This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: * General Basis and Bra-Ket Notation * Tensor Analysis * Elementary Differential Geometry * Differential Forms * Applications of Tensors and Differential Geometry * Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

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.

This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: * General Basis and Bra-Ket Notation * Tensor Analysis * Elementary Differential Geometry * Differential Forms * Applications of Tensors and Differential Geometry * Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

Aero and Vibroacoustics of Automotive Turbochargers is a topic involving aspects from the working fields of thermodynamics of turbomachinery, aerodynamics, rotordynamics, and noise propagation computation. In this broadly interdisciplinary subject, thermodynamics of turbomachinery is used to design the turbocharger and to determine its operating conditions. Aerodynamics is needed to study the compressor flow dynamics and flow instabilities of rotating stall and surge, which can produce growling and whining-type noises. Rotordynamics is necessary to study rotor unbalance and self-excited oil-whirl instabilities, which lead to whistling and constant tone-type noises in rotating floating oil-film type bearings. For the special case of turbochargers using ball bearings, some high-order harmonic and wear noises also manifest in the rotor operating range. Lastly, noise propagation computation, based on Lighthill's analogy, is required to investigate airborne noises produced by turbochargers in passenger vehicles. The content of this book is intended for advanced undergraduates, graduates in mechanical engineering, research scientists and practicing engineers who want to better understand the interactions between these working fields and the resulting impact on the interesting topic of Aero and Vibroacoustics of Automotive Turbochargers.

Rotordynamics of automotive turbochargers is dealt with in this book encompassing the widely working field of small turbomachines under real operating conditions at the very high rotor speeds up to 300000 rpm. The broadly interdisciplinary field of turbocharger rotordynamics involves 1) Thermodynamics and Turbo-Matching of Turbochargers 2) Dynamics of Turbomachinery 3) Stability Analysis of Linear Rotordynamics with the Eigenvalue Theory 4) Stability Analysis of Nonlinear Rotordynamics with the Bifurcation Theory 5) Bearing Dynamics of the Oil Film using the Two-Phase Reynolds Equation 6) Computation of Nonlinear Responses of a Turbocharger Rotor 7) Aero and Vibroacoustics of Turbochargers 8) Shop and Trim Balancing at Two Planes of the Rotor 9) Tribology of the Bearing Surface Roughness 10) Design of Turbocharger Platforms using the Similarity Laws The rotor response of an automotive turbocharger at high rotor speeds is studied analytically, computationally, and experimentally. Due to the nonlinear characteristics of the oil-film bearings, some nonlinear responses of the rotor besides the harmonic response 1X, such as oil whirl, oil whip, and modulated frequencies occur in Waterfall diagram. Additionally, the influences of the surface roughness and oil characteristics on the rotor behavior, friction, and wear are discussed. This book is written by an industrial R&D expert with many years of experience in the automotive and turbocharger industries. The all-in-one book of turbochargers is intended for scientific and engineering researchers, practitioners working in the rotordynamics field of automotive turbochargers, and graduate students in applied physics and mechanical engineering.

This book deals with rotordynamics of automotive turbochargers while encompassing the analysis of the dynamics of rotating machines at very high rotor speeds of 300,000 rpm and above. This interdisciplinary field involves 1. thermodynamics and turbo-matching knowledge to compute working conditions of turbochargers, 2. fluid and bearing dynamics to calculate various operating thrust loads and to design the rotating floating ring bearings (two-oil-film bearings), and 3. tribology to improve the rotor stability and to reduce the bearing friction. Mathematical background in modeling and simulation methods is necessary; however, the prerequisites have been kept to a minimum. The book addresses both practitioners working in the field of rotordynamics of automotive turbochargers and graduate students in mechanical engineering.

Aero and Vibroacoustics of Automotive Turbochargers is a topic involving aspects from the working fields of thermodynamics of turbomachinery, aerodynamics, rotordynamics, and noise propagation computation. In this broadly interdisciplinary subject, thermodynamics of turbomachinery is used to design the turbocharger and to determine its operating conditions. Aerodynamics is needed to study the compressor flow dynamics and flow instabilities of rotating stall and surge, which can produce growling and whining-type noises. Rotordynamics is necessary to study rotor unbalance and self-excited oil-whirl instabilities, which lead to whistling and constant tone-type noises in rotating floating oil-film type bearings. For the special case of turbochargers using ball bearings, some high-order harmonic and wear noises also manifest in the rotor operating range. Lastly, noise propagation computation, based on Lighthill's analogy, is required to investigate airborne noises produced by turbochargers in passenger vehicles. The content of this book is intended for advanced undergraduates, graduates in mechanical engineering, research scientists and practicing engineers who want to better understand the interactions between these working fields and the resulting impact on the interesting topic of Aero and Vibroacoustics of Automotive Turbochargers.

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.

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.