Page 82 - Analysis and Design of Machine Elements

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radial distance between centroid
r Analysis and Design of Machine Elements helix angle, ∘
i
and ith bolt centre, mm lead angle, ∘
S safety factor deflection, mm
S p safety factor for crushing tensile stress, MPa
T torque, N mm ca calculated tensile stress, MPa
T 1 frictional torque in the thread, p bearing stress, MPa
Nmm yield strength, MPa
s
T 2 frictional torque at bearing surface, [ ] allowable tensile stress, MPa
Nmm [ ] allowable bearing stress, MPa
p
W effective section modulus, mm 3 shear stress, MPa
z number of bolts in a joint group [ ] allowable shear stress, MPa
thread angle, ∘ equivalent frictional angle, ∘
v

3.1 Introduction

3.1.1 Applications, Characteristics and Structures
Machine joints are used to connect two or more components together. They form
indispensable parts in machine constructions, as they facilitate manufacturing and
assembly, accommodate shipping and handling, permit disassembly for repair, replace-
ment and maintenance. Virtually all machines comprise an assemblage of individual
parts, separately manufactured and joined together by various fastening methods [1].

For example, a jumbo jet such as Boeing’s 747 uses about 2.5 million fasteners [2].
Machine joints can be broadly classified as detachable and permanent joints. Detach-
able joints can be disassembled without damaging any element in the connection. Con-
nections using threaded fasteners, keys and splines are typical examples of detachable
joints. Permanent joints refer to connections like riveting, welding, bonding (brazing,
soldering, adhesive bonding) and so on that cannot be disassembled without damaging
elements of the joint.
As joints and connections cause geometrical and material discontinuities, high local
stresses and potential failures, the number of joints should be reduced [1–4]. As a mat-
ter of fact, joints remain the weakest link in a machine and their high safety concern
presents an incessant challenge to designers and engineers. It is therefore necessary to
have a thorough understanding of performance and careful analysis of joints under all
conditions of service, especially in cars, aeroplanes, steam and gas turbines and so on
where mechanical reliability and human safety are vital.
This chapter will discuss in detail the analysis and design of conventional standard
threaded fasteners. The detachable fastening methods for shaft and hub, as well as per-
manent connection methods will be introduced in the following chapters.

3.1.2 Selection of Fastening Methods
The selection of fastening methods depends upon many factors. The first is whether
the joint is to be permanent or detachable. The selection of permanent joints is
mainly due to the consideration of manufacturing and assembly costs; while the
selection of detachable joints considers far more factors, including structure, assembly,