Sizing the drive system - Propulsion Systems for Hybrid Vehicles - page 149

According to Table 4.2, speed reversal occurs between sun and ring gear ports
and the speed at these ports is scaled by the basic ratio, k . All other input-output
combinations preserve the direction of speed. The basic ratio, 1.5 < k < 4, is
determined by gear diameters.
There are variations of epicyclic gear sets in which combinations of epicyclic
gears and spur gears are used to realize dual stage epicyclic sets that are hard
connected and do not rely on clutches to ground any port. When clutches are used
to ground various ports of an epicyclic set, we have the essential ingredients of an
automatic transmission. All automatic transmissions are designed around epicyclic
stages with clutches to affect the step ratio changes plus an input torque converter
to smooth out the speed variations of the engine by inertia and fluid coupling.

4.1.1 Transmission selection
Passenger vehicle transmissions can be broadly grouped into manual shift, auto-
matic and continuously variable. Manual shift transmissions (MT) have pre-defined
step ratios that vary in a geometric progression. Modern MTs have an acceleration
factor on the geometric ratio to realize smoother transitions and better drive quality.
MTs are virtually always spur gear on a main and counter shaft, or layshaft, design.
Automatic transmissions are designed around planetary gear sets for power on
demand shifting.

4.1.2 Gear step selection
Transmission gear ratios follow a geometric progression that spans the desired
range of speed ratio or shift ratio coverage. For example, a 4-speed gearbox may
have a total speed ratio of 3.6:1 to 3.9:1, a 5-speed gearbox a ratio of 4.3:1 to 5.2:1
while a 6-speed gearbox will have a speed ratio of approximately 6:1. For example,
a 6-speed gearbox is assumed with an overall ratio of 6:1 such that the geometric
ratio for gear step is taken as the sixth root of six (e.g. r = 1.348 but < r > = 1.23 on
average over the range when using an acceleration factor). Depending on the gear
selected, an acceleration is given to the geometric ratio in order to smooth shift
busyness in the higher gears (i.e. smaller steps). In this chapter, an acceleration
factor a = 1.33 will be used. Gear ratio z x is defined according to the empirical
relation in (4.4). In (4.4), we set the highest gear to z 0 = 0.7, with x = {0,1,2,3,4,5}
in retrogression and x mx being the top gear. Ratio z 0 represents an overdrive con-
dition; that is, output torque is higher than input torque, meaning the engine is
lugging:

a

z x ¼ z 0 ð r Þ ð x mx x Þ ð 4 : 4 Þ

Equation (4.4) gives a very smooth transition in step ratios as higher gears are
engaged under load. The overall driveline tractive effort at the wheels follows a
hyperbola envelope. The step ratios predicted by (4.4) are listed in Table 4.3, where
x is the gear number.