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May 21, 2006
Basics
The FORCE applied by a wheel is always tangent to the wheel.
Force is measured in units of weight (lb, oz, N)
May 21, 2006
Basics
The required TORQUE to move a mobile 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)
May 21, 2006
Information Needed
• Estimated Weight• Number of wheels and motors• Maximum incline• Desired maximum velocity at worst
case• Push/Pull forces
May 21, 2006
Friction
• Static Friction– Used to determine traction failure
• Rolling Friction– Used to determine motor requirements
• Kinetic Friction
May 21, 2006
Rolling Friction
R Is the coefficient of Rolling friction– Using the coefficient of Static friction (S)
will typically be to high• To determine R:
– Roll a wheel at a initial velocity, v, and measure the time, t, in which it takes to stop
NF RR
gtv
R
May 21, 2006
Rolling Friction
• Some typical values for R
– Steel on steel: 0.001– Rubber on pavement: 0.015
May 21, 2006
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( RWF
EXR FWF )sincos(
WF R
EXR FWF
May 21, 2006
Other Cases
• Tracks– Set r=0– Use a spring scale to determine the force required to
pull the chassis in neutral and add that to the worst case force
• Gear Trains– Bulky gear trains may significantly affect the outcome– If this is a concern, it may be best to test in the same
way as tracks
May 21, 2006
Procedure
• Step One: Determine total applied force at worst case
• Step Two: Calculate power requirement
May 21, 2006
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 the number of motors if more than one motor is used
vFP
RULE OF THUMB: 3 TIMES MARGIN
May 21, 2006
Procedure
• Step One: Determine total applied force at worst case
• Step Two: Calculate power requirement• Step Three: Calculate torque and speed
requirement
May 21, 2006
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
rv
Speed requirement is in rad/sec
PT
May 21, 2006
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
May 21, 2006
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
May 21, 2006
Torque vs. Speed Curve
• Where T = Torque• TPK = Stall Torque
• SNL = No Load Speed = Speed
NL
PKPK S
TTT
May 21, 2006
Torque vs. Speed CurveTorque vs. Speed
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
7.00E-02
0 1000 2000 3000 4000 5000 6000 7000 8000
Speed, rpm
Torq
ue, N
m
From this plot, maximum speed can be determined for a
given load.
May 21, 2006
PowerPower vs. Speed
0.00E+00
2.00E+00
4.00E+00
6.00E+00
8.00E+00
1.00E+01
1.20E+01
0 1000 2000 3000 4000 5000 6000 7000
Speed, rpm
Pow
er, w
atts
PKNL
PK TSTP 2)(
May 21, 2006
PowerPower vs. Torque
0.00E+00
2.00E+00
4.00E+00
6.00E+00
8.00E+00
1.00E+01
1.20E+01
0 0.01 0.02 0.03 0.04 0.05 0.06
Torque, Nm
Pow
er, w
atts
TSTTSTP NLPK
NL 2)(
May 21, 2006
PowerPower vs. Speed
0.00E+00
2.00E+00
4.00E+00
6.00E+00
8.00E+00
1.00E+01
1.20E+01
0 1000 2000 3000 4000 5000 6000 7000
Speed, rpm
Pow
er, w
atts
Power vs. Torque
0.00E+00
2.00E+00
4.00E+00
6.00E+00
8.00E+00
1.00E+01
1.20E+01
0 0.01 0.02 0.03 0.04 0.05 0.06
Torque, Nm
Pow
er, w
atts
max21TT
max21
Peak power is obtained at half of maximum torque and speed
May 21, 2006
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
May 21, 2006
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)
dtdiLV
Flyback voltages can be very high and damage electronics, that is why a flyback diode in the
switching circuit is required.
May 21, 2006
Common Mistakes
• Using static or kinetic friction instead of rolling friction– If a wheel is rolling without slipping, the only
energy loss is due to deformations in the wheel/surface (rolling friction)
• Using PWM to control a motor reduces the available torque– The average power, speed and torque are
reduced, however, effective torque is not significantly effected