# Theory of Machines Questions and Answers – Bevel Gears

This set of Theory of Machines Multiple Choice Questions & Answers (MCQs) focuses on “Bevel Gears”.

1. Bevel gears are used to have a gear drive between two intersecting shafts. True or false?
a) True
b) False

Explanation: To have a gear drive between two intersecting shafts, bevel gears are used. Bevel wheels are used to work a gear to another gear. They are generally mounted on shafts which are perpendicular to each other but can be designed to work at other angles too. Thus, the statement is true.

2. Bevel gears are equivalent to rolling ________
a) cubes
b) cones
c) spheres
d) cuboids

Explanation: By geometry of bevel gears, it is evident that they are equivalent to rolling cones. Their pitch surface is a cone. Bevel gears exist as pairs which can be either straight or inclined at different angles.

3. Identify the given gear.

a) Spur
b) Helical
c) Worm
d) Bevel

Explanation: The given gear is bevel gear. Here, ƴg, ƴp = pitch angles of gear and pinion respectively.
rg, rp = pitch radii of gear and pinion respectively.

4. What is the formula to calculate the pitch angle of gear of a bevel gear using the radius?
a) yg = tan-1 ((cos θ)/((rg/rp)+sin θ))
b) yg = tan-1 ((cos θ)/((rp/rg)+sin θ))
c) yg = tan-1 ((sin θ)/((rp/rg)+cos θ))
d) yg = tan-1 ((sin θ)/((rg/rp)+cos θ))

Explanation: tan yg = ((sin θ)/((rp/rg)+cos θ))
Therefore, yg = tan-1 ((sin θ)/((rp/rg)+cos θ))
Similarly, tan yp = ((sin θ)/((rg/rp)+cos θ))
Therefore, yp = tan-1 ((sin θ)/((rg/rp)+cos θ)).

5. What is the formula to calculate the pitch angle of pinion of a bevel gear using the angular velocity?
a) yp = tan-1 ((cos θ)/((wg/wp)+sin θ))
b) yp = tan-1 ((cos θ)/((wp/wg)+sin θ))
c) yp = tan-1 ((sin θ)/((wg/wp)+cos θ))
d) yp = tan-1 ((sin θ)/((wp/wg)+cos θ))

Explanation: tan yp = ((sin θ)/((wp/wg)+cos θ))
Therefore, yp = tan-1 ((sin θ)/((wp/wg)+cos θ))
Similarly, tan yg = ((sin θ)/((wg/wp)+cos θ))
Therefore, yg = tan-1 ((sin θ)/((wg/wp)+cos θ)).

6. Which of the gears has the highest contact ratio?
a) Helical
b) Spur
c) Bevel
d) Worm

Explanation: Bevel gears increase the contact ratio. It avoids interference and results in stronger pinion teeth. The gear ratio can be determined from the number of teeth, pitch diameters or pitch cone angles.

7. What is the working depth of the gear and the pinion of the bevel gears?
a) 2 m, 0.7 m
b) 0.7 m, 2 m
c) 3 m, 0.4 m
d) 0.4 m, 3 m

Explanation: The working depth of the teeth is usually 2 m which is the same as for standard spur and helical gears, but the bevel pinion is designed with the larger addendum and has 0.7 m working depth. The gear addendum varies according to the gear ratio and is 1 m for a gear ratio 1.

8. A pair of bevel gears is mounted on two intersecting shafts who have a shaft angle of 70°. The velocity ratio of the gears is 2. Find the pitch angles.
a) 42.21°, 27.79°
b) 48.14°, 21.86°
c) 39.29°, 30.71°
d) 46.95°, 23.05°

Explanation: θ = 70°, wg/wp = 1/2
tan yg = ((sin θ)/((wg/wp)+cos θ)) = ((sin 70°)/((1/2)+cos 70°)) = 1.16
yg = 48.14°
tan yp = ((sin θ)/((wp/wg)+cos θ)) = ((sin 70°)/((2)+cos 70°)) = 0.4
yp = 21.86°
We can confirm this by checking that yg + yp = θ = 70°.

9. A pair of bevel gears is mounted on two intersecting shafts who have a shaft angle of 80°. The gear ratio of the gears is 1/3. Find the pitch angles.
a) 62.76°, 17.24°
b) 49.31°, 30.69°
c) 56.97°, 23.03°
d) 64.63°, 15.37°

Explanation: θ = 80°, wg/wp = 1/3
tan yg = ((sin θ)/((wg/wp)+cos θ)) = ((sin 80°)/((1/3)+cos 80°)) = 1.94
yg = 62.76°
tan yp = ((sin θ)/((wp/wg)+cos θ)) = ((sin 80°)/((3)+cos 80°)) = 0.31
yp = 17.24°
We can confirm this by checking that yg + yp = θ = 80°.

10. The gear ratio of bevel gears = tan yg = cot yp. True or false?
a) True
b) False

Explanation: The gear ratio of bevel gears can be given from the number of teeth, the pitch diameters or the pitch cone angles as i = ω12 = n1/n2 =d2/d1 = tan yg = cot yp. Thus, the statement is true.

Sanfoundry Global Education & Learning Series – Theory of Machines.

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