Muutke küpsiste eelistusi

E-raamat: Finite Element Modeling of Elastohydrodynamic Lubrication Problems [Wiley Online]

  • Formaat: 464 pages
  • Ilmumisaeg: 27-Apr-2018
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119225132
  • ISBN-13: 9781119225133
Teised raamatud teemal:
  • Wiley Online
  • Hind: 169,17 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Finite Element Modeling of Elastohydrodynamic Lubrication ProblemsSuurem pilt
  • Formaat: 464 pages
  • Ilmumisaeg: 27-Apr-2018
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119225132
  • ISBN-13: 9781119225133
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119225133

Covers the latest developments in modeling elastohydrodynamic lubrication (EHL) problems using the finite element method (FEM)

This comprehensive guide introduces readers to a powerful technology being used today in the modeling of elastohydrodynamic lubrication (EHL) problems. It provides a general framework based on the finite element method (FEM) for dealing with multi-physical problems of complex nature (such as the EHL problem) and is accompanied by a website hosting a user-friendly FEM software for the treatment of EHL problems, based on the methodology described in the book. Finite Element Modeling of Elastohydrodynamic Lubrication Problems begins with an introduction to both the EHL and FEM fields. It then covers Standard FEM modeling of EHL problems, before going over more advanced techniques that employ model order reduction to allow significant savings in computational overhead. Finally, the book looks at applications that show how the developed modeling framework could be used to accurately predict the performance of EHL contacts in terms of lubricant film thickness, pressure build-up and friction coefficients under different configurations.

Finite Element Modeling of Elastohydrodynamic Lubrication Problems offers in-depth chapter coverage of Elastohydrodynamic Lubrication and its FEM Modeling, under Isothermal Newtonian and Generalized-Newtonian conditions with the inclusion of Thermal Effects; Standard FEM Modeling; Advanced FEM Modeling, including Model Order Reduction techniques; and Applications, including Pressure, Film Thickness and Friction Predictions, and Coated EHL.

This book:

  • Comprehensively covers the latest technology in modeling EHL problems
  • Focuses on the FEM modeling of EHL problems
  • Incorporates advanced techniques based on model order reduction
  • Covers applications of the method to complex EHL problems
  • Accompanied by a website hosting a user-friendly FEM-based EHL software

Finite Element Modeling of Elastohydrodynamic Lubrication Problems is an ideal book for researchers and graduate students in the field of Tribology.

Preface xiii
Nomenclature xvii
About the Companion Website xxv
Part I Introduction
1(124)
1 Elastohydrodynamic Lubrication (EHL)
3(56)
1.1 EHL Regime
3(4)
1.2 Governing Equations in Dimensional Form
7(21)
1.2.1 Generalized Reynolds Equation
9(6)
1.2.2 Film Thickness Equation
15(3)
1.2.3 Linear Elasticity Equations
18(6)
1.2.4 Load Balance Equation
24(1)
1.2.5 Energy Equations
24(4)
1.2.6 Shear Stress Equations
28(1)
1.3 Governing Equations in Dimensionless Form
28(8)
1.3.1 Dimensionless Parameters
29(2)
1.3.2 Generalized Reynolds Equation
31(1)
1.3.3 Film Thickness Equation
32(1)
1.3.4 Linear Elasticity Equations
33(1)
1.3.5 Load Balance Equation
34(1)
1.3.6 Energy Equations
34(2)
1.3.7 Shear Stress Equations
36(1)
1.4 Lubricant Constitutive Behavior
36(8)
1.4.1 Pressure and Temperature Dependence
37(1)
1.4.1.1 Density
37(2)
1.4.1.2 Viscosity
39(2)
1.4.1.3 Thermal Conductivity and Heat Capacity
41(1)
1.4.2 Shear Dependence of Viscosity
41(2)
1.4.3 Limiting Shear Stress (LSS)
43(1)
1.5 Dimensionless Groups
44(2)
1.6 Review of EHL Numerical Modeling Techniques
46(6)
1.7 Conclusion
52(7)
References
52(7)
2 Finite Element Method (FEM)
59(66)
2.1 FEM: The Basic Idea
59(2)
2.2 Model Partial Differential Equation (PDE)
61(2)
2.3 Steady-State Linear FEM Analysis
63(36)
2.3.1 Elementary Integral Formulations
64(1)
2.3.1.1 Weighted-Residual Form
64(1)
2.3.1.2 Weak Form
65(1)
2.3.2 Solution Approximation
66(1)
2.3.2.1 Meshing and Discretization
67(2)
2.3.2.2 Lagrange Linear Elements
69(4)
2.3.2.3 Lagrange Quadratic Elements
73(2)
2.3.3 Galerkin Formulation
75(3)
2.3.4 Integral Evaluations: Mapping between Reference and Actual Elements
78(7)
2.3.5 Connectivity of Elements
85(1)
2.3.6 Assembly Process and Treatment of Boundary Conditions
86(4)
2.3.7 Resolution Process
90(1)
2.3.8 Post-Processing of the Solution
91(1)
2.3.9 One-Dimensional Example
92(7)
2.4 Steady-State Nonlinear FEM Analysis
99(10)
2.4.1 Newton Methods for Nonlinear Systems of Equations
99(1)
2.4.1.1 Newton Method
100(2)
2.4.1.2 Damped-Newton Method
102(3)
2.4.2 Nonlinear FEM Formulation
105(4)
2.5 Transient FEM Analysis
109(3)
2.5.1 Space-Time Discretization
110(1)
2.5.2 Time-Dependent FEM Formulation
111(1)
2.6 Multi-Physical FEM Analysis
112(6)
2.6.1 Multi-Physical FEM Formulation
113(2)
2.6.2 Assembly Process
115(1)
2.6.3 Coupling Strategies
116(1)
2.6.3.1 Weak Coupling
217(1)
2.6.3.2 Full/Strong Coupling
117(1)
2.7 Stabilized FEM Formulations
118(5)
2.7.1 Isotropic Diffusion (ID)
120(1)
2.7.2 Streamline Upwind Petrov--Galerkin (SUPG)
121(1)
2.7.3 Galerkin Least Squares (GLS)
121(2)
2.8 Conclusion
123(2)
References
123(2)
Part II Finite Element Modeling Techniques
125(214)
3 Steady-State Isothermal Newtonian Line Contacts
127(38)
3.1 Contact Configuration
127(1)
3.2 Geometry, Computational Domains, and Meshing
128(4)
3.2.1 Geometry
128(1)
3.2.2 Computational Domains
128(2)
3.2.3 Meshing and Discretization
130(2)
3.3 Governing Equations and Boundary Conditions
132(6)
3.3.1 Reynolds Equation
133(3)
3.3.2 Linear Elasticity Equations
136(2)
3.3.3 Load Balance Equation
138(1)
3.4 FEM Model
138(12)
3.4.1 Connectivity of Elements
139(1)
3.4.2 Weak Form Formulation
139(2)
3.4.3 Elementary Matrix Formulations
141(1)
3.4.3.1 Elastic Part
142(2)
3.4.3.2 Hydrodynamic Part
144(1)
3.4.3.3 Load Balance Part
145(1)
3.4.4 Stabilized Formulations
146(4)
3.5 Overall Solution Procedure
150(3)
3.6 Model Calibration and Preliminary Results
153(8)
3.6.1 Mesh Sensitivity Analysis
153(1)
3.6.2 Penalty Term Tuning
153(3)
3.6.3 Solid Domain Size Calibration
156(1)
3.6.4 Preliminary Results
157(4)
3.7 Conclusion
161(4)
References
161(4)
4 Steady-State Isothermal Newtonian Point Contacts
165(34)
4.1 Contact Configuration
165(1)
4.2 Geometry, Computational Domains, and Meshing
166(4)
4.2.1 Geometry
166(1)
4.2.2 Computational Domains
166(3)
4.2.3 Meshing and Discretization
169(1)
4.3 Governing Equations and Boundary Conditions
170(105)
4.3.1 Reynolds Equation
171(2)
4.3.2 Linear Elasticity Equations
173(1)
4.3.3 Load Balance Equation
174(1)
4.4 FEM Model
175(1)
4.4.1 Connectivity of Elements
175(1)
4.4.2 Weak Form Formulation
176(1)
4.4.3 Elementary Matrix Formulations
177(1)
4.4.3.1 Elastic Part
178(2)
4.4.3.2 Hydrodynamic Part
180(2)
4.4.3.3 Load Balance Part
182(1)
4.4.4 Stabilized Formulations
183(4)
4.5 Overall Solution Procedure
187(3)
4.6 Model Calibration and Preliminary Results
190(6)
4.6.1 Mesh Sensitivity Analysis
190(1)
4.6.2 Penalty Term Tuning
191(1)
4.6.3 Preliminary Results
192(4)
4.7 Conclusion
196(3)
References
196(3)
5 Steady-State Thermal Non-Newtonian Line Contacts
199(44)
5.1 Contact Configuration
199(1)
5.2 Geometry, Computational Domains, and Meshing
200(3)
5.2.1 Geometry
200(1)
5.2.2 Computational Domains
200(1)
5.2.3 Meshing and Discretization
201(2)
5.3 Governing Equations and Boundary Conditions
203(5)
5.3.1 Generalized Reynolds Equation
204(1)
5.3.2 Linear Elasticity Equations
205(1)
5.3.3 Load Balance Equation
205(1)
5.3.4 Energy Equations
205(2)
5.3.5 Shear Stress Equation
207(1)
5.4 FEM Model
208(19)
5.4.1 Connectivity of Elements
208(2)
5.4.2 Weak Form Formulation
210(3)
5.4.3 Elementary Matrix Formulations
213(2)
5.4.3.1 Elastic Part
215(1)
5.4.3.2 Hydrodynamic Part
215(3)
5.4.3.3 Load Balance Part
218(1)
5.4.3.4 Thermal Part
219(5)
5.4.3.5 Shear Stress Part
224(1)
5.4.4 Stabilized Formulations
225(2)
5.5 Overall Solution Procedure
227(1)
5.6 Model Calibration and Preliminary Results
228(12)
5.6.1 Mesh Sensitivity Analysis
230(1)
5.6.2 Full versus Weak Coupling
230(9)
5.6.3 Preliminary Results
239(1)
5.7 Conclusion
240(3)
References
241(2)
6 Steady-State Thermal Non-Newtonian Point Contacts
243(38)
6.1 Contact Configuration
243(1)
6.2 Geometry, Computational Domains, and Meshing
244(3)
6.2.1 Geometry
244(1)
6.2.2 Computational Domains
244(1)
6.2.3 Meshing and Discretization
245(2)
6.3 Governing Equations and Boundary Conditions
247(5)
6.3.1 Generalized Reynolds Equation
248(1)
6.3.2 Linear Elasticity Equations
249(1)
6.3.3 Load Balance Equation
249(1)
6.3.4 Energy Equations
249(3)
6.3.5 Shear Stress Equations
252(1)
6.4 FEM Model
252(22)
6.4.1 Connectivity of Elements
253(2)
6.4.2 Weak Form Formulation
255(3)
6.4.3 Elementary Matrix Formulations
258(2)
6.4.3.1 Elastic Part
260(1)
6.4.3.2 Hydrodynamic Part
261(3)
6.4.3.3 Load Balance Part
264(1)
6.4.3.4 Thermal Part
264(6)
6.4.3.5 Shear Stress Part
270(3)
6.4.4 Stabilized Formulations
273(1)
6.5 Overall Solution Procedure
274(1)
6.6 Model Calibration and Preliminary Results
275(5)
6.6.1 Mesh Sensitivity Analysis
276(1)
6.6.2 Preliminary Results
276(4)
6.7 Conclusion
280(1)
References
280(1)
7 Transient Effects
281(1)
7.1 Contact Configuration
281(1)
7.2 Geometry, Computational Domains, and Meshing
281(1)
73 Governing Equations, Boundary, and Initial Conditions
282(15)
7.3.1 Reynolds Equation
282(2)
7.3.2 Linear Elasticity Equations
284(1)
7.3.3 Load Balance Equation
284(1)
7.4 FEM Model
284(5)
7.4.1 Connectivity of Elements
285(1)
7.4.2 Weak Form Formulation
285(1)
7.4.3 Elementary Matrix Formulations
286(2)
7.4.3.1 Elastic Part
288(1)
7.4.3.2 Hydrodynamic Part
288(1)
7.4.3.3 Load Balance Part
289(1)
7.5 Overall Solution Procedure
289(2)
7.6 Preliminary Results
291(4)
7.7 Conclusion
295(2)
References
295(2)
8 Model Order Reduction (MOR) Techniques
297(42)
8.1 Introduction
297(2)
8.2 Reduced Solution Space Techniques
299(14)
8.2.1 Modal Reduction
302(1)
8.2.2 Ritz-Vector-Like Method
303(1)
8.2.3 EHL-Basis Technique
304(2)
8.2.3.1 Typical Test Case Results
306(4)
8.2.3.2 Performance Analysis: Reduced versus Full Model
310(3)
8.3 Static Condensation with Splitting (SCS)
313(22)
8.3.1 Static Condensation
315(1)
8.3.2 Splitting
316(1)
8.3.3 Overall Numerical Procedure
316(4)
8.3.4 Results and Discussion
320(1)
8.3.4.1 Typical Test Cases
320(1)
8.3.4.2 Splitting Algorithm Tuning
321(6)
8.3.4.3 Preservation of Solution Scheme Generality
327(2)
8.3.4.4 Performance Analysis
329(6)
8.4 Conclusion
335(4)
References
337(2)
Part III Applications
339(66)
9 Pressure and Film Thickness Predictions
341(20)
9.1 Introduction
341(1)
9.2 Qualitative Parametric Analysis
341(7)
9.2.1 Isothermal Newtonian Conditions
342(3)
9.2.2 Thermal Non-Newtonian Conditions
345(3)
9.3 Quantitative Predictions
348(3)
9.4 Analytical Film Thickness Predictions
351(6)
9.4.1 Numerical Experiments
352(1)
9.4.2 Correction Factors and Film Thickness Formulas
353(2)
9.4.3 Experimental Validation
355(2)
9.5 Conclusion
357(4)
References
359(2)
10 Friction Predictions
361(22)
10.1 Introduction
361(2)
10.2 Quantitative Predictions
363(6)
10.3 Friction Regimes
369(11)
10.3.1 Relevant Dimensionless Numbers
370(1)
10.3.1.1 Weissenberg Number
370(1)
10.3.1.2 Nahme--Griffith Number
370(1)
10.3.1.3 Limiting Shear Stress Number
370(1)
10.3.1.4 Roller Compliance Number
370(1)
10.3.2 Delineation of Friction Regimes
371(4)
10.3.2.1 Linear Regime
375(1)
10.3.2.2 Nonlinear Viscous Regime
376(1)
10.3.2.3 Plateau Regime
377(1)
10.3.2.4 Thermoviscous Regime
378(1)
10.3.3 Friction Regimes Chart
378(2)
10.4 Conclusion
380(3)
References
381(2)
11 Coated EHL Contacts
383(22)
11.1 Introduction
383(2)
11.2 Modeling Subtleties
385(3)
11.3 Influence of Coating Properties on EHL Contact Performance
388(14)
11.3.1 Pressure and Film Thickness
389(2)
11.3.2 Friction
391(3)
11.3.3 Discussion
394(1)
11.3.3.1 Influence of Coating Mechanical Properties
394(2)
11.3.3.2 Influence of Coating Thermal Properties
396(6)
11.4 Conclusion
402(3)
References
403(2)
Appendices
405(24)
A Numerical Integration
407(10)
A.1 Line Elements
412(1)
A.2 Triangular Elements
412(1)
A.3 Rectangular Elements
413(1)
A.4 Tetrahedral Elements
414(1)
A.5 Prism Elements
415(2)
B Sparse Matrix Storage
417(6)
B.1 Triplet Storage (TS)
418(1)
B.2 Compressed Row Storage (CRS)
419(1)
B.3 Compressed Column Storage (CCS)
419(4)
C Shell T9 Lubricant Properties
423(6)
C.1 Pressure and Temperature Dependence of Density
423(1)
C.2 Pressure and Temperature Dependence of Viscosity
424(1)
C.3 Shear Dependence of Viscosity
425(1)
C.4 Pressure Dependence of Limiting Shear Stress
426(1)
C.5 Pressure and Temperature Dependence of Thermal Properties
427(2)
References 429(2)
Index 431
WASSIM HABCHI, PHD, is an Associate Professor of Mechanical Engineering in the Department of Industrial and Mechanical Engineering at the Lebanese American University, Lebanon. His main area of expertise is in the finite element modeling of elastohydrodynamic lubrication problems. He is a leading authority in this field, and has published in numerous tribology journals.
Püsilink: https://www.kriso.ee/db/9781119225133_pe.html
Märksõnad: