MACHINE DESIGN – WORM, HELICAL AND BEVEL GEAR

PROBLEM SET # 4
INSTRUCTION: Encircle the letter that corresponds to the correct answer of your choice.
MULTIPLE CHOICE:

1. A work rotating at 1150 rpm drives a worm gear. The velocity ratio is 15 to 1. A 10 hp motor is used to supply
the worm with worm pitch gear diameter of 3 in. Find the tangential force on the worm.
A. 365.37 lbs B. 465.37 lbs C. 565.37 lbs D. 665.37 lbs

2. A double thread worm gear has a pitch of 1 1/8 and a pitch diameter of 3 in. It has a coefficient of friction of 0.20
and normal angle (pressure angle) of 14.5o. The worm is supplied by 12 hp at 1200 rpm motor. Find the
tangential force on the gear. The worm is left hand threads.
A. 597.08 lbs B. 697.08 lbs C. 797.08 lbs D. 897.08 lbs

3. A single worm gear has a pitch diameter of 2 in and a pitch of 1 in with coefficient of friction of 0.21. The normal
angle is 14.5 degrees with tangential force on gear of 1000 lbs. Find the separation force on gear and worm
considering a left-hand thread.
A. 171.23 lbs B. 271.23 lbs C. 371.23 lbs D. 471.23 lbs

4. A double thread worm gear has a lead angle of 7.25 degrees and pitch radius of 2 ½ in. Find the pitch of the
worm.
A. ¼ in B. ½ in C. 1 in D. 1 ½ in

5. A triple thread worm gear has a helix angle of 78 degrees. It has a pitch of ¾ in. Find the pitch diameter of the
gear.
A. 2.37 in B. 2.77 in C. 3.07 in D. 3.37 in

6. A double thread worm has a lead of 1.5 in and pitch diameter of 3.5 in. If normal pressure angle is 14.5 degrees,
find the pressure angle of the worm.
A. 11.68o B. 12.68o C. 13.68o D. 14.68o

7. A triple thread worm gear has pitch of ¾ in and pitch diameter of 2 ¼ in. Find the helix angle.
A. 72.34o B. 62.34o C. 52.34o D. 42.34o

8. A three-thread worm, rotating at 1,000 rpm, drives a 31-tooth gear. Find the speed of the gear.
A. 76.77 rpm B. 86.77 rpm C. 96.77 rpm D. 106.77 rpm

9. A double thread worm having a pitch of 1 in is used to drive a 40 teeth gear. Find the pitch diameter of the gear.
A. 9.73 in B. 10.73 in C. 11.73 in D. 12.73 in

10. A triple thread worm gear is used to drive a 25 teeth gear having a pitch of ¾ in. Find the center distance.
A. 2.34 in B. 3.34 in C. 4.34 in D. 5.34 in

11. A double thread worm has a helix angle of 82o and a pitch diameter of 1 ¾ in. The worm rotates at 800 rpm.
Find the linear speed of the worm.
A. 129.82 fpm B. 139.82 fpm C. 149.82 fpm D. 159.82 fpm

12. A triple thread worm gear having a diametral pitch of 5 in is used to deliver a gear. The speed ratio is 10. Find
the pitch line velocity of gear id the worm rotates at 600 rpm.
A. 64.25 fpm B. 74.25 fpm C. 84.25 fpm D. 94.25 fpm

13. A double thread worm gear having a pitch of 1 in and has a linear speed of 200 fpm. The pitch diameter of worm
is 4 in. Find the tangential speed of the worm.
A. 1,256.64 fpm B. 1,356.64 fpm C. 1,456.64 fpm D. 1,556.64 fpm

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14. A triple thread worm gear has a pitch of ¾ in and pitch diameter of 3.5 in. The normal pressure angle is 14.5
degrees and coefficient of friction is 0.10. Find the worm efficiency.
A. 50.05% B. 55.05% C. 60.05% D. 65.05%

15. A triple thread worm gear has normal pressure angle of 14.5o and coefficient of friction is 0.15. If worm efficiency
is 70%, find the lead angle.
A. 25.74o B. 27.74o C. 29.74o D. 31.74o

16. A worm has four threads of 14.5o normal pressure angle and pitch diameter of 4 ¼ in. The gear has 52 teeth of
1 ¾ in pitch. Find the center distance of the shafts.
A. 12.61 in B. 14.61 in C. 16.61 in D. 18.61 in

17. A worm has four threads of 14.5o normal pressure angle and pitch diameter of 4 ¼ in. The gear has 52 teeth of
1 ¾ in pitch. Find the efficiency of the worm if friction is 0.03.
A. 82.88% B. 86.88% C. 89.88% D. 92.88%

18. A triple thread worm has a pitch diameter of 3 inches. The wheel has 25 teeth and a pitch diameter of 5 inches.
Material for both the worm and the wheel is of phosphor bronze. Compute the helix angle.
A. 0.20 B. 0.30 C. 0.40 D. 14

19. A triple thread worm gear is used to drive a 25 teeth gear having a pitch of ¾ in. Find the center distance.
A. 2.34 in B. 3.34 in C. 4.34 in D. 5.34 in

20. A double threaded right-handed worm gear transmits 15 HP at 1150 rpm. The pitch of the worm is 0.75 inches
and pitch diameter of 3 inches. The pressure angle is 14 and ½ degrees and the coefficient of friction is 0.12.
Find the separating force in pounds.
A. 504 lbs B. 501 lbs C. 407 lbs D. 5091 lbs

21. A 20-tooth helical gear has a pitch diameter of 10 in. Find the diametral pitch of the gear.
A. 2 B. 3 C. 4 D. 5

22. A 28 –tooth helical gear having a pitch diameter of 7 has a helix angle of 22 degrees. Find the circular pitch in a
plane normal to the teeth.
A. 0.528 B. 0.628 C. 0.728 D. 0.828

23. A helical gear having a helix angle of 23o and pressure angle of 20o. Find the pressure angle normal to the teeth.
A. 0.235 B. 0.335 C. 0.435 D. 0.535

24. A 75 hp motor, running at 450 rpm is geared to a pump by means of helical gear having a pinion diameter of 8 in.
Find the tangential force of the gear.
A. 2,326 lbs B. 2,426 lbs C. 2,526 lbs D. 2,626 lbs

25. A turbine at 30,000 rpm is used to drive a reduction gear delivering 3 hp at 3,000 rpm. The gears are 20 degrees
involute herringbone gears of 28 pitch and 2 1/8 in effective width. The pinion has 20 teeth with a helix angle of
23 deg. Determine the load normal to the tooth surface.
A. 20.4 lbs B. 24.4 lbs C. 28.4 lbs D. 32.4 lbs

26. A helical gear having 20 teeth and pitch diameter of 5 in. Find the normal diametral pitch if helix angle is 22
degrees.
A. 3.31 in B. 4.31 in C. 5.31 in D. 6.31 in

27. A helical gear tangential load of 200 lbs and axial load of 73 lbs. Find the helix angle.
A. 14 degrees B. 16 degrees C. 18 degrees D. 20 degrees

28. A helical gear having 20 teeth and pitch diameter of 5 in. Find the normal diametral pitch if helix angle is 22
degrees.
A. 3.31 in B. 4.31 in C. 5.31 in D. 6.31 in

29. Two helical gear transmit 50 HP at 3600 rpm. What should be the bore diameter of each gear be if the allowable
stress in gear shafts is 12,500 psi?
A. 1.252 in B. 1.3275 in C. 1.4568 in D. 1.5276 in

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30. A 20o full depth straight tooth gear has a face width of 3 ¾ in and a pitch diameter of 12 in with cone pitch angle
of 37.5o. Find the mean diameter.
A. 6.72 in B. 7.72 in C. 8.72 in D. 9.72 in

31. A straight tooth bevel gear has a face width of 4” and a pitch diameter of 14 in with cone pitch angle of 40o. If the
torque on the gear is 8000 in-lb, what is the tangential force on the gear?
A. 1400 lbs B. 1400 lbs C. 1400 lbs D. 1400 lbs

32. A pair of straight tooth bevel gear connect a pair of shafts 90o. The velocity ratio is 3 to 1. What is the cone pitch
angle of smaller gear?
A. 71.57 deg B. 65.34 deg C. 18.43 deg D. 12.34 deg

33. A spiral bevel pinion with a left-hand spiral rotates clockwise transmits power to a mating gear with speed ratio of
2 to 1. Determine the pitch angle of the pinion.
A. 16.56 deg B. 20.56 deg C. 26.56 deg D. 32.56 deg

34. A spiral bevel pinion with a left-hand spiral transmits 4 hp at 1200 rpm to a mating gear. The mean diameter of
the pinion is 3 in. Find the tangential force at the mean radius of the gear.
A. 110 lbs B. 120 lbs C. 130 lbs D. 140 lbs

35. A pair of 4-pitch, 14.5o, involute bevel gears have 2:1 reduction. The pitch diameter of the driver is 1 0 in and
face width of 2 in. Determine the face angle of pinion. (Shafts at right angle)
A. 20.85 deg B. 23.85 deg C. 25.85 deg D. 27.85 deg

36. The cone angle of pinion of a pair of bevel gear is 30o while for the gear 60o. If the pinion turns at 300 rpm, find
the speed of the gear.
A. 173.21 rpm B. 183.21 rpm C. 193.21 rpm D. 203.21 rpm

37. The cone angle of pinion and the gear are 25o and 65o respectively. Find the speed ratio.
A. 1.5 B. 5.2 C. 4.23 D. 2.14

38. A pair of bevel gear having a speed ratio of 3 has a 5-pitch at 14.5 deg involute. The pitch angle of the pinion is
8 in. Find the addendum angle of the pinion. (At right angle between shafts)
A. 0.906o B. 1.45o C. 2.34o D. 3.20o

39. A pair of bevel gear having a speed ratio of 2 has 4-pitch at 14.5o involute. The pitch diameter of pinion is 7 in.
Find the dedendum angle of the gear.
A. 1.11 deg B. 2.11 deg C. 3.11 deg D. 4.11 deg

40. A class 3 pinion bevel gear is made of alloy steel hardened to 300 Brinell. The pinion runs at 850 rpm with 5 in
pitch diameter. Find the gear stress at factor of safety 3.
A. 35,023 psi B. 45,023 psi C. 55,023 psi D. 65,023 psi

41. Compute the pitch angle of a bevel gear given the pinion’s number of teeth of 14 and 42 teeth on the gear.
A. 18.4” B. 28.4” C. 33.4” D. 38.4”

42. In a standard bevel gear, the pinion rotates at 150 rpm, its number of teeth is 14 while the gear has 42 teeth,
what is the pitch angle of the pinion?
A. 18.4 degrees B. 20 degrees C. 14.5 degrees D. 20.5 degrees

43. A four-wheel vehicle must develop a drawbar pull of 17,500 lbs. The engine which develops 500 hp and drives
500 hp and drives through a gear transmission a 34-tooth spiral bevel pinion gear which meshes with a spiral
bevel gear having 51 teeth. This gear is keyed to the drive shaft of the 48 in diameter rear wheels of the vehicle.
What transmission gear ratio should be used if the engine develops maximum torque at 1500 rpm? Note: the
efficiency of the bevel gear differential is 80%.
A. 17.493:1 B. 16.667:1 C. 18.562:2 D. 11.492:2

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ANSWER KEY
1. A 2. D 3. B 4. C 5. D

6. D 7. A 8. C 9. D 10. B

11. B 12. D 13. A 14. D 15. A

16. C 17. D 18. A 19. B 20. B

21. A 22. C 23. B 24. D 25. A

26. B 27. D 28. B 29. D 30. D

31. D 32. A 33. C 34. D 35. D

36. A 37. D 38. A 39. B 40. A

41. A 42. A 43. B

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