1 Crore+ students have signed up on EduRev. Have you? 
INTRODUCTION
Fundamental Law of Gearing
Figure 72 shows two mating gear teeth, in which
Although the two profiles have different velocities V_{1} and V_{2} at point K, their velocities along N_{1}N_{2} are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Therefore, we have
(71)
or
(72)
We notice that the intersection of the tangency N_{1}N_{2} and the line of center O_{1}O_{2} is point P, and
(73)
Thus, the relationship between the angular velocities of the driving gear to the driven gear, or velocity ratio, of a pair of mating teeth is
(74)
Point P is very important to the velocity ratio, and it is called the pitch point. Pitch point divides the line between the line of centers and its position decides the velocity ratio of the two teeth. The above expression is the fundamental law of geartooth action.
Force Analysis
Lewis Equation
The first equation used for bending stress was the Lewis equation. This is derived by treating the tooth as a simple cantilever and with tooth contact occuring at the tip as shown below:
Only the tangent component(W_{t}) is considered. It is also assumed that only one pair of teeth is in contact. Stress concentrations at the tooth root fillet are ignored. It can be shown that the maximum bending stress occurs at the tangent points on the parabola shown above. Use of the standard equation for bending stress(σ=Mc/I) leads to:
The value of Y independent of the size of tooth and depend only on No. of teeth on gear and system of teeth.
Maximum tangential force P_{t} called beam strength and replaced by S_{b}.
known as Lewis equation.
Since torque developed by source and required by driven machine varies during working cycle. It is balanced by flywheel. In gear design maximum force is the criterion. This is accounted by means of a service factor.
Due to inability in calculation of dynamic load a velocity factor (Cv) developed,
d — diameter of gear (in mm)
Effective load
where, P_{d} is the dynamic load
6 videos89 docs55 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
6 videos89 docs55 tests
