Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Chapter 13, Problem 8P
To avoid the problem of interference in a pair of spur gears using a 20° pressure angle, specify the minimum number of teeth allowed on the pinion for each of the following gear ratios.
- (a) 2 to 1
- (b) 3 to 1
- (c) 4 to 1
- (d) 5 to 1
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1. To avoid the problem of interference in a pair of spur gears using a 20° pressure angle, specify the
minimum number of teeth allowed on the pinion (Np.act) for each of the following gear ratios, and the
corresponding maximum number of teeth on meshing gear (NG,act). Assume full depth tooth.
a. 1.25 to 1
b. 1.6 to 1
c. 2.5 to 1
d. 3.2 to 1
2. Repeat problem 1 for helical gears with normal pressure angle of 20° and helix angle of 30°.
Figure shown below illustrates the gears in a speed-change gearbox used in machine tool applications. By sliding the cluster gears on shafts Band C, nine speed changes can be obtained as shown in Table given below. The problem of the machine tool designer is to select tooth numbers for the various gears (2 to 10) so as to produce a reasonable distribution of speeds for the output shaft. The gears 2, 6 and 9 are having 20, 25 and 50 teeth respectively. The input shaft speed is 450 rpm and the output speed can vary from 137 rpm to 580 rpm depending on the sequence of the gears. If the output speed obtained through the gear sequence 2-5-5-8 is 257 rpm and if the minimum and maximum number of teeth in the gear system are 20 and 50 respectively,
(i) Suitable tooth numbers for the remaining gears (3,4,5,7,8 & 10)
A 28-tooth spur pinion mates with a 42-tooth gear. The diametral pitch is 4 teeth/in and the
pressure angle is 20.. Make a drawing of the gears showing one tooth on each gear. Find and
tabulate the following results: the addendum, dedendum, clearance, circular pitch, tooth
thickness, and base-circle diameters; the lengths of the arc of approach, recess, and action; and
the base pitch and contact ratio.
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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- Two straight-toothed bevel gears mesh with a shaft angle of 90° and a diametral pitch of 5. The pinion has 20 teeth, and the gear ratio is 2:1. The addendum and dedendum are the same as for 20 stub teeth. For the gear, determine the pitch radius, cone angle, outside diameter, cone distance, and face width.arrow_forwardA 21-tooth spur pinion mates with a 28-tooth gear. The diametral pitch is 3 teeth/in and the pressure angle is 20°. Make a drawing of the gears showing one tooth on each gear. Find and tabulate the following results: the addéndum, dedendum, clearance, circular pitch, tooth thick- ness, and base-circle diameters; the lengths of the arc of approach, recess, and action; and the base pitch and contact ratio.arrow_forwardthree spur gear arrangement are shown. it has a pinion gear A-driver that rotates for about 500 rpm. the second gear, gear B- an idler and the third gear, gear C- driven gear. the three gears have a diametral pitch of 5 and power of 10hp. The pressure angle is 20°.Number of teeth are shown in the figure. determine the following: i) The pitch diameters of each of the gears. ii) The torque that each shaft is required to transmit. iii) The forces on each of the gears, shown on a free body diagram. iv) The resultant force on the shaft carrying Gear B.arrow_forward
- Examine the gear drive system shown below. All the gears have a DP = 12. The smallest gear is the primary driver gear and has 15 Teeth, RPM = 3600, and Torque = 2.2 N-m. That small gear meshes with a 72-tooth gear which is connected to another gear that has 20 teeth. That 20-tooth gear connects to the final driven gear that has 64 teeth. What is the final output RPM of the 64-tooth gear? What is the final output Torque supplied by the 64 tooth gear?arrow_forwardThree 14.5° pressure angle spur gears with a diametral pitch of 8 are meshed. The input pinion on the left is running clockwise at 3101 rpm and transmits 3.2 Hp. Gear 1 (Pinion) Input N1 = 20 teeth Gear 2 Idler Gear 3 Output N3 = 25 teeth N2 = 75 teeth Answer the following: 1. Pinion (Gear 1) pitch diameter (1 mark) 2. Gear 2 pitch diameter (1 mark) 3. Gear 3 pitch diameter (1 mark) 4. Circular pitch (1 mark) 5. Addenda (1 mark) 6. Center distance from gear 1 to gear 3 (2 marks) 7. Line of action length for gear 1 contacting gear 2 (2 marks) 8. Contact ratio of gear 1 and 2 (2 marks) 9. Gear ratio from gear 1 to gear 3 (1 mark) 10. Draw a free-body diagram of Gear 2, showing the radial and tangential forces. Calculate these forces. What is the reaction force in the bearing? (3 marks)arrow_forward1. A reverted compound gear train with a gear train ratio of 40:9 is required. All available gears have module 1 and pressure angle 20 deg. Gears with N (number of teeth) between 4 and 25 are available. Please design the gear train. Please construct a table with all gears in the gear train and give the pitch diameter for all gears.arrow_forward
- 6. Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmits a torque of 20 N m. The torque transmitted by the gear is (a) 6.6 Nm (6) 20 Nm (c) 40 Nm (d) 60 Nm.arrow_forwardProblem 1. The spur gears shown in Figure 1 have a diametral pitch of 2 teeth per inch and a 20° - pressure angle. Gear 2 rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair in Gear 5 on shaft c. (a) Show fully labeled free-body diagrams of gear 2, and Gears 3 and 4; (b) What forces do gear 3 and 4 transmit to the idler shaft? (c) What is the train value? (d) What is the output speed? Gear 5 Gear 4 48Teeth 18Teeth Gear 3 32Teeth Gear 2 18Teeth Figure 1arrow_forwardFor a pair of spur gears, one design decision is to specify the pressure angles. Please select the common values of pressure angle per textbook. 300 200 250arrow_forward
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