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DC Permanent Magnet Motors A tutorial winch design David Giandomenico Lynbrook High School Robotics FIRST Team #846 DGiandomenico@lynbrookrobotics.com (408)343-1183 December 10, 2011 David Giandomenico - FIRST #846 2010 Breakaway December 10, 2011 David Giandomenico - FIRST #846 2004 FIRST Frenzy: Raising the Bar December 10, 2011 David Giandomenico - FIRST #846 What We Want. • Weight: 130 lbs • Distance: 1.5 feet • Time (speed): 5 seconds December 10, 2011 David Giandomenico - FIRST #846 What We’ve Got: Some of the Motors supplied in FIRST Robotics Kit December 10, 2011 David Giandomenico - FIRST #846 “CIM” Motor Specification December 10, 2011 David Giandomenico - FIRST #846 “CIM” Motor Performance December 10, 2011 David Giandomenico - FIRST #846 “CIM” Motor Performance Stall Current No Load Speed No Load Current Stall Torque December 10, 2011 David Giandomenico - FIRST #846 FUSE Limits on Motor Power Stall Current 40 A Fuse Limit ~100 Oz-In December 10, 2011 David Giandomenico - FIRST #846 Kit Motors – Which One? All Data at 12VDC Max Power (Watts) Stall Torque (oz-in) Free Speed (RPM) Free Current (A) Stall Current (A) BaneBots RS395 48.1 16.7 15,500 0.5 15 BaneBots RS540 123.5 39.5 16,800 1 42 BaneBots RS550 253.5 70.6 19,300 1.4 85 BaneBots RS775 83.1 61.1 7,300 1.1 30 CIM FR801-001 340.1 344.0 5,310 2.7 133 Denso 262100-3030-(Right) 23.5 1501.1 84 1.8 18.6 Denso 262100-3040-(Left) 23.5 1501.1 84 1.8 21 Fisher-Price 00801-0673-(2011) 291.6 75.4 20,770 0.82 108.7 Fisher-Price 00968-9015-(2010) 185.0 63.7 15,600 1.25 70 Make / Model December 10, 2011 David Giandomenico - FIRST #846 Motors - Sorted by Power Max Power (Watts) Stall Torque (oz-in) Free Speed (RPM) Free Current (A) Stall Current (A) CIM FR801-001 340.1 344.0 5,310 2.7 133 Fisher-Price 00801-0673-(2011) 291.6 75.4 20,770 0.82 108.7 BaneBots RS550 253.5 70.6 19,300 1.4 85 Fisher-Price 00968-9015-(2010) 185.0 63.7 15,600 1.25 70 BaneBots RS540 123.5 39.5 16,800 1 42 BaneBots RS775 83.1 61.1 7,300 1.1 30 BaneBots RS395 48.1 16.7 15,500 0.5 15 Denso 262100-3030-(Right) 23.5 1501.1 84 1.8 18.6 Denso 262100-3040-(Left) 23.5 1501.1 84 1.8 21 Make / Model December 10, 2011 David Giandomenico - FIRST #846 Choosing a motor based on Maximum Output Power 1. Calculate Energy required to lift load. 2. Given the Time & Energy, calculate the mechanical Power required. 3. Boost Power requirement to adjust for Friction in the gearbox and elsewhere. 4. Choose a motor whose Maximum Output Power is at least 4/3 * (safety margin) December 10, 2011 David Giandomenico - FIRST #846 Winch Design Input parameters Weight to lift (lbs) Height (ft) to lift in time T Time to lift seconds 130 1.5 5 Convert to MKS (metric system) Mass to lift (Kgs) Weight To lift (Newtons) Height (m) Time to Lift 59.1 579.1 0.457 5 Potential Energy Kp = mgh (Joules) 264.8 Weight & Mass conversions: 1Kg = 2.2 lbs-mass Weight in Newtons = mass x 'g' where g=9.8 m/s/s so a 1Kg mass weighs 9.8 Newtons Power needed to gain above energy in time T P = Kp / T (Watts) 53.0 December 10, 2011 David Giandomenico - FIRST #846 Motor Selection Max Power (Watts) Stall Torque (oz-in) Free Speed (RPM) Free Current (A) Stall Current (A) CIM FR801-001 340.1 344.0 5,310 2.7 133 Fisher-Price 00801-0673-(2011) 291.6 75.4 20,770 0.82 108.7 BaneBots RS550 253.5 70.6 19,300 1.4 85 Fisher-Price 00968-9015-(2010) 185.0 63.7 15,600 1.25 70 BaneBots RS540 123.5 39.5 16,800 1 42 BaneBots RS775 83.1 61.1 7,300 1.1 30 BaneBots RS395 48.1 16.7 15,500 0.5 15 Denso 262100-3030-(Right) 23.5 1501.1 84 1.8 18.6 Denso 262100-3040-(Left) 23.5 1501.1 84 1.8 21 Make / Model December 10, 2011 David Giandomenico - FIRST #846 www.johnsonmotor.com December 10, 2011 David Giandomenico - FIRST #846 2011 Fisher Price Motor All Data at 12VDC Make / Model Max Power (Watts) Stall Torque (oz-in) Free Speed (RPM) Free Current (A) Stall Current (A) Fisher-Price 00801-0673-(2011) 291.6 75.4 20,770 0.82 108.7 Convert oz-in to N-m: 1 oz-in = 0.007061552 N-m Make / Model Max Power (Watts) Stall Torque (N-m) Free Speed (RPM) Free Current (A) Stall Current (A) Fisher-Price 00801-0673-(2011) 291.6 0.532 20,770 0.82 108.7 December 10, 2011 David Giandomenico - FIRST #846 Fisher Price Motor 2010 Speed vs Torque V=12VDC 25000 Speed (RPM) 20000 15000 10000 5000 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 What is Torque? T F d But isn’t that “Work” W Finline d December 10, 2011 David Giandomenico - FIRST #846 Units of Work vs. Torque • Work (Energy) ft-lbf, Joules (=N-m), KWh, … • Torque pound feet(lbf-ft), ft-lbf, oz-in, N-m … December 10, 2011 David Giandomenico - FIRST #846 Work in a Rotating System T r December 10, 2011 r r W F x v r W F r v r W (F r ) W T David Giandomenico - FIRST #846 Power, Torque & Speed P Force dist / time P F r / t P ( F r ) / t P T 2 RPM P T 60 December 10, 2011 David Giandomenico - FIRST #846 Fisher Price Motor 2011 Speed vs Torque V=12VDC 25000 Speed (RPM) 20000 (speed,torque) 15000 10000 5000 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2011 Output Power vs Torque V=12VDC Mechanical Power (Watts) 350 300 250 200 150 100 50 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Normalized Speed vs Torque % No Load Speed V=Rated Voltage 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Torque (% Stall Torque) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Speed & Torque in a DC PM Motor • Let ={0,100%} such that N ( ) N s ( ) s T ( ) Ts (1 ) December 10, 2011 David Giandomenico - FIRST #846 Normalized Speed vs Torque % No Load Speed V=Rated Voltage 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Torque (% Stall Torque) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Speed & Torque in a DC PM Motor P( ) ( )T ( ) P( ) sTs (1 ) Using calculus, Max Power occurs when: dP ( ) 0 sTs (1 2 ) d Or, w/o calculus, Max occurs between two roots of quadratic, at =0, =1 that is, =½ or equivalently, when =50% December 10, 2011 David Giandomenico - FIRST #846 Output Power vs % Stall Torque V=Rated Voltage Power Out (% Max Power) 120% 100% 80% 75% 60% 40% 20% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Torque (% Stall Torque) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Max Power in a DC PM Motor PMax PMax December 10, 2011 Ts s 2 2 2 Ts N RPM max 4 60 David Giandomenico - FIRST #846 2011 Fisher Price Motor All Data at 12VDC Make / Model Max Power (Watts) Stall Torque (N-m) Free Speed (RPM) Free Current (A) Stall Current (A) Fisher-Price 00801-0673-(2011) 291.6 0.532 20,770 0.82 108.7 December 10, 2011 David Giandomenico - FIRST #846 Fisher Price Motor 2011 Output Power vs Torque V=12VDC Mechanical Power (Watts) 350 300 250 200 150 100 50 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2011 Input Power vs Torque Input Electrical Power (Watts) V=12VDC 1800 1600 1400 1200 1000 800 600 400 200 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) Current rises linearly with Torque December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Motor Current I ( ) I o ( I s I o )(1 ) Where α is the % No Load speed December 10, 2011 David Giandomenico - FIRST #846 Electrical Power P I V December 10, 2011 David Giandomenico - FIRST #846 Fisher Price Motor 2011 Input Power vs Torque V=12VDC Input Electrical Power (Watts) 1400 1200 1000 800 600 400 200 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) Input power is Current X Voltage December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2010 Output Power vs Torque V=12VDC Mechanical Power (Watts) 350 300 250 200 150 100 50 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2010 Electrical Power In & Mechanical Power Out vs Torque Electrical Power In & Mechanical Power Out (Watts) V=12VDC 1400 1200 1000 800 600 400 200 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2011 Efficiency vs Torque Efficiency V=12VDC 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Torque (N-m) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2011 Efficiency Efficiency vs Normalized Torque V=12VDC 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 7%-15% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Torque (% Stall Torque) December 10, 2011 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 DC PM Motor Summary • Max Power occurs at 50% No-Load Speed • Best efficiency typically occurs at about 80%-93% No-Load Speed • Most DC PM Motors will overheat if operated continuously at speeds less than 50% when full voltage is applied. December 10, 2011 David Giandomenico - FIRST #846 Gear Loss Estimate Suppose we have n=3 inline sets of gears, each with a 4:1reduction. What is the total efficiency if each gear set loses 4%? T = in or December 10, 2011 T = (100%-4%)3 = 88.5% David Giandomenico - FIRST #846 When x is small, x 1 1 x 1 nx n December 10, 2011 David Giandomenico - FIRST #846 Estimate of how many gear sets. • Suppose we want a gear reduction of 1200. How many gear sets with a reduction of 3 do we need? • Solve 3N = 1200 • N = ln(1200)/ln(3) = 6.45 December 10, 2011 David Giandomenico - FIRST #846 Gear loss estimate We need 6.45 3:1 gear sets. Assuming a loss of 4% for each gear set, T = in or T = (1-4%)6.45 = 76.8% December 10, 2011 David Giandomenico - FIRST #846 Putting it all together 1. Choose a winch drum size 2. Calculate the drum rpm 3. Choose the % motor operating speed 4. Calculate the required gear reduction to operate at that speed 5. Verify the output winch line force meets or exceeds the original specification, including gear box losses December 10, 2011 David Giandomenico - FIRST #846 Winch Design Specification Input parameters Weight to lift (lbs) Height (ft) to lift in time T Time to lift seconds Convert to MKS (metric system) Mass to lift (Kgs) Weight To lift (Newtons) Height (m) Time to Lift December 10, 2011 130 1.5 5 59.1 579.1 0.457 5 David Giandomenico - FIRST #846 Winch Drum Speed Winch Line Speed Distance (m) Time Speed (m/s) 0.4572 5 0.0914 Drum size (dictated by factors such as cable) Diameter (inches) 6 Diameter (m) 0.152 Circumference (m) 0.479 Drum speed Revolutions / second Revolutions / minute (rpm) December 10, 2011 0.191 11.46 David Giandomenico - FIRST #846 Determine the Gear Reduction December 10, 2011 Drum speed Revolutions / second Revolutions / minute (rpm) 0.191 11.46 Motor spec at 12VDC No load speed Stall Torque Stall Torque (1 Oz-In= 0.007061552 N-m) Max Power Output Free Current Stall Current 20770 RPM 75.4 oz0in 0.532 N-m 289.5 W 0.82 A 108.7 A Operating Point at FUSE current at 20A at 30A at 40A 17.8% 27.0% 36.3% Select Motor Speed and Torque % motor speed Motor current Motor Speed Torque Power out Required Gear Reduction 90% 11.6 A 18693 rpm 0.0532 N-m 104.2 W 1631.3 David Giandomenico - FIRST #846 Gear Loss Estimate Required Gear Reduction Loss estimate assuming 'n' small gear sets Individual gear set reduction ratio % Loss per gear set Number of gear reductions Total estimated gear efficiency December 10, 2011 1631.3 4 times 5% 5.336 sets 76.06% David Giandomenico - FIRST #846 Verify We Meet or Exceed Pull Strength Specification Winch line output at speed Motor torque at speed (above) Torque after gearbox (no loss) After gear box losses Force on Line Force on Line (lbs) December 10, 2011 0.0532 N-m 86.86 N-m 66.06 N-m 866.92 N 194.61 lbs David Giandomenico - FIRST #846 Feat Accomplished! 194 lb exceeds required spec of 130lbs December 10, 2011 David Giandomenico - FIRST #846 More than you wanted to know about Robot Winch Design David Giandomenico Lynbrook High School Robotics FIRST Team #846 DGiandomenico@lynbrookrobotics.com (408)343-1183 December 10, 2011 David Giandomenico - FIRST #846 Addendum: Interest or Time permitting December 10, 2011 David Giandomenico - FIRST #846 x y 1 1 x y x y 2 2 2 x y x 2xy y 3 3 2 2 3 x y x 3x y 3xy y 4 4 3 2 2 3 4 x y x 4x y 6x y 4xy y 0 December 10, 2011 David Giandomenico - FIRST #846 1 y 1 1 1 y 1 1 y 2 2 1 y 1 2 y y 3 2 3 1 y 1 3 y 3 y y 4 2 3 4 1 y 1 4 y 6 y 4 y y 0 1 b n December 10, 2011 1 n b ... David Giandomenico - FIRST #846 Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 December 10, 2011 x y 1 x y 1 x 1 y x y 2 x 2 2 xy y 2 x y 3 x 3 3 x 2 y 3 xy 2 y 3 4 x y x 4 4 x 3 y 6 x 2 y 2 4 xy3 y 4 0 David Giandomenico - FIRST #846 Binomial Theorem n n n n1 1 n 1 n1 n n a b a a b ... a b b 1 2 n 1 n n n n! k k!(n k )! December 10, 2011 David Giandomenico - FIRST #846