# Gears

 Question 1
A steel spur pinion has a module (m) of 1.25 mm, 20 teeth and $20^{\circ}$ pressure angle. The pinion rotates at 1200 rpm and transmits power to a 60 teeth gear. The face width (F) is 50 mm, Lewis form factor Y = 0.322 and a dynamic factor $K_v = 1.26$. The bending stress ($\sigma$) induced in a tooth can be calculated by using the Lewis formula given below.

If the maximum bending stress experienced by the pinion is 400 MPa. the power transmitted is __________ kW (round off to one decimal place).

Lewis formula: $\sigma =\frac{K_vW^t}{FmY}$, where $W^t$ is the tangential load acting on the pinion.
 A 10 B 20 C 30 D 40
GATE ME 2020 SET-2   Machine Design
Question 1 Explanation:
\begin{aligned} F_{t} \times c_{v} s &=b m y\left[\sigma_{b}\right]_{\max } \\ c_{v} &=1.26 \\ F_{t} \times 1.26 \times 1 &=50 \times 1.25 \times 0.322 \times 400 \\ F_{t} &=6388.88 \mathrm{N} \\ P_{\text {angle }} &=F_{t} \times v=\frac{F_{t} \times \pi D_{p} N}{60} \\ &=\frac{6388.88 \times \pi \times 1.25 \times 20 \times 1200}{60}=10 \mathrm{kW} \end{aligned}
 Question 2
A helical gear with $20^{\circ}$ pressure angle and $30^{\circ}$ helix angle mounted at the mid-span of a shaft that is supported between two bearings at the ends. The nature of the stresses induced in the shaft is
 A normal stress due to bending only B normal stress due to bending in one plane and axial loading; shear stress due to torsion C normal stress due to bending in two planes and axial loading; shear stress due to torsion D normal stress due to bending in two planes; shear stress due to torsion
GATE ME 2020 SET-1   Machine Design

 Question 3
Which one of the following is used to convert a rotational motion into a translational motion?
 A Bevel gears B Double helical gears C Worm gears D Rack and pinion gears
GATE ME 2014 SET-4   Machine Design
Question 3 Explanation:
Bevel gears: Rotational motion transfer between axes at right angle.
Worm gears: For large reduction ratio in a single stage.
Double helical gears: Rotational motion transfer between parallel axes.
Rack and Pinion gears: Rotational to linear motion conversion.
 Question 4
A spur pinion of pitch diameter 50 mm rotates at 200 rad/s and transmits 3 kW power. The pressure angle of the tooth of the pinion is 20$^{\circ}$. Assuming that only one pair of the teeth is in contact, the total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______
 A 638.5N B 548.6N C 985.6N D 784.5N
GATE ME 2014 SET-2   Machine Design
Question 4 Explanation:
Given,
\begin{aligned} d&=50 \mathrm{mm} \\ \omega&=200 \mathrm{rad} / \mathrm{s} \\ P&=3000 \mathrm{W} \\ \phi&=20^{\circ} \\ T&=\frac{P}{\omega}=\frac{3000}{200}=15 \mathrm{N.m} \end{aligned}

\begin{aligned} F_{T} \times r &=T \\ \therefore F_{T} &=\frac{T}{r}=\frac{15}{0.025}=600 \mathrm{N} \\ \therefore F_{T} &=F \cos \phi \\ F &=\frac{600}{\cos 20^{\circ}}=638.5 \mathrm{N} \end{aligned}
 Question 5
A pair of spur gears with module 5 mm and a center distance of 450 mm is used for a speed reduction of 5:1. The number of teeth on pinion is _______
 A 30 B 40 C 50 D 60
GATE ME 2014 SET-1   Machine Design
Question 5 Explanation:

\begin{aligned} \frac{N_{P}}{N_{G}} &=5=\frac{T_{G}}{T_{P}} \\ T_{G} &=5 T_{P} \\ C &=\frac{m}{2}\left(T_{P}+T_{G}\right) \\ T_{P}+T_{G} &=\frac{2 C}{m}=\frac{2 \times 450}{5} \\ &=180 \\ \text{or }\quad 6 T_{P}&=180 \\ \text{or }\quad T_{P}&=30 \end{aligned}

There are 5 questions to complete.

### 1 thought on “Gears”

1. QN 17 ANSWER IS 2