Concept explainers
Whether the rated power is valid.
Answer to Problem 10P
The rated power is valid.
Explanation of Solution
Write the expression for pitch diameter of gear.
Here, the pitch diameter of gear is
Write the expression for pitch diameter of pinion.
Here, the pitch diameter of pinion is
Write the expression for gear ratio of gear set.
Here, the gear ratio is
Write the expression for pitch line velocity.
Here, the pitch line velocity is
Write the expression for dynamic factor.
Here, dynamic factor is
Write the expression for constant
Here, the transmission accuracy number is
Write the expression for constant
Write the expression of size factor for
Here, size factor is
Write the expression for size factor of pitting resistance for
Here, size factor for pitting resistance is
Write the expression for load distribution factor.
Here, load distribution factor is
Write the general expression for stress cycle factor of pinion for
Here, the stress cycle factor for pinion is
Write the general expression for stress cycle factor of gear for
Here, the stress cycle factor for gear is
Write the expression for reliability factor for bending strength.
Here, the reliability factor is
Write the expression for reliability factor for pitting.
Write the expression for stress cycle factor for pitting resistance for pinion for
Here, the stress cycle factor for pitting resistance for pinion is
Write the critical expression for stress cycle factor for pitting resistance for gear for
Here, the stress cycle factor for pitting resistance for gear is
Write the expression for hardness ratio factor for pitting resistance for gear.
Here, hardness ratio factor for pitting resistance for gear is
Write the expression for constant
Here, the Brinell harness number for pinion is
Write the expression for allowable bending stress number.
Here, the allowable bending stress number is
Write the expression for permissible bending stress for pinion.
Here, the permissible bending stress for pinion is
Write the expression for permissible bending stress for gear.
Here, the permissible bending stress for gear is
Write the expression for bending stress for pinion.
Here, the bending stress in pinion is
Write the expression for bending stress for gear.
Here, the bending stress in gear is
Write the expression for transmitted load by pinion in bending.
Here, the transmitted load by pinion in bending is
Write the expression for transmitted load on gear in bending.
Here, the transmitted load on gear in bending is
Write the expression for allowable contact stress number.
Here, the allowable bending stress number is
Write the expression for permissible contact stress number for pinion.
Here, the permissible contact stress number for pinion is
Write the expression for permissible contact stress number for gear.
Here, the permissible contact stress for gear is
Write the expression for contact stress for pinion.
Here, the contact stress in pinion is
Write the expression for contact stress for gear.
Here, the contact stress in gear is
Write the expression for transmitted load by pinion for wear.
Here, the transmitted load by pinion for wear is
Write the expression for transmitted load on gear for wear.
Here, the transmitted load on gear for wear is
Write the expression for crowning factor for pitting of uncrowned tooth.
Here, the crowning factor for pitting is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to Figure 15-7 “Bending factor
Substitute
Substitute
Substitute
Refer to Figure 15-7 “Bending factor
Substitute
Substitute
Substitute
Substitute
Refer to Table 14-8 “Elastic Coefficient
Refer to Figure 15-6 “Contact geometry factor
Substitute
Substitute
Substitute
Substitute
Substitute
The power rating for a gearset is defined as minimum of power rating in wear for pinion and gear and in bending for pinion and gear so that the failure by bending and wear of teeth on both gear and pinion can be saved.
The calculated power rating for gearset is
Thus, the rated power is valid.
Want to see more full solutions like this?
Chapter 15 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_forward1. 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 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
- 2. 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_forwardA 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_forwardProblem 19-11 A pair of straight bevel gears, mounted on shafts which are intersecting at right angles, consists of a 24 teeth pinion meshing with a 32 teeth gear. The module at the large end of the tooth is 5 mm. Calculate : 1. the pitch circle diameters of the pinion and the gear; 2. the pitch angles for the pinion and gear; 3. the cone distance; 4. the formative number of teeth for the pinion and gear; and 5. the back cone radius for the pinion and gear?arrow_forward
- Required information A gearbox with a compound reverted gear train transmits 25 horsepower with an input speed of 2500 rev/min. Spur gears with a diametral pitch of 4 teeth/in anda 20° pressure angle are used with 15 teeth on the each of the small gears and 44 teeth on each of the larger gears. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the output torque, neglecting frictional losses. The output torque To is Ibf-in.arrow_forward6. 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_forwardSolve this problem in spur gearsA 17-tooth pinion meshes with an 84-tooth gear. The full-depth involute gear teeth have 20° pressureangle and a diametral pitch of 32. Determine the base pitch and the contact ratio. Also,calculate theaddendum, dedendum, circular pitch, tooth thickness, and the base diameter for the pinion and gear. Ifthe center distance isincreased by 0.125 in., what are the new valuesfor thecontact ratio and thepressureangle with complete solution and write in hand writing thank youarrow_forward
- 2. A pair of spur gears with 20°, full-depth, involute teeth transmits 7.5 hp. The pinion is mounted on the shaft of an electric motor operating at 1750 rpm. The pinion has 20 teeth and a diametral pitch of 12. The gear has 72 teeth. Compute the following: 1. The rotational speed of the gear 2. The velocity ratio and the gear ratio for the gear pair 3. The pitch diameter of the pinion and the gear 4. The center distance between the shafts carrying the pinion and the gear 5. The pitch line speed for both the pinion and the gear 6. The torque on the pinion shaft and on the gear shaft 7. The tangential force acting on the teeth of each gear 8. The radial force acting on the teeth of each gear 9. The normal force acting on the teeth of each geararrow_forwardA parallel helical gearset consists of a 19-tooth pinion driving a 57-tooth gear. The pinion has a left-hand helix angle of 30°, a normal pressure angle of 20°, and a normal module of 2.5 mm. Find: (a) The normal, transverse, and axial circular pitches (b) The transverse diametral pitch and the transverse pressure angle (c) The addendum, dedendum, and pitch diameter of each gear 20° are angle specifyarrow_forwardA pair of spur gears with 20°. full-depth, involute teeth transmits 7.5 hp. The pinion is mounted on the shaft of an electric motor operating at 1750 rpm. The pinion has 20 teeth and a diametral pitch of 12. The gear has 72 teeth. Compute the following: a. The rotational speed of the gear b. The velocity ratio and the gear ratio for the gear pair c. The pitch diameter of the pinion and the gear d. The center distance between the shafts carrying the pinion and the gear e. The pitch line speed for both the pinion and the gear f. The torque on the pinion shaft and on the gear shaft g. The tangential force acting on the teeth of each gear h. The radial force acting on the teeth of each gear i. The normal force acting on the teeth of each geararrow_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