Modeling and Analysis of Passive Vibration Isolation Systems

By Sudhir Kaul

Modeling and Analysis of Passive Vibration Isolation Systems discusses a wide range of dynamic models that can be used for the design and analysis of passive vibration isolation systems. These models range from linear viscoelastic single degree-of-freedom systems to multiple degree-of-freedom nonlinear systems. They can be used to evaluate hyperelasticity and creep, and to represent the inertia effect for an evaluation of vibroacoustic characteristics at high frequencies. This book also highlights specific nonlinear behavior, displacement-limiting designs, hyperelastic behavior, and characteristics associated with elastomeric materials for each model. It also identifies key attributes, limitations, and constraints, providing a holistic reference that can be used for the design and analysis of passive vibration isolators. Modeling and Analysis of Passive Vibration Isolation Systems serves as a reference for engineers and researchers involved in the design, development, modeling, analysis, and testing of passive vibration isolation systems and as a reference for a graduate course in vibration modeling and analysis.

• Outlines the use of multiple models for optimal passive vibration isolation system design
• Discusses the effects system design has on subsequent product development components and parameters
• Includes applied examples from the automotive, aerospace, civil engineering and machine tool industries
• Presents models that can be extended or modified to investigate different means of passive isolation, nonlinearities, and specific design configurations
• Considers specific elastomer characteristics such as Mullins and Payne effects for theoretical modeling and analysis

• Language: English
• Publisher: Elsevier Science
• Release date: Aug 31, 2021
• ISBN: 9780128194218

Sudhir Kaul

Sudhir Kaul is an Associate Professor of Mechanical Engineering in the School of Engineering and Technology at Western Carolina University in North Carolina, USA. Dr. Kaul earned his PhD from the University of Wisconsin-Milwaukee in 2006 and has held academic positions since 2008. His industry experiences include development of vibration isolation systems, design and development of motorcycle powertrains, and design of hydraulic systems. His research interests include dynamic modeling for vibration isolation, motorcycle dynamics, and fracture diagnostics. He has published more than sixty articles in peer-reviewed journals and conference proceedings.

Book preview

Chapter 1

Vibration isolation—background

Contents

1.1 Introduction 1

1.2 Isolator materials 2

1.3 Common elastomeric isolator designs 4

1.4 Stiffness and damping 6

1.5 Single-degree-of-freedom system 9

1.6 Multiple-degree-of-freedom system17

Review exercises 24

References 25

Abstract

This chapter provides a brief theoretical background for the modeling and analysis of a vibration isolator or a vibration isolation system. Some of the main concepts associated with vibration isolation systems and the theoretical solutions for single and multiple degree-of-freedom systems are presented in this chapter. The purpose of this chapter is to serve as a refresher on main concepts in the time domain and frequency domain analysis of vibrating systems. Furthermore, most commonly used materials for manufacturing passive isolators are also briefly discussed in this chapter.

Keywords

Vibration isolators; Elastomeric isolators; Single degree-of-freedom system; Multiple degree-of-freedom system; Frequency response

1.1 Introduction

The use of vibration isolators and vibration isolation systems is widely prevalent in multiple applications such as automotive, railroad, aerospace, heavy machinery, civil structures, etc. Some of the main reasons for using a vibration isolator include mitigation of resonance peaks, reduction of transmissibility, enhancement of fatigue life, improvement in ergonomics, etc. in the presence of external or internal sources of dynamic excitation. The design of a vibration isolator requires a close examination of multiple considerations such as the source of dynamic excitation, range of excitation frequency, excitation amplitude, allowable displacement, acceleration limits of the isolated system, available design envelope, etc. Additionally, considerations of environmental conditions, manufacturability, and material choice are also important. All these considerations accentuate the importance of a theoretical model that can reasonably predict the performance of the isolation system before finalizing the design and before manufacturing prototypes that can be used for testing. Therefore, it is critical to select a suitable model that can be correlated to test results and eventually used to finalize design details.

1.2 Isolator materials

Vibration isolation can be achieved by using materials capable of providing a combination of highly elastic behavior in conjunction with damping properties. Pneumatic, hydraulic, elastic metal, and elastomeric designs are commonly used in commercial vibration isolation applications. Elastomeric materials are arguably most common and are extensively used in the industry with a very commonly used design consisting of elastomeric material bonded to metal plates or a metal core. Such isolators are typically called elastomeric mounts. Natural rubber, neoprene, and butyl rubber are some of the commonly used elastomers in commercial vibration isolators. Elastomers provide a designer with a range of stiffness and damping characteristics as well as an ability to withstand different environmental conditions. This ability to satisfy performance requirements over a wide range of rugged conditions along with the ease of manufacturing through a molding process make elastomers a common choice for isolators during the design process. Table 1.1 lists some of the commonly used elastomers for manufacturing passive vibration isolators with a listing of some of their characteristics that can be considered during design. In addition to the commonly used elastomers, manufacturers often develop proprietary elastomeric recipes to serve the needs of a specific design that may require a combination of properties from different materials. Properties of elastomeric materials can be changed significantly by changing their composition or by using different blends. A typical manufacturing process of the raw material involves vulcanization by adding sulfur and by the addition of accelerators, fillers, and plasticizers (Mark, Erman, & Roland, 2013). The raw material is then used in a molding process to produce a vibration isolator of the designed shape and size to deliver the necessary stiffness and damping properties. While there are many characteristics that are sought from the design of a vibration isolator, some of the common technical properties that a designer seeks to comprehend are damping, dynamic stiffness, environmental resistance, and some of the inherent nonlinearities.

Table 1.1

Metal springs have been commonly used for vibration isolation applications as they can be designed to offer a range of stiffness properties in heavy machinery applications. Most of these designs do not allow much flexibility with damping as most metal springs offer relatively low material damping. Coil springs, disc springs, slotted springs, etc. are some examples of metal springs commonly used in vibration isolation applications (Rivin, 2003).

In some cases, it is common to use a separate damper to augment damping of the vibration isolation system. Viscous dampers are designed to offer resistance to relative motion between two surfaces that are typically separated through a fluid film. Some of these dampers can exhibit nonlinear behavior due to strong temperature dependence. Since the early 1990s, magnetorheological (MR) dampers have been developed by researchers and manufacturers to provide smart damping properties that can be controlled through input current to an electromagnet that in turn governs the behavior of the damper. MR fluids consist of micron-sized particles in a carrier fluid, an MR damper allows control over the apparent viscosity of the fluid by controlling the magnetic flux of the electromagnet. Such a damper is considered to be a semi-active system that can be used for vibration isolation and control (Choi & Wereley, 2008; Dominguez, Sedaghati, & Stiharu, 2004). Friction dampers and electromagnetic dampers are other examples of dampers that have been used in some vibration isolation applications.

A hydraulic mount, also called a hydromount, is another vibration isolator that has been used in automotive applications. Such an isolator provides properties that are amplitude dependent as well as frequency dependent. The isolator typically consists of two chambers connected through a channel that allows fluid passage from one chamber to the other. This design allows the vibration isolator to exhibit low stiffness and high damping for dynamic excitations with large amplitude and low frequency while demonstrating low damping at small amplitude and high frequency vibrations (Truong & Ahn, 2010). Different designs of hydromounts have been used in some automotive applications to provide dynamic characteristics that can be tuned to provide a frequency-dependent behavior.

1.3 Common elastomeric isolator designs

Some of the common designs of passive vibration isolators involve elastomeric material bonded to metal plates or a metal core with a static member that is assembled to a rigid frame and a dynamic member that separates the isolated components from the source of dynamic excitation. There are some designs that consist of elastomeric materials without being bonded to a metal plate or a metal core, such designs typically do not need to withstand high static loads. Passive elastomeric isolators are generally designed to be under compression loading or shear loading with circular or rectangular cross sections being the most commonly used. Grommets, bushings, etc. are also common examples of passive elastomeric isolators. Some of the commonly used design configurations of elastomeric isolators are shown in Table 1.2.

Table 1.2