Weight Reduction Case Study of a Premium Road Bicycle Crank Arm Set by Implementing Beralcast® 310 By: Sean Sullivan Chris Huskamp, IBC Advanced Alloys Date: March 4, 2013 Overview The crank set is the device responsible for converting the bicycle rider’s human power to rotational mechanical power. The crank set travels in a clockwise motion, propelling the bicycle forward. Figure 1 shows the first 180º of a complete crank rotation along with the corresponding torque curve. 180º was chosen because this represents the “power stroke”, the remaining portion of the crank rotation is the “dead stroke.” The dead stroke refers to the fact that no torque is generated by the crank, assuming pedal straps are not used. The two cranks which make up the complete crank set are 180º out of phase which allows for a continuous transfer of torque. As Figure 1 illustrates, the torque increases to a maximum at 90º and begins decreasing until once again reaching zero at 180º. The torque curve assumes that the rider applies a constant pedal force. In reality, the applied force drops off as the rider’s leg extends and the torque curve does not possess perfect symmetry about the 90º point. Therefore, the first 90º are of specific interest when examining the loading conditions. There are three main loading conditions which the crank undergoes: axial torque (torque transmitted to the bicycle’s wheel), side torque (bending the crank arm out, in, or twisting), and combined torque (combination of side and axial torque). The maximums for these conditions are: 0º for side torque, 45º for combined torque, and 90º for axial torque. Figures 2 to 4 show the free body diagrams and FEA stress distribution. Side bending on the crank arm without any torque being transferred to the bicycle wheel Figure 2: Maximum side torque at 0º. Side bending Twisting Axial bending Figure 3: Maximum combined torque at 45º. Twisting Axial bending Figure 4: Maximum Axial Torque at 90º Shimano Dura-Ace Crank Set The particular crank set examined in this study is the Shimano Dura-Ace crank set pictured in Figure 5. B A Figure 5-Shimano Dura-Ace Crank Set The individual crank arms are hollow forgings composed of 7050-T651 aluminum. The “sprocket arm” (Figure 5-A) is composed of a one piece arm and central hub. A sprocket ring bolts to the five central arms of the hub and is responsible for transferring torque to the bicycle’s rear wheel. The sprocket arm has an axle which passes through a bearing assembly on the bicycle’s frame. The “straight arm” (Figure 5-B) mounts to the axle by means of a splined hole which is tightly pinched on the axle end by tightening Project Definition This study explores the Shimano Dura-Ace crank set in the following manner: 1. Produce 3D CAD models of both crank arms. 2. Perform FE analysis on the crank arms based on the standard 7050-T651 aluminum; this establishes a baseline strength and weight. 3. Substitute the 7050-T651 Al with extruded Beralcast 310 alloy and observe the improvements in displacement and weight over the baseline figures. 4. Show the potential weight savings by creating alternative versions of the straight arm and compare them to the measured weight of the actual part. The following will first describe the CAD and FEA models created for the project and then outline the results obtained from the FE analysis. CAD Models Figure 6 shows photo renderings of the 3D CAD models. The models were created based on measurements of actual pieces. As mentioned previously, the two crank arms are hollow. However, because the internal geometry is not known, the CAD models are solid. The sprocket arm was modeled without the sprocket ring to simplify the FE analysis. This has no substantial effect on the final results. A B Figure 6: CAD models of the Shimano Dura-Ace crank arms FEA Models The FEA model of the straight arm is shown in Figure 7. 1.75in 500 lb. Remote Load Fixed Geometry Figure 7-Straight Arm FEA Model A fixed geometry constraint is applied to the inner surface of the axle mounting hole. The 500lb load is remotely applied to the inner surface of the pedal mounting hole. This load is located 1.75 in from the centerline of the crank arm (at the pedal mounting surface) and is concentric to the mounting hole; this simulates the use of a pedal. 500lb is beyond a reasonable design load and was chosen because it would produce noticeable displacements for comparison between the 7050-T651 Al and 310 Beralcast. A solid mesh was used. Since the study concerns a general comparison of materials, a course mesh was used to speed the simulation process. By changing the angle of the remote load, three different FEA models were produced to simulate the crank arm at the 0°, 45°, and 90° positions. The sprocket arm FEA models were similar to the straight arm versions, with only the application of the fixed constraint being different. Figure 8 shows that for the 0° position the fixed geometry was applied to the axle mounting hole, while for the 45° and 90° cases the fixed constraints were applied to the sprocket ring mounting holes. Fixed at axle mounting hole for 0° Fixed at sprocket ring mounting holes for 45° and 90° Figure 8-Sprocket Arm FEA Model Results Material Substitution: The first part of the study concerns the direct substitution of 7050-T651 Al with Beralcast 310. As mentioned previously, the crank arms are hollow forgings but the internal geometry is not known and was therefore not modeled. Figure 9 shows the deformed stress plot of the straight crank arm. Graph 1 outlines the final results of the substitution of Beralcast 310. The focus is on the relative differences between the two materials, therefore all of the results are shown as a percent difference. Figure 10 shows the deformed stress plot of the sprocket crank arm along with Graph 2 which displays the corresponding results. 0° 45° 90° Figure 9: Deformed stress plot of the straight crank arm. Straight Crank Arm Results 60.00% 42.86% 40.00% Weight Reduction = 26.64% 20.00% 7.54% 9.09% 0.00% 0° 45° 90° -20.00% Max Displacement Max Stress -40.00% -60.00% -67.54% -67.91% -67.06% -80.00% Graph 1: Straight crank arm results 0° 45° 90° Figure 10: Deformed stress plot of the sprocket crank arm. Sprocket Crank Arm Results 60.00% 50.26% Weight Reduction = 26.64% 35.22% 40.00% 24.81% 20.00% 0.00% 0° 45° 90° -20.00% Max Displacement Max Stress -40.00% -60.00% -67.21% -68.00% -67.80% -80.00% Graph 2: Sprocket crank arm results The deformed plots of Figure 9 and 10 show the characteristic side bending at 0°, combined side bending-axial bending-twist at 45°, and the axial bending-twist at 90°. Substituting Beralcast 310 produces a weight reduction of 26.64%, this is a direct result of 310’s lower density. There is a corresponding increase in stress ranging from 8 to 50%, the large variance is due to stress concentrations and FEA model accuracies. The increase in stress is expected given the Beralcast 310’s superior stiffness compared to 7050-T651 Al. This difference is most apparent in the 67 to 68% reduction in maximum displacement. Alternative Designs: For the second part of the study, the model of the standard Dura-Ace straight crank arm was modified in five unique ways to show the potential weight savings. The model weight is compared to the part’s actual weight of 0.3929lb (this is excluding all auxiliary hardware) which accounts for the internal cavity for the hollow forging process used by the Manufacturer. The maximum displacements are compared to the FEA 7050-T651 Al displacements: 0° = 0.069in, 45° = 0.0561in, 90° = 0.0422. An overview of the five unique models is outlined in Figure 11. Figure 11: Alternative design options overview. Below is a brief description of each separate crank arm, as well as the FEA results. Profile Reduction: 0° 45° 90° Max Stress (kpsi) 31.5 30.4 29.8 Max Displacement (in) 0.0404 0.0385 0.0362 % Difference Displacement -41.45% -31.37% -14.22% Weight (lb) 0.34894 % Difference Weight -11.19% The side and bottom profiles were reduced to produce a thinner overall shape. The weight is reduced by nearly 11% compared to the actual part. Pocket: Max Stress (kpsi) 30.9 29.9 28.8 Max Displacement (in) 0.0422 0.0341 0.0151 % Difference Displacement -38.84% -39.22% -64.22% Weight (lb) 0.33874 % Difference Weight -13.78% A pocket was created on the back side of the standard crank arm, leaving a shear plane on the forward face of the part. The weight is reduced by nearly 14% compared to the actual part with a 38 to 64% increase in stiffness. I-Beam: 0° 45° 90° Max Stress (kpsi) 32.5 31.7 30.6 Max Displacement (in) 0.0474 0.0463 0.04 % Difference Displacement -31.30% -17.47% -5.21% Weight (lb) 0.34959 % Difference Weight -11.02% Pockets were created along the sides on both the front and back to create a sort of I-beam cross section. The center and side supports provide side bending strength while the pocket floors provide axial bending strength. The weight reduction is approximately 0.04lb or 11%. Through Cut: 0° 45° 90° Max Stress (kpsi) 31.1 30.5 29.8 Max Displacement (in) 0.0401 0.0347 0.0246 % Difference Displacement -41.88% -38.15% -41.71% Weight (lb) 0.35388 % Difference Weight -9.93% In this case, contoured through cuts are made along the centerline of the crank arm.