GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 13 of 65

Marks: +1, -0

A spur gear with

20^{∘}

full depth teeth is transmitting

20 {kW}

200 {rad} {/} {s} .

The pitch circle diameter of the gear is

100 {mm}

. The magnitude of the force applied on the gear in the radial direction is

Solution:

{P}=20 {kW}, ω=200 {rad} {/ } {s}

D_{p}=100 {mm} ; r_{p}=50 {mm}

Using

P=T × ω

20 × 10^{3}=T × 200

⇒ T=100 N-m

T=F_{t} × r_{p}

⇒ 100=F_{t} × \;{50}/{1000}

F_{t}=2 {kN}

\;{F_{T}}/{F_{t}}=\tan θ

⇒ F_{r}=F_{t} \tan θ=2 × \tan 20=0.73 k N

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