Concept explainers
The power rating for new gear-set.
Answer to Problem 29P
The power rating for new gear-set is
Explanation of Solution
Write the expression for diameter of pinion.
Here, the number of teeth on pinion is
Write the expression for diameter of the gear.
Here, the number of teeth on gear is
Write the expression for velocity of the pinion.
Here, the number of rotation made by pinion is
Write the expression for constant of transmission accuracy level number.
Here, the transmission accuracy level number is
Write the expression for constant
Write the expression for dynamic factor.
Write the expression for allowable bending stress number through hardened steels.
Here, the brinel hardness number is
Write the expression for gear ratio.
Here, the number of teeth on gear is
Write the expression for stress cycle factor for bending for pinion.
Here, the number of cycles is
Write the expression for stress cycle factor for bending for gear.
Write the expression for allowable stress for pinion.
Here, the reliability factor is
Write the expression for allowable stress for gear.
Write the expression for load correction factor for uncrowned teeth.
Write the expression for pinion proportion factor.
Here, the face width is
Write the expression for pinion proportion modifier for straddle mounted pinion.
Write the expression for mesh alignment factor.
Here, the empirical constant is
Write the expression for mesh alignment correction factor.
Write the expression for load distribution factor
Write the expression for overload factor for pinion.
Here, the Lewis form factor for pinion is
Write the expression for overload factor for gear.
Here, the lewis form factor for gear is
Write the expression for transmitted load in pinion.
Here, the spur gear geometry factor for pinion is
Write the expression for power for pinion.
Write the expression for transmitted load for gear.
Here the spur gear geometry factor for gear is
Write the expression for power for gear.
Write the expression for pitting resistance stress cycle factor for pinion.
Write the expression for pitting resistance stress cycle factor for gear.
Write the expression for geometry factor.
Here, the pressure angle is
Write the expression for hardness ratio factor
Write the expression for contact fatigue strength for pinion.
Write the expression for contact fatigue strength for gear.
Write the expression for pinion contact endurance strength.
Write the expression for transmitted load.
Here, the elastic coefficient is
Write the expression for power of pinion.
Write the expression for gear contact strength.
Write the expression for transmitted load.
Write the expression for power of gear.
Write the expression for rated power.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to table 14-9, “Empirical constant
Substitute
Substitute
Refer Figure 14-6, “spur gear geometry factor”, to obtain the geometry factor for number of teeth
Since the thickness of gear is constant so
Rim thickness
Since the loading is uniform so
Refer table 14-2, “values of the lewis form factor
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the rating of speed reducer for power is
Want to see more full solutions like this?
Chapter 14 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- Two 20º full-depth steel gears are heat treated to BHN=350. AGMA Quality No.8 Pinionturns 860 rpm. N1=24c; N2=96; Pd=4, and b=2in. Find the horsepower the gears aretransmitting. Ans: hp=77.2arrow_forwardFor full depth of involute spur gears. minimum number of teeth of pinion to avoid interference depends upon (a) pressure angles B.Speed ratio C.circular pitch D pitch diameterarrow_forwardA pair of Straight teeth spur geard, having 2ó involutek full depth teerh is to halee tyanj mitted Power 12 KW at 30e rpm of the Pinich. The speed ratío is 3. The allowable s tati'c StYesse) for gear of cast brom and Pinion of steel are 6o Mpa and lo5 Mpa, respectilely. Assume the number of teeth Pinion as 16 and face width as 14 times of tha module. A SSume Steedy load Conditng and 8-10 hours of service per day. Given: be=84 Mpa, Ges=6o0 MPa, C=80,E, = 200000 HPa , Ea ノ HPa 4.5 4.5+earrow_forward
- 14-23 A spur gearset has 17 teeth on the pinion and 51 teeth on the gear. The pressure angle is 20° and the overload factor K, = 1. The diametral pitch is 6 teeth/in and the face width is 2 in. The pinion speed is 1120 rev/min and its cycle life is to be 10" revolu- tions at a reliability R = 0.99. The quality number is 5. The material is a through- hardened steel, grade 1, with Brinell hardnesses of 232 core and case of both gears. For a design factor of 2, rate the gearset for these conditions using the AGMA method.arrow_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_forwardA pair of gears with 14.5° full-depth teeth are to transmit 5 hp at 1800 rpm of the pinion; mw= 2.5; Np = 20 teeth; carefully cut teeth; intermittent service; Kf= 1.45. A. Determine the diametral pitch, B. face width, C. and tooth numbers if the pinionis to be made of phosphor gear bronze (SAE 65, Table AT 3arrow_forward
- 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_forwardOL Two involute gears of 20 pressure angie are in mesh. The nomber of teeth on pinion is 20 and the gear ratio is 2. If the pitch expressed in module is 5 mm and the pitch line speed is 1.2 m/s, assuming addendum as standard and equal to one module, find: 1 The angle turnad through by pinion when one pair of teeth is in mesh; and 2 The maximum veloctty of sitdingarrow_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_forward
- Problem 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_forwardA pair of helical gears are machined with a hob. The hob has a 20 degree pressure angle and machines circular pitch of 0.55 inch/tooth on a spur gear. Two gears are machined, the pinion has 18 teeth and the gear has 36 teeth. The measured transverse diametral pitch on the pinion is 5 inch/tooth. The pinion transmits 10 hp at 1,000 rpm. Calculate the helix angle of the gearset, in degrees.arrow_forwardA 57-tooth spur gear is in mesh with a 23-tooth pinion. The gearset transmits 125 hp at 1000 pinion rpm. Size the spur gears for a bending failure safety factor of at least 2 assuming a steady torque, 25∘ pressure angle, full-depth teeth, Qν = 9, an AISI 4140 steel pinion, and a class 40 cast iron gear. Part A Find the appropriate standard diametral pitch for the gearset. Part B Find the minimum required face width of the gears needed to satisfy the safety requirementsarrow_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