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VIZAG MT Mechanical: 2015 Official Paper

Option 4 : \(t = \frac{{2{A_p}}}{{\sqrt {1 ~+~ 3\;si{n^2}\phi } ~-~ 1}}\)

CT 1: Engineering Mathematics

477

10 Questions
5 Marks
15 Mins

**Concept:**

**The minimum number of teeth on the pinion is given by:**

\(t_{min} = \frac{{2{A_p}}}{{\sqrt {1 + \left( {\frac{t}{T}} \right)\left( {\frac{t}{T} + 2} \right)\;Si{n^2}ϕ } - 1}}\)

where, t_{min }= minimum number of teeth on the pinion, t = number of teeth on the pinion, T = number of teeth on the gear, A_{p} = Addendum fraction, ϕ = Pressure angle.

__Calculation:__

**Given:**

Pinion and gear have an equal number of teeth, i.e. t = T

Placing the value of \(\frac{t}{T} = 1\) in the above equation

we get,

\(t = \frac{{2{A_p}}}{{\sqrt {1 ~+~ 3\;Si{n^2}\phi } ~-~ 1}}\)

__Additional Information__

Increasing teeth decreases interference

**Interference is a phenomenon in which the addendum tip of gear undercuts into the addendum or base circle of a pinion.**

This tooth interface can be reduced by increasing the number of teeth above a certain minimum number.

System of gear teeth |
Minimum number of teeth on the pinion |

\(14\frac{1}{2}^\circ Composite\) |
12 |

\(14\frac{1}{2}^\circ fulldepthinvolute\) |
32 |

20° full depth involute |
18 |

20° Stub involute |
14 |