Finite Element Analysis of a Sandwich Composite Bicycle Frame

Transcription

1 1 Finite Element Analysis of a Sandwich Composite Bicycle Frame Andrew L. Hastert, Benjamin F. Barger, and Justin T. Wood Abstract When designing human-powered transportation vehicles like bicycles, given the sole bipedal power source, efficiency and weight are of the upmost importance. While lightweight materials like carbon fiber and titanium are often employed in bicycle construction, the state of the art in optimization of these highly engineered materials is still in its infancy. Many of these vehicles are created using hollow tubular space frames, but we hypothesize that an ovular or box crosssection beam frame is a more appropriate profile and topography when designing a recumbent-style vehicle. The scope of our project encompasses the design, finite element analysis, optimization through analysis, and real-world prototypic verification of sandwich composites, particularly for use in a bicycle space frame. Our investigation begins with the creation of a parametric cross-section and subsequent volume set that idealizes our final frame topography. While the core of the sandwich composite will be made of an isotropic material (high density polyester foam), the outside composite layer is made up of several layers of uni-directional carbon fiber. We mesh the foam with solid brick 186 elements and the composite layer with solid-shell 191 elements for future parametric optimization of the section data thus ply orientation of the composite sub-layers. We will apply various loading conditions in bending, shear, torsion, and tension to qualify the beam in real-life loading situations. Finally, we will construct sandwich composite beams, apply similar loading conditions, and compare results. Index Terms Finite Element Method, Sandwich Composites, Ply Orientation, Design Optimization, FEA Verification E I. INTRODUCTION NERGY price, depletion of fossil fuels, and increased usage of motorized vehicles are presenting new political, socioeconomic, and environmental complications for Americans every day. Human powered vehicles offer a unique and viable option for countering and potentially reversing these effects. However, speed, efficiency and dependability are critical in the appeal of these vehicles as people will be powering the vehicle themselves. One of the more important aspects of vehicle design is a strong yet lightweight space frame as this unit will be experiencing the loads of the driver as well as torsion pedaling forces and turning effects. To develop a model of the frame we first must size the frame to accommodate an average driver. This will determine where their distributed load of the rider s weight will be, as well as the distance to the crank. Due to low ride height, low drag coefficient, and high rider output efficiency, we have determined that the frame will follow a recumbent style. A general frame shape was designed and the determined loading conditions include rider weight force and pedal torsion on the crank. While many recumbent bicycles are built using metals like aluminum and steel, our interests lie with performance, thus we re incorporating uni-directional carbon fiber and high density foam in a functional sandwich composite. We ve employed the Finite Element Analysis (FEA) to obtain simulated physical loading, deformation, and stress. An industry-standard FEA package, ANSYS, will allow us to create our uni-directional carbon fiber layups to reduce weight and increase efficiency. These cross-sections and individual ply orientation will then be optimized to incorporate our desired factor of safety in accordance with the stresses. A. Design Idea II. METHOD As materials become highly engineered the use of technology has increased, so has the use of new and unique materials. Lighter and stronger materials, such as carbon fiber, have been used for many applications to optimize designs. Bicycle frames have become lighter and faster while maintaining, or improving, their strength with the use of these composites. For our design criteria, we chose to create our frame using a sandwich composite. The use of this type of composite will allow us to create a lightweight frame while maintaining a great amount of strength. Sandwich composites consist of a core, usually foam or honeycomb wrapped with a composite like carbon fiber. The medium we are planning to use for the core is a high density polyester foam. This foam will improve the integrity of the structure since it can transfer the shear stress applied to it in multi-axial bending. Our high density insert will then be wrapped with single direction carbon fiber layers. This specific type of composite consists of strands of carbon fiber oriented in a single direction. When viewing a single piece of this material, the modulus of elasticity is very high in the oriented direction of the strands of carbon fiber, but extremely weak in the opposing directions. To overcome this obstacle, plies are oriented at different angles to compensate for stresses at different angles. We plan to test the different angles of ply orientation to discover which assembly will produce the highest amount of strength and least amount of displacement.

2 2 For our design, we are using six layers of carbon fiber under two scenarios. The first test frame will consist of oriented layers at 0, 90, -45, 45, 90, and 0 degrees. The second test frame will be oriented in a fashion of 0, 90, -30, 30, 90, and 0 degrees. The third test frame will be oriented in a fashion of 0, 30, -45, 45, -30, and 0 degrees. These orientation angles will compensate for the forces that are applied to the bicycle frame. measurements, we were able to fix spaces for the crank, seat, fork, and front wheel. Having set locations for these segments allowed us to create a frame that could be employed by a number of different cyclists. After we appropriated our measurements to create an extruded cross section, we then had a recumbent bicycle frame with actual dimensions that could accommodate a various number of different travelers. B. Volume Generation Although the prominent cross sectional model for bicycles have been tubular, mainly hollow; our design method aspired to include an ovular design. First, the high density foam core is dimensioned to be 51mm tall by 32mm wide with 9.5mm radius rounds. Adopting rounded contours instead of cornered edges was conceived and utilized due to the transverse effects it has on the applied stresses. Under an applied load, a frame with cornered edges would institute stress concentrations at the edges, lowering its ultimate strength and weakening the structure. Rounded perimeters help to disperse any applied load along the cross section eliminating any stress concentrations and stress raisers. This decision also incorporates the safety and comfort of the prospective rider. Organic, rounded edges will provide a higher level of assurance and amenity rather than an abrupt angle as seen in Fig. 1. Fig. 2. Final extruded volume. C. Mesh Generation The mesh for this sandwich composite scenario will call for two different types of elements because the foam is isotropic while the composite material is functionally orthotropic. The foam is meshed with brick 186 elements and the composite shell is meshed with solid-shell 190 elements with section data defining ply orientation for all six layers. This will allow for parametric optimization. In order to determine our mesh size, we had to account for the different properties of the various elements we employed. For the foam core we used 200 nodes on the initial extruded area as showin in blue in Fig. 3. Fig. 1 Initial cross-sectional area. The blue area represents the high density foam while the purple area represents the composite solid-shell. Once the shape of the cross section was ultimately determined, our foam nucleus was wrapped in six layers of the uni-directional carbon fiber. These ply orientations were selected due to their ease of construction, and each layer is to be oriented in a said fashion according to our design specifications. Using ANSYS, each element in the cross section was given an area. Actual measurements and dimensions were input into the program to simulate a real life scenario. This sample was then extruded to take the form of a recumbent bicycle frame as shown in Fig. 2. To fabricate a practical model, we used average bicycle rider dimensions and correlated them to the cycle s components. From these Fig 3. Tetrahedral elements representing the high density foam in blue and the composite shell elements with unit thickness in purple.

3 3 The initial area was swept along the extrusion path with 20 elements per line. Overall, this develops over 23,000 nodes just for the foam. The composite elements are one unit thick but correspond to outside nodes on the foam core. This process allows the structure to be refined anywhere with stress concentrations, like abrupt changes in geometry. The mesh was particularly refined near fillets in the frame as shown in Fig. 4. direction oriented in a negative direction simulating actual rider weight. Applied dynamic also occurs near the frontal of the frame where the crank is located. A moment of 800N is applied in opposing directions at this region to simulate a torque and a moment as shown in Fig. 5. These forces will mimic the stresses created when a rider is pedaling. Fig. 4. Foam elements swept along the extruded path with increased element count at unique geometries. D. Boundary Conditions In order to attain accurate stress analysis for any application, boundary conditions must be defined. This will ensure that the solution incorporates the boundary of the domain. In our circumstance, several boundary conditions are to be set. Our first constraint will occur near the foremost portion of the frame where the front fork is housed. At this location, we will constrain movement in all directions, setting the degrees of freedom in the X, Y, and Z direction to be zero. Creating this constraint will allow us to attain accurate results of the frame materials without the frame itself rotating. Another of our boundary conditions occurs near the center of the frame. Since legions of frames adhere to a countless number of design specifications, we decided to simplify our makeup. Many unique variations in frame construction occur at the rear wheel of the cycle. To generalize our layout while striving to obtain the best results, we came to the conclusion that directly behind the seat of the vehicle, the frame should end and the terminal be fixed. The extremity of the frame will have zero degrees of freedom in all directions. This will condition will mimic a number of different combinations of rear wheel frame connections. With this end fixed, the frame will act as if there is a rear wheel, without us having to complicate our frame design. Following the creation of our boundary conditions, we then applied external forces our composite frame. Forces applied from a typical rider would immediately include their weight. A 800N force was applied over the entire seating plate distance where the seat would be located. This application was exercised the vertical Y Fig. 5. Fully constrained sections in light blue and applied loads in red. The weight of the rider is equally distributed across the area on the right where the seat rail is fixed while there is a moment applied on the left corresponding to maximum pedaling resulting forces. E. Iterative Solver For our design, we are using six layers of carbon fiber with opposing ply orientations. The first test frame will consist of oriented layers at 0, 90, -45, 45, 90, and 0 degrees as shown in Fig. 6. The second test frame will be oriented in a fashion of 0, 90, -30, 30, 90, and 0 degrees as shown in Fig. 7. The third test frame will be oriented in a fashion of 0, 30, -45, 45, -30, and 0 degrees as shown in Fig. 8. These orientation angles will compensate for the opposing forces that are applied to the bicycle frame and the standard angles make for easy manufacturing. A simulation will be conducted for each test frame and we will seek a low stress and deflection. Fig. 6 The ply orientation layup section data.

4 4 Our model also allowed us to solve for nodal stress and strain results. Fig. 10 shows the nodal Von Mises equivalent stress across the frame body. There are apparent stress concentrations near the head tube constraint, along the seating area, as well as near the torque crank moment arm. A closeup in Fig. 11 shows the nodes with maximum stress near the crank moment arm. Fig. 7 The ply orientation layup section data. Fig. 10 Nodal Von Mises stress results are plotted on the volume. Stress concentrations are visible at the head tube constraints as well as the applied moment for pedaling. Fig. 8 The ply orientation layup section data. III. RESULTS As shown in Fig. 9, the deformed shape and nodal results were calculated using our FEA model in ANSYS. Fig. 11 This view shows the highest stress concentration. This corresponds with the applied moment for pedaling. Table I lists the ply orientations for the three test frames. Through FEA we obtained nodal stress and strain results given our loading conditions and various stiffness matrices by way of the changing ply orientations. Table II lists maximum Von Mises equivalent stress for the three test frames. Table III lists the maximum deflection values for the various test frames in the x-axis, y-axis, z-axis, as well as equivalent total deflection. Fig. 9 The deformed results with extreme scaling effect. The major deflection in the y-axis corresponds with rider weight loading.

5 5 TABLE I PLY ORIENTATIONS FOR VARIOUS FRAME ITERATIONS These beams were tested to failure as shown in Fig. 13. The FEA model of the simple beam with similar constraints and loading showed very similar nodal displacement and deformed shape as shown in Fig. 14. The applied force and resulting displacement was measured by the testing apparatus as shown in Fig 15. The tested force vs. displacement results for the physical test and the FEA simulation are compared in Table IV. TABLE II MAXIMUM VON MISES STRESS VALUES FOR VARIOUS FRAME ITERATIONS TABLE III MAXIMUM DEFLECTION VALUES FOR VARIOUS FRAME ITERATIONS Fig. 13. Resulting failed prototype. The primary mode of failure is clearly caused by delamination and subsequent structural crushing. IV. FINITE ELEMENT ANALYSIS VERIFICATION While a dense mesh and detailed volumetric model can assure promising results, it s important to verify these results with prototype testing [1]. Several sandwich composite beams were constructed to mimic a sample of the bicycle frames cross-section. The beams were tested in three-point bending as seen in Fig. 12. Fig. 14 Corresponding FEA results of mimicked frame piece test. Note the similar mode of deformation and stress concentrations that initiate the delamination. Fig. 12. Three point bending test of composite frame prototype. These tests allow for verification of the overall frame FEA stress and deflection results.

6 6 REFERENCES [1] D. Onipede, I. Avdeev and G. Sterlacci, Finite Element Modeling of Smart Composite Plates Reinforced by NiTi Shape Memory Alloy Wires in Proceedings of SPIE, vol.4348, pp Fig. 15 Force / Displacement Curve for composite test specimen. TABLE IV FORCE AND DEFLECTION FOR TEST FRAME VS FEA RESULTS V. CONCLUSIONS Through FEA of our sandwich composite model, we were able to obtain stress and deflection results for the applied loads and make conclusions based on ply orientations. While the lowest maximum deflection values were observed on test frame 1 as shown in Table III, the lowest maximum stress was observed on test frame 2. Though generally a higher deflection tends to result in a higher stress, given the virtually unpredictable reaction of composite materials, one can assume this higher stress is due to a stress concentration at a corner or change in geometry. On a simple beam with a central loading, we observed higher stress concentrations at the fillets of the cross-section. Finally, we were able to verify our results using a simple beam section and three-point bending. Given the high variability in composite manufacturing, testing equipment, and calculation error, it is very impressive for this team to see such similar results in our verification trials. We are confident in our results. In future work we look to expand on our optimization by focusing on cross-sectional dimensions as well as local optimization of ply orientations. ACKNOWLEDGMENT The authors would like to acknowledge the support provided by the Department of Mechanical Engineering, the University of Wisconsin-Milwaukee, ANSYS Inc., the ANSYS Institute of Industrial Innovation at University of Wisconsin-Milwaukee, Dr. Rani El-Hajjar, Dr. Ilya V. Avdeev, Dr. Ben Church, and Mir Zunaid Shams.