1. Informally Parameters and properties of DC Motors

2. 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.

3. 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.
A. G. Billard

4. 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.
A. G. Billard

5. 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?
A. G. Billard

6. 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.
A. G. Billard

7. Formally Characterizing Electric Motors
Characterizing motors
Application of motor characteristics
Choosing motors and gears

8. Characterizing Motors
Power
Torque
Speed

9. Torque in DC Motors

10. 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

11. What is Torque? T=F·d Torque
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

12. 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.
A. G. Billard

13. 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.
A. G. Billard

14. 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.
No load, maximum speed but no power
A. G. Billard

15. Power Trends for Motors with linear torque speed curves
Use such curves. provided by the producer, for your calculations
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.

16. 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)?
A. G. Billard

17. From Motor Torque to wheel speed

18. Motors are characterized by Torque / Speed Curves
When speed grows, torque decreases

19. How can we use the torque speed curve from previous slide?
Our robot or vehicle has a wheel with radius r r F
1. Calculate or measure force required to propel device.
2. Determine torque by T=F·r
Wheel with radius r
E.g. 50 N force (~ 11 lbs.), m radius (~ 4 in)
T = 50*0.1 = 5 N-m F r T
Torque-Speed Curve
 (omega) r
3. Determine motor
speed (angular velocity)
from curve.
wheel speed V
1000 rpm
 (omega)
E.g.  = 1000*2*/60 = 105 rad/sec
V=.1*105 = 10.5 m/sec
4. Calculate wheel speed by V=r •

20. 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)

21. Power of a motor

22. 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

23. Power in DC Motors
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?

24. Calculating power from speed and torque of the motor
Spreadsheet application converts motor speed to rad/sec
Spreadsheet calculates power using P=T*
Revolutions per minute
Radians per revolution
Seconds per minute
100 * 2*3,14/60 = 10.5
Speed increases, torque decreases
First convert to radians per second

25. Motor Torque and Power verus Speed:

26. DC Motor Speed-Torque Curves

27. Torque, not speed as before
Speed, efficiency, power and current as function of torque of DC Motors
Maximum of speed
Maximum of power
Maximum of efficiency
Maximum of current
Torque
Now we have torque, not speed on x axis
Torque, not speed as before

28. 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.
How?
What do you think?
A. G. Billard

29. DC Motor Speed-Torque Curves with gears
Larger gear rotates slower but has more torque R1 R2
1,T1
2,T2
Shaft of motor
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

30. Gearing V1=V2 1R1=2R2 or 2 = 1R1 /R2 if R1=2*R2 then 2 =2*1
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 = F2 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.

31. Gear Ratio’s High gear ratio - high torque, low speed
Low gear ratio - low torque, high speed R1 R2
1,T1
2,T2
Keep in mind this figure when you will be:
Creating drive system for your wheeled robot and select the size of wheels.
Create a robot arm.

32. 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 R2
1,T1
2,T2

33. Choosing wheel size for your mobile robot
Question
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?

34. Choosing Gear ratios 9 N-m
Which gearing will give us a faster vehicle if our load is 9 Newton-meters?
No gearing, speed is 20 radians per second
1. Consider no gearing
Choosing Gear ratios
9 N-m
speed
Torque four times higher
2. Consider 4:1 gearing
4:1 gearing, speed is 42 radians per second
4:1 gearing R1 R2
1,T1
2,T2
Motor shaft
Maximum speed four times smaller

35. Choosing Gear ratios 5 N-m What is there is smaller load?
No gearing, 100 radians per second
Which gearing will give us a faster vehicle if our load is 5 Newton-meters?
Choosing Gear ratios
5 N-m
4:1 gearing, 46 radians per second
Conclusion
You must know the load and the curve of your motor when you design your mobile robot for speed.

36. Choosing wheel size for your mobile robot
Question
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?

37. Experimental Setup for Power
Governing Equations
v=d/t P=F ·v
P = F · d/t
Definition of Terms
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
P= m · g · d/t
You raise weight m by distance d
What power motor power do you need? r d
Experimental Parameters
d = 0.7 m g = 9.81 m/s2 r = m (1.91 cm)
F=m·g

38. 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
Knowing m,g, d, t you want to calculate power.
Knowing power and some other parameters, you want to find best combination.
Many practical problems can be formulated that relate power, speed, torque, efficiency, current, voltage and gears.
You can use some Excel calculator or write a GA algorithm to optimize your problem.
Formulating the problem is your creative task.
Solving the problem is either assuming and verifying or using some kind of more advanced optimization. d
F=m·g

39. Motor Selection Estimates

40. Motor Selection Estimates
You have a motor.
You are designing a mobile robot. You know the tasks of this robot, ramps, speeds, loads.
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

41. Motor Selection Estimates (cont)
Using Torque-Speed Curve to select the motor with sufficient power for your task. 1 2
Angular velocity
Power curve
current 3
Now you know what is the value of maximum power that you need.
torque
Can your motor deliver this power?
Good motor with this power may be expensive.
May be you need to have to cheap motors in parallel? 4

42. Motor Selection Comments: design a drive train.5
Do not be too optimistic, assume low efficiency.
Have conservative estimates on drops in drive efficiency!

43. 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.

44. Sources
A. G. Billard
Zachery L Olson