Page 282 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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[S] allowable safety factor [ ] allowable bending stress, MPa
−1
T torque, N mm shear stress, MPa
W section modulus, mm 3 endurance limit in shear at r =−1,
−1
W polar section modulus, mm 3 MPa
T
w weight of ith mass, N yield strength in shear, MPa
i s
y deflection, mm torsional shear stress, MPa
T
[y] allowable deflection, mm [ ] allowable shear stress, MPa
z number of segments in a stepped unit length angular deflection,
shaft ∘ m −1
correction coefficient [ ] allowable unit length angular
∘
slope, rad deflection, m −1
[ ] allowable slope, rad fundamental natural frequency,
n
normal stress, MPa rad s −1
−1 endurance limit at stress ratio of Subscripts
−1, MPa i values of ith segment in a stepped
a stress amplitude, MPa shaft
b ultimate tensile strength, MPa max maximum value
ca design stress, MPa S static state
m mean stress, MPa normal stress
s yield strength in tension, MPa shear stress

10.1 Introduction

10.1.1 Applications, Characteristics and Structures
Shafts are important elements in virtually all types of machinery. They are supported by
bearings, rotate and transmit power and thereby torque. A typical application of shafts
is input, output or intermediate shafts supporting gears in gear reducers.
Unlike standard elements, shafts are designed for specific applications individually,
considering the mounted elements, operating loads and service conditions. Power trans-
mission elements, such as gears, belt pulleys, chain sprockets, couplings and so on are
attached to the shafts by keys, splines, pins and other devices. When shafts rotate with
power transmission elements, power and rotational motion are transmitted from one
element to other rotating parts of shaft system [1–3].

10.1.2 Types of Shafts
A shaft is a long cylindrical element loaded torsionally, transversely and/or axially as a
machine operates. Consequently, shafts can be classified as transmission shafts, axles
and spindles according to the loads they carry [4]. Transmission shafts carry both bend-
ing and torsional moments, and are usually stepped, as shown in Figure 10.1a. They sup-
port gears, pulleys and so on and often transmit power. Axles carry bending moments
only. They are used to support rotating wheels, pulleys and the like. An axle can turn with
a wheel as a unit, like a railway car axle, as illustrated in Figure 10.1b, or is nonrotating,