Condition Control of Mechatronic Systems
Sustainable Development Goals
Learning Goals
Objectives:
1) To identify the framework of condition control under the Scientific areas of Vibration theory, Signal measure and analysis and Tribology.
2) To be able to diagnose and solve, by means of measure and calculation, problems of condition-based maintenance that may occur in industrial environment.
3) To measure acceleration with hand Vibrometers and Accelerometers connected to sinal aquisition racks
4) To know, in detail, linear vibration theory with 1 and n degrees-of-freedom and continuous systems (bars, beams and plates)
5) To be able to use measure software, signal processing software (Labview) and CAS software (Mathematica and Maple)
6) To know how to solve inverse problems in the response of n-DOF systems, to perform sensitivity analysis
7) To be precise, concise and fast answering maintenance problems, making use of measuring and calculation tools.
Contents
Syllabus:
1) Introduction to preventive and predictive maintenance. Condition-based maintenance. Classification of maintenance techniques, planning and the weight of the economic factor. Primary and Secondary functions, reliability.
2) Measurements and information gathering methods. Instrumentation.
3) Damage and degradation of Industrial equipments. Illustrations. Fatigue, plastic flow, creep and rupture. Typical mechanical failure: shafts, gearing, pipes, etc.
4) Mechanical vibrations in the context of maintenance: 1 DOF
4a) D'Alembert principle and the use of inertial forces in the free-body diagrams. Energy and energy-based methods to obtain the equilibrium in the sense of d'Alembert..
4b) Second-order ODEs: characteristic equation, types of response, stable and unstable systems. Damped and non-damped frequencies, damping ratio. Superposition principle and response shift.
4c) Response to non-zero initial conditions.
4d) Constant right-hand side. Static displacement. Harmonic right-hand side, critical frequency, phase diagram and frequency ration. Periodic right-hand side: Truncated Fourier series.
4e) Response to an arbitrary excitation: Dirac-Delta, equivalence to an initial velocity inversely proportional to the mass. Duhamel integral. General response.
4f) ODE integrators: reduction to a first-order system. Superposition response to a first-order ODE, central difference numerical integration, critical time step, Courant number.
4g) Stationarity of the Lagrangian, Euler-Lagrange equations.
5) Machine components as rigid bodies:
5a) Basis change and vector transformation: alibi-alias and orthogonal matrices.
5b) Rigid-body DOF. Euler angles and general rotation matrix. Euler theorem. Rotation matrix eigensystem. Chasles theorem. Angular velocity and acceleration, general case.
5c) General motion of a rigid body.
5d) Inertia matrix, general motion equations.
5e) Typical inertia matrices and solutions
5e) Bidimensional case.
6) N degrees-of-freedom:
6a) General motion equations by the Euler-Lagrange method.
6b) Free undamped case: orthogonality, eigenshapes and frequencies, modal basis.
6c) Modal decoupling in the proportional case. General response.
6d) Frequency response and basis motion. Accelerometer modus-operandi.
7) Fourier Series and Gibbs phenomenon. How to filter it.
8) Fourier transforms in detail.
9) Continuous media. Second order PDEs: classification and characterization of the solutions. Functional spaces and internal products, the introduction of a metric.
10) Beams and plates: modal basis and general solution. Boundary conditions by using distributions and integration of the motion equations.
11) Sensitivity analysis.
12) Lubricants: viscosity, indices, maintenance role.
13) Practical works and papers done by the students.
Teaching Methods
1) Theoretical Lectures using both transparencies and powerpoint presentations, as well as Mathematica experimentations. Cumbersome but important deductions (such as finite rotations and the Chasles theorem) are detailed deduced in the Whiteboard, with direct questions posed to the students. Students are stimulated to participate and deduce key aspects in the Whiteboard. Theoretical parts are presented between illustrations and appeal to intuition and empirical knowledge.
During the lecture, students are stimulated with questions and short exercises.
2) The practical classes resort to practical exercises and experimentations with the vibration equipment.
3) Work assignments performed by the students that must defend them in a meeting with the lecturer. One of the assignments is theoretical and of bibliography search and another one is experimental.
Assessment
Evaluation:
30% For the written examination
35% For the theoretical and bibliography search assignment
35% For the experimental assignment
Recommended Reading
G.Thompson, Design Review - The Critical Analysis of the Design of Production
Facilities, The Lavenham Press, Ltd, U.K., 1985.
Charles O. Smith, Introduction to Reliability in Design, McGraw-Hill, Ltd, Tokyo,
1976.
Machinery Malfunction Diagnosis and Correction, Robert C. Eisenman, Robert C.
Eisenman, Prentice Hall.
Mechanical Vibrations: International 4th edition, S. S. Rao, Prentice-Hall.
Write-ups and papers from Journals.
