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About this book

This monograph presents computational models that describe electro-mechanical characteristics of tapered and cylinder roller bearings in various industrial applications. Applying the Levenberg-Marquardt’s algorithm to solving strongly nonlinear coupled equation systems, the computational models consisting of many circular slices per rolling element enable computations of the local Hertzian pressures at the elastohydrodynamic (EHD) contact area, the relating oil-film thickness in elastohydrodynamic lubrication (EHL), the limiting voltage of electro-pitting, bearing frictions, and fatigue lifetimes of the bearings for various load spectra. Using the best-known machine-learning method for clustering, the load spectrum is clustered in k cluster means based on the invariant damage number to accelerate the load spectrum. Furthermore, the accelerated load spectrum is used for the testing procedure of the bearings to reduce the testing time and costs as well.

The target audience of this book primarily comprises graduate students in mechanical engineering and practicing engineers of electro-machines and transmission systems who want to computationally design tapered and cylinder roller bearings for the automotive industry and other industries, and to deeply dive into these relating working fields.

Table of Contents


Chapter 1. Tapered Roller Bearings

Tapered roller bearings (TRB) are normally used under large radial, axial loads, and bending moments at moderate shaft speeds and heavy-duty operations. Many applications of these bearings are found in the automotive industry (e.g. for front and rear wheels, differentials of trucks and buses), marine and aerospace industries (e.g. boats, ships, airplanes, and space shuttles), construction and mining industries (e.g. bulk conveyors, compact track loaders, concrete mixers, continuous miners, and tunnel drills), agricultural industries (e.g. mowers, tractors, and grain carts), machine tool spindles, and wind turbines.
Hung Nguyen-Schäfer

Chapter 2. Cylinder Roller Bearings

Cylinder roller bearings (CRB) are much simpler than tapered roller bearings (TRB). They are used under large radial loads and quite small axial loads depending on the bearing type at moderate shaft speeds and heavy-duty operations.
Hung Nguyen-Schäfer

Chapter 3. Loads Acting on Gears and Bearings

This chapter deals with the calculations of loads acting on helical gears and bearings used in transmission systems for the automotive industry. The gear loads depend only on the gear geometries and the driving torque on the shaft. As a result, the loads on the bearings result from the gear loads and the setup geometries. The loads on the bearings change with the operating conditions, such as forwards and backwards driving cycles, and recuperation phase.
Hung Nguyen-Schäfer

Chapter 4. Bearing Endplay Over Operating Temperatures

In the following section, the axial endplay of two single tapered roller bearings (TRB) in the X and O setups is computed over the operating bearing temperatures.
Hung Nguyen-Schäfer

Chapter 5. Accelerated Load Spectrum

In general, the load spectrum is too large and extensive to test the lifetime of a component. To hasten the testing time and to reduce costs, the load spectrum should be accelerated so that its much shorter testing time is equivalent to the real lifetime for the load spectrum. The equivalent load spectrum is called the accelerated load spectrum .
Hung Nguyen-Schäfer

Chapter 6. Solving Nonlinear Equation Systems

This chapter deals with solving nonlinear equation systems that describe the computational models for tapered and cylinder roller bearings in Chaps. 1 and 2. In general, the computational models consisting of a large number of coupled equations are strongly nonlinear. It is not easy to get converged solutions for large strongly nonlinear coupled equation systems. Therefore, an appropriate algorithm is required to solve such nonlinear equation systems. In the following sections, the Gauss-Newton and the Levenberg-Marquardt algorithm based on least squares method are mathematically derived for solving the computational models of tapered and cylinder roller bearings.
Hung Nguyen-Schäfer


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