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# chap06 - 81 Chapter 6 Spur Gears 6.1 Find the diametral...

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81 Chapter 6 Spur Gears 6.1 Find the diametral pitch of a pair of gears having 32 and 84 teeth, respectively, whose center distance is 3.625 in. 3 2 2 3 32 84 3.625 in 2 2 2 N N R R P P P + + = + = = ( 29 116 teeth 16 teeth/in 2 3.625 in P = = Ans. 6.2 Find the number of teeth and the circular pitch of a 6-in pitch diameter gear whose diametral pitch is 9 teeth/in. ( 29 ( 29 (2 ) 9 teeth/in 6.0 in 54 teeth N P R = = = Ans. ( 29 9 teeth/in 0.349 1 in/tooth p P π π = = = Ans. 6.3 Determine the module of a pair of gears having 18 and 40 teeth, respectively, whose center distance is 58 mm. ( 29 3 2 2 3 18 40 58.0 mm 2 2 2 m mN mN R R + + = + = = ( 29 2 58.0 mm 2.0 mm/tooth 58 teeth m = = Ans. 6.4 Find the number of teeth and the circular pitch of a gear whose pitch diameter is 200 mm if the module is 8 mm/tooth. ( 29 ( 29 (2 ) 200.0 mm 8 mm/tooth 25 teeth N R m = = = Ans. ( 29 8 mm/tooth 25.13 mm/tooth p m π π = = = Ans. 6.5 Find the diametral pitch and the pitch diameter of a 40-tooth gear whose circular pitch is 3.50 in/tooth. ( 29 3.500 in/tooth 0.897 6 teeth/in P p π π = = = Ans. ( 29 ( 29 2 40 teeth 0.897 6 teeth/in 44.563 in D R N P = = = = Ans.

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82 6.6 The pitch diameters of a pair of mating gears are 3.50 in and 8.25 in, respectively. If the diametral pitch is 16 teeth/in how many teeth are there on each gear? ( 29 ( 29 2 2 2 2 16 teeth/in 3.500 in 56 teeth N PR PD = = = = Ans. ( 29 ( 29 3 3 3 2 16 teeth/in 8.250 in 132 teeth N PR PD = = = = Ans. 6.7 Find the module and the pitch diameter of a gear whose circular pitch is 40 mm/tooth if the gear has 36 teeth. ( 29 40 mm/tooth 12.732 mm/tooth m p π π = = = Ans. ( 29 ( 29 2 12.732 mm/tooth 36 teeth 458.4 mm D R mN = = = = Ans. 6.8 The pitch diameters of a pair of gears are 60 mm and 100 mm, respectively. If their module is 2.5 mm/tooth, how many teeth are there on each gear? ( 29 ( 29 2 2 2 2 60 mm 2.5 mm/tooth 24 teeth N R m D m = = = = Ans. ( 29 ( 29 3 3 3 2 100 mm 2.5 mm/tooth 40 teeth N R m D m = = = = Ans. 6.9 What is the diameter of a 33-tooth gear if its circular pitch is 0.875 in/tooth? ( 29 ( 29 2 0.875 in/tooth 33 teeth 9.191 in D R pN π π = = = = Ans. 6.10 A shaft carries a 30-tooth, 3-teeth/in diametral pitch gear that drives another gear at a speed of 480 rev/min. How fast does the 30-tooth gear rotate if the shaft center distance is 9 in? ( 29 ( 29 2 2 2 30 teeth 2 3 teeth/in 5.000 in R N P = = = ( 29 3 2 3 2 9.000 in 5.000 in 4.000 in R R R R = + - = - = ( 29 3 2 3 2 4.000 in 480 rev/min 384 rev/min 5.000 in R R ϖ ϖ = = = Ans. 6.11 Two gears having an angular velocity ratio of 3:1 are mounted on shafts whose centers are 136 mm apart. If the module of the gears is 4 mm/tooth, how many teeth are there on each gear? ( 29 ( 29 2 2 3 2 2 2 3 3 136 mm 1 1 4 1 R R R R R ϖ ϖ + = = + = + = ÷ ÷ 2 34.0 mm R = ( 29 2 2 2 34.0 mm 2 17 teeth 4 mm/tooth R N m = = = Ans. ( 29 3 3 2 2 102.0 mm R R R R = + - = ( 29 3 3 2 102.0 mm 2 51 teeth 4 mm/tooth R N m = = = Ans.
83 6.12 A gear having a module of 4 mm/tooth and 21 teeth drives another gear at a speed of 240 rev/min. How fast is the 21-tooth gear rotating if the shaft center distance is 156 mm? ( 29 ( 29 2 2 2 4 mm/tooth 21 teeth 2 42 mm R mN = = = ( 29 ( 29 3 2 3 2 156 mm 42 mm 114 mm R R R R = + - = - = ( 29 3 2 3 2 114 mm 240 rev/min 651.4 rev/min 42 mm R R ϖ ϖ = = = Ans.

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chap06 - 81 Chapter 6 Spur Gears 6.1 Find the diametral...

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