dc permanent magnet motors a tutorial winch design

David Giandomenico - FIRST #846

DC Permanent Magnet MotorsA tutorial winch design

David Giandomenico

Lynbrook High School Robotics

FIRST Team #846

[email protected]

(408)343-1183

August 10, 2013

mailto:[email protected]

David Giandomenico

Start with:Robot features - what things move on a robot.Include drive train, arm, winch, lift.Winch is easy to specify.

2010 Breakaway

August 10, 2013 David Giandomenico - FIRST #846


2004 FIRST Frenzy: Raising the Bar

David Giandomenico

2004 FIRST CompetitionAttach to 10ft high bar andlift robot off ground


What We Want.• Weight:

• Distance:

• Time (speed):

130 lbs

1.5 feet

5 seconds


What We’ve Got:Some of the Motors supplied in FIRST Robotics Kit


Kit Motors – Which One?All Data at 12VDC 2013 choices (partial list!)

Make Model

Max Power (W)

Stall Torque (oz-in)

Free Speed (rpm)

Free Current (A)

Stall Current (A)

AndyMark am-0912 179 61 16000 1.2 64

AndyMark am-0915 45 1209 198 0.6 22

BaneBots M7-RS775-18 273 113 13000 1.8 87

BaneBots M5-RS550-12 M5-RS550-12-B

254 71 19300 1.4 85

BaneBots M5-RS540-12 123 39 16800 1 42

BaneBots M7-RS775-12 83 61 7300 1.1 30

BaneBots M5-RS545-12 74 24 16800 0.9 21

BaneBots M3-RS395-12 48 17 15500 0.5 15

CIM FR801-001 337 343 5310 2.7 133

VEX Mini CIM 217-3371 229 198 6200 1.8 86

VEX bag motor 217-3351 149 57 14000 1.8 41


Motors - Sorted by PowerMake Model

Max Power (W)


Free Speed (rpm)

Free Current (A)

Stall Current (A)

CIM FR801-001 337 343 5310 2.7 133

BaneBots M7-RS775-18 273 113 13000 1.8 87

BaneBots M5-RS550-12 M5-RS550-12-B

254 71 19300 1.4 85

VEX Mini CIM 217-3371 229 198 6200 1.8 86

AndyMark am-0912 179 61 16000 1.2 64

VEX bag motor 217-3351 149 57 14000 1.8 41

BaneBots M5-RS540-12 123 39 16800 1 42

BaneBots M7-RS775-12 83 61 7300 1.1 30

BaneBots M5-RS545-12 74 24 16800 0.9 21

BaneBots M3-RS395-12 48 17 15500 0.5 15

AndyMark am-0915 45 1209 198 0.6 22


“CIM” Motor Specification


“CIM” Motor Performance


“CIM” Motor Performance

StallTorque

No LoadCurrent

No Load Speed

StallCurrent


Current Limits (fuse) on Motor Power

StallCurrent

40 AFuse Limit

~100 Oz-In


Choosing a motor based onMaximum 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)

David Giandomenico

Design methodologyCoincidentally, a Motor at 75% speed delivers 75% of max output power. Since P(alpha) = 4* alpha(1-alpha)*Pmax, where alpha is %No load speed. So add factor of 1/75%, which is 4/3


www.johnsonmotor.com


Winch DesignInput parameters

Weight to lift (lbs) 130Height (ft) to lift in time T 1.5Time to lift seconds 5

Convert to MKS (metric system)Mass to lift (Kgs) 59.1Weight To lift (Newtons) 579.1Height (m) 0.457Time to Lift 5

Potential EnergyKp = mgh (Joules) 264.8

Power needed to gain above energy in time TP = Kp / T (Watts) 53.0

Weight & Mass conversions:1Kg = 2.2 lbs-mass

Weight in Newtons = mass x 'g'where g=9.8 m/s/sso a 1Kg mass weighs 9.8 Newtons


Motor SelectionMake Model

Max Power (W)


Free Speed (rpm)

Free Current (A)

Stall Current (A)

CIM FR801-001 337 343 5310 2.7 133

BaneBots M7-RS775-18 273 113 13000 1.8 87

BaneBots M5-RS550-12 254 71 19300 1.4 85

VEX Mini CIM 217-3371 229 198 6200 1.8 86

AndyMark am-0912 179 61 16000 1.2 64

VEX bag motor 217-3351 149 57 14000 1.8 41

BaneBots M5-RS540-12 123 39 16800 1 42

BaneBots M7-RS775-12 83 61 7300 1.1 30

BaneBots M5-RS545-12 74 24 16800 0.9 21

BaneBots M3-RS395-12 48 17 15500 0.5 15

AndyMark am-0915 45 1209 198 0.6 22

Make Model

Max Power (W)


Free Speed (rpm)

Free Current (A)

Stall Current (A)

CIM FR801-001 337 343 5310 2.7 133

BaneBots M7-RS775-18 273 113 13000 1.8 87

BaneBots M5-RS550-12 254 71 19300 1.4 85

VEX Mini CIM 217-3371 229 198 6200 1.8 86

AndyMark am-0912 179 61 16000 1.2 64

VEX bag motor 217-3351 149 57 14000 1.8 41

BaneBots M5-RS540-12 123 39 16800 1 42

BaneBots M7-RS775-12 83 61 7300 1.1 30

BaneBots M5-RS545-12 74 24 16800 0.9 21

BaneBots M3-RS395-12 48 17 15500 0.5 15

AndyMark am-0915 45 1209 198 0.6 22

Make Model

Max Power (W)


Free Speed (rpm)

Free Current (A)

Stall Current (A)

CIM FR801-001 337 343 5310 2.7 133

BaneBots M7-RS775-18 273 113 13000 1.8 87

BaneBots M5-RS550-12 254 71 19300 1.4 85

VEX Mini CIM 217-3371 229 198 6200 1.8 86

AndyMark am-0912 179 61 16000 1.2 64

VEX bag motor 217-3351 149 57 14000 1.8 41

BaneBots M5-RS540-12 123 39 16800 1 42

BaneBots M7-RS775-12 83 61 7300 1.1 30

BaneBots M5-RS545-12 74 24 16800 0.9 21

BaneBots M3-RS395-12 48 17 15500 0.5 15

AndyMark am-0915 45 1209 198 0.6 22


What is Torque?

dFW inline

dFT

But isn’t that “Work?”

David Giandomenico


Units of Work vs. Torque

• Work (Energy)

• Torquepound feet(lbf-ft), ft-lbf, oz-in, N-m …

ft-lbf, Joules (=N-m), KWh, …


Work in a Rotating System

Force

rT

David Giandomenico


Power, Torque & Speed

TP

60RPM 2TP

timedistForceP /

trFP /)( trFP /

0.00 0.10 0.20 0.30 0.40 0.50 0.600

5000

10000

15000

20000

25000

Speed vs Torque

Torque (N-m)

Spee

d (R

PM)

August 10, 2013 David Giandomenico - FIRST #846From FIRST_MOTOR_CALC.xls

V=12VDC

(speed,torque)

Where is Max Power?Fisher Price Motor 2011

David Giandomenico

Introduce Torque - Speed characteristic.Key Note: Voltage is fixed. Brake (load) is applied to slow down motor while maintaining supply voltage.

August 10, 2013 David Giandomenico - FIRST #846From FIRST_MOTOR_CALC.xls

V=12VDC

0.00 0.10 0.20 0.30 0.40 0.50 0.600

50

100

150

200

250

300

350

Output Power vs Torque

Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)

Maximum PowerFisher Price Motor 2011

Standardize through Normalization


http://www.mabuchi-motor.co.jp http://www.johnsonmotor.com


http://www.mabuchi-motor.co.jp

http://www.johnsonmotor.com

Simplified through Standardization


Normalized Speed vs Torque

0%10%20%30%40%50%60%70%80%90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Torque (% Stall Torque)

% N

o Lo

ad S

peed

V=Rated Voltage

85%+15%=100%

30%+70%=100%

50%+50%=100%

David Giandomenico

Which point is greatest power?Which box has greatest area?


Speed & Torque in a DC PM Motor

• Let ={0,100%}

such that

)1()(

)()(

s

s

s

TT

NN


Speed & Torque in a DC PM Motor

Or, w/o calculus, Max occurs between two roots of quadratic, at =0, =1 that is,

=½ or equivalently, when =50%

)()()( TP

Using calculus, Max Power occurs when:


Max Power in a DC PM Motor

604 2 max

RPMs

MaxNTP

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0%

20%

40%

60%

80%

100%

120%

Output Power vs % Stall Torque


Pow

er O

ut (%

Max

Pow

er)


V=Rated Voltage

75%

David Giandomenico

Normalized "Generic" power characteristics*) Max Power at 50%*) Power at 25% torque (75% no load speed) yields 75% of Max Power out.

David Giandomenico

Haven't defined Max Power yet, but I refer to it below.


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

0.00 0.10 0.20 0.30 0.40 0.50 0.600

50

100

150

200

250

300

350


Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)


Fisher Price Motor 2011

From FIRST_MOTOR_CALC.xls

V=12VDC

0.00 0.10 0.20 0.30 0.40 0.50 0.600

200400600800

10001200140016001800

Input Power vs Torque

Torque (N-m)

Inpu

t Ele

ctric

al P

ower

(Wat

ts)




V=12VDC

Current rises linearly with Torque


Motor Current

Where α is the % No Load speed

)1)(()( oso IIII


Electrical Power

VIP

0.00 0.10 0.20 0.30 0.40 0.50 0.600

200

400

600

800

1000

1200

1400

Input Power vs Torque

Torque (N-m)

Inpu

t Ele

ctric

al P

ower

(Wat

ts)




V=12VDC

Input power is Current X Voltage

0.00 0.10 0.20 0.30 0.40 0.50 0.600

50

100

150

200

250

300

350


Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)




V=12VDC




V=12VDC

0.00 0.10 0.20 0.30 0.40 0.50 0.600

200

400

600

800

1000

1200

1400

Electrical Power In & Mechanical Power Out vs Torque

Torque (N-m)

Elec

trica

l Pow

er In

&

Mec

hani

cal P

ower

Out

(Wat

ts)

0.00 0.10 0.20 0.30 0.40 0.50 0.600%

10%20%30%40%50%60%70%80%

Efficiency vs Torque

Torque (N-m)

Effic

ienc

y




V=12VDC

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0%

10%20%30%40%50%60%70%80%

Efficiency vs Normalized Torque


Effic

ienc

y

7%-15%



V=12VDC


Normalized Efficiency for IDEAL motor

Max Efficiency


Operating Point:

Efficiency:

0% 2% 4% 6% 8% 10%50%

60%

70%

80%

90%

100%

Io / Is

Bes

t Ope

ratin

g Po

int

...simplifying yields:

Derivation of: Max Efficiency


Find Maximum :

Efficiency: Where:

Use Quadratic Formula to find roots:


Derivation of: Max Efficiency continued

Substitute for (1-α) to get:


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.


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 T = (100%-4%)3 = 88.5%

David Giandomenico

Transistion Topic - Cut if short for time


When x is small, 1x

David

Commonly, I am asked why we don't just add the losses. The following slides explain why adding is a reasonable approximation.


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

David Giandomenico

In the final design, N must be an integer, but for the interim design, this method conveniently allows us to estimate the loss without committing to a specific gear selection.


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%


Putting it all together1. 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


Winch Design SpecificationInput parameters

Weight to lift (lbs) 130Height (ft) to lift in time T 1.5Time to lift seconds 5

Convert to MKS (metric system)Mass to lift (Kgs) 59.1Weight To lift (Newtons) 579.1Height (m) 0.457Time to Lift 5


Winch Drum SpeedWinch Line Speed

Distance (m) 0.4572Time 5Speed (m/s) 0.0914

Drum size (dictated by factors such as cable)Diameter (inches) 6Diameter (m) 0.152Circumference (m) 0.479

Drum speedRevolutions / second 0.191Revolutions / minute (rpm) 11.46


Determine the Gear Reduction

Required Gear Reduction 1021.0

Loss estimate assuming 'n' small gear sets

Individual gear set reduction ratio 4 times% Loss per gear set 5%

Number of gear reductions 4.998 setsTotal estimated gear efficiency 77.39%


Gear Loss Estimate

Winch line output at speedMotor torque at speed (above) 0.0798 N-mTorque after gearbox (no loss) 81.47 N-m

After gear box losses 63.05 N-mForce on Line 827.41 NForce on Line (lb) 185.75 lb

Margin

Weight of load 130 lbMargin (force:load at target speed) 1.43 : 1


Verify We Meet or ExceedPull Strength Specification


Feat Accomplished!185 lb exceeds required spec of 130lbs


More than you wanted to know about

Robot Winch Design

David Giandomenico

Lynbrook High School Robotics

FIRST Team #846

[email protected]

(408)343-1183

mailto:[email protected]


Addendum: Interest or Time permitting

David Giandomenico

Expand binomial polynomials to show second binomial coefficents, are 0,1,2,3,4...n

dc permanent magnet motors a tutorial winch design

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