motor calculations and power budgets

8/10/2019 Motor Calculations and Power Budgets

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Motor

n What motor are we using?q Manufacturer: Mabuchi Motors at

http://www.mabuchi-motor.co.jp/english/

q Part Number: RC-260RA-2670

q Operating Voltage: 4.5V (but can run at 6V)


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Step 1 Determine Your System

n Choose the speed that you would like theoutput action to occur at.q This is not the output of the motor, but whatever

action you are doing (eg. Spinning a wheel)

q Remember v=*r for a linear motion like a wheelturning

n Choose the time span you would like theaction to occur in.

n Determine any frictional coefficients, weights,diameters, forces, inertia that will be appliedto the system.


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Step 2 Determine the Torque

n Three regimes from the Trapezoidal Profile1. Inertia Limited (Acceleration)

2. Friction Limited

3.

Inertia Limited (Deceleration)

ta td

tc

Velocity

Time

321


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First Regime Inertia Limitedn When you first apply power to a motor, the dominant

torque is from trying to accelerate the inertia to thedesired speed.

q Think of accelerating your car out of a stop light, butwithout burning rubber.

n Motor has to accelerate in time ta to a certain velocity for a rotational motion or v for a linear motion.

n T = J* = m*a*r

q Know or v and know ta => can find acceleration forthe rotation or linear motion.

q For a car, it is easiest to use T = m*a*r with mass ofcar and acceleration desired.

q For a platter spinner, it is easiest to use T = J* withinertia of platter and wheel and desired acceleration.


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Second Regime Friction Limited

n Friction is always present and always worksagainst your applied force.

n Sources of friction in and on your machine:

q

Dynamic frictionq External passive loads

n Pulling pucks

n Pushing balls

q External active loadsn Battlebots


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Friction Funn Dynamic friction

q This is the hodge-podge friction that covers what happens butcant be predicted easily

q Includes internal friction of motor and bearings, odd shapes ofparts, and the actual friction force applied at the wheels (NOTthe force from static or kinematic coefficients of friction).

n External passive loadsq This is the force your machine must apply to move things on

the table, including balls, pucks, other robots, etc.

q Based on weight of object and its static coefficient of friction.

n External active loadsq This is the force your machine must apply to actively push

another machine around. At this case, you want to apply fullfrictional capacity of the wheels without slipping.


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Friction Funn So why not use F=s*n?

n This is the no-slip condition.n This condition means that the wheels are applying the maximum

force they can apply before they spin without applying any force.

n This is a lotta force which requires a whole lotta power from yourmotors!! This condition will cause your motor to fail by one of two

ways:1. Traction failure (T > *N*r) burning rubber! Your wheels will spin

at the maximum speed, but no power or force is applied.

2. Torque failure (T > Tstall) - Stall means the motors are applying theirmaximum torque with no speed.

q Maximum torque = maximum current = maximum heat = meltingwires after too long.

q Melting wires means magic smoke pours out of your motor! Magicsmoke means the motor has gone to a happier place and you haveto buy a new motor.


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Friction and Force Examples

n Imagine pushing your car up an incline plane.How much force does it take to push you up

the hill?

n Now you are on a flat surface. How muchforce does it take to push you?


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Third Regime Inertia Limitedn Now you must apply torque to stop your inertia

q Think of slamming on the brakes when you miss a stop sign,but without leaving tire marks on the road.

n Motor has to decelerate in time td to a certain velocity for a rotational motion or v for a linear motion.

n T = J* = m*a*rq Know or v and know td => can find deceleration for the

rotation or linear motion.

q For a car, it is easiest to use T = m*a*r with mass of car andacceleration desired. For a platter spinner, it is easiest to useT = J* with inertia of platter and wheel and desireddeceleration.

n This may not be important for spinning the platter ifyou are spinning it around, but it is very important foroscillating the platter. It is also very important forstopping your machine before you fall into the chasm!


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Step 3 Whats the Power?n Determine Power of system:

Power = Torque x Rotational Speed

= Force x Linear Speed

n What torque and speed do I use?

q Based on the velocity profile and frictionconsiderations, calculate the torque or force and

speed for each regime.

q Figure out the power in each regime.

q Pick the largest power as the most conservative.

n Quick sanity check your motors can supply 2W


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Step 4 Gear Ratios

n First order estimate without knowing gear train:q Assume gear ratio efficiency is 50%

(this is the worst case with some room to play)

q So set the torque output of the motor to 2X the

worst case torque from above.n If you know your exact gear train and frictional

situation, you can figure out an accurateestimate of the efficiency.

n Plots for the Tamiya motor kit on the websiteaccount for frictional loss and inertia of theincluded gear box.


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Step 5 Find the Torque on Curves

n Go to the torque speed curve for the motoralone (see website) or for the motor with the

appropriate gear box (see web if you know

your ratio)


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Step 7 Find the Motor Currentn Find current I on the chart corresponding to

your design torque

n You can also see how efficient the motor is

for your case


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Step 8 Total Current Draw

n We know the current from one motor.n Are there any other motors running?

q If yes, calculate the current (starting from step 1)

for each of those motors.

n Are you using solenoids?

q If yes, check web for more info.


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Step 9 Total Currents

n Sum up all of the currents that will be used atthe same time. This will require that you plan

out when your motors will be actuated.

q Itotal

=I1

+I2

+. . .+IN


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Step 10 Battery Power!

n Now look at the battery.q We know P=I*V

n I is current and V is voltage

n From the battery pack the max amount of voltage is 6

volts

n So power is 6*Itotal where Itotal is from step 9.


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Step 11 How the Battery Cell Worksn Note: A battery cell is a voltage source with a resistor in series. This

resistor will burn off some voltage before you can use it. Cell data (see

lecture notes on web) present examples of this curves as current isdrawn from the cell.

n Check to see if the cells can output this much.q We know V=I*R. Solving for current we get: I=V/R.

q Since there are 6 cells are in series, they have the same amount of current

running through each of them. Since there are two of these cells in parallel,the total output current is twice this amount.

q The current in one cell is I=1.5/0.18 = 8 Amps where 0.18 ohms is theinternal resistance of a cell. Using this current value, the cells are capable of8A*1.5V = 12 W per cell or 72 W per 6 cells or 144 W for the whole lot ofcells.

q BUT, this is the maximum possible current. At this current, no voltage isbeing supplied and nothing will work. Also, the cells will get reallllly hot at

this much current drain. Remember, a soldering iron is more than 15 W orthat a 40 W light bulb gets real hot real quick! Normal battery cells wontwork even close to this amperage.

q So, when the battery begins drawing current, it loses voltage across theresistor. Therefore, the maximum voltage is when only a little current isdrawn.


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Step 11 How the Battery Cell Works

n

Still checking to see if this works:q Combining the equation of current and power produces a

general formula for power:

n P=(Battery voltage-((internal resistance)*current))*current

n What is the maximum amount of current from the

cells?q Occurs when the internal resistance = external resistance.

n Pmax=(battery voltage)/(internal resistance*N cells).

q Max current for one set of six cells is:

n (9V - 4.8V)/(0.18 ohms*6)(4.8V is minimum voltage required for control system to operate)

n 3.88 Amps although you want to run at less. . .


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Step 12

n Reiterate if things dont work outq Perhaps change your rotational speed or some

other guestimated value.


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Power Budget Structure

Power in Batteries

Motor 1 Motor 2 Motor 3 Motor 4

Gear Box 1 Gear Box 2 Gear Box 3 Gear Box 4

Output 1 Output 2 Output 3 Output 4

Solenoid

Transmission

Output 5

To do a complete power budget, you should be able to fill in

force, torque, velocity, power and energy in each of the

above blocks, as required for your design. Also, you may

have additional blocks for triggers which you will have to

consider.


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Power Supply Elements

n

Motorsq Torque * angular speed or force * linear speed

n Spring

q Torsional

n Force * distance/time

q Extension

n Force * distance/time

n Solenoid

q Force * stroke/time

n Batteriesq Current * voltage

n Piston

q Force * distance/time


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Power and Energy Budgets

n How much power are you using at one time?q Ptotal =Pmotor+Pspring+Psolenoid+Ppistonq Pbattery>=Pmotor+Psolenoid+Ppiston

n

How much energy are you using?q Energy cells > total energy require by system

n Energy = Power *time

motor calculations and power budgets

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