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Transcript of Robotics 3
8/8/2019 Robotics 3
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May 21, 2006
EXPERT SYSTEMS AND SOLUTIONS
Email: [email protected]
Cell: 9952749533www.researchprojects.info
PAIYANOOR, OMR, CHENNAI
Call For Research Projects Final
year students of B.E in EEE, ECE, EI,
M.E (Power Systems), M.E (Applied
Electronics), M.E (Power Electronics)
Ph.D Electrical and Electronics.
Students can assemble their hardware in our
Research labs. Experts will be guiding the projects.
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Sizing Electric Motors for Mobile Robotics
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The Basics
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Unit Conversions
sec1
sec2
revrad !T
sec11
m N W att
!
sec111
CoulombV ol t AmpereV ol t W att !!
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Basics
The FORCE applied
by a wheel is alwaystangent to the wheel.
Force is measured in units of weight (lb, oz, N)
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Basics
The required
TORQUE to move amobile robot is the
force times the
radius of the wheel.
Torque is measured in units of weight x length
(lb·ft, oz ·in, N·m)
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Procedure for Sizing DC
Motors
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Information Needed Estimated Weight
Number of wheels and motors
Maximum incline
Desired maximum velocity at worst case
Push/Pull forces
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Procedure Step One: Determine total applied force
at worst case
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Friction Static Friction
± Used to determine traction failure
Rolling Friction
± Used to determine motor requirements
Kinetic Friction
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Rolling Friction
QR Is the coefficient of Rolling friction ± Using the coefficient of Static friction (QS)will typically be to high
To determine QR:
± Roll a wheel at a initial velocity, v, andmeasure the time, t, in which it takes tostop
N F R R !
g t
v
R
!
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Rolling Friction Some typical values for QR
± Steel on steel: 0.001
± Rubber on pavement: 0.015
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Other Forces
U
Usin!W F I
Gravity
External
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Total Force Calculate worst case
± Up hill with rolling friction
± Up hill with rolling friction, pushing
± Level ground with rolling friction
± Level ground with rolling friction, pushing
)sincos( UU Q ! RW F
EX R F W F ! )sincos( UU Q
W F R ! Q
EX R F W F ! Q
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Other Cases Tracks
± Set Qr =0
± Use a spring scale to determine the force requiredto pull the chassis in neutral and add that to the
worst case force
Gear Trains
± Bulky gear trains may significantly affect theoutcome
± If this is a concern, it may be best to test in the
same way as tracks
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Procedure Step One: Determine total applied force
at worst case
Step Two: Calculate power requirement
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Power Requirement Determine velocity, v, requirement
under maximum load (worst case force)
Using the worst case force and velocity,calculate the power requirement
This is the total power, divide by thenumber of motors if more than onemotor is used
v F P !
RULE OF THUMB: 3 TIMES MARGIN
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Procedure Step One: Determine total applied force
at worst case
Step Two: Calculate power requirement
Step Three: Calculate torque and speed
requirement
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Speed/Torque Requirements Using the velocity requirement, v, and
the radius of the wheel, r
Using the speed from above and the
power per motor
r
v![
Speed requirement
is in rad/sec
[
P T !
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Procedure Step One: Determine total applied force
at worst case
Step Two: Calculate power requirement
Step Three: Calculate torque and speed
requirement
Step Four: Find a motor that meets
these requirements
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Spec Sheet
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Spec Sheet
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Torque vs. Speed Curve
Where T = Torque
TPK = Stall Torque
SNL = No Load Speed [ = Speed
[ !
NL
PK PK
S
T T T
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Torque vs. Speed CurveTorque vs. Speed
0.00 +00
1.00 -02
2.00 -02
3.00 -02
4.00 -02
5.00 -02
6.00 -02
7.00 -02
0 1000 2000 3000 4000 5000 6000 7000 8000
Speed, rpm
T o r q u e ,
N m
From this plot,
maximum speed canbe determined for a
given load.
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Power Power vs. Speed
0 00 +00
2 00 +00
4 00 +00
6 00 +00
8 00 +00
1 00 +01
1 20 +01
0 1000 2000 3000 4000 5000 6000 7000
Speed, rpm
P o w e r , w a t t s
[ [ [ ! PK NL
PK
T S
T
P
2
)(
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Power Power vs. Torque
0 00 +00
2 00 +00
4 00 +00
6 00 +00
8 00 +00
1 00 +01
1 20 +01
0 0 01 0 02 0 03 0 04 0 05 0 06
Torque, Nm
P o w e r , w a t t s
T S T T
S
T P NL PK
NL
!
2
)(
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Power Power
¡
¢
£
¤
eed
0 00¦
§
00
2 00¦
§
00
̈
00¦
§
00
6 00¦
§
00
©
00¦
§
00
1 00¦
§
01
1 20¦
§
01
0 1000 2000
000 ̈
000
000 6000
000
Speed, r pm
P o w e r , w a t t s
Power vs. Tor
e
0 00¦
§
00
2 00¦
§
00
̈
00¦
§
00
6 00¦
§
00
©
00¦
§
00
1 00¦
§
01
1 20¦
§
01
0 0 01 0 02 0 0
0 0 ̈
0 0
0 06
Tor e, Nm
P o w e r , w a t t s
max2
1T T !
max2
1[ [ !
Peak power is obtained at half of
maximum torque and speed
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Procedure Step One: Determine total applied force
at worst case
Step Two: Calculate power requirement
Step Three: Calculate torque and speed
requirement
Step Four: Find a motor that meets
these requirements
Step Five: Plot motor characteristics
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A Few Extra Points
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Simple DC Motor Model
e R I V ! [ !e
k e [ !e
k R I V
I k T t !
2
max 1 ¹¹ º ¸©©
ª¨ !
P
NL
I I L
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Motor Inductance The windings of a DC motor creates an
Inductance, L
Change in current through an
inductance creates a voltage
Switching current to a motor causes
di/dt to spike (Flyback)
dt
di LV !
Flyback voltages can be very high and damage
electronics, that is why a flyback diode in the
switching circuit is required.
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Winches Similar to drive motors
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Common Mistakes Using static or kinetic friction instead of rolling
friction
± If a wheel is rolling without slipping, the onlyenergy loss is due to deformations in thewheel/surface (rolling friction)
Using PWM to control a motor reduces theavailable torque
± The average power, speed and torque arereduced, however, effective torque is notsignificantly effected
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Questions?