Lightweight Electric/Hybrid Vehicle Design
Lightweight Electric/Hybrid Vehicle Design
Lightweight Electric/Hybrid Vehicle Design
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Design</strong> for optimum body-structural and running-gear performance efficiency 229<br />
third and fourth gears respectively. Actual plots would of course depend on the torque/speed<br />
characteristics of electric drives.<br />
8.8.3 ROTARY INERTIA, ROLLING AND GRADIENT RESISTANCES<br />
While translatory-mass inertia calculation is relatively easy, that of rotary mass is more difficult.<br />
It is necessary to sum the rotating inertia of the separate transmission components by relating<br />
relative torque to the driving axle as T = ΣIaR i 2 – for moment of inertia I and angular acceleration<br />
a. Since wheel circumferential speed is equal to vehicle translatory velocity, an ‘equivalent mass’<br />
can be considered as concentrated at the rolling radius – having the same effect on the inertia of<br />
translatory motion as the summation of individual rotary inertias.<br />
Thus effective inertia mass M = M r i e 2αd = ΣIR2 where equivalent mass M = ΣIR e 2 /r2 , the effective<br />
mass being M = M + M = MY where Y is termed the rotary mass factor, a valuable tool of the<br />
i e<br />
method. To find its value, the rotary masses are divided into parts rotating with wheels – and those<br />
rotating with power unit. The latter gain in importance in the lower ranges since M is proportional<br />
e<br />
to R2 . Average values quoted in the literature for a fully laden commercial vehicle are fourth-gear,<br />
1.09, then 1.2, 1.6 through to 2.5 in first. The value of Y is obtained from<br />
Y = 1 + M e /M = 1 + [(ΣI w /Mr 2 ) + (ΣIR 2 /Tr 2 )]<br />
where ΣI w is wheel inertia and I e is that for ‘engine speed’ parts and typically Y = 1 + (0.4 +<br />
0.0025R 2 ).<br />
Rolling resistance R r can be expressed as a dimensionless coefficient f (= 0.013 for radial tyres)<br />
while transmission resistance is obtained from a summation of the power consumed at various<br />
stages along the powertrain. Overall efficiency E depends on the transmission system and is<br />
conventionally assumed as E = 0.90 in direct drive and 0.85 in lower gears. Air resistance is<br />
obtained from<br />
R a = C d AρV 2 /2g<br />
for vehicle speed V, gravity acceleration g, projected frontal area A and air density ρ (C d rising to<br />
0.8 for a bluff box van). Gradient resistance is the component of gravitational force parallel to<br />
vehicle attitude, (b). Since W d μ = fW + W tan θ max , maximum gradient = Wm − f.<br />
8.8.4 ACCELERATIVE PERFORMANCE<br />
Selection of gear ratio will depend upon the chosen operation for the vehicle. The ratio for maximum<br />
acceleration can be estimated from<br />
G max = (Rr/T e )±[(Rr 2 /T e ) + (Wr 2 /g + I w /r)/I e ] 1/2<br />
where motion resistance R = R r + R a and I e and I w are engine and wheel inertias. Engine speed<br />
relates to vehicle speed as<br />
V = 2pN e r . 3600/12 . 60E s G . 5280 = N e r/168GE s<br />
and tyre slip efficiency E s can be assumed equal to 0.965 for this calculation.<br />
Thus N e and T e for each gear reduction may be tabulated against road speed by means of the<br />
engine torque/speed curve. Motion resistance forces are subtracted from P to give free tractive