Mathematical model of brush seals for gas turbine engines: A nonlinear analytical solution

Presented herein is a mathematical model employing differential equations formulation for brush seals used in gas turbine engines. These components are used to seal the bearing chamber from the environment and reduce the loss of lubricant in the atmosphere, ensuring a MTBR long enough to have required the change the seals only during the engine overhaul operation. The model assumes a single curved bristle loop in the form of a curved-bridge beam subjected to the influences of complex external loads (static and dynamic). Further, a model for clustered bristles is proposed. Specifically, the static forces acting on the curved-bridge beam include the weight of the oil capillary attached to the beam, the weight of the beam itself, the capillary force developed between the surfaces of the bristles in the brush and the temperature gradient. The dynamic forces include the leakage oil pressure and the rotation of the shaft. This complex loading induces a nonlinear large deflection on the curved-bridge beam. Also, the temperature gradient present on the bristles during the gas turbine engine operation generates a change in the geometry of the beam and in the magnitude of the forces acting on the bristles modeled as beams. In the present model, the weights are assumed as uniformly distributed forces on the surface of the beam while the capillary forces and the force generated by the rotating shaft are considered to be non-uniform. The equation expressing the curvature of the beam under general loading force is developed and one can choose the appropriate method of solving the generated differential equation after the expression of the general force is defined. Hence, the ordinary differential equation describing the nonlinear large deflection of the curved-bridge beam will be derived using general nonlinear elasticity theory.

A Novel Orthogonally Separated Isolation System and Its Seismic Performance on a Curved Concrete Bridge

The seismic response of curved concrete bridges is complex because of the geometric irregularity and induced planar rotation of the deck, which can magnify the displacement of the deck and deformation of the bearings. To control the planar rotation and thus the seismic response of the curved bridge, an orthogonally separated isolation system (OSIS) is proposed, which consists of the upper and lower isolation parts. With this, the planar relative displacement of the common isolation system is decomposed into the relative displacement of the upper part in one direction and the relative displacement of the lower isolation part in the orthogonal direction. Therefore, the planar rotation can be restrained and the seismic demand of the isolation bearing is decoupled. The analytical models of a curved bridge and the OSIS are established in OpenSees. A suite of 118 ground motions, of which 80 are ordinary and 38 are pulse-like, is selected as input with 24 different angles of incidence so as to consider the seismic variation. Nonlinear dynamic time-history analyses of the two models are conducted to evaluate the effectiveness of the OSIS. The results show that the OSIS can effectively decrease the deck displacement, the bearing deformation and the pier column shear force, especially under the ground motions with higher intensities, while the shear force increases slightly on the abutment.

Curved Concrete Slab-On-Steel I-Girder Bridges

A parametric study was conducted, using the finite-element method, to study the load distribution characteristics of curved composite I-girder bridges under truck loading. The influence of several geometric parameters on the moment, and deflection distribution factors, as well as warping stresses in straight and curved composite I-girder bridges was examined. For straight bridges, the moment distribution factors were correlated with those specified in the Canadian Highway Bridge Design Code of 2000, CHBDC. Also the magnitudes of warping stresses in the steel bottom flanges were correlated with the specified limits in bridge codes. The results showed that the CHBDC moment distribution factors significantly overestimate the structural response of straight bridges considered in this study. It was also observed that the curvature limitation specified in the CHBDC to treat a curved bridge of low curvature as a straight one underestimate the structural response.

Curved Concrete Slab-On-Steel I-Girder Bridges

A parametric study was conducted, using the finite-element method, to study the load distribution characteristics of curved composite I-girder bridges under truck loading. The influence of several geometric parameters on the moment, and deflection distribution factors, as well as warping stresses in straight and curved composite I-girder bridges was examined. For straight bridges, the moment distribution factors were correlated with those specified in the Canadian Highway Bridge Design Code of 2000, CHBDC. Also the magnitudes of warping stresses in the steel bottom flanges were correlated with the specified limits in bridge codes. The results showed that the CHBDC moment distribution factors significantly overestimate the structural response of straight bridges considered in this study. It was also observed that the curvature limitation specified in the CHBDC to treat a curved bridge of low curvature as a straight one underestimate the structural response.

Shaking Table Test of High Pier and Small Radius Curved Bridge under Multi-point Excitation

The non-uniform stratum and uneven surface have the complicated seismic spatial variability. The seismic response of high pier and small radius curved bridge caused by the seismic specificity of this kind of terrain has not been systematically studied. According to the multi-point excitation theory of long-span structures and the similar theory of shaking table test in model structures, a high pier with small radius curved girder bridge was used as the research object. The shaking table test of real bridge model was carried out to study the seismic response laws of this kind of bridge under multi-point excitation. The results show that the designed seismic wave expansion device can meet the test requirements. The frequency of the model structure decreases rapidly and the damping ratio increases during the whole test process. The local terrain effect amplifies the seismic response of high pier and small radius curved bridge. The seismic response of high pier and small radius curved bridge is affected by different frequency spectrum seismic waves, and there is a big difference. Based on the above results, the impact of multi-point excitation should be considered in seismic design of high pier with small radius curved bridge.