Vibration Control Engineering

Passive and Feedback Systems

Ernesto Novillo

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9781032006994
• eBook ISBN: 9781000482195
• Topic: Technology & Engineering
• Subtopic: Industrial Design
• Index: Technology & Engineering

This book applies vibration engineering to turbomachinery, covering installation, maintenance and operation. With a practical approach based on clear theoretical principles and formulas, the book is an essential how-to guide for all professional engineers dealing with vibration issues within turbomachinery. Vibration problems in turbines, large fans, blowers, and other rotating machines are common issues within turbomachinery. Applicable to industries such as oil and gas mining, cement, pharmaceutical and naval engineering, the ability to predict vibration based on frequency spectrum patterns is essential for many professional engineers. In this book, the theory behind vibration is clearly detailed, providing an easy to follow methodology through which to calculate vibration propagation. Describing lateral and torsional vibration and how this impacts turbine shaft integrity, the book uses mechanics of materials theory and formulas alongside the matrix method to provide clear solutions to vibration problems. Additionally, it describes how to carry out a risk assessment of vibration fatigue. Other topics covered include vibration control techniques, the design of passive and active absorbers and rigid, non-rigid and Z foundations. The book will be of interest to professionals working with turbomachinery, naval engineering corps and those working on ISO standards 10816 and 13374. It will also aid mechanical engineering students working on vibration and machine design.

Part I Vibration Theory of SDOF, MDOF and Continuous Dynamic Systems

1 Dynamics of Linear SDOF Systems

DOI: 10.1201/9781003175230-2

1.1 Introduction to Machine’s Vibration

Mechanical vibration is a quick and small alternating motion experienced by a machine or mechanism. Technically speaking, it is a harmonic displacement of minimal amplitude produced by unbalanced rotating parts or transmitted by vibrating nearby machines. Under some circumstances, wave amplitudes rise to such an elevated level that dynamic forces may harm the rotating machine. This phenomenon is known as resonance. The ability to predict and mitigate or prevent vibration is of utmost importance for the machine’s life span and surrounding constructions.

Rotating machines are usually impacted by vibration because of the imbalance produced by shafts, wheels, and other rotating parts revolving at high speed. A centrifugal force deflects the axle as the shaft, wheels and other revolving parts are never perfectly straight and balanced. The axle reacts with a rigid force in opposition to the centrifugal force. It is trying to recover its initial straightness, which of course, is impossible in practice because the shaft is not entirely rigid. Thus, the axle is bent by its weight or mechanically attached unbalanced loads. Although rigid and centrifugal forces are in equilibrium, vibration and axle bending are inevitable aftermaths.

Turbomachine shafts and wheels behave like mass-spring sets known as the mechanical system, where the shaft is equivalent to a spring, and wheels are equivalent to rotating masses. Their combination has a characteristic frequency at which the system oscillates even if no external force is applied. This frequency is known as natural frequency. There is more than one natural frequency in machines as they are complex configurations of mass and springs. A harmonic disturbance with a frequency close to any natural frequency produces an abnormal amplification of the vibration amplitude.

The content of this chapter is to prepare for the following problems that usually affect rotating machines’ performance or are harmful to their mechanical integrity, such as:

• Vibration at a critical velocity
• Lateral vibration
• Torsional vibration
• Axial vibration
• Vibration transmission to foundations and other installations

Lateral or transverse vibration is due to shaft bending produced by transversal loads (see Figure 1.1). It is also known as bending or whirling vibration. This type of vibration is less harmful than torsional vibration but, in any case, requires strict monitoring due to associated risks of fatigue and eventual breakage. Another common cause of lateral vibration is when the shaft’s center of gravity does not lie on the shaft’s geometric axis of symmetry. This issue produces a centrifugal force that creates a cyclic shaking perpendicular to the axle, like a shaft bending.

Figure 1.1 Deflected shaft predicts lateral vibration.

Vibration puts many parts of rotating machines (i.e., bearings, blades and other moving parts) in danger of catastrophic damage. Therefore, it is essential to identify their origin and mitigate vibrations as soon as possible during the machine operation. Current state-of-the-art instrumentation is very sophisticated; it facilitates vibration measurements to help diagnose problems and guide design solutions. These measurements help to understand where the problems originate and to make decisions to prevent...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgements
• About the Author
• Abbreviations
• PART I Vibration Theory of SDOF, MDOF and Continuous Dynamic Systems
• PART II Turbo Machines And Ship Vibrations
• PART III Vibration Control Systems
• Index