Chris A. Papadopoulos

CRACK IDENTIFICATION IN FRAME STRUCTURES

Abstract In this paper the problem of crack depth and position identification in frame structures is examined, using eigenfrequency measurements. It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the crack size and position. The basic idea is to present in contour graph form the dependency of the first two structural eigenfrequencies on crack depth and location, using the finite element method. To identify the location and depth of a crack in a frame structure, one only needs to determine the intersecting point of the superposed contours that correspond to the measured eigenfrequency variations caused by the crack presence. A number of beam and frame examples are included in the present paper to verify the applicability of this combined computational-graphical or experimental-graphical method.

Crack identification in rotating shafts by coupled response measurements

In this paper a new method is applied in rotating cracked shafts to identify the depth and the location of a transverse surface crack. A local compliance matrix of different degrees of freedom is used to model the transverse crack in a shaft of circular cross section, based on available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. It is known that when a crack exists in a structure, such as a beam, then the excitation in one-direction causes coupled vibrations in other directions. This property is used here to identify the crack. The shaft is modeled as a rotating Timoshenko beam including the gyroscopic effect and the axial vibration due to coupling. The method used here is based on the measurements of the axial vibration response due to different excitation frequencies and shaft revolutions. The figures presented are used to identify the crack.

Crack identification in beams by coupled response measurements

In this paper a new method for the determination of the depth and the location of a transverse surface crack in a beam is presented. Simulating the crack by a local compliance matrix of six degrees of freedom has been used for crack modelling in the last decade. This matrix contains diagonal and non-diagonal terms, and thus coupling among different modes of vibration occurs. A harmonic force or a moment of known amplitude and frequency is used to dynamically excite the beam. The exciting frequency should be far from a system eigenvalue to avoid the effect of the damping near resonance. Two response measurements at a point are required by the method. The first measurement is taken in the direction of the excitation, while the second one in the direction where coupling effect occurs due to the crack. The crack is considered to always remain open. The identification of the existence of the crack will be shown to be feasible, if a response on a degree of freedom, other than the one of the excitation, exists. A Timoshenko beam finite element of six degrees of freedom per node, is used. This method can be applied in structures in air as well as under water.

Brakes and clutches using ER fluids

Abstract If an electro-rheological (ER) fluid is used in viscous coupling devices, such as clutches or brakes, then the possibility to control the output capacity of this device exists. The imposition of an electric field between the input and output parts alters the viscosity of the fluid and consequently the output torque for brakes or angular velocity for the clutches. In this paper the experimental investigation of a multiple disk electro-rheological viscous device, that can for experimental purposes be used as both brake and clutch, is presented. The device used has 10 pairs of rotating and stationary (or rotated) disks with 1 mm disk spacing. The apparatus is filled with ER fluid and an electric field of 0–2.1 kV\mm is applied. The ER fluid used is zeolite with oil. The input shaft speed can be changed from 0–2400 rpm using a 3 kW variable speed motor. In this paper, the driven shaft with its fixed disks is clamped with the aid of a beam on a spring measuring system in order to measure the resulting torque. As a consequence of this experimental configuration, the energy dissipation is high. As the temperature is increased, the viscosity is decreased. On the other side, as the applied electric field is increased the viscosity is also increased. So properties such as the torque capacity of the device, the wall shear stress and relative viscosity are experimentally determined and presented as functions of the two main parameters, electric field and temperature, as well as the input angular velocity.

Non-linearities in misaligned journal bearings

Abstract An analysis of hydrodynamic Newtonian lubrication for misaligned journal bearings is given. The primary aim of this paper is to model the non-linearities that occur in a hydrodynamic journal bearing in both aligned and misaligned conditions, and to present the non-linear stiffness, damping and hybrid coefficients in the form of diagrams that can be used in a dynamic analysis of journal bearings. The Reynolds equation is solved using the finite element solution technique. A two-dimensional Newton-Raphson method is used to locate the journal equilibrium position from which both linear and non-linear bearing dynamic coefficients are evaluated by means of the small perturbation technique. The bearing dynamic coefficients, linear and non-linear, due to displacements and to rotations for partial arc, and full journal bearings are calculated for various L / D ratios and misalignment conditions. The effects of misalignment on the linear and non-linear plain journal bearing characteristics are analysed and presented.

Torsional vibrations of rotors with transverse surface cracks

The torsional vibrations of a rotor with a transverse crack are investigated. The crack is modelled by way of a local flexibility matrix which is calculated analytically and measured experimentally. Good agreement between the two methods is obtained. The free vibration problem is solved and the three first eigenvalues are plotted versus the crack location and depth. The finite element method is used for the solution of any shaft system with a crack, using a modified stiffness matrix for the cracked element.

Analytical and experimental crack identification of beam structures in air or in fluid

Abstract In this paper a new method for crack identification in beams is presented. The transverse surface crack is considered to remain always open. Using this method the crack location and depth can be determined. The method is based on the basic observation that the eigenmodes of any cracked structure are different from those of the uncracked one. The differences are due to the slope discontinuity of the vibration eigenmodes at the crack location. The basic idea in this paper is to correlate the mode differences with the crack depth and location. These correlated differences are chosen to be (a) the ratio of two amplitude measurements in two positions and (b) the distance of the node of the vibrating mode from the left end, while the structure is vibrating under harmonic excitation in resonant condition. The analytical results presented here are also experimentally proven. In a free-free beam the two first eigenmodes are measured and the node distance of the uncracked and the cracked beam are used in pre-plotted diagrams to verify the crack location and depth. Here, it is also theoretically proved that the above results for the beam are the same in both the air and the water. This is valid irrespective of whether the damping effect is taken into consideration or not.

Modal Analysis of Rotor on Piecewise Linear Journal Bearings Under Seismic Excitation

A rotor bearing system is expected to exhibit large vibration amplitudes when subjected to a large seismic excitation. It is possible that these vibrations can lead to large values the eccentricity of the bearings. Then the bearing is operated in highly nonlinear region because the stiffness and the damping coefficients are nonlinear as functions of the eccentricity. To solve this problem numerical integration must be performed with high cost in computer time. The idea of this paper was to divide the nonlinear area into more areas where the stiffness and damping coefficients could be considered to be constants. In other words the bearing coefficients are considered to be piecewise constant. The excitation due to the earthquake is modelled as a movement of the base of the bearings using the El Centro data for the acceleration. Then a simplified modal analysis for each of these piecewise linear regions can be performed. The equation of motion of the rotor contains rotational speed depended terms, known as gyroscopic terms, and terms due to base excitation. The response and the variation of the dynamic properties of this complicated rotor bearing system are investigated and presented.

HIGH SPEED JOURNAL BEARINGS LUBRICATED WITH ELECTRO-RHEOLOGICAL FLUIDS: AN EXPERIMENTAL INVESTIGATION

It is well known that the imposition of an electric field on an Electro-Rheological (ER) fluid alters the viscosity and as a consequence the f flow properties of the f fluid. If such a fluid is used to lubricate a journal bearing system, it is expected that the imposition of an electric field between the rotor and the stator will cause the alteration of the dynamic properties of the journal bearing. For the present, it has been proved that this is valid only for low speeds and high radial clearances of Couette type viscometers. In this paper an experiment in a high speeds (16000 to 65000 s−1) journal bearing with small radial clearance is presented. The experiment performed has showed the phenomenon and has proved that the ER FLUID at high shear rates under constant temperature, follows the Bingham model in realistic bearings. Properties such as wall shear stress, dynamic yield stress relative viscosity are experimentally determined as functions of the electric field, for different particle concentrations and the shear strain rate under constant or free to vary temperature (due to operating conditions, angular velocity, friction). Concluding the ER fluids can be used to create “smart” journal bearings. Vibration controllers can be constructed to control the stability of the ER fluid lubricated bearings.

Dynamic stability of linear misaligned journal bearings via Lyapunov's direct method

One of the most important problems of rotor-bearing systems, the stability problem, especially in the case that the rotor is in misaligned position in respect with the bearing, is examined in this paper. Lyapunovs direct method was preferred in this analysis instead of a classical eigenvalue analysis in order to obtain the stability conditions in the form of analytical, expressions. The eight dynamic coefficients (four stiffness and four damping) for the aligned, journal bearing or the 32 dynamic coefficients (16 stiffness and, 16 damping) for the misaligned case can be used here, in order to obtain, the analytical stability conditions and the stability charts. The results of the present investigation are compared with the results and. experiments in the literature and are found to be in good agreement. The rigid, rotor model was chosen for work in order to concentrate on the misaligned bearing behavior, thus avoiding the flexible shaft influence on the system. The model used is comprised of a rigid roto...