Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.

Trend Prediction Method Based on the Largest Lyapunov Exponent for Large Rotating Machine Equipments

In order to predict electromechanical equipments＇ nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on chaos theory. The predict method of chaos time series and two methods of proposing f and F are dis- cussed. The arithmetic of max prediction time of chaos time series is provided. Aiming at the key part of large rotating mechanical equipments-bearing, used this prediction method the simulation experiment is carried out. The result shows that this method has excellent performance for condition trend prediction.

ON SEVERAL NEW METHODS TO POLAR DECOMPOSITION COMPUTATION

In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decompositioncomputation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis' s method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions.

Rotational Forms of Large Eddy Simulation Turbulence Models:Modeling and Mathematical Theory

In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary.After the derivation of the model,the authors prove some of the mathematical properties coming from the weighted energy estimates,which allow to prove existence and uniqueness of a class of regular weak solutions.

A Kind of Super-parametric Finite Element for Geometric Nonlinear Analysis of Plates and Shells

A new kind of super parametric finite elements for geometric nonlinear analysis of plates and shells is presented.Besides the nodes on the middle surface, additional virtual nodes are used to determine the normal to the middle surface.There are three displacement d.o.f.for each node of the element, and two transverse shear strains are taken as additional independent d.o.f.for each node on the middle surface.Therefore, the element is suitable for large rotation analysis of plates and shells. It can also be easily applied to the analysis of laminated and sandwich shells and plates.Numerical examples are given to show the accuracy and efficiency of the element.