theory and practice of permanent magnet, direct...

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Theory and Practice of Permanent Magnet, Direct Current (PMDC) Motors

or

How to Avoid that Burning SmellHow to Avoid that Burning Smell

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Two Pole, PMDC Motor

"Electric motor cycle 1, 2 & 3" by Wapcaplet. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Electric_motor_cycle_3.png#/media/File:Electric_motor_cycle_3.png

For a simple, two pole DC motor, power applied to the coils wrapped around the armature creates a magnetic field. The magnetic field repels the left permanent magnet and attracts the right permanent magnet thereby rotating the armature.

When the armature rotates to horizontal, the magnetic fields produce zero torque and cease acting to spin the armature. At this point, the commutator reverses current direction in the coils, reversing magnetic field polarity, and the armature continues to spin.

permanent magnet

armature

commutator

coils

Through electromagnetism, the Lorentz force, motors convert electrical energy into mechanical energy

The simple, two pole, PMDC motor is not the most effective implementation of a PMDC motor, but makes illustration of the theory of operation straightforward. Most implementations of PMDC motors will have three or more pole armatures.

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PMDC Motor: What goes on inside

Animation source: By Lookang many thanks to Fu-Kwun Hwang and author of Easy Java Simulation = Francisco Esquembre (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

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CIM Motor

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Conservation of Energy: It's the law

● Closed systems conserve energy over time

● Energy can neither be created nor destroyed

● Energy can change forms

– Potential energy due to height can become kinetic energy (mgh = 1/2mv2)

– Chemical energy can become kinetic energy (C4 anyone?)

– Electrical energy can become mechanical energy

● Power is the time rate of change of energy

In physics, the law of conservation of energy states that the total energy of an isolated system remains constant.

Common units of Energy

SI English Conversion

Joule (J) Btu 1 J = 9.4782E-04 Btu

newton-meter (N·m) foot-pound (ft·lb) 1 J = 1 N·m = 0.73756 ft·lb

Common units of Power


Watts (W) foot-pound per second (ft·lb/s) 1 W = 0.73756 ft·lb/s

newton-meter per second (N·m/s) Horsepower (hp) 1 W = 1 N·m/s = 1.3410E-03 hp

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Physical Parameters Governing Motor Operation

● Torque

● Speed

● Power

● Efficiency

● Voltage, electric potential tension, potential difference

● Current

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Torque

● Torque: The quantitative measure of the tendency of a force to cause or change rotational motion

● Torque turns dials, flips switches, drills holes, tightens bolts, spins wheels, ...

● Torque (τ) = applied force (F) * moment arm (l)= tangential force (Ftan) * r

● For a wheel, force is always tangential.τ = F * r

Common units of Torque


newton-meter (N·m) inch-pound (in·lb) 1 N·m = 8.8507 in·lb

foot-pound (ft·lb) 1 N·m = 0.73756 ft·lb

force

radius

torque

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Speed

● Speed, more specifically, angular velocity, is the rate of rotation around an axis

● Angular velocity, ω, may be expressed in many ways, but, for motors, is typically expressed as revolutions per minute (rpm)

● When performing computations involving angular velocity, particularly power computation, express angular velocity in radians per second

● One revolution is 360 degrees or 2π radians

● The tangential velocity at any point on a rotating wheel is the product of the distance from the center of rotation, r, and the angular velocity expressed in radians or vtan = r * ω

● When using the radius of the wheel, vtan, is the velocity of the vehicle or the linear speed of the rope on a winch

What goes around

1 revolution Conversion

2π radians 1 radian = (180/π)º

360 degrees 1º = (π/180) radians

ω

radius (r)

vtan

= r * ω

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Power

● If we move that object around the circle once every second, 1 revolution per second, then the power we are applying is

= F*2πr/sec

● Since we know that F * r is torque, we can rewrite that equation as= τ * 2π/sec or= τ * ω, where ω for this case is the specific speed of 2πr/sec

● In the general case, rotational power, P = τ * ω, with ω in radians/sec

Common units of Power


Watts (W) foot-pound per second (ft·lb/s) 1 W = 0.73756 ft·lb/s

newton-meter per second (N·m/s) Horsepower (hp) 1 W = 1 N·m/s = 1.3410E-03 hp

● Power is the time rate of change of work

● Work is force (F) applied over a distance (s)= F * s

● If we move an object around the circumference of a circle of radius, r, by applying a constant force, F, the work we perform is

= F * 2πr

Force

r

Circumference = 2πr

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Voltage, Current and Power

● Electric circuits function on the motion of electric charges

● Q usually denotes the basic quantity of electric charge with units of coulombs

● Potential difference, or voltage, is work performed per unit-positive charge moving that charge between two points in an electric field, W/Q

● We express voltage in volts (V)

● Current, I, is the rate of motion of charge in a circuit or Q/t

● We express current in amps (A)

● Since voltage is the available work per charge between two points in a circuit and current is the motion of that charge, then

V * I = * =WQ

Qt

Wt

● And, as we know, the time rate of change of work is power!

● P = V * I with units of watts (W)

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+

+

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Efficiency

● The world is not a perfect place

● Motors receive input power from some external source, e.g. a battery, and output mechanical, rotational energy, but not without energy loss due to

– Friction in bearings and the commutator

– Electrical resistance in the windings on the armature

– Electromotive backforce

– Rotor imbalance

– Etc.

● We express this power loss as the non-dimensional ratio of output power to input powerη = P/VI

● Efficiency, η, varies as a function of motor speed

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Motor Performance Model: Mini CIM Torque and Speed

0 1000 2000 3000 4000 5000 6000 70000

50

100

150

200

250

Speed (rpm)

To

rqu

e (

oz-

in)

τ = τs - (τs/ ωn) * ωω = ωn - (ωn / τs) * τ

Maximum torque is stall torque:

τs = 198.4 oz-in (1.401 N·m)

Maximum speed at free load:

ωn = 6200 rpm

● A linear model of torque versus speed, set by stall torque and no load speed, is a good performance approximation for typical PMDC motors at constant voltage

● Torque is inversely proportional to speed

Torque

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Motor Performance Model: Mini CIM Power

0 1000 2000 3000 4000 5000 6000 70000

50

100

150

200

250

Speed (rpm)

To

rqu

e (

oz-

in)

an

d P

ow

er

(wa

tts)

Maximum power occurs at half of maximum speed and torque

Maximum torque198.4 oz-in (1.401 N·m)

Maximum speed6200 rpm

Maximum power227.4 watts

• As we know, P = τ * ω• Substituting our linear

equation for torque or speed:

P = τs * ω - (τ

s/ ω

n) * ω2

P = ωn * τ - (ω

n / τ

s) * τ2

TorquePower

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0 1000 2000 3000 4000 5000 6000 70000

50

100

150

200

250

0

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

To

rqu

e (

oz-

in)

an

d P

ow

er

(wa

tts)

Effi

cie

ncy

(%

)

Motor Performance Model: Mini CIM Efficiency

Maximum torque198.4 oz-in (1.401 N·m)


Maximum output power227.4 W

Maximum efficiency

η = 65%

Note: Efficiencies are from CIM motor data scaled to Mini CIM speed range.

• Motor efficiency is the ratio of output power to input power

• Efficiency is characteristic to each motor

Torque

Power

Efficiency

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Vex Measured Motor Performance: Mini CIM

0 1000 2000 3000 4000 5000 60000

50

100

150

200

250

0.0

0.5

1.0

1.5

2.0

2.5

Current (A)

Torque (N·m)

Output Power (W)

Efficiency (%)

Speed (RPM)

Cur

rent

(A

), P

ow

er

(W),

and

Eff

icie

ncy

(%)

To

rque

(N

·m)

Maximum torque1.409 N·m

Maximum output power215.4 W @ 2919.8 RPM

Maximum speed5839.5 RPM

Max Current89.4 A

Maximum efficiencyη = 57.4%

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Motor Performance Model: Mini CIM Input Power

0 1000 2000 3000 4000 5000 6000 70000

100

200

300

400

500

600

0

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

To

rqu

e (

oz-

in)

an

d P

ow

er

(wa

tts)

Effi

cie

ncy

(%

)

Maximum torque198.4 oz-in


Maximum power227.4 watts

Maximum efficiency

η = 65%

Input power

What's happening toinput power here?

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0 1000 2000 3000 4000 5000 6000 70000

200

400

600

800

1000

1200

1400

1600

1800

2000

0

10

20

30

40

50

60

70

80

90

100

Input Power (W)

Output Power (W)

Efficiency (%)

Speed (RPM)

Inp

ut a

nd O

utp

ut P

ow

er

(W)

Eff

icie

ncy

(%)

Maximum efficiencyη = 57.4%Maximum input power

1,072.7 W

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Vex Measured Motor Performance: CIM

0 1000 2000 3000 4000 5000 60000

50

100

150

200

250

300

350

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Current (A)

Torque (N·m)

Output Power (W)

Efficiency (%)

Speed (RPM)

Cur

rent

(A

), P

ow

er

(W),

and

Eff

icie

ncy

(%)

To

rque

(N

·m)



Max Current131.1 A



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0 1000 2000 3000 4000 5000 60000

50

100

150

200

250

0.0

0.5

1.0

1.5

2.0

2.5

Current (A)

Torque (N·m)

Output Power (W)

Efficiency (%)

Speed (RPM)

Cur

rent

(A

), P

ow

er

(W),

and

Eff

icie

ncy

(%)

To

rque

(N

·m)




Max Current89.4 A


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Vex Measured Motor Performance: BAG

0 2000 4000 6000 8000 10000 12000 140000

20

40

60

80

100

120

140

160

180

200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Current (A)

Torque (N·m)

Output Power (W)

Efficiency (%)

Speed (RPM)

Cur

rent

(A

), P

ow

er

(W),

and

Eff

icie

ncy

(%)

To

rque

(N

·m)



Maximum speed13,177.7 RPM

Max Current52.6 A


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Vex Measured Motor Performance: 775Pro

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 200000

50

100

150

200

250

300

350

400

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Current (A)

Torque (N·m)

Output Power (W)

Efficiency (%)

Speed (RPM)

Cur

rent

(A

), P

ow

er

(W),

and

Eff

icie

ncy

(%)

To

rque

(N

·m)


Maximum output power347.2 W @ 9,367.0 RPM

Maximum speed18,734.0 RPM

Max Current133.6 A


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CIM vs 775Pro

CIM Motor 775Pro Motor

CIM Motor 775Pro MotorTorque(N·m)

Speed(rpm)

Current(amps)

Power(watts)

Torque(N·m)

Speed(rpm)

Current(amps)

Power(watts)

Free Load 0.0 5,330 2.7 0.0 0.0 18,734 0.7 0

At Max Power 1.21 2,665 66.9 336.7 0.35 9,367 67.2 347.2

At Stall 2.41 0 131.1 0.0 0.71 0 133.6 0

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BAG vs 775Pro

BAG Motor 775Pro Motor

BAG Motor 775Pro MotorTorque(N·m)

Speed(rpm)

Current(amps)

Power(watts)

Torque(N·m)

Speed(rpm)

Current(amps)

Power(watts)

Free Load 0.0 13,178 1.8 0.0 0.0 18,734 0.7 0

At Max Power 0.22 6,589 27.2 148.7 0.35 9,367 67.2 347.2

At Stall 0.43 0 52.6 0.0 0.71 0 133.6 0

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0 10 20 30 40 50 60 700.0

0.5

1.0

1.5

2.0

2.5

0

20

40

60

80

100

120

140

160

Time, s

To

rque

, N·m

Cur

rent

, A

Locked Rotor Stall Performance

CIM

Mini CIM

BAG

775 Pro

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Questions

??

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Mini CIM vs BAG

0 1000 2000 3000 4000 5000 6000 70000

100

200

300

400

500

600

0

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

Tor

que

(oz

-in)

and

Pow

er (

wat

ts)

Effi

cien

cy (

%)

0 2000 4000 6000 8000 10000 12000 14000 160000

100

200

300

400

500

600

0

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

To

rqu

e (

oz-

in)

an

d P

ow

er

(wa

tts)

Effi

cie

ncy

(%

)





BAG Motor Mini CIM Motor

Note: Efficiencies are from CIM motor data scaled to BAG and Mini CIM speed range.

BAG Motor Mini CIM MotorTorque(oz-in)

Speed(rpm)

Current(amps)

Power(watts)

Torque(oz-in)

Speed(rpm)

Current(amps)

Power(watts)

Free Load 0.0 14000 1.8 0 0.0 6200 1.5 0

At Max Power 28.4 7000 21.4 147 100.3 3100 43.8 230

At Stall 56.0 0 41.0 0 198.4 0 86.0 0

theory and practice of permanent magnet, direct...

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