DC Permanent Magnet Motors
A tutorial winch design
David Giandomenico
Lynbrook High School Robotics
FIRST Team #846
DGiandomenico@lynbrookrobotics.com
(408)343-1183
December 10, 2011
David Giandomenico - FIRST #846
2010 Breakaway
December 10, 2011
David Giandomenico - FIRST #846
2004 FIRST Frenzy: Raising the Bar
December 10, 2011
David Giandomenico - FIRST #846
What We Want.
• Weight:
130 lbs
• Distance:
1.5 feet
• Time (speed):
5 seconds
December 10, 2011
David Giandomenico - FIRST #846
What We’ve Got:
Some of the Motors supplied in FIRST Robotics Kit
December 10, 2011
David Giandomenico - FIRST #846
“CIM” Motor Specification
December 10, 2011
David Giandomenico - FIRST #846
“CIM” Motor Performance
December 10, 2011
David Giandomenico - FIRST #846
“CIM” Motor Performance
Stall
Current
No Load
Speed
No Load
Current
Stall
Torque
December 10, 2011
David Giandomenico - FIRST #846
FUSE Limits on Motor Power
Stall
Current
40 A
Fuse Limit
~100 Oz-In
December 10, 2011
David Giandomenico - FIRST #846
Kit Motors – Which One?
All Data at 12VDC
Max 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
Make / Model
December 10, 2011
David Giandomenico - FIRST #846
Motors - Sorted by Power
Max 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
Make / Model
December 10, 2011
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)
December 10, 2011
David Giandomenico - FIRST #846
Winch Design
Input parameters
Weight to lift (lbs)
Height (ft) to lift in time T
Time to lift seconds
130
1.5
5
Convert to MKS (metric system)
Mass to lift (Kgs)
Weight To lift (Newtons)
Height (m)
Time to Lift
59.1
579.1
0.457
5
Potential Energy
Kp = mgh (Joules)
264.8
Weight & Mass conversions:
1Kg = 2.2 lbs-mass
Weight in Newtons = mass x 'g'
where g=9.8 m/s/s
so a 1Kg mass weighs 9.8 Newtons
Power needed to gain above energy in time T
P = Kp / T (Watts)
53.0
December 10, 2011
David Giandomenico - FIRST #846
Motor Selection
Max 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
Make / Model
December 10, 2011
David Giandomenico - FIRST #846
www.johnsonmotor.com
December 10, 2011
David Giandomenico - FIRST #846
2011 Fisher Price Motor
All Data at 12VDC
Make / Model
Max Power
(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
Convert oz-in to N-m:
1 oz-in = 0.007061552 N-m
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
December 10, 2011
David Giandomenico - FIRST #846
Fisher Price Motor 2010
Speed vs Torque
V=12VDC
25000
Speed (RPM)
20000
15000
10000
5000
0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Torque (N-m)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
What is Torque?
T  F  d
But isn’t that “Work”
W  Finline  d
December 10, 2011
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 …
December 10, 2011
David Giandomenico - FIRST #846
Work in a Rotating System
T


r



December 10, 2011
r r
W  F x
v r
W  F  r
v r
W  (F  r )
W  T
David Giandomenico - FIRST #846
Power, Torque & Speed
P  Force  dist / time
P  F  r / t
P  ( F  r ) / t
P  T
2 RPM
P T
60
December 10, 2011
David Giandomenico - FIRST #846
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)
December 10, 2011
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)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Normalized Speed vs Torque
% No Load Speed
V=Rated Voltage
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Torque (% Stall Torque)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Speed & Torque in a DC PM Motor
• Let ={0,100%}
such that
N ( )  N s
 ( )   s
T ( )  Ts (1   )
December 10, 2011
David Giandomenico - FIRST #846
Normalized Speed vs Torque
% No Load Speed
V=Rated Voltage
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Torque (% Stall Torque)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Speed & Torque in a DC PM Motor
P( )   ( )T ( )
P( )  sTs  (1   )
Using calculus, Max Power occurs when:
dP ( )
0
  sTs (1  2 )
d
Or, w/o calculus, Max occurs between two roots of quadratic, at
=0, =1 that is,
=½ or equivalently, when =50%
December 10, 2011
David Giandomenico - FIRST #846
Output Power vs % Stall Torque
V=Rated Voltage
Power Out (% Max Power)
120%
100%
80%
75%
60%
40%
20%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90% 100%
Torque (% Stall Torque)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Max Power in a DC PM Motor
PMax
PMax
December 10, 2011
 Ts   s 
   
 2  2 
2 Ts N RPM  max

4  60
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
December 10, 2011
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)
December 10, 2011
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
December 10, 2011
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
December 10, 2011
David Giandomenico - FIRST #846
Electrical Power
P  I V
December 10, 2011
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
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Fisher Price Motor 2010
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)
December 10, 2011
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Fisher Price Motor 2010
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)
December 10, 2011
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)
December 10, 2011
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)
December 10, 2011
From FIRST_MOTOR_CALC.xls
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.
December 10, 2011
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
December 10, 2011
T = (100%-4%)3 = 88.5%
David Giandomenico - FIRST #846
When x is small,
x  1
1 x 1 nx
n

December 10, 2011
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
December 10, 2011
David Giandomenico - FIRST #846
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%
December 10, 2011
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
December 10, 2011
David Giandomenico - FIRST #846
Winch Design Specification
Input parameters
Weight to lift (lbs)
Height (ft) to lift in time T
Time to lift seconds
Convert to MKS (metric system)
Mass to lift (Kgs)
Weight To lift (Newtons)
Height (m)
Time to Lift
December 10, 2011
130
1.5
5
59.1
579.1
0.457
5
David Giandomenico - FIRST #846
Winch Drum Speed
Winch Line Speed
Distance (m)
Time
Speed (m/s)
0.4572
5
0.0914
Drum size (dictated by factors such as cable)
Diameter (inches)
6
Diameter (m)
0.152
Circumference (m)
0.479
Drum speed
Revolutions / second
Revolutions / minute (rpm)
December 10, 2011
0.191
11.46
David Giandomenico - FIRST #846
Determine the Gear Reduction
December 10, 2011
Drum speed
Revolutions / second
Revolutions / minute (rpm)
0.191
11.46
Motor spec at 12VDC
No load speed
Stall Torque
Stall Torque (1 Oz-In= 0.007061552 N-m)
Max Power Output
Free Current
Stall Current
20770 RPM
75.4 oz0in
0.532 N-m
289.5 W
0.82 A
108.7 A
Operating Point at FUSE current
at 20A
at 30A
at 40A
17.8%
27.0%
36.3%
Select Motor Speed and Torque
% motor speed
Motor current
Motor Speed
Torque
Power out
Required Gear Reduction
90%
11.6 A
18693 rpm
0.0532 N-m
104.2 W
1631.3
David Giandomenico - FIRST #846
Gear Loss Estimate
Required Gear Reduction
Loss estimate assuming 'n' small gear sets
Individual gear set reduction ratio
% Loss per gear set
Number of gear reductions
Total estimated gear efficiency
December 10, 2011
1631.3
4 times
5%
5.336 sets
76.06%
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 (lbs)
December 10, 2011
0.0532 N-m
86.86 N-m
66.06 N-m
866.92 N
194.61 lbs
David Giandomenico - FIRST #846
Feat Accomplished!
194 lb exceeds required spec of 130lbs
December 10, 2011
David Giandomenico - FIRST #846
More than you wanted to know about
Robot Winch Design
David Giandomenico
Lynbrook High School Robotics
FIRST Team #846
DGiandomenico@lynbrookrobotics.com
(408)343-1183
December 10, 2011
David Giandomenico - FIRST #846
Addendum: Interest or Time permitting
December 10, 2011
David Giandomenico - FIRST #846
x  y   1
1
x  y   x  y
2
2
2
x  y   x  2xy  y
3
3
2
2
3
x  y  x  3x y  3xy  y
4
4
3
2 2
3
4
x  y  x  4x y  6x y  4xy  y
0
December 10, 2011
David Giandomenico - FIRST #846
1  y   1
1
1  y   1  1 y
2
2
1  y   1  2 y  y
3
2
3
1  y   1  3 y  3 y  y
4
2
3
4
1  y   1  4 y  6 y  4 y  y
0
1  b
n
December 10, 2011
 1  n b  ...
David Giandomenico - FIRST #846
Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
December 10, 2011
x  y   1
x  y 1  x  1 y
x  y 2  x 2  2 xy  y 2
x  y 3  x 3  3 x 2 y  3 xy 2  y 3
4
x  y   x 4  4 x 3 y  6 x 2 y 2  4 xy3  y 4
0
David Giandomenico - FIRST #846
Binomial Theorem
 n  n  n  n1 1
 n  1 n1  n  n
a  b   a   a b  ...  a b  b
1 
 2
 n  1
 n
n
n
n!
  
 k  k!(n  k )!
December 10, 2011
David Giandomenico - FIRST #846