Decomposition Analysis of an Automotive Powertrain Design ...

educes fuel flow by 1.3%; the constraint on peak power, the constraint on compression ratio, and
the constraint on burn duration are active. The combustion stability constraint limited the egr factor
to 1.37. The change in egr and the change in bore-stroke ratio (from 1.11 to 1.04) both result in
better thermal efficiency and lower fuel flow. The bore-stroke ratio could change because of the
latitude in the peak power constraint which was the result of an improved manifold. The improved
volumetric efficiency allowed this change.
The first solution to SP was then used to generate a new fuel, emissions, and torque curve
to solve the MP. The results of this optimization are shown in columns VIII and IX of Table I. In
this iteration small changes were observed in the gear ratios, but the engine was downsized by 5%
effecting another 2% in fuel economy improvement. Again, the 0-60 constraint became active. In
this iteration, fuel economy was improved at the expense of 0-60 time until the 0-60 constraint
became active. Note the reduction in stall speed from 2728 to 2655 caused by the reduced torque
from engine down-sizing. Also, NOx is reduced 15%, the 5-20 time is virtually the same, and
only 3 mph has been sacrificed in cruising gradeability velocity compared to the original baseline.
A second set of optimal torque-speed points were generated to solve the second iteration of
SP (column X). In this iteration no improvement in the objective was obtained.
Not a surprising
result, since the starting point is at the peak power constraint boundary, and changes in bore-stroke
only improve the power at the expense of fuel. Similarly, the starting point is on the burn rate
boundary, and egr will improve fuel only at the expense of burn rate.
Figure 12 summarizes the iteration history of the master problem, and illustrates the fuel
economy/performance tradeoff as a function of engine displacement. In both iterations the 0-60
starts feasible, and the engine is downsized until the 0-60 constraint is active. The improvement in
volumetric efficiency by varying the manifold geometry allowed an additional 5% reduction in
engine displacement which resulted in an additional 2% improvement in metro-highway fuel