ME 314 HW#8

Important sections to study from Chapter-14

  • Section 14-3
  • Section 14-4
  • Section 14-5 to 14-18
  • Section 14-18 (only the two analysis summary: Figures 14-17 and 14-18
  1. A pair of spur gears are selected for a speed reduction application in windmills. The number of teeth in pinion and gear are 22 and 60 respectively. The diametral pitch is 4 and the pressure angle is 20 degrees. The geometric quality is specified to be Qv=10. The gear material is alloy steel 4340 through hardened to a Brinell hardness number of 250. The material quality is Grade-1. The face width is 3 inches. The pinion is expected to run at 1200 rpm and transmit 20 horsepower. The total number of pinion rotations (cycles) is expected to be 1 billion cycles. The power source is light shock and the load is uniform. The material strength data should conform to a reliability of 99%. The gears are specified to be crowned. The mounting is such that shaft deflection and slope effects can be ignored. The gears are ordered to have rigid and accurate mounting corresponding to “precision enclosed gear units”. The thickness of the rim is more than 1.2 times the tooth height. Adequate lubrication is applied and the temperatures are less than 200 degrees F. Determine:

a)Factor of safety guarding against eventual tooth breakage [~11]

b)Factor of safety guarding against eventual surface pitting [~2]

  1. A pair of helical gears are in mesh in a speed reduction application. The pinion and gear teeth numbers are 14 and 54 respectively. The normal diametral pitch in 7 teeth per inch. The normal pressure angle is 20 degrees and the helix angle is specified to be 30 degrees. The gears transmit 5 horsepower at 500 rpm. Determine the magnitude of tangential, radial, and axial forces. [545 lbs, 229 lbs, 315 lbs]
  1. A pair of straight bevel gears are in mesh in a speed reduction application. The intersecting shafts meet at 90 degrees. The pinion and gear teeth numbers are 15 and 25 respectively. The diametral pitch in 10 teeth per inch. The pressure angle is 20 degrees The gears transmit 5 horsepower at 500 rpm. Determine the magnitudes of tangential, radial, and axial forces on the pinion. [988 lbs, 308 lbs, 185 lbs]

Problem 4 is not assigned

  1. A double thread worm transmits ¾ of horsepower at 600 rpm. The worm in meshed to a 36-tooth gear with a normal diametral pitch of 8 teeth/inch. The worm has a pitch diameter of 1.5 inches. Use a coefficient of friction of 0.05 and determine the forces exerted by the gear on the worm (tangential, radial, and axial). [105 lbs, 174 lbs, 468 lbs]