Project 2: Torque-Arm Modeling, Simulation and Optimization

Date: April 3 1

Report Format

• Formal report, including title, summary, introduction, approach, results, discussion, appendix (programs), and/or references. • Report must be self-explanatory; define all terms that you use and explain clearly what you did.

• Submit report (Word or PDF file, Max 10 pages) and CAE file of optimum design by 12:00 PM in Sakai • Penalty or extra credit 4/19 4/20 4/21 4/22 4/23 4/24 4/25 4/26 4/27 +6 +5 +4 +3 +2 +1 0 -5 -10 • There will be additional extra credit of up to 10% for easy-to understand (and grade) reports that would be given to at least 20% of the reports.

2

Design of Torque Arm

• Used for transmitting load from a shaft to a wheel • Goal: design the lightest structure with stress constraints • Material properties – E = 206.8 GPa, Poisson’s ratio = 0.29, thickness = 1.0cm

, density = 7850 kg/m 3 – Use cm for the length unit and make other units consistent (need to convert all values in cm units).

3

Preliminary Analysis

• At the initial design (x 1 = 12, x 2 = 1, x 3 = 27), estimate the vertical displacement at the center of the right hole and maximum von Mises stress using Mechanics of Materials.

• Explain your assumptions and approaches in the report.

• Later, compare your hand calculation with FE results and discuss the difference between them • Remember that the purpose of preliminary analysis is to estimate the locations of max stress and displacement as well as their levels.

4

Abaqus Modeling

• First task is to sketch the section geometry with fully constrained (curves will change to green color) – This is necessary because you will change design and regenerate models several times • How to apply BCs and loads?

– MPC constraint (control point = reference point, slave nodes = nodes on the circumference of the hole, MPC type = Beam). 5

Effect of Element Types

• Compare results using different elements (CST, LST, Q4 and Q8).

• Turn off “reduced integration” option in Element Type command • Use plane stress element type • Compare the maximum displacement at the load application point and maximum von Mises stress (provide a table) • Try to use approximately the same number of nodes for all element types.

6

Convergence Study

• FEA at the initial design (x 1 = 12, x 2 = 1, x 3 = 27) with Q4 • Carry out convergence study on the vertical displacement at the center of right shaft • Determine reasonable mesh size (you are limited to 1,000 nodes!). Use this mesh size in the parameter study later.

• Use Richardson’s extrapolation to estimate the accurate vertical displacement at the load application point Displacement No. of Elements 7

Parameter Study

• Designer wants minimize subject to  max x i L  x i  240MPa  x i U • We simplify the design problem by one function with one variable (penalty parameter a = 100) f(d)  mass(d)    initial _ mass  a  max (d) 240  1  a  0 if a a if a  0 0 • The relationship between d and design variables is • Change in d     x 1 x x 2 3  12d       6  changes in x  d  [0,1] changes in FE geometry 8

Parameter Study

• Perform a parameter study by changing d between 0 and 1 with 10 increments • Plot a graph d versus f(d) and find an optimum design d opt that minimizes f(d) (graphically or approximated by polynomials) • Report optimum design in terms of mass, stress and (x1, x2, x3) f(d) d opt d 9