Page 314 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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S induced thrust load, N angular deviation, deg.
S ′ appended thrust load, N 1 angular velocity of inner ring,
S static safety factor rad s −1
0
S resolved axial load component, N angular velocity of rolling elements,
i 2
∘
t temperature, C rad s −1
X dynamic radial load factor angular velocity of outer ring,
3
X static radial load factor rad s −1
0
Y dynamic axial load factor angular velocity of retainer, rad s −1
4
Y static axial load factor
0
contact angle, deg. Subscripts
life-adjustment factor for reliability 1, 2 bearing number
1
load-life exponent m average value
11.1 Introduction
11.1.1 Applications, Characteristics and Structures
Rolling contact bearings (or rolling bearings) are standardized machine elements widely
used in various machines. They support rotating shafts while permitting relative motion
between two elements [1]. Rolling contact bearings have low starting and good operating
friction, and are ideal for applications with high starting loads, such as in vehicles, trains,
aeroplanes and mobile equipment in general [2].
Compared with sliding bearings, rolling contact bearings require minimum lubrica-
tion and less axial space. They have high efficiency and reliability, and minimum main-
tenance requirements. Besides, rolling contact bearings can be preloaded to eliminate
internal clearance, which is crucial for high precision rotation and fatigue life. As stan-
dardized products, rolling bearings are interchangeable among manufacturers. Never-
theless, high rotating speeds may lead to rapid accumulation of fatigue cycles and high
centrifugal force on rolling elements [2]. The noise level is usually high due to poor
damping capability of rolling bearings.
A typical rolling contact bearing composes of an inner ring (race), an outer ring
(race), rolling elements and a retainer. The inner ring and outer ring are called cone
and cup, respectively, for a tapered roller bearing [2]. Figure 11.1 shows the structure
of a single-row, deep-groove ball bearing. The inner ring is pressed onto a shaft with a
slight interference fit to ensure that it rotates with the shaft. The outer ring is usually
stationary and is held by the housing of machine. The inner ring and outer ring form
a narrow, dual, circular track within which rolling elements roll during operation
[2]. The presence of rolling elements allows a low friction rotation of shafts. Typical
rolling elements include spherical balls, cylindrical, tapered or spherical rollers, needles
and so on. The retainer, also called a cage or separator, is used to keep rolling elements
separated and evenly spaced around the raceway to prevent them contact with each
other during operation.
When a rolling contact bearing carries a load, the load is exerted on a small area where
rolling elements contact with the inner or outer rings. The resultant contact stresses are
usually quite high, regardless of bearing type. To withstand high stress and to resist wear,
rolling elements and races are normally made from hard, high strength steel or ceramic.
The most widely used bearing steel is high carbon chromium steels, including GCr15