Russ Hersberger

Motor Math for SUMO Robots

Russ Hersberger

Traction Force

• He who has the most friction wins• Two things determine the force of friction

– The coefficient of friction– The force pressing the SUMO onto the surface

• The equation is , where f is the coefficient of friction and fN is the force perpendicular to the motion.

f Nf f

Russ Hersberger

Three kinds of friction

• Static friction, the strong one, occurs when there is no relative motion between the SUMO and the surface.

• Dynamic friction, much less than static friction, occurs when SUMO is sliding

• Rolling friction always works against the owner but is usually very small

Russ Hersberger

Defeating Your Opponent

• You must overcome the static friction of your opponent.

• The contest places a mass limit on SUMO.

• You must pick the tires that provide the biggest coefficient of friction.

Russ Hersberger

Testing Coefficient of Friction

• Get some sewing thread.

• Attach it to SUMO in line with the axles so there is no lifting or pressing.

• Clamp the wheels so they don’t turn.

• Top off the mass to the max allowed.

• Drape the thread over a round “low friction” screwdriver shaft.

Russ Hersberger

Testing Coefficient of Friction

• Attach the thread to a plastic bottle. For accurate measurement, weigh the empty bottle.

• Slowly fill the bottle with water until SUMO starts to slide.

• Weigh the bottle, subtract the empty weight.• Multiply the kilograms by 9.8 to get the

force in Newtons.

Russ Hersberger

Testing Coefficient of Friction

• If you don’t care what the actual force is, then just record the height of water in the bottle.

• Try out different tire materials and choose the one the takes the most water to move.

Russ Hersberger

So Now the Motor

• What’s between the battery and the floor?– Opponents Friction that we have just discussed– The wheel diameter– The friction of the motor– Rolling friction– The motor torque constant– The motor resistance

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How much torque do you need?

• Bigger wheels need more torque from the motor, but have a higher top speed.

• Torque is the force applied where the wheel touches the floor multiplied by the radius of the wheel.

• Smaller wheels need a smaller motor for the same traction.

( ) times static rolling wheelf f r

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How much electricity do you need?

• You know the torque () you need, so divide by the torque constant.

• The equation is,

motorik

Russ Hersberger

How much electricity do you need?

• Multiply the current by the motor resistance. That’s how much voltage you need if your not moving and just pushing.

• If your moving then the rotating motor generates a voltage (called back EMF) that opposes the battery voltage, reducing the torque.

battery motor motor backEMFv i R V

Russ Hersberger

Summary

( )

friction f N

motor sliding rolling wheel

motormotor

battery motor motor BackEMF

f f

f f r

ik

V i R V

Russ Hersberger

OK so there is a catch!

• Firstly, this is the minimum current you need. You should double it. After all your opponent may have found better tires.

• Secondly, you can’t just increase the voltage to get the current you need. Too much power will dissipate in the motor resistance, and cause overheating.

Russ Hersberger

Selecting a motor

• Rule 1. Get a motor with a large torque constant.

• Rule 2. Get a motor with a very small motor resistance, also called armature resistance.

Russ Hersberger

Back to defeating your opponent

• If you and your opponent have excellent traction then the there are only two ways to win:

1. Your motor is stronger than his, which means that his wheels will rotate as you push him backwards.

2. Lifting your opponent will reduce his fN and increase yours. You need to transfer his weight to your wheels.

Russ Hersberger

If your motor is stronger than his

• If the wheels are turning then the motor generates a voltage.

• The voltage generated by the pusher’s motor reduces the available torque by decreasing the current flow.

• The voltage generated by the pushee’s motor increases the available torque by increasing the current flow.

• This effect is small for low speeds. Determines how fast you push him out of the ring.

Russ Hersberger

Lifting Your Opponent

• You should transfer as much of your opponents weight to your drive wheels as possible.

• This is what SUMO is about.

• Transferring to other points of contact with the floor is less effective.

Russ Hersberger

Breaking Static friction

• You need1. Lots of friction on your side

2. A strong motor

• Momentum– Momentum is mass times velocity– When you hit your opponent the impulsive

force is proportional to momentum

Russ Hersberger

Using Momentum

• Get your speed up and SMACK the other guy.

• Bigger wheels mean greater velocity.

• This means lower torque at low speeds.

• You may need a bigger motor.

• Be careful not to transfer your weight to the other guy or you will just be helping him.

Russ Hersberger

Summary

• Your enemy is STATIC FRICTION.

• Your friend is STATIC FRICTION.– You need

• Tires with a large coefficient of friction.

• Motors with:– A large torque constant.

– Low armature resistance.

• To lift your opponent.

Russ Hersberger

Measuring the Torque Constant

• Wrap sewing thread around the shaft of the motor without overlapping.

• There should be only one layer.• Use a bit of glue on the first wrap to keep it from

slipping.• Attach a known mass to the free end of the thread.• Releasing the mass will cause the motor to spin.• The mass applies a constant torque to the motor

Russ Hersberger

Measuring the Torque Constant

• On the electrical side, connect a current meter across the motor leads, effectively shorting them together.

• Release the mass and while it is moving at a constant speed, record the current.

• The applied torque is the mass times the acceleration due to gravity times the radius of the motor shaft.

• The torque constant is the torque divided by the armature current

Russ Hersberger

Summary

ampsin current armature theis

(N/A) ampper Newtonsin constant torque theis

metersin radiusshaft theis

m/s 9.81gravity todueon accelerati theis

(Kg) kilogramsin mass theis

m)-(N meters-Newtonin torque theis

where

and

2

i

k

r

g

m

τ

ikmgr

Russ Hersberger

There are two motor constants

• The torque constant (k) connects the armature current to the shaft torque.

• The back EMF constant (kB) connects the motor speed to voltage generated in the armature.

• Thus a motor can be used as a generator.• These are the same value if measured using

standard international units

Russ Hersberger

Back EMF Constant

• k is measured in volts per radians/second.• Often manufacturers use different units.• Always convert to the above units.• If a motor is spinning then it generates a voltage.• It does not matter how the motor is made to spin.

9.55 timesRPMin speed theislocity angular ve The

secondradians/ in locity angular ve theis

constant EMFback theis

:

times

ω

k

where

ωkV

B

BbackEMF

Russ Hersberger

Motor Equations Summary

9.55 timesRPM

constant emfBack

constant Torque

constants Conversion

Side Mechanical

Side Electrical

BbackEMF

armatureτ

wheelfriction

armature

backEMFappliedarmature

kV

ik

rf

R

VVi