Christos I. Papadopoulos

Geometry Optimization of Textured Three-Dimensional Micro- Thrust Bearings

This paper presents an optimization study of the geometry of three-dimensional micro-thrust bearings in a wide range of convergence ratios. The optimization goal is the maximization of the bearing load carrying capacity. The bearings are modeled as micro-channels, consisting of a smooth moving wall (rotor), and a stationary wall (stator) with partial periodic rectangular texturing. The flow field is calculated from the numerical solution of the Navier-Stokes equations for incompressible isothermal flow; processing of the results yields the bearing load capacity and friction coefficient. The geometry of the textured channel is defined parametrically for several width-to-length ratios. Optimal texturing geometries are obtained by utilizing an optimization tool based on genetic algorithms, which is coupled to the CFD code. Here, the design variables define the bearing geometry and convergence ratio. To minimize the computational cost, a multi-objective approach is proposed, consisting in the simultaneous maximization of the load carrying capacity and minimization of the bearing convergence ratio. The optimal solutions, identified based on the concept of Pareto dominance, are equivalent to those of single-objective optimization problems for different convergence ratio values. The present results demonstrate that the characteristics of the optimal texturing patterns depend strongly on both the convergence ratio and the width-to-length ratio. Further, the optimal load carrying capacity increases at increasing convergence ratio, up to an optimal value, identified by the optimization procedure. Finally, proper surface texturing provides substantial load carrying capacity even for parallel or slightly diverging bearings. Based on the present results, we propose simple formulas for the design of textured micro-thrust bearings.

Computational Fluid Dynamics Thermohydrodynamic Analysis of Three-Dimensional Sector-Pad Thrust Bearings With Rectangular Dimples

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of computational fluid dynamics (CFD) simulations, based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth, and texture density on the bearing performance indices (load carrying capacity, friction torque, and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

Evolutionary Optimization of Micro- Thrust Bearings With Periodic Partial Trapezoidal Surface Texturing

An optimization study of trapezoidal surface texturing in slider micro-bearings, via Computational Fluid Dynamics (CFD), is presented. The bearings are modeled as microchannels, consisting of a moving and a stationary wall. The moving wall (rotor) is assumed smooth, while part of the stationary wall (stator) exhibits periodic dimples of trapezoidal form. The extent of the textured part of the stator, and the dimple geometry are defined parametrically; thus, a wide range of texturing configurations is considered. Flow simulations are based on the numerical solution of the Navier-Stokes equations for incompressible isothermal flow. To optimize the bearing performance, an optimization problem is formulated, and solved by coupling the CFD code with an optimization tool based on genetic algorithms and local search methods. Here, the design variables define the bearing geometry, while load carrying capacity is the objective function to be maximized. Optimized texturing geometries are obtained for the case of parallel bearings, for several numbers of dimples, illustrating significant load carrying capacity levels. Further, these optimized texturing patterns are applied to converging bearings, for different convergence ratio values; the results demonstrate that, for small and moderate convergence ratios, substantial increase in the load carrying capacity, in comparison to smooth bearings, is obtained. Finally, an optimization study performed at a high convergence ratio shows that, in comparison to the parallel slider, the optimal texturing geometry is substantially different, and that performance improvement over smooth bearings is possible even for steep sliders.© 2010 ASME

Performance comparison between textured, pocket, and tapered-land sector-pad thrust bearings using computational fluid dynamics thermohydrodynamic analysis

Different geometry patterns of the surface of thrust bearings have been proven very beneficial in terms of bearing load-carrying capacity and friction coefficient. In this study, four different types of sector-pad thrust bearings have been cross-evaluated for operation under realistic operating conditions: (a) an open pocket bearing, (b) a closed pocket bearing, (c) a tapered-land bearing, and (d) a bearing partially textured with rectangular dimples. Bearing performance has been computed by means of computational fluid dynamics simulations based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Conjugate heat transfer at the bearing pad and rotor has been taken into account. Initially, for a reference design of each bearing, the effects of varying rotational speed and minimum film thickness have been investigated. Further, characterization of each bearing for a constant level of thrust load has been performed. Finally, the effects of varying the depth of each geometry pattern have been studied. The present results illustrate a superior performance of the open pocket bearing in comparison to the other bearing types.

Evolutionary Optimization of Micro-Thrust Bearings With Periodic Partial Trapezoidal Surface Texturing

An optimization study of trapezoidal surface texturing in slider micro-bearings, via computational fluid dynamics (CFD), is presented. The bearings are modeled as microchannels, consisting of a moving and a stationary wall. The moving wall (rotor) is assumed smooth, while part of the stationary wall (stator) exhibits periodic dimples of trapezoidal form. The extent of the textured part of the stator and the dimple geometry are defined parametrically; thus, a wide range of texturing configurations is considered. Flow simulations are based on the numerical solution of the Navier‐Stokes equations for incompressible isothermal flow. To optimize the bearing performance, an optimization problem is formulated and solved by coupling the CFD code with an optimization tool based on genetic algorithms and local search methods. Here, the design variables define the bearing geometry, while load carrying capacity is the objective function to be maximized. Optimized texturing geometries are obtained for the case of parallel bearings for several numbers of dimples, illustrating significant load carrying capacity levels. Further, these optimized texturing patterns are applied to converging bearings for different convergence ratio values; the results demonstrate that, for small and moderate convergence ratios, a substantial increase in load carrying capacity, in comparison to smooth bearings, is obtained. Finally, an optimization study performed at a high convergence ratio shows that, in comparison to the parallel slider, the optimal texturing geometry is substantially different, and that performance improvement over smooth bearings is possible even for steep sliders. DOI: 10.1115/1.4001990

CFD THERMOHYDRODYNAMIC ANALYSIS OF 3-D SECTOR-PAD THRUST BEARINGS WITH RECTANGULAR DIMPLES

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of Computational Fluid Dynamics (CFD) simulations, based on the numerical solution of the Navier-Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth and texture density on the bearing performance indices (load carrying capacity, friction torque and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

Characterization of Stiffness and Damping in Textured Sector Pad Micro Thrust Bearings Using Computational Fluid Dynamics

In the present paper, a study of stiffness and damping in sector-pad micro thrust bearings with artificial surface texturing is presented, based on computational fluid dynamics (CFD) simulations. The bearing pads are modeled as consecutive three-dimensional independent microchannels, each consisting of a smooth rotating wall (rotor) and a partially textured stationary wall (stator). CFD simulations are performed, consisting in the numerical solution of the Navier–Stokes equations for incompressible isothermal flow. The goal of the present study is to characterize the dynamic behavior of favorable designs, identified in previous optimization studies, comprising parallel and convergent thrust bearings with rectangular texture patterns. To this end, a translational degree of freedom (DOF) along the thrust direction and a rotational (tilting) DOF of the rotor are considered. By implementing appropriate small perturbations around the equilibrium (steady-state) position and processing the simulation results, the stiffness and damping coefficients of the bearing are obtained for each DOF. The computed dynamic coefficients of textured thrust bearings are compared to those of conventional (smooth slider) designs. It is found that the dependence of bearing stiffness and damping on geometrical parameters exhibits the same trends for both DOFs. Both stiffness and damping are found to increase with bearing width. In general, increasing the bearing convergence ratio results in increased bearing stiffness and decreased damping. Finally, the present results demonstrate that properly textured parallel sliders are characterized by an overall dynamic performance that is superior to that of smooth converging sliders.

Developing Pod Over the Complex Plane to Form a Data Processing Tool for Finite Element Simulations of Steady State Structural Dynamics

To analyze the steady state response of structural dynamical systems with multi-field response (example, Timoshenko shearable rod) given complex-valued databases (finite element simulations of complexified equations of motion), we have developed a Complex Proper Orthogonal Decomposition (CPOD) transform. Like the regular multi-field POD, the development of the C-POD is based on the primitive space and frequency auto-correlation operations. These data fusion operations give rise to complex Hermitian operators whose solution determines the C-POD transform. The eigen-values of the complex Hermitian operators are strictly positive and it is shown that they represent the energy fractions of the auto-correlation energy contained in the POD modes. The POD modes have both amplitudes and shapes that are complex-valued scalar functions. The C-POD transform is verified by applying it to characterize the finite element simulations of the steady state dynamics of planar beams and arches. It turns out that the real part of the shape of a POD mode coincides with the shape of the linear POD; whereas its amplitude is a localized function of frequency at a critical frequency which is identical to a natural frequency.Copyright

Geometry Optimization of Textured 3-D Micro-Thrust Bearings

The paper presents an optimization study of the geometry of three-dimensional micro-thrust bearings, in a wide range of convergence ratios. The optimization goal is the maximization of the bearing load carrying capacity. The bearings are modeled as microchannels, consisting of a smooth moving wall (rotor), and a stationary wall (stator) with partial periodic rectangular texturing. The flow field is calculated from the numerical solution of the Navier-Stokes equations for incompressible isothermal flow; processing of the results yields the bearing load capacity and friction coefficient. The geometry of the textured channel is defined parametrically for several width-to-length ratios. Optimal texturing geometries are obtained by utilizing an optimization tool based on genetic algorithms, which is coupled to the CFD code. Here, the design variables define the bearing geometry and convergence ratio. To minimize the computational cost, a multi-objective approach is proposed, consisting in the simultaneous maximization of the load carrying capacity and minimization of the bearing convergence ratio. The optimal solutions, identified based on the concept of Pareto dominance, are equivalent to those of single-objective optimization problems at different convergence ratio values. The present results demonstrate that the characteristics of the optimal texturing patterns depend strongly on both the convergence ratio and the width-to-length ratio. Further, the optimal load carrying capacity increases at increasing convergence ratio, up to an optimal value, identified by the optimization procedure. Finally, proper surface texturing provides substantial load carrying capacity even for parallel or slightly diverging bearings. Based on the present results, we propose simple formulas for the design of textured micro-thrust bearings.Copyright

Piston ring performance in two-stroke marine diesel engines: Effect of hydrophobicity and artificial surface texturing on power efficiency

In the present work, an algorithm for the solution of the Reynolds equation incorporating the Elrod–Adams cavitation model and appropriately modified to account for hydrophobic surfaces has been developed and solved by means of the finite difference method. The algorithm has been utilized to calculate the frictional characteristics of piston rings of a large two-stroke marine diesel engine, and to evaluate their performance, in terms of minimum film thickness, friction force, and power loss over a full-engine cycle, including time-dependent phenomena. For improving frictional behavior, two surface treatments of the piston ring surface have been studied, namely hydrophobicity and artificial surface texturing, which are introduced at appropriate parts of the ring face. Following a parametric analysis, optimal texturing and hydrophobicity design parameters have been identified for operation with maximum value of minimum film thickness and minimum friction losses. The present results demonstrate that substantial performance improvement can be achieved if hydrophobicity or artificial surface texturing is properly introduced at the faces of a piston ring.