Decomposition Analysis of an Automotive Powertrain Design ...

Powertrain Relationships
The principal behavior variables characterizing a powertrain are torque and speed
throughout the components. In analyzing a vehicle's performance, these behavior variables take
on various values that constitute a vector of states as the vehicle analysis is conducted: states
through a driving cycle, states when the engine is at maximum torque, and states effected by
steady state criteria imposed on the vehicle. In the development of the powertrain relationships,
the FDT partitions, and the coordination strategy, torque and speed are treated as only two
behavior variables in contrast to representing every state separately. Other potential methods of
representing state variables are discussed in the concluding remarks.
Figure 5 illustrates the power flow through the powertrain. The expressions relating
engine torque, T e , to torque at the driving wheel, T d , are given by Equations (14) - (17).
T i = T e - T acc - (π / 30) (I e + I acc + I i ) dN e /dt (14)
T gb =T i R t - (π /30) I t dN t /dt (15)
T fd = T gb η gb ξ gb - T ch - (π /30) (I gb + I ds ) dN ds /dt (16)
T d = T fd η fd ξ fd - (π /30) I fd dN d /dt (17)
These equations define the states (torque and speed) of each element in the powertrain at any point
in time. Two additional state equations are required to define the relationship between engine
actuation (throttle or manifold pressure) and driving force at the road. The first is given as part of
the engine model development; the second is given with the wheel model. Development of the
functional dependence of component efficiencies, and reduction ratios on geometric and control
variables will complete the model development.
Wheels
The geometric wheel variable of interest is the effective tire radius, r e . The principal
behavior variables of interest are the adhesion coefficient µ o , the traction coefficient µ, and the slip
ratio S. These quantify the interaction at the tire-road interface by the expression