advertisement

DC Permanent Magnet Motors A tutorial winch design David Giandomenico Lynbrook High School Robotics FIRST Team #846 [email protected] (408)343-1183 August 10, 2013 David Giandomenico - FIRST #846 2010 Breakaway August 10, 2013 David Giandomenico - FIRST #846 2004 FIRST Frenzy: Raising the Bar August 10, 2013 David Giandomenico - FIRST #846 What We Want. • Weight: 130 lbs • Distance: 1.5 feet • Time (speed): 5 seconds August 10, 2013 David Giandomenico - FIRST #846 What We’ve Got: Some of the Motors supplied in FIRST Robotics Kit August 10, 2013 David Giandomenico - FIRST #846 Kit Motors – Which One? All Data at 12VDC Make Model AndyMark am-0912 AndyMark am-0915 BaneBots M7-RS775-18 BaneBots M5-RS550-12 M5-RS550-12-B BaneBots M5-RS540-12 BaneBots M7-RS775-12 BaneBots M5-RS545-12 BaneBots M3-RS395-12 CIM FR801-001 VEX Mini CIM 217-3371 VEX bag motor 217-3351 August 10, 2013 2013 choices (partial list!) Max Power Stall Torque Free Speed Free Current Stall Current (W) (oz-in) (rpm) (A) (A) 179 61 16000 1.2 64 45 1209 198 0.6 22 273 113 13000 1.8 87 254 71 19300 1.4 85 123 39 16800 1 42 83 61 7300 1.1 30 74 24 16800 0.9 21 48 17 15500 0.5 15 337 343 5310 2.7 133 229 198 6200 1.8 86 149 57 14000 1.8 41 David Giandomenico - FIRST #846 Motors - Sorted by Power Make Model CIM FR801-001 BaneBots M7-RS775-18 BaneBots M5-RS550-12 M5-RS550-12-B VEX Mini CIM 217-3371 AndyMark am-0912 VEX bag motor 217-3351 BaneBots M5-RS540-12 BaneBots M7-RS775-12 BaneBots M5-RS545-12 BaneBots M3-RS395-12 AndyMark am-0915 August 10, 2013 Max Power Stall Torque Free Speed Free Stall Current (W) (oz-in) (rpm) Current (A) (A) 337 343 5310 2.7 133 273 113 13000 1.8 87 254 71 19300 1.4 85 229 198 6200 1.8 86 179 61 16000 1.2 64 149 57 14000 1.8 41 123 39 16800 1 42 83 61 7300 1.1 30 74 24 16800 0.9 21 48 17 15500 0.5 15 45 1209 198 0.6 22 David Giandomenico - FIRST #846 “CIM” Motor Specification August 10, 2013 David Giandomenico - FIRST #846 “CIM” Motor Performance August 10, 2013 David Giandomenico - FIRST #846 “CIM” Motor Performance Stall Current No Load Speed No Load Current Stall Torque August 10, 2013 David Giandomenico - FIRST #846 Current Limits (fuse) on Motor Power Stall Current 40 A Fuse Limit ~100 Oz-In August 10, 2013 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) August 10, 2013 David Giandomenico - FIRST #846 www.johnsonmotor.com August 10, 2013 David Giandomenico - FIRST #846 W inch D esig n In p u t p a ra m e te rs W eight to lift (lbs ) 130 H eight (ft) to lift in tim e T 1.5 Tim e to lift s ec onds 5 W eight & M as s c onvers ions : C o n ve rt to M K S (m e tric syste m ) M as s to lift (K gs ) 59.1 W eight To lift (N ew tons ) 579.1 H eight (m ) 0.457 Tim e to Lift 5 1K g = 2.2 lbs -m as s W eight in N ew tons = m as s x 'g' w here g= 9.8 m /s /s s o a 1K g m as s w eighs 9.8 N ew tons P o te n tia l En e rg y K p = m gh (Joules ) 264.8 P o w e r n e e d e d to g a in a b o ve e n e rg y in tim e T P = K p / T (W atts ) August 10, 2013 53.0 David Giandomenico - FIRST #846 Motor Selection Make Model CIM FR801-001 BaneBots M7-RS775-18 BaneBots M5-RS550-12 VEX Mini CIM 217-3371 AndyMark am-0912 VEX bag motor 217-3351 BaneBots M5-RS540-12 BaneBots M7-RS775-12 BaneBots M5-RS545-12 BaneBots M3-RS395-12 AndyMark am-0915 August 10, 2013 Max Power Stall Torque Free Speed Free Stall Current (W) (oz-in) (rpm) Current (A) (A) 337 343 5310 2.7 133 273 113 13000 1.8 87 254 71 19300 1.4 85 229 198 6200 1.8 86 179 61 16000 1.2 64 149 57 14000 1.8 41 123 39 16800 1 42 83 61 7300 1.1 30 74 24 16800 0.9 21 48 17 15500 0.5 15 45 1209 198 0.6 22 David Giandomenico - FIRST #846 What is Torque? T F d But isn’t that “Work?” W Finline d August 10, 2013 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 … August 10, 2013 David Giandomenico - FIRST #846 Work in a Rotating System W = F× x T q r W = F ´ rq W = (F ´ r )q W = Tq August 10, 2013 David Giandomenico - FIRST #846 Power, Torque & Speed P Force dist / time P F r / t P ( F r ) / t P T P T 2 RPM 60 August 10, 2013 David Giandomenico - FIRST #846 Where is Max Power? 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) August 10, 2013 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Maximum Power 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) August 10, 2013 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Standardize through Normalization http://www.mabuchi-motor.co.jp August 10, 2013 http://www.johnsonmotor.com David Giandomenico - FIRST #846 Simplified through Standardization http://www.mabuchi-motor.co.jp http://www.johnsonmotor.com August 10, 2013 David Giandomenico - FIRST #846 N ormalized S peed vs Torque V=Rated Voltage % N o L o a d Sp e e d 100% 85%+15%=100% 90% 80% 70% 60% 50%+50%=100% 50% 40% 30%+70%=100% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% T orque (% Sta ll T orque ) August 10, 2013 David Giandomenico - FIRST #846 Speed & Torque in a DC PM Motor • Let ={0,100%} such that N ( ) N s ( ) s T ( ) T s (1 ) August 10, 2013 David Giandomenico - FIRST #846 Speed & Torque in a DC PM Motor P ( ) ( )T ( ) P(a ) = w f a ´ Ts (1- a ) = w f Ts ´ a (1- a ) Using calculus, Max Power occurs when: dP(a ) 0= = w f Ts (1- 2a ) da Or, w/o calculus, Max occurs between two roots of quadratic, at =0, =1 that is, =½ or equivalently, when =50% August 10, 2013 David Giandomenico - FIRST #846 Max Power in a DC PM Motor P(a ) = w f a ´ Ts (1- a ) at a max = 50%, PMax = PMax August 10, 2013 TSw f 4 2 T s N RPM max 4 60 David Giandomenico - FIRST #846 Output Power vs % Stall Torque V=Rated Voltage Power Out (% Max Power) 120% 100% 80% 75% 60% 40% P (a ) TSw f a (1- a ) = Pmax TSw f / 4 20% 0% 0% 10% 20% 30% 40% 50% 60% Torque (% Stall Torque) August 10, 2013 70% 80% 90% = 4a100% (1- a ) P ( 25%) 1 3 = 4× × Pmax 4 4 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 August 10, 2013 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) August 10, 2013 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 August 10, 2013 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 August 10, 2013 David Giandomenico - FIRST #846 Electrical Power P I V August 10, 2013 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 August 10, 2013 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) August 10, 2013 From FIRST_MOTOR_CALC.xls David Giandomenico - FIRST #846 Fisher Price Motor 2011 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) August 10, 2013 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) August 10, 2013 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) August 10, 2013 David Giandomenico - FIRST #846 Normalized Efficiency for IDEAL motor August 10, 2013 David Giandomenico - FIRST #846 Operating Point: 1 a eff = 1+ I o / I s Best Operating Point Max Efficiency 100% 90% 80% 70% 60% 50% 0% 5% 10% Io / Is Efficiency: ù Tsw o é 1 hmax = ê ú VI s êë1+ I o / I S úû 2 August 10, 2013 David Giandomenico - FIRST #846 Derivation of: Efficiency: Max Efficiency Tsw o a (1- a ) h= VI s 1- ka Where: k º1- c =1- Io / I s Find Maximum : d a (1- a ) 0= da 1- ka ...simplifying yields: 0 = ka 2 - 2a +1 Use Quadratic Formula to find roots: 1± 1- k a eff = k August 10, 2013 David Giandomenico - FIRST #846 Derivation of: Max Efficiency continued Tsw o a (1- a ) h= VI s 1- ka at a = aeff , 2 0 = ka eff - 2a eff +1 2 0 = ka eff - a eff - a eff +1 2 1- a eff = a eff - ka eff = a eff (1- ka eff ) Substitute for (1-α) to get: h (a ) a =a August 10, 2013 eff Tswo 2 = aeff VI s 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. August 10, 2013 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 August 10, 2013 T = (100%-4%)3 = 88.5% David Giandomenico - FIRST #846 When x is small, x 1 (1 - x ) »1 - nx n August 10, 2013 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 August 10, 2013 David Giandomenico - FIRST #846 Gear loss estimate We need 6.45 3:1 gear sets. Assuming a loss of 5% for each gear set, T = in or T = (1-5%)6.45 = 71.8% August 10, 2013 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 August 10, 2013 David Giandomenico - FIRST #846 Winch Design Specification In p u t p aram eters W eight to lift (lbs) H eight (ft) to lift in tim e T T im e to lift seconds C o n v ert to M K S (m etric system ) M ass to lift (K gs) W eight T o lift (N ew tons) H eight (m ) T im e to Lift August 10, 2013 130 1.5 5 59.1 579.1 0.457 5 David Giandomenico - FIRST #846 Winch Drum Speed W in c h L in e S p e e d D is ta n c e (m ) T im e S p e e d (m /s ) 0 .4 5 7 2 5 0 .0 9 1 4 D ru m s ize (d ic ta te d b y fa c to rs s u c h a s c a b le ) D ia m e te r (in c h e s ) 6 D ia m e te r (m ) 0 .1 5 2 C irc u m fe re n c e (m ) 0 .4 7 9 D ru m s p e e d R e vo lu tio n s / s e c o n d R e vo lu tio n s / m in u te (rp m ) August 10, 2013 0 .1 9 1 1 1 .4 6 David Giandomenico - FIRST #846 Determine the Gear Reduction August 10, 2013 David Giandomenico - FIRST #846 Gear Loss Estimate Required Gear Reduction 1021.0 Loss estimate assuming 'n' small gear sets Individual gear set reduction ratio % Loss per gear set Number of gear reductions Total estimated gear efficiency August 10, 2013 4 times 5% 4.998 sets 77.39% 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 (lb) 0.0798 N-m 81.47 N-m 63.05 N-m 827.41 N 185.75 lb Margin Weight of load 130 lb Margin (force:load at target speed) 1.43 : 1 August 10, 2013 David Giandomenico - FIRST #846 Feat Accomplished! 185 lb exceeds required spec of 130lbs August 10, 2013 David Giandomenico - FIRST #846 More than you wanted to know about Robot Winch Design David Giandomenico Lynbrook High School Robotics FIRST Team #846 [email protected] (408)343-1183 August 10, 2013 David Giandomenico - FIRST #846 Addendum: Interest or Time permitting August 10, 2013 David Giandomenico - FIRST #846