Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780077591670
Author: BUDYNAS
Publisher: MCG
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Chapter 13, Problem 53P
A 2-tooth left-hand worm transmits
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A pair of helical gears transmit 15 KW power and the pinion is rotating at 1000 rpm. The helix angle is 0.50 radians and the normal pressure angle is 0.35 radians. The pitch diameter of the pinion is 70 mm and the pitch diameter of the gear is 210 mm. Determine the tangential, radial, and axial forces between the gear teeth.
A similar pair of helical gears , also on parallel axes, are to have involute teeth, of 20o normal pressure angle, and 3 mm normal module. The wheels are to have 26 and 34 teeth, and to work with a centre distance of 146 mm. Calculate the transverse pressure angle in degrees.
pinion having 20 involute teeth of module pitch 6 mm rotates at 200 r.p.m. and transmits 1.5 kW to a gear wheel having 50 teeth. The addendum on both the wheels is 1/4 of the circular pitch. The angle of obliquity is 20°. Find (a) the length of the path of approach ; (b) the length of the arc of approach; (c) the normal force between the teeth at an instant where there is only pair of teeth in contact.
Chapter 13 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 13 - A 17-tooth spur pinion has a diametral pitch of 8...Ch. 13 - A 15-tooth spur pinion has a module of 3 mm and...Ch. 13 - A spur gearset has a module of 6 mm and a velocity...Ch. 13 - A 21-tooth spur pinion mates with a 28-tooth gear....Ch. 13 - A 20 straight-tooth bevel pinion having 14 teeth...Ch. 13 - A parallel helical gearset uses a 20-tooth pinion...Ch. 13 - A parallel helical gearset consists of a 19-tooth...Ch. 13 - To avoid the problem of interference in a pair of...Ch. 13 - Prob. 9PCh. 13 - Prob. 10P
Ch. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - A parallel-shaft gearset consists of an 18-tooth...Ch. 13 - The double-reduction helical gearset shown in the...Ch. 13 - Shaft a in the figure rotates at 600 rev/min in...Ch. 13 - The mechanism train shown consists of an...Ch. 13 - The figure shows a gear train consisting of a pair...Ch. 13 - A compound reverted gear trains are to be designed...Ch. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - A gearbox is to be designed with a compound...Ch. 13 - The tooth numbers for the automotive differential...Ch. 13 - Prob. 26PCh. 13 - In the reverted planetary train illustrated, find...Ch. 13 - Prob. 28PCh. 13 - Tooth numbers for the gear train shown in the...Ch. 13 - The tooth numbers for the gear train illustrated...Ch. 13 - Shaft a in the figure has a power input of 75 kW...Ch. 13 - The 24T 6-pitch 20 pinion 2 shown in the figure...Ch. 13 - The gears shown in the figure have a module of 12...Ch. 13 - The figure shows a pair of shaft-mounted spur...Ch. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - A speed-reducer gearbox containing a compound...Ch. 13 - For the countershaft in Prob. 3-72, p. 152, assume...Ch. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - The figure shows a 16T 20 straight bevel pinion...Ch. 13 - The figure shows a 10 diametral pitch 18-tooth 20...Ch. 13 - Prob. 45PCh. 13 - The gears shown in the figure have a normal...Ch. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - The figure shows a double-reduction helical...Ch. 13 - A right-hand single-tooth hardened-steel (hardness...Ch. 13 - The hub diameter and projection for the gear of...Ch. 13 - A 2-tooth left-hand worm transmits 34 hp at 600...
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- simple gear train of 30 and 50 teeth for pinion and gear wheel respectively, is used to drive an electric wheelchair at a velocity that is double the maximum velocity of slip. The pinion has an equal addendum as the gear wheel, a module of 3 mm, and a pressure angle of 14.5o. The wheelchair has a maximum velocity of 5 m/s when its pinion rotates at 800 r.p.m. Calculate: 1. The magnitude of the velocity of slip of gears in mesh.2. The angular speed of the gear wheel in rad/s.3. The maximum length of a path of the approach in mm.arrow_forwardTwo parallel shafts have an angular velocity ratio of 4 to 1 are connected by gears, the largest of which has 40 teeth. Find the number of teeth of smaller gear.arrow_forwardA 220 mm diameter of 14.5 degrees involute gear is used to transmit 50 kW at 580 rpm Find the total force transmitted on the gear.arrow_forward
- A simple gear train of 30 and 50 teeth for pinion and gear wheel respectively,is used to drive an electric wheelchair at a velocity that is double the maximum velocity of slip. The pinion has an equal addendum as the gear wheel, a module of 3 mm, and a pressure angle of 14.5o. The wheelchair has a maximum velocity of 5 m/s when its pinion rotates at 800 r.p.m. Calculate: 1.1. The magnitude of the velocity of slip of gears in mesh. (2)1.2. The angular speed of the gear wheel in rad/s. (4)1.3. The maximum length of a path of the approach in mm. (2)1.4. The length of a path of a recess in mm. (7)1.5. The addendum of the gears in mm. (7)1.6. The contact ratio.arrow_forwardA simple gear train of 30 and 50 teeth for pinion and gear wheel respectively, is used to drive an electric wheelchair at a velocity that is double the maximum velocity of slip. The pinion has an equal addendum as the gear wheel, a module of 3 mm, and a pressure angle of 14.5o. The wheelchair has a maximum velocity of 5 m/s when its pinion rotates at 800 r.p.m. Calculate: a) The magnitude of the velocity of slip of gears in mesh. b)The maximum length of a path of the approach in mm c ) The length of a path of a recess in mm d) The addendum of the gears in mm e) The contact ratio.arrow_forwardA spur pinion of pitch diameter 50 mm rotates at 200 rad/s and transmits 3 kW power. The pressure angle of the tooth of the pinion is 20°. find the total force exerted by a tooth of the pinion on other gear?arrow_forward
- A straight gear with module m = 5 mm and face width bw = 40 mm has center distance cd = 0.1875m. The pinion has 25 teeth, the speed is 1000 rpm, and pressure angle ᶲ = 200. Find the Hertzian contact stress at the pitch point when the gear transmits 10 kW. Neglect friction forces. The gear steel has modulus of elasticity E = 207 GPa and a Poisson’s ratio of 0.30.arrow_forwardA single stage spur gear gearbox has a module of 1.5mm and an input speed of 1500.p.m. and a pinion with 15 teeth. The overall ratio of the gearbox is 6:1 and the gearbox is transmitting a power of 6000W. If the factor of safetv is to be reduced to an absolute minimum acceptable value and the gears are to be made from a material with a Yield stress of 540 MPa, what is the face width of the gears (in mm) Express your answer in the form 21.00 ie with two decimal place an no unitsarrow_forwardA three-thread worm gear, rotating at 1000 rpm, drives a 31-tooth worm gear and transmit 15 HP. Theworm has 14 ½ o teeth with ¾ pitch, 2 in pitch diameter, and an included face angle of 60o. The coefficientof friction is 0.05. (Assume Y = 0.322) A. Determine the helix angle of the worm. Ans. 70.30o B. Determine the speed ratio. Ans. 10.33C. Determine the center distance. Ans. 4.70 inD. Determine the apparent stress in the worm wheel teeth. Ans. 31,100 psiE. Determine the efficiency of this worm-gear set. Ans. 85.70%arrow_forward
- A double-threaded right-handed worm gear transmits 15 Hp at 1150 rpm. The pitch of the worm is 0.75 inch and the pitch diam of 3 inches. The pressure angle is 14.5° and the coefficient of friction is 0.12. b) Find tangential force on worm.arrow_forwardA simple gear train of 30 and 50 teeth for pinion and gear wheel respectively, is used to drive an electric wheelchair at a velocity that is double the maximum velocity of slip. The pinion has an equal addendum as the gear wheel, a module of 3 mm, and a pressure angle of 14.5o. The wheelchair has a maximum velocity of 5 m/s when its pinion rotates at 800 r.p.m. Calculate The magnitude of the velocity of slip of gears in mesh.arrow_forwardA 15 kW and 1200 r.p.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having 20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day under light shock conditions, find from the standpoint of strength, 1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear. Check the gears thus designed from the consideration of wear. The surface endurance limit may be taken as 700 MPaarrow_forward
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