Homework 3 - F23 (1) (1)

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University of Michigan *

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250

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Mechanical Engineering

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Dec 6, 2023

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10

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ME250 | F23 | University of Michigan HW3: Lectures 9, 10, 11, and 12 (67 pts) Engineering Drawings & Mfg Plans, Dimensions and Tolerances, Electric Motors, Machine Elements Due Friday, October 20th by 11:59 pm on Canvas This is an individual assignment, and your solution must be entirely prepared by you. Homework assignments must be completed on your own (unless they are team assignments), however you are encouraged to discuss the problems with your classmates. Upload a PDF of your solution to the Assignments tab on Canvas. Problem 1: Dynamic Analysis and Motors (20 points) Your ME250 team wants to use the planetary gearbox motor, available in your kit, to lift a very small load weighing 1.28oz. You have designed a lifting arm which weighs 0.488oz. Using SolidWorks, you determine that the center of gravity of the arm is 1.5 inches from the shaft. When lifting, the load will be 3 inches from the shaft. Note, the spec for the planetary gearbox motor states the parameters at 3V, but our battery pack will output 6V, so assume the motor will be operated at 6 V. Note that due to the large number of gears in mesh, the efficiency of the gearbox can be quite low: use γ = 0.3 in this case. Perform your calculations where the motor is operating in the region of its highest efficiency. (Choosing a correct gearbox-motor configuration for a cube lifting arm is one of the crucial tasks in RMP design. Therefore, an example procedure for the same called “Lifter example” is uploaded on canvas for your reference. You can find it in Files > Project Resources > First Principle Analysis Examples > Lifter Example.pdf .) A. Following the Lifter example and selecting from only the gear ratios available in the planetary gearbox motor kit [note: specs for the motor can be found by following the link on the kit materials spreadsheet], find the smallest gear ratio that will lift the load with a safety factor of two. Do your calculation assuming the worst-case orientation of the arm. (10 pts) B. Continuing to use the Lifter example, calculate the speed of the arm in units of RPM, when lifting the load using this gear ratio. (5 pts) C. If you use the highest available gear ratio to lift the load instead of the gear ratio that you selected in part a, what will be the speed of the arm in units of RPM? (5 pts)
Problem 2: Power Screws (10 pts) A standard 3/8-24 UNF threaded rod is used as a power screw to raise and lower a load. It has a lead of 0.0417 inches, a pitch diameter of 0.3479 inches, and a coefficient of friction of 0.3. A. When the power screw is used to raise the load, the input torque is 2.4 inch-pounds. What is the weight of the load that is being raised? (4 pts) B. How much torque does it take to lower this same load using the power screw? (4 pts) C. A lubricant is applied to the threads. How would this affect your answers to part B? (2 pts)
Problem 3: Stackup Analysis and GD&T (13 pts) When designing your RMP, you have a ¼-20 bolt that clamps three plates down to your aluminum base plate. The base plate (green) has a threaded hole, where the three clamp plates (blue, orange, pink) have clearance holes. You want to make sure you maintain enough thread engagement into the aluminum base plate. Upon researching stackup analysis, you learn that you can calculate expected thread engagement using Worst Case Scenario (WCS) analysis. The WCS is as expected, evaluating the thread engagement if all of your dimensions are at the maximum (or minimum!) of their tolerance band. Measurement Dimension (inch) Tolerance (inch) Bolt Length, L b 1.25 +/- 0.100 Plate a 1 thickness 0.2 +/- 0.050 Plate a 2 thickness 0.3 +/- 0.050 Plate a 3 thickness 0.1 +/- 0.010 Plate a 4 thickness 0.5 +/- 0.010 Thread Engagement, L e ? ? A. What is the nominal thread engagement? Does this meet the minimum thread engagement requirement? (2 pts) B. Calculate the WCS stackup for thread engagement. Does this meet the minimum thread engagement requirement? (2 pts)
C. Respond to and explain your answer to the following: a. Do you think the worst-case scenario (WCS) method used above is a good strategy for calculating tolerance stack ups? Explain. (1 pt) b. Is the WCS likely to occur? Explain. (1 pt) D. A different part in the same assembly has these two feature control frames. Translate each tolerance description into a feature control frame by filling in the provided blank feature control frames. (7 pts) a. Position of 0.005 at MMC to datum A, datum B at MMC, and datum C at LMC. b. Profile of a surface of 0.01 to datum E at MMC and datum C.
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