Single-Course Engelsk 5 ECTS

# Dynamics of machinery

## Overall Course Objectives

The aim of the course is to enable the students to: a) analyse and determine the dynamic loads and vibrations in mechanical systems, b) use and develop analysis methods suitable when designing machinery, c) read and evaluate the scientific literature in this field.

See course description in Danish

Learning Objectives

• Build mechanical and mathematical models and computationally implement them for simulating the dynamical behavior of rotating machines, mechanisms and structures.
• Deal with multibody systems (MBS) and finite element method (FEM) to describe the dynamic behavior of rigid and flexible machine components.
• Understand the interrelation among different disciplines, as dynamics, mechanical vibrations, experimental mechanics, machine elements, signal processing, fluid dynamics, magnetism, motion control and numerical analysis.
• Apply such an interrelation to achieve the coefficients of differential equations of motions, which can be constant or depending on the angular velocity of machine.
• Determine the dynamic coefficients of different types of hydrodynamic bearings.
• Deal with damped (non-symmetric) gyroscopic systems, calculate mode shapes, natural frequencies and damping factors as a function of the machine angular velocity with the aim of predicting critical speeds, vibration levels and stability limits.
• Understand the principles of experimental dynamic tests and the operational principles of sensor and actuators, among them accelerometers, displacement and force transducers and electromagnetic shakers.
• Understand the techniques of signal analysis and processing, which make possible the development of the experimental methodologies for validating mathematical models (digital twins) and for diagnosing rotating machinery malfunctions.
• Understand and use signal processing techniques to obtain auto and cross-correlation functions, power and cross-spectral density functions, frequency response functions and coherence function (digitalization).
• Validate mathematical models based on Experimental Modal Analysis (EMA).
• Account for simplifications and limitations of the theoretical and experimental methods (MBS, FEM, EMA) used, and predict the possible consequences for the dynamic behavior of flexible and rotating machine components.
• Write technical reports, with correct description of theoretical and experimental procedures, in a clear way, well structured language, using technical terms, giving physical interpretations and evaluations of results.

Course Content

Methods for the analytical and numerical treatment of the response of a mechanical system under periodic, transient and stochastic loading. The modal method, FEM method, transfer methods. Numerical methods for the analysis of torsional and lateral vibrations in rotors (optimization of dampers, vibrations caused by unbalance, balancing, and instability). Examples of self-induced vibrations and dynamic instability. The fundamental theory for vibrational analysis and treatment of vibrational data are given with the goal of building digital twins and monitoring/dignosing machine malfunctions inside the Industry 4.0 framework.

Recommended prerequisites

10022/41532/41560/41035/41535/41564

Teaching Method

Lessons and practical exercises with measurements. Based on the experiments and measurements 2 reports are prepared.

Faculty

See course in the course database.

## Registration

Language Engelsk 13 weeks DTU Lyngby Campus 41514 Candidate Week 6 Week 20 Fri 8-12
Price 9.250,00 DKK