Sıra | DOSYA ADI | Format | Bağlantı |
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01. | Distances Sprocket Calculations Motors | pptx | Sunumu İndir |
Transkript
Motors 101Tom MilnesBAA Team 2199 RepresentativePrincipal Mathematician JHU/APL
Why Use Electrical Motors?• High Torque or Speed Rotational Motion Is Needed– Low Torque, Speed, with finite rotation can achieved with Servos• Variable speed / force linear motion is needed over long distances (using cord or chain)– Two position linear motion better achieved with pneumatics over achievable ranges– Motion prevention is also better done with pneumatics Pneumatic device pins a manipulator part into place
What is an Electrical Motor?• Device which converts Electrical Power to Mechanical Rotational Power
What is Power?• Power is the rate of Energy production– Power = Energy / Time
What is Energy?• Physics Inspired English Definition– Energy is required to do Work• Energy Sources– Battery, Stretched Spring, Gasoline, Moving Object, Object at Height– Can be converted from / to various forms Total is conserved But some is usually converted to useless forms such as heat
What is Work?• Unlike say - a homework set – for physical tasks work has a precise definition– Linear Motion The product of distance moved times the opposing forceo Work = Force x Distance (pound – feet, Newton-meters)o Lifting Task = Object Weight x Distance Moved– Rotational Motion The product of angle rotated times the opposing torqueo Work = Torque x Angle (pound – feet, Newton-meters)
What is Power?• Power is required to Work Quickly• Precise definitions for Physical Tasks– Linear Motion The product of velocity moved times the opposing forceo Power = Force x Velocity (pound – feet/s, Newton-meter/s)o Lifting Task = Object Weight x Velocity– Rotational Motion The product of angle rate times the opposing torqueo Power = Torque x Angular Speed (pound – feet/s, Newton-meter/s)
Power• Power is conserved in a linked or closed loop system but not always in useful form.– Ratio of Output Power / Input Power is called efficiency – varies from 0 to 1– Heat loss is a double whammy• For Electrical Motors Mechanical Power is:– Torque x Angular Speed = τω
DC Motor Characteristics• Linear Relation between Torque and Angular SpeedAngular Speed (rpm)Torque (oz-in)0MaximumSpeedMaximumTorque
Power• Power is Torque x Angular SpeedAngular Speed (rpm)Torque (oz-in)0Max PowerMaximumSpeedMaximumTorquePower ( Watts)
Current Draw (Amperage)• Current draw is proportional to torqueAngular Speed (rpm)Torque (oz-in)0Max PowerMaximumSpeedMaximumTorqueCurrent (Amps)Power ( Watts)MaximumCurrent
Motor Limitations• In many cases motors are current limited with respect to maximum achievable power– See Example Next• Max torque / Max current is bad for motors!– Circuit breakers aren’t fast enough to prevent motor destruction – they are designed to keep wiring from burning!! “Magic Blue Smoke” results– Always protect against this! Time limit a motor that runs into a mechanical stop Place a detector to stop / reverse the motor before a mechanical stop
Practical Example40 AmpBreakerBanebots40 AmpCircuitBreaker
Using Motors• Electrical Motors are intrinsically high speed / low torque devices – not highly useful out of the box– Pulleys and Belts, Gears, Sprockets and Chain required to increase torque / lower speed for real utility
Pulley Exampler1v1st PulleyAttached to Motor2nd PulleyAttached to Device v =w1r1 v =w2r2 r2 =2r1
v1st PulleyAttached to MotorOutput PulleyAttached to DevicePulley Example v =w1r1 v =w2r2 If no belt slippagev =w1r1=w2r2 sow2=r1r2w1=12w1andif no power lossesP1=P2t1w1=t2w2so t2=r2r1t1=2t2 r1 r2 =2r1
Gear ExampleGear 1Gear 2Reversal of Direction # teeth ´tooth length =C =2pr# teeth1# teeth2=r1r2Consequently,w2=# teeth1# teeth2w1t2=# teeth2# teeth1t1 In this case,w2=2080w1=14w1t2=8020t1=4t1
Gears In Series
Gears In Series• Appears highly difficult but generalizing the original gear example for any two gears “n” and “n+1” we have• Applied recursively starting with gears 1 and 2 we have wn+1=# teethn# teethn+1wn, tn+1=# teethn+1# teethntn wLast=# teethFirst# teethLastwFirst, tLast=# teethLast# teethFirsttFirst
Gears In SeriesDon’t Effect Gear Ratio Calculations wLast=1260wFirst=15wFirst, tLast=5tFirst
Gears in Parallel – Compound GearsIndividual GearRatios Multiply In Compound Gears5:15:1Overall Ratio is 5:1 x 5:1 = 25:1
Planetary GearsPlanet Gears are Idler GearsIn a Planetary Gearbox Gear Ratio = # teeth in Ring Gear# teeth in Sun Gear
Planetary Gear StagesMotorInputOutput ShaftN:1N:1N:13-Stage GearboxEach Stage N:1Total N3:1Ring GearVery Compact!!!
Motors – Power is Key!• The most important thing to look for in a motor is its overall Power capability!– Then look at torque and speed individually• Use of gears, chains, belts will allow you to obtain the desired speed / torque combination for your application.
2017 Motors Ranked by PowerBrand Type Order #Max Power (Watts)Stall Torque (oz-in)Free Speed (rpm)RS775 Pro 217-4347 347.83 100.54 18700Many CIM Varies 337.34 343.40 5310BaneBots RS-775 M7-RS775-18 266.79 110.93 13000BaneBots RS-550 M5-RS550-12 245.83 68.85 19300VEX mini-CIM 217-3371 227.40 198.26 6200AndyMark 9015 am-0912 179.49 60.64 16000VEX BAG 217-3351 146.71 56.64 14000AndyMark RS775-125 am-2194 36.91 35.00 5700AndyMark RS775-5 am-2161 36.91 35.00 5700AndyMark Snow Blower am-2235 29.60 1600.00 100Denso Window 5-163800-RC1 21.81 1309.91 90Denso Throttle AE235100-0160 18.04 18.40 5300AndyMark NeveRest am-3104 14.00 8.75 6600Bosch Seat Motor 6004 RAE 194-06 13.83 3115.46 24
2017 Motors Ranked by TypeBrand Type Order #Max Power (Watts)Stall Torque (oz-in)Free Speed (rpm)RS775 Pro 217-4347 347.83 100.54 18700Many CIM Varies 337.34 343.40 5310BaneBots RS-775 M7-RS775-18 266.79 110.93 13000BaneBots RS-550 M5-RS550-12 245.83 68.85 19300VEX mini-CIM 217-3371 227.40 198.26 6200AndyMark 9015 am-0912 179.49 60.64 16000VEX BAG 217-3351 146.71 56.64 14000AndyMark RS775-125 am-2194 36.91 35.00 5700AndyMark RS775-5 am-2161 36.91 35.00 5700AndyMark Snow Blower am-2235 29.60 1600.00 100Denso Window 5-163800-RC1 21.81 1309.91 90Denso Throttle AE235100-0160 18.04 18.40 5300AndyMark NeveRest am-3104 14.00 8.75 6600Bosch Seat Motor 6004 RAE 194-06 13.83 3115.46 24
Drive Motors• CIM Motors– Heavy duty sealed bearing motor Can take continuous use and varying acceleration– Also physically heavy Best mounted low in your robot for stability– Use at least 4 in your Drive System Otherwise you will be pushed around by other robots Use 5th or 6th CIM for high power taskso 2015 “Recycle Rush” – Tote / Garbage Can Liftero 2016 “Stronghold” – Climbing Motoro 2017 “Steamworks” – Climbing Motor
High Power MotorsBanebots 775-18 273 Watts Banebots 550 254 Watts Mini-CIM 229 Watts Andy Mark 0912 179 Watts Bag Motor 149 Watts Use for high torque or high speed manipulators!!VexPro 775 Pro347 Watts
Low Power MotorsHighly UsefulRS-775-125 – am-2194RS-775-5 – am-2161Numerous Gearboxes,Encoder And Mounting KitFrom AndyMarkFor low power use (such asPrecision pointing)NeveRest MotorAndyMark’s principal FTC motorVery low power, precision movementNumerous Gearboxes,Encoders And Mounting KitsFrom AndyMark
Low Power Dubious UtilityDensoThrottle MotorAE235100-0160DensoWindow Motor262100-3030 (Right)262100-3040 (Left)AndyMarkSnow Blower Motoram-2235Bosch Seat Recliner Motor82794153-3 Motors already attached to gears so reduction ratio is fixed. Difficult to mount. Difficult to wire. Awkward shapes.
Gearboxes, Gears • CIM– Andymark - www.andymark.com – VexPro - www.vexrobotics.com/vexpro/– Banebots - www.banebots.com • Other High Power – Andymark, VexPro, Banebots• Low Power Highly Useful– AndyMark• Low Power Dubious Utility– Gearboxes built in – not neededAM Mini ToughboxVexPro VersaPlanetaryVexPro ShiftingGearboxBaneBots16:1AM-3106NeveRest 40AMPG-27
Other Means of Reduction• Sprocket / Chain, Pulley / Belt, External Gears– Typically used in single stage in combination with gearbox as manufactured to get the required speed torque
Drive Train Example• A single CIM is attached to a AndyMark Mini-Tough Box with 8.54:1 Reduction, the ½” output shaft is attached to a 1.45” diameter sprocket which is attached to a 2.683” sprocket on a 6” wheel. What is the maximum possible speed of the robot?
Speed Calculations• Maximum CIM Speed is Free Speed 5310 rpm or 88.5 rev/s• Total Reduction– 8.54 x 2.863”/1.45” = 16.86• Speed at Wheel– 88.5 rev/s / 16.86 = 5.25 rev /sMake Part NumberMax Power(W)Stall Torque(oz-in)Free Speed(rpm)CIM FR801-001 337 343 5310
Speed Calculations• Speed on 6” Wheel– 5.25 rev/s x Circumference = 5.25 rev/s x π x 6” = 99 “/ s = 8.2 ft/s
Lift Calculations• A Banebots 775-18 Motor is attached to a 64:1 Gearbox to 1” radius sprocket which is drives a chain to lift an object. How heavy can the object be? How fast could the maximum weight object be lifted?
40 Amp Circuit Breaker49.1 oz-in torque
Force Calculations• 49.1 oz-in torque with 40 amp circuit breaker• Increases to 49.1 oz-in x 64 = 3142.4 oz-in = 196.4 pound-in• Torque = Force x Distance– Force = Torque / Distance = 196.4 pound-in / 1” = 196.4 pounds max
Velocity Calculations• Motor Speed: 7422 rev/m at 40 amps = 123.7 rev/s• Gearbox shaft speed 123.7 / 64 = 1.93 rev/s• Velocity = 1.93 rev / s x Circumference = 1.93 rev/s x 2 x π x 1” = 12.14 in / s = 1.01 ft/s maximum
Warning!!• Theoretical maximum performance will not be achieved in practice due to various energy losses. – Always include a “performance margin” in your calculations!– Test your system to insure it meets your requirements!
Questions?• Contact Me– Tom Milnes – 443-778-4982 – thomas.milnes@jhuapl.edu