December 10, 2011 David Giandomenico - FIRST #846 DC Permanent Magnet Motors A tutorial winch design...

December 10, 2011 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

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



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


“CIM” Motor Specification


“CIM” Motor Performance


“CIM” Motor Performance

StallTorque

StallTorque

No LoadCurrentNo LoadCurrent

No Load Speed

No Load Speed

StallCurrentStallCurrent


FUSE Limits on Motor Power

StallCurrentStallCurrent

40 AFuse Limit40 AFuse Limit

~100 Oz-In~100 Oz-In


Kit Motors – Which One?

Make / ModelMax 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

All Data at 12VDC


Motors - Sorted by 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


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


Motor Selection


(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


(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


(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


www.johnsonmotor.com


2011 Fisher Price Motor


(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

All Data at 12VDC


(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

Convert oz-in to N-m: 1 oz-in = 0.007061552 N-m


Fisher Price Motor 2010

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 in a Rotating System

€

W = Tθ

€

W =v F ×

r r θ

€

W = (v F ×

r r )θ

€

W =r F ⋅

r x Force

€

θr

T

David Giandomenico


Power, Torque & Speed

TP

60

RPM 2TP

timedistForceP /

trFP /)( θtrFP /θ

December 10, 2011 David Giandomenico - FIRST #846From FIRST_MOTOR_CALC.xls

V=12VDC

(speed,torque)


David Giandomenico



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%

Torque (% Stall Torque)

% 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


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


2011 Fisher Price Motor

All Data at 12VDC


(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




V=12VDC




V=12VDC

Current rises linearly with Torque


Motor Current

Where α is the % No Load speed

)1)(()( oso IIII


Electrical Power

VIP




V=12VDC

Input power is Current X Voltage




V=12VDC




V=12VDC




V=12VDC




V=12VDC


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,

€

1− x( )n

≈1− nx

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 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 20770 RPMStall Torque 75.4 oz0inStall Torque (1 Oz-In= 0.007061552 N-m) 0.532N-mMax Power Output 289.5 WFree Current 0.82 AStall Current 108.7 A

Operating Point at FUSE currentat 20A 17.8%at 30A 27.0%at 40A 36.3%

Select Motor Speed and Torque% motor speed 90%Motor current 11.6 AMotor Speed 18693 rpmTorque 0.0532 N-mPower out 104.2 WRequired Gear Reduction 1631.3

Required Gear Reduction 1631.3

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

Number of gear reductions 5.336 setsTotal estimated gear efficiency 76.06%


Gear Loss Estimate

Winch line output at speedMotor torque at speed (above) 0.0532 N-mTorque after gearbox (no loss) 86.86 N-m

After gear box losses 66.06 N-mForce on Line 866.92 NForce on Line (lbs) 194.61 lbs


Verify We Meet or Exceed Pull Strength Specification


Feat Accomplished!

194 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


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...

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December 10, 2011 David Giandomenico - FIRST #846 DC Permanent Magnet Motors A tutorial winch design...

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