For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor a. Therefore, the Arrhenius equation is widely used due to its simple for...For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor a. Therefore, the Arrhenius equation is widely used due to its simple form and often leads to suitable results. Where, the Arrhenius equation presents a linear relation for the temperature-dependent shift factor in logarithmic scale ln（α） with the absolute inverse temperature （1/θ）. However, in cases with a large temperature range which eventually include more complex reaction processes, the functional relation between ln（α） and （1/θ） is nonlinear in the ＇Arrhenius plot＇. In those cases, the monotone change of the nonlinear range in the ＇Arrhenius plot＇ can be interpreted as a transient range between two approximately linear or constant regions. An extended application of the modified Arrhenius equation from Nakamura （1989） is presented in this study for this transient range. The introduced method was applied to describe the time-temperature equivalence in the relaxation analysis of restoring seal force of metal seals, which are used in lid-systems of transport and interim storage casks for radioactive materials. But, the method is widely valid and can be used for different objectives which are characterized by thermorheologically simple behavior with nonlinear sensitivity to inverse temperature.展开更多
Since the beginning of the 20th century, many researches on the sealing characteristic of mechanical seals were carried out broadly and in depth by various methods and some leakage models were built. But due to the la...Since the beginning of the 20th century, many researches on the sealing characteristic of mechanical seals were carried out broadly and in depth by various methods and some leakage models were built. But due to the lack of the way to characterize the main factors of influence on the leakage, most of the early researches were based on the assumptions that the seal faces topography and the frictional conditions were invariant. In the early built models, the effect of the surface topography change of the seal face on the leakage rate was neglected. Based on the fractal theory, the contact of end faces of the rotary and stationary rings was simplified to be the contact of a rough surface and an ideal rigid smooth surface, and the contact interface＇s cavity size-distribution function as well as the fractal characteristic of the cavity profile curve was discussed. By analyzing the influence of abrasion on the seal face topography and the leakage channel, the time-correlation leakage prediction model of mechanical seals based on the fractal theory was established and the method for predicting the leakage rate of mechanical seals with parallel plane was proposed. The values of the leakage rate predicted theoretically are similar to the measured values of the leakage rate in the model test and in situ test. The experimental results indicate that the leakage rate of mechanical seals is a transient value. The surface topography of the end faces of the seal tings and its change during the frictional wear of mechanical seals can be accurately characterized by the fractal parameters. Under the work conditions of changeless frictional mechanism, the fractal parameters measured or calculated based on the accelerated testing equation can be used to predict the leakage rate of mechanical seal in service. The proposed research provides the basis for determining the leakage state and predicting working life of mechanical seal.展开更多
Heat generated by friction between faces of mechanica l seals is a major factor that causes deterioration of the seals and shortens th eir service life. Excessive temperature rise can greatly alter the seal geometry a...Heat generated by friction between faces of mechanica l seals is a major factor that causes deterioration of the seals and shortens th eir service life. Excessive temperature rise can greatly alter the seal geometry and vaporize the sealing fluid, resulting in friction of boundary lubrication. These effects on face seals usually lead to excessive leakage and ultimately ren der the seal inoperable. In order to maintain the reliability of seals, high fri ction and unwanted wear must be avoided. Using the laser-texturing process to produce regular micro-surface structures is a fast and convenient technique compared to some more conventional etching or erosion technique currently used by the seal industry for various grooved face seals. Indeed, by using a pulse laser, better control is obtained on the geometr y, size and pore ratio of seal rings made of metallic or ceramic materials. In t his study, seal rings are made of silicon carbide and carbon. Mating faces of th e rings are polished and only silicon carbide rings are laser-textured. The las er texturing can be controlled to produce spherical pores at selected diameters, depths and pore ratio. The textured rings are then super-polished to remove th e bulges formed on the pores rims. After this process the average pore diameter, pore depth and pore ratio reach the predetermined parameter. Some untextured ri ngs are also treated to the same surface roughness and served as a reference for comparison of the textured rings. A special test rig is used to simulate a mech anical seal system and to measure the effect of the laser texturing on friction and seal performance. Tests are performed at various rotational speeds and vario us axial loads. Compared with the conventional mechanical seals, temperature rise, friction torq ue and friction coefficient of mechanical seals with laser-textured seal faces are much lower. These preliminary results show the potential of improving fricti on performance and increasing seal life with laser-textured seal faces.展开更多
To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficu...To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.展开更多
The loss in efficiency due to shroud leakage or tip clearance flow accounts for a substantial part of the overall losses in turbomachinery. It is important to identify the leakage loss characteristics in order to opti...The loss in efficiency due to shroud leakage or tip clearance flow accounts for a substantial part of the overall losses in turbomachinery. It is important to identify the leakage loss characteristics in order to optimize turbomachinery. At present, little information is available in the open literature concerning the effect of honeycomb seals on the loss characteristics in shroud cavities of an axial turbine, despite of the widespread use of the honeycomb seals. Therefore, interaction between rotor labyrinth seal leakage flow with and without honeycomb facings and main flow is investigated to provide the loss characteristics of the mixing process of the re-entering leakage flow into the main flow. The effects of honeycomb seals on the flow in shroud cavities and interaction with the main flow are analyzed. An additional study on the impact of subtle shroud cavity exit geometry is also presented. The investigation results indicate that the honeycomb seal affects the over tip leakage flow and reduces mixing losses when compared to the solid labyrinth seal. The leakage flow interactions with the main flow have considerably changed the flow fields in the endwall regions. The proposed research reveals the effects of honeycomb seals on the loss characteristics in shroud cavities and the impact of subtle shroud cavity exit geometry, and it is helpful for the design optimization of turbomachinery.展开更多
Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance...Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.展开更多
Bulk flow model with perturbation simplification has been used to calculate rotordynamic coefficients in annular seals which have significant influences on the dynamic behavior of rotors in turbomachinery. In this wor...Bulk flow model with perturbation simplification has been used to calculate rotordynamic coefficients in annular seals which have significant influences on the dynamic behavior of rotors in turbomachinery. In this work, a transient bulk flow model with arbitrary rotor motion is developed, and the boundary conditions and friction factor in the model are calibrated with steady Computational Fluid Dynamics（CFD） analysis. The numerical solution scheme is developed based on the finite element method to obtain the transient reaction force in the seal clearance. With a periodic circular rotor orbit, the transient forces at multiple whirling frequencies are used to evaluate the rotordynamic coefficients. The leakage flowrate of CFD analysis has good agreement with experimental results and the calibrated parameters in bulk flow model are dependent on operating conditions. Although CFD calibration improves the accuracy of the perturbed bulk flow model, the direct damping is overestimated and the cross-coupled damping is underestimated. Compared with the perturbed model, the predictions of the transient bulk flow model are more agreeable with the experiment.展开更多
The sealing rings are one of the most important components as the sealing devices in the wet clutch unit of a heavy vehicle. The sealing ring, made from PTFE composites, was subjected to serious wear on the sealing su...The sealing rings are one of the most important components as the sealing devices in the wet clutch unit of a heavy vehicle. The sealing ring, made from PTFE composites, was subjected to serious wear on the sealing surface, but the mating metal surface only had slight abrasion. A specialized test rig was designed for wear research and failure analysis of the sealing ring. The composition analyses of the ring material, working conditions and wear surface characteristics by visual inspection and tribological properties as well as microscopic analysis with scanning electron microscope was performed to determine the wear mechanism and failure causes. Results revealed that the wear of PTFE composites was characterized by abrasion and adhesion after a certain duration testing, and the wear mechanism changed to thermal fatigue and abrasive wear in the stage of intense wear. The thermal deformation and fatigue were primarily responsible for the rapid wear of the PTFE composites for the sealing rings.展开更多
Hydrostatic mechanical face seals for reactor coolant pumps are very important for the safety and reliability of pressurized-water reactor power plants.More accurate models on the operating mechanism of the seals are ...Hydrostatic mechanical face seals for reactor coolant pumps are very important for the safety and reliability of pressurized-water reactor power plants.More accurate models on the operating mechanism of the seals are needed to help improve their performance.The thermal fluid–solid interaction（TFSI）mechanism of the hydrostatic seal is investigated in this study.Numerical models of the flow field and seal assembly are developed.Based on the mechanism for the continuity condition of the physical quantities at the fluid–solid interface,an on-line numerical TFSI model for the hydrostatic mechanical seal is proposed using an iterative coupling method.Dynamic mesh technology is adopted to adapt to the changing boundary shape.Experiments were performed on a test rig using a full-size test seal to obtain the leakage rate as a function of the differential pressure.The effectiveness and accuracy of the TFSI model were verified by comparing the simulation results and experimental data.Using the TFSI model,the behavior of the seal is presented,including mechanical and thermal deformation,and the temperature field.The influences of the rotating speed and differential pressure of the sealing device on the temperature field,which occur widely in the actual use of the seal,are studied.This research proposes an on-line and assembly-based TFSI model for hydrostatic mechanical face seals,and the model is validated by full-sized experiments.展开更多
Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. On...Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.展开更多
The loads acting on the sealing elements of balanced mechanical seals are analyzed. When the balance factor approaches the back pressure factor, the spring pressure will become main part of the face pressure. The leak...The loads acting on the sealing elements of balanced mechanical seals are analyzed. When the balance factor approaches the back pressure factor, the spring pressure will become main part of the face pressure. The leakage model of balanced mechanical seals is established on the base of M-B model for rough surface. Several GY-70 type balanced mechanical seals are tested. The influences of the spring pressure both on the leakage rate and on the friction characteristic of balanced mechanical seals are investigated. The research results indicate that as spring pressure increases, both the clear-ance between two end faces and the leakage rate will decrease, and the friction will be more serious because lubrication medium between the rotating ring and the stationary ring reduces, though the increase of the spring pressure may not be enough to change the face friction state of mechanical seals. There exists an optimum spring pressure for mechanical seal operation. Under this spring pres-sure, not only leakage rate is small, but also the seal end surfaces have a fine friction characteristic. Under different operating conditions, identical type mechanical seals may possess different spring pressure. Appropriate selection of spring pressure is valuable to realize long-period and small leakage rate operating of balanced mechanical seals.展开更多
Experimental investigation has been performed to study the leakage and wear characteristics of carbon seal working at high circumferential speed. To expand the scope of application, two newly designed carbon seals wer...Experimental investigation has been performed to study the leakage and wear characteristics of carbon seal working at high circumferential speed. To expand the scope of application, two newly designed carbon seals were compared: #1 Carbon Seal(CS1) with the inner diameter of136 mm and including 4 segments, #2 Carbon Seal(CS2) with the inner diameter of 212 mm and including 6 segments. Air leakage tests were firstly conducted in the Medium-speed Seal Test Rig. The pressure ratio changed from 1.04 to 2.02 with the rotating speed varying from 0 to18300 r/min. Of paramount concern was the durability test, including 300 h running time accumulated by three different working conditions, which was separately implemented on each carbon seal.The morphology variation of the friction surface, wear and leakage were recorded. Results indicated that the leakage monotonously increases with the pressure ratio and decreases with the rotating speed. Comparing with CS1, more typical features exist on the friction surface of CS2, which are generated by more severe wear. Continually, leakage characteristics deteriorate. Furthermore, fitted formula has been educed for the life prediction of carbon seal, which could provide some supports for aero-engine design.展开更多
Swirl brakes are usually introduced at the seal entrance in industry to improve the seal stability,especially for labyrinth seals suffering low seal clearance and high inlet preswirl ratio.However,how to arrange swirl...Swirl brakes are usually introduced at the seal entrance in industry to improve the seal stability,especially for labyrinth seals suffering low seal clearance and high inlet preswirl ratio.However,how to arrange swirl brakes at the seal entrance to obtain better seal stability retains unknown,such as the axial distance between the brake trailing edge and the first tooth.To this end,the effects of the distance between brakes and the first tooth on the leakage flow rate and seal rotordynamic coefficients were numerically investigated at typical inlet preswirl ratios of 0.45 and0.8,and the predicted results were in comparison with the results for no-brake configuration.The obtained results disclose that the brake configuration arranged against the first tooth produces lower circumferential velocity in the downstream of the brakes as a result of the larger counterclockwise vortex moving from the brake trailing edge to the brake leading edge when compared to the brake configuration away from the first tooth.Besides,the dropped circumferential velocity in the downstream of brakes will cause larger pressure fluctuation in the circumferential direction and thus generates larger tangential force to restrain the rotor forward whirl.On the other hand,the effective damping is further increased when the distance between brakes and the first tooth decreases to zero,that is,the crossover frequency is even disappeared at the inlet preswirl ratio of 0.45 and successfully drops from 69.9 Hz to 32.7 Hz at the preswirl ratio of 0.8.展开更多
The test results of sealing performance and a comparison between three types of honeycomb seals and a type of labyrinth seal are presented, which have different seal clearances and work under various rotor speeds. It ...The test results of sealing performance and a comparison between three types of honeycomb seals and a type of labyrinth seal are presented, which have different seal clearances and work under various rotor speeds. It has been found that the honeycomb seal leakage during a rotor speed of 6000 r/min decreases by about 4.8 percent as compared with that during a rotor speed of 0 r/min. At a radial clearance of 0.12 mm the honeycomb seal with a cell size of 1.6 mm enjoys the best sealing performance. The leakage flow of the labyrinth seal with a radial clearance of 0.06 mm is smaller than that of the honeycomb seals.展开更多
The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system fa...The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.展开更多
The charge valve is an important element in the charging port of a high-pressure hydrogen storage cylinder(HP-HSC).It is normally closed after the HP-HSC is filled with hydrogen.If the seal of the charge valve is dama...The charge valve is an important element in the charging port of a high-pressure hydrogen storage cylinder(HP-HSC).It is normally closed after the HP-HSC is filled with hydrogen.If the seal of the charge valve is damaged,it will seriously affect the stable operation of the hydrogen supply system and may even cause safety problems.Therefore,the seal performance of the charge valve is important.In this paper,finite element analysis(FEA)is carried out to analyze the seal contact performance of hydrogenated nitrile rubber(HNBR)gaskets in the seal pair of a charge valve.The effects of different pre-compressions,seal widths,and hydrogen pressures on the seal contact performance of the charge valve are analyzed.The contact pressure on the seal surface increases with the increase of pre-compression.With a pre-compression of 2.5 mm,the maximum contact pressure without and with hydrogen pressure are 68.51 and 107.38 MPa,respectively.A contact gap appears in the inner ring of the seal surface with pre-compression below 0.15 mm.The contact gap occurs between the entire seal surface with a seal width of1 mm.The contact pressure on the seal surface and the width of the separation area between the seal surfaces increase with the increase of the seal width.The contact gap between the seal surfaces is zero with a width of 2.5 mm.The width of the separation area between the seal surfaces decreases with the decrease of the hydrogen pressure.The width of the separation area is reduced from 0.5 mm at 35 MPa to 0.17 mm at 15 MPa.This work can be useful for improvement of the seal performance and of the design of the charge valve used in the HP-HSC.展开更多
The nitrile butadiene rubber(NBR)hardness effect on the sealing characteristics of hydraulic O-ring rod seals is analyzed based on a mixed lubrication elastohydrodynamic model.Parameterized studies are conducted to re...The nitrile butadiene rubber(NBR)hardness effect on the sealing characteristics of hydraulic O-ring rod seals is analyzed based on a mixed lubrication elastohydrodynamic model.Parameterized studies are conducted to reveal the mechanism of the influence of rubber hardness on the static and dynamic behavior of seals.The optimized selections of rubber hardness are then investigated under different conditions.Results show that the low hardness seal is prone to stress concentration due to the extrusion effect under high pressure conditions;it is also more prone to leaking.A high hardness seal can better prevent leakage by reducing film thickness but it will cause large frictional power loss and increase the probability of wear failure.The choice of low hardness is recommended to reduce friction with the premise that leakage requirements are met.展开更多
Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the b...Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.展开更多
The current research on secondary O-ring seals used in mechanical seals has begun to focus on their dynamic properties. However, detailed analysis of the dynamic properties of O-ring seals in spiral groove gas face se...The current research on secondary O-ring seals used in mechanical seals has begun to focus on their dynamic properties. However, detailed analysis of the dynamic properties of O-ring seals in spiral groove gas face seals is lacking. In particular a transient study and a difference analysis of steady-state and transient performance are imperative. In this paper, a case study is performed to gauge the effect of secondary O-ring seals on the dynamic behavior（steady-state performance and transient performance） of face seals. A numerical finite element method（FEM） model is developed for the dynamic analysis of spiral groove gas face seals with a flexibly mounted stator in the axial and angular modes. The rotor tilt angle, static stator tilt angle and O-ring damping are selected to investigate the effect of O-ring seals on face seals during stable running operation. The results show that the angular factor can be ignored to save time in the simulation under small damping or undamped conditions. However, large O-ring damping has an enormous effect on the angular phase difference of mated rings, affecting the steady-state performance of face seals and largely increasing the possibility of face contact that reduces the service life of face seals. A pressure drop fluctuation is carried out to analyze the effect of O-ring seals on the transient performance of face seals. The results show that face seals could remain stable without support stiffness and O-ring damping during normal stable operation but may enter a large-leakage state when confronting instantaneous fluctuations. The oscillation-amplitude shortening effect of O-ring damping on the axial mode is much greater than that on the angular modes and O-ring damping prefers to cater for axial motion at the cost of angular motion. This research proposes a detailed dynamic-property study of O-ring seals in spiral groove gas face seals, to assist in the design of face seals.展开更多
The oxidation of Kovar alloy was investigated, the wetting and spreading behavior of hard and soft glasses on Kovar alloy were studed by using the sessile drop method, and the quality and the seal strength of glass-Ko...The oxidation of Kovar alloy was investigated, the wetting and spreading behavior of hard and soft glasses on Kovar alloy were studed by using the sessile drop method, and the quality and the seal strength of glass-Kovar seals were tested. The experimental results indicated that the preoxidation of Kovar alloy for approximately 10 min at 700℃ in air resulted in excellent adherence in glass-Kovar seals. The wetting and spreading behavior of glass on preoxidized Kovar alloy were superior to that on nonoxidized Kovar alloy. The wetting ability of ASF110 glass, at 950℃ and 980℃ in Ar and N2 atmospheres, was significantly superior to that of ASF200R and ASF700 glasses. The seal quality of the glass-preoxidized Kovar seal was superior to that of the glass-nonoxidized Kovar seal. The shear strength of the ASFll0 glass-preoxidized Kovar seal, which was prepared at 980℃ for 20 min in an Ar atmosphere, was approximately 3.9 MPa.展开更多
文摘For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor a. Therefore, the Arrhenius equation is widely used due to its simple form and often leads to suitable results. Where, the Arrhenius equation presents a linear relation for the temperature-dependent shift factor in logarithmic scale ln（α） with the absolute inverse temperature （1/θ）. However, in cases with a large temperature range which eventually include more complex reaction processes, the functional relation between ln（α） and （1/θ） is nonlinear in the ＇Arrhenius plot＇. In those cases, the monotone change of the nonlinear range in the ＇Arrhenius plot＇ can be interpreted as a transient range between two approximately linear or constant regions. An extended application of the modified Arrhenius equation from Nakamura （1989） is presented in this study for this transient range. The introduced method was applied to describe the time-temperature equivalence in the relaxation analysis of restoring seal force of metal seals, which are used in lid-systems of transport and interim storage casks for radioactive materials. But, the method is widely valid and can be used for different objectives which are characterized by thermorheologically simple behavior with nonlinear sensitivity to inverse temperature.
基金supported by China Postdoctoral Science Foundation (Grant No. 20070410323)Jiangsu Provincial Planned Projects for Postdoctoral Research Funds of China (Grant No. 0701001C)Jiangsu Provincial Planned Projects for Fostering Talents of Six Scientific Fields of China (Grant No. 07-D-027)
文摘Since the beginning of the 20th century, many researches on the sealing characteristic of mechanical seals were carried out broadly and in depth by various methods and some leakage models were built. But due to the lack of the way to characterize the main factors of influence on the leakage, most of the early researches were based on the assumptions that the seal faces topography and the frictional conditions were invariant. In the early built models, the effect of the surface topography change of the seal face on the leakage rate was neglected. Based on the fractal theory, the contact of end faces of the rotary and stationary rings was simplified to be the contact of a rough surface and an ideal rigid smooth surface, and the contact interface＇s cavity size-distribution function as well as the fractal characteristic of the cavity profile curve was discussed. By analyzing the influence of abrasion on the seal face topography and the leakage channel, the time-correlation leakage prediction model of mechanical seals based on the fractal theory was established and the method for predicting the leakage rate of mechanical seals with parallel plane was proposed. The values of the leakage rate predicted theoretically are similar to the measured values of the leakage rate in the model test and in situ test. The experimental results indicate that the leakage rate of mechanical seals is a transient value. The surface topography of the end faces of the seal tings and its change during the frictional wear of mechanical seals can be accurately characterized by the fractal parameters. Under the work conditions of changeless frictional mechanism, the fractal parameters measured or calculated based on the accelerated testing equation can be used to predict the leakage rate of mechanical seal in service. The proposed research provides the basis for determining the leakage state and predicting working life of mechanical seal.
文摘Heat generated by friction between faces of mechanica l seals is a major factor that causes deterioration of the seals and shortens th eir service life. Excessive temperature rise can greatly alter the seal geometry and vaporize the sealing fluid, resulting in friction of boundary lubrication. These effects on face seals usually lead to excessive leakage and ultimately ren der the seal inoperable. In order to maintain the reliability of seals, high fri ction and unwanted wear must be avoided. Using the laser-texturing process to produce regular micro-surface structures is a fast and convenient technique compared to some more conventional etching or erosion technique currently used by the seal industry for various grooved face seals. Indeed, by using a pulse laser, better control is obtained on the geometr y, size and pore ratio of seal rings made of metallic or ceramic materials. In t his study, seal rings are made of silicon carbide and carbon. Mating faces of th e rings are polished and only silicon carbide rings are laser-textured. The las er texturing can be controlled to produce spherical pores at selected diameters, depths and pore ratio. The textured rings are then super-polished to remove th e bulges formed on the pores rims. After this process the average pore diameter, pore depth and pore ratio reach the predetermined parameter. Some untextured ri ngs are also treated to the same surface roughness and served as a reference for comparison of the textured rings. A special test rig is used to simulate a mech anical seal system and to measure the effect of the laser texturing on friction and seal performance. Tests are performed at various rotational speeds and vario us axial loads. Compared with the conventional mechanical seals, temperature rise, friction torq ue and friction coefficient of mechanical seals with laser-textured seal faces are much lower. These preliminary results show the potential of improving fricti on performance and increasing seal life with laser-textured seal faces.
基金Project supported by the National Natural Science Foundation of China （Nos. 51005209 and 51375449）
文摘To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.
基金supported by National Natural Science Foundation of China (Grant No. 50776021)Doctoral Fund of Ministry of Education of China (Grant No. 20092304110004)
文摘The loss in efficiency due to shroud leakage or tip clearance flow accounts for a substantial part of the overall losses in turbomachinery. It is important to identify the leakage loss characteristics in order to optimize turbomachinery. At present, little information is available in the open literature concerning the effect of honeycomb seals on the loss characteristics in shroud cavities of an axial turbine, despite of the widespread use of the honeycomb seals. Therefore, interaction between rotor labyrinth seal leakage flow with and without honeycomb facings and main flow is investigated to provide the loss characteristics of the mixing process of the re-entering leakage flow into the main flow. The effects of honeycomb seals on the flow in shroud cavities and interaction with the main flow are analyzed. An additional study on the impact of subtle shroud cavity exit geometry is also presented. The investigation results indicate that the honeycomb seal affects the over tip leakage flow and reduces mixing losses when compared to the solid labyrinth seal. The leakage flow interactions with the main flow have considerably changed the flow fields in the endwall regions. The proposed research reveals the effects of honeycomb seals on the loss characteristics in shroud cavities and the impact of subtle shroud cavity exit geometry, and it is helpful for the design optimization of turbomachinery.
基金funded by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.
基金supported by the National Natural Science Foundation of China(No.11176010)
文摘Bulk flow model with perturbation simplification has been used to calculate rotordynamic coefficients in annular seals which have significant influences on the dynamic behavior of rotors in turbomachinery. In this work, a transient bulk flow model with arbitrary rotor motion is developed, and the boundary conditions and friction factor in the model are calibrated with steady Computational Fluid Dynamics（CFD） analysis. The numerical solution scheme is developed based on the finite element method to obtain the transient reaction force in the seal clearance. With a periodic circular rotor orbit, the transient forces at multiple whirling frequencies are used to evaluate the rotordynamic coefficients. The leakage flowrate of CFD analysis has good agreement with experimental results and the calibrated parameters in bulk flow model are dependent on operating conditions. Although CFD calibration improves the accuracy of the perturbed bulk flow model, the direct damping is overestimated and the cross-coupled damping is underestimated. Compared with the perturbed model, the predictions of the transient bulk flow model are more agreeable with the experiment.
基金Funded by the National Natural Science Foundation of China(Nos.51005104, 51105288)Jiangsu Province Basic Research Program(Natural Science Foundation) (No.BK2011477)+1 种基金China Postdoctoral Science Foundation(No.20110491355)Young Excellent Teachers Training Project of Jiangsu University
文摘The sealing rings are one of the most important components as the sealing devices in the wet clutch unit of a heavy vehicle. The sealing ring, made from PTFE composites, was subjected to serious wear on the sealing surface, but the mating metal surface only had slight abrasion. A specialized test rig was designed for wear research and failure analysis of the sealing ring. The composition analyses of the ring material, working conditions and wear surface characteristics by visual inspection and tribological properties as well as microscopic analysis with scanning electron microscope was performed to determine the wear mechanism and failure causes. Results revealed that the wear of PTFE composites was characterized by abrasion and adhesion after a certain duration testing, and the wear mechanism changed to thermal fatigue and abrasive wear in the stage of intense wear. The thermal deformation and fatigue were primarily responsible for the rapid wear of the PTFE composites for the sealing rings.
基金Supported by National Basic Research Program of China(973 Program,Grant No.2009CB724304)National Key Technology R&D Program(Grant No.2011BAF09B05)National Natural Science Foundation of China(Grant No.50975157)
文摘Hydrostatic mechanical face seals for reactor coolant pumps are very important for the safety and reliability of pressurized-water reactor power plants.More accurate models on the operating mechanism of the seals are needed to help improve their performance.The thermal fluid–solid interaction（TFSI）mechanism of the hydrostatic seal is investigated in this study.Numerical models of the flow field and seal assembly are developed.Based on the mechanism for the continuity condition of the physical quantities at the fluid–solid interface,an on-line numerical TFSI model for the hydrostatic mechanical seal is proposed using an iterative coupling method.Dynamic mesh technology is adopted to adapt to the changing boundary shape.Experiments were performed on a test rig using a full-size test seal to obtain the leakage rate as a function of the differential pressure.The effectiveness and accuracy of the TFSI model were verified by comparing the simulation results and experimental data.Using the TFSI model,the behavior of the seal is presented,including mechanical and thermal deformation,and the temperature field.The influences of the rotating speed and differential pressure of the sealing device on the temperature field,which occur widely in the actual use of the seal,are studied.This research proposes an on-line and assembly-based TFSI model for hydrostatic mechanical face seals,and the model is validated by full-sized experiments.
基金supported by National Basic Research Program of China(973 Program,Grant No. 2009CB724304)Key Research Program of the State Key Laboratory of Tribology of Tsinghua University,China (Grant No. SKLT08A06)National Natural Science Foundation of China(Grant No. 50975157)
文摘Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.
基金This project is supported by Provincial Natural Science Foundation of Educa-tion Office of Jiangsu, China (No. 04KJD530090)Innovating Founda-tion for Doctoral Dissertation of Nanjing University of Technology, China (No. BSCX200510).
文摘The loads acting on the sealing elements of balanced mechanical seals are analyzed. When the balance factor approaches the back pressure factor, the spring pressure will become main part of the face pressure. The leakage model of balanced mechanical seals is established on the base of M-B model for rough surface. Several GY-70 type balanced mechanical seals are tested. The influences of the spring pressure both on the leakage rate and on the friction characteristic of balanced mechanical seals are investigated. The research results indicate that as spring pressure increases, both the clear-ance between two end faces and the leakage rate will decrease, and the friction will be more serious because lubrication medium between the rotating ring and the stationary ring reduces, though the increase of the spring pressure may not be enough to change the face friction state of mechanical seals. There exists an optimum spring pressure for mechanical seal operation. Under this spring pres-sure, not only leakage rate is small, but also the seal end surfaces have a fine friction characteristic. Under different operating conditions, identical type mechanical seals may possess different spring pressure. Appropriate selection of spring pressure is valuable to realize long-period and small leakage rate operating of balanced mechanical seals.
基金supported by the National Natural Science Foundation of China(No.51976214)National Science and Technology Major Project(2017-Ⅳ-0010-0047)。
文摘Experimental investigation has been performed to study the leakage and wear characteristics of carbon seal working at high circumferential speed. To expand the scope of application, two newly designed carbon seals were compared: #1 Carbon Seal(CS1) with the inner diameter of136 mm and including 4 segments, #2 Carbon Seal(CS2) with the inner diameter of 212 mm and including 6 segments. Air leakage tests were firstly conducted in the Medium-speed Seal Test Rig. The pressure ratio changed from 1.04 to 2.02 with the rotating speed varying from 0 to18300 r/min. Of paramount concern was the durability test, including 300 h running time accumulated by three different working conditions, which was separately implemented on each carbon seal.The morphology variation of the friction surface, wear and leakage were recorded. Results indicated that the leakage monotonously increases with the pressure ratio and decreases with the rotating speed. Comparing with CS1, more typical features exist on the friction surface of CS2, which are generated by more severe wear. Continually, leakage characteristics deteriorate. Furthermore, fitted formula has been educed for the life prediction of carbon seal, which could provide some supports for aero-engine design.
基金funded by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Swirl brakes are usually introduced at the seal entrance in industry to improve the seal stability,especially for labyrinth seals suffering low seal clearance and high inlet preswirl ratio.However,how to arrange swirl brakes at the seal entrance to obtain better seal stability retains unknown,such as the axial distance between the brake trailing edge and the first tooth.To this end,the effects of the distance between brakes and the first tooth on the leakage flow rate and seal rotordynamic coefficients were numerically investigated at typical inlet preswirl ratios of 0.45 and0.8,and the predicted results were in comparison with the results for no-brake configuration.The obtained results disclose that the brake configuration arranged against the first tooth produces lower circumferential velocity in the downstream of the brakes as a result of the larger counterclockwise vortex moving from the brake trailing edge to the brake leading edge when compared to the brake configuration away from the first tooth.Besides,the dropped circumferential velocity in the downstream of brakes will cause larger pressure fluctuation in the circumferential direction and thus generates larger tangential force to restrain the rotor forward whirl.On the other hand,the effective damping is further increased when the distance between brakes and the first tooth decreases to zero,that is,the crossover frequency is even disappeared at the inlet preswirl ratio of 0.45 and successfully drops from 69.9 Hz to 32.7 Hz at the preswirl ratio of 0.8.
基金National Emphases Basis Research Development and Programming Project(G1999022304)
文摘The test results of sealing performance and a comparison between three types of honeycomb seals and a type of labyrinth seal are presented, which have different seal clearances and work under various rotor speeds. It has been found that the honeycomb seal leakage during a rotor speed of 6000 r/min decreases by about 4.8 percent as compared with that during a rotor speed of 0 r/min. At a radial clearance of 0.12 mm the honeycomb seal with a cell size of 1.6 mm enjoys the best sealing performance. The leakage flow of the labyrinth seal with a radial clearance of 0.06 mm is smaller than that of the honeycomb seals.
基金supported by the National Natural Science Foundation of China(Nos.51875015,51620105010)。
文摘The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.
基金supported by the National Natural Science Foundation of China(No.52175067)the Science and Technology Department of Zhejiang Province(No.2021C01021),Chinathe Young Elite Scientist Sponsorship Program by China Association for Science and Technology(No.YESS20200154)。
文摘The charge valve is an important element in the charging port of a high-pressure hydrogen storage cylinder(HP-HSC).It is normally closed after the HP-HSC is filled with hydrogen.If the seal of the charge valve is damaged,it will seriously affect the stable operation of the hydrogen supply system and may even cause safety problems.Therefore,the seal performance of the charge valve is important.In this paper,finite element analysis(FEA)is carried out to analyze the seal contact performance of hydrogenated nitrile rubber(HNBR)gaskets in the seal pair of a charge valve.The effects of different pre-compressions,seal widths,and hydrogen pressures on the seal contact performance of the charge valve are analyzed.The contact pressure on the seal surface increases with the increase of pre-compression.With a pre-compression of 2.5 mm,the maximum contact pressure without and with hydrogen pressure are 68.51 and 107.38 MPa,respectively.A contact gap appears in the inner ring of the seal surface with pre-compression below 0.15 mm.The contact gap occurs between the entire seal surface with a seal width of1 mm.The contact pressure on the seal surface and the width of the separation area between the seal surfaces increase with the increase of the seal width.The contact gap between the seal surfaces is zero with a width of 2.5 mm.The width of the separation area between the seal surfaces decreases with the decrease of the hydrogen pressure.The width of the separation area is reduced from 0.5 mm at 35 MPa to 0.17 mm at 15 MPa.This work can be useful for improvement of the seal performance and of the design of the charge valve used in the HP-HSC.
基金supported by the National Natural Science Foundation of China(No.52005470)the Natural Science Foundation of Zhejiang Province(No.LQ21E050020)the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.2021YW17),China.
文摘The nitrile butadiene rubber(NBR)hardness effect on the sealing characteristics of hydraulic O-ring rod seals is analyzed based on a mixed lubrication elastohydrodynamic model.Parameterized studies are conducted to reveal the mechanism of the influence of rubber hardness on the static and dynamic behavior of seals.The optimized selections of rubber hardness are then investigated under different conditions.Results show that the low hardness seal is prone to stress concentration due to the extrusion effect under high pressure conditions;it is also more prone to leaking.A high hardness seal can better prevent leakage by reducing film thickness but it will cause large frictional power loss and increase the probability of wear failure.The choice of low hardness is recommended to reduce friction with the premise that leakage requirements are met.
基金co-supported by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.
基金Supported by National Key Basic Research Program of China(973Program,Grant No.2012CB026003)National Science and Technology Major Project of China(Grant No.ZX06901)
文摘The current research on secondary O-ring seals used in mechanical seals has begun to focus on their dynamic properties. However, detailed analysis of the dynamic properties of O-ring seals in spiral groove gas face seals is lacking. In particular a transient study and a difference analysis of steady-state and transient performance are imperative. In this paper, a case study is performed to gauge the effect of secondary O-ring seals on the dynamic behavior（steady-state performance and transient performance） of face seals. A numerical finite element method（FEM） model is developed for the dynamic analysis of spiral groove gas face seals with a flexibly mounted stator in the axial and angular modes. The rotor tilt angle, static stator tilt angle and O-ring damping are selected to investigate the effect of O-ring seals on face seals during stable running operation. The results show that the angular factor can be ignored to save time in the simulation under small damping or undamped conditions. However, large O-ring damping has an enormous effect on the angular phase difference of mated rings, affecting the steady-state performance of face seals and largely increasing the possibility of face contact that reduces the service life of face seals. A pressure drop fluctuation is carried out to analyze the effect of O-ring seals on the transient performance of face seals. The results show that face seals could remain stable without support stiffness and O-ring damping during normal stable operation but may enter a large-leakage state when confronting instantaneous fluctuations. The oscillation-amplitude shortening effect of O-ring damping on the axial mode is much greater than that on the angular modes and O-ring damping prefers to cater for axial motion at the cost of angular motion. This research proposes a detailed dynamic-property study of O-ring seals in spiral groove gas face seals, to assist in the design of face seals.
文摘The oxidation of Kovar alloy was investigated, the wetting and spreading behavior of hard and soft glasses on Kovar alloy were studed by using the sessile drop method, and the quality and the seal strength of glass-Kovar seals were tested. The experimental results indicated that the preoxidation of Kovar alloy for approximately 10 min at 700℃ in air resulted in excellent adherence in glass-Kovar seals. The wetting and spreading behavior of glass on preoxidized Kovar alloy were superior to that on nonoxidized Kovar alloy. The wetting ability of ASF110 glass, at 950℃ and 980℃ in Ar and N2 atmospheres, was significantly superior to that of ASF200R and ASF700 glasses. The seal quality of the glass-preoxidized Kovar seal was superior to that of the glass-nonoxidized Kovar seal. The shear strength of the ASFll0 glass-preoxidized Kovar seal, which was prepared at 980℃ for 20 min in an Ar atmosphere, was approximately 3.9 MPa.
