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Electric motors
KON-C2004 Mechatronics Basics
Tapio Lantela, Nov 7nd, 2016
Applications
Power range
http://www.dmaeuropa.com/Clients/Sulzer/News/tabid/3546/itemid/3334/Default.aspx
From milliwatts
http://small-generator.com/buy/index.php?main_page=product_info&cPath=2&products_id=44&zenid=7am2ohqmufajn06bafie386007
to megawatts
Speed range
http://www.celeroton.com/en/products/motors.html
From a couple hundred rpm
to hundreds of
thousandsof rpm
http://www.ebikes.ca/learn/hub-motors.html
Electric motors
DC
- Brushed
- Brushless
AC
- Synchronous
• Permanent magnet motor
• Field excitation
• Reluctance
- Asynchronous (Induction)
• Squirrel cage
• Wound rotor
Physics of a generic electric motor
Magnetic flux
density B
Radius r
Stator
Current -I
Force F
Current I
Angle ϑ
Rotor
Force F
Torque T
Magnetic flux density B
Current I
Length l
Number of turns N
Force F = BlI
Torque T = 2rF
2rFcos(ϑ)
= 2NrBlI = KtI
Induced voltage = Blv
=2NBlv
Blrω =2NBlrω = Keω
DC motor working principle
Simple two pole example
- In practise motors have three or more poles
http://www.pcbheaven.com/wikipages/How_DC_Motors_Work/
https://en.wikipedia.org/wiki/Brushed_DC_electric_motor
Brushed DC motor construction
http://www.electrical-knowhow.com/2012/05/classification-of-electric-motors.html
DC motor commutator
DC motor field generation
Permanent magnet
- Permanent magnet rotor (Brushless)
- Permanent magnet stator (Brushed)
Material saturation
limits field magnitude
Field coils (Brushed)
- Series wound
- Parallel (shunt) wound
- Separately excited
http://www.electrical4u.com/dc-servo-motors-theory-and-working-principle/
Electrical models of a DC motor
Equivalent circuit
http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed&section=SystemModeling
Mathematical model
Mechanical models of an electric motor
Physical model
Mathematical model
Time constants of a motor
Winding
inductance &
resistance
Rotor & load
inertia
Power losses
Resistive losses
- Proportional to the square of the current (torque)
- Resistance depends on temperature (0.4%/K)
Core losses
- Proportional to the rotating speed
Mechanical losses
- Bearing friction
• proportional to the rotating speed
- Damping (air etc.)
• proportional to the square of rotating speed
Additional losses
- Variable frequency drive harmonics etc.
Motor equations
Input power Pin = UI
Output power Pout = Tω
Resistive loss in windigs Pres = RI2
Back electromagnetic force Vbemf = Keω
Characteristics of a PMDC motor
Maximum torque and efficiency are speed dependent
Operating limits of a PMDC motor
http://www.electrocraft.com/products/pmdc/DPP720/
Field weakening
Reduce magnetic field flux density B
- Smaller B -> smaller torque constant Kt and BEMF constant Ke
- Smaller Kt -> less torque
- Smaller Ke -> more angular velocity
Field weakening
http://ecomodder.com/forum/showthread.php/bsfc-chart-thread-post-em-if-you-got-1466-26.html
Operating limits of a motor
Temperature
- Winding insulation melting temperature
- Permanent magnet demagnetization temperature
Voltage
- Winding insulation breakdown voltage
Mechanical strength
- Rotor breakdown speed
Commutation speed
- Drive/controller speed
Characteristics of a DC motor
Motor data
Assigned power rating
1 Nominal voltage
2 No load speed
3 No load current
4 Nominal speed
5 Nominal torque
6 Nominal current
7 Stall torque
8 Starting current
9 Max. efficiency
10 Terminal resistance
11 Terminal inductance
12 Torque constant
13 Speed constant
14 Speed / torque gradient
15 Mechanical time constant
16 Rotor inertia
12 W
12 V
12100 rpm
155 mA
8060 rpm
10.1 mNm
1.25 A
31.3 mNm
3.47 A
63 %
3.46 Ω
0.121 H
9.02 mNm / A-¹
1060 rpm / V-¹
406 rpm / mNm-1
9.56 ms
2.25 gcm²
Source: Maxon corp.
Four quadrant operation
Brushed DC motor velocity control
The torque is proportional to the current in the winding
Current is controlled by voltage
- Or usually with pulse width modulation, PWM
- If the PWM frequency is high enough, the current stays almost constant (small
fluctuations)
Brushed DC motor control
Motor needs large currents
- E.g. microcontroller signal not powerful enough for running the motor
- A separate motor drive circuit controls the motor current according to the
microcontroller signal
One signal for PWM, one for direction
M
M
Brushless DC motor (BLDC)
Permanent magnet rotor
Stator with windings
External commutation
- integrated position sensosr,
usually hall sensors
Almost service free
Withstands well short term overloading
- heat is transported effectively from the stator into the environment
More complex control system
BLDC commutation
http://www.mpoweruk.com/motorsbrushless.htm
BLDC commutation
AC motor
Two categories
- Asynchronous
- Synchronous
Input usually three phase sinusoidal AC voltage
Only bearings need service
Control with variable frequency drive
http://www.pump-zone.com/topics/motors/ac-motors-part-two-three-phase-operation/page/0/1
AC field generation
Three field coils (per pole)
- 120 °phase difference
http://tdflashzone.net23.net/1_6_Physics-Flashes.html
Synchronous AC: Permanent magnet
Permanent magnet AC motor is almost the same as BLDC.
Synchronous AC: Permanent magnet
https://www.ecnmag.com/article/2009/10/comparing-motor-control-techniques
Asynchronous AC: Induction
Stator field induces current in the bars which causes torque
- Requires slip to create induced currents
Types
- Squirrel cage
• Rotor made of conducting short circuited bars in steel frame
- Wound rotor
http://www.nidec.com/en-IN/technology/motor/basic/00026/?prt=1
AC motor control
Rotational speed is determined
by the frequency of the input voltage
Frequency is controlled with variable frequency drive/inverter
(taajuusmuuttaja in Finnish)
- Rectification of the three phase voltage to DC voltage
- The rectified DC voltage is converted e.g. with pulse width
modulation (PWM) to AC voltage with the needed frequency
- The AC voltage is fed to one of the three coils of the stator
according to the sensors of the control system.
Rated values of an induction motor
Rated values are for continuous duty
-
Rated voltage – winding insulation
Rated current – ohmic resistive losses
Rated field – magnetic saturation of the material
Rated power = T*omega
For a dimensioning a motor for a variable load, it is possible to
calculate an equivalent constant load or simulate the system
Motors for servo systems
Many designs: DC (brushed or brushless), AC
Integrated feedback sensors
Ability to tolerate short term overloads
Low inductance
- Small electric time constant
Low rotor inertial mass
- Small mechanical time constant
http://www.ustudy.in/node/5789
http://www.exlar.com/press_releases/1868
Summary
Electric motors can be found anywhere and for any power rating
They have excellent efficiency at proper loading conditions
- Usually this means a large enough rpm
Output power limited by temperature
- Can be overloaded for a short while
Maximum rotating speed limited by back emf / supply voltage
Questions?
More info on electric drives
- Advanced courses
• ELEC-E8407 – Electromechanics
• ELEC-E8405 - Electric Drives