1. The pressure angle of two gears in a mesh is φ = 22.5°. The number of teeth on the pinion is 25 and the gear ratio is 2. The module is 7 mm and addendum = 1 module. Find the angle of action of these two gears.
a) 32.056°
b) 34.697°
c) 22.72°
d) 28.531°
Explanation: φ = 22.5°, t = 25 and T = 25 x 2 = 50, m = 7 mm and addendum = 7 mm.
r = mt/2 = 87.5 mm and ra = r + a = 94.5 mm
R = mT/2 = 175 mm and Ra = R + a = 182 mm
Path of contact = (Ra2 – R2cos2 φ)0.5 + (ra2 – r2cos2 φ)0.5 – (R + r)sinφ = 32.056 mm
Arc of contact = Path of contact/cos φ = 32.056/cos 22.5° = 34.697 mm.
Angle of action = Arc of contact / r = 0.3965 rad = 22.72°.
2. The pressure angle of two gears in a mesh is φ = 25°. The number of teeth on the pinion is 45 and the gear ratio is 2. The module is 6 mm and addendum = 1.1 module. Find the contact ratio of these two gears.
a) 1.7
b) 2.3
c) 4.2
d) 3.5
Explanation: φ = 25°, t = 45 and T = 45 x 2 = 90, m = 6 mm and addendum = 6.6 mm.
r = mt/2 = 135 mm and ra = r + a = 141.6 mm
R = mT/2 = 270 mm and Ra = R + a = 276.6 mm
Path of contact = (Ra2 – R2cos2 φ)0.5 + (ra2 – r2cos2 φ)0.5 – (R + r)sinφ = 29.068 mm
Arc of contact = Path of contact/cos φ = 29.068/cos 25° = 32.073 mm.
Contact ratio = Arc of contact / Circular pitch = 32.073 / πm = 32.073 / (πx6) = 1.7.
3. Identify the given gear.
a) Spur gear
b) Helical gear
c) Worm and worm gear
d) Bevel gear
Explanation: The given diagram is of a helical gear. In helical gears, the teeth are inclined to the axis of the gear. The gears can be either left handed or can be right handed depending on the direction in which the helix slopes when viewed. Here, 1 is left handed gear and 2 is a right handed gear.
4. The angle at which the teeth of the gear are inclined to the axis of a gear is called as __________
a) pitch angle
b) normal angle
c) helix angle
d) gear angle
Explanation: Helix angle is the angle at which the teeth are inclined to the axis of a gear.
In the diagram above, Ψ is called as helix angle. Depending upon the direction of this angle, the gear can be either left handed or right handed.
5.The distance between the corresponding points on adjacent teeth measured on the pitch circle is called ______________
a) helical pitch
b) normal pitch
c) gear pitch
d) circular pitch
Explanation: Circular pitch is the distance between the corresponding points on adjacent teeth measured on the pitch circle.
Here, the distance p is called as circular pitch.
p = πm, where m is the module.
6. The shortest distance measured along the normal to the helix between corresponding points on the adjacent teeth is called ____________
a) gear pitch
b) helical pitch
c) circular pitch
d) normal circular pitch
Explanation: Normal circular pitch or normal pitch is the shortest distance measured along the normal to the helix between corresponding points on the adjacent teeth.
In the given figure, pn is the normal circular pitch.
pn = p cos Ψ
Therefore, mn = m cos Ψ.
7. Two spiral gears have a normal module of 10 mm and the angle between the skew shaft axes is 50°. The driver has 20 teeth and the helix angle of it is 30°. If the velocity ratio is 1/3 and the driver as well as the follower are both left handed, find the centre distance between the shafts.
a) 434.72 mm
b) 452.83 mm
c) 582.19 mm
d) 523.39 mm
Explanation: Ψ1 = 30°, mn = 10 mm and Ψ2 = 50° – 30° = 20°, T1 = 20.
VR = 1/3 = T1/T2
T2 = 3 x T1 = 3 x 20 = 60
Centre distance = C = (mn/2) ((T1/cos Ψ1) + (T2/cos Ψ2)) = 434.72 mm.
8. The centre distance between two meshing gears is 250 mm and the angle between the shafts is 60°. The normal circular pitch is 10 mm and the gear ratio is 2. Ψ1 = 35°. Find the value of number of teeth on both the wheels.
a) 46,92
b) 45, 90
c) 54,108
d) 62, 124
Explanation: Given: Ψ1 = 35°, Ψ2 = 60° – 35° = 25°, G = T2/T1 = 2, pn = 10 mm and C = 250 mm
Centre distance = C = 250 = (mn/2) ((T1/cos Ψ1) + (T2/cos Ψ2)) = (pn/2π) ((T1/cos Ψ1) + (T2/cos Ψ2)) = 1.59 x (1.22T1 + 2.207T1) = 5.45 T1
T1 = 250/5.45 = 45.88 ~ 46
T2 = 2 x T1 = 92.
9. The centre distance between two meshing gears is 250 mm and the angle between the shafts is 60°. The normal circular pitch is 10 mm and the gear ratio is 2. Ψ1 = 35°. Find the exact centre distance.
a) 248.992 mm
b) 250.934 mm
c) 251.831 mm
d) 251.029 mm
Explanation: Ψ1 = 35°, Ψ2 = 60° – 35° = 25°, pn = 10 mm
We found out that T1 = 46 and T2 = 92.
Centre distance = (pn/2π) ((T1/cos Ψ1) + (T2/cos Ψ2)) = 250.934 mm.
10. The centre distance between two meshing gears is 250 mm and the angle between the shafts is 60°. The normal circular pitch is 10 mm and the gear ratio is 2. Ψ1 = 35°.Find the efficiency if the friction angle is 6°.
a) 89.23 %
b) 91.02 %
c) 88.58 %
d) 85.69 %
Explanation: Given: φ = 6°, Ψ1 = 35°, Ψ2 = 60° – 35° = 25°
Efficiency = η = (cos (Ψ2+ φ) x cos Ψ1¬)/ (cos (Ψ1 – φ) x cos Ψ2 ¬) = 0.8858 = 88.58 %.