM

Since the titanium alloy used in this study is a ductile material, the maximum von Mises stress failure criteria was used to determine the results of the loading. Accordingly, we find that the current handlebar design exceeds the 500 MPa material yield stress, meaning that the part will fail under this load. Further, we find that the maximum displacement at the location of loading also exceeded industry standards, as shown in Figure # below. Therefore, two design requirements were defined for the redesign of this handlebar: (a) decrease maximum stress displacement in the handlebar to comply with industry standards and (b) stiffen the handlebar to provide less deflection per the client's request.

Max Stress (MPa) Max. Disp. at load application (mm)

Design Requirements 500 15

Shell Model 1660.9 18.64

Solid Model 1641.2 17.26 Table 8

Implications for Design

In many cases, the structural performance of a component can be improved by changing significant geometries, such adding additional bodies or redesigning the shape of existing bodies. Alternatively, performance can be improved by changing the material used. In our case, neither of these options was feasible since the particular shape of the handle bar was desirable to the client. Furthermore, changing the material would make the experimental validation of our model obsolete, thus we would be less confident with our FEA results. Therefore we decided to change the thickness of the handlebar, allowing us to maintain the material and its shape. Changing only the thickness also allowed us to simplify the iterative design process by making use of SolidWorks Shell Definition feature, shown in Fig. #. Doing so required the use of our shell model, which we’ve deemed sufficient for our purpose. Therefore, we decided to omit solid meshing from our final design phase. In Shell Definition, we modified the thicknesses of the handlebar, stem, and welds, through several iterations and ran simulations until arriving to a modified design that met both design requirements. Fig. # shows all iteration of our redesign. A simulation was run for each iteration, changing the thickness at various points to see how the resulting stress and deflection changed. The goal was to specify a thickness where the max stress on the bars would be under the required 500 MPa while deflecting a maximum of no more than 15mm. Green cells indicate iterations that achieve those goals while red cells indicates the contrary. Note that Mod.7 was our final satisfactory design with a maximum Y-displacement of 7.35 mm and a σ-max in-x of 496.52 MPa.

Figure 26

MOD.1 MOD.2 MOD.3 MOD.4 MOD.5 MOD.6 MOD.7 MOD.8

Stem thick. (mm) 1.55 1.55 2 2 2.5 2.5 2.5 2.5

Fillet thick. (mm) 3 5 5 7 7 5 6 6

H-bar. thick. (mm) 1.2 1.55 1.55 1.55 1.55 1.55 1.55 1.2

dmax Y-axis (mm) 12+ 10.08 8.7 7.95 7.1 7.65 7.35 8.66

σmax X-axis (MPa) >1000 948.69 629.56 640.41 457.77 525.63 496.52 559.87 Table 9

Conclusion In this project, we assumed the task of redesigning an integrated handlebar-stem for a client that desired greater stiffness in its performance. Further, we took initiative to determine if the current design satisfied Industry Safety standards and if they didn't, to ensured that the redesigned handlebar did so. In our study we took advantage of the linear behavior of SolidWorks solver by performing experiments on the actual handlebar components and using the gathered strain and displacement values to validate our model for future simulations. We found that our two meshing strategies, solid and shell meshing, yielded slightly different but acceptable results in comparison to our experimental measurements. Convergence studies for both maximum stress and maximum displacement yielding results that indicated that our current handlebar design did not meet industry standards. An iterative design process was then underwent using SolidWorks shell mesh definition feature to determine an optimize design. In our final design, the maximum stress was decreased by roughly 69%. Furthermore our final maximum displacement reached 7.35 mm (~59% decrease), which meets both industry standards and is deemed satisfactory for the client based on its significant decrease from the original design.