325-midterm-2014W with MC SA answers
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University of British Columbia *
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Course
325
Subject
Mechanical Engineering
Date
Oct 30, 2023
Type
Pages
12
Uploaded by ColonelHyenaMaster902
Page 1
MECH 325 – Midterm Book 1
Tuesday, October 21, 2014
Name: _____________________________________
Student Number: _____________________________
Circle your section
Section 101:
T1A (11:00am tutorial)
T1B (3:30pm tutorial)
Section 102:
T1C (2:00pm tutorial)
T1D (5:00pm tutorial)
Signature: ___________________________________
Part 1 MC Mark _____ / 14
Part 1 SA Mark _____ / 16
Part 2 LA Mark _____ / 30
Total _____ / 60
Instructions
There are two parts to this exam with different instructions for each.
Please read carefully.
Part 1 – Closed-Book (30 marks)
Multiple choice (14 marks: 1 marks per question)
. Complete all 14 questions by marking your
response
in pencil in the computer score card
.
Write your name and student number on the computer
card and mark your student number in the “ID Field”.
Short answer (16 marks: 2 or 4 marks per question).
Complete all 6 questions by marking your
response in this exam booklet.
After you have completed Part 1, hand in your booklet and Scantron scorecard and you will receive a
handout for Part 2 and a separate exam booklet for your answers.
You may not return to Part 1 after you
hand it in.
Part 2 – Open-Book (30 marks)
Long answer (30 marks)
: Complete all parts to the questions for Part 2 by marking your responses in the
separate exam booklet.
This portion of the exam is open-book and open-notes.
Only non-programmable calculators may be used
(or programmable calculators
with purged memories)
.
Page 2
Part
1
A
: Multiple Choice
Answer all 14 questions.
Each is worth 1 mark.
Choose the single best response – a given question may
have more than one choice that is correct but marks will only be given for the
best
answer.
1.
Which of the following types of gears is appropriate for high-efficiency, smooth (low-noise)
transmission of motion between parallel shafts with minimal axial loading on either shaft?
a)
Bevel
b)
Spur
c)
Worm
d)
Herringbone
e)
Helical
2.
A spur gear has 40 teeth, a 14° pressure angle, and a pitch diameter of 2.0 in.
What is the
diametral pitch of the gear?
a)
0.05
b)
1.42
c)
2.86
d)
7.0
e)
20.0
3.
The worm gear shown has a 1” pitch diameter and has
two threads. The gear has an 8” pitch diameter and 96
teeth.
If the worm turns 24 revolutions in the direction
indicated, how far does the gear turn?
a)
4 rotations clockwise
b)
1 rotation clockwise
c)
½
rotation clockwise
d)
1 rotation counter-clockwise
e)
4 rotations counter-clockwise
4.
In the worm from Question 3, the bearing at A is the locating bearing.
What direction are the
forces from the worm shaft onto bearing A?
a)
- x
+ y
- z
b)
+ x
- y
+ z
c)
+ x
- y
- z
d)
- x
- y
+ z
e)
- x
- y
- z
5.
A spur gearset has an input gear with 15 teeth and an output gear with 60 teeth.
If 4 N·m of
torque is supplied to the input gear at 50 rad/sec, approximately how much power is delivered
by the output gear to the load?
a)
16 W
b)
60 W
c)
75 W
d)
200 W
e)
800 W
A
B
x
y
(
z
out of
page)
Page 3
6.
For the planetary gear train shown, the sun gear rotates
at 2000 rpm clockwise and the arm is fixed.
How fast
does the ring gear rotate and in which direction?
a)
4,000 rev/min (clockwise)
b)
2,500 rev/min (clockwise)
c)
300 rev/min (counter-clockwise)
d)
300 rev/min (clockwise)
e)
2,500 rev/min (counter-clockwise)
7.
Comparing a square vs. an ACME power screw, which of
the following is true regarding the use of a split-nut:
a)
A split nut reduces friction on both types of power screw
b)
A split nut allows for backlash adjustment on an ACME power screw
c)
A split nut allows for backlash adjustment on a square power screw
d)
A split nut is required when using a bushing for a friction collar on both types of power screw
e)
A split nut is required when an ACME power screw is non-reversing
8.
Which of the following components of belt tension present in V-Belts but normally ignored in
flat belts that is the main consideration when calculating belt life?
a)
Initial tension (F
i
)
b)
Bending tension (F
b
)
c)
Centrifugal tension (F
c
)
d)
Tight-side tension (F
1
)
e)
Slack-side tension (F
2
)
9.
A V-belt drive has a driving pulley operating at 200 rpm, a drivetrain value of e = 0.25, a
nominal power of H
nom
= .75 hp, a service factor of K
s
= 2.5, and a design factor of n
d
= 1.5.
TWO belts are to be used in parallel.
The following belts are available in the catalogue. Which
is the smallest belt that will satisfy the design requirements?
a)
Allowable power H
a
= 0.7 hp
b)
Allowable power H
a
= 1.1 hp
c)
Allowable power H
a
= 1.5 hp
d)
Allowable power H
a
= 2.9 hp
e)
Allowable power H
a
= 5.7 hp
10.
A timing belt has a driving pulley with pitch diameter of 20 cm and 50 teeth, and a driven
pulley with 100 teeth.
The wrap angle is 130°.
During operation, the tight side tension is 130 N,
slack side tension is 40 N, and the driving pulley rotation rate is 120 rad/sec.
What is the torque
transmitted from the motor shaft to the driving pulley?
a)
6.0 N·m
b)
9.0 N·m
c)
60.0 N·m
d)
100.0 N·m
e)
600 N·m
100T
30T
15T
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Page 4
11.
Which of the following design or operating parameters should be increased in order to be able
to reduce the required bushing length of a boundary-lubricated bearing in service?
(assume all
other parameters remain fixed)
a)
Operating rotation speed,
N
b)
Applied force,
F
c)
Coefficient of friction,
f
s
d)
(PV) rating of the bushing
e)
Wear factor,
K
12.
A tapered-roller bearing is best suited for:
a)
Only large radial loads
b)
Only large axial loads
c)
Small radial loads, plus large axial loads in both directions
d)
Large radial loads, plus large axial loads in both directions
e)
Large radial loads, plus large axial loads in one direction only
13.
Which of the following statements is true for the Soderberg, Gerber, Modified Goodman and
ASME-elliptic fatigue failure criteria:
a)
All criteria predict fatigue failure will occur before yielding
b)
Only the Modified Goodman criterion is valid for tensile stresses
c)
The zone to the left of each of the fatigue criteria lines represents the design domain where n < 1
d)
When
σ
a
= 0, the safety factor n
≥
1 when
σ
m
≤
S
y
for all criteria
e)
When
σ
m
= 0, the safety factor n = 1 when
σ
a
= 0.5 * S
e
for all criteria
14.
A motor drives a gearbox input shaft (top
shaft in figure to right) at 1200 rpm.
The
gearbox uses a worm gear to drive a constant
torque load attached to the output shaft via a
flexible coupling.
In addition to torsional
shear and direct shear due to the worm
gearset, the output shaft is subject to stresses
best characterized by:
a)
steady bending stress plus alternating axial
stress
b)
steady bending stress plus steady axial stress
c)
zero midrange stress and steady axial stress
d)
partially but not fully-reversed bending
stress only
e)
alternating bending stress in the
z
-axis only,
plus alternating axial stress
Page 5
P
art 1B
–
Short
-
Answer Questions
(16
marks
)
Answer all 7 questions in the spaces provided.
Each question is worth 2 marks.
15.
The larger helical gear shown has a normal pressure angle of
20°, a helix angle
ψ
of 30°, N = 35 teeth, and a pitch diameter
of 5”.
What is the normal pitch in inches? Show your
calculations.
(2 marks)
Diametral pitch P = N/d = 35/5” = 7 in
-1
P * p =
π
, so p =
π
/7 = 0.45”
Normal pitch = _0.45”_____
16.
Based on the shaft loading
shown in the top diagram,
complete the diagrams for
axial
force,
shear
force,
bending
moment
and
torsion. Notes: The moments
shown are oriented along the
x-axis. You do not need to
indicate
values
in
your
diagrams,
but
they
must
follow
the
usual
sign
convention. (4 marks)
Page 6
17.
Given that the total raising torque,
T
T
, for an ACME power screw is given by the sum of the
raising torque at the threads (
T
R
) and collar friction torque (
T
C
):
What is the efficiency,
e
, which is defined as the ratio of the total raising torque when friction
has been eliminated divided by the total raising torque?
Simplify the expression, and leave the
denominator as
T
T
. (2 marks)
=
F l
/ (2
π
T
t
)
18.
The shaft shown has a pair of tapered roller bearings, a helical gear, a spur gear, and a
cylindrical roller bearing.
Power is transmitted to the large helical gear via a smaller pinion
gear and runs in one direction only, with smooth torque delivery.
Assuming proper shaft
accessories, what are the TWO most significant changes you would suggest to this design and
why?
(2 marks)
Change #1.
Shorten shaft to increase stiffness and critical speed
Change #2.
Replace tapered roller bearings with a single angular ball bearing to reduce cost
T
T
=
T
R
+
T
C
=
Fd
m
2
π
fd
m
sec
α
+
l
π
d
m
−
fl
sec
α
"
#
$
$
%
&
'
'
+
Ff
c
d
c
2
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Page 7
19.
The diagram shown below is the tension profile for a flat belt.
On this diagram, sketch the
tension profile for a V-belt belt that is transmitting the same torque, but otherwise has the same
linear speed, initial tension, pulley diameters, and belt weight per unit length.
(2 marks)
20.
A) For synchronous power transmission with a flexible element, what is the principal
operating
difference between roller chains and timing belts? Exclude materials and secondary effects such
as lubrication, dirt, and maximum capacity. (1 mark)
B) What is the simplest way to minimize this difference? (1 mark)
A:
Chordal speed variation
B:
Increase number of teeth on the sprocket
B
C
D
E
F
A
B
∆
F
/2
∆
F
/2
Page 8
(page intentionally left blank)
Page 1
MECH 325 – Midterm Book 2
Tuesday, October 21, 2014
Name: _____________________________________
Student Number: _____________________________
Circle your section
Section 101:
T1A (11:00am tutorial)
T1B (3:30pm tutorial)
Section 102:
T1C (2:00pm tutorial)
T1D (5:00pm tutorial)
Signature: ___________________________________
Q21 _____ / 4
Q22 _____ / 4
Q23 _____ / 6
Q24 _____ / 8
Q25 _____ / 8
Q26 _____ / 6 (bonus)
Total _____/ 30 + 6
Instructions
Please read carefully.
Part 2 – Open-Book (30 pts)
Long answer
: Complete all parts to the question by marking your response in the booklet provided.
This
portion of the exam is open-book and open-notes.
At the end of the exam, return this handout with
your answers in the booklet.
This is a multi-part problem.
For each part, use the parameter values given.
Do not carry your answers
forward from one part to the next except for dimensions on the figure.
If you cannot complete one
part, you may move on and still receive full marks for subsequent parts.
Do not try to back-calculate to
previous parts, since the new parameters given are incorrect and contradictory on purpose.
Clearly
indicate your final answer to each part by drawing a box around it.
Separate different parts with a line
drawn across the page.
Only non-programmable (or purged) calculators may be used.
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Page 2
Long Answer Problem (3
0
marks)
NOTE: The non-SI tables required are appended at the back of the handout.
SUGGESTION: Remove the handout staple so you can refer to the figure and the questions at the
same time.
Page 3
21.
The motor connected to shaft (a) delivers a power of
H
nom
= 2.00 kW at a speed of 3000 revolutions
per minute in a counter-clockwise direction, as shown in the figure.
Spur gears 2 and 3 deliver the
power with an efficiency of 97% to shaft (b) at location D.
Shafts (a) and (b) are aligned on the y-
axis.
The V-belt on Pulley 4 at location B has a wrap angle of 180°.
Forces
F
top
and
F
bottom
are
parallel to the z-axis.
Determine the magnitude of the torque on shaft (b) delivered to the V-belt
sheave (4) and the linear speed of the V-belt in ft/min, not in m/s. (4 marks)
22.
Regardless of the answers to the previous question, assume
T
b
= 4.87 Nm at a rotational speed of 157
rad/sec (=1500 RPM) in a clockwise direction. Assume a “V V’ configuration (V-belt sheaves on
driving and driven ends), so
K
1
= 1.
Assume a length factor of
K
2
= 1, a service factor
K
s
= 1.3 and a
design factor of 1.5.
Determine the smallest type of belt that will suffice from Table 17-12 (from
types A through E), and justify your answer.
(4 marks)
23.
Regardless of the answers to the previous question, assume
F
top
= 400 N and
F
bottom
= 1100 N.
The
geometry of the shaft is as follows:
x1
= 8 cm;
x2
= 8 cm;
x3
= 4 cm.
The pressure angle of the gears
is 20°, and
W
t
= 1200 N. The bearings at A and C are self-aligning.
Determine the reaction forces
on the shaft from bearing A and bearing C in the X-Z plane ONLY. (6 marks)
24.
Regardless of the answers to the previous question, assume the bearing reaction force magnitudes are
F
A
= 1600 N and
F
C
= 1100 N. Select a single-row, 02-series, deep-groove bearing from Table 11-2
that will be appropriate for both locations A and C.
Use an application factor of 1.2, a life of
x
=20
and a reliability of
R
= 0.995. Use these parameters:
L
10
= 10
6
x
0
= 0.02
θ
= 4.459
b
= 1.483
Determine the
C
10
value required and the bearing bore diameter at the more critical location of
the two (A or C). (8 marks)
25.
Regardless of the answers to the previous question, assume the following for a calculation of stresses
at B (the pulley): the shaft is made of steel with
S
ut
= 820 MPa and
S
y
= 650 MPa, and it has a fully-
corrected endurance limit of
S
e
= 280 MPa at this location.
The pulley is restrained to the shaft using
a key and keyway (for the keyway, assume
q
= 0.75,
q
s
= 0.85,
K
t
= 2.2,
K
ts
= 3.0,
K
f
= 1.75,
K
fs
=
2.2,).
The following loading information is to be used: the fully-reversed bending moment magnitude
at B due to the power transmission forces is 95 Nm. The steady torque
T
transmitted by the shaft from
gear 3 to the pulley is 52 Nm
.
To assure a factor of safety of 1.8, determine the minimum shaft
diameter needed at location B (the pulley) to prevent fatigue failure, based on the Soderberg
criterion.
(8 marks)
26.
BONUS:
Regardless of the answers to the previous question, assume a Type “C” V-belt (
K
b
= 1600
and
K
c
= 1.716), H
d
= 2 HP at the rotational speed for shaft (b) of 2000 RPM with a pulley diameter
of 5”, so V = 2617 ft/min.
The belt tension friction coefficient
f
= 0.5.
Find hoop tension
F
c
, belt
tensions
F
top
and
F
bottom
, and the minimum initial tension
F
i
. (6 marks)
Page 4
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- I need answer within 20 minutes please please with my best wishesarrow_forward27. You have the following compound machine. For S and ins a. What is the ideal mechanical advantage of this system? The inclined plane dimensions are 7.2 meters length and 1.8 meters height. What effort force is required to move the 600N create? In practice, you need to supply an effort force of 75 N to lift the crate. What is the efficiency? C. How could you redesign this compound d. machine so that the effort force needed was 50 N in practice? Assume the efficiency is your response from part C no matter what changes you make. Be specific with the changes you propose (if you add pulleys state how many, if you change the inclined plane dimensions state the new dimensions, etc.).arrow_forwardplease answer question 7arrow_forward
- TYPEWRITTEN ONLY PLEASE FOR UPVOTE. DOWNVOTE FOR HANDWRITTEN. DO NOT ANSWER IF YOU ALREADY ANSWERED THIS. I'LL DOWNVOTE.arrow_forwardI Review Learning Goal: To be able to find the center of gravity, the center of mass, and the centroid of a composite body. Part A A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the bodyng the weighted average Find the area of the body. (Figure 1) Express your answer numerically in feet squared to three significant figures. into regular shaped segments, and then by calculating i of the segments' centroids.An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.55 ft , where a is the diameter of the semi- circle,b = 3.74 ft, and c = 2.35 ft . A hole with diameter d = 0.750 ft is centered at (1.26, 0.775). > View Available Hint(s) Vol AEO It vec ? A = ft? Submit Part B Find a, the a-coordinate of the body's centroid. (Figure 1) Express your answer numerically in feet to three significant figures. > View…arrow_forwardPart E Learning Goal: To calculate the moment of inertia for areas Where is the centroid of the section, y shown in (Figure 2), located? composed of simpler shapes. Express your answer in cm to three significant figures. The beam section shown in (Figure 1) is composed of two horizontal flanges and a vertical web with dimensions H = 24 cm , W1 = 33 cm , and W2 = 23 cm , and the plates all have thickness 2 cm . View Available Hint(s) %3D Calculate the moment of inertia of the section about ΑΣφ ? vec the centroid axis parallel to the x-axis. cm Submit Part F What is the moment of inertia of the section about its centroidal axis parallel to the x-axis? Express your answer in cm to three significant figures. Figure 2 of 2 • View Available Hint(s) vec ? I : cm4 Submitarrow_forward
- How come h2 is 424.25?arrow_forward24 Problem: Mathematics in Wind Energy Production Wind power is defined as the use of air flow through wind turbines to provide the mechanical force to generate electricity. Wind power is an alternative to burning fossil fuels, and is renewable and produces no greenhouse gas emissions during operation. Modern horizontal-axis wind turbines often use three blades. Theoretically, the maximum power P (unit: watts) that a three-blade wind turbine can extract from the wind power can be calculated as: Blade 1. %3D (Equation 1) dɔzayd² = d where p is the air density (kg/m'), A is the sweep area of the turbine (m²) and can be calculated from the length of the turbine blades, and v is the wind speed (m/s). C, is the power coefficient that is unique to each turbine type. This coefficient represents the amount of kinetic energy from the wind that is captured by the turbine. From the Betz's limit law we know that the best power conversion possible is Cp,max = 0.59. Part 1 Given the following data:…arrow_forwardHand written plz asap please fast... I'll give you multiple upvote hand written plz.... Solve all parts but fastarrow_forward
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