4.1 Shift types and smooth curve
One may postulate three kinds of state transition
as follows. Shift is conducted by disengaging
one clutch and by engaging another clutch with
different ratios. Smooth slip (speed) shift occurs
first, which tries to make the slip speed of new
clutch change from its initial speed to zero in a
smooth manner.
During shift, the clutch torque is decided entirely
by the applied pressure. However, the engaged
clutch torque is independent of the actuating
pressure. It generally decreases after upshift. So,
changing the clutch torque from old engaged
torque, TEo, to new engaged torque, TEn> smoothly
while satisfying the shift condition may accomplish
the shift process. This will be called the
smooth (engaged clutch) torque shift.
Substituting Eqs. (8b) - (8c) to Eq. (14b) , a
dynamic shift condition in terms of the vehicle
acceleration gives The vehicle acceleration before and after the
shift is given by Eq. (15). It generally decreases
after upshift. Thus, moving the vehicle from its
initial acceleration to the final state smoothly
while satisfying condition (20) will be called the
smooth (vehicle) acceleration shift.
Now, let us consider what is the smooth transition
from one state to another while satisfying the
shift condition. In the context of variational calculus,
the problem may be written It is difficult to find the analytical solution for
this problem. As an approximation of a smooth
function solution, cycloidal curve (21) may be
chosen. It is shown in Fig. 3 (a) where Yo and Yn