problems for practice

PROBLEMS FOR PRACTICE

1. Two spur gears, having 20 and 60 teeth, are meshing with each other. If the module be 5, find the pitch circle diameters of the two gears. Calculate also circular and diametrical pitches of these gears. 

[Ans. 100 mm; 300 mm; 15.7 mm; 0.2]

2. The following data relate to a pair of involute spur gears in mesh: 

Teeth on pinion 25, Teeth on gear = 48; Pressure angle =20°. Pitch in module = 5 mm and pitch line velocity of pinion = 1.2 m/s. Determine the velocity of sliding at the beginning of engagement, at the end of engagement and at the pitch point, if addendum is equal to one module. 

[Ans. 38.46 cm/s; 35.49 cm/s and 0 cm/s]

3. Two gears in mesh have a module of 10 mm and a pressure angle of 25°. The pinion has 20 teeth and the gear has $2. The addendum on both the gears is equal to one module. Determine:

(i) the number of pairs of teeth in contact,

(ii) the angles of action of the pinion and the wheel, and

(iii) the ratio of the sliding velocity to the rolling velocity at the pitch point and at the beginning and end of engagement.

 [Ans. (i) 1.475; (ii) 26°36'; 10°13'; (iii) zero; 0.304; 0.278] 

4. Two spur wheels have 30 teeth each of involute shape. The circular pitch is 25 mm and pressure angle is 20°. Deternfine the addendum of the wheels, if the arc of contact is twice the circular pitch.

 [Ans. 9.9 mm]

5. A gear wheel having 20 teeth of involute form of module pitch 6 mm and an angle of obliquity of 20°, drives another wheel of the same dimensions. Calculate the length of arc of contact if the addendum is one module.

If the addendum was altered so that the arc of contact was the possible what would be the length of this arc, and the addendum required for this?

[Ans. 35.5 mm; 9.72 mm; 43.68 mm] 

6. Find the length of the path of contact when a pinion with 18 teeth meshes with an internally toothed wheel with 72 teeth, when the pressure angle is 20 degrees, modulę pitch is 4 and the addenda of pinion and wheel are 8.7 mm and 3.7 mm respectively.

[Ans. 14.9 mm]

7. A pair of involute spur gears with 14½° pressure angle and having 6 mm module are in mesh. The number of teeth on the pinion is 16 and its rotational speed is 300 rpm. When the gear ratio is 2, find the addendum on the pinion in order to avoid interference.

[Ans. 18.78 mm] 

8. Determine the minimum number of teeth required on a pinion, in order to avoid interference which is to gear with (i) a wheel to give a gear ratio of 4 to 1; and (ii) an equal wheel. The pressure angle is 20° and a standard addendum of 1 module for the wheel may be assumed. 

[Ans. (i) 16; (ii) 13]

9. Two 20° involute spur gear mesh externally and give a velocity ratio of 3. Module is 3 mm and the addendum is equal to 1.1 module. If the pinion rotates ar 120 rpm, determine:

(i) the minimum number of teeth on pinion and gear to avoid interference, and

(ii) the number of pair of teeth in contact.

 [Ans. (i) TG = 50; TP = 17; (ii) 1.78 pairs]

10. Following data refers to two meshing gears having 20° involute teeth:

Number of teeth of gear wheel 52; Number of teeth of pinion = 20; Speed of pinion 360 rpm; Module = 8 mm

If addendum of each gear is such that the path of approach and path of recess are half of their maximum possible values, determine the addendum for the gear and the pinion and the length of arc of contact. 

[Ans. 5.07 mm; 18.04 mm; 52.4 mm]

11. Following data relate to two meshing involute gears:

Number of teeth on gear wheel = 60; Pressure angle = 20°; Gear ratio 1.5; Speed of gear wheel = 100 rpm; Module = 8 mm

The addendum on each wheel is such that the path of approach and the path of recess on each side are 40% of the maximum possible length each.

Determine:

(i) the addendum for the pinion and the gear,

(ii) the length of path of contact,

(iii) the length of arc of contact, and

(iv) the contact ratio.

 [Ans. (i) 8.3 mm; 14 mm; (ii) 54.72 mm; (iii) 58.23 mm; 2.3 pairs] 

12. A 20° involute pinion with 20 teeth drives a gear having 60 teeth. Module is 8 mm and addendum of each gear is 10 mm.

(i) State whether interference occurs or not. Give reasons.

(ii) Find the length of path of approach and arc of approach, if pinion is the driver.

[Ans. (i) Since KP < MP (i.e., 25.79 mm < 27.26 mm), therefore no interference occurs; (ii) 27.36 mm, 29.1 mm]