Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Chapter 7, Problem 25P
To determine
The design parameter of the shaft.
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A steel shaft 800 mm long transmitting 15 kW at 400 r.p.m. is supported at two bearings at the twoends. A gear wheel having 80 teeth and 500 mm pitch circle diameter is mounted at 200 mm from theleft hand side bearing and receives power from a pinion meshing with it. The axis of pinion and gearlie in the horizontal plane. A pulley of 300 mm diameter is mounted at 200 mm from right hand sidebearing and is used for transmitting power by a belt. The belt drive is inclined at 30° to the vertical inthe forward direction. The belt lap angle is 180 degrees. The coefficient of friction between belt andpulley is 0.3. Design and sketch the arrangement of the shaft assuming the values of safe stresses as :τ = 55 MPa; σt= 80 MPa. Take torsion and bending factor 1.5 and 2 respectively.
2. A shaft is supported on bearings A and B, 800 mm between centres. A 20 degrees straight tooth spur gear having 600 mm pitch diameter, is located 200 mm to the right of the left hand bearing A, and a 700 mm diameter pulley is mounted 250 mm towards the left of bearing B. The gear is driven by a pinion with a downward tangential force while the pulley drives a horizontal belt having 180 degrees angle of wrap. The pulley also serves as a flywheel and weighs 2000 N. The maximum belt tension is 3000 N and the tension ratio is 3: 1. Determine the maximum bending moment and the necessary shaft diameter if the allowable shear stress of the material is 40 MPa.
A transmission shaft supporting
a helical gear B and an overhung bevel gear D is
shown in Fig.
bearings, A and C. The pitch circle diameter of
the helical gear is 450 mm and the diameter of
the bevel gear at the forces is 450 mm. Power is
transmitted from the helical gear to the bevel gear.
The gears are keyed to the shaft. The material of
the shaft is steel 45C8
400
The shaft is mounted on two
400
400
270
250
]640
210 640
The factors k, and k, of ASME code are 2.0
and 1.5 respectively. Determine the shaft diameter
using the ASME code.
100
Chapter 7 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 7 - A shaft is loaded in bending and torsion such that...Ch. 7 - The section of shaft shown in the figure is to be...Ch. 7 - The rotating solid steel shaft is simply supported...Ch. 7 - A geared industrial roll shown in the figure is...Ch. 7 - Design a shaft for the situation of the industrial...Ch. 7 - The figure shows a proposed design for the...Ch. 7 - For the problem specified in the table, build upon...Ch. 7 - Prob. 8PCh. 7 - For the problem specified in the table, build upon...Ch. 7 - For the problem specified in the table, build upon...
Ch. 7 - In the figure is a proposed shaft design to be...Ch. 7 - The shaft shown in the figure is proposed for the...Ch. 7 - Prob. 20PCh. 7 - The shaft shown in the figure is proposed for the...Ch. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - A 25-mm-diameter uniform steel shaft is 600 mm...Ch. 7 - Prob. 29PCh. 7 - Compare Eq. (727) for the angular frequency of a...Ch. 7 - Prob. 31PCh. 7 - The steel shaft shown in the figure carries a...Ch. 7 - A transverse drilled and reamed hole can be used...Ch. 7 - Prob. 34PCh. 7 - The shaft shown in Prob. 721 is proposed for the...Ch. 7 - A guide pin is required to align the assembly of a...Ch. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - A ball bearing has been selected with the bore...Ch. 7 - Prob. 41PCh. 7 - A gear and shaft with nominal diameter of 35 mm...
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- Figure below shows a portion of a pump that is gear-driven at uniform load and speed. The 25 mm diameter solod shaft supported by the bearings is to be made of machined AISI 1045 CD steel. The helical gear is subjected to the axial force F-498 y a radial load F- 750 N and a tangential load of F-1.995 N. Assume the component is g at room temperature of 70F and the material has s0s reliability factor. Hint: Be careful when you calculate the bending moment at the fillet, as all the three forces on the helical gear cause bending moment at the fillet. Calculate resultant bedina moment from all the three forces. Bending moment is completely reversed loading.) 25-mm solid round shaft Fillet Bending K, = 2.0 Torsional k, = 1.5 Axial K,18 F. F, F Pump Helical spur gear -50 mm -250-mm dia FIGURE 1. Identify the critical locations) of stress and show it clearly in a diagram. 2 Identity cleary, all the components of stresses (at the critical point) that will be calcurated (by drawing and clearty…arrow_forwardFigure below shows a portion of a pump that is gear-driven at uniform load and speed. The 25 mm diameter solod shaft supported by the bearings is to be made of machined AISI 1045 CD steel. The helical gear is subjected to the axial force F =499 y a radial load F = 741 N and a tangential load of F=2,006 N. Assume the component is operating at room temperature of 70°F and the material has 50% reliability factor. 25-mm solid Bending K, = 2.0 round shaft Fillet Torsional K = 1.5 F. F, Axial K, = 1.8 F Pump Helical spur gear 50 mm -250-mm dia.- FIGURE 1. Identify the critical location(s) of stress and show it clearly in a diagram. 2. Identify cleary, all the components of stresses (at the critical point) that will be calculated (by drawing and clearly showing the XYZ axes) and show it in a matrix form. Show which components of stresses will have a value zero or non-zero. 3. Calculate the principal stresses and principal directions. Show the principal stresses clearly in a stress element…arrow_forward8.10 Two equal involute gear wheels of 40 teeth each, 3 mm module and 20° pressures angle are in mesh. Determine the minimum addendum if 2 pairs of teeth are always in mesh. The gear wheels rotate at 750 r.p.m. and transmit 4.6 kW. Find the normal force at each pair assuming equal direction of load between the pairs. Neglect friction.arrow_forward
- In the double-reduction gear train shown (dimensions are in inches), shaft a is driven by a motor attached by a flexible coupling attached to the overhang. The motor provides a torque of 2500 lbf-in at a speed of 1200 rpm. The gears have 20° pressure angles, with diameters shown in the figure. Use an AISI 1020 cold-drawn steel. Design Shaft CD with a design factor of 1.5 by performing the following tasks. (a) Sketch a general shaft layout, including means to locate the gears and bearings, and to transmit the torque. (b) Perform a force analysis to find the bearing reaction forces, and generate shear and bending moment diagrams. (c) Determine potential critical locations for stress design. (d) Determine critical diameters of the shaft based on fatigue and static stresses at the critical locations. (e) Make any other dimensional decisions necessary to specify all diameters and axial dimensions. Sketch the shaft to scale, showing all proposed dimensions. (f) If any of the deflections…arrow_forwardA transmission shaft supporting a helical gear B and an overhung bevel gear D is shown in Fig. bearings, A and C. The pitch circle diameter of the helical gear is 450 mm and the diameter of the bevel gear at the forces is 450 mm. Power is transmitted from the helical gear to the bevel gear. The gears are keyed to the shaft. The material of the shaft is steel 45C8 The factors k, and k, of ASME code are 2.0 and 1.5 respectively. Determine the shaft diameter using the ASME code. 400 The shaft is mounted on two 400 400 270 250 210 640i ]640 100arrow_forwardA gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another gear with the transmitted force FA applied at the 20 pressure angle as shown. The power is transmitted through the shaft and delivered through gear B through a transmitted force Fg at the pressure angle shown. For the steel countershaft shown below, assume the bearings have a maximum slope specification of 0.064" for good bearing life. Does the dia shown below meet the requirement? if not determine a suitable shaft diameter. 1.25-in da Gear A F₁-300- Gear B Sindia The minimum shaft diameter is in.arrow_forward
- 3. A 15 kW and 1200 rp.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having 20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day under light shock conditions, find from the standpoint of strength, 1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear. Check the gears thus designed from the consideration of wear. The surface endurance limit may be taken as 700 MPa.[Ans. m 6 mm ; b = 60 mm; Tp= 24; T=96; D, = 144mm; De= 576 mm]arrow_forwardEx: The second shaft on a parallel-shaft 25-hp foundry crane speed reducer contains a helical gear with a pitch diameter of S.08 in. Helical gears transmit components of force in the tangential, radial, and axial directions. The components of the gear force transmitted to the second shaft are shown in Fig. (8) at point A. The bearing reactions at C and D, assuming simple- supports, are also shown. A ball bearing is to be selected for location C to accept the thrust, and a cylindrical roller bearing is to be utilized at location D. The life goal of the speed reducer is 10 kh, with a reliability factor for the ensemble of all four bearings (both shafts) to equal 1 (90% reliability) with light to moderate impact. (a) Select the roller bearing for location D. (b) Select the ball bearing (angular contact) for location C, assuming the inner ring rotates. *- 20 Fig (8)arrow_forwardThe shaft shown in figure below rotating at 310 rpm carries a spur pinion E. The teeth are of the 20°, full-depth, involute form. The pinion delivers 20 hp to a gear to the left as shown. Compute the torque delivered by the shaft to the pinion E and the tangential and radial forces exerted on the shaft by the pinion. Include the weight of the pinion. A B E -12- Flywheel 1550 lb 22-in dia. V-belt sheave 120 lb 9 A 20° 6-in spur gear 20° FD 45 lb WEE Q E drives Q WrE 45 16.arrow_forward
- The reducer input shaft shown in the figure is taperedIt transmits moment with the help of a gear wheel.On the spindle, Fa = 552 N, Fr = 457 N, Ft = 1960 Nfrom gear forces and belt mechanismincoming Fk = 2600 N radial force impact. The shaft rotates with n = 1090 rpm.Accept the shaft diameter in the A bearing as dA = 35 mm.Fixed ball bearing for Lh = 13500 hselectarrow_forwardCalculate the angle of twist at point A. A for the following diagrammed problem. There is a 1600 lb-in torque T applied at A. Shaft AB is 12 in. long, and shaft CD is 8 in. long. Gear B has 8 in. diameter, and Gear C has 5 in. diameter. Both shafts have diameter 1 in. Assume that there is no slip between the gears, and that all components are made of steel with shear modulus G-29 × 10° psi. TA = 1600 lb in A 12 in B C 8 in Darrow_forwardThe reducer input shaft shown in the figure is tapered It transmits moment with the help of a gear wheel. On the spindle, Fa = 552 N, Fr = 457 N, Ft = 1960 N from gear forces and belt mechanism incoming Fk = 2600 N radial force impact . The shaft rotates with n = 1090 rpm. Accept the shaft diameter in the A bearing as dA = 35 mm. Fixed ball suitable for Lh = 13500 h select bearing.arrow_forward
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