Concept explainers
The countershaft in Prob. 3–73, p. 152, is part of a speed reducing compound gear train using 20° spur gears. A gear on the input shaft drives gear A with a 2 to 1 speed reduction. Gear B drives a gear on the output shaft with a 5 to 1 speed reduction. The input shaft runs at 1800 rev/min. All gears are to be of the same material. Since gear B is the smallest gear, transmitting the largest load, it will likely be critical, so a preliminary analysis is to be performed on it. Use a module of 18.75 mm/tooth, a face-width of 4 times the circular pitch, a Grade 2 steel through-hardened to a Brinell hardness of 300, and a desired life of 12 kh with a 98 percent reliability. Determine factors of safety for bending and wear.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
SHIGLEY'S MECH.ENGINEERING DESIGN-EBK>I
- A gear train is composed of four helical gears with the three shaft axes in a single plane, as shown in the figure. The gears have a normal pressure angle of 20 and a 30 helix angle. Gear is the driver, and is rotating counterclockwise as viewed from the top. Shaft b is an idler and the transmitted load from gear 2 to gear 3 is 500 Ibf. The gears on shaft b both have a normal diametral pitch of 7 teeth/in and have 54 and 14 teeth, respectively. Find the forces exerted by gears 3 and 4 on shaft barrow_forwardI n a reverted gear train, as shown in Fig. Q2, two shafts A and B are in the same straight line andare geared together through an intermediate parallel shaft C. The gears connecting the shafts Aand C have a module of 2 mm and those connecting the shafts C and B have a module of 4.5 mm.The speed of shaft A is to be about but greater than 12 times the speed of shaft B, and the ratio ateach reduction is same. Find suitable number of teeth for all gears. The number of teeth of eachgear is to be a minimum but not less than 16. Also find the exact velocity ratio and the distance ofshaft C from A and Barrow_forwardA 220 mm diameter of 14.5 degrees involute gear is used to transmit 50 kW at 580 rpm Find the total force transmitted on the gear.arrow_forward
- A gear train is composed of four helical gears with the tree shaft axes in a single plane, as shown in the figure. The gears have a normal pressure angle of 20° and a 30°helix angle. Gear 2 is the driver, and is rotating counterclockwise as viewed from the top. Shaft b is and idler and the transmitted load from gear 2 to gear 3 is 500 lbf. The gears on shaft b both have a normal diametral pitch of 7 teeth/in and have 54 and 14 teeth, respectively. Find the forces exerted by gears 3 and 4 on shaft b.arrow_forwardThe upper half of a compound Epicyclic gearset is shown in Figure, with input shaft I rotating at a constant speed of 700 rpm in a clockwise direction and generating 12 kW input power. The Annulus wheel A2 is coupled to an auxiliary gear N on shaft X and forms a compound wheel with gear O. The Annulus A1 rotates in a counter-clockwise direction at a speed of 5,300 rpm. Calculate the following using this condition: Number of gear teeth:P1 = 30 , A1 = 120P2 = 50 , A2 = 140N = 60 , O = 120 a) The output shaft O (NO), shaft X (NX), and gear ratio speed and direction (n). b) Calculate the speed and direction of output shaft O (NO), shaft X (NX), and gear ratio if Annulus wheel A1 is locked (n). c) The braking torque (Tb) that must be applied to Annulus wheel A1 to keep it stationary (magnitude and direction), assuming gear transmission efficiency of 90%.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_forward
- The double-reduction helical gearset shown in the figure is driven through shaft a at a speed of 700 rev/min. Gears 2 and 3 have a normal diametral pitch of 12 teeth/in, a 30° helix angle, and a normal pressure angle of 20°. The second pair of gears in the train, gears 4 and 5, have a normal diametral pitch of 8 teeth/in, a 25° helix angle, and a normal pressure angle of 20°. The tooth numbers are: N, = 12, N, = 48, N4 = 16, N, = 36. Find: (a) The directions of the thrust force exerted by each gear upon its shaft (b) The speed and direction of shaft c (c) The center distance between shaftsarrow_forwarda in the figure has a power input of 75 kW at a speed of 1000 rev/min in the counterclock-wise direction. The gears have a module of 5 mm and a 20° pressure angle. Gear 3 is an idler.(a) Find the force F3b that gear 3 exerts against shaft b.(b) Find the torque T4c that gear 4 exerts on shaft Please solve with step wise given data must write....arrow_forwardA pair of straight-tooth bevel gears (as shown in the figure above) are in mesh transmitting 35 hp at 1000 rpm (pinion speed). The gear rotates at 400 rpm. The gear system has a pitch of 6 and a 20-degree pressure angle. The face width is 2 inches and the pinion has 36 teeth. Determine the tangential, radial, and axial forces acting on the pinionarrow_forward
- The motor shown in Fig. P6-47 develops 100 hp at a speed of 360 rpm. Gears A and B deliver 40 hp and 60 hp, respectively, to operating units in a factory. If the maximum shearing stress in the shafts must be limited to 12 ksi, determine a. The minimum satisfactory diameter for the motor shaft. b. The minimum satisfactory diameter for the power shaft. (1 hp=745,7 watts); (1 ksi=6,89 MPa); (1 ft=0,30 m)arrow_forwardA compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze [G = 6,500 ksi] tubes, which have an outside diameter of 2.40 in. and a wall thickness of 0.1375 in. Segments (3) and (4) are solid 1.00-in.-diameter steel [G = 11,500 ksi] shafts. The shaft lengths are L1 = 58 in., L2 = 16 in., L3 = 16 in., and L4 = 28 in. The torques applied to the shafts have magnitudes of TB = 970 lb·ft, TD = 430 lb·ft, and TE = 170 lb·ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign convention presented in Section 6.6., calculate: (a) the magnitude of the maximum shear stress in the compound shaft. (b) the rotation angle of flange C with respect to flange A. (c) the rotation angle of gear E with respect to flange A.arrow_forwardThe shafts are made of steel with shear modulus of 75 GPa. Determine the angle of twist of gear B if a torque of 30 kN·m is applied to gear B. Both shafts have the same diameter of 90 mm. (Hint: for the meshing cylindrical gears, i.e. gear C and D, the angle of twist need to time the radius of the gear while applying the equation of compatibility.)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