Transcript MOTOR PARAMETERS

Informally
Parameters and
properties of DC
Motors
Operating Voltage
• Operating Voltage is the voltage recommended for powering
the motor
• A motor requires a power source within its operating voltage,
• i.e., the recommended voltage range for best efficiency of the
motor.
• The motor will work fine on lower voltages (not always). But it
will work at a lower power.
• The motor can operate at higher voltages.
• The power is increased!!
• This will however shorten the operating life of the motor.
Current and Work
• When constant voltage is applied, a DC motor draws current in the
amount proportional to the work it is doing.
• E.g., if a robot is pushing against a wall, it is drawing more current (and
draining more of its batteries) than when it is moving freely in open
space.
• The reason is the resistance to the motor motion introduced
by the wall.
• When there is no resistance to its motion, the motor
draws the least amount of current;
• When there is so much resistance as to cause the motor
to stall, it draws the maximal amount of current.
Copyright @ 2002 A. G. Billard
Stall Current
• If the resistance is very high (i.e.,
the wall won't
move no matter how hard the robot
pushes against it), the motor draws a maximum
amount of power, and stalls.
• The stall current of the motor is the most current it can
draw at its specified voltage.
Copyright @ 2002 A. G. Billard
Motor Inefficiency
• As any physical system, DC motors are not
perfectly efficient.
• The energy is not converted perfectly.
• Some energy is wasted as heat generated by friction
of mechanical parts.
• Inefficiencies are minimized in well-designed
(more expensive) motors, and their efficiency can
be high.
• How high?
Copyright @ 2002 A. G. Billard
Level of Efficiency of DC motors
• Good DC motors can be made to be efficient in
the 90th percentile.
• Cheap DC motors can be as low as 50%.
• Other types of effectors, such as miniature
electrostatic motors, may have much lower
efficiencies still.
Copyright @ 2002 A. G. Billard
Formally
Characterizing
Electric Motors
Characterizing motors
Application of motor characteristics
Choosing motors and gears
Characterizing Motors
Power
Torque
Speed
Torque in DC Motors
Speed, Angular Acceleration, and Torque
•  (omega)
• Motor speed is commonly measured in:
• rpm (revolutions per minute)
• or rad/sec (radians per second)
•  (alpha)
• Angular acceleration is commonly measured in rad/sec2
•T
• Torque is measured in:
• N-m (Newton-meters)
• or ft-lbs (foot pounds) commonly
What is Torque?
Torque
• T=F·d
Where force has the units of N (Newtons) and distance has the
units of m (meters) resulting in torque units of N-m
Newton
meters
F
d
Torque at the Motor Shaft
• Within a motor's operating current range, the
more current is used, the more torque or
rotational force is produced at the shaft.
• The strengths of the magnetic field generated in
the wire loops is directly proportional to the
applied current and thus the produced torque at
the shaft.
Copyright @ 2002 A. G. Billard
Stall Torque
• Besides stall current, a motor also has its stall
torque.
• Stall torque is the amount of rotational force
produced when the motor is stalled at its
operating voltage.
Copyright @ 2002 A. G. Billard
Free Spinning and Stalling
• When the motor is stalled, it is producing maximum torque,
but the rotational velocity is 0, so the output power is 0 again.
• Between free spinning and stalling, the motor does useful
work, and the produced power has a characteristic parabolic
relationship
• A motor produces the most power in the middle of its
performance range.
Power vs. Speed
Power (Watts)
600
No load, maximum
speed but no power
500
400
300
200
100
0
0
500
1000
1500
2000
2500
Speed (rpm)
Copyright @ 2002 A. G. Billard
Power Trends for Motors with linear torque speed curves
Power vs. Speed
Power (Watts)
600
Use such curves. provided
by the producer, for your
calculations
500
400
300
200
100
0
0
500
1000
1500
Speed (rpm)
2000
2500
SPEED
• The amount of power a motor generates is the product of the
shaft's rotational velocity and its torque.
• If there is no load on the shaft, i.e., the motor is spinning freely,
then the rotational velocity is the highest
• but the torque is 0, since nothing is being driven by the motor.
• The output power, then, is also 0.
Speed and Torque
• Most DC motors have unloaded speeds in the range of
3,000 to 9,000 RPM (revolutions per minute), or 50
to 150 RPS (revolutions per second).
• This puts DC motors in the high-speed but low-torque
category (compared to some other actuators).
• How often do you need to drive something very light that
rotates very fast (besides a fan)?
Copyright @ 2002 A. G. Billard
From Motor
Torque to wheel
speed
Motors are characterized by Torque /
Speed Curves
Torque vs. Speed
Torque (N-m)
12
10
8
6
4
2
0
0
500
1000
1500
w (rpm)
When speed grows, torque decreases
2000
2500
How can we use the torque speed curve
from previous slide?
r
F
1. Calculate or measure force required to propel device.
Our robot or vehicle
has a wheel with
radius r
2. Determine torque by T=F·r
Wheel with radius r
E.g. 50 N force (~ 11 lbs.),
.1 m radius (~ 4 in)
r
T
T = 50*0.1 = 5 N-m
TorqueSpeed Curve
 (omega)
F
r
Torque vs. Speed
3. Determine motor
from curve.
Torque (N-m)
speed (angular velocity)
12
wheel speed V
10
8
1000 rpm
6
4
2
0
0
500
 (omega)
1000
1500
2000
2500
w (rpm)
E.g.  = 1000*2*/60 = 105 rad/sec
4. Calculate wheel speed by V=r •
V=.1*105 = 10.5 m/sec
Power is the rate at which work is done
•Light bulb use about 100 Watts
•Economy automobiles produce about 120 HP
(90,000 W)
•High performance jet engines produce about
50,000 HP (37 million Watts)
Power of
a motor
Power of a motor
•P=T•
•Power is the torque times the angular
velocity
•If T is in N-m and  is in rad/sec, power
has the units of Watts
Power in DC Motors
Power vs. Speed
Power (Watts)
600
500
400
300
200
100
0
0
500
1000
1500
Speed (rpm)
2000
2500
• Think about a robot arm, you are
trying to select the motors for
shoulder.
• How many motors?
• How long the arm?
• How many motors in the lower part of
the arm?
• How to transmit motion to fingers?
Calculating power from speed and
torque of the motor
• Spreadsheet application converts motor speed to rad/sec
• Spreadsheet calculates power using P=T*
1rev 2rrad 1 min
min 1rev 60 sec
Revolutions
per minute
Radians per
revolution
Seconds per minute
100 * 2*3,14/60 = 10.5
Speed (rpm) Speed (rad/s) Torque (N-m) Power (W)
0
0.0
10
0
100
10.5
9.5
99
200
20.9
9
188
300
31.4
8.5
267
400
41.9
8
335
First convert to radians per second
Speed increases, torque
decreases
Motor Torque and Power verus Speed:
torque
power
speed
DC Motor Speed-Torque Curves
Power vs. Speed
Power (Watts)
600
500
400
300
200
100
0
0
500
1000
1500
Speed (rpm)
2000
2500
Speed, efficiency,
power and current as
function of torque of
DC Motors
Maximum
of speed
Maximum
of
efficiency
Maximum
of power
Maximum of
current
Torque
Now we have torque, not speed
on x axis
Torque, not speed as before
Motors and Robots
• DC motors are best at high speed and low torque.
• In contrast, robots need to pull loads
• (i.e., move their bodies and manipulators, all of which have
significant mass),
• thus requiring more torque and less speed.
• As a result, the performance of a DC motor typically
needs to be adjusted.
What do you
think?
• How?
Copyright @ 2002 A. G. Billard
DC Motor SpeedTorque Curves with
gears
Larger gear
rotates slower
but has more
torque
R1
1,T1
R2
of motor
Shaft
2,T2
• The current increases linearly with torque. Current is independent of applied voltage.
Maximum
of speed
Smaller
current for
smaller
torque
This is what we get
from the motor
Max voltage
This is what we get from
the same motor geared
down with coefficient G
G=R1/R2
smaller
voltage
Speed decreased
G times
Torque increased
G times
Smaller voltage,
smaller speed for the
same torque
Torque
Torque
Gearing
R1
1,T1
R2
2,T2
Here there are equal speeds and equal forces
• V1=V2
1R1=2R2 or 2 = 1R1 /R2
if R1=2*R2 then 2 =2*1
• F1 = F 2
T1/R1=T2/R2 or T2=T1R2/R1
if R1=2*R2 then T2 =T1/2
These formulas will be a base
when we will calculate robot
arms and mobile robots.
Gear Ratio’s
•High gear ratio - high torque, low speed
•Low gear ratio - low torque, high speed
R1
1,T1
R2
2,T2
Keep in mind this figure
when you will be:
1. Creating drive system for
your wheeled robot and
select the size of wheels.
2. Create a robot arm.
Wheel size affects gear ratio
•If the wheel size is doubled, the gear ratio is
cut in half
•Larger wheels can increase the speed of a
vehicle.
•Smaller wheels can increase the torque of a
vehicle.
R1
1,T1
R2
2,T2
Choosing wheel
size for your
mobile robot
• Question
1.
2.
3.
4.
5.
We have a mobile robot.
We assume some load.
What is the relation between speed and gear ratio?
Which means, how to select your gear ratio to have an assumed speed?
Or, I have some gearbox with a gear ratio, what will be the speed?
Torque vs. Speed for motor with no gearing
12
No gearing, speed
is 20 radians per
second
Torque (N-m)
10
1. Consider
no gearing
8
6
4
2
0
0
50
100
9 N-m
Torque four
times higher
2. Consider
4:1 gearing
4:1 gearing
R1
Motor 1,T1
shaft
R2
2,T2
150
200
w (rad/sec)
Torque (N-m)
Choosing Gear ratios
Which gearing
will give us a
faster vehicle
if our load is 9 Newtonmeters?
250
speed
Torque vs. Speed curve for same motor with 4:1 gear ratio
45
40
35
30
25
20
15
10
5
0
4:1 gearing, speed
is 42 radians per
second
0
10
20
30
w (rad/sec)
40
50
60
Maximum speed four times smaller
What is there is
smaller load?
Torque vs. Speed curve for motor with no gearing
12
No gearing, 100
radians per second
Torque (N-m)
Which gearing
will give us a
faster vehicle
if our load is 5
Newton-meters?
8
6
4
2
0
0
50
100
5 N-m
Conclusion
You must know the load
and the curve of your
motor when you design
your mobile robot for
speed.
150
200
250
w (rad/sec)
Torque vs. Speed curve for motor with 4:1 gearing
Torque (N-m)
Choosing Gear ratios
10
45
40
35
30
25
20
15
10
5
0
4:1 gearing, 46
radians per second
0
10
20
30
w (rad/sec)
40
50
60
Choosing wheel
size for your
mobile robot
• Question
1.
2.
3.
4.
5.
We have a mobile robot.
We assume some load.
What is the relation between speed and gear ratio?
Which means, how to select your gear ratio to have an assumed speed?
Or, I have some gearbox with a gear ratio, what will be the speed?
Experimental
Setup for Power
Governing Equations
v=d/t
P=F ·v
P = F · d/t
Definition of Terms
You raise weight
m by distance d
What power
motor power do
you need?
r
d
d - distance weight was lifted
t - total lifting time
v - average velocity during lift
F - force required to lift object
r - radius of motor pulley
P - motor power during lift
Experimental Parameters
F=m·g
d = 0.7 m
g = 9.81 m/s2
r = 0.019 m (1.91 cm)
P= m · g · d/t
Speed, vs Current, vs
Torque, vs Power
Governing Equations
v=d/t
P=F ·v
P = F · d/t
P= m · g · d/t
You raise weight
m by distance d
Practical problems
What power
motor power do
you need?
r
d
F=m·g
1. Knowing m,g, d, t you want to calculate
power.
2. Knowing power and some other parameters,
you want to find best combination.
3. Many practical problems can be formulated
that relate power, speed, torque, efficiency,
current, voltage and gears.
4. You can use some Excel calculator or write a
GA algorithm to optimize your problem.
5. Formulating the problem is your creative task.
6. Solving the problem is either assuming and
verifying or using some kind of more
advanced optimization.
Motor Selection
Estimates
Motor Selection Estimates
1. You have a motor.
2. You are designing a mobile robot. You know the tasks of this robot, ramps, speeds,
loads.
3. Is my motor good enough?
This is the power that my
application requires
From torque calculated
for your design
This is the power that
my motor gives
These data you find experimentally or in catalog for your motor
Motor Selection Estimates (cont)
1
• Using Torque-Speed Curve to select the motor with sufficient power for
your task.
2
Angular
velocity
Power
curve
current
3
torque
4
Now you know what is the
value of maximum power that
you need.
1. Can your motor deliver this power?
2. Good motor with this power may be expensive.
3. May be you need to have to cheap motors in parallel?
Motor Selection Comments:
design a drive train.
5
• Do not be too optimistic,
assume low efficiency.
• Have conservative
estimates on drops in
drive efficiency!
• We have many motors in the lab.
• You can purchase cheap good motors from Army Surplus Stores, and similar.
• You can purchase good gears and complete drives, look also to Ebay.
Sources
• Copyright @ 2002 A. G. Billard
• Zachery L Olson