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Introduction to Motors Kurt Heinzmann DEKA Research & Development Corp. Christopher Mikus BAE Systems January 2005 Introduction to Motors Topics 1. Manufacturers' torque curves and specification sheets 2. How to manage motor temperature rise 3. Gear ratio 4. Review of motors from the Kit of Parts 5. Which motor for which application on a robot? Note • These slides have been edited since the presentation on 7 Jan 2005. – Distinction has been made between torque constant Kt and voltage constant Ke, because, although in an ideal motor, K = Kt = Ke, Kt and Ke differ significantly in a gearmotor. Some of the motors in the kit are gearmotors. – New material was added • Advice balloons • Comparison of motors in the Kit • Clarification of gear ratio selection Steps • • • • • • • • • • • • Assumptions and approximations Power Power loss in the mechanism Power required at the motor Power loss in the motor Basic motor theory Important motor parameters Power loss in the motor Power loss in other electrical components Gear ratios Comparison Batteries Assumptions and Approximations • Steady operation – We will not discuss acceleration requirements • Linear systems – We will represent nonlinear phenomena as linear • Simple motor analysis – Study only two power loss parameters • Loss due to electrical resistance • Loss due to friction and damping, combined in one fixed value Example: Simplify. Assume fixed free current (combine the effects of friction and damping) Example motor 3.0 2.5 y = 0.11x + 0.53 Ifree, A 2.0 Current 1.5 Linear (Current) Free current per data sheet 1.0 0.5 0.0 0 2 4 6 8 Voltage, V 10 12 14 Power • Power is a measure of how fast work gets done. • POWER = EFFORT x FLOW “EFFORT” – force – torque – pressure – voltage – thinking “FLOW” –travel speed –rotating speed –flow of fluid –flow of electrons –doing Power Loss in the Mechanism • Some power from the motor is lost due to friction in the mechanism – Gears, belts, cables – Bearings, guides – Tires, balls, or other deformable items – Damage Cooling a hot motor with snow or cold spray is not a – Contamination suggested solution to heat • Power loss is heat generation. Changing the temperature of a motor’s components too quickly can cause permanent damage. Design your robot well to prevent motor overheating Power required at the motor • Power at the motor = power required at the point of use + power lost in the mechanism • Power loss is heat Power loss in the motor • Power is lost in the motor due to friction, damping, and electrical resistance • Power loss is heat Design your robot’s drive train such that it won’t bind under stress and add excessive friction to your system. Reduce friction and loading by properly supporting axles with bearings and pillow blocks. Reduce side loading by supporting both ends of axles and drive shafts. Basic Motor Theory • Torque is rotating EFFORT, speed is rotating motion (“FLOW”) – Torque = force x radius • Voltage is electrical EFFORT, current is FLOW of electrons • Power = EFFORT x FLOW – Mechanical power P(out) = torque x speed – Electrical power P(in) = voltage x current • Shaft power = power in – power loss – Power loss is sum of electrical loss and mechanical loss Basic Motor Theory Important motor parameters • Stall torque ( stall ) • Stall current ( istall ) • Free speed ( free ) • Free current ( ifree ) Basic Motor Theory • Important motor parameters Torque constant ( Kt ) –Torque is proportional to current – Units: newton-metres ampere (Nm/A) • Voltage constant ( Ke ) –Motor internal voltage is proportional to speed volts _ – Units: V/(rad/s) radian/second • Torque loss ( loss) – We will derive this from free current – Unit: newtons (N) • Resistance (R) – Ohm’s law – Unit: ohm () Units, Conversions International System (SI) of units Item Force Distance Speed Torque Angle Speed Time Voltage Current Power Resistance Energy Pressure Flow Symbol used Comment here Mechanical effort Mechanical displacement Travelling speed Turning effort Angular displacement Rotating speed Don’t have much V Electrical effort i P R AbbrevSI unit iation newton N metre m metre/second m/s newton metre Nm radian rad radian/second rad/s second s volt V Electrical flow ampere Rate of work watt Cause of power loss as heat ohm Work A W Alternate unit lb. In. mph lb-in degree rpm min., h hp Conversion 4.45 N = 1lb. 0.0254 m = 1 in. 0.45 m/s = 1 mph 2 rad = 360° 0.105 rad/s = 1 rpm 3600 s = 1 h 746 W = 1 hp joule (Nm) J pascal (N/m2) Pa Fluid effort 3 Fluid flow (at stated pressure) cubic metre/s m /s ft-lb psi CFM 6900 Pa = 1 psi 0.00047 m3/s = 1 CFM Prefixes: m = milli- = one thousandth (mm, mNm) k = kilo- = one thousand (km, kW) Why use SI units? • Easier than U.S. Customary units • Electrical power gets converted to mechanical power. – If you express electrical power and mechanical power in watts, you know what’s happening at both ends of the motor. – Would you like to convert volts-times-amperes to horsepower? • Advice: Convert to SI units before doing any other calculation. • Consolation: you can always convert back. Basic Motor Theory Direct Current (DC), Permanent-Magnet (PM), BrushCommutated Motor FIRST rules do not allow you to modify the internal components of a motor. Read the current year's rules to understand how you may modify gear boxes if at all. Basic Motor Theory Important motor parameters Given: stall, istall, free, ifree and V, Find: Kt, Ke, loss(free), and R. Some motors have an internal circuit breaker, which will stop the motor, or PTC thermistor*, which will stop or slow the motor by increasing its electrical resistance, if the motor gets too hot. After the motor cools, it runs normally again. Examples: Window motor Sliding door motor *PTC thermistor - resistor with a positive temperature coefficient Find torque constant Kt and voltage constant Ke Find torque loss loss(free) Find resistance R Calculate current, speed, power and efficiency Example Motor From data sheet: stall = 0.65 Nm istall = 148 A free = 2513 rad/s ifree = 1.5 A From equation 3a: Kt = 0.65 Nm / (148.0-1.5) A = 0.0044 Nm/A From equation 3b: Ke = (12 V -1.5 A*0.081 )/ 2513 rad/s = 0.0047 V/(rad/s) From equation 4: loss(free) = 0.0044 Nm/A x 1.5 A = 0.0066 Nm From equation 5: R = 12 V /148 A = 0.081 Equations 6 - 11 allow us to calculate the following performance curves as a function of torque (with constant voltage): • • • • • • current speed output power input power power loss efficiency (6) (7) (8) (9) (10) (11) Example Motor - Current Example motor 160 148 A Speed (rad/s); Power (W) 140 120 100 80 60 40 20 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Example Motor - Speed Example motor 2500 Speed (rad/s); Power (W) 2000 1500 1000 500 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Example Motor - Power output Example motor Speed (rad/s); Power (W) 2000 1500 1000 500 407 W 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Example Motor - Input Power Example motor 2000 1800 W Speed (rad/s); Power (W) Output power, W Input power, W 1500 1000 500 407 W 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Example Motor - Power loss Example motor 2000 1800 W Output power, W Speed (rad/s); Power (W) Power loss, W Input power, W 1500 1000 Best operation is to the left of where these lines cross. 500 407 W 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Example Motor - Efficiency Example motor 100 90 Speed (rad/s); Power (W) 80 76% 70 60 50 40 30 20 10 0 0.00 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0.70 Motor performance based on data sheet Example motor 2500 250 Output power, W Speed, rad/s Power loss, W Current, A Efficiency 200 1800 W 148 A 1500 1000 150 100 76% 500 50 133 W 0 0.00 407 W 0.10 0.20 0.30 0.40 Torque (Nm) 0.50 0.60 0 0.70 Current (A); Efficiency (%) Speed (rad/s); Power (W) 2000 Real World: Power loss 14 AWG wire: 12 AWG wire: 10 AWG wire: 6 AWG wire: 3.0 m/ft. 1.9 m/ft. 1.2 m/ft. 0.5 m/ft. (Copper at 65 °C) Example motor, stalled for approximately 2 s 160 16 140 14 Example motor, stalled for approximately 2 s 120 12 100 10 Motor winding temperature measurement 80 8 Current Motor terminal voltage 60 Voltage, V Current, A; Temperature, °C; Resistance, mOhm ~ Smoke ~ 6 Battery voltage 40 4 20 2 0 0 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time, s •This circuit was not properly protected (wrong circuit breaker) •Measuring thermocouple was inserted near windings (windings got hotter than thermocouple) •Brushes got hotter than windings Example motor, stalled for approximately 2 s 160 Temperature, °C; Resistance, mOhm 140 Example motor, stalled for approximately 2 s ~ Smoke ~ 120 100 Motor winding temperature measurement 80 Total circuit resistance Motor resistance 60 Resistance of wires, connectors, breakers, etc. 40 Battery resistance 20 0 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time, s •Motor resistance increased from 67 m to 96 m (43%) in two seconds •Battery resistance = 18 m •Resistance of wires (5 ft. of 14 AWG), connectors, breakers, etc. = 25 m •Total circuit resistance increased to about twice the initial motor resistance Performance of the system compared with motor performance based on data sheet Example motor 2500 250 Output power, W Speed, rad/s Power loss, W 200 Current, A Efficiency 1500 150 1240 W 1000 100 95 A 500 68% 50 DATA SHEET 126 W 0 0.00 278 W 0.10 0.20 SYSTEM 0.30 0.40 Torque, Nm 0.50 0.60 0 0.70 Current (A); Efficiency (%) Speed (rad/s); Power (W) 2000 CIM motor (a.k.a. Chiaphua, a.k.a. Atwood) Be aware that a motor may have other names. CIM motor data and curves Stall torque stall = 347 oz-in = 2.4 Nm Stall current istall = 114 A Free speed free = 5342 rpm = 560 rad/s Free current ifree = 2.4 A CIM motor performance curves CIM motor You will need to operate within the limits of the circuit breakers supplied with the kit! (20 A, 30 A, or 40 A) Speed (rad/s); Power (W) 1200 140 Output power, W Speed, rad/s 120 Power loss, W Current, A 1000 100 Efficiency 800 80 600 60 400 40 200 20 0 0 0.5 1 1.5 Torque, Nm 2 0 2.5 Current (A); Efficiency (%) 1400 Comparison of power available from example motor and CIM motor Comparison of power available from example motor and CIM motor 450 Example motor CIM motor 400 Output power, W 350 300 250 200 150 100 50 0 0 0.5 1 1.5 Torque, Nm 2 2.5 Simple strategy • Calculate (or read from data sheet) the motor resistance R • Increase R by 50% - 100% • Calculate power curve • Operate at half of new peak power Performance curves re-calculated with R increased by 75% Comparison of power available from example motor and CIM motor 2500 500 Speed, Example motor Speed, CIM motor Example motor, R increased by 75% CIM motor, R increased by 75% 2000 450 400 1500 300 250 <--- Stay to the left of the peak power point 1000 200 150 500 100 50 0 0 0 0.2 0.4 0.6 0.8 Torque, Nm 1 1.2 1.4 Output power, W Speed, rad/s 350 "Gear" ratio: Mechanical power transmission efficiency is important • • • • • • • Spur gears: 90% per pair Worm and gear: 10%-60% Nut on a screw (not ball nut): 10%-60% Twist cables: 30%-90% Chain: 85%-95% Wire rope (cables): up to 98% Rack and pinion 50%-80% Example: Gear ratio out = 1.5 Nm; out = 100 rad/s Pmotor = Pout / g (12) Gear ratio example Output power = 1.5 Nm • 100 rad/s = 150 W Try: Spur gears (assume 90% efficiency per stage) Power required at motor Pmotor = Pout / g one stage: Pmotor = 150 W / 0.9 = 167 W two stages: Pmotor = 150 W / 0.9 /0.9 = 185 W three stages: Pmotor = 150 W / 0.9 /0.9 /0.9 = 206 W four stages: Pmotor = 150 W /0.9/0.9/0.9/0.9 = 229 W Gear ratio example Estimate torque by inspection, then calculate an approximate gear ratio to determine how many gear stages are required. Rule of thumb for spur gears: max. ratio per stage = 5:1 Comparison of power available from example motor and CIM motor 2500 500 Speed, Example motor Speed, CIM motor Example motor, R increased by 75% CIM motor, R increased by 75% 4 stages 3 stages 2 stages 1 stage 1500 400 300 1000 200 0.1 Nm? 0.4 Nm? 500 100 0 0 0 0.1 0.2 0.3 0.4 Torque, Nm 0.5 0.6 0.7 0.8 Output power, W Speed, rad/s 2000 Gear ratio Example motor Gear ratio - example motor Choosing operating point for example motor 2500 500 Speed, Example motor Power, example motor, R increased by 75% 2000 1500 300 1000 200 Tw o stages: 185 W 500 100 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Torque, Nm Check: gear ratio Ng = motor/out = 1850 / 100 = 18.5:1 = 4.3 • 4.3 Operating point looks good (comfortably to the left of the peak power point) Output power, W Operating point 1850 rad/s Speed, rad/s 400 Gear ratio CIM motor Gear ratio - CIM motor Choosing operating point for CIM motor 2500 500 Speed, CIM motor Power, CIM motor, R increased by 75% 2000 400 1500 300 1000 200 One stage: 167 W 500 100 388 rad/s 0 0 0.1 0.2 0.3 0.4 0.43 Nm Torque, Nm 0.5 0.6 0.7 Gear ratio Ng = motor/out = 388 / 100 = 3.9:1 Moderately heavy load for this motor (near peak power) 0 0.8 Output power, W Speed, rad/s Operating point Gear ratio example • Calculate current – Should not exceed breaker current • Choose motors based on – Power – Gearing required – Possibility of stalling and heating – Weight – All motor tasks Summary of motors in the 2005 Kit of Parts Sorted by peak output power Number on Supplier motor Motor name Fisher- 74550-0642 Power Wheels Price CIM FR801-001 (Chiaphua, Atwood) Fisher- 74550-0642 Power Wheels Price Globe 409A586 2WD/4WD transfer mtr. Taigene 16638628 Sliding (van) door Globe 409A587 2WD/4WD transfer mtr. Nippon- E6DFWindow Lift Denso 14A365-BB Jideco Window Lift Mabuchi RS454SH W/spur gear ccw Description Motor only Keyed output shaft, ccw Motor and gearbox Motor only Peak power, Reference Stall torque Stall Stall Free Free Free 10.5 V Voltage on Gear (as from torque current speed speed current supply data sheet ratio data sheet) (Nm) (A) (rpm) (rad/s) (A) (W) 12 647 mNm 12 346.9 oz-in 12 181 12 Worm Gearmotor Planetary Gearmotor Worm Gearmotor Worm Gearmotor Spur pinion on shaft 35 oz in 34 Nm cw, 30 Nm ccw 10.5 12 117 0.647 148 24000 2513 1.5 312 2.45 114 5342 559 2.3 261 77 148 133 13.9 2.5 203 0.247 21.5 9390 983 0.4 46 30 44 75 7.9 2.7 44 13 21.5 80 8.4 0.58 24 12.6 9.2 Nm 9.2 24.8 92 9.6 2.8 16 12 8.33 Nm 8.33 21 85 8.9 3 14 12 620 g-cm 0.061 5.2 4700 492 0.22 5.7 Comparison of motors in the 2005 Kit of Parts Speed and torque at peak power with 10.5 V supply 100000 Speed, rad/s 10000 Fisher-Price motor alone 1000 Globe motor alone 500 W 200 W Mabuchi CIM 100 W 100 50 W 20 W 10 W 10 5W Nippon Taigene Jideco Globe with gearhead 1 0.01 0.1 1 Torque, Nm 10 FisherPrice with gearbox 100 Keep batteries charged. Battery voltage and breaker panel voltage with pulse load: Discharge current: 50 A (shared between two 30 A breakers); duty cycle: 10 s on, 10 s off. Battery nominal capacity @ 20 hour discharge rate: 18 Ah Discharged capacity, Ah; Voltage, V 16 14 12 10 Battery voltage 8 Discharged capacity 6.3 Ah 6 Panel voltage 4 2 0 0 5 10 Time, minutes 15 Keep batteries charged. Battery DC resistance during pulsed discharge. Pulse: 50 A for 10 s, 0 A for 10 s Resistance calculated from voltage drop and pulse current, at 1 s intervals throughout the pulse. 16 140 10 s 14 120 5s 12 4s 3s Battery resistance 100 10 2s Panel plus wire resistance 80 8 Battery open-circuit voltage 1 second 60 6 40 4 20 2 0 0 0.0 1.0 2.0 3.0 4.0 5.0 Discharged capacity, Ah 6.0 7.0 8.0 Battery open circuit voltage, V DC resistance, milliohms 160 Conclusion • Proper planning up front will keep you alive in the heat of the battle. • Wisely choose the role that a motor will play on your robot. Remember that most of these motors were originally designed for applications other than a competition robot. • Test the conditions in which a motor is used and calculate conditions when possible. If you operate below the limits recommended here, your motors are likely to be be trouble-free. • Good Luck