Decomposition Analysis of an Automotive Powertrain Design ...

The U.S. metro-highway fuel economy, expressed in units of miles per gallon, represents
a weighted average of the fuel consumed over the city and highway driving cycles. In the U.S.
Emissions Federal Test Procedure No. 75, oxides of nitrogen (NOx), carbon monoxide (CO),
and hydrocarbons (HC) emissions are collected and 'bagged' over a three phase driving cycle.
Standards set by the Clean Air Act (CAA) and the California Air Resources Board (CARB) dictate
acceptable levels (i.e., set the constraint values). Bosch (1986) provides a good description of
legislated driving cycles and test procedures worldwide. Only the emissions NO and NO 2 ,
collectively referred to as NOx, are considered here.
Hydrocarbons are ignored since
approximately 80% of the total hydrocarbon emissions are emitted during the first 120 seconds of
the cycle as the catalyst warms up to maximum efficiency; they are managed with control strategies
for cold transient behavior which is beyond the scope of the problem formulated here. Similarly,
catalyst efficiencies for CO are sufficient to the extent that CO emissions would rarely become an
active design constraint.
Vehicle Relationships
Appendix A has the complete nomenclature used to describe the vehicle dynamics and
Figure 4 shows a free body diagram for the vehicle. The driving equation for all the criteria is
simply the balance of forces on the vehicle,
M dV/dt = F d - F roll - F grade - F aero . (1)
The vehicle acceleration is proportional to the driving force at the road-wheel interface and the
resistive forces of rolling friction, gravity, and air drag. The rolling resistance is the sum of tire
friction and brake drag on the wheels; tire friction is the product of the coefficient of rolling
resistance and the normal force at the wheels; brake drag is measured or modeled and for
decomposition analysis is given as function of wheel speed,
F roll = C roll F nnd + C roll F nd + (T bd (N d ) + T bnd (V/r e ))/r e (2)
The rolling coefficient, C roll , is often determined experimentally by using the test procedure
SAEJ1269 or can be represented analytically with an expression like (Gillespie 1992)