Shock and Vibration

Volume 2016 (2016), Article ID 7846369, 14 pages

http://dx.doi.org/10.1155/2016/7846369

## Influence of Sandwich-Type Constrained Layer Damper Design Parameters on Damping Strength

^{1}Tecnun-University of Navarra, Manuel Lardizabal 13, 20018 San Sebastián, Spain^{2}CEIT, Manuel Lardizabal 15, 20018 San Sebastián, Spain^{3}CEIT and Tecnun-University of Navarra, Manuel Lardizabal 15, 20018 San Sebastián, Spain^{4}CAF, Jose Miguel Iturrioz 26, 20200 Beasain, Spain

Received 21 August 2015; Accepted 2 February 2016

Academic Editor: Emiliano Mucchi

Copyright © 2016 Inaki Merideno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a theoretical study of the parameters that influence sandwich-type constrained layer damper design. Although there are different ways to reduce the noise generated by a railway wheel, most devices are based on the mechanism of increasing wheel damping. Sandwich-type constrained layer dampers can be designed so their resonance frequencies coincide with the wheel’s resonant vibration frequencies, and thus the damping effect can be concentrated within the frequency ranges of interest. However, the influence of design parameters has not yet been studied. Based on a number of numerical simulations, this paper provides recommendations for the design stages of sandwich-type constrained layer dampers.

#### 1. Introduction

The environmental requirements for railway operation are becoming more and more demanding. In particular, railway noise has to be taken into account as freight traffic increases and urban trams, metro lines, and high speed lines spread all over the world. Noise reduction at the source is more attractive than the use of noise barriers, but this requires a thorough understanding of the noise source mechanisms as well as methodologies to evaluate the effectiveness of proposed solutions [1].

Different sources may contribute to the total noise level, but wheel/rail noise is the most important noise source at middle speed ranges (50–250 km/h), where the vast majority of trains run [2]. At low frequencies the noise is mainly radiated by the sleeper and the rail, whereas at high frequencies (around 1500 Hz), the wheel is the dominant noise source [3]. Thus, the wheel is one of the most critical components of railway noise emission, and the study of its vibroacoustics has attracted the attention of many researchers due to its significant complexity [4].

The main wheel/rail noise sources are rolling noise, impact noise, or squeal noise, this last one being the most difficult to mitigate. Wheel squeal is considered to be caused by an instability in wheel vibrations [4–6], so sufficient positive damping, which is only a small fraction of critical damping, can actually stabilize these wheel vibrations and reduce squeal.

Different ways of increasing wheel damping have been reported in the literature, the most important ones being resilient wheels [7–10], ring dampers [7, 11–14], CAF dampers [15, 16], and constrained layer dampers (CLD) [17–20], either as a treatment applied on the wheel web [1, 7, 9, 21–25] or as tuned absorbers [1, 7, 26–28].

This paper is focused on sandwich-type CLD tuned absorbers, which are frequently employed in metro wheel cases. Sandwich-type CLDs are devices that combine metallic sheets with viscoelastic layers, and they increase the damping of the railway wheel modes. The damping is due to the energy dissipation that occurs through the deformation of the viscoelastic material.

A sandwich-type CLD can be designed to reduce both squeal and rolling noise, depending on the treatment configuration. One advantage of the sandwich-type CLD is that it ages well, and it can be removed from a worn wheel and installed on a new one [7]. It can be designed so its resonance frequencies will coincide with wheel resonant vibration frequencies [7, 29], and thus its damping effect can be concentrated within the frequency ranges of interest. The possibilities are endless, and the same problem can often be solved by a number of different solutions.

Merideno et al. [30, 31] highlighted the need to develop a specific model that calculates the damping added by sandwich-type CLD to the railway wheel, in order to avoid experimental measurements. They presented a procedure that could be employed in design stages where the damping device is not available. The calculated damping can then be used to simulate the noise generated by a railway wheel [32, 33].

This paper makes use of the damping prediction model developed by Merideno et al. [30] to analyse several design parameters of the sandwich-type CLD solution and study their influence on the resulting total damping of the wheel-damper system. The effective noise reduction is not investigated in this paper, since the influence of wheel/rail contact on the radiated noise is out of the scope of this paper. The objective is that the results presented in this paper will be able to serve as a guideline for sandwich-type CLD designs, even for structures other than the railway wheel.

#### 2. Objective Function and Design Parameters

According to Merideno et al. [30], the final modal damping ratio (the damping ratio of the wheel with the damping solution) can be calculated as(see [30]) where represents the total number of sandwich-type devices attached to the railway wheel and refers to the sum of the base reaction forces (the imaginary part) appearing in each damper. The theoretical development of this equation can be found in the literature, and so it is not repeated here.

In this equation, the terms , , and are specific to the undamped wheel, so if we only aim to study the damping strength of a given sandwich-type CLD in the frequency domain and independently of the railway wheel, these parameters should not be considered. The term refers to all the reaction forces in the damper base nodes, making it directly related to the damping strength that a particular sandwich-type CLD design would have, independent of the railway wheel. The term refers to the wheel’s natural frequencies, but when a given sandwich-type CLD is attached to a given railway wheel, corresponds to the vibration frequency at which the damper is excited. Therefore, instead of understanding this frequency term as the natural frequency of the railway wheel, it must be understood as the vibration frequency at which the damper is excited. However, when comparing different sandwich-type CLD designs that concentrate their damping strength on different frequency ranges, the reaction forces are normally higher for higher vibrational frequencies. Because of this, we define the concept of* damping potential* as normalizing in terms of frequency the damping strength of a damping solution:where is related to the total amount of damper base nodes. This damping potential frequency-dependent value is the objective function in our study, since it defines the potentiality of a sandwich-type CLD to add damping to a given structure in the frequency domain. The frequency at which the sandwich-type CLD has a high damping potential value must then coincide with the frequency at which the designer wants to add damping in the structure to ensure the effectiveness of the sandwich-type CLD.

Now that the objective function has been defined, the design parameters under study will be described. The nomenclature that will be used hereafter for the geometric design parameters of a sandwich-type CLD is illustrated in Figure 1, which shows a scheme of a four-layer sandwich-type CLD, where refers to the thickness of the th metallic sheet (where 0 corresponds to the base sheet), refers to the thickness of the th viscoelastic layer, and refers to the angle of the viscoelastic layers. This is a typical design employed in railway wheels for squeal noise. As it is usually an arc-type design, angle is preferable to referring to the length of the viscoelastic layer.