Resonance phenomena of an elastic ring under a moving load

This study investigates the response of a circular ring under a moving load. Past work on shells under the influence of moving loads is consolidated, with explanation of the formation of the unique quasi-stationary mode shapes, which are seen under these conditions. This work presents an alternate method of solution for problems for which moving loads are present and encourages distinguishing between normal mode shape methods and the solution methods for the proposed quasi-stationary resonance problems. This alternate method is then followed through to a general solution for quasi-stationary mode shapes, with specific solutions presented for the following three cases: magnitude-varying moving point load, phase varying moving point load and a non-uniform continuous moving load, all applied to a stationary ring

The Effect of Distribution for a Moving Force

Many types of slender or thin walled structures experience forces which traverse across them. For example: vehicles passing over a bridge, overhead crane operations and liquid "slug" movement in spanning pipelines. This moving force can initiate a large dynamic stress within the structure and is often important for assessing structural fatigue. For many of these force/structure scenarios, modelling of the force as a concentrated point force would be an adequate simplifying approximation. In some cases, however, it may not be appropriate to simplify the distributed force into a single point force. For instance, slug lengths in pipelines can be significant in relation to span lengths. There is currently no guidance in the literature regarding the distribution effect of the force on the response of a structure under a moving force. This paper investigates the dynamic response of an elastic, simply supported beam under the influence of a moving distributed force, with varying distribution to span length ratios. In addition, it examines the speed of the traversing force, which is also highly influential on the dynamic response of the beam. This investigation is undertaken using an explicit transient dynamic finite element formulation of a simply supported beam. Guidelines are provided to discriminate between those scenarios when it is appropriate to simplify a distributed moving force as a concentrated force, and those when it must be modelled as the original distributed force

Estimation of Turbine Blade Natural Frequencies from Casing Pressure and Vibration Measurements

Non-contact measurement of gas turbine rotor blade vibration is a non-trivial task, with no method available which achieves this aim without some significant draw-backs. This paper presents a truly non-contact method to estimate rotor blade natural frequencies from casing vibration measurements at a single engine operating speed. An analytical model is derived to simulate the internal casing pressure in a turbine engine including the effects of blade vibration on this pressure signal. It is shown that the internal pressure inside a turbine contains measureable information about the rotor blade natural frequencies and in-turn the casing vibration response also contains this information. The results presented herein show the residual, pressure and casing vibration, spectrum can be used to determine the rotor blade natural frequencies with validation provided for the analytical model by experimental measurements on a simplified test rig. A simulated blade fault in one of the rotor blades is introduced with successful estimation of the simulated faulty blade natural frequency

Relationship between the pressure at the casing wall and at the blade tip for a vibrating turbine blade

A recent research program has identified the possibility of using the analysis of casing wall pressures in the indirect measurement of gas turbine rotor blade vibration amplitudes [1]. Analytical modelling of the casing wall pressures and reconstruction of rotor blade vibration amplitudes from the analysis of these simulated pressure signals have shown potential advantages over current non-contact rotor blade vibration measurement methods. However, the modelling made some fundamental assumptions about the casing wall pressure. One of the assumptions made was that the pressure at the blade tip is not significantly different from that measured across the clearance gap at the casing wall. This fluid-structure hypothesis is investigated in this paper. Unsteady computational fluid dynamic modelling of the flow conditions around the blade surface, combined with the blade structural motion, is performed numerically, and the distributions of the pressure across the rotor blade tip and casing clearance gap are investigated and reported

Gas turbine blade natural frequency measurement using external casing vibrations

Currently tip timing methods are the pseudo industry standard for measuring Gas Turbine blade vibration. The physical placement of tip timing probes is however reasonably prohibitive due to the high pressure/temperature environment of a turbine. A simpler method of sensor setup would be through the use of externally mounted accelerometers to measure the casing vibration response and relate this back to the internal blade vibration.The vibration of a gas turbine casing is driven by the strong rotating pressure which develops around the rotating blade stages. The oscillating motion of the rotor blades phase modulates this pressure signal. An analytical formulation of the internal pressure signal is developed in this paper. The effects of blade motion on this internal pressure signal is then investigated as the speed of the engine is increased/decreased such that the driving frequency traverses a rotor blade natural frequency. Experimental measurements on a simplified test turbine are presented comparing the results of the analytical internal pressure signal along with results of the measured casing vibration during engine run up/down. It is shown that the spectrum of the internal pressure and casing vibration signal contains information which can be used to estimate the rotor blade natural frequencies

Computational Fluid Dynamic Analysis of a Vibrating Turbine Blade

This study presents the numerical fluid-structure interaction (FSI) modelling of a vibrating turbine blade using the commercial software ANSYS-12.1. The study has two major aims: (i) discussion of the current state of the art of modelling FSI in gas turbine engines and (ii) development of a “tuned” one-way FSI model of a vibrating turbine blade to investigate the correlation between the pressure at the turbine casing surface and the vibrating blade motion. Firstly, the feasibility of the complete FSI coupled two-way, three-dimensional modelling of a turbine blade undergoing vibration using current commercial software is discussed. Various modelling simplifications, which reduce the full coupling between the fluid and structural domains, are then presented. The one-way FSI model of the vibrating turbine blade is introduced, which has the computational efficiency of a moving boundary CFD model. This one-way FSI model includes the corrected motion of the vibrating turbine blade under given engine flow conditions. This one-way FSI model is used to interrogate the pressure around a vibrating gas turbine blade. The results obtained show that the pressure distribution at the casing surface does not differ significantly, in its general form, from the pressure at the vibrating rotor blade tip

Low cost remote data acquisition system

Remote data acquisition (RDAQ) is required in a number of vibration and noise measurement settings. Specialised systems exist for RDAQ, however they require significant investment to set up. This paper describes a low cost method of RDAQ which utilises a laptop computer, data acquisition system and a USB internet dongle. The system described in this paper would allow a professional vibration/noise measurement specialist to modify their existing data acquisition system for remote use with minimal cost. The system was tested both in an industrial and an academic setting for verification

A review of major centrifugal pump failure modes with application to the water supply and sewerage industries

Centrifugal pumps are one of the world?s most widely used type of pump, having an extensiverange of applications, from food processing to water or sewage transportation. Problems that arisewithin these machines decrease the flow of the fluid within the pipelines, thus interrupting theproduction and transport of the fluid to its destination within the process. This may lead to other partsof the process system slowing down or behaving undesirably. As a result, it is imperative that thesepumps be correctly monitored, diagnosed, maintained or replaced prior to the pump failing catastrophically to reduce downtime, material cost, and labour costs. This paper reviews the major faultmodes that are found in centrifugal pumps, especially those in the water and sewage industry. Attentionis given to the nature of the faults, symptoms shown within the pump that could be utilised for specificfault detection and diagnosis, and any mechanical corrective procedures that exist to help alleviate theproblem. In addition, this paper contains a comparison and critique of previously published work thathas attempted to diagnose the fault modes of centrifugal pumps

A vibration cavitation sensitivity parameter based on spectral and statistical methods

Cavitation is one of the main problems reducing the longevity of centrifugal pumps in industry today. If the pump operation is unable to maintain operating conditions around the best efficiency point, it can be subject to conditions that may lead to vaporisation or flashing in the pipes upstream of the pump. The implosion of these vapour bubbles in the impeller or volute causes damaging effects to the pump. A new method of vibration cavitation detection is proposed in this paper, based on adaptive octave band analysis, principal component analysis and statistical metrics. Full scale industrial pump efficiency testing data was used to determine the initial cavitation parameters for the analysis. The method was then tested using vibration measured from a number of industry pumps used in the water industry. Results were compared to knowledge known about the state of the pump, and the classification of the pump according to ISO 10816

Separation of Excitation Forces from Simulated Gas Turbine Casing Response Measurements

Condition monitoring of blades within gas turbines has been and will continue to be of importance in all areas of their use, for maintenance and reliability purposes. Non-intrusive measurement of blade condition is the ambition of most techniques for this endeavour, with a number of methods proposed, investigated and employed for such measurement, with the current dominant method using proximity probes to measure blade arrival time for subsequent processing. It is proposed, however, that the measurement of the casing vibration, due to the aerodynamic-structural interaction within a gas turbine, could provide a means of blade condition monitoring and modal parameter estimation, without requiring perforation of the casing. An analytical model of a gas turbine casing and simulated pressure signal associated with the rotating blades, individual blade vibrations and transfer of stator blade vibrations has been developed in order to understand the complex relationship between casing response and the most important excitation forces. Due to the force interaction being through a fluid medium, a certain degree of randomness is introduced into the excitations, and the viability of this inherent randomness as a useful aid for separation of the contributing excitation forces from the system response is explored