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