STATIC AND DYNAMIC ANALYSIS OF TWO–LOBE FLOATING BUSH BEARING IN TURBULENT REGIME WITH NON–NEWTONIAN LUBRICANTS\ud

Modern large capacity turbo generators usually produce power in a range of 500–1200 MW running at 3000/3600 rpm. These turbo generators use rotor bearings which have diameter of 0.50m or more, leading to high journal surface speeds. The flow behaviour of the lubricant used in these bearings is in the super laminar regimes. In the published literature, Reynolds number as high as 7500 have already been reported. Still higher trends for Reynolds number are expected for larger turbo generators likely to be used in future. Further, to improve the characteristics of lubricants, the additives are added for specific engineering requirements. The viscosity of these lubricants having additives is not constant and usually some nonlinear relation between the shear stress and shear strain rate is found. In the field of hydrodynamic lubrication no significant progress has been made to find the performance characteristics of bearings using non-Newtonian lubricant due to difficulties involved in analytical treatment.\ud In high speed applications, where stiffness and stability are major considerations, non-circular bearings (two-lobe, three-lobe etc.) are used. The non-circular bearing configuration, in general, gives better dynamic stability, reduced power loss and also provides larger oil flow as compared to plain journal bearing.\ud The floating-bush bearings have definite advantage compared to the conventional journal bearings. The purpose of the ring is to reduce the shear losses by decreasing the relative speed between the matting surfaces.\ud In the present work, static and dynamic performance characteristics of two-lobe floating bush bearing operating in turbulent regime using non-Newtonian lubricants have been studied.\ud The modified Navier-Stokes equations along with the continuity equation in cylindrical co-ordinates, representing the flow-field in the clearance space of hydrodynamic journal bearing, are solved by Finite Element Method applying the Galerkin’s technique to obtain the bearing characteristics. A three-dimensional isoparametric element using 20 nodes for velocity and 8 nodes for pressure are used. The quadratic shape function for velocity distribution and linear for pressure distribution is employed to solve the Navier-Stokes and continuity equations. Mixed type of formulation for the interpolation function has been adopted for generating the element matrix as well as global fluidity matrix.\ud To obtain a solution for non-Newtonian lubricant, firstly the three dimensional momentum and continuity equations for Newtonian lubricant are solved and then the solution is upgraded iteratively. The non-Newtonian effect is incorporated in each iteration by modifying the viscosity term using the cubic shear stress law and power law model. The nodal pressure and velocity components obtained for the Newtonian case is taken as initial trial solution for the non-Newtonian models. The shear strain rate for the respective non-Newtonian model is computed at each gaussian integration point for every element of the positive pressure fluid film region. The Newton-Raphson method has been used to compute the value of shear stress. The non-linear theory proposed by Elrod and Ng has been used to compute the turbulent viscosity coefficient. A direct iteration scheme with nested iteration is used first to upgrade the viscosity term and then to upgrade the local shear stress. The iterations are continued till the convergence criteria is achieved or the number of iteration exceeds a prescribed limit.\ud As both the turbulence lubrication theory as well as the non-Newtonian lubricant models are non-linear, successive iterative scheme is used for computing the bearing characteristics. The static and dynamic characteristics are computed at various eccentricities over a range of Reynolds number up to 12000. The results for laminar condition are also obtained.\ud A computer software in FORTRAN has been developed for computing the various static and dynamic characteristics of the bearing.\ud Static characteristics of two-lobe floating bush bearing in terms of load carrying capacity, attitude angle, axial oil flow, friction coefficient and temperature rise parameter are computed for various Reynolds numbers in turbulent regime using both non-Newtonian models.\ud Dynamic characteristics of the bearing in terms of four stiffness coefficients and four damping coefficients are calculated for various Reynolds numbers. The dynamic stability characteristics in terms of critical journal mass is also computed using routh's criteria.\ud The results obtained revealed better performance in turbulent regime as compared to laminar condition for both non-Newtonian models. Two-lobe floating bush bearing has better dynamic stability in comparison to circular floating bush bearing.\u