Decomposition Analysis of an Automotive Powertrain Design ...

6 COORDINATED OPTIMIZATION SOLUTION
Assume a vehicle segment has been selected with the acceleration targets 0-60 time τ 0 =
11.0 sec, 5-20 time τ 1 = 1.81 sec, four second distance S base = 88.4 ft. Assume body and chassis
decisions have yielded the vehicle parametervalues given in the appendix. This leaves as variables
the engine geometry and egr schedule, x 1 = (b, s, c r , d i , d e , L mi , D mi , L me , D me i vo , i vc , e vo , e vc ,
d bm , l bm , d br , l br , i lift , e lift, F egr ), and transmission gears and torque converter size, x 2 = (ξ 1 , ξ 2 ,
ξ 3 , ξ 4 , ξ fd , ξ span , α t ,i gear ) to be optimized. The coordination strategy begins by solving for all
initial values in SP to create a starting point for MP (a map of fuel flow, NOx emissions, and
manifold pressure as a function of engine speed and torque based on the initial engine design, and
a wide-open throttle torque curve).
Table I summarizes the results of the strategy. The first column identifies geometric and
behavior variables in the MP and SP; the second lists the variable name; the third gives the units.
The initial values of the variables of interest (geometric and behavior) are given in the fourth
column. The next seven columns give results as the strategy sequences through optimization in the
MP and SP. Note that the final point of MP defines the displacement of the engine in the initial
point of SP. Similarly, the final point of SP defines the fuel flow and emissions used in MP.
The coordination strategy converged in two overall iterations and improved the fuel
economy by 10.8% (3 mi/gal) relative to the baseline powertrain. At the feasible starting point,
(column IV) none of the acceleration constraints are active: τ 0-60, τ 5-20, and S base are within the
bounds by 0.7 seconds, 0.1 seconds, and 4.0 feet respectively. In the solution to the first iteration
of MP (column V), the step-down ratio ξ 1 /ξ 2 is reduced, the final drive ratio is nearly unchanged,
the size factor on the torque converter α t , is increased, the engine is down-sized by 8%, and the
gear box span is increased by 0.1 ratios. First gear ratio ξ 1 is reduced by 20%; the second ξ 2 by
10%; and the fourth ξ 4 by 18%. The active constraints are the 0-60 time τ 0-60 and the bound on
the torque converter scaling factor α t . The fuel economy is improved by 7.9%. Gradeability
criteria are virtually unaffected.