Particulars of a spur gear are Gear ratio 10 ∶ 1, distance between centers - 660 mm, pinion transmits 500 kW at 1800 rpm.

Involute teeth of standard proportion (addendum = m) with pressure angle of 22.5°. Minimum number of teeth on pinion in order to avoid interference will be

Concept:

Interference:

Contact of portions of tooth profiles that are not conjugate is called interference.

It occurs when contact occurs below the base circle.

The minimum number of teeth on the pinion (TP) in order to avoid interference may be obtained from the following relation :

\(T_P= \frac{2A_w}{G\left[\sqrt{1+\frac{1}{G}\left(\frac{1}{G}+2\right)\sin^2ϕ }-1\right]}\;\)

where, A_w = Coefficient of the addendum of wheel, G = Gear ratio or velocity ratio = TG/TP = DG/DP,

ϕ  = Pressure angle or angle of obliquity.

Calculation:

Given:

G = 10, Center distance = 660 mm, P = 500 kW at 1800 rpm, A_w = 1, ϕ = 22.5

Now we have to put all required values in the formula for the minimum number of teeth in opinion,

\(T_P= \frac{2 \times 1}{10\left[\sqrt{1+\frac{1}{10}\left(\frac{1}{10}+2\right)\sin^2{22.5} }-1\right]}\;\)

T_P = 13.11 ≈ 14

So, the minimum number of teeth on the pinion is 14.