Question

If T is the actual number of teeth on a helical gear and φ is the helix angle for the teeth, the formative number of teeth is written as

(a) T sec^3 φ

(b) T sec^2 φ

(c) T/sec^3φ

(d) T cosec φ

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The origin of the question is Standard Proportions of Gear Systems in portion Toothed Gearing & Gear Trains of Machine Kinematics

Answer 1

Correct answer is (a) T sec^3 φ

To elaborate: The formative or equivalent number of teeth for a helical gear may be defined as the number of teeth that can be generated on the surface of a cylinder having a radius equal to the radius of curvature at a point at the tip of the minor axis of an ellipse obtained by taking a section of the gear in the normal plane. Mathematically, formative or equivalent number of teeth on a helical gear,

              T sec^3 φ