This course aims at introducing the main concepts related of rotor dynamics and diagnostics.

Rotor dynamics is the key for the design and operation of many machines: turbine of any kind used for power generation, aircraft engines, electrical motors, centrifugal compressors, etc. Thus, the dynamics of the complete machine and of its main components, like shafts, bearings, seals and blades is presented in detail. Several design tools and examples are introduced.

Diagnostics is an emerging requirement in modern mechanical systems in order to shorten out-of-service and reduce operation costs. Very often, the faults are affecting the same components analysed by rotor dynamics and this makes the two parts of the course strictly connected. State-of-the-art techniques, based on both system model and data analysis, are introduced.

All the topics are analysed under practical and theoretical points of view, with several examples of application in real machines, of design cases and of case histories. The seminars, conducted by industry experts, are essential parts of the course.

More in detail, the aims of the course are:

• To provide tools and methods to define the mathematical model of a rotor system, by considering its main sub-components
• To provide the basics for the mechanical analysis of rotating machinery
• To provide tools and methods to perform diagnostics of mechanical systems, by considering their main sub-components
• To provide the basics for fault and damage diagnostics in mechanical systems
• To provide the morphological description of the main sub-components of rotor systems

Knowledge and understanding

After passing the exam, the student:

• knows the methodologies and the principles to describe in mathematical terms a rotor system and its main sub-components;
• understands and knows how a rotor system is composed;
• knows the basic aspects of diagnostics of mechanical systems;
• knows the methodologies to perform diagnostics of some components of mechanical systems;
• learns the methods of modeling rots systems;

Ability to apply knowledge and understanding

After passing the exam, the student:

• is able to perform the modeling of rotor systems;
• is able to understand and describe the functioning of a rotor system;
• can calculate the dynamic response of a rotor system;
• is able to address and analyze basic problems of diagnostics in a mechanical system;
• can effectively communicate the results of the analysis performed on the dynamics of a rotor system;
• can effectively communicate the results of the diagnostics of a mechanical system.

Rotor dynamics

• Finite beam models for lateral and torsional vibrations. Supporting structure modelling. Review of design standards (API, ISO). Flexible rotors balancing
• Critical speeds, Campbell diagram, System response to common linear (unbalance, bow, misalignment, cracks) and non linear (rub, magnetic fields) excitations
• Stability (effects of fluid film bearings, of steam flow, of magnetic bearings/fields)

Fluid-film bearings

• Hydrodynamic lubrication, computational hydrodynamics, Geometry of fluid film bearings
• Bearing design (static and dynamic characteristics), Journal bearing testing, Thrust bearing testing, Bearing coating materials, Bearing damages
• Effects of electrical pitting

Seals

• Geometry, modelling (bulk-flow, and CFD), dynamic characteristics calculation

Blade dynamics

• Excitation causes
• Design, HCF, Correction, LCF, Correction
• Damping, snubbing, friction, vibration measurements

Diagnostics

• Maintanance policies, condition monitoring, setting of alarms and trips, review of current standards
• Model based approach (inverse dynamic problem), with case history analysis (steam, gas and hydro turbines)
• Data driven approach (advanced signal analysis: time-frequency transformations, 2nd order cyclostationarity, envelope analysis, spectral kurtosis), with case histories (turbine gearbosx, train traction systems, engine firing)

Special topics

• Wind turbine diagnostics
• Roller element bearings diagnostics
• Gear diagnostics

Seminars (speakers from industry)

1. Industrial steam turbine design and operational requirements
2. Rolling element bearing diagnostics

A good knowledge of calculus is required, especially regarding linear differential equations, matrix algebra and partial differential equations. The knowledge of finite element approach is suggested, but not mandatory. Similarly, the knowledge of basics of fluid mechanics and of signal processing is useful.

Organization of the course and methods of verification

The course is divided into a series of lessons and practical exercises, related to the topics of the lessons, aimed at consolidating the knowledge and methods learnt during the lessons.

The exam consists of an oral exam.

The oral exam consists in answering questions, in open form, that focus on all the topics covered in the course, accompanying the answering with equations, graphs, sketches, in a synthetic and complete exposition. Depending on specific logistics problems, it could be required to perform the oral exam by answering the questions by composing a written document, which will be discussed with the teacher.

The purpose of the oral test is to verify the knowledge underlying the study of rotordynamics and diagnostics, and the applications covered in the course, evaluating both the understanding of physical phenomena and their mathematical implementation (demonstration). The oral test also verifies the ability to transmit the results of the analyses carried out both in mathematical terms and with graphic representations.

Slides of the lessons, which include all the topics of the course, are provided via BeeP. The bibliography is suggested and can be fruitful consulted for individual in-depth analysis.

Slides of the lessons

Available on www.biblio.polimi.it - The book is useful for the description of main components of typical rotating machines

Some hardcopies are available in Polimi libraries

Available on www.biblio.polimi.it

Some hardcopies are available in Polimi libraries

Available on www.biblio.polimi.it

Available on www.biblio.polimi.it