Transcript Speeds & Torques in DC Permanent Magnet Motors

More than you wanted to know about
Robot Winch Design
David Giandomenico
Lynbrook High School Robotics
FIRST Team #846
[email protected]
(408)343-1183
September 15, 2007
D.Giandomenico
A few common tasks robots might do:
• Robot may move itself
• Robot often has an arm to lift or grasp objects
• Robot might have to lift itself or pull an object
September 15, 2007
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Three functions we may consider:
• Design a robot arm
• Design the drive train
• Design a lifting winch
We will consider the winch, which is
arguably the most simply specified of the
three robotic functions.
September 15, 2007
D.Giandomenico
2004 FIRST National Robotics
Competition
• Endgame Task:
Robot must
suspend itself from
a bar located 10
feet above the floor
• Our task: Design a
winch to lift robot
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Design Criterion for the Winch
• How much weight to lift?
• How far?
• How fast?
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What We Want.
• Weight:
130 lbs
• Distance:
1.5 feet
• Time (speed):
5 seconds
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What we have:
(Some of the Motors supplied in FIRST Robotics Kit)
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Globe, motor/gearbox
Delphi Seat Motor (Mfg:
Keyang)
Delphi Window Motor
(Mfg: Valeo)
Peak Power
Globe, motor only
FreeCurrent
Fisher-Price,
motor/gearbox
Delphi Sliding Door Motor
(Mfg: Taigene)
FreeSpeed
Fisher-Price, motor only
StallCurrent
Bosch, motor/gearbox in
high
Bosch, motor/gearbox in
low
StallTorque
Bosch, motor only
Gearbox Efficiency
All data approximate at
12 VOLTS
Gearbox Ratio
FIRST MOTOR COMPARISON (2002-2003)
-
-
0.65
114 A
20,000 RPM
2.5 A
340 W
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
-
-
.36 N-m
57 A
15,000 RPM
?
140 W
147:1
65%
35 N-m
57 A
100 RPM
?
91 W
-
-
35 N-m
40 A
75 RPM
?
69 W
-
-
.21 N-m
21 A
11,500 RPM
.82 A
63 W
117:1
77%
19 N-m
21 A
100 RPM
.82 A
50 W
-
-
2 N-m
20 A
600 RPM
?
31 W
-
-
12 N-m
20 A
70 RPM
?
22 W
data from www.usfirst.org
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“CIM” Motor Specification
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“CIM” Motor Performance
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“CIM” Motor Performance
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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
September 15, 2007
D.Giandomenico
Globe, motor/gearbox
Delphi Seat Motor (Mfg:
Keyang)
Delphi Window Motor
(Mfg: Valeo)
Peak Power
Globe, motor only
FreeCurrent
Fisher-Price,
motor/gearbox
Delphi Sliding Door Motor
(Mfg: Taigene)
FreeSpeed
Fisher-Price, motor only
StallCurrent
Bosch, motor/gearbox in
high
Bosch, motor/gearbox in
low
StallTorque
Bosch, motor only
Gearbox Efficiency
All data approximate at
12 VOLTS
Gearbox Ratio
FIRST MOTOR COMPARISON (2002-2003)
-
-
0.65
114 A
20,000 RPM
2.5 A
340 W
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
-
-
.36 N-m
57 A
15,000 RPM
?
140 W
147:1
65%
35 N-m
57 A
100 RPM
?
91 W
-
-
35 N-m
40 A
75 RPM
?
69 W
-
-
.21 N-m
21 A
11,500 RPM
.82 A
63 W
117:1
77%
19 N-m
21 A
100 RPM
.82 A
50 W
-
-
2 N-m
20 A
600 RPM
?
31 W
-
-
12 N-m
20 A
70 RPM
?
22 W
data from www.usfirst.org
September 15, 2007
D.Giandomenico
Choosing a motor based on
Maximum Motor Output Power
• The max power of a DC PM magnet motor cannot be sustained
without burning out the motor!
• As a rule of thumb, operate motor at 70%-80% of the
no-load speed.
• Power output = Pmax * 4(1-)
where   % no-load speed
• Coincidentally,
At 75% no-load speed, Pout = 75% Pmax
• Need to consider losses in Gear sets
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September 15, 2007
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Estimate gear loss for
a large gear reduction
Consider a large gear reduction of 1200
First, estimate number of small gears sets
(Typical gear sets might have a ratio of 3:1)
Second, estimate the loss in for n gear sets
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Gear loss estimate for a set of gears
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%
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D.Giandomenico
Estimate of how many gears to
make a large gear reduction.
• 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
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.
September 15, 2007
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Gear loss estimate
From before, we need around n=6.45 gear
sets. Assuming a loss of 4% for each gear
set,
T = in
or
T = (1-4%)6.45 = 76.8%
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Fisher Price Motor Data 2004
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Fisher Price Motor 2004
SPEED
V=12VDC
16000.0
14000.0
Speed (RPM)
12000.0
10000.0
8000.0
6000.0
4000.0
2000.0
0.
36
0.
34
0.
31
0.
29
0.
26
0.
24
0.
22
0.
19
0.
17
0.
14
0.
12
0.
10
0.
07
0.
05
0.
02
0.
00
0.0
Torque (N-m)
Speed decreases as motor is braked
September 15, 2007
From FIRST_MOTOR_CALC.xls
D.Giandomenico
What is Torque?
T  F  d
But isn’t that “Work”
W  Finline  d
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Units of Work vs. Torque
• Work (Energy)
ft-lbf, Joules (=N-m), KWh, etc.
• Torque
pound feet(lbf-ft), ft-lbf, oz-in,
N-m etc.
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Power, Torque & Speed
P  F d /t
P  F  r / t
P  ( F  r ) / t
P  T
2 RPM
P T
60
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D.Giandomenico
Fisher Price Motor 2004
POWER
V=12VDC
160.0
Mechanical Power (Watts)
140.0
120.0
100.0
80.0
60.0
40.0
20.0
0.
36
0.
34
0.
31
0.
29
0.
26
0.
24
0.
22
0.
19
0.
17
0.
14
0.
12
0.
10
0.
07
0.
05
0.
02
0.
00
0.0
Torque (N-m)
From FIRST_MOTOR_CALC.xls
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Speed & Torque in a DC PM Motor
• Let ={0,100%}
such that
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
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Speed & Torque in a DC PM Motor
Using calculus, Max Power occurs when:
Or, w/o calculus, Max occurs between two roots
of quadratic, at =0, =1 that is,
=½ or equivalently, when =50%
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
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Max Power in a DC PM Motor
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Fisher Price Motor Data 2004
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
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Power input into a DC PM Motor
Device Under Test (DUT) conditions:
V = 12VDC (fixed)
Load is varied using some type of brake
Under these conditions, a good model for the
current is:
September 15, 2007
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Power input into a DC PM Motor
P  I V
Power is small when =100%, and increases
linearly as  decreases
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
September 15, 2007
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
September 15, 2007
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Fisher Price Motor 2004
V=12VDC
From FIRST_MOTOR_CALC.xls
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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 cannot sustain operating
with full voltage applied at speeds less than 50%
No-Load.
September 15, 2007
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Putting it all together
1.
2.
3.
4.
Choose a winch drum size
Calculate the drum rpm
Choose the % motor operating speed
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
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Winch Design Specification
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Winch Drum Speed
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Determine the Gear Reduction
Drum speed
Revolutions / second
Revolutions / minute (rpm)
0.191
11.46
Motor spec at 12VDC
No load speed
Stall Torque
Pout max
15000 RPM
0.36 N-m
141.37 W
Motor speed and torque
% motor speed
Motor Speed
Torque
Required Gear Reduction
80%
12000
0.0720 N-m
1047.2
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Gear Loss Estimate
Required Gear Reduction
1047.2
Loss estimate assuming 'n' small gear sets
Individual gear set reduction ratio
4 times
% Loss per gear set
5%
Number of gear reductions
Total estimated gear efficiency
September 15, 2007
5.016
77.31%
D.Giandomenico
Verify We Meet or Exceed Pull
Strength Specification
Total estimated gear efficiency
77.31%
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)
0.0720
75.40
58.29
765.00
171.74
September 15, 2007
N-m
N-m
N-m
N
lbs
D.Giandomenico
Feat Accomplished!
• 171lb exceeds required spec of 130lbs
• What does this mean?
• Things to think about:
– Could it be that we overdesigned the winch?
– How will the winch respond when lifting 130lbs if it is pulling with
171lbs?
– And of course, how do we build this winch?
September 15, 2007
D.Giandomenico
More than you wanted to know about
Robot Winch Design
David Giandomenico
Lynbrook High School Robotics
FIRST Team #846
[email protected]
(408)343-1183
September 15, 2007
D.Giandomenico