Numerical simulation model of reciprocating rod seal systems with axial wear texture on rod surface

In this paper, a simulation model of reciprocating rod seal systems when there is axial texture on the rod surface due to wear is studied. The model includes macroscopic solid mechanics analysis, microscopic contact mechanics analysis and fluid mechanics analysis, and on this basis, the change of surface pressure when the sealing ring fall into a texture is calculated by the micro‐deformation mechanics analysis of the seal surface. Then, the stiffness matrix method is used to find the film thickness when the three pressures in the sealing area are in equilibrium, completing the fluid–solid coupling calculation. Combined with the above simulation process, the performance parameters of the sealing system such as leakage and friction can be obtained. Results show that axial texture will degrade sealing performance, which increases leakage and friction. The simulation results can quantitative characterise the influence of rod wear on sealing performance and provide some theoretical basis for the study of seal failure mechanism and prediction of seal life.


| INTRODUCTION
The reciprocating rod seal is an indispensable component in hydraulic systems because it undertakes the responsibility of maintaining medium pressure and preventing environmental pollution. As a typical dynamic seal, it is required to prevent medium leakage under conditions of a continuously moving sealing surface and an extremely high-pressure difference between inside and outside, which means that designing a qualified seal is quite a challenge.
To overcome this challenge, many scholars have conducted experiments and theoretical research on reciprocating rod seals since the 1930s. 1 In experimenting, Karaszkiewicz 2 found that no matter how well sealed, when the piston rod extends out of the hydraulic cylinder, which called outstroke, the rod always carries out some medium. If the condition of no leakage is required, the medium must be completely brought back when the piston rod retracts into hydraulic cylinder. On this basis, many sealing performance analysis methods that can calculate the flows of medium through the sealing surface during the out-and instrokes have been proposed, including the IHL (Inverse hydrodynamic lubrication) theory [3][4][5][6][7] and EHL (Elastohydrodynamic lubrication) theory. [8][9][10][11][12] The IHL theory is based on the full film lubrication, the load is entirely borne by the fluid film, so the fluid film pressure is equal to the load of the seal ring on the piston rod which can be obtained by finite element analysis. Then the leakage rate can be calculated by solving Reynolds equation in reverse. Different from the IHL theory, the EHL theory considers mixed lubrication conditions. In this theory, the fluid film pressure and asperities contact pressure under the specified film thickness can be obtained by means of forward solution of Reynolds equation and microscopic contact analysis, and then the film thickness is corrected to make the sum of the above two forces equal to the load of the seal ring on the piston rod. Many experiments later have shown that asperities contact exists in reciprocating seal system, 13,14 so the EHL theory is more reliable and becoming the main simulation method.
The above research provides sufficient theoretical analysis methods for the static performance of reciprocating seals, but for the prediction of seal life, there are still some problems. As the seals are more fragile than other components in mechanical systems, most current research has only focused on the deterioration of the seal during use. However, in practice, the phenomenon that the metal rod is worn by the seal often occurs (see Figure 1). The texture depth may be of the same order as the film thickness or even greater, so the effect of texture on sealing performance cannot be ignored. Therefore, it is of significance to establish a simulation model considering the texture of the rod surface to enable the model to more accurately evaluate the performance of a sealing system and predict the life of the sealing system when rod wear occurs.
Since the trace produced by wear is always parallel to the direction of friction, the wear texture would be parallel to the axial direction of the piston rod in the reciprocating seal system, as shown in Figure 2. It is not easy to analyse the effect of axial texture on sealing performance because the seal ring would be trapped in the texture which would cause the surface deformation and alter the stress distribution of the sealing ring surface. In traditional reciprocating seal lubrication analysis, because the film thickness is much smaller than the scale in other directions, the dimension of the film thickness direction is simplified, and the axial symmetry characteristics simplify the circumference dimension, so a quasi-one-dimensional lubrication analysis can be used. However, since the axial texture destroys the axial symmetry of the piston rod, the mixed lubrication calculate process is transformed into a twodimensional problem, and the surface deformation stress analysis is a three-dimensional problem. What's more, when the texture has varying depth axially, the simulation would be a time dependent problem, but considering that the depth of actual observed wear is relatively uniform, this paper makes a simplification that the texture depth is constant. Since the above problems have not been solved, there is currently no analysis method for the axial texture.
In this work, a numerical simulation model of a reciprocating rod seal which includes analyses of fluid mechanics, contact mechanics, and solid mechanics is established. On this basis, considering that the sealing ring would deform following the texture of the rod surface and change the surface pressure, a microscopic deformation mechanics analysis is conducted to correct the surface pressure. The stiffness matrix method, which has high stability and calculation efficiency, is then used to find the fluid film thickness when the fluid film pressure, asperities contact pressure and static contact pressure is in balance, completing the numerical simulation calculation of the seal system.

| ANALYSIS
Most researchers currently believe that a reciprocating seal works when the fluid and asperities contact both exist and the state of the sealing zone is as shown in Figure 3. The static contact pressure p sc on the seal ring surface can be obtained from macroscopic solid mechanics and microscopic deformation mechanics analyses, while the fluid film pressure p f and asperity contact pressure p con can be calculated by microscopic fluid mechanics and microscopic contact mechanics analyses, respectively. The film thickness distribution is then corrected by fluid-structure coupling analysis to satisfy the balance relation of three forces p sc= p con+ p f . F I G U R E 2 Schematic of O ring reciprocating seal system and axial texture on the rod.

| Analysis of solid mechanics
The simulation method introduced in this paper is universal and applicable to various types of reciprocating seals, so only two seal forms are simulated, the O-ring which represents traditional rubber seal and VL seal ring which represents combined seals. Figure 4 is the schematic diagram of the two sealing systems before assembly. In subsequent finite element simulations, the rigid body parts are moved to the correct position to simulate the state of the seal after assembly. The material of the Oring is NBR (nitrile butadiene rubber) and a threeparameter Mooney-Rivlin model is used to describe its static material mechanical properties. The model parameters can be obtained by fitting the stress-strain data from a tensile-compression test: C 10 = 2.51 MPa, C 01 = À0.27 MPa, and d = 0.0090. The material of plastic seal ring is PTFE (polytetrafluoroethylene). Its compressive stress-strain curve is shown in Figure 5. The curve shown in the figure are engineering stress-strain curve. When constructing the plastic model, it is necessary to convert the engineering stress-strain data into the real stress-strain data. The plastic model based on Von Mises criterion is used to describe its mechanical properties. The rod and groove are considered rigid because their deformations are very small. The rod and groove are moved to the assembly position and pressure is applied to the fluid side to simulate conditions of the actual seal system. After the simulation, the contact pressure between the seal ring and the rod can be extracted for conditions when the rod is smooth.

| Analysis of deformation mechanics
The contact pressure when the rod is smooth and there is no fluid film between the interfaces can be calculated by finite-element simulation described above. In the previous numerical simulation method of reciprocating seals, it is considered that the fluid film would not affect the static contact pressure because the fluid film is too thin to affect the overall strain of the seal ring and the film thickness changes gently, which causes the seal ring surface to remain flat. Therefore, in the subsequent fluidstructure interaction calculation, the static contact pressure caused by the deformation of the seal ring is regarded as constant.
In this study, because the magnitudes of film thickness and texture are small, the overall deformation of the sealing ring is still consistent with the results calculated by the finite-element method. However, because of the texture, there is circumferential micro-deformation on the surface of the seal ring, resulting in a change of surface contact pressure distribution (see Figure 6, direction of motion is perpendicular to the plotting plane). What's more, since the thickness of the fluid film is on the same order of magnitude as the size of the texture, the effect of the fluid film on the circumferential micro-deformation cannot be ignored.  In summary, in order to evaluate the effect of axial texture on seal performance, the following two problems need to be solved: 1. The micro-deformation of seal surface should be calculated according the texture shape and fluid film thickness distribution in the fluid-structure interaction calculation. 2. A method which can calculate the change of static contact pressure when the seal surface undergoes micro-deformation is needed to establish.
For first problem, since the fluid film thickness is determined by continuous correction according to the mixed lubrication equilibrium conditions, the micro-deformation also needs to be constantly changed with the correction process. In EHL theory, a film thickness distribution is obtained before each calculation cycle by assuming the initial fluid film thickness or the modified fluid film thickness, and the micro-deformation can be calculated by: where u y ð Þ is the micro-deformation of the sealing surface, δ y ð Þ is the shape of the axial texture and h y ð Þ is the thickness of the fluid film.
The contact pressure distribution when there is micro-deformation on the surface is then calculated. Westerggard 15 suggested that in two dimensional contact, the deformation caused by a sinusoidal pressure distribution has a linear relationship between the pressure, and on this basis, the shape variation and contact stress distribution were solved for any surface deformation.
Johnson 16 then extended this theory to three-dimensional contact problem. Based on the above research, Stanley et al. 17 put forward an analytical solution of the relationship between any surface pressure and deformation using the fast Fourier transform (FFT).
First, although the surface micro-deformation could be very complicated, it always can be transformed into a series of cosine deformation superpositions using the discrete Fourier transform. Then, the pressure change under the cosine form deformation can be obtained by the following formula 17 : All cosine deformations can be converted to a corresponding pressure change, which are then added to get the total pressure change. Theoretically, a twodimensional discrete Fourier transform is requiring, but the contact width of the seal ring in the axial direction is about 1 mm, and the width of the surface texture of the piston rod is much narrower, only 40 μm. Therefore, the sealing zone can be regarded as infinitely long for the ratio of radial length to circumferential length in the analytical model is much larger than 6, so it can be treated with a two-dimensional analysis. Finally, the static contact pressure p sc can be obtained by adding the contact pressure calculated by the finite-element simulation to the total pressure change. Combined with the static contact pressure simulated by finite element, the static contact pressure caused by the deformation of the seal ring of the seal ring can be obtained, the computational procedure is shown in Figure 7.
Influence of texture on seal ring surface deformation and contact pressure.
Since the analysis method described is applicable to all shapes of axial textures, only the texture consisted of a series of square grooves is analysed in this paper. The groove width is 20 μm and reciprocating rod seal systems with different groove depths and spacings are simulated. Figure 6 shows the meanings of the different groove parameters.

| Analysis of fluid mechanics
Fluid mechanics analysis can obtain fluid film pressure, in this part, the IHL theory is used to get an approximate initial film thickness distribution which then is modified by the EHL theory.
In IHL theory, the simplified one-dimensional Reynolds equation is used to obtain the initial thickness distribution of which the accuracy does not have to be too high, 13 where the lubrication film pressure distribution p can be considered to be consistent with the static contact pressure which has been obtained in solid mechanics analysis, and h 0 is the film thickness at maximum pressure. By further simplifying the equation, the cubic equation of the film thickness can be obtained, and the film thickness distribution can be solved. [3][4][5][6][7] After IHL analysis, a one-dimensional film thickness is obtained, which is then extended to a two-dimensional film thickness with axial symmetry in the circumferential direction, and further corrected by EHL method. Because the seal system loses its axisymmetric characteristic due to the axial worn rod, a two-dimensional fluid analysis is required because the rod is no longer axisymmetric. Therefore, the governing equation selected is as follows 18 : where x is the direction of the motion, y is circumferential, the flow factors ϕ xx , ϕ yy , ϕ s:c:x can be obtained from Refs. 19,20, where F is the cavitation index, Φ is the average density/pressure function and b h T is the truncated film thickness, and they are obtained from: In applying the finite volume method, Equation (2) can be discretized and linear equations for the pressure of five adjacent nodes are obtained. The boundary conditions in x direction are fixed pressure, and the boundary conditions in y direction are cyclic boundary conditions. And according to grid independent analysis, the grid size is determined as 5 μm. Then the fluid film pressure distribution is obtained by solving the linear equations using the method of inverse coefficient matrix. The dimensionless flow rate and dimensionless fluid shear stress are then calculated from F I G U R E 7 Computational procedure of deformation mechanics analysis.

| Analysis of contact mechanics
Contact mechanics analysis can obtain asperities contact pressure and asperities contact friction through film thickness. For the same reason with fluid mechanics analysis, it is described here briefly too. A contact model that is proposed by Persson,21 in which the shape of the asperities and interactions between the asperities can be considered by fractal theory and power spectrum analysis, is used to calculate the contact pressure: where α and β can be calculated from the Hurst exponent in accordance with the results of Ref. 21.

| Fluid-solid coupling calculation
The author 22 first proposed a method that considers the relationship between film thickness and fluid film pressure, asperities contact pressure and static contact pressure. According to the influence of film thickness on static contact pressure, fluid film pressure, and asperities contact pressure, the relationship between the three pressures and film thicknesses can be simplified as three springs (Figure 8). When the film thickness changes, the three pressures also change. Therefore, when p f þ p con ≠ p sc , the correction of film thickness can be calculated according the stiffness of three springs, denoted K con , K f , and K dc : For the sealing ring deformation is much greater than the film thickness, K sc ( K f þ K con , then Equation (6) can be simplified to: When the fluid film thickness changes, both fluid film and asperities contact pressures change (the change in static contact pressure is ignored), and the amount of change in pressure per unit change in film thickness represents the stiffness of the sealing system. Therefore, the total stiffness matrix can be obtained by the following steps: first, apply a unit increment to the film thickness of each node successively; second, calculate the sum of the fluid film pressure and asperities contact pressure after the film thickness changes; finally, extract the pressure increment after each change to obtain the total stiffness matrix K. Then, inverting the total stiffness matrix to get the total flexibility matrix I and the fluid film thickness correction Δh is calculated (Figure 9).

| Computational procedure
An outline of the computational procedure is as follows (see Figure 10): 1. Contact pressure is calculated considering that the rod is smooth using finite-element simulation. 2. Given an initial film thickness distribution h, the static contact pressure caused by the deformation of the seal ring p sc , fluid pressure p f , and asperities contact pressure p con are calculated. 3. If jp sc À p f À p con j < ε 1 , the calculation result is output; if not, the film thickness correction Δh is calculated using the stiffness matrix method, the film thickness distribution is updated, and Step (2) is repeated.

| RESULTS AND DISCUSSION
The simulation method introduced in this paper is universal and applicable to various types of reciprocating seals, so only two seal forms are simulated, the O-ring which represents traditional rubber seal and VL seal ring which represents combined seals. Table 1 lists all the parameters required for the simulation calculation, and these parameters also represent all the parameters F I G U R E 8 Simplified model of pressure in sealing zone.
affecting the sealing performance that can be considered by the theory used in this paper. These parameters are derived from an actual sealing system. The sealing system has low pressure and speed, and would not run continuously for a long time, and the friction heat is small, so it can be regarded as the system has always maintained the operating temperature. What's more, it's important to note that the grids number has great influence on the accuracy and efficiency of calculation and it is generally believed that the more grids number, the more the calculation can reflect the actual process, which means that the calculation results would be more accurate, but at the same time, the amount of calculation would also increase. Therefore, the verification of the irrelevance between the grids number and calculation results needs to be carried out and the specific method is increasing the grids number by reducing grid size, until the grids number increased, the calculation result changed very little. Through this process, it can be found that the size of grids should be less than or equal to 5 μm if the accuracy of calculation is to be guaranteed.

| Results for rubber O-ring
3.1.1 | Distributions of seal surface deformation, film thickness, and pressure Figure 11 shows the distribution of seal surface deformation and the rod surface, wherein the zero of height is F I G U R E 9 Flow chart of the calculation for the fluid film thickness correction. Boldface lowercase letters represent column vectors, boldface uppercase letters represent matrices; other letters represent scalars.
F I G U R E 1 0 Computational procedure of the algorithm.
T A B L E 1 Basic parameters and settings. . Under these conditions, we found that the seal ring would sink into the grooves, which causes large strain on the surface of the sealing ring and thus affecting the static contact pressure distribution.

Seal material NBR
On the basis of the results in Figure 11 and the contact pressure calculated by finite-element simulation, p sc is obtained through deformation mechanics analysis. Figure 12 shows the distributions of p sc and the contact pressure calculated by finite-element simulation. By comparing the two pressures, we found that the pressure would drop where the seal ring is sunk into the groove and increases at other locations.
On the basis of Figure 11, the film thickness distribution ( Figure 13) is obtained by subtracting the height of the rod surface from that of the sealing surface. The film thickness should be consistent in the circumferential direction when the rod is smooth; when the rod is axialtextured, the film thickness in the groove would be greater. Although the sealing ring would sink into the groove under these conditions, the deformation is insufficient to compensate for the depth of the groove.
On the basis of the film thickness distribution, p con is calculated (Figure 14). Through theoretical analysis, it can be known that p con is inversely proportional to film thickness, so the distribution of p con is opposite to that of the film thickness. p f is obtained by solving the Reynolds equation based on the film thickness ( Figure 15). Unlike p con , p f is almost unchanged in the circumferential direction. The main reason for the change of p f is resistance of the flow channel, so the p f would not change very much if the spacing is very small. However, p con is related to the film thickness and can mutate.

| Results of sealing performance
Although the above results show the working mechanism of a seal system with an axial-textured rod, friction and leakage need to be calculated to evaluate the sealing performance.
It is difficult to evaluate the influence of the texture on the average friction force of the seal system in three dimensions, so p f and p con are averaged in the circumferential direction (add the pressure values of all circumferential nodes with the same axial coordinates and divide by the number of circumferential nodes) for comparison ( Figure 16). The p f decreases and p con increases when there is an axial texture in the rod surface. This trend increased as the depth and density (width/spacing) of the texture increased.
It can be found that only during instroke, there are two turning points in the fluid pressure. This phenomenon can be explained by the Reynolds equation. For the quasi-one-dimensional Reynolds equation suitable for reciprocating seals, it can be transformed into the following form: From this equation, we can see that the gradient of fluid pressure is positive when the film thickness is large. At the outlet of fluid film, the film thickness is very large which means the gradient of fluid pressure is positive. When the contact force is high, the fluid pressure is also high, and its maximum value will be greater than the outlet pressure. Due to the gradient of fluid pressure at F I G U R E 1 1 Distribution of seal surface deformation (surface of the rod is also indicated).
the outlet is positive, there would always be another turning point between the point of maximum pressure and the outlet of the fluid film. However, for outstroke, the fluid pressure at the outlet is zero, so the gradient of fluid pressure at the outlet cannot be positive (otherwise there would be negative pressure), which means there would not be two turning points during outstroke.
The total friction is equal to the asperities contact friction (asperities contact pressure times dry friction coefficient) plus the fluid shear friction. Owing to the increase of p con , the total friction force increased with the increase of depth and density (width/spacing) of texture ( Figure 17). During the outstroke, the average friction force is 18.08 N without texture and 19.87 N with the deepest and densest texture, which is an increase of 9.92%; F I G U R E 1 2 Distributions of (a) static contact pressure; (b) contact pressure calculated by finite-element simulation.
F I G U R E 1 3 Distribution of film thickness.
during instroke, the corresponding values are 34.91 N and 37.32 N, demonstrating an increase of 6.91%.
Maximum asperities contact pressure is also a friction performance parameter (see Figure 18). The trend of maximum asperities contact pressure is the same as that of the average friction force, but the variation is larger. During outstroke, the maximum asperities contact pressure is 3.56 MPa without texture and 5.50 MPa with the deepest and densest texture, representing an increase of 54.5%; the corresponding instroke values are 5.31 MPa and 7.43 MPa, representing a difference of 39.9%. This is because axial texture results in asperities contact pressure in the non-grooved section that is higher than the average pressure, and the gap increases with the depth and density of the texture. At the same time, the average asperities contact pressure increases with depth and density of the texture. The maximum asperities contact pressure therefore changes more obviously. Combining the calculation results of maximum asperities contact pressure and average friction force, it can be concluded that axial texture will degrade the friction performance of the seal system.
Leakage is the most important parameter used to evaluate sealing performance. For a reciprocating rod seal system, leakage is equal to the flowrate during the outstroke minus the flowrate during the instroke. These flowrates therefore need to be calculated to obtain the leakage. Figure 19 shows the calculation results. The flowrate is lower in the seal system with the axialtextured rod, and the trend increased as the depth and density of the texture increased. During outstroke, the flowrate is 20.43 mL/h without texture and 20.14 mL/h with the deepest and densest texture, which is a decrease of 1.48%; during instroke, the flowrate is 17.18 mL/h without texture and 16.64 mL/h with the deepest and densest texture, an increase of 3.18%. The flowrate during the instroke decreases more than during the outstroke. thickness and the Poiseuille flowrate has a cubic relationship to the fluid film thickness. Because the flowrate decreases when there is texture, it can be inferred that the film thickness also decreases; however, the presence of texture causes the film thickness to vary circumferentially, actually increasing the maximum film thickness, so the Poiseuille flowrate may increase because it has a cubic relationship with the fluid film thickness, which means it is more sensitive to the maximum film thickness. The direction of Poiseuille flow is consistent with the direction of pressure decrease, so an increase of Poiseuille flow would further decrease the flowrate during the instroke, which causes the flowrate during the instroke to further decrease. Figure 20 shows the leakage calculated on the basis of the flowrates during the outstroke and instroke. Because the flowrate during the instroke decreases more, the leakage increases with depth and density of the texture. The leakage is 3.24 mL/h without texture and 3.51 mL/h with the deepest and densest texture, which is an increase of 8.15%. This means that axial texture would degrade the performance of the seal system.
Through the above analysis and interpretation of various calculation results, it can be found that the obtained results conform to the physical laws of solids and fluids, which can verify the reliability of the model to some extent.

| Results for VL sealing ring
3.2.1 | Distributions of seal surface deformation, film thickness, and pressure Figures 21,22,23,24,25 shows the distribution of seal surface deformation and the rod surface, the distributions of p sc and the contact pressure calculated by finite-element simulation, the film thickness distribution, the asperities contact pressure distribution, fluid film pressure distribution for VL seal ring respectively. The simulation results are similar to those of O-ring, the seal ring would sink into the grooves (see Figure 21), causing the stress to decrease (see Figure 22) and film thickness to increase in the groove (see Figure 23). For p con is inversely proportional to film thickness, the distribution of p con is opposite to that of the film thickness and for the spacing is very small, so the p f would not change very much. Figure 26 shows the average fluid film pressure and average asperity contact pressure calculated under different conditions. The presence of axial texture would also increases p con and decreases p f of VL sealing ring, but different from the calculation result of O-ring, during instroke, because the basic value of p con is much larger than p f , and the sum of the two is fixed, the increase of p con is less. Figure 27 shows the total friction calculated under different conditions. During the outstroke, the average friction force is 100.99 N without texture and 107.23 N with the deepest and densest texture, which is an increase of 6.18%; during instroke, the corresponding values are 71.20 N and 71.88 N, demonstrating an increase of 0.96%. The trend of the average friction force is consistent with that of p con . Figure 28 shows the maximum asperities contact pressure under different conditions. During outstroke, the maximum asperities contact pressure is 37.35 MPa without texture and 45.31 MPa with the deepest and densest texture, representing an increase of 21.31%; the corresponding instroke values are 33.26 MPa and 41.70 MPa, representing a difference of 25.38%. The overall trend is consistent with the O-ring, but due to the material characteristics, the increase of the maximum asperities contact pressure is relatively small. Figure 29 shows the calculation results of flowrate during outstroke and instroke. During outstroke, the flowrate is 12.79 mL/h without texture and 12.70 mL/h with the deepest and densest texture, which is a decrease of 0.71%; during instroke, the flowrate is 16.11 mL/h without texture and 15.64 mL/h with the deepest and densest texture, an increase of 2.86%. Similar to the simulation results of O-ring, the flowrate of instroke decreases more obviously.

| Results of sealing performance
F I G U R E 2 1 Distribution of seal surface deformation (surface of the rod is also indicated).
F I G U R E 2 2 Distributions of (a) static contact pressure; (b) contact pressure calculated by finite-element simulation. Figure 30 shows the leakage calculated on the basis of the flowrates during the outstroke and instroke. Because the flowrate during the instroke decreases more, the leakage increases with depth and density of the texture. The leakage is À3.32 mL/h without texture and À 2.94 mL/h with the deepest and densest texture,   which is an decrease of 11.45%. This means that axial texture would degrade the performance of the seal system. What's more, it can be found that the leakage is negative. In the reciprocating seal theory, when the piston rod extends out of the hydraulic cylinder, which called outstroke, the rod always carries out some medium and the medium would be brought back when the piston rod retracts into hydraulic cylinder. When the flowrate during outstroke is less than that during instroke, the average leakage rate would be negative. When the leakage rate calculated is negative, it actually shows 0 leakage in the actual use of the sealing system, and if medium is artificially added to the outside of the seal, the medium would be brought back to the piston chamber.

| CONCLUSIONS
In this work, static contact pressure is calculated by macroscopic solid mechanics analysis and microdeformation analysis, and on the basis of a prior numerical simulation model, the fluid pressure p f , and asperities contact pressure p con can be calculated under a given film thickness distribution h. Then the stiffness matrix method is used to determine the film thickness when the three pressures are in equilibrium to achieve fluid-solid coupling in the sealing zone. Finally, a simulation model, which can predict performance of reciprocating rod seal systems when there is a axial texture in the rod surface, is established.
A sealing system with different axial texture parameters is simulated and analysed. The results show that the seal would sink into the texture, which causes the static contact pressure to drop where the seal ring sinks into the groove and to increase at other locations. At the same time, the film thickness and asperities contact pressure in the groove would be greater, while the fluid film pressure is almost unchanged in the circumferential direction.
Friction and leakage are calculated on the basis of the above result. The average friction force and maximum asperities contact pressure increase as the depth and density (width/spacing) of the texture increase, which means that an axial texture would degrade the friction performance of the seal system. Furthermore, flowrates during the outstroke and instroke both decrease as the depth and density (width/spacing) of the texture increase, but the latter decreases more, which increases leakage. These results show that axial texture would reduce the sealing effect which means the wear of rod would reduce seal life.