SAN JOSÉ STATE UNIVERSITY
Department of Mechanical and Aerospace Engineering
ME 106 Fundamentals of Mechatronics
Homework #6: Motor Sizing – Due on 11/4/10
Attach the cover sheet (filled out) to your homework responses. Where written responses are
requested, please type them. Make sure that you show how you arrive at any answers involving
numerical calculations. Answers that do not show intermediate steps will likely not get any
points. Photocopy, photograph, or scan your work, so that you have a back up copy and upload
to the D2L Dropbox.
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1. (25 pts) Construct plots of the important motor data for the motor selected in the motor sizing
example from lecture (Maxon A-max, 22mm dia, 6W, model 110162). Your plots must
include:





The speed vs. torque line that passes through the operating point of the motor. The operating
point is the peak torque and angular speed of the motor shaft that we found in the sizing
calculation.
o This line corresponds to a particular voltage applied to the motor. What voltage does the
line correspond to?
The speed vs. torque line if 18V is applied to the motor. This line will not pass through the
operating point, but should be above it.
o What no-load speed would be achieved if 18V is applied to the motor?
The current vs. torque line (assume 18V applied to the motor). Hint: torque is related to current.
The output power vs. torque line (assume 18V applied to the motor). Hint: output power can be
found from torque and speed.
The efficiency vs. torque line (assume 18V applied to the motor). Efficiency is defined as
(Motor shaft power out) / (Electrical power in)
Review your notes from lecture where we derived the torque-speed relationship for a PMDC
motor. In lecture, we solved for torque as a function of speed. You could just as easily have
solved for speed as a function of torque, and many manufacturers show the performance of
their motors on a speed vs. torque graph (Maxon does this). See if you can get this relation
from what we derived in class:

V
R
T  in
KT K E
KE
 = motor shaft speed (units are rad/s)
T = torque (units are N-m)
KT = Torque constant (units are N-m/A)
KE = Back EMF constant ( = 1/(speed constant), units are V/(rad/s)
BJ Furman | ME 106 Intro to Mechatronics | HW6_Motor_Sizing.doc | 21OCT2010
Page 1 of 4
SAN JOSÉ STATE UNIVERSITY
Department of Mechanical and Aerospace Engineering
ME 106 Fundamentals of Mechatronics
2. (20 pts) Given a linear stage like the one shown in lecture, size a stepper motor (i.e.,
determine the peak torque, the RMS torque, and the speed at the motor shaft, assuming that
the motor couples directly to the leadscrew) that would be able to move a 10 kg load
following a motion profile like:
Velocity
s1
t1
t2
t3
t4
Time
Where:
t1=0.5 s
t2=1.5 s
t3=2.0 s
t4=3.0 s
s1=1.0 inch/s (note that this is the velocity of the mass, NOT the angular speed of the
leadscrew)
(If you don’t remember what the stage looks like, see: http://agsmotion.com/parker1p3.jpg
for a stage that is somewhat similar.)
Assume that the pitch of the leadscrew is 10 threads per inch, and that the friction torque
opposing the motor shaft amounts to 1 oz-in.
Note that in order to find the torques, you will need to determine an equivalent inertia, Jtot,
for the inertial effects of all the moving components in the system. You can find the formulas
in the handout, “Motion Control Mechanics”, which was given in lecture (and also available
on the ME 106 website at:
http://www.engr.sjsu.edu/bjfurman/courses/ME106/ME106pdf/MotionControlMechanics.pdf).
Assume that you can neglect the contributions of the leadscrew and motor rotor inertias1 to
Jtot .
1
It is a worthwhile exercise to calculate what the leadscrew actually contributes to J tot to see if the assumption that it
can be neglected is warranted. The inertia of the rotor is unknown, because the motor has not been selected! One can
estimate what the inertia of the motor rotor is by using the peak torque and maximum speed to ‘ballpark’ the torque
or peak power that the motor must put out and then going to a catalog to see what the rotor inertias are for motors
that are in the ballpark for meeting the torque or power requirements. Another way is to use a rule of thumb that the
rotor inertia should be in the range of 0.1  J net  1 , where Jnet is the contribution to Jtot from all the moving
J motor
components except the motor rotor. In our case Jnet would be the just the contribution to Jtot from the 10 kg mass.)
BJ Furman | ME 106 Intro to Mechatronics | HW6_Motor_Sizing.doc | 21OCT2010
Page 2 of 4
SAN JOSÉ STATE UNIVERSITY
Department of Mechanical and Aerospace Engineering
ME 106 Fundamentals of Mechatronics
3. (5 pts) Develop a flowchart for a program to drive the printer carriage in this week’s lab
experiment between the photoreflective and photo interrupter switches.
4. (10 pts) Write the C code that implements the logic developed in Problem 3.
5. (10 pts) Simulate the program from Problem 4 in the AVR simulator. Show the contents of
the appropriate registers to demonstrate that your program functions properly.
BJ Furman | ME 106 Intro to Mechatronics | HW6_Motor_Sizing.doc | 21OCT2010
Page 3 of 4
SAN JOSÉ STATE UNIVERSITY
Department of Mechanical and Aerospace Engineering
ME 106 Fundamentals of Mechatronics
Homework Cover Sheet
Date
Name (print)
Last Name
HW #
First Name
Lab Section
Title
Summary
BJ Furman | ME 106 Intro to Mechatronics | HW6_Motor_Sizing.doc | 21OCT2010
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