DC Permanent Magnet Motors
A tutorial winch design
David Giandomenico
Lynbrook High School Robotics
FIRST Team #846
DGiandomenico@lynbrookrobotics.com
(408)343-1183
August 10, 2013
David Giandomenico - FIRST #846
2010 Breakaway
August 10, 2013
David Giandomenico - FIRST #846
2004 FIRST Frenzy: Raising the Bar
August 10, 2013
David Giandomenico - FIRST #846
What We Want.
• Weight:
130 lbs
• Distance:
1.5 feet
• Time (speed):
5 seconds
August 10, 2013
David Giandomenico - FIRST #846
What We’ve Got:
Some of the Motors supplied in FIRST Robotics Kit
August 10, 2013
David Giandomenico - FIRST #846
Kit Motors – Which One?
All Data at 12VDC
Make
Model
AndyMark
am-0912
AndyMark
am-0915
BaneBots
M7-RS775-18
BaneBots
M5-RS550-12
M5-RS550-12-B
BaneBots
M5-RS540-12
BaneBots
M7-RS775-12
BaneBots
M5-RS545-12
BaneBots
M3-RS395-12
CIM
FR801-001
VEX Mini CIM
217-3371
VEX bag motor
217-3351
August 10, 2013
2013 choices (partial list!)
Max Power Stall Torque Free Speed Free Current Stall Current
(W)
(oz-in)
(rpm)
(A)
(A)
179
61
16000
1.2
64
45
1209
198
0.6
22
273
113
13000
1.8
87
254
71
19300
1.4
85
123
39
16800
1
42
83
61
7300
1.1
30
74
24
16800
0.9
21
48
17
15500
0.5
15
337
343
5310
2.7
133
229
198
6200
1.8
86
149
57
14000
1.8
41
David Giandomenico - FIRST #846
Motors - Sorted by Power
Make
Model
CIM
FR801-001
BaneBots
M7-RS775-18
BaneBots
M5-RS550-12
M5-RS550-12-B
VEX Mini CIM
217-3371
AndyMark
am-0912
VEX bag motor
217-3351
BaneBots
M5-RS540-12
BaneBots
M7-RS775-12
BaneBots
M5-RS545-12
BaneBots
M3-RS395-12
AndyMark
am-0915
August 10, 2013
Max Power Stall Torque Free Speed
Free
Stall Current
(W)
(oz-in)
(rpm)
Current (A)
(A)
337
343
5310
2.7
133
273
113
13000
1.8
87
254
71
19300
1.4
85
229
198
6200
1.8
86
179
61
16000
1.2
64
149
57
14000
1.8
41
123
39
16800
1
42
83
61
7300
1.1
30
74
24
16800
0.9
21
48
17
15500
0.5
15
45
1209
198
0.6
22
David Giandomenico - FIRST #846
“CIM” Motor Specification
August 10, 2013
David Giandomenico - FIRST #846
“CIM” Motor Performance
August 10, 2013
David Giandomenico - FIRST #846
“CIM” Motor Performance
Stall
Current
No Load
Speed
No Load
Current
Stall
Torque
August 10, 2013
David Giandomenico - FIRST #846
Current Limits (fuse)
on Motor Power
Stall
Current
40 A
Fuse Limit
~100 Oz-In
August 10, 2013
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)
August 10, 2013
David Giandomenico - FIRST #846
www.johnsonmotor.com
August 10, 2013
David Giandomenico - FIRST #846
W inch D esig n
In p u t p a ra m e te rs
W eight to lift (lbs )
130
H eight (ft) to lift in tim e T
1.5
Tim e to lift s ec onds
5
W eight & M as s c onvers ions :
C o n ve rt to M K S (m e tric syste m )
M as s to lift (K gs )
59.1
W eight To lift (N ew tons )
579.1
H eight (m )
0.457
Tim e to Lift
5
1K g = 2.2 lbs -m as s
W eight in N ew tons = m as s x 'g'
w here g= 9.8 m /s /s
s o a 1K g m as s w eighs 9.8 N ew tons
P o te n tia l En e rg y
K p = m gh (Joules )
264.8
P o w e r n e e d e d to g a in a b o ve e n e rg y in tim e T
P = K p / T (W atts )
August 10, 2013
53.0
David Giandomenico - FIRST #846
Motor Selection
Make
Model
CIM
FR801-001
BaneBots
M7-RS775-18
BaneBots
M5-RS550-12
VEX Mini CIM
217-3371
AndyMark
am-0912
VEX bag motor
217-3351
BaneBots
M5-RS540-12
BaneBots
M7-RS775-12
BaneBots
M5-RS545-12
BaneBots
M3-RS395-12
AndyMark
am-0915
August 10, 2013
Max Power Stall Torque Free Speed
Free
Stall Current
(W)
(oz-in)
(rpm)
Current (A)
(A)
337
343
5310
2.7
133
273
113
13000
1.8
87
254
71
19300
1.4
85
229
198
6200
1.8
86
179
61
16000
1.2
64
149
57
14000
1.8
41
123
39
16800
1
42
83
61
7300
1.1
30
74
24
16800
0.9
21
48
17
15500
0.5
15
45
1209
198
0.6
22
David Giandomenico - FIRST #846
What is Torque?
T  F  d
But isn’t that “Work?”
W  Finline  d
August 10, 2013
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 …
August 10, 2013
David Giandomenico - FIRST #846
Work in a Rotating System
W = F× x
T
q
r
W = F ´ rq
W = (F ´ r )q
W = Tq
August 10, 2013
David Giandomenico - FIRST #846
Power, Torque & Speed
P  Force  dist / time
P  F  r / t
P  ( F  r ) / t
P  T
P T
2 RPM
60
August 10, 2013
David Giandomenico - FIRST #846
Where is Max Power?
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)
August 10, 2013
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Maximum Power
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)
August 10, 2013
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Standardize through Normalization
http://www.mabuchi-motor.co.jp
August 10, 2013
http://www.johnsonmotor.com
David Giandomenico - FIRST #846
Simplified through Standardization
http://www.mabuchi-motor.co.jp
http://www.johnsonmotor.com
August 10, 2013
David Giandomenico - FIRST #846
N ormalized S peed vs Torque
V=Rated Voltage
% N o L o a d Sp e e d
100%
85%+15%=100%
90%
80%
70%
60%
50%+50%=100%
50%
40%
30%+70%=100%
30%
20%
10%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90% 100%
T orque (% Sta ll T orque )
August 10, 2013
David Giandomenico - FIRST #846
Speed & Torque in a DC PM Motor
• Let ={0,100%}
such that
N ( )  N s
 ( )   s
T ( )  T s (1   )
August 10, 2013
David Giandomenico - FIRST #846
Speed & Torque in a DC PM Motor
P ( )   ( )T ( )
P(a ) = w f a ´ Ts (1- a )
= w f Ts ´ a (1- a )
Using calculus, Max Power occurs when:
dP(a )
0=
= w f Ts (1- 2a )
da
Or, w/o calculus, Max occurs between two roots of
quadratic, at =0, =1 that is,
=½ or equivalently, when =50%
August 10, 2013
David Giandomenico - FIRST #846
Max Power in a DC PM Motor
P(a ) = w f a ´ Ts (1- a )
at a max = 50%,
PMax =
PMax 
August 10, 2013
TSw f
4
2 T s N RPM
 max
4  60
David Giandomenico - FIRST #846
Output Power vs % Stall Torque
V=Rated Voltage
Power Out (% Max Power)
120%
100%
80%
75%
60%
40%
P (a ) TSw f a (1- a )
=
Pmax
TSw f / 4
20%
0%
0%
10%
20%
30%
40%
50%
60%
Torque (% Stall Torque)
August 10, 2013
70%
80%
90%
= 4a100%
(1- a )
P ( 25%)
1 3
= 4× ×
Pmax
4 4
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
August 10, 2013
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)
August 10, 2013
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
August 10, 2013
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
August 10, 2013
David Giandomenico - FIRST #846
Electrical Power
P  I V
August 10, 2013
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
August 10, 2013
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)
August 10, 2013
From FIRST_MOTOR_CALC.xls
David Giandomenico - FIRST #846
Fisher Price Motor 2011
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)
August 10, 2013
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)
August 10, 2013
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)
August 10, 2013
David Giandomenico - FIRST #846
Normalized Efficiency for IDEAL motor
August 10, 2013
David Giandomenico - FIRST #846
Operating Point:
1
a eff =
1+ I o / I s
Best Operating Point
Max Efficiency
100%
90%
80%
70%
60%
50%
0%
5%
10%
Io / Is
Efficiency:
ù
Tsw o é
1
hmax =
ê
ú
VI s êë1+ I o / I S úû
2
August 10, 2013
David Giandomenico - FIRST #846
Derivation of:
Efficiency:
Max Efficiency
Tsw o a (1- a )
h=
VI s 1- ka
Where:
k º1- c =1- Io / I s
Find Maximum :
d a (1- a )
0=
da 1- ka
...simplifying yields:
0 = ka 2 - 2a +1
Use Quadratic Formula to find roots:
1± 1- k
a eff =
k
August 10, 2013
David Giandomenico - FIRST #846
Derivation of:
Max Efficiency
continued
Tsw o a (1- a )
h=
VI s 1- ka
at a = aeff ,
2
0 = ka eff
- 2a eff +1
2
0 = ka eff
- a eff - a eff +1
2
1- a eff = a eff - ka eff
= a eff (1- ka eff )
Substitute for (1-α) to get:
h (a ) a =a
August 10, 2013
eff
Tswo 2
=
aeff
VI s
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.
August 10, 2013
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
August 10, 2013
T = (100%-4%)3 = 88.5%
David Giandomenico - FIRST #846
When x is small,
x  1
(1 - x ) »1 - nx
n
August 10, 2013
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
August 10, 2013
David Giandomenico - FIRST #846
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%
August 10, 2013
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
August 10, 2013
David Giandomenico - FIRST #846
Winch Design Specification
In p u t p aram eters
W eight to lift (lbs)
H eight (ft) to lift in tim e T
T im e to lift seconds
C o n v ert to M K S (m etric system )
M ass to lift (K gs)
W eight T o lift (N ew tons)
H eight (m )
T im e to Lift
August 10, 2013
130
1.5
5
59.1
579.1
0.457
5
David Giandomenico - FIRST #846
Winch Drum Speed
W in c h L in e S p e e d
D is ta n c e (m )
T im e
S p e e d (m /s )
0 .4 5 7 2
5
0 .0 9 1 4
D ru m s ize (d ic ta te d b y fa c to rs s u c h a s c a b le )
D ia m e te r (in c h e s )
6
D ia m e te r (m )
0 .1 5 2
C irc u m fe re n c e (m )
0 .4 7 9
D ru m s p e e d
R e vo lu tio n s / s e c o n d
R e vo lu tio n s / m in u te (rp m )
August 10, 2013
0 .1 9 1
1 1 .4 6
David Giandomenico - FIRST #846
Determine the Gear Reduction
August 10, 2013
David Giandomenico - FIRST #846
Gear Loss Estimate
Required Gear Reduction
1021.0
Loss estimate assuming 'n' small gear sets
Individual gear set reduction ratio
% Loss per gear set
Number of gear reductions
Total estimated gear efficiency
August 10, 2013
4 times
5%
4.998 sets
77.39%
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 (lb)
0.0798 N-m
81.47 N-m
63.05 N-m
827.41 N
185.75 lb
Margin
Weight of load
130 lb
Margin (force:load at target speed) 1.43 : 1
August 10, 2013
David Giandomenico - FIRST #846
Feat Accomplished!
185 lb exceeds required spec of 130lbs
August 10, 2013
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
August 10, 2013
David Giandomenico - FIRST #846
Addendum: Interest or Time permitting
August 10, 2013
David Giandomenico - FIRST #846