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Introduction to Electrical Drives
By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering
Dr. Ungku Anisa, December 2009 1
EEEB443 - Control & Drives
Definition of Electrical Drives
 Drives – system employed
for motion control
 Motion control requires
prime movers
 Electrical Drives – Drives
that employ Electric
Motors as prime movers
Electrical Drives -> Electric
Motor as Prime Mover
Prime Mover
Drives -> Motion Control
Dr. Ungku Anisa, December 2009 2
EEEB443 - Control & Drives
Advantages of Electrical Drives
 Flexible control characteristic
 particularly when power electronic converters are
employed
 Wide range of speed, torque and power
 High efficiency – low no load losses
 Low noise
 Low maintenance requirements, cleaner operation
 Electric energy easily transported
 Adaptable to most operating conditions
 Available operation in all four torque-speed quadrants
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 3
Conventional Electric Drives
 Ward-Leonard system –
introduced in 1890s
 Disadvantage :
 Bulky
 Expensive
 Inefficient
 Complex
Dr. Ungku Anisa, December 2009 4
EEEB443 - Control & Drives
Modern Electric Drives
 Small (compact)
 Efficient
 Flexible
 Interdisciplinary
Power Source Power Processing Unit Motor Load
Control
Reference
Control
Unit
feedback
Dr. Ungku Anisa, December 2009 5
EEEB443 - Control & Drives
Electric Drives Application
 Line Shaft Drives
 Oldest form
 Single motor,
multiple loads
 Common line
shaft or belt
 Inflexible
 Inefficient
 Rarely used
Dr. Ungku Anisa, December 2009 6
EEEB443 - Control & Drives
Electric Drives Application
 Single-Motor, Single-
Load Drives
 Most common
 Eg: electric saws,
drills, fans, washers,
blenders, disk-
drives, electric cars.
Dr. Ungku Anisa, December 2009 7
EEEB443 - Control & Drives
Electric Drives Application
 Multimotor Drives
 Several motors,
single mechanical
load
 Complex drive
functions
 Eg: assembly
lines, robotics,
military airplane
actuation.
Dr. Ungku Anisa, December 2009 8
EEEB443 - Control & Drives
Basic Components of Electric
Drives
 Power Source
 Motor
 Power Processing Unit (Electronic Converter)
 Control Unit
 Mechanical Load
Power Source
Power
Processing Unit
Motor Load
Control
Reference
Control
Unit
feedback
Dr. Ungku Anisa, December 2009 9
EEEB443 - Control & Drives
Basic Components of Electric
Drives - Motor
• Obtain power from electrical sources
• DC motors - Permanent Magnet or wound-field (shunt,
separately excited, compound, series)
• AC motors – Induction, Synchronous (wound –rotor, IPMSM,
SPMSM), brushless DC
• Selection of machines depends on many factors, e.g.:
Dr. Ungku Anisa, December 2009 10
EEEB443 - Control & Drives
Electrical
energy
Mechanical
energy
Motor
• application
• cost
• efficiency
• environment
• type of source available
Basic Components of Electric
Drives – Power Source
• Provides energy to electric motors
• Regulated (e.g: utility) or Unregulated (e.g. : renewable
energy)
• Unregulated power sources must be regulated for high
efficiency – use power electronic converters
• DC source
• batteries
• fuel cell
• photovoltaic
• AC source
• single- or three- phase utility
• wind generator
Dr. Ungku Anisa, December 2009 11
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Power Processing Unit
• Provides a regulated power supply to motor
• Enables motor operation in reverse, braking and variable
speeds
• Combination of power electronic converters
 Controlled rectifiers, inverters –treated as ‘black boxes’ with
certain transfer function
More efficient – ideally no losses occur
Flexible - voltage and current easily shaped through
switching control
Compact
Several conversions possible: AC-DC , DC-DC, DC-AC, AC-AC
Dr. Ungku Anisa, December 2009 12
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Power Processing Unit
 DC to AC:
Dr. Ungku Anisa, December 2009 13
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Power Processing Unit
 DC to DC:
Dr. Ungku Anisa, December 2009 14
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Power Processing Unit
 AC to DC:
Dr. Ungku Anisa, December 2009 15
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Power Processing Unit
 AC to AC:
Dr. Ungku Anisa, December 2009 16
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Control Unit
• Supervise operation
• Enhance overall performance and stability
• Complexity depends on performance requirement
• Analog Control – noisy, inflexible, ideally infinite bandwidth
• Digital Control – immune to noise, configurable, smaller
bandwidth (depends on sampling frequency)
• DSP/microprocessor – flexible, lower bandwidth, real-time
• DSPs perform faster operation than microprocessors
(multiplication in single cycle), complex estimations and
observers easily implemented
Dr. Ungku Anisa, December 2009 17
EEEB443 - Control & Drives
Basic Components of Electric
Drives – Component Selection
• Several factors affecting drive selection:
• Steady-state operation requirements
• nature of torque-speed profile, speed regulation, speed range,
efficiency, quadrants of operations, converter ratings
• Transient operation requirements
• values of acceleration and deceleration, starting, braking and reversing
performance
• Power source requirements
• Type, capacity, voltage magnitude, voltage fluctuations, power factor,
harmonics and its effect on loads, ability to accept regenerated power
• Capital & running costs
• Space and weight restrictions
• Environment and location
• Efficiency and reliability
Dr. Ungku Anisa, December 2009 18
EEEB443 - Control & Drives
DC or AC Drives?
DC Drives
AC Drives
(particularly Induction Motor)
Motor • requires maintenance
• heavy, expensive
• limited speed (due to
mechanical construction)
• less maintenance
• light, cheaper
• high speeds achievable (squirrel-
cage IM)
• robust
Control Unit Simple & cheap control even
for high performance drives
• decoupled torque and flux control
• Possible implementation using
single analog circuit
Depends on required drive
performance
• complexity & costs increase with
performance
• DSPs or fast processors required in high
performance drives
Performance Fast torque and flux control Scalar control – satisfactory in some
applications
Vector control – similar to DC drives
Dr. Ungku Anisa, December 2009 19
EEEB443 - Control & Drives
Torque Equation for Rotating
Systems
 Motor drives a load through a transmission system (eg. gears,
V-belts, crankshaft and pulleys)
 Load may rotate or undergo translational motion
 Load speed may be different from motor speed
 Can also have multiple loads each having different speeds,
some may rotate and some have translational motion
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 20
Motor Load
Te , m TL
Represent motor-load
system as equivalent
rotational system
Torque Equation for Rotating
Systems
• First order differential equation for angular frequency (or velocity)
• Second order differential equation for angle (or position)
 
2
2
dt
d
J
dt
d
J
T
T m
L
e





With constant inertia J,
 
dt
J
d
T
T m
L
e




Te , m
TL
Dr. Ungku Anisa, December 2009 21
EEEB443 - Control & Drives
Torque equation for equivalent motor-load system:
where:
J = inertia of equivalent motor-load system, kgm2
m = angular velocity of motor shaft, rads-1
Te = motor torque, Nm
TL = load torque referred to motor shaft, Nm
(1)
(2)
Torque Equation for Rotating
Systems with Gears
 Low speed
applications use
gears to utilize high
speed motors
 Motor drives two
loads:
 Load 1 coupled
directly to motor
shaft
 Load 2 coupled via
gear with n and n1
teeth
 Need to obtain
equivalent motor-
load system
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 22
Motor
Te
Load 1,
TL0
Load 2,
TL1
J0
J1
m
m
m1
n
n1
TL0
TL1
Motor
Te
J
Equivalent
Load , TL
m
TL
Torque Equation for Rotating
Systems with Gears
 Gear ratio a1 =
 Neglecting losses in the transmission:
 Hence, equivalent motor-load inertia J is:
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 23
Kinetic energy due
to equivalent inertia
=  kinetic energy of moving parts
1
2
1
0 J
a
J
J 

(3)
(4)
Torque Equation for Rotating
Systems with Gears
 If 1 = transmission efficiency of the gears:
 Hence, equivalent load torque TL is:
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 24
Power of the equivalent
motor-load system
=  power at the loads
1
1
1
0

L
L
L
T
a
T
T 
 (5)
Torque Equation for Rotating
Systems – Example 1
 Figure below shows a motor driving three loads. Assuming there are no
losses in the system, calculate the:
 total moment of inertia of the system referred to
the motor shaft
 amount of torque the motor must produce
to drive the loads
 output power of the motor
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 25
Motor
T e
Load 1,
T L1 = 10 Nm
Load 2,
T L2 = 10 Nm
Jm=1.5kgm-2
m 1500 rpm
N1
N2
N3
Load 3,
T L3 = 6 Nm
J1 = 2kgm-2
J2= 7kgm-2
J3= 5kgm-2
m3
500 rpm
m2
300 rpm
Torque Equation for Rotating
Systems with Belt Drives
 By neglecting slippage,
equations (4) and (5) can
still be used.
 However,
where:
Dm = diameter of wheel driven by motor
DL = diameter of wheel mounted on load shaft
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 26
L
m
D
D
a 
1 (6)
Torque Equation for Rotating
Systems with Translational Motion
 Motor drives two
loads:
 Load 1 coupled
directly to motor
shaft
 Load 2 coupled via
transmission
system converting
rotational to linear
motion
 Need to obtain
equivalent motor-
load system
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 27
Motor
Te
J
Equivalent
Load , TL
m
TL
Torque Equation for Rotating
Systems with Translational Motion
 Neglecting losses in the transmission:
 Hence, equivalent motor-load inertia J is:
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 28
Kinetic energy due
to equivalent inertia
=  kinetic energy of moving parts
2
1
1
0 









m
v
M
J
J

(7)
 If 1 = transmission efficiency of the transmission system:
 Hence, equivalent load torque TL is:
Torque Equation for Rotating
Systems with Translational Motion
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 29
Power of the equivalent
motor-load system
=  power at the loads and motor










m
L
L
v
F
T
T


1
1
1
0
(8)
Relation between Translational and
Rotational Motions
 The relationship between the torques and linear forces are:
 Relationship between linear and angular velocity:
 Hence, assuming the mass M is constant:
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 30
1
1 rF
T  m
m rF
T 

r
v 
dt
dv
M
F
Fm 
 1
dt
d
Mr
T
Tm

2
1 

Torque Equation for Rotating
Systems – Example 2
 An example of a hoist drive employing gears is shown below.
The system can be represented by an equivalent system shown
on the right. Write down the equation for the:
 Equivalent system moment of inertia
 Equivalent system load torque
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 31
Hoist drive
Equivalent system
Torque Equation for Rotating
Systems – Example 3
 If the motor is rated at 19kW, is the motor sufficient to drive
the two loads?
 The translational motion load now has to lift a weight of 1200
kg at the same speed of 1.5m/s. Is the motor still capable to
drive both loads at the same motor speed of 1420 rpm?
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 32
Components of Load Torque
• Load torque can be divided into:
• Friction torque – present at motor shaft and in various
parts of load.
• Viscous friction torque Tv – varies linearly with speed (Tv  m).
Exists in lubricated bearings due to laminar flow of lubricant
• Coulomb friction torque TC – independent of speed. Exists in
bearings, gears coupling and brakes.
• Windage torque Tw – exists due to turbulent flow of air or
liquid.
• Varies proportional to speed squared (Tw  m
2).
• Mechanical Load Torque TL - torque to do useful
mechanical work.
Dr. Ungku Anisa, December 2009 33
EEEB443 - Control & Drives
Mechanical Load Torque
• Torque to do useful mechanical work TL – depends on
application.
• Load torque is function of speed
• where k = integer or fraction
• Mechanical power of load:
• and
k
m
L
T 

m
L
T
P 
 m
m n
60
2
 
Angular speed
in rad/s
Speed
in rpm
Dr. Ungku Anisa, December 2009 34
EEEB443 - Control & Drives
Mechanical Load Torque
Dr. Ungku Anisa, December 2009 35
EEEB443 - Control & Drives
Mechanical Load Torque
 Torque independent
of speed , k = 0
 Hoist
 Elevator
 Pumping of water
or gas against
constant pressure
Dr. Ungku Anisa, December 2009 36
EEEB443 - Control & Drives
Mechanical Load Torque
 Torque proportional
to square of speed ,
k = 2
 Fans
 Centrifugal pumps
 Propellers
Dr. Ungku Anisa, December 2009 37
EEEB443 - Control & Drives
Mechanical Load Torque
 Torque inversely
proportional to
speed , k = -1
 Milling machines
 Electric drill
 Electric saw
Dr. Ungku Anisa, December 2009 38
EEEB443 - Control & Drives
Motor T- characteristic – variation of motor torque with speed
with all other variables (voltage and frequency) kept constant.
Loads will have their own T- characteristics.
Steady State Operating Speed
Synchronous motor
Induction motor
Separately excited
/ shunt DC motor
Series DC motor
SPEED
TORQUE
Dr. Ungku Anisa, December 2009 39
EEEB443 - Control & Drives
Steady State Operating Speed
• At constant
speed, Te= TL
• Steady state
speed is at
point of
intersection
between Te
and TL of the
steady state
torque
characteristics
TL
Te
Steady state
Speed, r
Torque
Speed
r2
r3
r1
Dr. Ungku Anisa, December 2009 40
EEEB443 - Control & Drives
By using power
electronic
converters, the
motor characteristic
can be varied
Steady State Stability
 Drives operate at steady-state speed (when Te = TL) only if the
speed is of stable equilibrium.
 A disturbance in any part of drive causes system speed to
depart from steady-state point.
 Steady-state speed is of stable equilibrium if:
 system will return to stable equilibrium speed when
subjected to a disturbance
 Steady-state stability evaluated using steady-state T-
characteristic of motor and load.
 Condition for stable equilibrium:
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 41
m
e
m
L
d
dT
d
dT


 (9)
Steady State Stability
 Evaluated using steady-state T- characteristic of motor and
load.
 Assume a disturbance causes speed drop to r’
 At the new speed r’,
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 42
Te TL
Steady-state point A
at speed = r
r
r’
Te’
TL’
Te’ > TL’
motor accelerates
operation restored to steady-
state point
m
T
Steady-state speed is of
stable equilibrium
m
e
m
L
d
dT
d
dT



 
dt
d
J
T
T m
L
e



Steady State Stability
 Let’s look at a different condition!
 Assume a disturbance causes speed drop to r’
 At the new speed r’,
Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 43
Te
TL
Steady-state point B
at speed = r
r
r’
TL’
Te’
Te’ < TL’
motor decelerates
operation point moves away
from steady-state point
m
T
Point B is at UNSTABLE
equilibrium
m
e
m
L
d
dT
d
dT



 
dt
d
J
T
T m
L
e



Torque-Speed Quadrant of
Operation
m
Te
Te
m
Te
m
Te
m

T
•Direction of positive
(forward) speed is
arbitrary chosen
•Direction of positive
torque will produce
positive (forward) speed
Quadrant 1
Forward motoring
Quadrant 2
Forward braking
Quadrant 3
Reverse motoring
Quadrant 4
Reverse braking
Dr. Ungku Anisa, December 2009 44
EEEB443 - Control & Drives
P = +ve
P = -ve
P = -ve
P = +ve
m
e
T
P 

Electrical energy
Mechanical energy
MOTOR
P = + ve
References
 El-Sharkawi, M. A., Fundamentals of Electric Drives,
Brooks/Cole Publishing Company, California, 2000.
 Dubey, G.K., Fundamentals of Electric Drives, 2nd ed., Alpha
Science Int. Ltd., UK, 2001.
 Krishnan, R., Electric Motor Drives: Modelling, Analysis and
Control, Prentice-Hall, New Jersey, 2001.
 Nik Idris, N. R., Short Course Notes on Electrical Drives,
UNITEN/UTM, 2008.
 Ahmad Azli, N., Short Course Notes on Electrical Drives,
UNITEN/UTM, 2008.
Dr. Ungku Anisa, December 2009 45
EEEB443 - Control & Drives

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459112057-1-Introduction-to-Electrical-Drives-ppt.ppt

  • 1. Introduction to Electrical Drives By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, December 2009 1 EEEB443 - Control & Drives
  • 2. Definition of Electrical Drives  Drives – system employed for motion control  Motion control requires prime movers  Electrical Drives – Drives that employ Electric Motors as prime movers Electrical Drives -> Electric Motor as Prime Mover Prime Mover Drives -> Motion Control Dr. Ungku Anisa, December 2009 2 EEEB443 - Control & Drives
  • 3. Advantages of Electrical Drives  Flexible control characteristic  particularly when power electronic converters are employed  Wide range of speed, torque and power  High efficiency – low no load losses  Low noise  Low maintenance requirements, cleaner operation  Electric energy easily transported  Adaptable to most operating conditions  Available operation in all four torque-speed quadrants Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 3
  • 4. Conventional Electric Drives  Ward-Leonard system – introduced in 1890s  Disadvantage :  Bulky  Expensive  Inefficient  Complex Dr. Ungku Anisa, December 2009 4 EEEB443 - Control & Drives
  • 5. Modern Electric Drives  Small (compact)  Efficient  Flexible  Interdisciplinary Power Source Power Processing Unit Motor Load Control Reference Control Unit feedback Dr. Ungku Anisa, December 2009 5 EEEB443 - Control & Drives
  • 6. Electric Drives Application  Line Shaft Drives  Oldest form  Single motor, multiple loads  Common line shaft or belt  Inflexible  Inefficient  Rarely used Dr. Ungku Anisa, December 2009 6 EEEB443 - Control & Drives
  • 7. Electric Drives Application  Single-Motor, Single- Load Drives  Most common  Eg: electric saws, drills, fans, washers, blenders, disk- drives, electric cars. Dr. Ungku Anisa, December 2009 7 EEEB443 - Control & Drives
  • 8. Electric Drives Application  Multimotor Drives  Several motors, single mechanical load  Complex drive functions  Eg: assembly lines, robotics, military airplane actuation. Dr. Ungku Anisa, December 2009 8 EEEB443 - Control & Drives
  • 9. Basic Components of Electric Drives  Power Source  Motor  Power Processing Unit (Electronic Converter)  Control Unit  Mechanical Load Power Source Power Processing Unit Motor Load Control Reference Control Unit feedback Dr. Ungku Anisa, December 2009 9 EEEB443 - Control & Drives
  • 10. Basic Components of Electric Drives - Motor • Obtain power from electrical sources • DC motors - Permanent Magnet or wound-field (shunt, separately excited, compound, series) • AC motors – Induction, Synchronous (wound –rotor, IPMSM, SPMSM), brushless DC • Selection of machines depends on many factors, e.g.: Dr. Ungku Anisa, December 2009 10 EEEB443 - Control & Drives Electrical energy Mechanical energy Motor • application • cost • efficiency • environment • type of source available
  • 11. Basic Components of Electric Drives – Power Source • Provides energy to electric motors • Regulated (e.g: utility) or Unregulated (e.g. : renewable energy) • Unregulated power sources must be regulated for high efficiency – use power electronic converters • DC source • batteries • fuel cell • photovoltaic • AC source • single- or three- phase utility • wind generator Dr. Ungku Anisa, December 2009 11 EEEB443 - Control & Drives
  • 12. Basic Components of Electric Drives – Power Processing Unit • Provides a regulated power supply to motor • Enables motor operation in reverse, braking and variable speeds • Combination of power electronic converters  Controlled rectifiers, inverters –treated as ‘black boxes’ with certain transfer function More efficient – ideally no losses occur Flexible - voltage and current easily shaped through switching control Compact Several conversions possible: AC-DC , DC-DC, DC-AC, AC-AC Dr. Ungku Anisa, December 2009 12 EEEB443 - Control & Drives
  • 13. Basic Components of Electric Drives – Power Processing Unit  DC to AC: Dr. Ungku Anisa, December 2009 13 EEEB443 - Control & Drives
  • 14. Basic Components of Electric Drives – Power Processing Unit  DC to DC: Dr. Ungku Anisa, December 2009 14 EEEB443 - Control & Drives
  • 15. Basic Components of Electric Drives – Power Processing Unit  AC to DC: Dr. Ungku Anisa, December 2009 15 EEEB443 - Control & Drives
  • 16. Basic Components of Electric Drives – Power Processing Unit  AC to AC: Dr. Ungku Anisa, December 2009 16 EEEB443 - Control & Drives
  • 17. Basic Components of Electric Drives – Control Unit • Supervise operation • Enhance overall performance and stability • Complexity depends on performance requirement • Analog Control – noisy, inflexible, ideally infinite bandwidth • Digital Control – immune to noise, configurable, smaller bandwidth (depends on sampling frequency) • DSP/microprocessor – flexible, lower bandwidth, real-time • DSPs perform faster operation than microprocessors (multiplication in single cycle), complex estimations and observers easily implemented Dr. Ungku Anisa, December 2009 17 EEEB443 - Control & Drives
  • 18. Basic Components of Electric Drives – Component Selection • Several factors affecting drive selection: • Steady-state operation requirements • nature of torque-speed profile, speed regulation, speed range, efficiency, quadrants of operations, converter ratings • Transient operation requirements • values of acceleration and deceleration, starting, braking and reversing performance • Power source requirements • Type, capacity, voltage magnitude, voltage fluctuations, power factor, harmonics and its effect on loads, ability to accept regenerated power • Capital & running costs • Space and weight restrictions • Environment and location • Efficiency and reliability Dr. Ungku Anisa, December 2009 18 EEEB443 - Control & Drives
  • 19. DC or AC Drives? DC Drives AC Drives (particularly Induction Motor) Motor • requires maintenance • heavy, expensive • limited speed (due to mechanical construction) • less maintenance • light, cheaper • high speeds achievable (squirrel- cage IM) • robust Control Unit Simple & cheap control even for high performance drives • decoupled torque and flux control • Possible implementation using single analog circuit Depends on required drive performance • complexity & costs increase with performance • DSPs or fast processors required in high performance drives Performance Fast torque and flux control Scalar control – satisfactory in some applications Vector control – similar to DC drives Dr. Ungku Anisa, December 2009 19 EEEB443 - Control & Drives
  • 20. Torque Equation for Rotating Systems  Motor drives a load through a transmission system (eg. gears, V-belts, crankshaft and pulleys)  Load may rotate or undergo translational motion  Load speed may be different from motor speed  Can also have multiple loads each having different speeds, some may rotate and some have translational motion Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 20 Motor Load Te , m TL Represent motor-load system as equivalent rotational system
  • 21. Torque Equation for Rotating Systems • First order differential equation for angular frequency (or velocity) • Second order differential equation for angle (or position)   2 2 dt d J dt d J T T m L e      With constant inertia J,   dt J d T T m L e     Te , m TL Dr. Ungku Anisa, December 2009 21 EEEB443 - Control & Drives Torque equation for equivalent motor-load system: where: J = inertia of equivalent motor-load system, kgm2 m = angular velocity of motor shaft, rads-1 Te = motor torque, Nm TL = load torque referred to motor shaft, Nm (1) (2)
  • 22. Torque Equation for Rotating Systems with Gears  Low speed applications use gears to utilize high speed motors  Motor drives two loads:  Load 1 coupled directly to motor shaft  Load 2 coupled via gear with n and n1 teeth  Need to obtain equivalent motor- load system Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 22 Motor Te Load 1, TL0 Load 2, TL1 J0 J1 m m m1 n n1 TL0 TL1 Motor Te J Equivalent Load , TL m TL
  • 23. Torque Equation for Rotating Systems with Gears  Gear ratio a1 =  Neglecting losses in the transmission:  Hence, equivalent motor-load inertia J is: Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 23 Kinetic energy due to equivalent inertia =  kinetic energy of moving parts 1 2 1 0 J a J J   (3) (4)
  • 24. Torque Equation for Rotating Systems with Gears  If 1 = transmission efficiency of the gears:  Hence, equivalent load torque TL is: Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 24 Power of the equivalent motor-load system =  power at the loads 1 1 1 0  L L L T a T T   (5)
  • 25. Torque Equation for Rotating Systems – Example 1  Figure below shows a motor driving three loads. Assuming there are no losses in the system, calculate the:  total moment of inertia of the system referred to the motor shaft  amount of torque the motor must produce to drive the loads  output power of the motor Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 25 Motor T e Load 1, T L1 = 10 Nm Load 2, T L2 = 10 Nm Jm=1.5kgm-2 m 1500 rpm N1 N2 N3 Load 3, T L3 = 6 Nm J1 = 2kgm-2 J2= 7kgm-2 J3= 5kgm-2 m3 500 rpm m2 300 rpm
  • 26. Torque Equation for Rotating Systems with Belt Drives  By neglecting slippage, equations (4) and (5) can still be used.  However, where: Dm = diameter of wheel driven by motor DL = diameter of wheel mounted on load shaft Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 26 L m D D a  1 (6)
  • 27. Torque Equation for Rotating Systems with Translational Motion  Motor drives two loads:  Load 1 coupled directly to motor shaft  Load 2 coupled via transmission system converting rotational to linear motion  Need to obtain equivalent motor- load system Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 27 Motor Te J Equivalent Load , TL m TL
  • 28. Torque Equation for Rotating Systems with Translational Motion  Neglecting losses in the transmission:  Hence, equivalent motor-load inertia J is: Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 28 Kinetic energy due to equivalent inertia =  kinetic energy of moving parts 2 1 1 0           m v M J J  (7)
  • 29.  If 1 = transmission efficiency of the transmission system:  Hence, equivalent load torque TL is: Torque Equation for Rotating Systems with Translational Motion Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 29 Power of the equivalent motor-load system =  power at the loads and motor           m L L v F T T   1 1 1 0 (8)
  • 30. Relation between Translational and Rotational Motions  The relationship between the torques and linear forces are:  Relationship between linear and angular velocity:  Hence, assuming the mass M is constant: Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 30 1 1 rF T  m m rF T   r v  dt dv M F Fm   1 dt d Mr T Tm  2 1  
  • 31. Torque Equation for Rotating Systems – Example 2  An example of a hoist drive employing gears is shown below. The system can be represented by an equivalent system shown on the right. Write down the equation for the:  Equivalent system moment of inertia  Equivalent system load torque Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 31 Hoist drive Equivalent system
  • 32. Torque Equation for Rotating Systems – Example 3  If the motor is rated at 19kW, is the motor sufficient to drive the two loads?  The translational motion load now has to lift a weight of 1200 kg at the same speed of 1.5m/s. Is the motor still capable to drive both loads at the same motor speed of 1420 rpm? Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 32
  • 33. Components of Load Torque • Load torque can be divided into: • Friction torque – present at motor shaft and in various parts of load. • Viscous friction torque Tv – varies linearly with speed (Tv  m). Exists in lubricated bearings due to laminar flow of lubricant • Coulomb friction torque TC – independent of speed. Exists in bearings, gears coupling and brakes. • Windage torque Tw – exists due to turbulent flow of air or liquid. • Varies proportional to speed squared (Tw  m 2). • Mechanical Load Torque TL - torque to do useful mechanical work. Dr. Ungku Anisa, December 2009 33 EEEB443 - Control & Drives
  • 34. Mechanical Load Torque • Torque to do useful mechanical work TL – depends on application. • Load torque is function of speed • where k = integer or fraction • Mechanical power of load: • and k m L T   m L T P   m m n 60 2   Angular speed in rad/s Speed in rpm Dr. Ungku Anisa, December 2009 34 EEEB443 - Control & Drives
  • 35. Mechanical Load Torque Dr. Ungku Anisa, December 2009 35 EEEB443 - Control & Drives
  • 36. Mechanical Load Torque  Torque independent of speed , k = 0  Hoist  Elevator  Pumping of water or gas against constant pressure Dr. Ungku Anisa, December 2009 36 EEEB443 - Control & Drives
  • 37. Mechanical Load Torque  Torque proportional to square of speed , k = 2  Fans  Centrifugal pumps  Propellers Dr. Ungku Anisa, December 2009 37 EEEB443 - Control & Drives
  • 38. Mechanical Load Torque  Torque inversely proportional to speed , k = -1  Milling machines  Electric drill  Electric saw Dr. Ungku Anisa, December 2009 38 EEEB443 - Control & Drives
  • 39. Motor T- characteristic – variation of motor torque with speed with all other variables (voltage and frequency) kept constant. Loads will have their own T- characteristics. Steady State Operating Speed Synchronous motor Induction motor Separately excited / shunt DC motor Series DC motor SPEED TORQUE Dr. Ungku Anisa, December 2009 39 EEEB443 - Control & Drives
  • 40. Steady State Operating Speed • At constant speed, Te= TL • Steady state speed is at point of intersection between Te and TL of the steady state torque characteristics TL Te Steady state Speed, r Torque Speed r2 r3 r1 Dr. Ungku Anisa, December 2009 40 EEEB443 - Control & Drives By using power electronic converters, the motor characteristic can be varied
  • 41. Steady State Stability  Drives operate at steady-state speed (when Te = TL) only if the speed is of stable equilibrium.  A disturbance in any part of drive causes system speed to depart from steady-state point.  Steady-state speed is of stable equilibrium if:  system will return to stable equilibrium speed when subjected to a disturbance  Steady-state stability evaluated using steady-state T- characteristic of motor and load.  Condition for stable equilibrium: Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 41 m e m L d dT d dT    (9)
  • 42. Steady State Stability  Evaluated using steady-state T- characteristic of motor and load.  Assume a disturbance causes speed drop to r’  At the new speed r’, Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 42 Te TL Steady-state point A at speed = r r r’ Te’ TL’ Te’ > TL’ motor accelerates operation restored to steady- state point m T Steady-state speed is of stable equilibrium m e m L d dT d dT      dt d J T T m L e   
  • 43. Steady State Stability  Let’s look at a different condition!  Assume a disturbance causes speed drop to r’  At the new speed r’, Dr. Ungku Anisa, December 2009 EEEB443 - Control & Drives 43 Te TL Steady-state point B at speed = r r r’ TL’ Te’ Te’ < TL’ motor decelerates operation point moves away from steady-state point m T Point B is at UNSTABLE equilibrium m e m L d dT d dT      dt d J T T m L e   
  • 44. Torque-Speed Quadrant of Operation m Te Te m Te m Te m  T •Direction of positive (forward) speed is arbitrary chosen •Direction of positive torque will produce positive (forward) speed Quadrant 1 Forward motoring Quadrant 2 Forward braking Quadrant 3 Reverse motoring Quadrant 4 Reverse braking Dr. Ungku Anisa, December 2009 44 EEEB443 - Control & Drives P = +ve P = -ve P = -ve P = +ve m e T P   Electrical energy Mechanical energy MOTOR P = + ve
  • 45. References  El-Sharkawi, M. A., Fundamentals of Electric Drives, Brooks/Cole Publishing Company, California, 2000.  Dubey, G.K., Fundamentals of Electric Drives, 2nd ed., Alpha Science Int. Ltd., UK, 2001.  Krishnan, R., Electric Motor Drives: Modelling, Analysis and Control, Prentice-Hall, New Jersey, 2001.  Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.  Ahmad Azli, N., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008. Dr. Ungku Anisa, December 2009 45 EEEB443 - Control & Drives