Page 198 - Mechatronics with Experiments

184 MECHATRONICS

Gear: F1 C1 4 4 B5

3 3
2 2
4
1 1

Input
shaft Main
shaft
Stages: 1, 2, 3, 4, 5
FIGURE 3.28: Automatic transmission used in heavy equipment applications showing the use
of planetary gears, controlled clutches, and brakes to select gear ratios: condition for gear
Forward 1 (F1) (Reproduced with permission from Volvo Trucks).

to disengaged or from disengaged to engaged state is important for smoothness of the
shift quality. To this end, the transition of the clutch/brake engagement/disengagement is
controlled by pressure regulating valves that control the fluid flow to the clutches/brakes.
Consider the clutch and brake engagement conditions for forward gear 1: F1 (Fig-
ure 3.28).

1. Clutch 1 (C1) locks the input shaft to the main shaft.
2. Brake 5 (B5) locks the planetary carrier of stage 5 to the transmission housing. As a
result, the planetary stage 5 is in the idling condition, which means that it is acting as
a regular gear since its planetary carrier is fixed.
3. This forces the ring gear of stage 4 (item 4,4), which is shared by stages 4 and 5, to
rotate in the opposite direction relative to the sun gear numbered (4,1) in the figure.
The output shaft (connected to sun gear of stage 5, number (5,1) in the figure) is then
driven in the opposite direction to the ring gear. The net result is that output shaft and
input shaft are in the same direction, hence the forward gear.

The gear ratio between input and output shaft speeds can be found as follows. Note that
the gear numbers of each stage are defined as follows, N , where i is the planetary stage
i,j
number (1, 2, 3, 4, 5), and j is the gear number in that stage: 1 for sun gear, 2 for planetary
carrier, 3 for planetary gear, 4 for ring gear. The speeds are also defined with the same
notation, w , where i is the planetary stage number (i = 1, 2, 3, 4, 5), and j = 1, 2, 3, 4 the
i,j
component numbers of that stage, sun, carrier, planet, and ring gears, respectively. The
output shaft speed (the shaft speed of the sun gear of planetary stage 5) is determined by
the ring gear speed of stage 4 as follows. Stage 5 operates in idle condition because its
planetary carrier is fixed, and the ring gear of stage 4 and stage 5 are the same, and the
speed of the output shaft is the same as the speed of the planetary carrier of stage 4,

w out = w 5,1 (3.286)
= w 4,2 (3.287)
w 5,1 N 5,4
=− (3.288)
w 5,4 N 5,1
w = w (same component) (3.289)
5,4 4,4
N 5,4
w =− ⋅ w (3.290)
out 4,4
N
5,1