Cavitation Boundary Conditions Research Articles

Optimization of surface texture distribution on the thrust bearing using the mass-conserving cavitation boundary condition: Theory and experiments

This study developed a numerical optimization model for the texture distribution in thrust bearings, employing the flat-headed chevron and circular dimple, and utilizing a mass-conserving cavitation boundary. A hybrid of the genetic algorithm and sequential quadratic programming algorithm is utilized. The results indicate the highest load-carrying capacity can be obtained by optimizing the texture distribution based on the flat-headed chevron. The primary mechanism is that the optimal distribution can efficiently harness the collective effect of texture, thereby effectively building up pressure. The optimal distributions of the flat-headed chevron and circular dimples exhibit asymmetric chevron and herringbone shapes, respectively. Furthermore, verification experiments show that the optimal distribution can shift the transition point to a lower rotation speed and higher normal load.

Multi-objective optimization of surface texture shape in fluid mechanical face seals using mass-conserving cavitation boundary condition

Surface texture shape significantly influences the tribological and sealing properties of fluid mechanical face seals. Considering that it is a contradiction to simultaneously improve load capacity and reduce leakage, a numerical multi-objective optimization model is proposed herein to improve the load-carrying capacity while reducing the volume leakage rate via texture shape optimization. The mass-conserving cavitating boundary condition and the non-dominated sorting genetic algorithm II are employed for the optimization. The numerical results indicate that the optimal texture shape is spiral-like under the lowest volume leakage rate, which becomes an asymmetric flat-front chevron with increasing load-carrying capacity and volume leakage rate. The optimal shape outperforms four regular shapes (all obtained by multi-objective optimization) at different rotation speeds and sealing pressures. The cavitation within the optimal shape ensures zero leakage in fluid face seals. The comprehensive performance of the texture shape obtained by multi-objective optimization is superior to that obtained by single-objective optimization.

Fusion of Multi-scale Features Seal End Face Fluid Characterization

The composite weaving of dynamic and static ring friction end faces with multi-scale features can improve the sealing performance of mechanical seals, but there is no clear mechanism of weaving action, and it is difficult to optimize seal surface weaving. In this study, a mathematical model is developed to analyze the fluid sealing performance of the composite textured mechanical seal end face with a combination of a 5-sided micro-pit and T-slot according to the mass conservation cavitation boundary condition. The change in sealing performance between the composite texture and single texture in terms of opening force and leakage volume was investigated. Numerical analysis shows that compared with a single texture, the multi-scale texture end face creates a coupling effect between the micro-pit and T-slot, which has a stronger dynamic pressure lubrication effect and improves the sealing performance of the sealing sub-seal with increased pressure. The research results can be applied to the design optimization of mechanical seal surface textures.

Performance analysis of two-dimensional section of partially textured piston ring with cavitation boundary conditions

The lubrication problems for cavitation are solved using the Elrod algorithm/its modifications, which are extremely nonlinear in nature due to binary switch function, lead to convergence issues, consequently, prone to numerical instabilities. In the present study, a continuous switch function is used to avoid these issues, which has not been explored yet for investigating performance behaviours (minimum film thickness, friction force, and power-loss) of piston ring/cylinder liner pair. The modified Reynolds equation is discretized using the Finite Difference Method (FDM). The algebraic equations have been solved by employing the Elrod and Vijayaraghavan-Keith algorithm with a modified switch function proposed by Fesanghary-Khonsari, which satisfies the mass-conservative cavitation. On the other hand, the total computational domain plays a significant role in predicting accurate numerical results. Therefore, in the present investigation, a piston ring segment of 3 mm × 1.20 mm has been investigated, which comprises larger computational domains ever considered in previous studies. The textures are cylindrical and situated at both ends of the piston ring, leaving the center portion untextured in the axial direction. The minimum film thickness change with time (squeeze film action) and lubricant’s (SAE 20W-40 engine oil) viscosity change with operating temperature have been incorporated in the spectrum of this study. The textured piston ring demonstrated an increase up to 7.2% of the minimum film thickness, friction reduction up to 30%, and reduction in power-loss up to 11% compared to the conventional (un-textured) piston ring.

Study on Sealing Performance of Oil Seal with Micro-pores Textured in Rotary Shaft Surface

In order to improve the reliability and the long life cycle of the lip seals, comprehensive consideration of the liquid film cavitation and JFO mass conservation boundary conditions, the geometry model of the oil seal with micro-diamonds textured on the shaft surface is given, and its mathematical model is built, the relevant numerical calculation method is used, eventually that the film pressure distribution and the micro diamond pores structure parameters effect on the seal performance are obtained under the different operating conditions. The results showed that the dynamic pressure effect caused by the diamond pores can make the oil film pressure field between the axial surface and the lip produced regular axial and radial wave change. At the same time, the change of working conditions strengthen or weaken the change law of the oil film pressure field, so which make the reliability of the liquid pressure, lubricating property and pump suction effect also change accordingly. The size, shape and pores direction of the micro-diamonds texture have great influence on the oil seal performance and lubrication characteristics, which can help to reduce the leakage rate, control the pump suction direction, stable the liquid pressure and reduce the friction. In order to improve the stability of the liquid film and pump suction effect, reduce the leakage rate, friction and wear, the axial surface micro-diamond pores texture of which the cone width ratio is 0.4-0.6, the pores depth is 1.5-4.5μm and the tilt angle is 40°-50° shall be selected for the oil seals.

Thermo-elasto-hydrodynamic analysis of triangular textured mechanical face seals

A 3D thermo-elasto-hydrodynamic (TEHD) model is presented to study the effects of triangular dimples on the loadcarrying capacity, leakage and friction of a mechanical seal operated under mixed or full film lubrication conditions. The model is solved by the finite element method (FEM), which takes into account the effects of the Jakobsson-Floberg-Olsson (JFO) cavitation boundary condition, surface roughness, elastic-plastic contact, thermo-elastic deformation, and the temperature-viscosity relation. The numerical results of the TEHD model are quite different from those of the hydrodynamic (HD) and thermo-hydrodynamic (THD) models, especially at high speeds. In order to obtain the optimum shape and distribution of the triangular dimples, a comparative study is conducted to investigate different distributions of equilateral triangles and isosceles right triangles. The results show that a surface textured mechanical seal with isosceles right triangular dimples has the most significant hydrodynamic and pumping effects which, in turn, are beneficial to sealing face opening behavior and leakage limitation. The theoretical results are in good agreement with the experimental ones, and offer new guidance for the future design and development of high-speed mechanical seals for aviation piston pumps.

Analysis of dynamic characteristics of spiral groove liquid film seal considering cavitation

PurposeThe purpose of this paper is to investigate the dynamic characteristics of a spiral groove liquid film seal considering the effect of cavitation.Design/methodology/approachA mathematical model of a spiral groove liquid film seal was established based on the mass-conserving Jakobsson–Floberg–Olsson cavitation boundary condition. The film rupture and film reformation boundaries were assumed to be unchanged under infinitesimal perturbation conditions. Governing equations under steady and perturbed states were solved by the finite element method, and then the dynamic characteristics of the spiral groove liquid film seal were theoretically investigated considering the effect of cavitation.FindingsThe results indicate that dynamic coefficients considering cavitation are smaller than those neglecting cavitation. The difference value is consistent with the change in cavitation area. The liquid film seal does not suffer axial instability whether considering cavitation, but its angular instability is more likely to occur when cavitation is considered.Originality/valueFor liquid lubricated non-contacting mechanical seals, the dynamic characteristics considering cavitation are investigated. The results are expected to provide a theoretical basis for improving the design method of liquid film seals.

Influence of dimple geometry and micro-roughness orientation on performance of textured hybrid thrust pad bearing

The present study deals with numerical simulation of textured hybrid thrust pad bearing. Influence of providing micro-dimples of different cross-sectional shapes on the bearing surface has been theoretically investigated on the performance of thrust pad bearing. Reynolds equation has been solved using mass-conserving algorithm based on Jakobsson–Floberg–Olsson cavitation boundary conditions. A parametric study is carried out to optimize dimple shapes from the viewpoint of load carrying capacity of bearings. The textured bearing surface is noticed to be beneficial in reducing the frictional power losses. Providing half-section dimples (second half in the direction of runner rotation) towards the leading edge of thrust pad, enhance the load carrying capacity and fluid film stiffness coefficient of bearings. Micro-roughness in a textured surface having transverse orientation is seen to improve the dynamic characteristics of hybrid thrust pad bearings.

A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves

• A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves is proposed. • The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. • The method facilitates the accurate calculation of the fluid film force of a journal bearing and saves computational costs. • The effects of the bearing parameters on the nonlinear fluid film forces are analyzed. A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves under the cavitation boundary condition is proposed. The pressure distribution of the Reynolds equation of a finitely long journal bearing with axial grooves is expressed as a particular solution and a homogeneous solution. The particular solution and the homogeneous solution are separated, respectively, into an additive form and a multiplicative form by the method of separation of variables. The circumferential separable function of the homogeneous solution can be expanded on the basis of the infinite series of trigonometric functions. The pressure distribution of the particular solution is obtained by the Sommerfeld transformation. The termination positions of the fluid film are determined by the continuity condition. The analytical expressions for the nonlinear fluid film forces of a finitely long journal bearing with two axial grooves are obtained. The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. The effects of the bearing parameters on the nonlinear fluid film forces are analyzed.

Viscosity wedge effect of dimpled surfaces considering cavitation effect

Abstract A thermohydrodynamic model is developed to study the viscosity wedge effect associated with dimpled surfaces considering the cavitation effects. The Streamline-Upwind/Petrov-Galerkin (SUPG) finite element method was applied to solve the energy and Reynolds equations combined with the Jakobsson–Floberg–Olsson (JFO) cavitation boundary conditions. The performance of a slider surface with an array of dimples are studied and the geometrical parameters of the dimples are optimized for enhancing the load-carrying capacity (LCC) and coefficient of friction (COF). The film pressure and temperature distribution at different conditions are analyzed. The simulation results show that the viscosity wedge effect has a more pronounced influence on the LCC and COF than the cavitation effect. The dimples with dimensionless depth hg/h0 = 0.6 and no more than 25% dimple area ratio are recommended.

The effect of lubricant inertia on fluid cavitation for high-speed squeeze film dampers

This work studies the effect of lubricant inertia on the fluid cavitation for partially sealed high-speed squeeze film dampers (SFDs) executing small amplitude circular-centered orbits (CCOs). The lubricant cavitation is modeled by both the Elrod algorithm and the Gumbel’s cavitation boundary condition to provide the comparison between the most common lubricant cavitation models. Additionally, the fluid inertia is integrated by adapting a finite-length SFD model for partially sealed dampers. The integrated SFD model is incorporated into a numerical simulation model and the results are validated by comparison with experimental data. The results of the analysis demonstrate that the fluid inertia effects significantly extend the cavitation region and influence the cavitation onset and the film reformation.

Study of Separation Characteristics of Micro-groove Rotary Seal Considering Different Cavitation Boundary Conditions

Micro-grooves have superior hydrodynamic characteristics; therefore, the operating state of the micro-groove rotary seals (MGRSs) used in wet clutches of vehicles change from mixed lubrication to full-film hydrodynamic lubrication with increased rotating speed. These transition characteristics of the lubrication state of the MGRS are called “separation characteristics.” However, simultaneously the increase in rotating speed also leads to the cavitation effect. In contrast to the convergent wedge-shaped gap, “negative effects” exist in the diverging gap that lead to the reduction in the hydrodynamic pressure on the sealing end face. When the pressure is less than the cavitation pressure, the oil film undergoes cavitation and then ruptures. Thus, a large cavitation region reduces the bearing capacity of the oil film. Cavitation effects significantly influence the separation characteristics of the MGRS. Here we report on a theoretical model that has been developed through coupling asperity contact, fluid lubrication with micro-grooves and axial motion dynamic characteristics of the seal. Separation characteristics of the MGRS under Reynolds and Jakobsson–Floberg–Olsson (JFO) cavitation boundary conditions are systematically investigated in this study. The results show that pressure distribution and fluid bearing force under the Reynolds cavitation boundary condition are larger than those under the JFO condition, while friction torques are almost the same under both conditions. The cavitation region is observed in experiments and found to become larger with increases in speed. The JFO cavitation boundary condition predicts larger separation speed of the MGRS than does the Reynolds cavitation boundary, and the separation speed predicted by the JFO cavitation boundary condition is significantly closer to the experimental result than that predicted by the Reynolds condition. For the best separation characteristics of the MGRS, selected micro-groove parameters are as follows: N g = 35–40, β = 17–23° and h g = 15–25 μm.

Numerical study on the lubrication performance of compression ring-cylinder liner system with spherical dimples.

The effects of surface texture on the lubrication performance of a compression ring-cylinder liner system are studied in this paper. By considering the surface roughness of the compression ring and cylinder liner, a mixed lubrication model is presented to investigate the tribological behaviors of a barrel-shaped compression ring-cylinder liner system with spherical dimples on the liner. In order to determine the rupture and reformulation positions of fluid film accurately, the Jacoboson-Floberg-Olsson (JFO) cavitation boundary condition is applied to the mixed lubrication model for ensuring the mass-conservative law. On this basis, the minimum oil film thickness and average friction forces in the compression ring-cylinder liner system are investigated under the engine-like conditions by changing the dimple area density, radius, and depth. The wear load, average friction forces, and power loss of the compression ring-cylinder liner system with and without dimples are also compared for different compression ring face profiles. The results show that the spherical dimples can produce a larger reduction of friction in mixed lubrication region, and reduce power loss significantly in the middle of the strokes. In addition, higher reduction percentages of average friction forces and wear are obtained for smaller crown height or larger axial width.

Friction losses modeling of piston rings for various combustion pressures in diesel engine

This paper describes a numerical simulation of the lubrication between the first compression piston ring and the cylinder liner in a typical diesel engine, using the one-dimensional Reynolds equation. The geometric profiles of piston rings are axisymmetric. The inlet boundary is assumed to be fully flooded, but Reynolds cavitation boundary conditions are assumed for the outlet boundary. Cavitation boundaries, frictional forces, friction coefficients, lubrication regimes and power losses are determined for various combustion pressures, which were induced by varying the injection strategy at fixed injection quantity and constant engine speed. Results of the simulation show a dependence of the frictional force on the combustion pressure. Power losses due to the frictional force are obtained as a function of crank angle.

Effect of Surface Roughness on the Pressure Generation in a Finite Rough Hydrodynamic Journal Bearing under Micropolar Lubrication in Steady-State

In hydrodynamic lubrication of journal bearing pressure of the fluid film is generated as a result of the viscous drag of the fluid into the wedge shaped gap between the journal and bearing due to relative motion of the journal with respect to the bearing. The pressure development of fluid is important in this type of lubrication to ensure performance of journal bearing. On the other hand, every surface has some degree of roughness that affects relative motion of the journal bearing system. This paper, thus, aims to present a detailed study of hydrodynamic pressure built up of a journal bearing including the roughness of the surfaces. The modified Reynolds equation is derived on the basis of theory of micropolar lubrication incorporating suitable roughness model. The resulting equation is solved numerically at steady state operating condition using cavitation boundary condition to observe distribution of pressure. The effects of variations in operating variables in terms of characteristic of lubricant and parameters defining roughness model are computed. The analytical results are compared with the available published results to validate the theory and computer code. The numerical result shows that for same geometrical condition maximum pressure developed in micropolar fluid always remain higher than that in Newtonian fluid. The steady state pressure is found to be decreased as the values of the roughness parameters are increased.

The validity of the Reynolds equation in spool valve analysis considering cavitation

Abstract The purpose of this research is to investigate the validity of the Reynolds equation in spool valve analysis under cavitation. This study is carried out for a laminar and isothermal flow between a sleeve and spool with grooves. The pressure and lateral force obtained from the Reynolds equation and the Navier-Stokes equation are compared with variations of aspect ratio, cross sectional area, and number of grooves. The cavitation phenomenon is considered by using a cavitation model in the Navier-Stokes equation and the Reynolds cavitation boundary condition in the Reynolds equation. A large difference of more than 20% is found between the equations for a lateral force of spool valve with many grooves. It was found that the Reynolds equation is not suitable for calculation of a lateral force of the spool valve with multiple-grooves of which the width and depth are even larger than the clearance under cavitation.

Numerical modeling of lubrication of piston ring of two-stroke marine diesel engine considering the effect of multi-scale grooves on the cylinder liner

The method of lubrication for piston ring in some types of low-speed two-stroke marine diesel engines is completely different from those in medium- or high-speed diesel engines since the inner surface of cylinder liners are textured with elliptical grooves in macroscale and honing texture in microscale. In this paper, a numerical model has been developed to study the potential of use of cylinder bore surface texturing, in the form of circumferential oil grooves with different dimensions and densities, to improve the tribological properties of piston ring–cylinder liner tribosystem. The average Reynolds equation has been employed in the area of microscale texture and the effect of macroscale grooves has been incorporated to improve the currently lubrication model. The focus is put on cavitation formation condition and boundary condition in grooves within the area of lubrication, analysis of the effect of macrogroove dimension characters and distribution of grooves on the tribological performance of piston compression ring. The solution provides the hydrodynamic friction force, boundary friction force, coefficient of friction, and the total friction force. The results show that the cylinder liner oil grooves can efficiently be used to maintain hydrodynamic effect. It is also shown that optimum surface texturing may substantially reduce the friction losses between piston ring and cylinder liner.

Mixed-lubrication analysis of marine stern tube bearing considering bending deformation of stern shaft and cavitation

A mixed-lubrication model has been developed to study tribological characteristics of a marine stern tube bearing. The finite difference method is employed to obtain numerical solutions of the Reynolds equation using combined Newton–Raphson and iterative relaxation methods. The differential equation of deflection curve of the propeller shaft is used to describe the bending deformation of propeller shaft. The displacement superposition method is used to solve the differential equation of deflection. The influences of cavitation and different boundary conditions, the Reynolds boundary condition and Jacobsson–Floberg and Olsson (JFO) boundary condition, as well as the bending deformation of shaft, on the Stribeck Curves are discussed in this paper.

Modeling of a Grooved Parallel Bearing with a Mass-Conserving Cavitation Algorithm

Several load-supporting mechanisms have been studied to deal with the cavitation problem in parallel bearings. The formation of cavities and their disposition affect the pressure generated in a continuous thin film and hence the load capacity of bearings. In solving the Reynolds equation, proper cavitation boundary conditions must be applied. In this article, the mass-conserving Vijayaraghavan-Keith cavitation algorithm is utilized to analyze the hydrodynamic lubrication performance of parallel bearings with one or more grooves. Using the finite difference method, a one-dimensional Reynolds equation is discretized. Gauss-Seidel iteration is used to solve the obtained set of linear algebraic equations. For a given lubricant, sliding speed, and minimum film thickness, several comparative studies are made between the Vijayaraghavan-Keith cavitation algorithm and a published analytic solution. Several factors affecting the hydrodynamic lubrication performance are considered, such as cavitation pressure, inlet length, groove number, and textured pattern. The analysis results validate the Vijayaraghavan-Keith cavitation algorithm. It is found that the Vijayaraghavan-Keith algorithm is not sensitive to the textured groove depth. In addition, inlet roughness, inlet suction, and quasi-antisymmetric integration are identified to be the essential features that generate hydrodynamic pressure in parallel bearings.

Comparison of Mobility Method and Mass Conservation Method in a Study of Dynamically Loaded Journal Bearings

The inverse problem of dynamically loaded journal bearings was solved using generalized Reynolds equation coupled with a complete mass conservative cavitation boundary conditions, as outlined by the Jacobsson-Floberg and Olsson (JFO) cavitation theory. In the course of solution, the modi®ed Thomas algorithms was employed, instead of standard Gauss±Jordan reduction method, which fully utilizes the sparse character of the system matrix, and thus greatly reduces computational time. The developed model was tested against the well-known mobility method for the case of journal bearings in a commercial reciprocating air compressor. It was found that the mobility method overestimates minimum ®lm thickness and underestimates such parameters as lubricant ow rate and bearing power loss. In general, the level of error is acceptable for most industrial applications. However, for the journal bearing where the feed pressure is time dependent and starvation e€ects are predominant, the mobility method may produce large not acceptable errors.