How does a DC Motor work?

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DC Motors & Generator. ▻Note that a DC motor always begins to act like a generator once the rotor wires start to move through the magnetic field. ▫ the induced ...
DC Motors

How does a DC Motor work?

26.1

CrossCross-section of DC motor Soft Iron Core (Rotor)

Magnetic field vector, B Wire length vector, dL

N

S

N

X

Force vector, df Permanent Magnet (Stator) Current, i

CrossCross-section of DC motor Rotor supported on bearings (free to rotate)

N

X

S

Generating ___________ torque

CrossCross-section of DC motor Switch direction of current flow after 90 degrees (the current switching process is called _______________) X

N

N

Rotation past 90 degrees

N

S

N X

Now generating _____ torque!

2 Commutator Bars DC

Two segment commutation on rotor

X

N

S

N

S

Now generating ______ torque!

%Torque vs. Angular Position

Torque

N

CrossCross-section of DC motor

100 50 0 0

90

180

270

Angular Position

360

DC Motors

26.2

4 Commutator Bars

24 Commutator Bars DC

DC

Torque

%Torque vs. Angular Position

N

S

N

Sixteen segment commutation on rotor

N

50 0

0

90

180

270

360

%Torque vs. Angular Position

100 50 0 0

Angular Position

Wire length vector, dL

Velocity vector, v Induced EMF, dV (voltage)

Note that an induced EMF always gives rise to a current whose magnetic field opposes the original change in magnetic flux - Lenz’s Law

ME 372 Circuit Model for Permanent Magnet DC Motor

Va

ia

La

360

that a DC motor always begins to act like a generator once the rotor wires start to move through the magnetic field  the induced “back EMF” is proportional to ____________________________  “back EMF” generates a ___________________ which opposes the applied current,  _________________ the force (torque) output of the motor

ME 360 Circuit Model for Permanent Magnet DC Motor ia +

Vb -

-

+

Ra

Va -

Va= applied armature voltage

Vb= back EMF

Ra= armature resistance

ia= armature current

La= armature inductance

270

DC Motors & Generator

+

Ra

180

► Note

Magnetic field vector, B

Assuming B, v, and dL are mutually perpendicular,

90

Angular Position

How does a DC Generator work?

+

S

N

100

Torque

Four segment commutation on rotor

Va= applied armature voltage Ra= armature resistance

Vb -

Vb= back EMF ia= armature current

DC Motors

26.3

PMDC Motor SteadySteady-State Equations ia =

1 Ra

(

)

from circuit

PMDC Motor SteadySteady-State Equations ► For

a given motor, Ra, Ka, and Kb are _________________

► Armature

Vb =

from dV= B v dL and v = rω

τ=

from df = ia dL X B and τ = rf

voltage Va, speed ω, and output torque τ are related by the 3 equations

► If

InIn-Class Exercise #1 =

Ra

=

Plot for InIn-Class Exercise #1 10

48 volts

=

0.17 N-m/amp

=

0.17 volt/rad/s 0.9 ohms

Determine the output torque, τa, for the speed assigned to your group 1) find back-EMF, Vb for your speed 2) find current, ia for your speed 3) find torque, τa for your speed

9 8 Torque, N-m

A small DC motor V a has these Ka parameter constants Kb

we know 2 of these, can solve for 3rd one

7 6 5 4 3 2 1 0 0

500

1000

1500

2000

2500

3000

Speed, RPM

Manufacturer’s Data

2nd InIn-Class Exercise A small DC motor V a has these Ka parameter constants Kb

=

Ra

=

?

volts

=

3.60 oz-in/amp

=

2.67 volt/KRPM 50 ohms

On a single graph, we will plot the torque vs. speed relationship for different input voltages 24, 18, 12, 6 VDC

DC Motors

InIn-Class Exercise #2

26.4

DC Tachometer Equations

2.00

Mechanical construction of a DC tachometer is essentially identical to DC motor

1.80

Torque, oz-in

1.60 1.40

ia =

1.20 1.00

1 (Va − Vb ) = 0 Ra

High impedance load, No current

0.80

Vb = k bω = Va

0.60 0.40 0.20

Output voltage proportional to angular velocity, ω

τ = k aia = 0

0.00 0

No current

1000 2000 3000 4000 5000 6000 7000 8000 9000 Speed, RPM

PMDC Motor Equation Part #2

Unit Conversions 1V = 1

N ⋅m →1 = A⋅ s

Substitute into units for the back-EMF constant, kb,

kb :

Vb = k bω

Va = R a i a + Vb

V N ⋅m = ⋅ rad / s rad V ⋅ A ⋅ s

Va = R a i a + k bω

τ = k a ia

k b = k a →τ = k bia

Multiply both sides by ia

Conclusion: __________________________ Electrical Power = Power Dissipated + Mechanical Power (Input) (as heat) (useful output)

PMDC Motor Equation Part #2 Va = R a i a + Vb

Vb = k bω

Va = R a i a + k bω

τ = k a ia

k b = k a →τ = k bia

PMDC Motor Equation Part #2b Va ia = R a ia2 + τω Electrical Power = Power Dissipated + Mechanical Power (Input) (as heat) (useful output)

Multiply both sides by ia

Efficiency = Electrical Power = Power Dissipated + Mechanical Power (Input) (as heat) (useful output)

Power Out Power In

DC Motors

Circuit Model for Permanent Magnet DC Generator

PMDC Generator Equations Vgen + R a ia = Vb

DC Motor/Generator

ia +

Vgen

Rexternal

-

k b = k a →τ = k bia

-

PMDC Motor Equation Part #3

Torque, τ

τ = k a ia

Multiply both sides by ia

Vb

Vgen= generated armature voltage Vb= back EMF Ra= armature resistance ia= armature current

τ stall

Vb = k bω

R externalia + R a ia = k bω

+

Ra

26.5

ω =0

Va = R a i a,stall → τ stall = k a

constant Va Speed, ω

At any point on load curve,

V − k bω Ra = a ia

ωNL=“no-load” speed (ia=0)

Va = k bω NL

DC Motor Commutation ► DC

motors require periodic switching of currents to maintain rotation (“commutation”)  conventional DC motors use ______________ to provide commutation, but  "brushless" DC motors which use ________________________ commutation have been developed.

Va Ra

Electrical Power + Power Dissipated = Mechanical Power (useful output) (as heat) (Input)

DC Motors

DC Brushed Motor Advantages ► _________________________________, _________________________________,

requiring only a voltage source, power opopamp, and analog control input for variable speed operation. ► __________________________________ through design variations ► __________________________________ without additional power input

26.6

DC Brushed Motor Disadvantages ► ____________________________, ____________________________,

the wear producing small particles which can affect the cleanliness of surrounding operations. ► High current through the brushes can cause them to burn out rapidly ► _________________________________________ which is primarily conducted away through the rotor shaft ► _______________________ are generated at the brush/rotor interface

DC Brushless Motor

DC Brushless Motor

► The

magnetic field in the rotor is provided by permanent magnets on the ___________

Permanent Magnet Rotor

► Hall

effect sensors (or resolver output) are used to signal a motor driver when to switch the current in the ___________ windings

► Motor

driver depends on the controller to set desired torque output Wound Wire Stator

DC Brushless Motor Disadvantages

DC Brushless Motor Advantages ► _________________________________________

and hence the heat conducted to the shaft is minimized. ► Due to the lack of brushes, motors can be operated at high torque and zero rpm indefinitely as long as the winding temperature does not exceed the limit. ► ________________________________________ or contaminate the surroundings

► Torque

ripple ____________________________ by design ► Motor operation requires the purchase of an _______________________________________ ► Rotor magnets can become demagnetized in high current or temperature environments ► Most motor drivers brake DC brushless motors by applying reverse current, in which almost as much power is expended to stop the motor as was required to start it moving