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- 1. Analysis of a Recumbent, Three Wheeled Tricycle Frame Michael Hamman, William Steppe Abstract-The recumbent trike was designed for an upcoming tricycle competition in May of 2016. A finite element analysis was performed on the frame to ensure the safe operation under competition loading constraints. After the initial model was analyzed using Von Mises Stress and Total Displacement methods, it was reiterated twice to lower the stress and increase the Factor of Safety. A CFD analysis was performed on a model fairing to determine an approximate drag force at the maximum riding velocity. The drag force was found to be negligible and was omitted from the analysis loading configuration. A mesh independent study was performed on the final design to ensure accurate results. I. Introduction he American Society of Mechanical Engineers is competing in the Human Powered Vehicle Competition in May, 2016, and must build a recumbent tricycle. This paper involves a static analysis of tricycle frame for supporting the tricycle design. Figure 1 presents a CREO 3.0 [1] model of the competition design. The frame will be custom built to support an 81.6 Kg person pedaling with a force of 1000 N [1]. The forces from the mass of the rider equated to 800 N, with a 1000 N force applied in the negative x-direction and an 800 N force applied in the negative y- direction. Figure 2provides a model with the constraints and forces. Figure 1: Frame model Figure 2: Loading and Constraints on Frame The tubing will be welded together at all angles for ease of connection and the weight savings it will offer compared to brackets or nuts and bolts. The frame will be designed using a factor of safety of 1.5, since it is only being used in a certain scenario, and the goal is to make the bike as light as possible while still being structurally sound. II. Methodology The trike model was designed with CREO 3.0. This software was used because there will have to be many changes to the geometry in order to optimize the frame, and CREO makes it relatively easy to apply those changes. ANSYS 14.5 Workbench [3] was used to perform a stationary Finite Element Analysis on the model. The Shear Strain Energy theory was used as the design failure criteria so Von Mises Stress and T
- 2. Total Displacement distributions were analyzed through the simulation process. The geometry was iteratively modified based on the results attained in CREO. Star- CCM+ [4] was used once to perform a CFD analysis on the fairing, Figure 3, which will fully enclose the bike and rider reducing drag force effects. Figure 3: Fairing Shell Model III. Initial Simplification The model from Figure 1 was simplified on the basis that certain objects are not required for the frame analysis. Figure 4provides the simplified model that was imported to ANSYS. Figure 4: Initial Simplification of Frame The rear wheel was removed. The rear wheel was analyzed as a frictionless support because it is mounted on the frame as a bearing instead of a static object. The front wheels and the suspension were removed and analyzed as a vertical constraint on the bolt holes where the suspension components would mount to the frame. This is because the wheels will not be able to change their vertical displacement, but they can change their horizontal displacement if the force is strong enough. IV. Initial Analysis and Results The initial design was modeled with square tubing having cross-sectional dimensions of 0.0381 m for height and width, and a wall thickness of 0.003175 m. The material chosen for the frame tubing 6061-T6 Aluminum because of its success in commercial bike frames thus far. The mass for the frame will equate to 2.4 Kg using this material for all of the beams. The static analysis was performed on the model to obtain the initial stress and displacement results. Figure 5 and Figure 6 provide the Von Mises stress and total displacement results, respectively. Figure 5: Initial Von Mises Stress Analysis Figure 6: Initial Total Displacement Analysis
- 3. The Von Mises stress analysis resulted in a maximum stress of 3.81 MPa. This stress would result in failure according to Von Mises failure criterion since 6061-T6 Aluminum has a yield stress of nearly 2.16 MPa. The maximum displacement that occurred was 0.0115 m at the pedal location, which, if under continuous fatigue could lead to failure if the maximum stress was not reached first. V. CFD Analysis and Results A CFD analysis was performed using STARCCM+ computational software to determine the influence of the air drag on the structural frame members [2]. STARCCM+ is a finite volume modeling software. A non-structured block mesh was used with a boundary laying scheme for the near wall regions. Figure 7 shows the mesh domain for the fairing CFD analysis along the fairing’s symmetry line. The fairing was treated as a wind tunnel flow with 1m spacing from the tunnel walls to the fairing top and sides. Standard air conditions where used for defining the air fluid properties. The Reynolds number defined by the fairing height is given in Table 1 is clearly in the turbulence flow regime. The turbulence was modeled using the steady state Realizable k- ε Reynolds Averaged Naiver-Stokes turbulence model. The model used a two- layer y+ wall treatment. Since the Mach number was nearly .08 the flow was highly incompressible and an uncoupled solver configuration was used to improve the computational speed. Figure 7: Fairing mesh and dimensions The simulation converged to a nearly 20N for several mesh refinement configurations. A drag coefficient was defined using the largest normal fairing cross-sectional area and is given in Table 1. The drag force was considered to have adequately converged since the drag coefficients predictions of same order of magnitude and nearly have the Reynolds number are reported for a CFD study of an Ahmed body [5]. This included several numerical schemes for turbulence treatment and reported an experimental baseline coefficient. Table 1: CFD flow condition and results summary. Re (-) Drag Force (N) Drag Coefficient (-) Elements 1.3E6 20 .0404 2.5E6 Figure 8 presents a velocity distribution along the symmetry plane. The flow profiles shown correspond with typical blunt body flows. Since the predicted drag force of 20N corresponding to maximum trike speed of 64.37kph is minimal compared to pedaling and rider loads it was considered negligible in the FEA. Figure 8: Velocity profile of fairing along symmetry plane.
- 4. VI. Second Simplification In attempting to achieve a higher accuracy in the meshes, the computer started to fail at completing the analysis. To remedy this, symmetry was introduced to the model, and the roll cage was removed, which is describe in Figure 9. Figure 9: Second Simplification Model Figure 10: Second Simplification Loading and Constraints Symmetry, Figure 10, was able to be applied because the frame is symmetric about the vertical plane that is normal to the direction of motion. This reduced the computational effort. The roll cage was able to be removed because there was no displacement and minimal stress applied to it, so the need to analyze the material there was unnecessary. VII. Second Analysis and Results The first step taken to decrease the stresses on the bike frame was to change the material, which was also the easiest. The material chosen was Alclad 2014-T6. The new material only has 0.1 g/cc higher density than 6061-T6 Aluminum, which lead to a new mass of 2.49 Kg. It also has a higher yield stress, at 414 MPa, compared to 6061-T1 at 110 MPa. The second step taken to reduce the stresses on the frame was to add fillets at some of the critical locations. The final step taken was to increase the height of the tube cross-section to 0.04445 m. This would assist in decreases the stresses since they are not applied horizontally on the tube. The static analysis was run on the new model; Figure 11provides the corresponding Von Mises stress and Figure 12provides the corresponding Total Displacement: Figure 11: Second Von Mises Stress Analysis Figure 12: Second Total Displacement Analysis The new Von Mises stress analysis provided a maximum stress of 2.6878 MPa, which provides a factor of safety of 1.540. Although this is slightly larger than the initial design goal, a third analysis was performed with an updated model in an attempt to minimize the maximum Von
- 5. Mises stresses, which will provide an increased factor of safety. VIII. Final Analysis and Results The only step taken to decrease the stresses on the bike frame after the second analysis was to increase the size of the fillets on the previous model and add a few more to some the high stress locations. Figure 13 and Figure 14 provide the corresponding Von Mises stress results and total displacement results, respectively. Figure 13: Final Von Mises Stress Analysis Figure 14: Final Total Displacement Analysis The final Von Mises stress analysis recorded a maximum stress of 2.678 MPa. This provided a factor of safety of 1.549. This meant, unless the material was changed, the wall thickness was increased, or the height of the beam was increased again, there was not much room for improvement on the design. IX. Mesh Independent Study A series of static structural simulations were performed with decreasing element size for eliminating the influence of element size on the accuracy of the simulation. Figure 15 presents the results of the mesh independence study. Both maximum Von Mises Stress and Total Deformation were monitored for convergence. The deformation converges quickly while the Von Mises stress converges at nearly half a million elements. Figure 15: Mesh Independence Study X. Natural Frequency Analysis Following the mesh convergence study a modal analysis was performed using the .002m mesh size from the convergence study. The modal study resulted in an approximation of the first 6 modal frequencies and the respective shapes. Figures Figure 16 through Figure 21. Figure 16: Modal shape at resonance frequency of 65.759Hz
- 6. Figure 16 major deformation occurring in the vicinity of the main frame member. Figure 17: Modal shape at resonance frequency of 92.756Hz Figure 17 shows a single high deformation near the axel mounts. Figure 18: Modal shape at resonance frequency of 100.82Hz Figure 18 show two dominate loading locations one near the rear axial mount and a second near the lower seat mount. Figure 19: Modal shape at a 215.89Hz resonance frequency Figure 19 gives a single dominate deformation near the pedal bearing mount. Figure 20: Modal shape at a 334.32Hz resonance frequency Figure 20 shows high deformation due to buckling near the rear axel mount. Figure 21: Modal shape at a 558Hz resonance frequency Figure 21shows twisting and buckling of the frame member near the rear axel mount. XI. Conclusions The frame for a recumbent tricycle must be able to support many large forces and remain rigid. The frame being analyzed was modeled in CREO 3.0 and analyzed in ANSYS Workbench. The analysis used the Von Mises Stress and total displacement criterion to measure the factor of safety and displacement from loading, respectively. A CFD analysis was applied to the fairing which produced drag forces of only 20 N at a maximum riding velocity of 64.37 Kph. Because the drag forces were small compared to the rider mass and pedaling force, they were able to be ignored. The
- 7. initial material was 6061-T6 aluminum because of its known success in commercially designed tricycles and low density, which resulted in a bike frame that only weighed 2.39 kg. After the initial analysis however the mechanical properties, specifically the yield strength of 2.16 MPa, were unacceptable. The first modification to decrease the maximum Von Mises stress was to change the material that had a higher yield strength, with a similar density in order to keep the mass similar. The new material chosen was Alclad2014-T6 Aluminum, which has a yield strength of 414 MPa and a provided a new mass of 2.48 Kg. The beam height was also increased to 0.044 m in order to increase the strength of the beam in the main directions that the forces were applied, without bulking it up too much. The final results provided a factor of safety of 1.55, which was almost exact to the desired factor of safety. These results end in a frame that has a low weight, high strength, and optimal performance. A modal analysis was performed determining the modal shapes corresponding six approximated resonance frequency. Though not in the scope of this study these modal result could be used in conjunction with dynamic loading to evaluate the fatigue life and design against harmonic loading. XII. Works Cited [1 ] PTC, "PTC CREO," [Online]. Available: http://www.ptc.com/product/creo/ne w. [Accessed December 2015]. [2 ] J. Stokes, Marshall Space Flight Center, 1976. [3 ] ANSYS INC, "ANSYS.com," ANSYS INC, 2015 . [Online]. Available: http://www.ansys.com/. [Accessed NA]. [4 ] CD-adapco, "cd-adapco.com," 2014. [Online]. Available: http://www.cd- adapco.com/. [Accessed 31 11 2015]. [5 ] A. M. Y. Liu, "Numerical modeling of airflow over the Ahmed body," in Eleventh annual conference of the CFD Society of Canada, 2003.

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