Unified Coordinate System Model for Performance Calculation of Fix-pad Journal Bearing with Different Pad Preload

Traditional model for calculating performance parameters of a fix-pad journal bearing leads to heavy workload, complicated and changeable formulae as it requires deriving various geometric formulae with different bearing types such as circular journal bearing, dislocated bearing and elliptic bearing. Considering different pad preload ratios for non-standard bearing, traditional model not only becomes more complicated but also reduces scalability and promotion of the calculation programs. For the complexly case of traditional model while dealing with various fix-pad journal bearings, unified coordinate system model for performance calculation of fix-pad journal bearing is presented in the paper. A unified coordinate system with the bearing center at the origin is established, and the eccentricity ratio and attitude angle of axis relative to each pad are calculated through the coordinates of journal center and each pad center. Geometric description of fix-pad journal bearing is unified in this model, which can be used for both various standard bearing and non-standard bearing with different pad preload ratios. Validity of this model is verified with an elliptical bearing. Performance of a non-standard four-leaf bearing with different pad preload ratios is calculated based on this model. The calculation result shows that increasing preload ratio of the pad 1 and keeping that of the left three pads constant improves bearing capacity, stiffness and damping coefficients. This research presents a unified coordinate system model unifies performance calculation of fix-pad journal bearings and studied a non-standard four-leaf bearing with different pad preload ratios, the research conclusions provides new methods for performance calculation of fix-pad journal bearings.

The Unified Coordinate System in Computational Fluid Dynamics

A fundamental issue in CFD is the role of coordinates and,in particular,the search for“optimal”coordinates.This paper reviews and generalizes the recently developed unified coordinate system(UC).For one-dimensional flow,UC uses a material coordinate and thus coincides with Lagrangian system.For two-dimensional flow it uses a material coordinate,with the other coordinate determined so as to preserve mesh othorgonality(or the Jacobian),whereas for three-dimensional flow it uses two material coordinates,with the third one determined so as to preserve mesh skewness(or the Jacobian).The unified coordinate system combines the advantages of both Eulerian and the Lagrangian system and beyond.Specifically,the followings are shown in this paper.(a)For 1-D flow,Lagrangian system plus shock-adaptive Godunov scheme is superior to Eulerian system.(b)The governing equations in any moving multi-dimensional coordinates can be written as a system of closed conservation partial differential equations(PDE)by appending the time evolution equations–called geometric conservation laws–of the coefficients of the transformation(from Cartesian to the moving coordinates)to the physical conservation laws;consequently,effects of coordinate movement on the flow are fully accounted for.(c)The system of Lagrangian gas dynamics equations is written in conservation PDE form,thus providing a foundation for developing Lagrangian schemes as moving mesh schemes.(d)The Lagrangian system of gas dynamics equations in two-and three-dimension are shown to be only weakly hyperbolic,in direct contrast to the Eulerian system which is fully hyperbolic;hence the two systems are not equivalent to each other.(e)The unified coordinate system possesses the advantages of the Lagrangian system in that contact discontinuities(including material interfaces and free surfaces)are resolved sharply.(f)In using the UC,there is no need to generate a body-fitted mesh prior to computing flow past a body;the mesh is automatically generated by the flow.Numerical examples are given to confirm these properties.Relations of the UC approach with the Arbitrary-Lagrangian-Eulerian(ALE)approach and with various moving coordinates approaches are also clarified.

T-duality as permutation of coordinates in double space

We introduce the 2D dimensional double space with the coordinates Z^M=（x~μ,y_μ）,whose components are the coordinates of initial space x~μ and its T-dual y_μ.We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates x^a,along which we want to perform T-duality,and the corresponding dual coordinates y_a.In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group.So,in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.

Numerical Study of the Unsteady Aerodynamics of Freely Falling Plates

The aerodynamics of freely falling objects is one of the most interesting flow mechanics problems.In a recent study,Andersen,Pesavento,and Wang[J.Fluid Mech.,vol.541,pp.65-90(2005)]presented the quantitative comparison between the experimental measurement and numerical computation.The rich dynamical behavior,such as fluttering and tumbling motion,was analyzed.However,obvious discrepancies between the experimental measurement and numerical simulations still exist.In the current study,a similar numerical computation will be conducted using a newly developed unified coordinate gas-kinetic method[J.Comput.Phys,vol.222,pp.155-175(2007)].In order to clarify some early conclusions,both elliptic and rectangular falling plates will be studied.Under the experimental condition,the numerical solution shows that the averaged translational velocity for both rectangular and elliptical plates are almost identical during the tumbling motion.However,the plate rotation depends strongly on the shape of the plates.In this study,the details of fluid forces and torques on the plates and plates movement trajectories will be presented and compared with the experimental measurements.