Estimated Motor and Transmission Inertia and Drive Requirements
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 (kg-m2, g-mm2) ??=Nm*0.5*Mr*(Dm/2)2
If known, enter motor inertia (else, enter "0"), Jm (kg-m2, g-mm2) Enter motor inertia in g-mm2 if different than above
Motor operating efficiency, etamotor
Given
Max motor torque, gammax (m-N-m, N-m) Given
Max motor speed, wmax (rpm, rad/s) Given
Motor speed at maximum efficiency, wmaxeff (rpm, rad/s) Given
Steepness S (N-m-s/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 (kg-m2)
??=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 (kg-m2)
??=0.5*Mouts*(Douts/2)2
Total Nm planetary transmissions' rotary inertia, Jtrans (kg-m2)
??=Nm*(Jplanets+Jouts)
Transmisssion efficiency (includes car wheels), etatrans
??=etastage^(Nstage+1): drive train efficiency
If known, enter transmission inertia (else, enter "0"), Jt (kg-m2, g-mm2) 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*m2)
Given from simulation results
Equivalent linear inertia of wheels,mwheel
??=Jwheel*Nm/rwheel2
Max wheel angular acceleration, wwacc (rad/s2)
See Eq(12)
Max car acceleration, acar (m/s2, g) ??=wwacc*rwheel
External loads, friction... Fext (N)
Enter the external load, or the push force
2Wd or 4WD, Nwd
Enter 2 for 2-wheel drive, 4 for 4-wheel drive
Coefficient of friction wheel-to-ground, 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_t2*(Jtrans+Jmotor)/rwheel2
Total actual sysetm equivelent inertia, Mtotal (kg)
??=mtrans+Mcar+mwheels
Total inertia, Jtotal
See Eq(2)
Power rates
Motors' total power rate, PRmotor
??=Nm*(gammax2/(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
Start-to-stop 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=N-m)
??=Pbat*t
List of Equations Used
 

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