frc robot mechanical principles

FRC Robot Mechanical Principles

• 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

Continuing Subjects:

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?

– How do you get Fast?– How do you get good pushing power?– How do you get both?

• Chassis & Drive train layout defined by middle of week 1?

1 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

1.46875

2.3523.5wide x 10 length

23.5 wide x 16" (6wd) =

23.5" wide x 10" long

2.35:1

An example of an 8WD agile & stable tank drive layout

FrictionClassical 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 Friction coefficient x Weight on wheel = m * m * g

Weight = mass*gravity =

m*g

Drive Force = Torque/radius=m*m*g

Torque

Friction reaction force

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

Whee

l

Motor

Sprocket

Transm

ission


• Simple Transmission Gearbox (as in the CIMple Gear box)– 2 CIM motor input

65 teeth

14 teeth

14 teeth

5300 RPMCIM Motor Free Speed

5300 RPMCIM Motor Free Speed

Output Speed = 5300 * 14/65 = 1150 RPM

Basic Relationships - Review

Wheel / Transmission Mechanics• Torque = Radius x Force = T (in-lbs)• Rotational speed = w (rpm)• Velocity = v = (w*2*P*r)/(60 *12) (ft/sec)• Frictional Coefficient = m “empirical” – test wheel grip to carpet, with

weight• Maximum Traction Force = FT = m x W (weight of the robot = mg)• 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

w

Fw

Ft

T

r

Wv


Whee

l

Moto

r

SprocketTra

nsm

ission

Drive Motor RPM - no Load 5300 RPM CIM motorTransmission gear ratio 4.65 :1 CIMple gearboxTranmission output speed 1139.8 RPMSprocket 1 number teeth 12 s1Sprocket 2 number teeth 24 s2 Sprocket ratio 2.00 :1 s2 / s1Wheel Speed (no load) 569.9 RPMWheel Diameter 4 inchesLinear speed (no load) 9.95 feet per secondsMotor Load speed loss coef 0.81 acquired by measurement of loaded robotLinear speed (loaded) 8.06 feet per seconds

w (RPM)Velocity = v = (w*2*P*r)/(60 *12) (ft/sec)

COTS Drive Transmission Options

Drive Transmissions - CIM motor inputsName Vendor Gear Ratio # CIMsCIMple AM 4.65 2Toughbox AM 12.75 2Toughbox mini AM 10.71 2Supershifter AM 6 & 24 2 other ratios availableBall Shifter VexPro 3.66 & 8.33 2 other ratios availableSingle Speed Vexpro 7 or 6 or 5.33 3Dual Speed WCP 15 & 5.6 2 other ratios availableSingle Speed WCP various 2


• Spreadsheet simulations allow quick iterations to explore different combinations of gearboxes, sprockets and wheel diameters.

1-Speed Drivetrain

Free Speed (RPM)

Stall Torque (N*m)

Stall Current (Amp)

Free Current (Amp)

Speed Loss Constant

Drivetrain Efficiency

Motor Stall Torque (in lbs)

Max (Stall) Acceleration

in/s2

CIM 5310 2.43 133 2.7 81% 90% 21.5055 1068.39 T = W*mu*R1104 W = mg = T/(mu*R)

# Gearboxes in Drivetrain

# Motors per Gearbox

Total Weight

(lbs)

Weight on Driven

Wheels Wheel Dia. (in) Wheel Coeff

Max wheel torque

(breakaway) in lbs.

Max acceleration (breakaway)

in / s2

2 3 140 100% 4 1.3 364 502.32 F = ma

F= T/R

Driving Gear

Driven Gear

Drivetrain Free-Speed

Drivetrain Adjusted

Speed

Pushing Match Current per

Motor

Wheel Max (Stall)

Torque (in-lbs)

Max continuous (40 Amp)

wheel torque

Max cont. acceleration

in / s2a = T/(R*m)

1 6 15.45 ft/s 12.51 ft/s 70.76 Amps 774.20 437.63 603.92 m=W/g g=386.4 in/s2

1 1.00 6.00 : 1 <-- Overall Gear Ratio m=T/(mu*R*g)1 1 1.55 Breakaway Amp a= mu*g1 1 33.27 1.202267179

Wheel Torque = Motor torque*Gear ratio

Gear Ratio Effects Gear Ratio Optimization Trades Off Speed and Torque

• 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

• Torque decreases with speed

• Wheel friction limits amount of Torque that can be transmitted without spinning wheels

– 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?

Torque=>

<= Speed

<= Distance

m = 1.3

m = 1.1

m = 0.9

Gear Ratio Max Speed

11.42 : 1

7.30 : 1

5.03 : 1 14.9 ft/s

10.3 ft/s

6.6 ft/s

2CIMS in each of 2 single speed gearboxes

Time (seconds)

Gear Ratio Effects

2 Speed Gearbox Allows Optimization of Speed and Torque

Torque=>

<= Speed

<= Distance

m = 1.3

m = 1.1

m = 0.9


11.42 : 1

7.30 : 1

5.03 : 1 14.9 ft/s

10.3 ft/s

6.6 ft/s

2CIMS in each of 2 two speed gearboxes

Time (seconds)

• Desire to “shift” when acceleration (or Torque) crosses– Here shift from 11.43 ratio to 5.03 ratio

at about 25 in-lbs and 16 fps– Very slight advantage in distance /

time

• If m = 1.1 then get up to 320 in-lbs torque at low speed

• And up to 15 fps!

• Only is advantage if shifted at right times

• Driver shifting is difficult – Automation opportunity?– Read speed on encoder and shift

automatically?

2 CIM vs 3 CIM Drive3 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


11.42 : 1

7.30 : 1

5.03 : 1 14.93 : 1

10.28 : 1

6.58 : 1

Torque=>

<= Speed

<= Distance

m = 1.3

m = 1.1

m = 0.9

3 CIMS in each of 2 single speed gearboxes

2 CIM vs 3 CIM DriveWhen 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

Torque=>

<= Speed

<= Distance

m = 1.3

m = 1.1

m = 0.9


9.50 : 1

5.33 : 1

3.44 : 1 21.8 ft/s

14.1 ft/s

7.9 ft/s

Drive SimulationAllows 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.

frc robot mechanical principles

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