DC Brushed Motors
& Power Transmission
2014 FRC
Ken Stafford
Permanent Magnet Brushed?
• Stator (Field) made
of permanent
magnets
• Rotor (Armature)
made with wire coils
(electromagnets)
• Commutator has
brushes to pass
current
2
The Basics…
• Imperfect Transducers
– Electrical Power to Mechanical Power
– Electrical Power to Thermal Power!
• Electrical Power (input)
– Volts times Amps (Watts)
– EG: CIM @ 40A has 480W input @12V
• Mechanical Power (output)
– Work divided by Time or
– RPM times Torque (Watts or Hp)
– EG: CIM (40A/12V) 3800rpm/6.15
inlbs=275W
The more basic Basics…
• Torque “twisting effort”
– EG: shaft turning, force at the end of an arm,
force at the circumference of wheel…
“pushing/pulling strength”
– Unlimited torque available through any motor
with appropriate transmission
• Power “rate of doing work”
– EG: speed of lifting, torque times rpm, force
times velocity… “robot/mechanism speed”
– Maximum is set by motor design—only
decreases through transmission
Motor Parameters
• Manufacturers provide varying data
• Not too difficult to obtain experimentally with
basic lab equipment
• You need only four values to predict ideal
performance
– At full speed (no load)
• Motor Speed (rpm)
• Current (Amps)
– At maximum torque (stall)
• Torque (inlbs)
• Current (Amps)
Example: Taigene (Van Door)
• Motor clamped in vise hooked
to calibrated power supply
• Free-running rpm by timed
counting
• Stall torque by linear force
balance at end of measured
arm
• Current measured directly from
power supply
• Results:
– Free running: 47.5 rpm @ 1.23 A
– Stall: 360 in lbs @ 24.2 A
Extrapolate Motor Performance
Performance Map
60
50
40
Speed (rpm)
Power (Watts)
30
Efficiency (%)
Current (Amps)
20
Heating (Watts)
10
0
Note: This is at
full rated voltage
0
50
100
150
200
250
Torque (in lbs)
300
350
So…what does this mean?
• Max Torque occurs at zero rpm
(stall)
– Also produces zero Mech Power and
Max Thermal Power
– Lightweight, air-cooled motors will
smoke in seconds
More on Motors…
• Max Power occurs at 50% Stall Torque, ~
50% Stall Current, and 50% Free-running
speed
• Any sub-maximum power is available at
2 different operating conditions
– High speed/low torque
– Low speed/high torque
• Max Efficiency occurs at ~25% Stall
Torque or ~60% Max Power
Typical FRC Motors
• Sealed vs Fan-Cooled
• Thermal Protection
• Anti-backdrive vs backdrive
resistant
• Built in transmissions
Motor Selection Criterion
1 Power Requirement
2 Weight of Motor &
Transmission
3 Physical Size of Motor & Transmission
4 Backdrive Characteristics
5 Continuous vs Intermittent Operations
6
Efficiency
7
Availability
Specific Recommendations
• Sealed motors (eg CIM)
– High torque, can handle
intermittent high loads
– Heavy
• Application:
– Driveline or other high power accessories
– Must be kept LOW in chassis
Recommendations Cont.
• Fan-cooled motors (eg FP)
– Very high power/low weight/
intolerant of high load
• Applications:
– Shooters/fans
Recommendation Cont.
• Worm Gear Motors (eg
Van Door)
– Thermal protection,
backdrive resistant, low
power, heavy
• Applications:
– Arm shoulder, turret
– Low in chassis
Design Example
• Build a winch to lift a
100 lb robot 3 ft in 10
secs:
– Mech Power =
Work/Time * Conversion
– Required Power = ((100
lb)(3 ft)/10 sec)(746
W/550 ft-lb/sec) = 40W
– 12 of the 20 allowed
2014 FRC motors > 40W
Taigene Performance Map
60
50
40
Speed (rpm)
Power (Watts)
30
Efficiency (%)
Current (Amps)
20
10
0
0
50
100
150
200
250
Torque (in lbs)
300
350
Design Example (cont)
• From the Performance Map
– It produces 40 W at either 100 or 275 in-lb
• At 100 in-lbs it’s ~45% efficient; at 275, it’s ~18%!
– Design your drum radius so it develops 50
lbs of force with 100 in-lbs of torque
• Radius = 100in-lbs/100 lbs = 1 in
100 lbs
2 in
100 in-lbs
Design Result
Drum Radius
Motor Condition
Time to Lift
<1.0 in
Happy—cool
>3.0 secs
=1.0 in
Working easy
=3.0 secs
>1.0; <2.75 in
Getting warm…
<3.0 secs
=2.75 in
Working hard
=3.0 secs
>2.75 in
Unhappy—hot!
>3.0 secs
Design Details Cont.
• If holding a lifter/arm in position is important
do not rely upon motor torque (overheating)
Design aexample:
mechanical
one-way
clutch/
• Previous
~30W
to hold
@ 1.0 in
retractable
ratchet
or @
balance
drum;
~180W
to hold
2.75 inmechanism
drum!
Transmission Essentials
• Unless you are VERY lucky…you will need ‘em
• Transmissions can:
1) Modify output speed/torque.
Transmission Essentials
• Unless you are VERY lucky…you will need ‘em
• Transmissions can:
1) Modify output speed and torque
2) Change direction of rotation
3) Physically separate motor from device
• They will ALWAYS
4) Reduce power through losses
More Basics
• For spur gears and chain/sprockets, it’s all
about the number of teeth!
• “Gear Train”, aka “Speed Ratio”
e = Product of Drivers / Product of Driven
= Speed out / Speed in
= (Torque in / Torque out) * Sys efficiency
Speed Example
• Driving elements:
– 16 T gear
– 18 T sprocket
• Driven elements:
– 54 T gear
– 28 T sprocket
• e = (16 * 18)/(54 * 28) = .19
• With motor @ 5000 rpm
Roller speed = 5000 *.19 = 950 rpm
Torque Example
• Same transmission: e =.19
• Losses occur at each “stage”
– Typically 5% loss (η = .95)
• You calculate you need 20 lbs
force at the 2 inch dia roller
Torque out = 20 lbs * 1 in = 20inlb
Torque in = (.19 * 20 inlb) / (.95 * .95) = 4.2 inlb
• Note: this would result in a 28 A load with
the small CIM as shown
“Roller” Chain and Sprockets
• Parameters (ANSI)
– Chain Number:
• 1st digit = pitch in 1/8 inches
• 2nd digit = “roller” (0), “lightweight”
(1), or “bushed” (5)
• EG: #25: ¼ inch pitch without rollers,
#35: 3/8 inch pitch without rollers
– Strength (breaking/working):
• #25 = 875/140 lbs
• #35 = 2100/480 lbs
– “Working” implies industrial duty/life expectancy
Chain Design Details
• Sprocket sizes
– Recommend 12T to 75T
• Smaller causes vibration & excess wear
• Larger leads to chain loss
• Chain Wrap
– 120 degree minimum for any drive or driven
sprocket
– Change routing, add idlers if necessary
• Design in adjusters for long runs
– Adjustment range should ideally be 2 pitch
lengths (to avoid half-links)
Gears, gears, gears!
• Parameters (ANSI)
– (Diametral) Pitch:
P = Number of Teeth/ Pitch Diameter
• Integer number, normally divisible by 4
• EG: 32, 28, 24, 20, etc
• Larger the P, the smaller/weaker the teeth
– Pressure Angle: the actual off-tangent angle force
transmission
• Typically 14.5 or 20 degrees
• 14.5 degrees weaker, more efficient
Spur Gear Design Details
• Gear sizes
– Recommend 12T to Infinity! (rack)
• Smaller (“pinions”) are weak from undercutting—esp 14.5 degree PA
– All gears with same P and PA will fit
• Transmission axle separation
– An exact, easily computed distance
D = (Total number of teeth/P) / 2
– EG: 16T & 42T, 24 Pitch gears
D = ((16 + 42) / 24) / 2 = 1.208 inches
• Can be 95-98% efficient/stage
16T
42T
Other Gear Stuff
50T
• Worm Gears
– Antibackdrive (Helix angle dependent,
Window--yes; Van Door--no)
– Woefully inefficient: η = .25-.75
– Very compact
e = Number leads on worm / Teeth on
Worm Gear
= 4 / 50 = .08
– DO NOT USE FOR HI-POWER
– Requires VERY secure bearing
support
4
General Suggestions
• Operate motors on left side of perf map
• Air-cooled motors cannot operate near
stall for more than a few seconds
• Control top speed of operation by
suitable gearing not by reduced voltage
• Avoid powered anti-backdrive
• Driveline ROT: no wheel-spin when
blocked? = TOO HIGH GEARED!
Overall Caveats
• Real world motors in robots will not operate at
the peak values predicted on the performance
maps
– Batteries will sag, voltage will be lost through
conductors, etc
• You need to consider mechanical
transmission efficiency when calculating
motor requirements
• Be careful to note reference voltage in
manufacture’s data—automotive use 10.5V
commonly
Questions?