Vullo V., Vivio F. Rotors: Stress Analysis and Design

Springer-Verlag Italia, 2013. XXVI, 339 p. 120 illus. — ISBN: 978-88-470-2561-5, ISBN: 978-88-470-2562-2 (eBook), DOI 10.1007/978-88-470-2562-2 — (Mechanical Engineering Series).Addresses analysis of stress and strain analysis in rotating disks and cylinders subjected to surface and body loads (a classic subject of machine design)
Treats not only classic subjects, but also includes advanced scientific contributions by the authors
Emphasizes a solid and early conceptual approach for design onset
Also useful as a reference in both academic and industrial courses
Stress and strain analysis of rotors subjected to surface and body loads, as well as to thermal loads deriving from temperature variation along the radius, constitutes a classic subject of machine design. Nevertheless attention is limited to rotor profiles for which governing equations are solvable in closed form. Furthermore very few actual engineering issues may relate to structures for which stress and strain analysis in the linear elastic field and, even more, under non-linear conditions (i.e. plastic or viscoelastic conditions) produces equations to be solved in closed form. Moreover, when a product is still in its design stage, an analytical formulation with closed-form solution is of course simpler and more versatile than numerical methods, and it allows to quickly define a general configuration, which may then be fine-tuned using such numerical methods.
In this view, all subjects are based on analytical-methodological approach, and some new solutions in closed form are presented. The analytical formulation of problems is always carried out considering actual engineering applications. Moreover, in order to make the use of analytical models even more friendly at the product design stage, a function is introduced whereby it is possible to define a fourfold infinity of disk profiles, solid or annular, concave or convex, converging or diverging. Such subjects, even derived from scientific authors’ contributions, are always aimed at designing rotors at the concept stage, i.e. in what precedes detailed design.Content Level » Research
Keywords » Conical Disks - Rotating Disk - Stress Rotors - Thermal Load
Related subjects » Mechanical Engineering - Mechanics.Mono-Dimensional Elastic Theory of Thin DiskEquilibrium Equations
Compatibility Equations
General Differential Equation for Rotating Disk Subjected to Thermal LoadConstant Thickness Rotating DiskGeneral Equations
Non-Rotating Annular Disk, Loaded at the Outer Radius
Non-Rotating Annular Disk, Loaded at the Inner Radius
Non-Rotating Solid Disk, Loaded at the Outer Radius
Rotating Annular Disk
Example
Rotating Solid Disk
Constant Thickness Disk Subjected to Angular Acceleration
Summary of Results for Constant Thickness Disk Loaded at the Inner and Outer Radius and Subjected to Centrifugal LoadThermal Loads and Fictitious Density Variation Along the RadiusAnnular Disk, Subjected to Thermal Load
Function T Given by an n-th Degree Function
Function T Given by an n Degree Polynomial
General Function T
Example
Solid Disk, Subjected to Thermal Load
Function T Given by an n-th Degree Function
Function T Given by an n Degree Polynomial
General Function T
Summary of Results for Constant Thickness Disk Subjected to Thermal Load
Constant Thickness Disk Subjected to Centrifugal and Thermal Loads
Stresses in Rotating Disks Having a Fictitious Density Variation Along the RadiusHyperbolic DisksAnnular Disk, Subjected to Centrifugal Load
Non-Rotating Annular Disk, Loaded at the Outer Radius
Non-Rotating Annular Disk, Loaded at the Inner Radius
Rotating Annular Disk
Example
Annular Disk, Subjected to Thermal Load
ExampleDisk of Uniform StrengthProfile Definition
Technical Solutions
Crown Ring Design
ExampleConical DiskConical Profile Geometry and General Differential Equations
Rotating Conical Disk Having Constant Density
cular Integral and Corresponding Stress and Strain State
Solution of Homogeneous Differential Equation and Corresponding Stress and Strain State
General Integral and Corresponding Stress and Strain State
Conical Disk Having Constant Density Subjected to Thermal Load
Rotating Disk Having Density Variation on Radius
Conical Disk with Density Variation Subjected to Centrifugal and Thermal Loads
Examples of Conical Disks
Rotating Solid Conical Disk with Apex Singularity and Having Constant Density
Rotating Annular Conical Disk with Apex Singularity and Having Constant Density
Rotating Solid Conical Disk with re R and Having Constant Density
Rotating Annular Conical Disk Without Singularities (ri 0 and re R) and Having Constant Density
Rotating Conical Disk with Hub and Crown Ring and H aving Constant Density
Conical Disk Without Singularities and Subjected to Temperature Gradient
Conical Disk Without Singularities and Having Density Variation on Radius
Rotating Conical Disk Without Singularities, with Density Variation on Radius and Subjected
to Temperature GradientNon-Linearly Variable Thickness DisksGeneral Differential Equations and Variable Thickness Profile Geometry
Rotating Disk Having Constant Density
Vicular Integral and Corresponding Stress and Strain State
Solution of Homogeneous Differential Equation and Corresponding Stress and Strain State
General Integral and Corresponding Stress and Strain State
Non-Linearly Variable Thickness Disks Having Constant Density and Subjected to Thermal Load
Non-Linearly Variable Thickness Disks Having Density Variation on Radius
Non-Linearly Variable Thickness Disks with Density Variation and Subjected to Thermal and Centrifugal Loads
Examples of Non-Linear Variable Thickness Disks
Rotating Solid Disk with Apex Singularity and Having Constant Density
Rotating Annular Disk with Apex Singularity and Having Constant Density
Rotating Solid Disks with re R and Having Constant Density
Rotating Annular Disks with re R and Having Constant Density
Rotating Disks with Hub and Crown Ring and Having Constant Density
Annular Disks Having Constant Density and Subjected to Temperature Gradient
Rotating Annular Disks Having Density Variation on Radius
Rotating Annular Disks Having Density Variation on Radius and Subjected to Thermal Load
Comparing Various Disk Types
Non-Linearly Variable Thickness Disks Subjected to Angular AccelerationDisk Having Arbitrary ProfileTimoshenko-Grammel’s Method
Example
Manson’s Method
ExampleDesign of Rotating Disks and Stress ConcentrationsFailure Criteria
General Considerations on the Use of Failure Criteria
Effects of Stress ConcentrationsStress Analysis of Rotating Cylinders in the Linear Elastic FieldPrinciples and General Equations
Circular Cylindrical Body with Clamped Ends or Indefinitely Extended in the Direction of its Axis Subjected to Centrifugal and Thermal Loads
Circular Cylindrical Body with Clamped Ends or Indefinitely Extended in the Direction of its
Axis Subjected to Centrifugal Load
Circular Cylindrical Body with Clamped Ends or Indefinitely Extended in the Direction of its Axis Subjected to Thermal Load
Circular Cylindrical Body of Finite Length with Free Ends Subjected to Centrifugal and Thermal Loads
Circular Cylindrical Body of Finite Length with Free Ends Subjected to Centrifugal Load
Circular Cylindrical Body of Finite Length with Free Ends Subjected to Thermal Load
Edge Effect in a Circular Cylindrical Body of Finite Length with Free Ends Subjected to Thermal Load
Solid Cylindrical Body of Finite Length and with Free Ends, Subjected to Transient Thermal Load
Stress Analysis in Rotating Disks Loaded Beyond Yielding: Non-Hardening Materials
Basic Hypotheses and Their Limitations in Disks Made of Non-Hardening Materials
Yield Criteria
Annular Disk
Elastic Limit Angular Velocity
Elastic-Plastic Analysis of Rotating Annular Disks
Residual Stresses
Example
Solid Disk
Elastic Limit Angular Velocity
Elastic-Plastic Analysis of Rotating Solid Disks
Residual Stresses
Bursting Angular SpeedStress Analysis in Rotating Disks Loaded Beyond Yielding: Hardening MaterialsGeneral
Millenson-Manson’s Method
Effect of Plastic Flow
Effect of Previous Plastic History
Effect of Creep
Analytical Method
Elastic Analysis
Solution of Homogeneous Differential Equation
Circular Integral
General Solution and Corresponding Stress and Strain State
Boundary Conditions and Integration Constants
Examples
Elastic-Plastic Analysis
Theoretical–Numerical Solution Case Studies and FEM Tests
Residual and Service Stresses
Design-Related Use of Plasticization and Limit-Design Factor
Appendices
Appendix A: Rotating Bars, Paddles and Blades
Appendix B: In-Depth Analysis of the Solution of the Hypergeometric Differential Equation
Appendix C: The Finite Element Method for Elastic-Plastic Problems