Concept explainers
Repeat Prob. 14-19 using helical gears each with a 20° normal pitch angle and a helix angle of 30° and a normal diametral pitch of 6 teeth/in.
14-19 A commercial enclosed gear drive consists of a 20° spur pinion having 16 teeth driving a 48-tooth gear. The pinion speed is 300 rev/min, the face width 2 in, and the diametral pitch 6 teeth/in. The gears are grade 1 steel, through-hardened at 200 Brinell, made to No. 6 quality standards, uncrowned, and are to be accurately and rigidly mounted. Assume a pinion life of 108 cycles and a reliability of 0.90. Determine the AGMA bending and contact stresses and the corresponding factors of safety if 5 hp is to be transmitted.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- A pair of helical gears mounted on parallel shafts have P, = 6, d, - 20°, and b= 4 in. The 32-tooth pinion and 48-tooth gear are made of steel having 400 Bhn and 350 Bhn, respectively. Manufacturing precision corresponds to curve C of Velocity factor chart. Use a mounting factor of 1.6. Center distance is 7.5 in. 1. What helix angle is required? 2. Estimate the horsepower that can be transmitted for 10 pinion revolutions with 99% reliability and a safety factor of 1.5 if the driving motor rotates 1200 rpm and involyes light shock and the driven load involves medium shock. Check for bending fatigue only.arrow_forward2. A pair of bevel gears have their shafts at right angles. The larger gear has 50 teeth of 4 diametral pitch and is made of SAE 1045 steel. The pinion has 20 teeth and runs at 850 rpm and transmit 30 hp. Determine: A. the gear diameter B. the pinion diameter C. the length of contact D. the pitch line velocity of the pinion E. the tangential force Ans. 12.5 in Ans. 5 in Ans. 6.73 in Ans. 1,112 fpm Ans. 890 lbsarrow_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_forward
- A pair of steel gears have a design life of a million cycles. They have 20° full-depth teeth with a diametral pitch of 8. Both gear and pinion are made of steel heat-treated to 350 Bhn, and both have a face width of 1.0 in. The teeth are machined with the highest quality hobbing operation. The pinion has 35 teeth and rotates 2000 rpm. The gear diameter over pinion diameter ratio is 2. The gears stay below a temperature of 140 °F. Assume a mounting correction factor of Km = 1.6 and an overload factor of Ko = 1. Use a reliability of 99.9% and a safety factor of 1.5. Use the pinion for the bending fatigue calculations and assume that there is no load sharing. A. What is the fatigue strength for these conditions. B. What is the tangential force acting on the gear teeth? C. Estimate the horsepower that can be transmitted, based only on bending fatigue.arrow_forwardAsaparrow_forwardA commercial enclosed spur gearset has 22 teeth on the pinion and 60 teeth on the gear. The pressure angle is 20° and the overload factor Ko =1. The diametral pitch is 8 teeth/in and the face width is 5 in. The pinion speed is 1000 rev/min and its cycle life is to be 10° revolutions at a reliability R =0.50. The quality number is 5 and the tooth are crowned. The material is a through-hardened steel, grade 2, with Brinell hardnesses of 250 core and case of both gears. For a conservative design and bending stress design factor of 2, rate the pinion (power) for these conditions using the AGMA method.arrow_forward
- 1. The figure shows a pair of shaft-mounted spur gears having a diametrical pitch of 6 teeth/in with a 14 tooth pinion (gear 2) driving a 49 tooth gear at a pressure angle of 20°. The power input is 3/4 hp at 2400 rpm cw. A, B, C, and D are bearings. 3. 3 in 3 in Determine the following: a. The Free Body Diagram for both gears. b. The pitch diameters of gears 2 and 3. c. The transmitted load. d. The torque Tin on the pinion shaft. e. The radial and tangential forces on gear 3 f. The output torque of gear 3 shaft.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 N2 = 75 teeth Gear 3 Output N3 = 25 teeth Answer the following: 1. Pinion (Gear 1) pitch diameter 2. Gear 2 pitch diameter 3. Gear 3 pitch diameter 4. Circular pitch 5. Addenda 6. Center distance from gear 1 to gear 3 7. Line of action 8. Contact ratio of gear 1 and 2 9. Gear ratio from gear 1 to gear 3( for gear 1 contacting gear 2, 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?arrow_forwardProvide the complete step-by-step solution, given data, conversion of units, and sketch for this problem. A turbine at 30,000 rpm is used to drive a reduction gear delivering 3 hp at 3,000rpm. The gears are 20 degrees involute herringbone gears of 28 pitch and 2 1/8 ineffective width. The pinion has 20 teeth with a helix angle of 23 deg. Determine theload normal to the tooth surface. A. 20.4 lbs B. 24.4 lbs C. 28.4 lbs D. 32.4arrow_forward
- 187 13-40 The figure shows a pair of shaft-mounted spur gears having a diametral pitch of 5 teeth/in with an 18-tooth 20° pinion driving a 45-tooth gear. The power input is 32-hp at 1800 rev/min. Find the direction and magnitude of the forces acting on bearings A, B, C, and D. 13-41 The figure shows the electric-motor frame dimensions for a 30-hp 900 rev/min motor. The frame is bolted to its support using four -in bolts spaced 11 in apart in the view shown and 14 in apart when viewed from the end of the motor. A 4 diametral pitch 20° spur pinion having 20 teeth and a face width of 2 in is keved to and fluch with 3 in 3 in Problem 13-40arrow_forwardQ8:- An epicyclic gear speed reduction is shown in the Fig. below. The driving shaft carries on the arm A a pin on which the compound wheels B and C are free to revolve. Wheel C meshes with the fixed wheel E and wheel B meshes with the wheel D which is keyed to the driven shaft. The number of teeth on the wheels are:- Zg=27, Z,=30, Zp=24 and ZĘ=21. Find the ratio of the speed of the driving shaft to the speed of the driven shaft. A Input output Earrow_forward2 spur gears connected externally were produced having M-2.5. They were mounted on 2 different shafts with a center distance of 9cm. The speed ratio is 3:1. Using 14.5° determine the following: 1. Pitch Diameter (Driver Diameter) mm 2. Pitch Diameter (Driven Diameter) = mm 3. Number of Teeth (Driver) = teeth 4. Number of Teeth (Driven) = teeth 5. Circular Pitch = mm 6. Addendum = in 7. Clearance = in 8. Dedendum D in 9. Whole Depth in 10. Working Depth in %!arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY