Electric motors KON-C2004 Mechatronics Basics Tapio Lantela, Nov 2nd, 2015

Applications

Power range From milliwatts to megawatts

Speed range From a couple hundred rpm to hundreds of thousandsof rpm

Electric motors DC -Brushed -Brushless AC -Synchronous Permanent magnet motor Field excitation Reluctance -Asynchronous (Induction) Squirrel cage Wound rotor

Force F Magnetic flux density B Current I Force F = B l I Torque T Radius r Torque T = 2rFcos(ϑ) Angle ϑ Current I Current -I Magnetic flux density B Force F Torque T = 2rF = 2NrB l I = K t I Stator Rotor Induced voltage = B l v = B l rω Induced voltage = 2NB l v =2NB l rω = K e ω Physics of a generic electric motor

DC motor working principle Simple two pole example In practise motors have three or more poles

Brushed DC motor construction

DC motor commutator

DC motor field generation Permanent magnet -Permanent magnet rotor (Brushless) -Permanent magnet stator (Brushed) Field coils(Brushed) -Series wound -Parallel (shunt) wound -Separately excited Material saturation limits field magnitude

Electrical models of a DC motor Equivalent circuit Mathematical model

Mechanical models of an electric motor Physical model Mathematical model

Motor equations Input power P in = UI Electromagnetic torque T = K t I Output power P out = Tω Resistive loss in windigs P res = RI 2 Back electromagnetic force V bemf = K e ω

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.

Characteristics of a PMDC motor Maximum torque and efficiency are speed dependent

Operating limits of a PMDC motor

Field weakening Reduce magnetic field flux density B -Smaller B -> smaller torque constant K t and BEMF constant K e -Smaller K t -> less torque -Smaller K e -> more angular velocity

Field weakening

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

Source: Maxon corp. Characteristics of a DC motor Motor data Assigned power rating12 W 1 Nominal voltage12 V 2 No load speed12100 rpm 3 No load current155 mA 4 Nominal speed8060 rpm 5 Nominal torque10.1 mNm 6 Nominal current1.25 A 7 Stall torque31.3 mNm 8 Starting current3.47 A 9 Max. efficiency63 % 10 Terminal resistance3.46 Ω 11 Terminal inductance0.121 H 12 Torque constant9.02 mNm / A-¹ 13 Speed constant1060 rpm / V-¹ 14 Speed / torque gradient406 rpm / mNm Mechanical time constant9.56 ms 16 Rotor inertia2.25 gcm²

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 Commutating with integrated hall sensors and external electronics Almost service Withstands well short term overloading (heat is transported effectively from the stator into the environment) More complex control system

BLDC commutation

AC motor Several types Asynchronous Synchronous Input voltage one or three phase sinusoidal AC voltage Only bearings need service Control with variable frequency drive

AC field generation Three field coils (per pole) -120 °phase difference

Synchronous AC Permanent magnet AC motor is almost the same as BLDC.

Induction motor Conducting short circuited bars embeddes in steel frame Stator field induces current in the bars which causes torque

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

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.

small DC servo controller (8-30W) BIG AC servo controller (5-120kW) Source: and Servo controllers Decentralised controllers

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 Motors can be overloaded for a short while Output rpm limited by voltage

Questions? More info on electric drives Advanced courses ELEC-E Electromechanics ELEC-E Electric Drives