Decomposition Analysis of an Automotive Powertrain Design ...

the optimization study are given in Appendix B. For decomposition the specific valvetrain friction
is represented implicitly as
F spvt = f(v type , N e ). (54)
The friction mean effective pressure for the oil pump is computed by scaling with respect to
displacement volume between two baseline designs according to
P foil = (O ld (N e ) - O hd (N e )) (4.6 - b 2 s π /4 n c x 10 -6 )/ 2.7 + O hd (N e ) (55)
where O ld and O hd are measured pumping losses for a 1.9L I-4 engine and a 4.6L V-8
respectively.
Similarly, the friction mean effective pressure for the water pump is computed by scaling
relative to two baseline designs with respect to power density according to
P fh2o =H lpd (N e ) + (H hpd (N e )-H lpd (N e ))(P bmep (N pp )N pp /895.2-54)/16. (56)
H lpd and H hpd are the water pumping losses of two engines of low and high power density
respectively. The values for O and H are given in Appendix B.
The total expression for friction is
P fmep = P fpu + P fpr + P fmb + P fvt + P foil + P fh2o. (57)
At a specified engine torque, speed, air-fuel ratio, and egr level, the fuel flow rate (ṁ f) is
the air flow rate (ṁ a) divided by the air-fuel ratio. The air flow rate is simply the product of air
density and volume displaced by the piston motion,
.
m f = ṁ a / R af
= 3.479 x10 -9 (p i /T m ) N e n c b 2 s π /(480 R af ). (58)
In the practical control of an engine at a given engine speed, four degrees of freedom exist
in obtaining a desired torque: manifold pressure, spark advance, air-fuel ratio, and exhaust gas
recirculation (egr). The control strategy aims to operate the engine at the air-fuel ratio, egr, and
spark advance values that minimize fuel consumption, meet emissions constraints and maintain