Milwaukee School of Engineering Mechanical Engineering Department ME460 Finite Element Analysis. Design of Bicycle Wrench Using Finite Element Methods

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1 Milwaukee School of Engineering Mechanical Engineering Department ME460 Finite Element Analysis Design of Bicycle Wrench Using Finite Element Methods Submitted by: Max Kubicki Submitted to: Dr. Sebastijanovic Submitted on: 30 October 2014

2 Abstract With growing concerns of pollution and a trending desire to start taking care of the environment, the popularity of biking has increased greatly over the last couple years. With this growing popularity comes an increased need in durable, yet affordable tools. This project set out to design a hex cone wrench which is a staple in any respectable bike mechanic s toolbox. The dimensional specifications and load requirements came from the sponsor of the project, Bob s Bike Barn, where the prices are so low you ll have a cow. The design consisted of recommending a material and selecting a thickness based on finite element analysi. The material choices were narrowed down to 6150 Alloy Steel, 8650 Alloy Steel, AL 6061-T6 and AL 5052-H34. The analysis showed that the thickness required for both of the aluminum allows given the load was much too large for the intended application of this tool. The final selection was chosen to be the AISI 6150 with a 3.5 mm thickness. This decision was made based on the acceptable material properties of the steel, the lower relative cost and the broad use of it in hand tool design.

3 Problem Investigation The purpose of this experiment was to design a bicycle wrench with the dimensions shown in Figure 1. The parameters that were to be designed were the thickness of the tool and the material of the tool, which was limited to either an aluminum or steel alloy. The thickness was to be determined based on the maximum distortion energy theory and a factor of safety of 1.5 against yielding. Figure 1: Bicycle Wrench Dimensions

4 Methods For this design finite element analysis was performed using ANSYS. The material selection was narrowed down to four choices that are commonly used for hand tools: 6150 Alloy Steel, 8650 Alloy Steel, AL 6061-T6 and AL 5052-H34. Set up of the FEA model consisted of placing a fixed support along the inside of the leftmost hexagonal cavity. The distributed load was replaced with an equivalent load of 400 N along the appropriate edge as shown in Figure 2. Figure 2: Support and Load Setup in ANSYS In order to determine which element to use for the mesh a convergence comparison was performed between triangular and quadrilateral elements. As it is a representative structural response, the maximum displacement was recorded for comparison. The results for the triangular and quadrilateral elements are shown in Table 1 and Table 2, respectively. The plot of these results is shown in Figure 3. It can be seen that the quadrilateral elements converged faster than the triangular and allows the system to be solved with fewer nodes. As the time required to solve the simulation did not change drastically with a decrease in size, 0.7 mm quadrilateral elements were selected for the mesh. It is also important to note that both of the convergence curves approaches the asymptote from below, thus it can be determined that this solution always underestimates the deformation. The mesh of the wrench is shown in Figure 3: Element Convergence PlotFigure 4.

5 Table 1: Triangular Element Convergence Data Triangular Element Size (mm) Number of Nodes Max Deformation (mm) Percent Change % % % % % % % % % Table 2: Quadrilateral Element Convergence Data Element Size (mm) Number of Nodes Quadrilateral Max Deformation (mm) Percent Change % % % % % % % %

6 Max deformation (mm) Convergence Study Triangular Quadrilateral Number of Nodes Figure 3: Element Convergence Plot Figure 4: Quadrilateral Mesh with Elements With the mesh method chosen and the proper fixtures and loads set up the simulation was ready to run. The analysis was done on each of the four materials chosen for this design and the equivalent stress and deformation were examined. The yield stress of the material, the maximum allowable stress with the given factor of safety, the final thickness and corresponding maximum stress and deformation are shown for each material in Table 3. Plots of the max principal stress, max equivalent stress and max deformation are shown for the AISI 6150 wrench.

7 Table 3: FEA Results for Different Design Materials with a Factor of Safety of 1.5 Material Yield Stress (Mpa) Max Allowable Stress (Mpa) Thickness (mm) Max Stress (Mpa) Max Deformation (mm) AL 5052-H AL 6061 T AISI AISI Figure 5: Equivalent (Von Mises) Stress with 261 MPa maximum for AISI 6150 bike wrench Figure 6: Maximum Principal Stress with 264 MPa maximum for AISI 6150 bike wrench

8 Figure 7: Total Deformation with mm maximum for AISI 6150 bike wrench From the results it can be seen that using either of the aluminum materials would require a thickness over 5 mm. Though not explicitly stated in the design specifications, the form of this wrench suggests it is most likely a cone wrench which is designed to reach axles that are hard to reach and are typically 2mm thick 1. Thus the design was narrowed down to AISI 6150 and AISI 8650 steel. The mechanical properties considered in this study were very similar between the two, however the 6150 steel allowed a slightly smaller thickness to the tool, albeit with one and a half times the displacement. Research showed 2 that the bicycle component this tool would be used for, a hub cone locking nut, on average only needs to be tightened down to 150 in-lbs based on common components. This corresponds to approximately a 50 N/cm distributed load as opposed to the specified 100 N/cm load. Given the over specified requirements and the factor of safety the displacement of the AISI 6150 steel will not be a concern. In addition the 6150 steel, or chrome vanadium steel, has a lower price than the 8650 steel and is a tried-andtrue material choice for hand tools 3. 1 Brown, Sheldon ( ). "Tool Tips: Cone Wrenches". Bicycling. Retrieved "Torque Specifications and Concepts." Web log post. Park Tool. N.p., 08 June Web. 29 Oct < 3 "Protanium High Torque Steel." Bondhus. N.p., n.d. Web. 29 Oct <