Concept explainers
A 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1120 rev/min, and drives a gear at a speed of 544 rev/min. Find the number of teeth on the gear and the theoretical center-to-center distance.
The number of teeth on the gear.
The theoretical center to-center distance.
Answer to Problem 1P
The number of teeth on the gear is
The theoretical center to-center distance is
Explanation of Solution
Write the expression for the diametrical pitch for the pinion.
Here, the number of teeth on pinion is
Write the expression of velocity ratio in terms of the number tooth.
Here, the rotational speed of the gear is
Write the relation between number of tooth on pinion and gear and diameters of the pinion and gear.
Here, the pitch circle diameter of the gear is
Write the expression for the centre distance between gear and pinion.
Conclusion:
Substitute
Substitute
Thus, the number of teeth on the gear is
Substitute
Substitute
Thus, the centre distance is
Want to see more full solutions like this?
Chapter 13 Solutions
SHIGLEY'S MECHANICAL ENGR DESIGN (LL)
- Solve 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_forwardAn epicyclic gear shown in figure below consists of ring gear, planet gear and sun gear. The ring gear has 72 internal teeth and sun gear has 32 external teeth. Planet gear meshes with both ring and sun gears and is carried on an arm which rotates about the centre of the ring gear at 20 r.p.m. If the gear A is fixed, Calculate the speed of plane gear.arrow_forwardA 17-tooth pinion meshes with an 84-tooth gear. The full-depth involute gear teeth have 20°pressure angle and a diametral pitch of 32. Determine the base pitch and the contact ratio.Also,calculate the addendum, dedendum, circular pitch, tooth thickness, and the base diameterfor the pinion and gear. If the center distance is increased by 0.125 in., what are the newvaluesfor the contact ratio and the pressure angle.arrow_forward
- 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.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_forwardColegio de Muntinlupa fabricated a pair of spur gear 2.5 module (20° full depth involute tooth) and to be mounted on shafts with a centerline distance of 90 mm. The speed ratio required is 3:1. Determine the following: a. Pitch diameter of pinionb. Pitch diameter of gearc. Number of teeth of piniond. Number of teeth of geare. Circular pitch of pinionf. Circular pitch of gearg. Addendumh. Dedendumi. Clearancej. Whole depthk. Working Depthl. Backlashm. Tooth thicknessn. Tooth space widtho. Outside diameter of pinionp. Outside diameter of gearq. Root diameter of pinionr. Root diameter of gears. Base diameter of piniont. Base diameter of geararrow_forward
- Two equal spur gears of 48 teeth mesh together with pitch radii of 4.0 in. and addenda of 0.1670in. If the pressure angle is 14 1⁄2 deg, calculate the length of action and contact ratio.arrow_forwardA parallel helical gearset uses a 20-tooth pinion driving a 36-tooth gear. The pinion has a right-hand helix angle of 30°, a normal pressure angle of 25°, and a normal diametral pitch of 4 teeth/in. Find: (a) The normal, transverse, and axial circular pitches (b) The normal base circular pitch (c) The transverse diametral pitch and the transverse pressure angle (d) The addendum, dedendum, and pitch diameter of each geararrow_forwardTwo mating involute spur gears of 20 pressure angle have a gear ratio of 2. The number of teeth on the pinion is 20 and its speed is 250 r.p.m. The module pitch of teeth is 10 mm. If the addendum on each wheel is such that the path of approach and the path of recess on each side are half the maximum possible length cach, find: i) the addendum for pinion and gear wheel, i) the length of arc of contact, iiithe maximum velocity of sliding during approach and recess. Assume pinion to be driver.arrow_forward
- A pinion having 40 teeth drives a gear having 80 teeth. the profile of the gear is involute with pressure angle ( 22), 12 mm module and (14) mm addendum. Find 1-the length of contact2-Arc of contact 3-Contact ratioarrow_forwardA pair of gear/pinion of 42 tooth and 18 tooth with a diametral pitch of 0.7874 teeth/cm and the addendum is 0.8/p and dedendum 1/p. The gear pressure angle is 200 . Compute the center distance of the pair of gears in meters.arrow_forwardA pinion with known module and number of teeth rotates at 2400 rpm and drives a gear at 800 rpm.Assume the spur gears mesh along their pitch circles.Determine the number of teeth on the gear, circular pitch,and theoretical center distance.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