Homework 3 - F23 (1) (1)
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University of Michigan *
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Course
250
Subject
Mechanical Engineering
Date
Dec 6, 2023
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Pages
10
Uploaded by CaptainPartridgePerson774
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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