FRC Robot Mechanical Principles
Continuing Subjects:
• Review understanding from last week
– Robot agility and maneuverability?
– Chassis types & options
– Speed and Torque?
• Torque vs. Speed
–
–
–
–
–
Gear ratios
Breakaway torque limit
2 speed
3 CIM vs. 2 CIM
3 CIM + 2 Speed – vs. 3 CIM single speed
• Wheels: Friction
FRC Engineering/Design
Review:
• Every year our Strategic Design has called for:
– “Fast, Stable, Maneuverable With Good, Pushing Power”
– How do you get maneuverable – agile – quick turning?
– How do you get stable?
– How do you get both?
1
– How do you get Fast?
– How do you get good pushing power?
– How do you get both?
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
23.5" wide
x 10" long
2.35:1
23.5wide x 10 length
23.5 wide x 16" (6wd) =
2.35
1.46875
An example of an 8WD
agile & stable tank drive layout
• Chassis & Drive train layout defined by middle of week 1?
Friction
Classical Friction Theory
• Torque at wheel imparts a “Drive force” at wheel carpet contact point
• This is reacted by a “Friction Force” of up to the “Friction
coefficient” times the weight on the wheel
– The friction coefficient is a characteristic of the materials involved
– If the Drive force is greater than the Friction force, the wheels will slip
• The maximum Torque that can be transmitted
by the drivetrain is the “Breakaway Torque”
that creates a Drive force equal the
Weight =
Friction coefficient x Weight on wheel
mass*gravity =
=m*m*g
m*g
Friction reaction force
=m*m*g
Torque
Drive Force =
Torque/radius
Drive Motors, Transmissions, Sprockets and
Wheel Diameter
• How to translate speed of motor to speed of robot?
– Motor speed inputs into transmission with a gear ratio
• Motor load results in speed loss
– Transmission output to sprockets connected by chain
• Ratio of sprocket teeth decreases speed
• Overall Ratio includes motors, transmissions,
sprockets/belts, wheel diameter
Drive Motors, Transmissions, Sprockets and
Wheel Diameter
• Simple Transmission Gearbox (as in the CIMple Gear box)
– 2 CIM motor input
Output Speed
= 5300 * 14/65
= 1150 RPM
5300 RPM
CIM Motor
Free Speed
65 teeth
14
teeth
14
teeth
5300 RPM
CIM Motor
Free Speed
Basic Relationships - Review
Wheel / Transmission Mechanics
•
Torque = Radius x Force = T (in-lbs)
•
Rotational speed = w
•
Velocity = v = (w*2*P*r)/(60 *12)
•
Frictional Coefficient =
•
Maximum Traction Force = FT = m x W (weight of the robot = mg)
•
(rpm)
m
(ft/sec)
“empirical” – test wheel grip to carpet, with weight
Maximum Torque at wheel that can be transferred by friction
– Tm= m * W * radius
•
Max torque delivered by motor is at stall
•
Torque decreases with speed
T
Fw r
v
W
Ft
w
Drive Motors, Transmissions, Sprockets
and Wheel Diameter
Drive Motor RPM - no Load
Transmission gear ratio
Tranmission output speed
Sprocket 1 number teeth
Sprocket 2 number teeth
Sprocket ratio
Wheel Speed (no load)
Wheel Diameter
Linear speed (no load)
Motor Load speed loss coef
Linear speed (loaded)
w (RPM)
Velocity = v =
(w*2*P*r)/(60 *12)
(ft/sec)
5300 RPM
CIM motor
4.65 :1
CIMple gearbox
1139.8 RPM
12
s1
24
s2
2.00 :1
s2 / s1
569.9 RPM
4 inches
9.95 feet per seconds
0.81
acquired by measurement of loaded robot
8.06 feet per seconds
COTS Drive Transmission Options
Drive Transmissions - CIM motor inputs
Name
CIMple
Toughbox
Toughbox mini
Supershifter
Ball Shifter
Single Speed
Dual Speed
Single Speed
Vendor Gear Ratio # CIMs
AM
4.65
2
AM
12.75
2
AM
10.71
2
AM
6 & 24
2
other ratios available
VexPro 3.66 & 8.33
2
other ratios available
Vexpro 7 or 6 or 5.33
3
WCP
15 & 5.6
2
other ratios available
WCP
various
2
Drive Motors, Transmissions, Sprockets
and Wheel Diameter
1-Speed Drivetrain
Free Speed Stall Torque
(RPM)
(N*m)
CIM
5310
# Gearboxes # Motors per
in Drivetrain Gearbox
2
3
2.43
Stall
Current
(Amp)
133
Free Current
(Amp)
2.7
Total
Weight
(lbs)
Weight on
Driven
Wheels
140
100%
Max (Stall)
Acceleration
in/s 2
81%
90%
1068.39
1104
Max
Max wheel
acceleration
torque
Wheel Dia. (in) Wheel Coeff
(breakaway) (breakaway)
in lbs.
in / s 2
4
1.3
364
502.32
Speed Loss
Constant
Drivetrain
Efficiency
Motor Stall
Torque
(in lbs)
21.5055
T = W*mu*R
W = mg = T/(mu*R)
Wheel Torque =
Motor torque*Gear ratio
F = ma
F= T/R
Driving
Gear
Driven
Gear
1
1
1
1
6
1.00
1
1
Wheel
Max
Max cont.
Pushing Match
Max (Stall) continuous
acceleration
Current per
Torque
(40 Amp)
2
Motor
in / s
(in-lbs)
wheel torque
15.45 ft/s 12.51 ft/s
70.76 Amps
603.92
774.20
437.63
6.00 : 1 <-- Overall Gear Ratio
1.55
Breakaway Amp
33.27
1.202267179
Drivetrain
Free-Speed
Drivetrain
Adjusted
Speed
a = T/(R*m)
m=W/g
g=386.4 in/s
m=T/(mu*R*g)
a= mu*g
• Spreadsheet simulations allow quick iterations to explore different
combinations of gearboxes, sprockets and wheel diameters.
2
Gear Ratio Effects
Gear Ratio Optimization Trades Off Speed and Torque
2CIMS in each of 2 single speed gearboxes
• Higher gear ratio
– Lower max speed
– More low end torque
– May not be able to use all of Torque?
• Lower Gear Ratio
– Higher max speed
– Less max torque
– May not ever get to top speed?
• Torque provides acceleration
– T=F*r =m*a *r
– increasing speed
m = 1.3
Gear Ratio Max Speed
m = 1.1
5.03 : 1
14.9 ft/s
7.30 : 1
10.3 ft/s
11.42 : 1
6.6 ft/s
m = 0.9
Torque=>
• Torque decreases with speed
• Wheel friction limits amount of Torque
that can be transmitted without
spinning wheels
<= Speed
<= Distance
– Only get advantage of higher gear ratio if
friction is high
– For Instance: m = 0.9 there is no advantage to a
gear ratio above 7.3
• For typical m = 1.1 What is optimum
gear ratio?
Time (seconds)
Gear Ratio Effects
2 Speed Gearbox Allows Optimization of Speed and Torque
2CIMS in each of 2 two speed gearboxes
• Desire to “shift” when acceleration
(or Torque) crosses
m = 1.3
– Here shift from 11.43 ratio to 5.03 ratio
at about 25 in-lbs and 16 fps
– Very slight advantage in distance / time
m = 1.1
Gear Ratio Max Speed
5.03 : 1
14.9 ft/s
7.30 : 1
10.3 ft/s
11.42 : 1
6.6 ft/s
m = 0.9
• If m = 1.1 then get up to 320 in-lbs
torque at low speed
• And up to 15 fps!
Torque=>
<= Speed
• Only is advantage if shifted at
right times
• Driver shifting is difficult
– Automation opportunity?
– Read speed on encoder and shift
automatically?
<= Distance
Time (seconds)
2 CIM vs 3 CIM Drive
3 CIM / Gearbox Drive Eliminates Need For 2 Speed Gearbox
• 3 CIMs provide 50% more torque
at any gear ratio
• Minimal benefit for 2 speed
gearbox
– Friction becomes more important
than gear ratio
• Can have ~14 fps robot (very
fast) and have max
transmittable torque
• 3 CIMs provide quicker
acceleration – getting more
distance vs. time.
– Equal to 2 CIM – 2 speed
3 CIMS in each of 2 single speed gearboxes
m = 1.3
m = 1.1
Gear Ratio Max Speed
5.03 : 1
14.93 : 1
7.30 : 1
10.28 : 1
11.42 : 1
6.58 : 1
m = 0.9
Torque=>
<= Speed
<= Distance
2 CIM vs 3 CIM Drive
When May 3 CIM – 2 Speed Make Sense?
• Low gear ratio – high speed
– High gear ratio set at level of
max useful torque benefit
• and not trip breakers
• Here for m = 1.2, Ratio~ 9:1
– Low gear maintains high
acceleration
– Makes difference only if
accelerating over 15 feet
distance
• At 20 feet may get up to
3-5 foot advantage
• May not be controllable
m = 1.3
m = 1.1
Gear Ratio Max Speed
3.44 : 1
21.8 ft/s
5.33 : 1
14.1 ft/s
9.50 : 1
7.9 ft/s
m = 0.9
Torque=>
<= Speed
<= Distance
Drive Simulation
Allows Convenient Evaluation Of Different Drive Train Configurations
• Useful to understand trends
– But make sure to anchor to test data
• Includes considerations for:
– Speed loss coefficient – how much slower motor is under load
• Free speed is 5300 RPM, loaded speed ~ 4300 RPM (81%)
• May be dependent on gear ratio – further test data needed
– Torque accelerates speed, but torque reduces with speed
– Speed desired called by voltage
– Voltage drops when load is first applied, current spike
• Simulation
– Iterative time step solution - excel
– Test data can be taken to improve simulations
– Spreadsheets from team 33 and 148 (JVN) used and here-bye credited
• Modified both in calculations and display.