41514 Dynamics of Machinery
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1 41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar (Iumár) Ferreira Santos 1. Course Structure 2. Objectives 3. Theoretical and Experimental Example 4. Industrial Applications 5. Mathematical ing & Steps 6. Examples
2 This image cannot currently be displayed. Home Page 1. Course Structure Grade = (1/3) * Project I + (2/3) * Project II Project I ing & Experimental Validation via Experimental Modal Analysis Project II FEM ing, Experimental Validation & Prediction of Rotor Stability
3 Home Page 1. Course Structure It is important to highlight that the selected pages of some reference books and manuscripts are very useful, if you attend the classes. The material is not ready yet to be used as a textbook and the structure of the course simulates the routine of a consulting engineer, who has to search for information in several sources in order to deal with the project challenges. In real life such information sources are frequently fragmented in several books and articles, and to facilitate and speed up the students learning process the sources are collected in the last column of the website. Remember though, that the discipline Dynamics of Machinery demands a strong integration of several disciplines, as dynamics, mechanical vibration, strength of materials, fluid mechanics, mathematics, numerical methods among others. There will be two educational projects and they were carefully formulated with the goal of integrating all these disciplines and strengthening the students background. While writing the final project reports all apparently fragmented information will be nicely linked together and the student will be able to understand Dynamics of Machinery in a holistic way, as it is in the reality.
4 2. Objectives Multidisciplinary Approach Physical System Mechanical Mathematical Assumptions (simplifications) Newton, Euler, D Alembert, Lagrange, Hamilton, Jourdain (principles & axioms) * Mass Elements M Particle Rigid Body Distributed * Spring Elements K Elasticity Theory & Material Magnetism * Damping Elements D Contact Mechanics (friction) Static Equilibrium Position (Linearization) Solution: (eigenvalues) (eigenvectors) (structure) (machine)
5 3. Theoretical and Experimental Example Physical System Mechanical Mathematical Ω u1 u2 u3 Eigenvalues: Eigenvectors: u1(ω) u2(ω) u3(ω) Application Examples: - seals (rotor-stator contact) - positioning of dampers - gearboxes
6 This image cannot currently be displayed. 4. Industrial Examples (Application) Tradicional Compressor (supported by fluid film bearings) Integrated Motorized Compressor (supported by magnetic bearings)
7 5. Mathematical ing & Steps Physical System Mechanical Mathematical Assumptions (simplifications) Newton, Euler, D Alembert, Lagrange, Hamilton, Jourdain (principles & axioms) * Mass Elements M Particle Rigid Body Distributed * Spring Elements K Elasticity Theory & Material Magnetism * Damping Elements D Contact Mechanics (friction) Static Equilibrium Position (Linearization) Solution: (eigenvalues) (eigenvectors) (structure) (machine)
8 5. Mathematical ing & Steps Physical System Mechanical Mathematical Assumptions (simplifications) Newton, Euler, D Alembert, Lagrange, Hamilton, Jourdain (principles & axioms) * Mass Elements M Particle Rigid Body Distributed * Spring Elements K Elasticity Theory & Material Magnetism * Damping Elements D Contact Mechanics (friction) Kinematics 1. Reference Frames (systems of coordinates) 2. Transformation Matrices 3. Position Vectors 4. Velocity Vectors (linear and angular) 5. Acceleration Vectors (linear and angular) Dynamics 6. Mass Properties (mass center, moments of inertia) 7. Force and Moment Vectors 8. Dynamic Equilibrium: (Newton, Euler, Lagrange ) 9. Equilibrium Poition (Linearization, Vibration Analysis)
9 This image cannot currently be displayed. 6. Examples Particle in 3D (Three Equations) Thank you for your attention!
10 6. Examples Particle in 3D (Three Equations) GOAL: Two Dynamic Reaction Forces (dimensioning & design) (machine elements, strength of materials) & One Equations of Motion (stability analysis and vibrations) (mechanical vibrations)
11 This image cannot currently be displayed. 6. Examples Particle in 3D (Three Equations) GOAL: Two Dynamic Reaction Forces (dimensioning & design) (machine elements, strength of materials) & One Equations of Motion (stability analysis and vibrations) (mechanical vibrations)
41514 Dynamics of Machinery
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