
Enter number data in appropriate fields  calculated results in RED


Motor (torque and
speed are NOT at absolute max values, but rather at max efficiency)

Descriptions

Rotor mass,
Mr (grams, kg)



Given

Diameter, Dm
(mm, m)



Given

Length, Lm
(inches, m)



Given

Number of
drive motors, Nm



Enter number of drive
motors

Nm Motors'
rotary inertia, Jmotor (kgm^{2}, gmm^{2})



??=Nm*0.5*Mr*(Dm/2)^{2}

If known,
enter motor inertia (else, enter "0"), Jm (kgm^{2}, gmm^{2})



Enter motor inertia
in gmm^{2} if different than above

Motor
operating efficiency, etamotor



Given

Max motor
torque, gammax (mNm, Nm)



Given

Max motor
speed, wmax (rpm, rad/s)



Given

Motor speed
at maximum efficiency, wmaxeff (rpm, rad/s)



Given

Steepness S
(Nms/rad)



See Eq (1)

Transmission
(Planetary or known transmisssion ratio and inertia)


Planet
carrier assembly mass Mplanet, (grams, kg)



Given

Planet
carrier outer diameter, Dpod (mm, m)



Given

Planet
carrier inner diameter, Dpid (mm, m)



Given

Number of
stages, Nstage



Nstage=2 for
transmission ratios 1:16 and 1:20; Nstage=3 for 1:25 and 1:100; =4 for 1:400

Efficiency
per stage, etastage



Given

Planetary total rotary inertia, Jplanets (kgm^{2})



??=0.5*Nstage*Mplanet*((Dpod/2)^{2}+(dpid/2)^{2})

Output shaft
mass, Mouts (grams, kg)



Given

Output shaft
diameter, Douts



Given

Output shaft
rotary inertia, Jouts (kgm^{2})



??=0.5*Mouts*(Douts/2)^{2}

Total Nm
planetary transmissions' rotary inertia, Jtrans (kgm^{2})



??=Nm*(Jplanets+Jouts)

Transmisssion
efficiency (includes car wheels), etatrans



??=etastage^(Nstage+1): drive train efficiency

If known,
enter transmission inertia (else, enter "0"), Jt (kgm^{2}, gmm^{2})



Enter transmission
inertia if different

If known,
enter transmission efficiency, etat (else enter "0")



Enter drive train
efficiency if different

Car


Mass of car,
Mcar (kg)



Enter mass of car in
kg

Diamter of
wheel, Dwheel (mm, m)



Given

Number of
wheels

4


Enter number of
wheels

Rotational
inertia of one wheel, Jwheel (kg*m^{2})



Given from simulation
results

Equivalent
linear inertia of wheels,mwheel



??=Jwheel*Nm/rwheel^{2}

Max wheel
angular acceleration, wwacc (rad/s^{2})



See Eq(12)

Max car
acceleration, acar (m/s^{2}, g)



??=wwacc*rwheel

External
loads, friction... Fext (N)



Enter the external
load, or the push force

2Wd or 4WD,
Nwd



Enter 2 for 2wheel
drive, 4 for 4wheel drive

Coefficient
of friction wheeltoground, mu (static friction coefficient)??



mu=force required to
move the car/weight of car

Coefficient
of dynamic friction fk



fk=force required to
move the car (with transmission detached) in constant speed/weight of car

Optimal
Transmission ratio by Matched Inertia Doctrine


Optimal
transmission ratio, ntrans




Confirm:
Number of stages = # required to achieve desired ntrans

yes



Actual
transmission ratio to be used, r_t



Enter transmission
ratio to be used

Actual
equivelent linear inertia of motor and tranny, mtrans (kg)



??= r_t^{2}*(Jtrans+Jmotor)/rwheel^{2}

Total actual
sysetm equivelent inertia, Mtotal (kg)



??=mtrans+Mcar+mwheels

Total
inertia, Jtotal



See Eq(2)

Power rates


Motors' total
power rate, PRmotor



??=Nm*(gammax^{2}/(Jtrans+Jmotor)/Nm))

Load power
rate, PRload



??=(Mcar*acar+Fext)*acar

System
goodness (should be >1): PRmotor/(4PRload/etatrans)



??=PRmotor/(4*PRload/IF(etat>0,
etat,etatrans))

Triangular
Velocity Profile Motion Results


Starttostop
travel distance, Xdes (m)



Enter desired travel
distance

Max.
potential tractive effort (even mass distribution), Ftraction (N)



Traction force when
the wheels slip

Max. motor
tractive effort (even mass distribution), Ftractive (N)



Maximum motor
traction force??

Can wheels
slip?



The wheels will slip
if the static traction force is less than the maximum motor traction force

Net steepness
(Sbar)



See Eq(8)

Net torque
(Gammabar)



See Eq(7)

Maximum
theoretical car speed vmaxpot (m/s)



??=(Dwheel/2)*(wmax/r_t)

Maximum
analytical car speed, vmax (m/s)



See Eq(11)

Car speed at
max motor h, vmaxeff (m/s)



??=(Dwheel/2)*(wmaxeff/r_t)

Time to
accelerate to speed at max motor h (theoretical), taccel (seconds)



See Eq(14)

Distance
travelled during acceleration to vmaxeff, Xaccel (m)



See Eq(15)

Taylor series prediction of time to accelerate &
deccelerate to Xdes

Time to
travel the desired travel distance (full speed at end of move)



See Eq(18)

Time to
travel the desired travel distance (stop at end of move: triangular velocity
profile)



If the car
accelerates, decelerates and then stops at a distance Xdes, estimate using
Eq(19)

Battery Requirements


Estimated
maximum power draw from batteries, Pbat (W)



??=vmaxeff*MIN(Ftractive,
Ftraction)/(etamotor*IF(etat>0, etat,etatrans))

Estimated
maximum energy draw from batteries, Ebat (J=Nm)



??=Pbat*t





List of Equations Used




