Question

The maximum efficiency of spiral gears is

(a) sin (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1

(b) cos(ϴ – ɸ) +1/sin (ϴ + ɸ) + 1

(c) cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1

(d) cos(ϴ – ɸ) +1/cos (ϴ + ɸ) + 1

The question was posed to me during an online exam.

This interesting question is from Minimum Number of Teeth on a Pinion for Involute Rack in Order to Avoid Interference topic in chapter Toothed Gearing & Gear Trains of Machine Kinematics

Answer 1

Right answer is (c) cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1

Easy explanation: The maximum efficiency of spiral gears is

 cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1

where, ϴ = Shaft angle

and ɸ = Friction angle.