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Enter number data in appropriate fields - calculated results in RED
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Motor (torque and
speed are NOT at absolute max values, but rather at max efficiency)
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Descriptions
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Rotor mass,
Mr (grams, kg)
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Given
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Diameter, Dm
(mm, m)
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Given
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Length, Lm
(inches, m)
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Given
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Number of
drive motors, Nm
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Enter number of drive
motors
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Nm Motors'
rotary inertia, Jmotor (kg-m2, g-mm2)
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??=Nm*0.5*Mr*(Dm/2)2
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If known,
enter motor inertia (else, enter "0"), Jm (kg-m2, g-mm2)
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Enter motor inertia
in g-mm2 if different than above
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Motor
operating efficiency, etamotor
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Given
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Max motor
torque, gammax (m-N-m, N-m)
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Given
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Max motor
speed, wmax (rpm, rad/s)
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Given
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Motor speed
at maximum efficiency, wmaxeff (rpm, rad/s)
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Given
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Steepness S
(N-m-s/rad)
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See Eq (1)
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Transmission
(Planetary or known transmisssion ratio and inertia)
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Planet
carrier assembly mass Mplanet, (grams, kg)
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Given
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Planet
carrier outer diameter, Dpod (mm, m)
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Given
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Planet
carrier inner diameter, Dpid (mm, m)
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Given
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Number of
stages, Nstage
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Nstage=2 for
transmission ratios 1:16 and 1:20; Nstage=3 for 1:25 and 1:100; =4 for 1:400
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Efficiency
per stage, etastage
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Given
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Planetary total rotary inertia, Jplanets (kg-m2)
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??=0.5*Nstage*Mplanet*((Dpod/2)2+(dpid/2)2)
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Output shaft
mass, Mouts (grams, kg)
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Given
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Output shaft
diameter, Douts
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Given
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Output shaft
rotary inertia, Jouts (kg-m2)
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??=0.5*Mouts*(Douts/2)2
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Total Nm
planetary transmissions' rotary inertia, Jtrans (kg-m2)
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??=Nm*(Jplanets+Jouts)
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Transmisssion
efficiency (includes car wheels), etatrans
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??=etastage^(Nstage+1): drive train efficiency
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If known,
enter transmission inertia (else, enter "0"), Jt (kg-m2, g-mm2)
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Enter transmission
inertia if different
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If known,
enter transmission efficiency, etat (else enter "0")
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Enter drive train
efficiency if different
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Car
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Mass of car,
Mcar (kg)
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Enter mass of car in
kg
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Diamter of
wheel, Dwheel (mm, m)
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Given
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Number of
wheels
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4
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Enter number of
wheels
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Rotational
inertia of one wheel, Jwheel (kg*m2)
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Given from simulation
results
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Equivalent
linear inertia of wheels,mwheel
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??=Jwheel*Nm/rwheel2
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Max wheel
angular acceleration, wwacc (rad/s2)
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See Eq(12)
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Max car
acceleration, acar (m/s2, g)
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??=wwacc*rwheel
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External
loads, friction... Fext (N)
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Enter the external
load, or the push force
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2Wd or 4WD,
Nwd
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Enter 2 for 2-wheel
drive, 4 for 4-wheel drive
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Coefficient
of friction wheel-to-ground, mu (static friction coefficient)??
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mu=force required to
move the car/weight of car
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Coefficient
of dynamic friction fk
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fk=force required to
move the car (with transmission detached) in constant speed/weight of car
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Optimal
Transmission ratio by Matched Inertia Doctrine
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Optimal
transmission ratio, ntrans
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Confirm:
Number of stages = # required to achieve desired ntrans
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yes
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Actual
transmission ratio to be used, r_t
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Enter transmission
ratio to be used
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Actual
equivelent linear inertia of motor and tranny, mtrans (kg)
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??= r_t2*(Jtrans+Jmotor)/rwheel2
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Total actual
sysetm equivelent inertia, Mtotal (kg)
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??=mtrans+Mcar+mwheels
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Total
inertia, Jtotal
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See Eq(2)
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Power rates
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Motors' total
power rate, PRmotor
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??=Nm*(gammax2/(Jtrans+Jmotor)/Nm))
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Load power
rate, PRload
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??=(Mcar*acar+Fext)*acar
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System
goodness (should be >1): PRmotor/(4PRload/etatrans)
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??=PRmotor/(4*PRload/IF(etat>0,
etat,etatrans))
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Triangular
Velocity Profile Motion Results
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Start-to-stop
travel distance, Xdes (m)
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Enter desired travel
distance
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Max.
potential tractive effort (even mass distribution), Ftraction (N)
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Traction force when
the wheels slip
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Max. motor
tractive effort (even mass distribution), Ftractive (N)
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Maximum motor
traction force??
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Can wheels
slip?
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The wheels will slip
if the static traction force is less than the maximum motor traction force
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Net steepness
(Sbar)
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See Eq(8)
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Net torque
(Gammabar)
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See Eq(7)
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Maximum
theoretical car speed vmaxpot (m/s)
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??=(Dwheel/2)*(wmax/r_t)
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Maximum
analytical car speed, vmax (m/s)
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See Eq(11)
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Car speed at
max motor h, vmaxeff (m/s)
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??=(Dwheel/2)*(wmaxeff/r_t)
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Time to
accelerate to speed at max motor h (theoretical), taccel (seconds)
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See Eq(14)
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Distance
travelled during acceleration to vmaxeff, Xaccel (m)
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See Eq(15)
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Taylor series prediction of time to accelerate &
deccelerate to Xdes
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Time to
travel the desired travel distance (full speed at end of move)
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See Eq(18)
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Time to
travel the desired travel distance (stop at end of move: triangular velocity
profile)
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If the car
accelerates, decelerates and then stops at a distance Xdes, estimate using
Eq(19)
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Battery Requirements
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Estimated
maximum power draw from batteries, Pbat (W)
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??=vmaxeff*MIN(Ftractive,
Ftraction)/(etamotor*IF(etat>0, etat,etatrans))
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Estimated
maximum energy draw from batteries, Ebat (J=N-m)
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??=Pbat*t
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List of Equations Used
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