Decomposition Analysis of an Automotive Powertrain Design ...

Regarding valve timing, a number of design limitations exist for the valvetrain to function
successfully. First the events are bounded so they occur in the appropriate region of the
thermodynamic cycle. Second, the difference,
g 25 : (i vo - e vc ) / 50 - 1.0 ≤ 0 (88)
is bounded to preclude excessive residual fraction at idle conditions. Third, limits exist on the
valvetrain acceleration. For both intake and exhaust cams, the acceleration is defined as the second
derivative of the lift profile as a function of cam angle and expressed in units of cm/deg 2 .
For
decomposition analysis purposes they are expressed as
g 26 : -.008 ≤ acc iv (i vo , i vc, i lift ) ≤ 0.011 (89)
g 27 : -.008 ≤ acc ev (e vo, e vc, e lift ) ≤ 0.011 (90)
The specific bounds depend on the valvetrain type, -0.008 and 0.011 correspond to the pushrod
valvetrain used in the example.
Appendix A summarizes the complete model as presented. Defining equations are treated as
zero-valued equalities and each function is given a unique name and number. These identifiers are
used in annotating the FDT and corresponding adjacency matrices of the optimization model. The
optimal design problem statement is then as follows.
maximize MPG m-h Metro-highway fuel economy
subject to
g 1 : NOx/0.4 -1 ≤ 0 CAA driven constraint on NOx
g 2 : τ 0-60 /τ ο -1 ≤ 0 0-60 mph time; τ ο = 11.0 sec
g 3 : τ 5-20 /τ 1 -1 ≤ 0 5-20 mph time; τ 1 = 1.81 sec.
g 4 : S base /S 0-4 - 1 ≤ 0 Launch distance; S base =88.4 ft.
g 5 : 30.0 /α s - 1 ≤ 0 Starting gradability ( > than 30%)
g 6 : 65 / V c - 1 ≤ 0 Cruising velocity ( > 65 mph @ 6% grade)
g 7 : T e (N e )/T emax (N e ) -1 ≤ 0 Lugging limits
g 8 : c r - 13.2 + 0.045 b ≤ 0 Knock limited bore
g 9 : θ 0−90 / 70 -1 ≤ 0 Combustion stability constraint
g 10 : 2. - ξ fd ≤ 0 Final drive ratio constraint
g 11 : ξ fd - 5 ≤ 0 Final drive ratio constraint
g 12 : 1.6 - ξ 1 / ξ 2 ≤ 0 Step down ratio constraint