Tutorial Machine Design Worm & Bevel gears

By Prof S S Chauhan, IEC College of Engineering & Technology, Greater Noida
Unit-2 Worm gears, Bevel gears
Objective: Student should have knowledge about the design of worm, Bevel and Hypoid gear and also have an idea about their different engineering applications.
Objective type Questions

1. When bevel gears having equal teeth and equal pitch angle connect tow shafts whose axes intersect at right angle, then they are known as:
(a) angular bevel gears (b) crown bevel gears (c) internal bevel gears (d) mitre gears

2. The worm gears are widely used for transmitting power at ………velocity ratios between non-intersecting shafts.
(a) high (b) low

3. In worm gears, the angle between the tangent to the thread helix on the pitch cylinder and the Plane normal to the axis of worm is called:
(a) pressure angle (b) lead angle (c) helix angle

4. The number of starts on the worm for a velocity ratio of 40 should be
(a) single (b) double (c) triple (d) quadruple

Numerical Questions

1. Define the virtual no. of teeth for a bevel gear.

2. What are the advantages of spiral bevel gears over straight bevel gears?

3. Differentiate between the mitre and crown bevel gear.

4. A cast iron bevel gear has a pitch diameter of 600mm and a pitch angle of 30degree. The module is 2.5. Determine the permissible endurance load. The teeth are 20-degree full depth.

5. Two cast iron bevel gears having pitch diameters of 80 mm and 100mm respectively and to transmit 11/4 Kw at 1100RPM of the pinion. The tooth profile are of 20 degree full depth. Take (s0=55MN/ m2)
(a) determine the face width and the required module from stand point of strength
(b) Check the design from stand point of dynamic load and wear C=110 kN/m

6. A cast steel (s0=100MN/ m2) bevel gear pinion has pitch diameter of 225mm and pitch angle of 30 degree. The module is 4. The gear rotates at 600RPM. From the standpoint of strength only how much power should this gear be capable of transmitting?

7. Two steel bevel gears connects shaft at right angle. The pinion has a BHN of 300 and the gear has hardness 200. The teeth are 14.5 full depth and the module is 3. The number of teeth on pinion has 64. The face width is 40mm. determine the wear load.

8. A 100 kW, 750-RPM motor is required to drive a centrifugal pump continuously at 250 RPM by means of straight bevel gears connected at 90m-degree shaft angle. The starting torque is 20% greater that rated torque (a) Design the gears. (b) Could the same pinion is use to drive the another pump at 150RPM? Give brief explanation.

9. A pair of 4 pitch 20 degree involutes machine cut bevel gear have a2:1 reduction . The pitch diameter of the driver is 250mm and runs at 200RPM. Selecting the suitable material for the pinion and the gear determine the various parameter of gear set.

10. A pair of bevel gear are mounted on shafts that are at 90 degree apart. The set is to transmit 90 Kw at 300RPM. The pinion has 150mm outside pitch diameter; 50 mm face width, a diametral pitch of 6, and 20 degree full depth. For a velocity ratio 0.4. Determine the forces acting on gear tooth.

11. Find the power transmitted by a pair of 20o bevel gears with Tp = 40 and Tg = 60 teeth. Gears are made of steel and are hardened to 350BHN. Module is 6.5mm. width of face is 60mm but thickness of the blanks is 35mm. Pinion rotates at 600rpm. The shaft angle is 90o. Safe static stress for gears = 105Mpa. Assume Kv =6 / (6 +v); C for dynamic load calculation = 250 kN/m.

12. Design a pair of bevel gears to transmit 12kW at 600rpm. Gear ratio is 2: 1 and pinion has 24 teeth of 20o involute full depth. The material for both the wheels is the same with safe static stress of 105Mpa. b = l/3. Find module, face width, cone distance and pitch circle diameters of both the wheels.
Assume Kv =3.5/(3.5+ √V), Where V is peripheral velocity in m/sec. Shaft angle is 90o. Check the design for wear strength and dynamic tooth load. Given that Ses = 600Mpa, Ep=Eg= 2x105 Mpa, c = dynamic load tooth factor = 300kN/m,
Y= Lawis form factor = 0.154 – (0.912/Tf).

13. For the above example determine the diameter of the shaft carrying gear if the mean plane of the gear is 150mm away from the bearing.

14. A pair of straight bevel gear is used to transmit 18.5kW at 600rpm. The gear ratio is 2 and shaft angle is 90o. Pinion has 28 teeth of 20o involute profile. The safe static stress for the pinion as well as gear material may be taken as 105Mpa. The module is 6mm. Determine the necessary face width b of the gears to carry the given safety.

15. A spindle of a drilling machine is to be driven by means of a pair of 20o straight bevel gears. The pinion is to be mounted on horizontal drive shaft. The reduction ratio is 3.5:1. The drilling operation requires 195Nm at 350rpm design the gear pair, if the safe static stress for the gears is limited to 145Mpa.

16. A double threaded worm has a pitch circle diameter of 84mm with a axial pitch of 20 mm determine the helix angle

17. A hardened steel worm transmits power to a phosphor bronze with a velocity ratio 20 the centre ceutic distance is 400 mm determine,
a)Axial module
b) Lead Angle (helix angle) c)Power rating based on heat dissipation criterion d)Power rating based on wear if worm rotates at750 rpm

18. For a worm and worm wheel the a centre distance is given as 225mm worm is made of hardened steel and rotates at 1250 rpm worm transmits power to a phosphor bronze gear (σb=35 Mpa with a transmission ratio of 15 the tooth on gear are 20 degree full depth involute(y=0.125) determine all the design parameters and recommitted safe power that the drive can transmit.

19. Or the above example , determine the diameter of the shaft of worm as well as the worm gear for the arrangement of the bearing assume coefficient of friction M=0.1

20. Design a pair of bevel gears for two shafts whose axes are at right angles. Speed of pinion shaft is 300 rpm and that of Gear shaft is 120 rpm. The power transmitted is 80 kW.