Finite Element Analysis ENG4025/5294 Project November 2022 Structural stress analysis of a bearing bracket Full details of the project submission and the submission procedure are provided on Moodle The relative weighting of each question is indicated in square brackets Ensure that you use consistent units and that you state the units used in the plots and calculations Bearing brackets are widely used in machinery to connect rotating parts, such as shafts, wheels, idler gears, etc., to stationary parts – an example of a ball bearing bracket is shown in Figure 1. A simplified two-dimensional (2D) schematic of a bearing bracket with dimensions is shown in Figure 2. The bracket is rigidly fixed to the base and a load of P = [-150, 100]T kN is applied. Figure 1: Bearing brackets Figure 2: Schematic of a bracket subjected to loading (dimensions in metres) The bracket is made of aluminium with a modulus of elasticity (Young’s modulus) of E = 70 GPa and a Poisson’s ratio of n = 0.33. The bracket’s thickness is 0.1 m. 2 Tips: 1- In sketch of the 2D part, use the Save Sketch As… tool in the toolbox. Once in the sketch of the new 3D part, use Add Sketch to add the saved sketch 2- For the 3D model, use Menu/Tools/Datum to create a point midway between the two centre points of the inner cylinder and use this point to locate the position of RP. To ensure correct position of the 3 nodes, partition to create two cells. Sketch a further partition on the new face, with two lines with endpoints at the desired positions 3- Use Tools/Partition/Face/Sketch to partition the mesh around holes. Use your existing 2D model of the bracket, and standard 6-noded modified quadratic plane stress triangle (CPS6M) elements to perform the following calculations: 1- Plot, in a single graph, the relationship between the von Mises stress at points A, B and C (see Figure 2), and the number of elements for different levels of mesh refinement corresponding to global seed sizes of 0.028, 0.014, and 0.007. Would further mesh refinement be required for results that are sufficiently accurate for engineering purposes – when justifying your answer, you might need to perform additional simulations. [10] 2- To investigate the computational expense associated with increasing the number of element as you refine the mesh, create a graph of the number of elements (x-axis) versus the TOTAL CPU TIME (TCT) (y-axis). Briefly explain the trend displayed in the graph. TCT is the CPU time required to solve the problem. It can be obtained from the job monitor after completing the analysis of each refinement case. Note: you should run this comparison on the same machine under simil
ar conditions. [10] 3- Plot the contours of the von Mises stress and the displacement magnitude distributions over the deformed bracket geometry for the various refinement levels investigated in Q1. Comment on the variation in the plots as the mesh gets finer. Note: images should be produced using the print command in Abaqus and not by using a screenshot, as the latter will produce poor quality images. You are advised to hide the mesh from the model to obtain better quality images. Ensure the legend is legible. [15] 3 The 2D plane stress model was an efficient way to begin the engineering design process. Now create a three-dimensional (3D) model as shown in Figure 3 and undertake a static stress analysis using standard, 3D stress 10-noded quadratic tetrahedron elements (C3D10). 4- As in Q1, repeat the analysis using the different level of mesh refinement and create a single graph of the relationship between the number of elements and the maximum von Mises stress at points A, B and C. In addition, compare the results of the 2D and 3D models and comment on the differences between the solutions. [15] 5- The bracket will now be fixed to the stationary component using bolts. In order to choose a suitable bolt size, calculate the optimum hole radius when (a) only a vertical load of 100 kN is applied, (b) only a horizontal load of -150kN is applied. Consider a bolt design tensile strength of 48 MPa and a design shear strength of 39 MPa. [15] 6- Create the two holes for the bolts in your model. Change the fixed BC indicated in Figure 2 to be located under the heads of the bolts as shown in Figure 4. The radius of the bolt head circle is 1.8 times the radius of the hole calculated in the previous question (use the worst-case loading scenario). Undertake a static stress analysis to calculate the maximum von Mises stress when a load of P = [-150, 100]T kN is applied. Present your results as contours plots of the von Mises stress and the magnitude of the displacement distribution over the deformed geometry. Compare your results to those obtained previously when the bracket was fully-fixed to the base – comment on any differences. [20] 7- Based on the results obtained from the stress analysis, how can the bracket be improved so as to both maintain engineering integrity and to minimise weight Provide a brief description of the rationale behind your solution. [15] 4 Figure 3: 3D model of the bracket Figure 4: Placement of holes for bolts