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MAE 150 HW 3

1

winter 2013

Professor Frank E. Talke MAE 150 Homework 3 Due: Jan 31, 2013
Problem #1: Read pages 53-68 and 88-108 in the course reader. Problem 2
In a sliding contact between a brush and a rotor in an electrical motor, the resonance frequency of the brush fibres is important in order to minimize wear. The manufacturer is interested in a statistical analysis of the brushfibres. The resonance frequency for a single brush fibre with circular cross section as a function of the manufacturing and material parameters is given by:

f res

0.56 ED 2  2 L 16 

 = Density
L = length of fibre D = diameter of fibre E = Young‟s modulus
Nom. Value Deviation 8960 ± 10 2 E-6 ±0.01 E-6 3 E-4 ±0.03 E-4 128.8 E+9 0

Variable ρ D L E

Unit kg/m³ m m Pa

a) Calculatethe nominal value of the resonance frequency of a brush fibre, using the numbers in the table. Also, calculate the worst case error and the statistical error. Hand in:  Nominal value, worst case error and statistical error.  Check whether the statistical error is smaller than the worst case error.  Attach your analytical calculations (no credit will be given for just the numbers). b) Perform aMonte Carlo Analysis of the resonance frequency using 10,000 points. In the normal distribution, the given tolerances correspond to 3 . Create a graph with 4 subplots showing the resonance frequency distribution (subplot 1), the distribution of the diameter (subplot 2), the distribution of the length (subplot 3) and

University of California San Diego

MAE 150 - Computer Aided Design andAnalysis

MAE 150 HW 3

2

winter 2013

the distribution of the density (subplot 4). Use 50 bins to create the histograms. Include labels and titles on all subplots. Do this for 2 cases: 1. Assume a uniform distribution for all independent variables. 2. Assume a normal distribution for all independent variables. Hand in:  A graph with 4 subplots for the uniform case and a graph with 4subplots for the normal case.  Attach your Matlab m-file. c) If all independent variables have the same distribution, will the dependent variable also have the same distribution? Hand in:  Discussion

Problem #3: Cam Design
Design a zero off-set plate cam with harmonic rise and 3-4-5 polynomial fall with the following data: Cam specifications: - Harmonic rise (0° θ 120° ) from 0 mm to 20 mm -Dwell (120° θ 180°) - 3-4-5 polynomial fall (180° θ 270°) back to 0 mm - Dwell (270° θ 360°) The cam is driven by a constant speed motor rotating counter-clockwise at 600 rpm The radius of the base circle = 35 mm The radius of the roller follower = 10 mm

a) Using MATLAB, hand in a plot of the displacement profile, the velocity profile and the acceleration profile of the follower as a function ofthe angle θ for every 1°. Use the subplot command. b) Hand in a plot of the pressure angle for every 1°. Show a table with the pressure angle for every 30 degrees, that is for θ=0°, 30°, 60°, …, 360°. Discuss your results. Note: If a cam profile does not start at   0 °, you must shift the profile for calculating and plotting the results compared to the case that the profile starts at   0 °.Hand in a hard copy of the MATLAB file you wrote to solve this problem!

University of California San Diego

MAE 150 - Computer Aided Design and Analysis

MAE 150 HW 3

3

winter 2013

Problem #4: SolidWorks
Complete the SolidWorks tutorial lessons 5 and 6 that are posted on the class website. All part files will be posted on TED in case you didn‟t finish the first 4 tutorials Submit ascreen shot as follows for each lesson. Remember to include the SolidWorks window with a time/date stamp. Please print the screen shots in color for this homework. Lesson 5: 2 Screen shots: 1) Fully assembled w/color 2) Exploded view w/color Lesson 6: Screen Shots 1) Displacement figure showing exagerated deformed shape. Additionally, print out the maximum deflection as seen in the scale bar on...