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El. knyga: Rotordynamics of Automotive Turbochargers

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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.
1 Turbocharging Concepts
1(20)
1.1 Introduction
1(4)
1.2 Applications of Turbochargers to Downsized Engines
5(9)
1.3 Regulation of Charge-Air Pressure
14(2)
1.4 Required Charge-Air Pressure of Downsized Engines
16(5)
References
20(1)
2 Thermodynamics of Turbochargers
21(16)
2.1 Thermodynamic Characteristics
21(1)
2.2 Efficiencies of Compressor and Turbine
22(2)
2.3 Turbocharger Equations
24(6)
2.4 Response Time of Turbochargers
30(3)
2.5 Turbocharger Matching
33(4)
References
36(1)
3 Vibrations of Turbochargers
37(28)
3.1 Introduction
37(2)
3.2 Vibration Modes of Turbochargers
39(2)
3.3 Vibration Characteristics of Turbochargers
41(3)
3.3.1 In Frequency Domain
41(1)
3.3.2 In Time Domain
42(2)
3.4 Linear and Nonlinear Vibrations of Turbochargers
44(2)
3.5 Measurement of the Rotor Locus
46(3)
3.5.1 Working Principle of the Eddy-Current Sensor
46(1)
3.5.2 Measurement of the Rotor Locus
47(2)
3.5.3 Studying Cases of the Rotor Orbit
49(1)
3.6 Study of Case Histories
49(16)
References
62(3)
4 Stability Analysis of Rotordynamic Behaviors
65(34)
4.1 Introduction
65(1)
4.2 Stability Analysis of Linear Rotordynamics
66(12)
4.2.1 Eigenvalues of the Free Vibration Response
66(3)
4.2.2 A Study Case of Calculating the Eigenvalues
69(5)
4.2.3 Stability Analysis with Routh--Hurwitz Criterion
74(4)
4.3 Stability Analysis of Nonlinear Rotordynamics
78(21)
4.3.1 Vibration Equations in the Autonomous Systems
78(2)
4.3.2 Stability Analysis with Bifurcation Theory
80(1)
4.3.3 Characteristics of Hopf Bifurcation Theory
80(4)
4.3.4 Classification of Hopf Bifurcation
84(1)
4.3.5 Coordinate Transformation in the Bifurcation
85(2)
4.3.6 Jacobian Matrix of the Vibration Equations
87(1)
4.3.7 A Study Case of the Subcritical Hopf Bifurcation
88(2)
4.3.8 Stability with Neimark--Sacker Torus Bifurcations
90(5)
4.3.9 Vibration Equations of the Nonautonomous Systems
95(2)
References
97(2)
5 Linear Rotordynamics of Turbochargers
99(40)
5.1 Introduction
99(2)
5.2 Vibration Response of the Linear Rotordynamic System
101(6)
5.3 Bearing Force Acting on the Flexible Rotor
107(3)
5.4 Gyroscopic Effect of the Rotor System
110(3)
5.5 Vibration Equations of Turbochargers
113(10)
5.6 Transient Response at the Run-Up
123(3)
5.7 Frequency Analysis in Campbell Diagram
126(6)
5.8 Computations of Linear Rotordynamics
132(7)
References
136(3)
6 Bearing Dynamics of Turbochargers
139(66)
6.1 Introduction
139(3)
6.2 Reynolds Lubrication Equation
142(3)
6.3 Lubrication Regimes in the Stribeck Curve
145(3)
6.4 Thrust Bearings
148(18)
6.4.1 Working Principle
148(2)
6.4.2 Calculation of the Thrust Load on the Rotor
150(5)
6.4.3 Design of Thrust Bearings
155(8)
6.4.4 Influential Parameters of Thrust Bearings
163(3)
6.5 Fluid Film Radial Bearings
166(22)
6.5.1 Theory of Fluid Film Bearings
168(6)
6.5.2 Nonlinear Bearing Forces on the Journal
174(8)
6.5.3 Floating Ring Bearings
182(5)
6.5.4 Influential Parameters of RFRB
187(1)
6.6 Rolling Element Bearings
188(17)
6.6.1 Characteristics of the Rolling Element Bearings
189(6)
6.6.2 Squeeze Film Damper with Ball Bearings
195(5)
6.6.3 Bearing Defect-Related Frequencies
200(3)
References
203(2)
7 Nonlinear Rotordynamics of Turbochargers
205(62)
7.1 Boundary Conditions of Rotordynamics
205(2)
7.2 Vibration Equations of the Rotor with RFRBs
207(5)
7.3 Synchronous and Asynchronous Vibrations
212(4)
7.4 Frequency Analysis in Waterfall Diagram
216(3)
7.5 Oil Whirl and Oil Whip in the Turbochargers
219(8)
7.5.1 Root Cause of the Oil Whirl
221(3)
7.5.2 Threshold of Instability
224(3)
7.6 Modulations of Vibrations
227(9)
7.6.1 Responses of Nonlinear Vibration Systems
228(1)
7.6.2 Modulated Sideband Frequencies
229(7)
7.7 Induced Airborne Noises in Automotive Turbochargers
236(5)
7.7.1 Classification of Noises
236(2)
7.7.2 Unbalance Whistle and Constant Tone
238(3)
7.8 Aliasing in DFT and Nyquist Frequency
241(5)
7.8.1 Discrete Fourier Transform (DFT)
241(3)
7.8.2 Aliasing in DFT
244(1)
7.8.3 Nyquist Frequency
244(2)
7.9 Computations of Nonlinear Rotordynamics
246(21)
7.9.1 Two-Phase Reynolds Lubrication Equation
247(2)
7.9.2 Results of Nonlinear Rotordynamics
249(16)
References
265(2)
8 Rotor Balancing in Turbochargers
267(24)
8.1 Reasons for Rotor Balancing
267(1)
8.2 Kinds of Rotor Balancing
268(1)
8.3 Two-Plane Low-Speed Balancing of a Rigid Rotor
268(10)
8.4 Two-Plane High-Speed Balancing of a Flexible Rotor
278(13)
8.4.1 Modal Balancing Theory
278(4)
8.4.2 Influence Coefficient Method
282(6)
8.4.3 Comparison Between Modal Balancing and ICM
288(1)
References
289(2)
9 Applied Tribology in the Oil-Film Bearings
291(40)
9.1 Introduction
291(1)
9.2 Characteristics of Lubricating Oils
291(2)
9.3 HTHS Viscosity of Lubricating Oils
293(5)
9.4 Viscosity Index of Lubricating Oils
298(2)
9.5 Stribeck Curve
300(2)
9.6 Surface Texture Parameters
302(11)
9.6.1 Surface Height Profile
303(2)
9.6.2 Surface Tribological Parameters
305(8)
9.7 Elastic and Plastic Deformations in the Bearings
313(9)
9.7.1 Normal Stress
314(1)
9.7.2 Shear Stress
315(1)
9.7.3 Friction Force in the Bearings
316(2)
9.7.4 Friction Power in the Bearings
318(2)
9.7.5 Mohr's Circle Diagram
320(2)
9.8 Wear Mechanisms in the Oil-Film Bearings
322(9)
References
330(1)
10 Design of Turbocharger Platforms
331(12)
10.1 Introduction
331(1)
10.2 Market Analyses of Combustion Engines
331(2)
10.3 Calculating Sizes of Compressor and Turbine Wheels
333(3)
10.4 Calculating Diameters of the Rotor Shaft
336(4)
10.5 Design of CHRA Geometry for the Platform
340(3)
References
341(2)
Appendix A Transformation Between the Precessing and Inertial Coordinates 343(4)
Appendix B Calculation of the Value x from the Value X in the log10 Scale 347(4)
Appendix C Solutions of the Characteristic Equation with Complex Coefficients 351(2)
Appendix D Normal Distribution Density Function and Probability Function 353(4)
Further Readings 357(2)
Index 359
Dr. Hung Nguyen-Schäfer is a senior technical manager in development of electric machines for hybrid and electric vehicles at EM-motive GmbH, a joint company of Daimler and Bosch in Germany. He received B.Sc. and M.Sc. in mechanical engineering with nonlinear vibrations in fluid mechanics from the University of Karlsruhe (KIT), Germany in 1985; and a Ph.D. degree in nonlinear thermo- and fluid dynamics from the same university in 1989. He joined Bosch Company and worked as a technical manager on many development projects. Between 2007 and 2013, he was in charge of rotordynamics, bearings, and design platforms of automotive turbochargers at Bosch Mahle Turbo Systems in Stuttgart. He is also the author of a professional engineering book Aero and Vibroacoustics of Automotive Turbochargers, Springer (2013) and coauthor of a mathematical engineering book Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, Springer (2014).
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