6 Lab: Motor Constants: 6.1 Prelab
6 Lab: Motor Constants: 6.1 Prelab
6 Lab: Motor Constants: 6.1 Prelab
√ √√ √ √√ √ √√ Name:
+ −0 + −0 + −0
Tm = km im vm = kv ωm
where Tm is the motor torque, im is the current passing through the motor, vm is motor
back-EMF voltage, and ωm is the motor’s angular speed.
The values of these constants are usually found on a motor specification sheet
that is experimentally determined by the motor’s manufacturer. The motors and encoders
used in this lab were purchased second-hand. Since the motor constants are not known,
we will run an experiment to determine their values.
6.1 PreLab
Soon, you will do your own MIPSI lab. You will choose a physical system, and use the
MIPSI technique, i.e., Model, Identifiers, Physics, Simplify and Solve, and Interpret
your results. To prepare for the future MIPSI lab, brainstorm two physical systems that
have an interesting question to be answered and are not a Ph.D. dissertation.
Short system description and question to be answered Rough system schematic
20
No load speed
Shown to the right is the linear relationship be-
tween the motor’s steady-state angular speed ωm 16
Write the ODE governing TLoad when both vi and ωm are constant and determine the
steady-state part of TLoad as a function of ωm and vi when both vi and ωm are constant.
Result:
Lm ṪLoad + Rm TLoad = km vi − (Rm b + km kv ) ωm
TLoad | vi is constant = ωm + vi
ωm is constant
Solve for km in terms of the steady-state value of TLoad when vi is constant and the motor
is stalled, i.e., ωm (t) = 0.
km = TLoad
While the motor is stalled, use the multi-meter to measure the resistance of the motor
coil at several angular positions.
Using the motor attached to the cart via the wire, measure the stall torque for an
appropriate range of vi from 3 to 5 volts. Assume the spring is linear. Note the length of
the moment arm. Do not stall the motor for long or it will overheat and burn out.
Approx. vi Measured vi Cart Displacement Force Torque km
3.0
4.0
5.0
Average km
kv =
and bits of zero (“low bits”). The value τperiod is the time interval
from a transition from low to high to the next transition from low
to high, e.g., measured in microseconds (10-6 seconds).
Using a motor without load, measure the steady-state value of ωm (use the oscilloscope
and a single output channel of the encoder) for an appropriate range of vi from 0 to 6 volts.
11
The definition of “volt” unit leads to (for an ideal DC motor) km = kv when SI units are used.