Individual Engineering Trade Study: Analysis of Frame Structure Feasibility using Aluminum, Study Guides, Projects, Research of Aerospace Engineering

Download Individual Engineering Trade Study: Analysis of Frame Structure Feasibility using Aluminum and more Study Guides, Projects, Research Aerospace Engineering in PDF only on Docsity! University of Notre Dame Department of Aerospace and Mechanical Engineering Date: October 12, 2006 To: AME 40463 Project Management From: Dan Turnure Subject: Individual Engineering Trade Study Purpose The purpose of this study was to determine the feasibility of the proposed frame structure for the Leg O’Maniacs’ concept design, based on the use of aluminum at a given cross sectional area. A structural analysis was performed using Matlab to determine the stresses present in the frame during the course of normal motion of the injured leg. Calculations for the worst-case buckling condition of the frame were performed as well, including consideration of stress concentrations due to the holes that will accommodate the wing nuts used in the height adjustment. The results of the study will be used to determine the materials to be purchased for the construction of the prototype. Sources of Information The equations and formulas used in the analysis for this trade study, along with the value for the modulus of elasticity of aluminum come from Fundamentals of Machine Elements by Hamrock, Schmid, and Jacobson1. The equations for static failure of elements were used to determine whether or not the support shafts will buckle or yield. A Matlab code was written to calculate the stresses present in the elements so that the maximums could be read from the graphs. The affect of stress concentrations at the holes in the shafts 1 Hamrock, Schmid, Jacobson, Fundamentals of Machine Elements McGraw-Hill. 2005 were taken into account by deriving the concentration factors from standard charts. Also, the maximum shear stress theory for static failure was used to calculate the safety factor for the part given the calculated stress and the yield strength. There were several important assumptions and simplifications made in the analysis. The most basic was the decision to treat the system as two dimensional. The system was only considered to move in the x-y plane (the plane of motion of a leg swinging forward), while motion in the third dimension was ignored. This was done to simplify the calculations, and can be justified because the range of motion in the third dimension will be very small compared the other two. Another simplifying assumption was that the strain in the supports will be greatest when the frame is oriented at θ=0°, which is approximated as being a purely axial stress state. This is the only case for which the simplified Hooke’s Law is valid. It was also assumed that the system would approximate a buckling condition for a column which has one end fixed to ground and the other end free. The system was simplified for calculation of the stress concentration factors as well. Half of the surface area of the tubing was approximated as a flat plane with a hold present so that the tables in the Hamrock book could be utilized. Design and State Variables In the study, the angle of orientation of the supports was considered a design variable although a minimum constraint of -10° and a maximum constraint of 30° were set. The The stress concentrations due to the screw holes in the shafts were determined according to the assumed geometry of the tubing, and based on a ¼” screw diameter. The concentration factor for the bending case was found to be 1.6, while for the axial loading it was 2.5. These factors were multiplied by the maximum stresses in the member, and this total was compared the yield strength according the MSST theory for static failure in order to determine the safety factor built in to the system. The above analysis was completed for the main support shafts, and also for the smaller supports that extend from the main shaft out to the ends of the foot piece of the device. Due to the smaller size of these supports, the maximum bending stress was lower and therefore of no concern. If the device fails it will fail on the large supports. Results The completed analysis yielded values for the maximum bending and axial stresses, maximum axial strain, critical buckling load, and safety factors for the main supports shaft, and the smaller supports on the foot. The results for the main support will be presented, while the inconsequential results for the smaller supports will be ignored. It was found that the maximum bending stress present in one leg of the frame would be 100 ksi, and the maximum axial stress for one side would be 1.2 ksi. These can be read from the graphs shown in Appendix B. The figures were the outputs of the Matlab code which was discussed earlier. The critical buckling load was found to be 300 lb for the chosen geometry and material properties, which is less than the 375 lbs constraint that was placed on the weight of the user. After the stress concentration factors were accounted for, the total stress in one support in the frame came to 163 ksi. This stress results in a safety factor of 0.24, which is less than one, meaning that the device would fail if it were subjected to these conditions. Based on Hooke’s Law, the strain in the support was calculated to be .012%. Even though the design seems to be inadequate to support the functional requirements placed on it, there are several reasons why the prototype will still be feasible for aluminum. First, none of the persons who will be testing the prototype weigh more than 250 lbs, much less than the 375 lbs weight constraint. Second, the calculations were performed considering on one piece of tubing. In reality, there will be overlap between a large diameter tube and a small diameter tube halfway up the frame. This will affectively halve the inner radius of the tubing, and subsequently raise the critical buckling load and decrease the maximum stresses. The chart below shows the effect of these factors on the state variables. σB (ksi) σA (psi) Buckling Load (lb) Original Size and Weight 100 1200 300 Reduced Weight, Original Size 70 840 Reduced Size, Original Weight 55 590 540 Reduced Weight, Reduced Size 36 390 540 Figure 1: Chart showing change in state variables for change in dimensions and operator weight The fourth set of conditions refers to a user weight of 250 lbs, an outer radius of 0.4375 in and an inner radius of 0.3 in. This most closely resembles the actual condition the frame will be in during testing of the prototype. Influence The results of this study affected the chosen material, and also the cross sectional area of the support shafts. Aluminum 6061, with a yield strength of approximately 40 ksi will be suitable for the construction of the prototype. Even though the safety factor is less than unity for the case of the main shafts, the proposed geometry and material are still being endorsed. This is because the calculations were made considering a user weight of 375 lbs, and this is far beyond the weight of any of the design engineers who will be testing the prototype. It seems that buckling will not become an issue for the proposed shaft size of ro=0.44 in and ri=0.37 in because the overlap in the area of the greatest stress (the mid point of the shaft) will effectively reduce the inner radius to 0.3 in, resulting in a buckling load of over 500 lbs. It is recommended that the smaller shafts be constructed of aluminum 6061 as well, and that their proposed orientations and geometries remain the same. They will not be susceptible to failure by buckling or to failure by yielding due to bending and axial stresses. The strain caused by the stresses will not be of any consequence.