Explanation Given information: The outer diameter of shaft is 50 mm . The transmitted power, P is 10 kW . The allowable shear stress ( τ all ) is 60 MPa . The motor speed ( N ) is 240 rpm . Calculation: Sketch the circular section as shown in Figure 1. Convert the unit of power in kW to Watts . P = 10 kW ( 10 3 W 1 kW ) = 10 , 000 W Find the frequency ( f ) using the relation: f = N 60 (1) Here, N is the number of revolutions. Substitute 240 rpm for N in Equation (1). f = 240 rpm 60 = 4 Hz Find the value of torque ( T ) for shaft ABC as follows: T = P 2 π f (2) Here, P is the power and f is the frequency. Substitute 10 , 000 W for P and 4 Hz for f in Equation (2). T = 10 , 000 2 π × 4 = 10 , 000 25.1327 = 397.887 N ⋅ m Gear A : Find the force using equilibrium equation as follows: F r A − T = 0 F = T r A (3) Here T is the torque and r A radius at point A . Substitute 397.887 N ⋅ m for T and 90 mm for r A in Equation (3). F = 397.887 90 mm ( 1 m 10 3 mm ) = 397.887 0.09 = 4 , 420.96 ≃ 4 , 421 N Calculate the bending moment at B as follows: Refer to Figure P8.25 in the textbook. M B = L A B × F (4) Here, F is the force and L A B is the length of AB . Substitute 100 mm for L A B and 4 , 421 N for F in Equation (4). M B = 100 mm ( m 10 3 mm ) × 4 , 421 = 0.1 × 4 , 421 = 442.1 N ⋅ m Find the value of outer radius ( c o ) as follows: c o = d o 2 (5) Here, d o is outer diameter. Substitute 50 mm for d o in Equation (5). c o = 50 2 = 25 mm Find the value of c using the relation: τ all = c o J M 2 + T 2 J c o = M 2 + T 2 τ all Substitute π 2 ( c o 4 − c i 4 ) c o for J c o

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves…

Videos

Question

Chapter 8.2, Problem 28P

To determine

The largest permissible inner diameter of the shaft.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 27P

Chapter 8.2, Problem 29P

Students have asked these similar questions

The design specifications for the gear-and-shaft system shown require that the same diameter be used for both shafts and that the angle through which pulley A will rotate when subjected to a 2-kip·in. torque TA while pulley D is held fixed will not exceed 7.5°. Determine the required diameter of the shafts if both shafts are made of a steel with G= 11.2 × 106 psi and τall= 12 ksi.assuming that both shafts are made of a brass with G= 5.6 × 106 psi and τall= 8 ksi.

The electric motor below, exerts a torque of 800 N.m on the steel shaft ABCD when it rotates at constant speed. Design specifications require that the shaft diameter be uniform from A to D and that the angle of twist between A and D not exceed 1.5°. Knowing that tmax < 60 MPa e G = 77.2 GPa, determine the minimum shaft diameter that can be used. 300 N-m 500 N-m B D 0.4 m 0.6 m 0.3 m

Three shafts and four gears are used to form a gear train that will transmit 6.7 kW from the motor at A to a machine tool at F. (Bearings for the shafts are omitted in the sketch.) Knowing that the frequency of the motor is 30 Hz and that the allowable stress for each shaft is 60 MPa, determine the required diameter of each shaft. The required diameter of shaft AB is mm. The required diameter of shaft CD is mm. The required diameter of shaft EF is mm.

Chapter 8 Solutions

EBK MECHANICS OF MATERIALS

Ch. 8.2 - A W10 = 39 rolled-steel beam supports a load P as...Ch. 8.2 - Solve Prob. 8.1, assuming that P = 22.5 kips and a...Ch. 8.2 - An overhanging W920 449 rolled-steel beam...Ch. 8.2 - Solve Prob. 8.3, assuming that P = 850 kN and a =...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The largest permissible inner diameter of the shaft.

Solution Summary: The author calculates the unit of power in kW and the motor speed (N) using the relation.

Concept explainers

Videos

The largest permissible inner diameter of the shaft.

Want to see the full answer?

Chapter 8 Solutions