F'I'R'S'T' Motors

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F.I.R.S.T. Motors Drive System Fundamentals
December 7, 2002 Team Ford FIRST Paul
Copioli Utica Community Schools Ford Motor
Company The ThunderChickens (Team 217)
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Agenda
1. Introduction (why we are here) 2. Intro to
Things Mechanical 3. First Motor
Characteristics 4. Robot Drive Systems - Design
Objectives 5. Questions Answers
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Introduction

• Who am I?
• Paul Copioli
• Bachelors of Science - Aeronautical Engineering
• U.S. Air Force Academy
• M.S.E. - Aerospace Mechanical Engineering
• University of Michigan
• FANUC Robotics North America
• Senior Product Development Engineer
• 4th Season with FIRST

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Intro to Things Mechanical

• Force - units are Pounds (Lbf) Newtons (N)
• Velocity - meters/sec, ft/sec, MPH
• Acceleration - m/s2, ft/s2, g 9.81 m/s2
• Angular Velocity - RPM, rad/sec, deg/sec
• Torque - Nm, ftLbf
• Torque Force Lever Arm (Wheel Radius)
• Velocity Ang. Velocity Wheel Radius

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Formulas Units

• Unit conversions of interest
• 1lbs 4.45 N
• 1 inch 0.0254 meters
• 1 in-lbs 0.11 N-m
• 1 RPM 60 Rev / Hour 0.105 Rad / Sec
• 1 mile 5280 X 12 inches 63,000 inches
• Power Force (N) X Velocity (m/s)
• Power Torque (N-m) X Angular Velocity (Rad/Sec)
• Electrical Power Voltage X Current

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FIRST Motors
1. Motor Characteristics (Motor Curve) 2. Max
Power vs. Power at 30 Amps 3. Motor
Comparisons 4. Combining Motors
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Motor Characteristics

• Torque v Speed Curves
• Stall Torque (T0)
• Stall Current (A0)
• Free Speed (Wf)
• Free Current (Af)

K (slope)
T0
Torque, Current
A0
Af
Speed
Wf
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Slope-Intercept (YmX b)

• YMotor Torque
• mK (discuss later)
• XMotor Speed
• bStall Torque (T0)

K (slope)
T0
Torque, Current
A0
Af
Speed
Wf
What is K? It is the slope of the line. Slope
change in Y / change in X (0 - T0)/(Wf-0)
-T0/Wf K Slope -T0/Wf
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(YmX b) Continued ...

• YMotor Torque
• mK -T0/Wf
• XMotor Speed
• bStall Torque T0

T0 (b)
K (-T0/Wf)
Torque, Current
A0
Af
Speed
Wf
Equation for a motor Torque (-T0/Wf)
Speed T0
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Current (Amps) and FIRST

• What are cutoff Amps?
• Max useable amps
• Limited by breakers
• Need to make assumptions

Can our Motors operate above 30 amps? -
Absolutely, but not continuous.
When designing, you want to be able to perform
continuously so finding motor info at 30 amps
could prove to be useful.
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Torque at Amp Limit

• T30 Torque at 30 Amps
• W30 Speed at 30 Amps

Current Equation Current (Af-A0)/Wf Speed
A0
Motor Equation Torque (-T0/Wf) Speed T0
S _at_ 30A (W30) (30 - A0) Wf / (Af-A0) T _at_ 30A
(T30) (-T0/Wf) W30 T0
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Power - Max vs. 30 Amps
Power Torque Speed Must give up torque for
speed Max Power occurs when T T0/2
WWf/2 What if max power occurs at a current
higher than 30A?
Pauls Tip 1 Design drive motor max power for
30A!
Power is Absolute - It determines the Torque -
Speed tradeoff!
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Motor Comparisons
Lets Look at Some FIRST Motors

• Chiaphua Motor
• Drill Motor
• Johnson Electric Fisher-Price Motor

We will compare T0, Wf, A0, Af, T30, W30, max
power (Pmax), amps _at_ max power (Apmax), and power
at 30 amps (P30).
We will be using Dr. Joes motor spreadsheet
updated to handle the new motors.
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Motor Comparisons
Motor Equations 1. Fisher-Price T
(-0.51/20,000) W 0.51 2. Bosch Drill T
(-0.65/20,000) W 0.65 3. Chiaphua T
(-2.2/5,500) W 2.2
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Combining Motors
Using multiple motors is common for drive trains.
We will look at matching the big 3 motors. I try
to match at free speed, but you can match at any
speed you like!! FP and drill will match 11 Wf
FP(drill) / Wf Chiaphua 20000/5500 40/11 Gear
ratio to match Chip FP(drill) is 40/11. We will
use an efficiency of 95 for the match gear. More
to come on Gear Ratio Efficiency in the Second
Half!
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Combined Motor Data
Motor Equations 1. F-P Drill T
(-1.16/20,000) W 1.16 2. F-P Chip
T (-3.96/5,500) W 3.96 3. Drill Chip
T (-4.45/5,500) W 4.45 4. F-P, Drill,
Chip T (-6.21/5,500) W 6.21
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Motor Q A
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Robot Drive Systems
1. Drive System Terms 2. Types of
Mechanisms 3. Traction Basics 4. Gearing
Basics 5. Design Condition
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Drive System Terms
1. Gear Ratio Can be described many ways -
Motor Speed / Output Speed - When GR gt 1 ?
Torque Increaser 2. Efficiency - Work lost due
to drive losses - Friction, heat,
misalignment 3. Friction Force - Tractive
(pushing) force generated between
floor and wheel. 4. W is rotational speed V
is linear Speed (velocity) 5. N1 is of teeth
on input gear/sprocket 6. N2 is of teeth on
output gear/sprocket
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Types of Drive Mechanisms
1. Chain Belt Efficiency 95 - 98 GR
N2/N1
2. Spur Gears Efficiency 95 - 98 GR N2/N1
N2
N1
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Types of Drive Mechanisms
3. Bevel Gears Efficiency 90 - 95 GR
N2/N1
N1
N2
4. Other Types - Worm Gears Efficiency
40 - 70 - Planetary Gears Efficiency
80 - 90
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Traction BasicsTerminology
maximum tractive force
normal force
friction coefficient
x

torque turning the wheel
weight
tractive force
normal force
Friction coefficient Mu
The friction coefficient for any given contact
with the floor, multiplied by the normal force,
equals the maximum tractive force can be applied
at the contact area. Tractive force is
important! Its what moves the robot.
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Traction FundamentalsNormal Force
weight
front
normal force (rear)
normal force (front)
The normal force is the force that the wheels
exert on the floor, and is equal and opposite to
the force the floor exerts on the wheels. In the
simplest case, this is dependent on the weight of
the robot. The normal force is divided among the
robot features in contact with the ground.
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Traction FundamentalsWeight Distribution
more weight in back due to battery and motors
less weight in front due to fewer parts in this
area
EXAMPLE ONLY
front
more normal force
less normal force
The weight of the robot is not equally
distributed among all the contacts with the
floor. Weight distribution is dependent on where
the parts are in the robot. This affects the
normal force at each wheel.
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Traction FundamentalsWeight Distribution is Not
Constant
arm position in rear makes the weight shift to
the rear
arm position in front makes the weight shift to
the front
EXAMPLE ONLY
front
normal force (rear)
normal force (front)
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Traction FundamentalsWeight Distribution is Not
Constant
Where the weight is in the robot is only part of
the story! When the robot accelerates (changes
speed), inertial forces tend to change the weight
distribution. (Example of inertial force the
force exerted by the seat on your back in a Z06
Corvette as it accelerates.) So, it is
important to consider how the weight distribution
changes when the robot changes speed.
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Traction FundamentalsWeight Transfer
robot accelerating from 0 mph to 6 mph
inertial forces exerted by components on the
robot
EXAMPLE ONLY
less normal force is exerted on the front wheels
because inertial forces tend to rotate the robot
away from the front
more normal force is exerted on the rear wheels
because inertial forces tend to rotate the robot
toward the rear
In an extreme case (with rear wheel drive), you
pull a wheelie In a really extreme case (with
rear wheel drive), you tip over!
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Gearing Basics

• Consecutive gear stages multiply

• Gear Ratio is (N2/N1) (N4/N3)
• Efficiency is .95 .95 .90

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Gearing Basics - Wheel Attachment
Wheel Diameter - Dw Dw Rw 2
Motor Shaft
Fpush

• Gear 4 is attached to the wheel
• Remember that T F Rw
• Also, V W Rw
• T4 T1 N2/N1 N4/N3 .95 .95
• W4 W1 N1/N2 N3/N4
• F T4 / Rw
• V W4 Rw

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Design Condition

• Assumptions
• Each of the 4 wheels have their own motor.
• Weight is evenly distributed.
• Using all spur gears.
• Terms
• W Weight of robot
• Wt Weight transferred to robot from goals
• n of wheels on the ground (4)
• p driving wheels per transmission (1)
• q of transmissions (4)
• Tout wheel output Torque
• Find the gear ratio wheel diameter to maximize
  push force.

The maximum force at each wheel we can attain is
??? Fmax Ffriction Mu(W Wt)/n on a
flat surface Now T F Rw ----gt F Tout / Rw
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Design Condition Continued

• Tout T30 GR eff _at_ each wheel

Ffriction Tout / Rw Mu(W Wt)/n T30 GR
eff / Rw
Mu(W Wt) GR/Rw --------------------------
- nT30eff
The above gives you the best combination of gear
ratio and wheel diameter for maximum pushing
force!
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Design Condition Continued
O.K. So what is my top speed? 0.85 Wfree
p 2 Rw Vmax m/sec
------------------------------ 60
GR Where Wfree is in RPM, Dw is in meters. The
0.85 accounts for drive friction slowing the
robot down.
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Design Condition Continued
0.85 Wfree p 2 Rw 0.85 Wfree
p 2 n T30 eff Vmax
---------------------------------
--------------------------------------------
60 GR 60 Mu (W
Wt) T30 GR eff Fmax
-------------------- Mu (W Wt) Rw
Max force and max velocity are fighting each other
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Drive System Fundamentals
QUESTIONS?