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 5, Problem 73P
To determine
The factor of safety against the fracture in the gear hub due to the shrink fit by using modified Mohr theory.
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A helical cast steel gear with 30o helix angle has to transmit 35 kW at 2000 rpm. If the gears has 25 teeth, find the necessary module, pitch diameters and face width for 20o full depth involute teeth. The static stress for cast steel may be taken as 100 MPa. The face width may be taken as 3 times to normal pitch. The tooth form factor is given by the expression y'= 0.154-0.912/TE, where TE represents the equivalent number of teeth. the velocity factor is given by Cv=6/(6+v), where v is the peripheral speed of the gear in m/s.
A short stub shaft, made of SAE 1035, as rolled, receivers 30 hp at 300 rpm via a 12-in. spur gear, the power being delivered to another shaft through a flexible coupling. The gear is keyed (profile keyway) midway between the bearings. The pressure angle of the gear teeth 20o, N = 1.5 based on the octahedral shear stress theory with varying stresses. (a) Neglecting the radial component R of the tooth load W , determine the shaft diameter. (b) Considering both the tangential and the radial components, compute the shaft diameters. (c) Is the difference in the results of the parts (a) and (b) enough to change your choice of the shaft size?
A helical cast steel gear with 30° helix angle has to transmit 35
kW at 2000 r.p.m. If the gear has 25 teeth, find the necessary
module, pitch diameters and face width for 20° full depth
involute teeth. The static stress for cast steel may be taken as
100 MPa. The face width may be taken as 3 times the normal
pitch. The tooth form factor is given by the expression
y'=0.154 – 0.912/T, where T represents the equivalent num-
ber of teeth. The velocity factor is given by C, =
6 + v
where
v is the peripheral speed of the gear in m/s.
Chapter 5 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 5 - A ductile hot-rolled steel bar has a minimum yield...Ch. 5 - A ductile hot-rolled steel bar has a minimum yield...Ch. 5 - A ductile hot-rolled steel bar has a minimum yield...Ch. 5 - A ductile hot-rolled steel bar has a minimum yield...Ch. 5 - A ductile hot-rolled steel bar has a minimum yield...Ch. 5 - Prob. 6PCh. 5 - 5-7 to 5-11 An AISI 1018 steel has a yield...Ch. 5 - 5-7 to 5-11 An AISI 1018 steel has a yield...Ch. 5 - 5-7 to 5-11 An AISI 1018 steel has a yield...Ch. 5 - 5-7 to 5-11 An AISI 1018 steel has a yield...
Ch. 5 - 5-7 to 5-11 An AISI 1018 steel has a yield...Ch. 5 - A ductile material has the properties Syt = 60...Ch. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - 5-14 to 5-18 An AISI 4142 steel QT at 800F...Ch. 5 - 5-14 to 5-18 An AISI 4142 steel QT at 800F...Ch. 5 - 5-14 to 5-18 An AISI 4142 steel QT at 800F...Ch. 5 - A brittle material has the properties Sut = 30...Ch. 5 - Repeat Prob. 519 by first plotting the failure...Ch. 5 - For an ASTM 30 cast iron, (a) find the factors of...Ch. 5 - For an ASTM 30 cast iron, (a) find the factors of...Ch. 5 - Prob. 23PCh. 5 - For an ASTM 30 cast iron, (a) find the factors of...Ch. 5 - 5-21 to 5-25 For an ASTM 30 cast iron, (a) find...Ch. 5 - 5-26 to 5-30 A cast aluminum 195-T6 exhibits Sut =...Ch. 5 - 5-26 to 5-30 A cast aluminum 195-T6 exhibits Sut =...Ch. 5 - 5-26 to 5-30 A cast aluminum 195-T6 exhibits Sut =...Ch. 5 - 5-26 to 5-30 A cast aluminum 195-T6 exhibits Sut =...Ch. 5 - 5-26 to 5-30 A cast aluminum 195-T6 exhibits Sut =...Ch. 5 - 5-31 to 5-35 Repeat Probs. 526 to 530 using the...Ch. 5 - 5-31 to 5-35 Repeat Probs. 526 to 530 using the...Ch. 5 - Repeat Probs. 526 to 530 using the modified-Mohr...Ch. 5 - Repeat Probs. 526 to 530 using the modified-Mohr...Ch. 5 - Repeat Probs. 526 to 530 using the modified-Mohr...Ch. 5 - This problem illustrates that the factor of safety...Ch. 5 - For the beam in Prob. 344, p. 147, determine the...Ch. 5 - A 1020 CD steel shaft is to transmit 20 hp while...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - 5-39 to 5-55 For the problem specified in the...Ch. 5 - Prob. 42PCh. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - Prob. 45PCh. 5 - 5-39 to 5-55 For the problem specified in the...Ch. 5 - Prob. 47PCh. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - 5-39 to 5-55 For the problem specified in the...Ch. 5 - 5-39 to 5-55 For the problem specified in the...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - For the problem specified in the table, build upon...Ch. 5 - Build upon the results of Probs. 384 and 387 to...Ch. 5 - Using F = 416 lbf, design the lever arm CD of Fig....Ch. 5 - A spherical pressure vessel is formed of 16-gauge...Ch. 5 - This problem illustrates that the strength of a...Ch. 5 - Prob. 60PCh. 5 - A cold-drawn AISI 1015 steel tube is 300 mm OD by...Ch. 5 - Prob. 62PCh. 5 - The figure shows a shaft mounted in bearings at A...Ch. 5 - By modern standards, the shaft design of Prob. 563...Ch. 5 - Build upon the results of Prob. 340, p. 146, to...Ch. 5 - For the clevis pin of Prob. 340, p. 146, redesign...Ch. 5 - A split-ring clamp-type shaft collar is shown in...Ch. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Two steel tubes have the specifications: Inner...Ch. 5 - Repeal Prob. 5-71 for maximum shrink-fit...Ch. 5 - Prob. 73PCh. 5 - Two steel lubes are shrink-filled together where...Ch. 5 - Prob. 75PCh. 5 - Prob. 76PCh. 5 - Prob. 77PCh. 5 - Prob. 78PCh. 5 - Prob. 79PCh. 5 - Prob. 80PCh. 5 - Prob. 81PCh. 5 - For Eqs. (5-36) show that the principal stresses...Ch. 5 - Prob. 83PCh. 5 - A plate 100 mm wide, 200 mm long, and 12 mm thick...Ch. 5 - A cylinder subjected to internal pressure pi has...
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- A helical cast steel gear with 30° helix angle has to transmit 35 kW at 2000 r.p.m. If the gear has 25 teeth, find the necessary module, pitch diameters and face width for 20° full depth involute teeth. The static stress for cast steel may be taken as 100 MPa. The face width may be taken as 3 times the normal pitch. The tooth form factor is given by the expression y'=0.154– 0.912/T; , where Tg represents the equivalent num- ber of teeth. The velocity factor is given by C, where 6 + v v is the peripheral speed of the gear in m/s.arrow_forwardFigure below shows a rotating shaft simply supported in ball bearings at A and D and loaded by a nonrotating orce Fof 6.8 kN. Using ASTM "minimum" strengths, estimate the life of the part. 6T td7 (a) Shaft drawing showing all dimensions in millimeters; all fillets 3-mm radius. The shaft rotates and the load is stationary; material is machined from AISI 1050 cold-drawn steel. (b) Bending moment diagram.arrow_forward1.Please design a pair of spur gears in the milling machine. It is known that power input is 7.5kW, Ni 1450r /min, and the %3D transmission ratio is required to be u = 2.08. F1. If there is slight impact, the supplementary conditions for trial design of this pair of gears: primary selection k = 1.8, number of smaller gear teeth Z1 = 26. The allowable stress and factors for material %3D is: [0]= 600 MPa, [o„]z= 599 MPa, [0,]ı= 220 MPa, [0,]= 213 MPa. E=1.693, Z, =1898/mpa Z„ = 2.5 K =1.25 Ky =1.1 K K =1.2 На K =1.35 Y =2.65, Y = 2.28 Y =1.58 Y =1.76 %3D Fa2 Fal sa1arrow_forward
- A rotating shaft of 40×4 mm AISI 1018 cold-drawn steel tubing has a 6 mm diameter hole drilled transversely through it. Estimate the factor of safety guarding against fatigue and static failures using the Gerber and Langer failure criteria for the following loading conditions: a. The shaft is subjected to a completely reversed torque of 120 N.m in phase with a completely reversed bending moment of 150 N.m. b. The shaft is subjected to a pulsating torque fluctuating from 20 to 160 N.m and as steady bending moment of 150 N.m.arrow_forwardA motor is used to drive a gear assembly at 200 rpm. The main gear is in the center of a 1 m long (0.5 m to the left and right of the gear) 50 mm diameter solid circular shaft, and power is taken from the two shaft ends. 25 kW is taken on the left end and an unknown amount of power is taken at the right end. the torque to the left side of the gear is? maximum shear stress to left of gear? If the maximum shear stress on the shaft to the right of the gear is 125 MPa, approximately how much power is being drawn off from the right side of the shaft? The shaft can be made from 6061-T6 aluminum. It has adequate strength to withstand the loading conditions in the scenario, including the loading on the right side of the shaft. true or false?arrow_forwardUse the general shaft layout given and determine critical diameters of the shaft based on infinite fatigue life with a design factor of 1.5. Check for yielding. Check the slopes at the bearings for satisfaction of the recommended limits in Table 7-2. Assume that the deflections for the pulleys are not likely to be critical. 500 lbf 75 lbf 8-in dia. Bearing at O 500 lb d 10.0" 75 lb Material 1040 Q and T 18 in Use the following shaft layout assuming a pulley transmits torque through a key and keyseat at location A to another pulley at location B. Assume the tensions in the belt at pulley B are T₁ and T2, where T₁ is 15% of T2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 10-in dia. 12 in T₂ T₁ The mean torque is 0 lb-in. The alternating torque is 2125 lb-in. The mean moment is 0 lb-in. The alternating moment is 5000 lb-in. 18.0" pulley diameter = 8.0" Sut 113 kpsi 10.0 B T2 T1 pulley diameter = 10.0" Sy 86 kpsi 12.0"…arrow_forward
- Torque in = 40nm Holding torque out = 896nm 8.Using your answers from the gear box above, and given that the input shaft has a diameter of 12 mm and the output shaft has a diameter of 15 mm, both shafts are made from aluminium. When this transmission system was operated, it failed. Identify the position where the failure occurred and the reason for this failure. Suggests improvements to the system to overcome the failure mode. The shear strength of aluminium is 207 MPa.arrow_forwardProduced from xCy steel material by machining method, the shaft is bedded at C and D points. With the shaft, constant Fy= 820 N forces in the vertical direction and constant Fx= 4,2 kN forces in the axial direction, which do not rotate together. The tensile strength of the shaft material is (sigma)tensile = (sigma)ut = 620 MPa and the yield strength is (sigma)yield = 420 MPa. For 50% reliability, analyze the fatigue damage condition of the shaft sections A and B separately.arrow_forwardUse the general shaft layout given and determine critical diameters of the shaft based on infinite fatigue life with a design factor of 1.5. Check for yielding. Check the slopes at the bearings for satisfaction of the recommended limits in Table 7-2. Assume that the deflections for the pulleys are not likely to be critical. 10 in 500 lbf 75 lbf 8-in dia. Bearing at O 10.0" 500 lb d 75 lb Material 1040 Q and T 18 in Use the following shaft layout assuming a pulley transmits torque through a key and keyseat at location A to another pulley at location B. Assume the tensions in the belt at pulley Bare T₁ and T2, where T₁ is 15% of T2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 10-in dia. 12 in T₂ 8.0⁰ T₁ 18.0" 10.0" I B pulley diameter = 8.0" Sut 113 kpsi T2 T1 pulley diameter = 10.0" Sy 86 kpsi 12.0" Bearing at C Using the DE-Goodman criteria and a design factor of 1.5, calculate the diameter based on the shaft's loadings…arrow_forward
- Q1 The rotating solid steel shaft is simply supported by bearings A and B, the gear has 500-mm pitch diameter. The shaft transmits a torque, T. The shaft is machined from steel AISI 1040 CD. Using a factor of safety of 2.5, determine a- The torque T b- Reactions RA and Rc c- Draw th Bending Diagram d- Maximum bending moment e- the minimum allowable diameter of the shaft using DE_Goodman theory. Assume sharp fillet radii at the bearing shoulders. 450 mm B A 500-mm dia. Fy = 8000 N 550 mm 00 C Dearrow_forwardQ1 The rotating solid steel shaft is simply supported by bearings A and B, the gear has 500-mm pitch diameter. The shaft transmits a torque, T. The shaft is machined from steel AISI 1040 CD. Using a factor of safety of 2.5, determine a- The torque T b- Reactions RA and Rc c- Draw th Bending Diagram d- Maximum bending moment e- the minimum allowable diameter of the shaft using DE_Goodman theory. Assume sharp fillet radii at the bearing shoulders. 450 mm B 550 mm C 500-mm dia. Fy = 8000 Narrow_forwardTwo designs for a shaft are being considered. Both have an outside diameter of 60 m and are 800 mm long. One is solid but the other is hollow with an internal diameter of 40 mm. Both are made from steel (G=70 GPa). Compare the torsional shear stress, angle of twist of the two designs if they are subjected to a torque of T N. m. Use the last THREE digit of your ID Number for the missing Torque (T). 575arrow_forward
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