Seal Groove Research Articles

Optimization of Tip Seal Grooves for Aerodynamic and Durability Improvements of Small-Core Turbines

Abstract While the gap between the turbine rotor tip and the outer case in a gas turbine engine is necessary for engine function, the gap is kept as small as possible due to the detrimental effect of the flow over the turbine tip. With the increased investments in ultra-high bypass turbofans, blade tip clearances are increasing in relative size to the turbine rotor, as engines move towards smaller cores. In this work, an optimization of a rotor tip seal with discrete axisymmetric grooves was explored computationally using RANS simulations. The optimization was applied at two tip clearances representing a nominal and small-core-scaled geometry, and with both flat- and squealer-tipped blades. The multi-objective optimization was designed to maximize rotor efficiency and minimize tip heat load. Several casing designs were identified for each tip configuration that both increased efficiency and reduced the heat load into the rotor tip. However, some optimal tip seal designs were composed of grooves that were demonstrated to be detrimental in prior work. Furthermore, grooves were more effective at increasing efficiency when applied to flat tipped geometries – increasing efficiency by 0.9 points over the ungrooved baseline with flat tipped blades, as opposed to 0.25 points over the ungrooved case with squealer tipped blades. Finally, optimal seal geometries that were obtained from the small-core scaled clearance gap optimizations maintained near optimal performance when evaluated at the design tip clearance, while those geometries developed at the design clearance experienced greater tip gap sensitivity.

A model of contact deep groove seals based on partition model and JFO boundary condition

Unlike nuclear main pump seals, deep groove seals in aero-engines operate on a contact basis. However, the precise working mechanism and accurate quantitative methods for assessing their sealing performance remain elusive. This paper introduces a fluid-solid-thermal coupling model for contact deep groove seals, utilizing a partition model and considering JFO boundary condition, mixed lubrication, and detailed heat calculations. The model significantly enhances accuracy compared to original approaches. It comprehensively accounts for contact effects, thermal deformations, convergence wedges, radial waviness, hydrodynamic pressures, groove drainage, and convection, revealing characteristics of contact deep groove seals such as high stiffness, effective heat dissipation, wear resistance, and prolonged service life. The proposed model and working mechanism provide theoretical guidance for designing diverse deep groove seal structures.

Evolution mechanism and parametric investigation of relative negative pressure zone in spiral groove gas face seal for aero-engine at high rotational speed

As an advanced sealing technology, spiral groove gas face seal has excellent sealing performance. However, it is rarely used in aero-engine. Previous investigation proposed that the relative negative pressure zone (RNPZ) in the spiral groove gas face seal can regulate the sealing performance. In this paper, further numerical simulation work is carried out. By quantifying the obstruction effect, viscous pumping effect and shear effect, the evolution mechanism of RNPZ under different film thicknesses and groove depths is revealed. Then, the parametric analysis of spiral groove configuration and groove number is carried out. Through the sub-regional quantitative analysis of the groove, the influence mechanism of structural configuration on RNPZ is revealed. Finally, combined with the hydrodynamic performance analysis, the spiral groove seal structure under optimal conditions is obtained. It is found that under the condition of high speed and low inlet pressure of aero-engine, RNPZ is suppressed by adjusting the structure of the spiral groove to enhance the shear effect, the pumping effect at the top of the groove and reduce the pumping effect at the bottom of the groove. When the number of grooves is 20 and the groove depth is 3 μm, the stiffness-leakage ratio of structure B and C can be increased by 10.15 % and 12.68 %, and the sealing performance is the strongest. This work can provide a theoretical and data basis for the subsequent optimization design of aero-engine gas face seals.

Study on working mechanism and performance of deep groove seal at high temperature and high speed in mixed lubrication

The deep groove seal is a kind of mechanical seal with millimeter depth grooves on the end face of the sealing ring, widely used in aviation and nuclear fields. However, its working mechanism and sealing performance are still unclear. In this research, a fluid-solid-thermal coupling numerical analysis model at high temperature and high speed in mixed lubrication is established to solve these problems. Mechanism analysis indicates that deep grooves cause circumferential waviness of micron level on the end face, strongly affecting the sealing performance. A quantitative characterization method is proposed, solving the characteristic parameters and analytical expression of deep groove seal waviness, so that the deep groove seal can be approximately equivalent to the waviness seal and be explained by the law of the waviness seal. The sealing performance can be controlled through the design of groove parameters. The results have been verified by the experiment. The fluid-solid-thermal coupling model and characterization method of equivalent waviness parameters for the deep groove seal proposed in this article provide a theoretical basis for further study of the mechanism and performance of the deep groove seal.

Compact design of the 166.6 MHz superconducting cavity and its beamline elements for HEPS

The High Energy Photon Source (HEPS) is a 6 GeV diffraction-limited synchrotron light source under construction in Beijing. It will use five 166.6 MHz superconducting radio frequency (rf) cavities to accelerate the 200 mA electron beam in the storage ring. In the current lattice design, each straight section is 6 meters long to accommodate two 166.6 MHz cavities. The cavity adopts β=1 quarter-wave geometry, and the damping of the higher order modes is realized by using an enlarged cavity beam pipe to 505 mm and a ferrite absorber installed on the beam pipe. The low rf frequency, as well as the large beam aperture, added great challenges to the design of the 166.6 MHz cavity module to fit into a strictly limited longitudinal space. In addition, heat load optimization for the transition from room temperature to the cryogenic temperature, smooth tapering from the 505 mm beam aperture to the small diameter of the gate valves for impedance control, proper collimation of the synchrotron light to prevent thermal damage of delicate components, are also demanding requirements for a compact design. Accessibilities are also preserved for tuners and vacuum components to enable online maintenance. Finally, rf field leakage in the vacuum seal groove of the cavity is carefully examined to prevent overheating on the superconducting flange, which, in the worst scenario, may cause a thermal runaway, thus limiting the achievable accelerating gradient of the cavity. This paper presents the first compact design of the 166.6 MHz srf section for HEPS.

Form Shear Stress Correction in Bulk Flow Analysis of Grooved Seals Based on Effective Film Thickness

Abstract Bulk flow models for grooved annular seals provide computationally efficient static and dynamic response predictions, though heavy reliance on empirical relationships often leads to undesirable levels of uncertainty. The flow complexity caused by the grooves adds difficulty to shear stress modeling for these seals. This study seeks to improve shear stress modeling for grooved seals through the identification and quantification of the additional bulk flow shear stress contributions within the groove region. Through single groove computational fluid dynamics (CFD) simulations and an effective film thickness analysis framework, the additional groove shear stress component is identified as a form shear stress (FSS) due to its clear relationship to the effective film thickness behavior. The FSS is quantified as a correction to traditional shear stress definitions. Predictive models for the FSS are developed as functions of the ratio of circumferential to axial Reynolds number and the total resultant Reynolds number. Implementation of the FSS models into a simplified bulk flow method delivers leakage predictions for three seal cases within 10% of the experimental results and qualitative agreement in predicted circumferential velocity profiles while eliminating the need for an assumed groove loss coefficient. This is the first paper to utilize an effective film thickness-based procedure to quantify and model the FSS component in grooved seal bulk flow analysis. The demonstrated predictive capability and widespread applicability of the models and approach presented in this paper provide an avenue for significant improvements in grooved seal bulk flow prediction accuracy through improved shear stress modeling.

Investigation on hydrodynamic lubrication effect of micro groove seal in pharmaceutical kettle.

To improve the lubrication conditions of the seal in the pharmaceutical kettles, a specific shape groove with micrometer level on the sealing end face is set up to fully utilize the fluid dynamic pressure effect under given working conditions. A numerical model is developed to solve the pressure distribution in the micro groove, where any groove shape can be used. The numerical form of the model is derived using the principle of mass conservation without considering the film thickness derivative term, and the coordinate transformation is introduced to adapt to the curved shape of the groove. The cavitation phenomenon is taken into account in the flow field of the seal, and the JFO cavitation model is introduced to modify the Reynolds equation. The diversity of groove shapes is considered, and the node adsorption method is adopted to approximate the groove shape. The model is established based on the principle of mass conservation, which can adapt to any different groove shapes and has a strong scalability. By mathematical modeling and solving, the performances of the micro groove seal under different groove shapes are analyzed, providing a basis for the micro groove design of seal in pharmaceutical kettles.

Simulation of Air Ingestion in a Mechanical Seal With Inward Pumping Spiral Grooves

Abstract Inward pumping spiral groove seals are used in many applications, such as transmission gearboxes or electric vehicles, as they can provide zero leakage and very low operating friction. The spiral grooves are connected to the low pressure side (typically atmosphere) and pump the fluid inward that is to say toward the high pressure side (inlet). If the rotational speed is high enough, the low pressure fluid (air) completely occupies the sealing area and is used as a low friction lubricant. However, for lower operating speeds or higher fluid pressures, the seal can be lubricated by both fluids simultaneously. This occurs particularly during start-up and shutdown. In this work, a numerical simulation of the two phases in the sealing gap of an upstream pumping spiral groove seal during start-up is performed. The establishment of the film is analyzed and the effect of the rotational speed and operating pressure on the fluid composition (air and liquid) in the sealing interface is studied. For the analyzed seal, it is shown that the amount of air pumped in the sealing area is controlled by the duty parameter.

Computational Fluid Dynamics Prediction of Rotordynamic Coefficients for Grooved Seals: Model and Numerical Sensitivity

Abstract Computational fluid dynamics (CFD) studies for annular seals continues to gain popularity as a powerful tool for seal rotordynamic analysis, but the wide variety in setup and modeling choices without sufficient justification prevent more widespread use of these methods. This study applies the quasi-steady (QS) method for rotordynamic coefficient prediction to an incompressible grooved seal model in order to rigorously quantify the influence of various prominent modeling choices on prediction results. Variation of the upstream region configuration confirms the dependence of the cross-coupled stiffness on the development of circumferential velocity, which is a strong function of upstream geometry. An axial inlet upstream region is shown to be a sufficient approximation to a radial inlet with axial symmetry, representative of a back-to-back seal configuration. Significant stiffness variation is observed for particular downstream region configurations, though the additional pressure perturbation is mostly confined to the downstream region itself. When no downstream region is included, sensitivity to the amount of pressure profile blending enforced at the seal outlet plane is demonstrated, further underscoring the need for an experimentally accurate downstream geometry. This is the first paper dedicated to a quantitative sensitivity investigation of this nature specific to incompressible grooved seals that examines upstream and downstream region configuration, rotor centrifugal growth effects, and modeling whirl amplitude. Use of these results will foster more accurate application of the QS method for rotordynamic predictions of incompressible grooved seals, ultimately enabling more widespread use of CFD methods for general seals predictions.

Active Probe Atomic Force Microscopy with Quattro-Parallel Cantilever Arrays for High-Throughput Large-Scale Sample Inspection.

An Atomic Force Microscope(AFM) isa powerful and versatile tool for nanoscale surface studies to capture 3D topography images of samples. However, due to their limited imaging throughput, AFMs have not been widely adopted for large-scale inspection purposes. Researchers have developed high-speed AFM systems to record dynamic process videos in chemical and biological reactions at tens of frames per second, at the cost of a small imaging area of up to several square micrometers. In contrast, inspecting large-scale nanofabricated structures, such as semiconductor wafers, requires nanoscale spatial resolution imaging of a static sample over hundreds of square centimeters with high productivity. Conventional AFMs use a single passive cantilever probe with an optical beam deflection system, which can only collect one pixel at a time during AFM imaging, resulting in low imaging throughput. This work utilizes an array of active cantilevers with embedded piezoresistive sensors and thermomechanical actuators, which allows simultaneous multi-cantilever operation in parallel operation for increased imaging throughput. When combined with large-range nano-positioners and proper control algorithms, each cantilever can be individually controlled to capture multiple AFM images. With data-driven post-processing algorithms, the images can be stitched together, and defect detection can be performed by comparing them to the desired geometry. This paper introduces principles of the custom AFM using the active cantilever arrays, followed by a discussion on practical experiment considerations for inspection applications. Selected example images of silicon calibration grating, highly-oriented pyrolytic graphite, and extreme ultraviolet lithography masks are captured using an array of four active cantilevers ("Quattro") with a 125 µm tip separation distance. With more engineering integration, this high-throughput, large-scale imaging tool can provide 3D metrological data for extreme ultraviolet (EUV) masks, chemical mechanical planarization (CMP) inspection, failure analysis, displays, thin-film step measurements, roughness measurement dies, and laser-engraved dry gas seal grooves.

A hybrid Gaussian mutation PSO with search space reduction and its application to intelligent selection of piston seal grooves for homemade pneumatic cylinders

To make the motion tracking control of the homemade pneumatic cylinder as accurate as possible, it is necessary to properly match the seal groove and seal ring on the piston to generate the appropriate friction. However, since the relationship between friction and motion control accuracy is not yet clear, and the friction affected by many factors cannot be accurately modeled, it is impossible to design the optimal seal groove with the highest possible motion control accuracy for pneumatic cylinder through theoretical calculation or simulation optimization. For this reason, an experimental optimization method is considered to select the optimal one from the six empirically designed seal grooves through a particle swarm optimization (PSO) algorithm. To cope with the shortcomings of slow convergence rate and the tendency to fall into local optimum of the basic PSO algorithm (BPSO), three improved PSO algorithms (HGMPSO-0, HGMPSO and HGMPSO-SSR) are successively proposed in this study. The first two improved algorithms are compared with other PSO variants on 23 benchmark functions tested, and the results show that HGMPSO has better overall performance. To significantly improve the search space search efficiency and make the algorithm converge faster, the search space contraction mechanism is introduced into the HGMPSO algorithm to form the HGMPSO-SSR algorithm. The experimental results show that the HGMPSO-SSR algorithm significantly outperforms other PSO variants used for comparison and successfully achieves intelligent selection of piston seal grooves for the designed homemade pneumatic cylinder.

Study on the hydrodynamic performance of two typical groove liquid film seals considering cavitation

PurposeThe purpose of this paper is to investigate the hydrodynamic performance of liquid film seals with oblique grooves (OGs) and spiral grooves (SGs), considering cavitation, compare and analyze the differences between them.Design/methodology/approachConsidering cavitation effect, the incompressible steady-state Reynolds equation was solved to obtain the sealing performance parameters of the liquid film seal with oblique groove and spiral groove.FindingsThe hydrodynamic performance of oblique groove seal (OGS) and spiral groove seal (SGS) shows a similar trend with the change of operating parameters. When the groove angle is less than 20°, the load-carrying capacity of SGS is better than that of OGS, while when the groove angle continues to increase, the hydrodynamic performance of OGS is slightly better than that of SGS, and more suitable for use under small differential pressure and high speed.Originality/valueThe hydrodynamic characteristics of liquid film seals with oblique grooves and spiral grooves considering cavitation effect were studied, which provides a theoretical reference for the application of oblique groove seal.

Numerical Simulation of a New Designed Mechanical Seals with Spiral Groove Structures

The spiral groove seal has a strong hydrodynamic effect, but it has poor pollution resistance at the seal’s end and has unfavorable sealing stability. Circumferential waviness seals can use the fluid to clean the surface and have a strong ability to self-rush, protecting the main cover from contamination. This study presents a novel wave-tilt-dam seal design that integrates spiral groove structures to enhance the hydrodynamic performance of circumferential waviness seals. The objective of the research is to evaluate the mechanical effectiveness of this new design through simulation modeling, with a focus on the impact of structural parameters such as rotational speed and seal pressure on the hydrodynamic behavior under various operating conditions. The results of the study indicate that the new structure effectively improves the hydrodynamic performance of the liquid seal, resulting in a significant increase in film rigidity. Additionally, the study identifies optimal values for structural parameters under specific conditions. By addressing the limitations of traditional spiral groove seals and improving their hydrodynamic performance, this research contributes to the advancement of seal technology.

Circumferentially Grooved Seal Flow Field Analysis Based on Effective Film Thickness to Improve Bulk Flow Models

Abstract Bulk flow methods for circumferentially grooved seals use simplified physics models to predict leakage and rotordynamic coefficients efficiently, but uncertainty in empirical quantities like friction factors and loss coefficients leads to limited accuracy. To develop a more fundamental understanding of incompressible grooved seal flow, this study utilizes computational fluid dynamics (CFD) and an effective film thickness, a physical boundary between the jet and recirculating flows, to investigate Reynolds number effects on flow fields and shear stresses. Simulations are run using ansyscfx for a single groove seal model where streamlined analysis produces the effective film thickness. Flow structures, film thicknesses, shear stresses, and net flow expansion into the groove are found to be described completely by the ratio of circumferential to axial Reynolds number and the total resultant Reynolds number. Decreases in leakage with rotor speed are found to be dictated by increased land shear stresses and a decreased role of the groove in inducing pressure drop. An optimal groove aspect ratio between 0.07 and 0.19 is presented based on maximizing expanded film area while retaining a main groove recirculation region. This is the first paper to analyze circumferentially grooved seal flow from an effective film thickness standpoint. The results highlight bulk flow analysis areas where an effective film thickness approach could lead to new, physics-motivated model development and the elimination of particular empirical coefficients, thus providing a foundation on which substantial improvements in bulk flow modeling accuracy can be achieved.

Temperature Distribution Measurement and Internal Flow Visualization in the Lubrication Film of Non-contacting Mechanical Seals

The surface textures of non-contacting mechanical seals form a few micrometers thick lubrication film that aids in achieving high performance of the seal. Improved texture design can control internal fluid flow, improving the sealing performance and lubrication characteristics. However, film thickness is sensitive to thermal deformation, making seals vulnerable to heat. Excessive temperature increases and deviations in temperature distribution can cause performance degradation or damage to seals. Previous studies have suggested that heat transfer impacting these thermal issues may be influenced by the internal flow, however, experimental studies examining flow fields have not been conducted yet. This study presents the design of experimental equipment, measurement of temperature distributions and observation of flow fields in lubrication films with three different textures—non-textured, Rayleigh step, and spiral groove. Furthermore, the results were compared with those of numerical analysis. Temperature was found to be higher at the downstream end of the flow. In particular, the Rayleigh step seal exhibited a nonuniform temperature distribution that alternated between low and high-temperature areas. This was caused by cooling related to radial grooves that had a pumping effect. In contrast, a uniform temperature distribution was confirmed in the case of the spiral groove seal, which was formed by mixing outer and inner side fluids. The results indicate that the temperature distribution in lubrication films can be controlled via flow field by the surface texture shape or depth to protect against thermal degradation and to achieve high reliability of non-contacting mechanical seals.Graphical

Experimental study on transient frictional features of herringbone-grooved mechanical face seals in start-up and stop stages

Evolutions of frictional features of herringbone-grooved face seals during start-up and stop stages are focused on. Transient frictional torques are measured for outer-diameter-side, middle and inner-diameter-side grooved seals and a smooth-face seal based on a formerly developed dedicated test rig. Development of fluid carrying capacity can be deduced for all four seals according to torque evolutions, and lift-off mechanisms are analyzed. Hydrodynamic effect gets smaller with grooves apart from pressurized fluid side, and thereby hydrostatic effect due to face coning by heat generation dominates the fluid film formation as it is for the smooth-face seal. Thermal characteristic time due to thermal lag effect is smaller than accelerating periods. The squeeze effect indicated by the smaller torque of stop stages is also playing a role in transient operation.

Computational Fluid Dynamics Analysis of the Influence of Gas Content on the Rotordynamic Force Coefficients for a Circumferentially Grooved Annular Seal for Multiple Phase Pumps

Abstract Pumping efficiency and rotordynamic stability are paramount to subsea multiphase pump operation since, during the life of a well, the process fluid transitions from a pure liquid to a mixture of gas in the liquid to just gas. Circumferentially grooved seals commonly serve as balance pistons in pumps while also restricting secondary flow. Prior experimental results obtained with a grooved seal operating with a mixture of air and mineral oil show the seal rotordynamic force coefficients vary significantly with the gas volume fraction (GVF). This paper, complementing an exhaustive experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage and dynamic force coefficients of a circumferentially grooved seal supplied with air in an oil mixture with a GVF varying from 0 to 0.7. The test seal has 14 grooves, an overall axial length of 43.6 mm, and radial clearance of 0.211 mm. The 127 mm diameter rotor spins at constant angular speed (Ω = 3500 rpm). The mixture enters the seal at a supply pressure (Pin) of 2.9 bar(a), and the seal exit pressure (Pout) is 1 bar(a). The CFD two-phase flow simulations utilize the Euler–Euler multiphase model to predict the mass flowrate and the pressure field as a function of the operating conditions. Using a multi-frequency shaft orbit motion method, the CFD simulations deliver the variations of reaction force on the rotor with respect to the excitation frequency. For a pure liquid condition (GVF = 0), both the CFD and experimental results produce constant stiffness, damping, and added mass coefficients. The experimental and CFD results demonstrate the seal rotordynamic force coefficients are quite sensitive to the GVF. When introducing a small amount of air into the oil (GVF = 0.1), the direct damping coefficient increases by approximately 10%. For operation with a mixture with inlet GVF > 0.1, the cross-coupled stiffness coefficients develop strong frequency-dependent characteristics. In contrast, the direct damping coefficient has a negligible variation with excitation frequency. The CFD predictions, as well as the experimental results, evidence that air injection in a liquid stream can significantly change the seal rotordynamic characteristics, and thus can affect the rotordynamic stability of a pump. An accurate CFD analysis provides engineers to design reliable grooved seals operating under two-phase flow conditions.

General Approach to Modeling of Non-Contact Seals and Their Effect on the Dynamics of a Centrifugal Machine Rotor

There is a constant demand for higher equipment parameters, such as pressure of a sealing medium and shaft rotation speed. However, as the parameters rise it becomes more difficult to ensure hermetization efficiency. Moreover, sealing systems affect the overall operational safety of the equipment, especially vibratory. Non-contact seals are considered as hydrostatodynamic supports that can effectively damp rotor oscillations. Models of an impulse and a groove seals, models of rotor-seals system and rotor-auto-unloading system, model of a shaftless pump are studied to evaluate an effect of these sealing systems on oscillatory characteristics of rotor. Analytical dependencies for computation the dynamic characteristics of impulse seals, hydromechanical systems rotor-seals and rotor-auto-unloading, as well as shaftless pumps are obtained. These dependencies describe the radial-angular vibrations of a centrifugal machine rotor in seals-supports. Equations for computation the amplitude-frequency characteristics are given. The directions of improving the оperational safety of critical pumping equipment by purposefully increasing the rigidity of non-contact seals that leads to higher rotor vibration stability have been determined.

Effect of pressure fluctuation in oil-gas multiphase pump on cavitation and performance of sealing liquid film

During the operation of the oil-gas multiphase pump, due to the variable gas content of the incoming flow, the medium pressure at the high-pressure end fluctuates widely, which is easy to cause the stress change at both ends of the mechanical seal compensation ring and “instability” phenomenon. In this paper, a three-dimensional spiral groove seal film model is established. Considering the cavitation effect of liquid film gap, the variation law of end face cavitation and sealing performance of liquid film seal is explored according to the effect of pressure pulsation in the pump on the inner diameter side (Static mechanical seal, PLAN74 flushing scheme in API 682) and outer diameter side (Rotary mechanical seal, PLAN53A flushing scheme in API 682). The results show that the local pressure drop in the sealing liquid film is the main cause result to cavitation of liquid film. The inner diameter side pressure fluctuation has a great impact on the end face cavitation, and the wave peak is about 100 times that of the outer diameter side pressure. The inner diameter side pressure fluctuation should be avoided in engineering application. There is hysteresis between gas volume fraction (GVF) and boundary pressure fluctuation. The synchronization between sealing performance parameters and outlet pressure fluctuation is good, but there is phase difference with inlet pressure fluctuation. The inner diameter side pressure fluctuation has a great change on the sealing performance. The peak is about 5–20 times that of the outer diameter side pressure, which is easy to cause vibration of the mechanical seal. The amplitude and period of pressure fluctuation have a great impact on the GVF and sealing performance. The larger the fluctuation period is, the less obvious the hysteresis of GVF is, and the closer to the variation law of pressure fluctuation. During the actual operation of the oil-gas multiphase pump, the mechanical seal connected with the medium in the pump is rotary, and the flushing scheme ought to be PLAN53A to ensure the safe and stable operation of the oil-gas multiphase pump.

Experimental and theoretical investigations on dry gas seal transient performance and its disparity with steady performance

Through high-speed dry gas seal test rig, the real-time film thickness and leakage rate of spiral grooved dry gas seal have been monitored under different closing forces which are changed by adjusting spring compression. Under the conditions of different spring pressures and seal face deflection rates, the change rules of transient opening force and leakage rate are obtained by solving the transient-state Reynolds equation based on the measured real-time film thickness. Meanwhile, the steady opening force and leakage rate are figured out by solving the steady-state Reynolds equation using the average value of the real-time film thickness. Results show that the variation trends of calculated results based on steady-state or transient-state theory coincide well with experimental results. But with the influence of nonlinear effect, the average value of transient opening force and leakage rate are larger than steady opening force and leakage rate calculated with the average value of real-time film thickness, and compared with the value of steady leakage rate, the average value of transient leakage rate considered seal face deflection is closer to the experimental monitoring results.