Fundamental law of Gearing- Theory of Machines

According to the law of gearing, the common normal at the point of contact between a pair of teeth must always pass through the pitch point. The following points in connection with the gears are worth noting :

1.  The velocity of siliding of teeth is the velocity of one relative to its mating tooth along the common tangent at the point of contact.
2.  The velocity of sliding is directly proportional to the distance of the point of contact from the pitch point.
3.  The length of arc of contact ,,,…..

= Length of path of contact / cosφ  [φ = Pressure angle.]

4. Contact ratio or number of pairs of teeth in contact,…

= Length of arc of contact / Circular pitch

5. The phenomenon when the tip of a tooth under cuts the root on its mating gear, is known as interference.

6. The interference may only be avoided, if the addendum circles of the two mating gears cut the common tangent to the base circles between the points of tangency.

7. The maximum number of teeth on the pinion order to avoid interference for 14 1/20 full depth involute are 32 and for 200 full depth involute teeth are 18.

8. The maximum efficiency of spiral gears is given by,…

ηmax = cos(θ+Φ) + 1 / cos(θ-Φ) -1    [θ= Shaft angle, and Φ= Friction angle]