Prediction of the Contact Behavior of Stepseals: Experimental and Numerical Investigations

Abstract

The contact behavior of a stepseal affects its reliability and remaining life. In this study, experimental and numerical analyses were performed to investigate the contact behavior of a typical stepseal. Its dimensions and material properties were also tested. The Mooney–Rivlin hyperelastic model was used to fit the stress–strain data of the rubber. A static contact pressure of 105.1 MPa was obtained using the Fujifilm pressure measurement film. A finite element model of a stepseal with reasonable element sizes was established. A comparison between the experimental results and finite element (FE) predictions shows that the finite element method underpredicts the maximum static contact pressure and contact length. For the maximum contact pressure, the test results were approximately 30.4% higher than those of the FE predictions.

1. Introduction

Seals are the most important elements used in hydraulic machinery to maintain the pressure and volume of a working medium [1,2,3]. Stepseals, which possess the advantages of a high dynamic sealing effect, low friction characteristics, and superior leakage control, are widely used in the stuffing boxes of reciprocating pumps [4,5,6]. Most problems associated with hydraulic components are dominated by the contact behaviors of the stepseal–rod sealing pairs. Hence, investigations of the contact behaviors of stepseals are both desirable and important.

Many studies have been carried out to investigate the sealing mechanism and performance of different reciprocating seals via experimental and numerical methods.

Nikas [7] developed a numerical model with which to study the elastohydrodynamics and mechanics of rectangular elastomeric seals for reciprocating piston rods under a wide range of temperatures and sealing pressures. Yang and Salant [8] compared the lubricating characteristics of U seals and stepseals via finite element analyses and found that the rod seal leakage is strongly dependent on the rod speed, sealed pressure, and seal roughness. Oliver and Hubertus [9] developed a test rig and conducted an experimental study on the influences of acceleration, sealed pressure, and temperature on a polytetrafluoroethylene (PTFE) stepseal.

Zhang et al. [10] performed an experimental study in conjunction with a finite element analysis of the contact pressure distributions of a bud-shaped composite sealing ring. Wang et al. [11] developed a soft elastohydrodynamic lubrication (EHL) model to investigate the effects of the non-Newtonian flow characteristics of lubricating oil on the sealing behavior of a hydraulic reciprocating stepseal. Xiang et al. [12] established a thermo-elastohydrodynamic lubrication model to analyze the thermal-viscous effects on a typical VL seal–reciprocating rod sealing pair. Ran et al. [13] developed a numerical model to analyze the effects of microscopic factors, such as rod speed and seal pressure, on reciprocating rod stepseal wear.

In this study, the dimensions and material properties of a typical stepseal, namely, the Turcon 2 K Stepseal RSK300500, were obtained and used to establish finite element models. A method of measuring the contact stress of stepseal by pressure measurement films is presented. The contact behaviors of the stepseal under different conditions were numerically investigated using a series of finite element analyses. The test results for the static contact pressure were compared with those of the finite element analyses. The effects of the radial compression and sealing pressure on the sealing performance are discussed.

2. Methods

2.1. Stepseal Dimensions and Material Properties

The tested stepseal, namely, the Turcon 2 K Stepseal RSK300500, consists of an O-ring and a PTFE-based seal ring. The dimensions of the stepseal are 50 × 65.1 × 6.3 mm, and the geometry of the seal ring can be measured in detail using a profilometer. The densities of the O-ring and PTFE seal ring, which are 1.25 g/cm³ and 2.075 g/cm³, respectively, were measured using the BSA224S electronic balance.

To obtain the material constants of the O-ring and the PTFE-based seal ring, a Z005 tensile-compression test machine was used in conjunction with a VML400 3D vision measuring machine [14]. The O-ring is made of PTFE and has an obvious linear elastic interval, which can be characterized by Young’s modulus and Poisson’s ratio. The O-ring is made of NBR, which is a typical hyperelastic material. The Mooney–Rivlin hyperelastic mode is used to characterize its material properties, and parameters need to be fitted to achieve its characterization.

The Mooney–Rivlin hyperelastic model [15,16,17] can be used to describe the elastic deformation of incompressible rubbers, for example, the O-ring. The strain energy function for this process is given in Equation (1):

W = C₁₀(I₁ − 3) + C₀₁(I₂ − 3) + (1/d)(J − 1)

(1)

where I₁ and I₂ represent the first and second deviatoric strain invariants, respectively; J is the deformation gradient; and C₁₀, C₀₁, and d are the material constants. For incompressible rubber materials, J = 1. Hence, Equation (1) can be simplified as follows:

W = C₁₀(I₁ − 3) + C₀₁(I₂ − 3)

(2)

Figure 1 shows the curve fitting of the uniaxial tensile tests of the O-ring and PTFE-based seal ring. Similar to ductile metals, a linear elastic region can be observed for the PTFE-based sealing ring which is expressed effectively by Young’s modulus and Poisson’s ratio. This region is applicable in describing the contact performance of the stepseal.

Table 1. The material constants for the components of the stepseal.

Materials	C10 (MPa)	C01 (MPa)	d	E (MPa)	υ
O-ring	5.58 × 10−2	1.18 × 10−1	0	-	-
PTFE-based seal ring	-	-	-	289	0.3

lists the material constants for the O-ring and PTFE-based seal ring, as obtained from the curve fitting of the uniaxial tensile tests.

2.2. Testing Static Contact Pressure Distributions

Fujifilm Prescale-type pressure measurement films (Tokyo, Japan) were used to confirm the distribution of the contact pressure at the lip of the stepseal assembled in the sealing box. At room temperature and pressure, the stepseal was installed in the sealing groove, and a film was fixed on the seal lip, and then the plunger chamfer end was slowly squeezed into the tool until the plunger was completely in the tool. It was held for 15 min, then the plunger was removed and the film was sent for inspection. Because the radial compression of the assembled stepseal could not be detected accurately, it was ignored in the experimental study.

Using the Fujifilm pressure distribution mapping system, namely, Prescale FPD-8010E, the contact pressure at the lip of the stepseal can be obtained, as shown in Figure 2. Figure 3 illustrates the contact pressure profile extracted from the mapping system. It has a maximum contact pressure of 105.1 MPa. However, due to the influence of the test tool on the friction interference of the pressure-sensitive sheet, the maximum stress reliability of the experimental results is high, and the contact width is inaccurate.

3. Finite Element Analyses

3.1. Finite Element Model

A two-dimensional (2D) axisymmetric finite element (FE) model was created. The model consisted of a seal housing, rods, and the tested stepseal, and was built using the commercial ABAQUS Professional 2022 [18] software package, as shown in Figure 4. Four-noded bilinear plane strain (CPS4E) elements were used for the mesh of the O-ring and PTFE-based seal ring, with a global mesh size of 0.125 mm, which allowed for the modeling of large strains and deformations [19,20]. In the vicinity of the contact surfaces between the sealing lip and rod, a relatively small mesh size of 0.035 mm was used to provide sufficiently accurate results, which resulted in 5495 elements. Surface-to-surface contacts were employed for both housing-to-stepseal and stepseal-to-rod contacts. A small sliding assumption was made for the two contacts [21,22]. The coefficient of friction was taken to be a constant value, i.e., 0.01, for all contacts. The material constants listed in Table 1 were used in the FE model. Two loading steps are used in the FE model. First, the plunger rod was moved upward by a certain displacement to represent the amount of installed precompression. Second, the fluid side of the stepseal was pressurized to represent the compression that resulted in hydraulic pressure. Then, a pressure penetration interaction method was used to automatically determine the critical point at which the hydraulic pressure was greater than the contact stress. The geometry model of the sealing groove is set as a fixed constraint, and the piston rod only retains the freedom to simulate interference fit and exerts pressure load on the stepseal.

3.2. Mesh Sensitivity Study

To obtain sufficiently accurate results while minimizing time consumption, a mesh independence study was performed. Figure 5 shows the contact pressure distribution on the contact interface between the stepseal and rod using three different numbers of elements: 819, 3303, and 5495. As shown in Figure 5, when the number of elements increases from 819 to 3303, significant changes in the contact pressure distribution and contact width are observed. The tendencies of the contact pressure distribution and peak value of the contact pressure for the FE model with 5495 elements, i.e., 73.2 MPa, are similar to those of the FE model with 3303 elements, i.e., 76.7 MPa. Hence, choosing 5495 elements for the FE model was reasonable to obtain sufficiently accurate results.

3.3. Contact Behavior Prediction

The sealing performance and service life of the sealing components are closely related to the contact behavior between the stepseal and the rod. The von Mises stress, contact length, and contact stress distribution of the stepseal are important indicators for evaluating static sealing performance. Figure 6a,b show the FE-predicted contact behaviors of the stepseal under 0.4 mm radial compression and a combination of 0.4 mm radial compression and a working pressure of 3 MPa. A close-up view of the stress distribution under 0.4 mm radial compression is shown in Figure 6c. The maximum stress occurred at the lip position of the PTFE seal ring with a value of 23.82 MPa. Figure 6b,d show the von Mises stress and contact stress distribution under a combination of 0.4 mm radial compression and a working pressure of 3 MPa, with maximum values of 50.77 and 8.03 MPa.

4. Results and Discussion

4.1. Static Contact Behavior of Stepseals

Figure 7 shows a comparison between the experimental static contact pressure profile obtained from the Fujifilm pressure distribution mapping system and the FE-predicted contact pressure profile. As shown in Figure 7, the experimental static contact pressure profile exhibited a higher maximum contact pressure and contact length than that predicted by the FE. Moreover, the tested maximum contact pressure was approximately 30.4% higher than that predicted by the FE. The FE model underpredicted the contact behavior of the stepseal, which may have led to an exaggerated remaining life of the stepseal.

4.2. Effects of Radial Compression on Contact Behavior

Figure 8 shows the stress distributions of the stepseal under radial compression of 0.2, 0.4, and 0.6 mm, combined with a working pressure of 3 MPa. As shown in Figure 8, the maximum stress occurred at the lip of the PTFE ring, whereas the stress level of the O-ring was relatively small. Based on the stress distribution results shown in Figure 8, variations in the maximum stress and contact length of the stepseal are shown in Figure 9. The maximum stress as well as the contact length increase with the increase in the amount of radial compression.

The contact pressure distributions of the stepseal under a combination of three radial compression amounts and a working pressure of 3 MPa are shown in Figure 9. Moreover, Figure 10 shows that the static contact pressure in the contact area rapidly increases to its peak in the initial stage and then slowly decreases to zero. The asymmetric distribution of the static contact pressure was partly due to the cross-sectional asymmetry of the PTFE ring, where the angle of the contact area between the slip of the PTFE ring and the rod on the high-pressure fluid side was greater than that on the low-pressure side. The asymmetric structural features of this PTFE ring played an important role in ensuring the sealing effect of the stepseal. However, this was because of the asymmetric deformation of the PTFE ring caused by the high-pressure fluid on one side of the fluid. As shown in Figure 10, the maximum contact stress was not sensitive to an increase in the amount of radial compression, whereas the contact length showed an increasing trend. As shown in Figure 8, the stress level of the O-ring is relatively small, which indicates that the O-ring plays an auxiliary sealing role in compression and compensates for minor wear.

4.3. Effects of Sealing Pressure on Contact Behavior

Figure 11 shows the FE-predicted stress distribution of the stepseal under different sealing pressures, combined with a radial compression of 0.6 mm. Moreover, Figure 11 shows that the maximum stresses corresponding to the three sealing pressures occurred at the lip of the PTFE ring. The maximum stress of the stepseal increased with an increase in the sealing pressure. Figure 12 shows that the maximum stress and contact length increase with different radial compression levels. Figure 13 shows the variations in the maximum stress and contact length of the stepseal under three different sealing pressures, combined with a radial compression of 0.6 mm. In a static sealing system, a larger contact length indicates a larger contact area of the sealing surface and better sealing performance, whereas a larger contact area is likely to increase the wear surface of the PTFE ring.

Figure 14 shows the static contact pressure profiles of the stepseal under three different sealing pressures. As shown in Figure 14, the static contact pressure profiles exhibit asymmetric characteristics for different sealing pressures. The maximum static contact pressure and contact length increase with an increase in the sealing pressure. Furthermore, the peak values of the contact pressure of the stepseal are larger than those of the corresponding sealing pressures. For instance, the peak value of the static contact pressure is approximately 26.7 times the sealing pressure of 3 MPa.

5. Conclusions

In this study, to explore the contact behavior of the Turcon 2 K Stepseal RSK300500, experimental and numerical studies were conducted. The conclusions are as follows:

Experimental studies were initially conducted to determine the dimensions and material constants of the stepseal used for the FE analyses. The stress–strain curves and material constants were obtained by a uniaxial experiment of rubber and plastic materials. The static contact pressure was obtained using a Fujifilm pressure measurement film with a value of 105.1 MPa.

A finite element model of the stepseal was established using the dimensions and material constants obtained from experimental studies. A mesh sensitivity study was conducted and an element size of 0.035 mm in the vicinity of the lip of the PTFE-based sealing ring was able to provide sufficiently accurate results.

Compared with the experimental results, the FE model underpredicted the maximum static contact pressure and contact length. The effects of radial compression and sealing pressure on the contact behavior were investigated using a series of FE analyses. The FE-predicted maximum contact stress was not sensitive to an increase in the amount of radial compression, whereas the contact length showed an increasing trend. The FE model predicted that the maximum static contact pressure and contact length would increase with an increase in the sealing pressure. This study only introduces the static sealing scenario, reciprocating sealing and microscopic leakage channels are also worthy of further study.