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## Über dieses Buch

This book comprehensively presents the computational design of rolling bearings dealing with many interdisciplinary difficult working fields. They encompass elastohydrodynamics (EHD), Hertzian contact theory, oil-film thickness in elastohydrodynamic lubrication (EHL), bearing dynamics, tribology of surface textures, fatigue failure mechanisms, fatigue lifetimes of rolling bearings and lubricating greases, Weibull distribution, rotor balancing, and airborne noises (NVH) in the rolling bearings. Furthermore, the readers are provided with hands-on essential formulas based on the up-to-date DIN ISO norms and helpful examples for computational design of rolling bearings.

The topics are intended for undergraduate and graduate students in mechanical and material engineering, research scientists, and practicing engineers who want to understand the interactions between these working fields and to know how to design the rolling bearings for automotive industry and many other industries.

## Inhaltsverzeichnis

### Chapter 1. Fundamentals of Rolling Element Bearings

Abstract
The main purpose of this book is not to deal with the rolling element bearings in general as a normal textbook of bearings but to focus on the computational design of bearings, especially ball and roller bearings that are used in automotive industries. Only essential things about the rolling bearings are briefly handled with the motto “the shorter the better.” Therefore, some issues of technical constructions for all types of bearings are intentionally not discussed in this book. The readers can find them in other literatures, e.g., [1–3]. However, some fundamental characteristics of the rolling bearings are recapitulated and discussed. They are essential for the computational design of bearings.
Hung Nguyen-Schäfer

### Chapter 2. Design of Rolling Bearings

Abstract
To design bearings for rotating machines, such as electric machines, turbochargers, and aircraft turbojets, the following development steps should be carried out:
Hung Nguyen-Schäfer

### Chapter 3. Contact Stresses in Rolling Bearings

Abstract
The Hertzian pressure (normal stress) in the contact zone between the ball/roller and raceways causes a plastic deformation of the ball/roller contour. In the contact area, the oil-film thickness is nearly constant at the height h c and reduces to the height at h min at the outflow of the contact zone (cf. Chap. 4). The Hertzian pressure p H in the oil film at the contact zone is calculated in the following section.
Hung Nguyen-Schäfer

### Chapter 4. Oil-Film Thickness in Rolling Bearings

Abstract
There are two kinds of lubrication for the bearings, oil and grease lubrications. In fact, the base oil dissolved in grease is separated from grease due to the centrifugal force of oil at increasing oil temperatures, and it is in fact used to lubricate the rolling bearings (cf. Chap. 5). As a result, the oil-film thickness is created between the rolling elements (balls and rollers) and raceways to keep the rotating rotor in balance with the external forces acting upon it.
Hung Nguyen-Schäfer

### Chapter 5. Tribology of Rolling Bearings

Abstract
Tribology is derived from the Greek word tribos, which means rubbing. It deals with the tribological phenomena, such as lubrication, friction, and wears in the moving parts. Thus, tribology becomes more and more important in automotive industry in terms of synthetic lubricating oils, friction reduction, adhesion and abrasion friction, and wear reduction in the oil-film bearings including radial and thrust bearings.
Hung Nguyen-Schäfer

### Chapter 6. Lifetimes of Rolling Bearings

Abstract
Under high Hertzian and EHD pressures in the contact zone, the rolling elements (balls and rollers) and raceways are deformed elastically (s. Chaps. 3 and 4). As soon as the rolling elements leave the lowest position in the bearing, the surface contours of rolling elements and raceways return to the initial forms. As a result, the surface contours of the balls, rollers, and raceways take turns cyclically changing between the elastically deformed and initial forms. After a certain number of cycles, the material fatigue occurs in the bearing and leads to the bearing failure. The of the bearing is limited by the number of cycles (revolutions).
Hung Nguyen-Schäfer

### Chapter 7. Reliability Using the Weibull Distribution

Abstract
To analyze the reliability of lifetime of products, the Weibull distribution plays a key role in many industries. In the following section, the Weibull distribution is used to predict the fatigue-related lifetime of rolling bearings at any reliable probability statistically.
Hung Nguyen-Schäfer

### Chapter 8. Bearing Friction and Failure Mechanisms

Abstract
The total friction torque acting on the bearing is caused by the bearing loads, viscous friction of oil, and seals of the bearing:
$${M}_t={M}_l+{M}_v+{M}_s$$
where
Hung Nguyen-Schäfer

### Chapter 9. Rotor Balancing and NVH in Rolling Bearings

Abstract
Production process of the rotor causes a primary unbalance where the mass center of the rotor does not locate in its rotation axis. Excessively large unbalance force and moment induce large amplitudes of the rotor response that leads to the bearing wear, bearing failure, and rub contact between the rotor and stator of electric machines. Additionally, the rotor unbalance generates unbalance whistle that is synchronous with the rotor frequency (frequency order 1×). The unbalance whistle is one of the undesirable airborne noises in electric vehicles.
Hung Nguyen-Schäfer

### Backmatter

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