Resilient Bearings Research Articles

Reducing ground borne noise due to railways: A practical application

The construction of new buildings very close to existing tracks, with heavy commuting traffic, requires careful design. Such projects must be accompanied with noise and vibration reduction measures. The practical case here considered has been analysed by first assessing the existing situation prior to construction (type of soil and traffic). In a second stage, we have proposed and quantified solutions to reduce vibration and ground-borne noise levels inside the buildings. A 2.5D FEM/BEM commercial software (Mefissto), developed by CSTB, has been employed in what is a very challenging numerical context: multi-layered ground, large multi-levels buildings, large frequency range (10–250 Hz). In every situation, the use of an original 2.75D approach leads to the low frequency noise levels inside the buildings. As the trackwork cannot, in this case, be modified the solutions tested consist in inserting different types of barriers in the ground or in inserting either spring of resilient bearings (decoupling) in the lower part of the structure. Results are compared to target values in terms of vibration and ground-borne noise levels selected in order to limit dwellings occupants’ annoyance. Satisfactory results can only be achieved with the use of the decoupling solution.

A numerical and experimental investigation of a special type of floating-slab tracks

Floating-Slab Tracks (FST) are predominantly used for mitigating railway-induced vibrations where the concrete slab is mounted on soft resilient bearings to provide vibration isolation. This paper presents a research study on the dynamic behavior of a special type of FST used in the recently built subway system in Doha, Qatar. The special FST has a continuous concrete slab with periodic grooves. Therefore, the track can be modeled as a periodic structure with a slab unit having two elements with different cross-sections. Extensive numerical and experimental investigations were conducted on a multi-unit full-scale mockup track representing the special FST. A fast running model based on the Dynamic Stiffness Method was developed and examined, in an initial numerical exercise, against a detailed Finite Element model for a track with a finite length. In the experimental campaign, a test was performed with an impact hammer to identify the actual vibration response of the mockup track. Results from the experimental investigations were then used for model updating of the fast running model. The model updating process was carried out according to an automated hybrid optimization approach that combines genetic algorithms with a local search method. Finally, the updated model was extended to an infinite model to investigate the influence of varying grooves thickness on the dynamic behavior of the special track with infinite length for both bending and torsion scenarios. The investigations suggested that reducing the thickness below 50% of the full thickness of the slab significantly affects the dynamic behavior of the special FST.

Isolation of structure-borne noise in buildings from exterior sources

The increasing frequency of construction of new performance, residential and other noise sensitive facilities in locations with high amplitudes of ground-borne noise has required development of effective building isolation design configurations to reduce to acceptable values the structure-borne noise transmitted into the buildings from the foundation. Isolating a large building such as a concert hall or multi-story residence necessarily requires structurally separating the isolated building, or isolated parts of the building, from the foundation. The structural support is then provided by resilient bearings that must properly support the building gravity load, provide a controlled seismic restraint and structural stability, and provide the noise reduction required. The goal of this presentation is to demonstrate that the technology and materials now exist to allow placement of any large noise sensitive building, either a performance facility or a residential building, in any location where it is subject to ground-borne vibration and noise that would normally cause intrusion and be incompatible with the intended occupancy. The development of the gravity load support bearings and the preloaded seismic restraint rubber bearing concepts are presented along with examples of successful applications.

Large building isolation with seismic restraint.

Isolating a large building such as a concert hall or multi‐story condominium necessarily requires structurally separating the isolated building from the foundation. The structural support is then provided by resilient bearings which must properly support the building gravity load and provide seismic restraint and structural stability. The best acoustical results are achieved with natural rubber bearings sized to support the gravity load at columns and loadbearing walls. Lateral support for wind and seismic loads is then achieved, without compromising the isolation, through the installation of lateral support bearings in equal and opposite pairs in both directions. The lateral loads are transmitted to the columns or loadbearing walls via the structural floor above the bearings functioning as a transfer slab. The equal and opposite preloaded pair concept for lateral restraint was developed to achieve an assembly with the bearings always in compression regardless of load or deflection. This avoids any need for embedded plates or bolts which could cause tension in the concrete structural elements. The history of the development of the preloaded lateral restraint rubber bearing concept is presented along with examples of successful application to concert halls and other structures.

A continuous model approach for cross-coupled bending vibrations of a rotor-bearing system with a transverse breathing crack

Abstract In this paper, the cross-coupled bending vibrations of a rotating shaft, with a breathing crack, mounted in resilient bearings are investigated. The equations of motion of the continuum and isotropic rotating model of the shaft follow the theory of Rayleigh. The governing equations are coupled in the two main directions, and the partial solution is obtained by solving a linear system of equations, for each time step, taking into account the non-linearity due to the breathing crack. The coupling is introduced in three different ways: the equations of motion, the resilient bearings and the crack. A main focus is made in the coupling introduction due to crack compliance variance while rotation with the cross-coupling terms of the local compliance matrix due to the crack to be calculated analytically as functions of the rotational angle. The three causes of coupling between the vertical and horizontal vibrations should be distinguished with regard to the effects that each one of them has on the dynamic response of the rotor. Inversely, the existence of each type of coupling in the frequency response could be used to identify the respective cause.

Dynamic behavior analysis of cracked rotor

In the present study, the additional slope is used to consider the crack breathing, and is expressed explicitly in the equation of motion as one of the inputs to produce the bending moment at the crack position. Inversely, the additional slope is calculated by integrating on the crack region based on a fracture mechanics concept. The response of a cracked rotor is formulated based on the transfer matrix method. The transient behavior due to the crack breathing is considered by introducing a ‘moving’ Fourier-series expansion concept to the additional slope. The time-varying harmonic components of the additional slope are used to calculate the harmonic responses. The application considered is a general rotor model composed of multiple shafts, disks and cracks, and resilient bearings at both ends. Verification analysis is carried out for a simple rotor model similar to those found in the literature. Using the additional slope, the cracked rotor behavior is explained by the crack depth and rotation speed increase. It is shown that region on the crack front line having the dominant stress intensity factor value moves from the central area to both ends, as the crack depth increases. The result matches well with the crack propagation pattern shown in a bench mark test in the literature. Whirl orbits near the critical and sub-critical speed ranges of the rotor are discussed. It is shown that there exists some speed range near the critical speed, where the temporary whirl direction reversal and phase shift exist. When an unbalance is applied, the peculiar features, such as the whirl direction reversal and phase shift, disappear.

Influence coefficients on rotor having thick shaft elements and resilient bearings

Timoshenko beam theory is introduced for modelling the behavior of shaft. Complex variables are used to represent the displacement, slope, moment and shear force, and the complex transfer matrix between the variables at both ends of the shaft element is derived and the influence coefficients are analytically derived for the general flexible rotor having two resilient bearings at both ends. Modelling and derivation of the influence coefficients are based on the transfer matrix method. Simulated influence coefficients are compared to the results using the finite element method based on Timoshenko beam theory. Simulation of the influence coefficients could suggest the guideline for determining the positions of the balancing and measuring planes and the running speed.

Free Vibration Analysis of Shafts on Resilient Bearings Using Timoshenko Beam Theory

This paper presents an analytical method adopted for the free vibration analysis of a shaft, both ends of which are supported by resilient bearings. The shaft is modeled by Timoshenko beam theory. Based on this model exact frequency equation to calculate complex eigenvalues is derived and presented in complex compact form for the first time. Explicit expressions to compute the corresponding mode shapes are also presented.

Surface pretreatment of thin inconel X-750 foils for improved coating adherence

Solid lubricant coatings are applied by spraying onto the foil in hydrodynamic resilient bearings; the foil provides the bearing surface. The foil surface should be roughened in order to achieve a good bond with the coatings. Mechanical, chemical and electrolytic treatments designed to roughen the surface were tested. Mechanical means of surface treatment were too severe and distorted the foil; chemical etching could not provide a suitable without loss of mechanical strength. The surfaces could be roughened adequately by electrolytic etching without loss of any mechanical strength. Since the thickness of the oxide layer and of other foreign material varied from piece to piece, some judgment was required as far as etching time was concerned. Metallurgical examinations, tensile tests and fatigue tests on etched foils showed that there was no loss of strength of the foil and that etching roughened the foil surfaces adequately. Generally, the wear life of the coating could be increased considerably by the use of etching before coating.

Floating track slab isolation for railways

Where an underground railway is in existence, it is up to the developer to take what precautions may be necessary to provide an acceptable interior environment. Many a building has been isolated on resilient bearings from the ground-borne vibrations produced by an adjacent railway with the result that the occupants are unaware of the trains running underneath the building. The technique for the resilient mounting of large structures has been well developed, and there is a B.S.I. Draft for Development in which some guidelines have been established. Where a new underground railway is to be constructed close to or under existing properties it may be more expedient to isolate the railway. Several design of a track slab have been constructed, usually with very beneficial effect. Some of these floating track slabs are described in this contribution.