## Nl

since — = k (a constant) Nh gear G3 — G2 — G2K — (GiK)K

G1K2

G1K3

Hence the ratios form a geometric progression. 0 v, Vî V, Vj vs

Vehicle speed (km/h|

Fig. 3.35 Gear ratios selected on geometric progression

The following relationship will also apply for a five speed gearbox:

G1 Gi

Hence K

Gi or

In general, if the ratio of the highest gear (GT) and that of the lowest gear (Gb) have been determined, and the number of speeds (gear ratios) of the gearbox nQ is known, the constant K can be determined by:

nQ-1

So gt Kkq+1 Gb nQ

For commercial vehicles, the gear ratios in the gearbox are often arranged in geometric progression. For passenger cars, to suit the changing traffic conditions, the step between the ratios of the upper two gears is often closer than that based on geometric progression. As a result, this will affect the selection of the lower gears to some extent.

Example A transmission system for a vehicle is to have an overall bottom and top gear ratio of 20:1 and 4.8 respectively. If the minimum to maximum speeds at each gear changes are 2100 and 3000 rev/min respectively, determine the following:

a) the intermediate overall gear ratios b) the intermediate gearbox and top gear ratios.

 K= Nl Nh 2100 3000 0.7 a) 1st gear ratio G1 = = 20.0:1 2nd gear ratio G2 = G1K = = 20 > 0.7 = = 14.0:1 3rd gear ratio G3 = G1K2 = 20 x 0.72 = 9.8:1 4th gear ratio G4 = G1K3 = 20 < 0.73 = 6.86:1 5th gear ratio G5 = = G1K4 = 20 0.74 = 4.8:1

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