December 2009 David Giandomenico DC Permanent Magnet Motors A tutorial winch design David...

December 2009 David Giandomenico

DC Permanent Magnet MotorsA tutorial winch design

David Giandomenico

Lynbrook High School Robotics

FIRST Team #846

[email protected]

(408)343-1183

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.


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


“CIM” Motor Specification


“CIM” Motor Performance


“CIM” Motor Performance

StallCurrentStallCurrent

StallTorque

StallTorque

No LoadCurrentNo LoadCurrent

No Load Speed

No Load Speed


All data approximate at 12 VOLTS

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Bosch, motor only - - 0.65 114 A 20,000 RPM 2.5 A 340 W

Bosch, motor/gearbox in high

20:1 80% 10 N-m 114 A 1,000 RPM 2.5 A 260 W

Bosch, motor/gearbox in low

64:1 70% 29 N-m 114 A 300 RPM 2.5 A 230 W

Fisher-Price, motor only - - .36 N-m 57 A 15,000 RPM ? 140 W

Fisher-Price, motor/gearbox

147:1 65% 35 N-m 57 A 100 RPM ? 91 W

Delphi Sliding Door Motor (Mfg: Taigene)

- - 35 N-m 40 A 75 RPM ? 69 W

Globe, motor only - - .21 N-m 21 A 11,500 RPM .82 A 63 W

Globe, motor/gearbox 117:1 77% 19 N-m 21 A 100 RPM .82 A 50 W

Delphi Seat Motor (Mfg: Keyang)

- - 2 N-m 20 A 600 RPM ? 31 W

Delphi Window Motor (Mfg: Valeo)

- - 12 N-m 20 A 70 RPM ? 22 W

data from www.usfirst.org

FIRST MOTOR COMPARISON (2002-2003)


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20:1 80% 10 N-m 114 A 1,000 RPM 2.5 A 260 W


64:1 70% 29 N-m 114 A 300 RPM 2.5 A 230 W



147:1 65% 35 N-m 57 A 100 RPM ? 91 W


- - 35 N-m 40 A 75 RPM ? 69 W




- - 2 N-m 20 A 600 RPM ? 31 W


- - 12 N-m 20 A 70 RPM ? 22 W




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


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



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20:1 80% 10 N-m 114 A 1,000 RPM 2.5 A 260 W


64:1 70% 29 N-m 114 A 300 RPM 2.5 A 230 W



147:1 65% 35 N-m 57 A 100 RPM ? 91 W


- - 35 N-m 40 A 75 RPM ? 69 W




- - 2 N-m 20 A 600 RPM ? 31 W


- - 12 N-m 20 A 70 RPM ? 22 W




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20:1 80% 10 N-m 114 A 1,000 RPM 2.5 A 260 W


64:1 70% 29 N-m 114 A 300 RPM 2.5 A 230 W



147:1 65% 35 N-m 57 A 100 RPM ? 91 W


- - 35 N-m 40 A 75 RPM ? 69 W




- - 2 N-m 20 A 600 RPM ? 31 W


- - 12 N-m 20 A 70 RPM ? 22 W




www.johnsonmotor.com


Fisher Price Motor Data 2004

All data approximate at

12 VOLTS

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Fisher-Price, motor only

- - .36 N-m 57 A 15,000 RPM 2 140 W


Speed vs Torque

0

2000

4000

6000

8000

10000

12000

14000

16000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Spee

d (R

PM)

Fisher Price Motor 2004

From FIRST_MOTOR_CALC.xls

V=12VDC

David Giandomenico

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


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, Torque & Speed

€

W = Tθ

€

W =v F •

v d

€

W = (v F ×

r r )θ

€

W =v F ×

v r θ

€

vd ⊥

v r

€

vd =

v r θ but


Power, Torque & Speed

TP

60

RPM 2TP

timedistForceP /

trFP /)( trFP /


Speed vs Torque

0

2000

4000

6000

8000

10000

12000

14000

16000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Spee

d (R

PM)



V=12VDC

(speed,torque)

David Giandomenico



Output Power vs Torque

0

20

40

60

80

100

120

140

160

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)



V=12VDC


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 L

oad

Spee

d


V=Rated Voltage

David Giandomenico



Speed & Torque in a DC PM Motor

• Let ={0,100%}

such that

)1()(

)(

)(

s

s

s

TT

NN


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%


% N

o L

oad

Spee

d


V=Rated Voltage

David Giandomenico

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


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:

)21()(

0

ssTd

dP

)1()( ssTP


Output Power vs % Stall Torque

0%

20%

40%

60%

80%

100%

120%

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


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.


Max Power in a DC PM Motor

22ss

Max

TP

604

2 max

RPMs

Max

NTP


Fisher Price Motor Data 2004

All data approximate at

12 VOLTS

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Fisher-Price, motor only

- - .36 N-m 57 A 15,000 RPM 2 140 W

David Giandomenico

Do power calculation, to see if it matches spec.



0

20

40

60

80

100

120

140

160

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)



V=12VDC


Current vs Torque

0

10

20

30

40

50

60

70

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Cur

rent

(A

mps

)



V=12VDC

Current rises linearly with Torque


Motor Current

Where α is the % No Load speed

)1)(()( oso IIII


Electrical Power

VIP


Input Power vs Torque

0

100

200

300

400

500

600

700

800

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Inpu

t Ele

ctri

cal P

ower

(Wat

ts)



V=12VDC

Input power is Current X Voltage



0

20

40

60

80

100

120

140

160

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Mec

hani

cal P

ower

(Wat

ts)



V=12VDC


Electrical Power In & Mechanical Power Out vs Torque

0

100

200

300

400

500

600

700

800

0.00 0.10 0.20 0.30 0.40

Torque (N-m)

Ele

ctri

cal P

ower

In

& M

echa

nica

l Pow

er O

ut (W

atts

)



V=12VDC


Speed vs Torque

0%

10%

20%

30%

40%

50%

60%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Torque (N-m)

Eff

icie

ncy



V=12VDC


DC PM Motor Summary

• Max Power occurs at 50% No-Load Speed

• Best efficiency typically occurs at about 75%-85% 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,

nxx n 11

1x

David

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


222 2 yxyxyx

32233 33 yxyyxxyx

yxyx

yx

1

0 1

4322344 464 yxyyxyxxyx

David Giandomenico

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


4324

323

22

1

0

46411

3311

211

111

11

yyyyy

yyyy

yyy

yy

y

...11 bnb n

David Giandomenico

Note coefficients of second term are 1,2,3,4...n


Pascal’s Triangle

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

4322344

32233

222

1

0

464

33

2

1

1

yxyyxyxxyx

yxyyxxyx

yxyxyx

yxyx

yx

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

David Giandomenico

Extra (digression): some math students may be interested to see quick methods of determining coefficients. Depends on audience--skip as needed.


Binomial Theorem

nnnnn bn

nba

n

nba

na

nba

1111

1...

21

)!(!

!

knk

n

k

n

David

Present Binomial Theorem only if asked...


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 4% for each gear set,

T = in

or

T = (1-4%)6.45 = 76.8%


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


Winch Design Specification

Input parametersWeight 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 ReductionDrum speed

Revolutions / second 0.191Revolutions / minute (rpm) 11.46

Motor spec at 12VDCNo load speed 15000 RPMStall Torque 0.36 N-mPout max 141.37 W

Motor speed and torque% motor speed 80%Motor Speed 12000Torque 0.0720 N-mRequired Gear Reduction 1047.2


Gear Loss Estimate

Required Gear Reduction 1047.2

Loss estimate assuming 'n' small gear setsIndividual gear set reduction ratio 4 times% Loss per gear set 5%

Number of gear reductions 5.016Total estimated gear efficiency 77.31%


Verify We Meet or Exceed Pull Strength Specification

Total estimated gear efficiency 77.31%

Winch line output at speedMotor torque at speed (above) 0.0720 N-mTorque after gearbox (no loss) 75.40 N-m

After gear box losses 58.29 N-mForce on Line 765.00 NForce on Line (lbs) 171.74 lbs


Feat Accomplished!

171 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]

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December 2009 David Giandomenico DC Permanent Magnet Motors A tutorial winch design David...

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