# Motors and Generators

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1 Motors and Generators Electro-mechanical devices: convert electrical energy to mechanical motion/work and vice versa Operate on the coupling between currentcarrying conductors and magnetic fields Governed by a set of fundamental principles

2 Magnetism Magnets are composed of north and south pole pairs. B-field lines go from the north to the south poles. N S

3 Principle #1 Current in a conductor results in a magnetic field around the conductor. Use the righthand rule to determine the field direction. i B

4 Principle #2 Moving a conductor in a magnetic field induces a voltage across the conductor according to B S N

5 Motion of a Coil in a B-Field

6 Commutation

7 Motion of a Coil in a B-Field

8 Motion of a Coil (cont.)

9 Commutation

10 Commutation (cont.)

11 Commutation: Multiple Coils

12 Principle #3 Passing a current through a conductor in a magnetic field will result in a force acting on the conductor according to B S N

13 B S i - v F + V app Step 1: Conductor initially at rest. Apply voltage; produces current; produces downward force; conductor accelerates downward; sees non-zero downward velocity. N

14 B S - + v V back F i - + V app Step 2: Conductor moving downward; produces voltage in conductor; superimposes with applied voltage; reduces effective voltage; reduces current; force reduced, still accelerating. N

15 B S - + V back - + V app Step 3: Conductor downward velocity produces V back equal to V app ; zero current flowing in conductor; zero force; constant velocity. v N

16 How does a DC Motor work? Wire length vector, dl

17 Cross-section of DC motor Soft Iron Core (Rotor) N N S Permanent Magnet (Stator)

18 Cross-section of DC motor Rotor supported on bearings (free to rotate) N X N S Generating torque

19 Cross-section of DC motor N N S X Still generating torque

20 Cross-section of DC motor Rotation past 90 degrees: N N S X Now generating torque!

21 Cross-section of DC motor of current flow after 90 degrees (the current switching process is called ) X N N S Now generating torque!

22 2 Commutator Bars DC Brushes; fixed Two segment commutation on rotor N X N S %Torque vs. Angular Position Torque Angular Position

23 4 Commutator Bars DC Four segment commutation on rotor N N S %Torque vs. Angular Position Torque Angular Position

24 24 Commutator Bars DC Sixteen segment commutation on rotor N N S %Torque vs. Angular Position Torque Angular Position

25 How does a DC Generator work? Wire length vector, dl

26 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 back EMF is to angular velocity back EMF generates a current which the applied current, reduces the force (torque) output of the motor

27 Circuit Model for Permanent Magnet DC Motor i a + + V a R a V b - V a = applied armature voltage R a = armature resistance - V b = back EMF i a = armature current

28 PMDC Motor Steady-State Equations from circuit from dv= B v dl and v = rω from df = i a dl X B and τ = rf

29 PMDC Motor Steady-State Equations For a given motor, R a, K a, and K b are constants Armature voltage V a, speed ω, and output torque τ are related by the 3 equations

30 PMDC Motor Equation Part #3 τ stall Torque, τ Speed, ω At any point on load curve, ω NL = no-load speed (i a =0)

31 Number Assignments - Exercise #1 Student Group Speed (RPM) Speed (rad/sec) Student Group Speed (RPM) Speed (rad/sec) # # # # # # # #

32 In-Class Exercise #1 A small DC motor has these parameter constants V a = 48 volts K a = 0.17 N-m/amp K b = 0.17 volt/rad/s R a = 0.9 ohms Determine the output torque, τ a, for the speed assigned to your group 1) find back-emf, V b for your speed 2) find current, i a for your speed 3) find torque, τ a for your speed

33 Plot for In-Class Exercise #1 Torque, N-m Speed, RPM

34 Manufacturer s Data

35 2nd In-Class Exercise A small DC motor has these parameter constants V a =? volts K a = 3.60 oz-in/amp K b = 2.67 volt/krpm R a = 50 ohms On a single graph, we will plot the torque vs. speed relationship for different input voltages - 24, 18, 12, 6 VDC

36 Number Assignments - Exercise #2 Both 1000 and 3000 RPM Group V a, volts Group #1 24 VDC #5 #2 18 VDC #6 #3 12 VDC #7 #4 6 VDC #8 Both 5000 and 7000 RPM

37 In-Class Exercise #2 Torque, oz-in Speed, RPM

38 In-Class Exercise - Solution volts 12 volts 18 volts 24 volts Torque, oz-in Speed, RPM

39 In-Class Exercise - Solution Torque, oz-in Speed, RPM

40 PMDC Motor Equation Part #2 V = R i + V V = ω a a a b b k b τ = k i a a

41 PMDC Motor Equation Part #2b V i a a = R a i 2 a +τω Electrical Power = Power Dissipated + Mechanical Power (Input) (as heat) (useful output)

42 Circuit Model for Permanent Magnet DC Generator i a DC Motor/Generator + V gen R a V b + - R external - V gen = generated armature voltage V b = back EMF R a = armature resistance i a = armature current

43 PMDC Generator Equations V + R i = V V = ω gen a a b b k b τ = k i a a

44 DC Motor Commutation DC motors require periodic switching of currents to maintain rotation ( commutation ) conventional DC motors use brushes to provide commutation, but "brushless" DC motors which use electronic commutation have been developed.

45 DC Brushed Motor Advantages Simplicity of operation, requiring only a voltage source, power op-amp, and analog control input for variable speed operation. Torque ripple can be easily minimized through design variations Dynamic braking capability without additional power input

46 DC Brushed Motor Disadvantages The brushes wear, 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 Heat is generated in the rotor windings which is primarily conducted away through the rotor shaft Small sparks are generated at the brush/rotor interface

47 DC Brushless Motor The magnetic field in the rotor is provided by permanent magnets on the Hall effect sensors (or resolver output) are used to signal a motor driver when to switch the current in the Motor driver depends on the controller to set desired torque output

48 DC Brushless Motor Permanent Magnet Rotor Wound Wire Stator

49 DC Brushless Motor Advantages No appreciable heat is generated in the rotor 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. No brushes to wear out or contaminate the surroundings

50 DC Brushless Motor Disadvantages Torque ripple is hard to minimize by design Motor operation requires the purchase of an electronic motor driver 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

51 Experimental Results #1 8 Torque, N-m Find the motor constants: k b, k a, R a Va = 40 volts Va = 60 volts Va = 80 volts Va = 100 volts Speed, rad/sec

52 DC Tachometer Equations i Mechanical construction of a DC tachometer is essentially identical to DC motor a = 1 R a ( V V ) a b = 0 High impedance load, No current V b = k b ω = V a Output voltage proportional to angular velocity, ω τ = k a i a = 0 No current

53 DC Motor - Magnetic Field Generation Magnetic field on the stator can be generated two ways with a permanent magnet (PM) electro-magnetically with wound coils Wound DC motors Series wound Shunt wound Compound wound ( series and shunt windings)

54 Series Wound DC Motor i f = i a + + V in R f R a V b - - V in = input voltage R a = armature resistance R f = field resistance V b = back EMF i a = armature current i f = field current

55 Series Wound DC Motor Large starting torque available R f is small a few turns of large gage wire are used Torque Speed

56 Shunt Wound DC Motor i f + i a i a + + V in R f R a V b - i f -

57 Shunt Wound DC Motor Used for both fixed & variable speeds R f is large several turns of small gage wire are used Torque Speed

58 Wound Motor Speed Control Change V in increase or reduce speed Increase field resistance reduces i f reduces K a and K b Increase armature resistance reduces V b reduce ω

59 Compound Wound DC Motor i f1 i a V in + - R f1 R f2 R a V b i f2 - + Has both a series and a shunt wound field

60 Separately Excited DC Motor i a V in - R a V b - i f - V f Acts like a permanent magnet DC motor (if a constant field excitation is used)

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