Session #18 Motors. R w+ - T, ω. Dan Frey. Figure by MIT OCW.

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1 Session #18 Motors Figure by MIT OCW T, ω R w - E i V Dan Frey -

2 Current versus Externally Applied Load I used a NiCd battery pack I discharged it across a (physically) big variable resistance i meas i pred ( R) The model can t fit the data well 10 5 data Or else the model must include a resistance that is a function of current R i () j 2 1 internal resistance model R L, R i measj

3 A Better Way to Understand a Battery e e LOAD Separator Positive Electrode (Cathode) Negative Electrode (Anode) Electrolyte Figure by MIT OCW

4 A Better Model for Battery i = kce E A / RT The variable E A denotes the reaction s required activation energy which is proportional to voltage So, we expect current (i) and terminal voltage (v) will be related by a rate equation of the form i = cv ke 25 ln i = ln k cv 2 log i 15 1 data model Voltage

5 DC Permanent Magnet Motor Parts of an Electric Motor NORTH F = q( E v B) FIELD MAGNET Armature Axle Commutator F Brushes SOUTH To Battery Figure by MIT OCW

6 Discussion Question: How can I design a DC motor to provide high stall torque? Parts of an Electric Motor NORTH F = q( E v B) FIELD MAGNET Armature Axle Commutator F Brushes SOUTH To Battery Figure by MIT OCW

7 A Model of a Motor (Steady State) E = V R w i T, ω R w - E i V - back emf

8 What is the Purpose of These Features? "" Tab Notch Figure by MIT OCW

9 N Brush Generator Mechanical Motor A B o F α Axis Neutral S Figure by MIT OCW

10 Torque Speed Curves Note, conventionally, speed is on the x axis and Torque is on the Y Speed (rpm) No load speed 7V 6V 4V 3V Stall torque Torque (Nm)

11 Torque Current Curves 7 6 Same behavior at all voltages! Current (Amps) Why doesn t the origin? Stall torque No load speed Torque (Nm) 7V 6V 4V 3V

12 Back emf versus speed 7 6 Back EMF (V) V 6V 4V 3V pred w (rad/sec)

13 Concept Question Variable resistance Coupling BATTERY DC Permanent magnet motors Variable resistance As the resistance is increased: 1) The shaft speed rises monotonically 2) The shaft speed drops monotonically 3) The shaft speed rises, reaches a maximum, then falls 4) The shaft speed fall, reaches a minimum, then rises Figure by MIT OCW

14 Discussion Question: How do the things I might do to raise stall torque affect back emf? E = V R w i T, ω R w - E i V -

15 First Law Applied to a Motor (Steady State) Tω = ηvi T, ω R w - E i V - back emf

16 Speed Control for DC Motors Figure removed for copyright reasons See datasheet information for Jeti 300 MC brush motor controller

17 Modeling for Optimization BATTERY LIFETIME MOTOR POWER OUTPUT Duration (minutes) Throttle = 10% Output Power (Watts) Throttle = 100% 10 5 Throttle = 100% Shaft Speed (rad/s) Throttle = 10% Shaft Speed (rad/s)

18 Brushless DC Motors Shaft position sensed Based on position, different stator windings are energized Rotor Stator Pros More efficient Higher power density Less noise Longer life Permanent Magnet Cons Control electronics Cost Figure by MIT OCW

19 High Power Electric Motors: Brushless vs Brushed Predator by Plettenberg Motors (Germany) DC Brushless for R/C Aircraft Peak Output: 11KW (1475 HP) Speed: 6,000 RPM Power In: 51 V, 215 A Mass: 1550 g (342 lbs) Power Density: 71 KW/Kg S28-BP-400X by Magmotor Corporation DC Brushed Motor Peak Output: 6 KW (8HP) Speed: 4900 RPM Power In: 48 V, 125 A Mass: 313 Kg (69 lbs) Power Density: 19 KW/Kg

20 Stepper Motors Radially magnetized permanent magnet Diagrams removed for copyright reasons Variable reluctance (no permanent magnet)

21 Single phase AC Motors S N S N S N S N - STEP - 1 STEP - 2 S N N S N S N S - STEP - 3 STEP - 4 Figure by MIT OCW

22 Three phase AC Motors Winding 2a Winding 3a Winding 1a S Winding 1b Winding 3b N Winding 2b A phase sequence of will spin the magnet in a clockwise direction A phase sequence of will spin the magnet in a counter-clockwise direction Figure by MIT OCW

23 Figures removed for copyright reasons Several screenshots of McMaster-Carr online catalog: NEMA DC motors Brushless NEMA DC motors NEMA dual-mount single-phase AC motors NEMA dual-mount three-phase AC motors

24 Next Steps Friday 28 April Lab at 2PM Now that there is no HW, lab is voluntary I will tailor it to projects as requested Tuesday 2 May Actuators?