Lubrication Characteristics of a Warhead-Type Irregular Symmetric Texture on the Stator Rubber Surfaces of Screw Pumps

Abstract

A theoretical model for the micro-texture on the inner wall of the stator rubber in screw pumps was developed. The finite element analysis method was employed. The pressure and streamline distributions for warhead-type, concentric circle-type, and multilayer rectangular-type textured surfaces were calculated. The effects of textured morphology, groove depth, groove width, and other parameters on the lubrication field were systematically investigated and analyzed. A nanosecond laser was employed to process the textured rubber surface of the stator in the screw pump. Subsequently, a micro-texture friction performance test was conducted on the rubber surface of the stator in actual complex well fluids from shale oil wells. Given the results of the simulation analysis and experimental tests, the lubrication characteristics of textured rubber surfaces with varying texture morphologies, rotational speeds, and mating loads were revealed. Furthermore, it indicated that the irregular symmetric warhead-type micro-texture exhibited excellent dynamic pressure lubrication performance compared with concentric circle-type and multilayer rectangular-type textures. The irregular symmetry enhanced the dynamic pressure lubrication effect, enhanced the additional net load-bearing capacity of the oil film surface, and reduced friction. As the groove depth increased, the volume and number of vortices within the groove also increased. The fluid kinetic energy was transformed into vortex energy, leading to a reduction in wall stress on the surface of the oil film, thereby affecting its bearing capacity. Initially, the maximum pressure on the wall surface of the oil film increased and then decreased. The optimal dynamic pressure lubrication effect was achieved with a warhead-type texture size of 3 mm, a groove width of 0.2 mm, and a groove depth of 0.1 mm. Well-designed texture morphology and depth parameters significantly enhanced the oil film-bearing capacity of the stator rubber surface, improving the dynamic pressure lubrication effect, and consequently extending the service life of the stator–rotor interface in the screw pump.

1. Introduction

Screw pump oil extraction has emerged as a pivotal method for lifting oil and gas in ultradeep wells, highly deviated wells, and horizontal wells. This is attributable to its high efficiency in medium conveyance, low energy consumption, and strong adaptability [1,2,3,4,5]. The mechanical wear behavior between stator–rotor contact surfaces critically impacts the service life and operational efficiency of screw pumps. Consequently, mitigating the wear between the stator and rotor is essential to prolonging the operational life of screw pumps, enhancing the efficiency of oilfield recovery operations.

Recently, studies have proposed surface texture technology to enhance the friction and wear performance of contact surfaces in relative motion. This involves designing and processing various micro-textures, such as micro-pits, micro-bulges, and micro-grooves, with specific patterns on the material surface. These micro-textures significantly reduce surface friction and enhance the load-bearing capacity of the oil film (Figure 1) [6,7,8,9,10,11,12,13]. Wang and Yu et al. engineered pit and groove micro-textures on bearing surfaces, demonstrating that the average friction coefficient of pit micro-textured surfaces decreased by 41.4% compared with non-textured surfaces. Furthermore, they emphasized that the careful selection of groove morphology is critical for optimizing bearing lubrication performance [14,15]. Additionally, Jia et al. developed a plunger texture lubrication model that accounts for plunger deformation and eccentricity. Their findings indicated that laser-etched pit-type micro-textures on the plunger surface significantly enhance lubrication performance, resulting in a 27.8% reduction in the average friction coefficient [16]. Zhang et al. analyzed the surface texturing of polymer polyethylene materials by establishing a theoretical model aimed at optimizing the load-carrying capacity, friction, and drag reduction of four texture shapes: circular, rectangular, square, and triangular. It was observed that the texture area rate, width, and depth strongly influence the load-carrying capacity of the oil film, with the optimal texture area rate for superior tribological performance ranging between 12% and 36% [17]. Bai et al. conducted hydrodynamic simulations to investigate the lubrication properties of micro-groove textures on surfaces at various flow rates. Their results revealed that vortices in the near-wall flow field on textured surfaces exhibited greater stability compared with those on smooth surfaces [18]. Ma et al. designed a sinusoidal groove texture employing both simulation analysis and friction experiments. It was observed that the optimal groove spacing enhanced the dynamic pressure effect and improved the oil film condition, with a texture area rate of 25%, resulting in optimal tribological performance [19]. Han and Shen employed theoretical analysis and numerical simulation. It was observed that asymmetric rectangular micro-textures exhibited exceptional lubrication performance compared with symmetric rectangular textures [20,21]. Wang et al. investigated the stator–rotor interference fit conditions in screw pumps and introduced micro-textures to the rotor surface to analyze the influence of texture, shape, and angle on the tribological performance between the stator and rotor. The results indicated that the average coefficient of friction was reduced to ~62% compared with non-textured surfaces. Additionally, the tribological performance under various lubrication conditions was examined by applying micro-textures to both stator and rotor surfaces. The study revealed that at a texture angle of 0° under dry friction conditions, the presence of micro-textures significantly enhanced the tribological performance of the stator–rotor interface [22,23]. Zhang Baoling employed fluid dynamics methods to analyze and compare the friction characteristics, pressure distribution, and flow field distribution of surfaces with no texture, as well as circular, spherical, or V-shaped textures. By conducting tests under water lubrication, oil lubrication, and oil–water mixing lubrication conditions, Zhang verified the theory of stator rubber surface texturing lubrication for screw pump stators. This study highlighted that optimizing texturing parameters significantly improved the friction characteristics of stator–rotor pairs, thereby demonstrating a significant enhancement in screw pump performance [24].

Surface texturing technology has shown significant promise in enhancing the tribological properties of materials. However, current studies predominantly focused on hard materials such as metals, commonly employed in bearings, gears, and cutting tools. Soft materials such as the rubber stator found in screw pumps, have received considerably less attention [25,26,27,28,29,30,31,32,33,34]. Therefore, this study addressed this gap by proposing the design of an irregular high-lubrication and friction-reducing texture, drawing inspiration from concentric circular patterns and multilayer rectangular textures. Based on fluid dynamic pressure lubrication theory, a mathematical model for stator rubber lubrication was established. Subsequently, finite element analysis was employed to simulate the impact of texture type, groove depth, and groove width on lubrication performance under actual shale oil well conditions. This study offered guidance for the optimal design of the textured surface of screw pump stator rubber, thereby advancing texturing design theory.

2. Theoretical Model of the Textured Surface of the Stator Rubber

2.1. Geometric Modeling of the Stator Rubber Textured Surface

Screw pumps, integral to rodless lift oil recovery systems, often face mechanical wear at the stator–rotor interface due to prolonged exposure to oil pressure, temperature, and viscosity. This wear can lead to pump failure. The application of surface texturing on the stator rubber can significantly enhance lubrication between the stator and rotor, thereby enhancing pump performance and longevity. In this study, a textured unit on the rubber surface of the screw pump stator was selected for analysis.

The warhead-type texture is designed based on a combination of warhead-type, concentric circle-type, and multilayer rectangular-type texture morphology, incorporating irregular symmetry to enhance the dynamic pressure lubrication effect in the grooves. Geometric models of the warhead-type, concentric circle-type, and multilayer rectangular-type textures were established sequentially (Figure 2). Textures were arranged in layers, starting from the center of the L × L unit area and expanding outward. The grooves of the textures have a width of w and a depth of h, with the overall texture size controlled by adjusting the dimensions of the outermost layer.

2.2. Mathematical Modeling of the Stator Rubber Textured Surface

Assuming a constant fluid flow, the Reynolds number (R_e) is employed to determine the flow regime. The flow is considered laminar when R_e ≤ 2300 and turbulent when R_e ≥ 4000 [35,36].

The actual Reynolds number of the fluid within the stator–rotor friction pair of a screw pump is calculated using the following formula:

$$R_e={\displaystyle \frac{\rho U{h}_0}{\eta }}$$

(1)

where U is the sliding velocity on the upper surface of the oil film (m/s), h₀ is the thickness of the oil film (m), ρ is the density of the shale oil (kg/m³), and η is the coefficient of dynamic viscosity of the shale oil (m²/s).

When the Reynolds number indicates turbulent flow, the k–epsilon model [37,38] was selected, introducing the turbulent kinetic energy k and dissipation rate ε to enhance computational accuracy.

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left[\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right]{\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(2)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \epsilon u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }$$

(3)

where C_1ε, C_2ε are empirical constants, and σ_k as well as σ_ε are the Prandtl numbers corresponding to the turbulent kinetic energy and dissipation rate, respectively.

Based on the theory of elastohydrodynamic lubrication, and considering the influence of inertial forces, the Navier–Stokes (N–S) equations describe incompressible Newtonian fluids in a Cartesian coordinate system [39,40,41,42,43,44]:

$${\displaystyle \frac{\partial \left(\rho u\right)}{\partial t}}+div\left(\rho \eta u\right)={\displaystyle \frac{\partial \tau xx}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yx}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zx}}{\partial z}}-{\displaystyle \frac{\partial P}{\partial x}}+F_x$$

(4)

$${\displaystyle \frac{\partial \left(\rho \nu \right)}{\partial t}}+div\left(\rho \eta \nu \right)={\displaystyle \frac{\partial {\tau }_{xy}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yy}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zy}}{\partial z}}-{\displaystyle \frac{\partial P}{\partial y}}+F_y$$

(5)

$${\displaystyle \frac{\partial (\rho w)}{\partial t}}+div(\rho \eta w)={\displaystyle \frac{\partial {\tau }_{xz}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zz}}{\partial z}}-{\displaystyle \frac{\partial P}{\partial z}}+F_z$$

(6)

where η is the dynamic viscosity of the fluid (Pa·s); ρ is the density of the fluid (kg/m³); u, v, and w are the components of the velocity vector in the x-, y-, and z-axis directions (m/s), respectively. τ_xx, τ_xy, and τ_xz are the components of viscous action at a point, respectively. P is the pressure of the fluid at a point (Pa). F_x, F_y, and F_z are the components of the volumetric force of the fluid in the x-, y-, and z-axis directions (N), respectively.

The oil film-bearing capacity was obtained by integrating the pressure distribution region of the wall shear stress over the region [45,46,47]:

$$F={\displaystyle {\int }_0^L{\displaystyle {\int }_0^{L}Pdxdy}}$$

(7)

where P is the pressure of the shale oil film in Pascals (Pa), L is the boundary for calculations in the x and y-axis directions (m).

The oil film friction was obtained by integrating the region of wall shear stress on the oil film [48,49,50]:

$$f={\displaystyle {\int }_0^L{\displaystyle {\int }_0^L\tau dxdy}}$$

(8)

where τ is the shear stress of the oil film (Pa).

The coefficient of friction on the rubber surface of the textured stator in the screw pump is calculated as the ratio of the friction force to the load-carrying capacity:

$$\mu ={\displaystyle \frac{f}{F}}$$

(9)

3. Simulation Analysis of Stator Micro-Texture Surface Lubrication Flow Field

3.1. Simulation Model of the Rubber Texture Surface Flow Field of a Screw Pump Stator

The number of mesh elements directly affects the accuracy of simulation analysis, which is crucial for determining the distribution of the wall pressure field and lubrication flow field on the oil film. Therefore, maintaining the number of mesh elements within a reasonable range is essential [51,52]. Computational fluid dynamics was employed to delineate the stator rubber surface warhead-type micro-texture geometric model mesh, solving for the oil film wall pressure field and lubrication flow field. Furthermore, for the warhead-type texture model, mesh independence validation was conducted using the radial pressure on the oil film wall as the target parameter. The validation of mesh independence for the stator rubber warhead-type micro-texture is illustrated in Figure 3a. Subsequently, with varying numbers of meshes, the radial pressure along the oil film wall was relatively constant. Given both the calculation accuracy and computation time, the mesh was determined at 470,000 (Figure 3b). Under varying tolerance values, the maximum pressure on the upper surface of the stator rubber microstructure oil film decreases as the tolerance value is reduced, initially declining rapidly before reaching a more gradual trend. When the tolerance values are set to 1 × 10⁻⁵ and 1 × 10⁻⁸, the calculation error for the maximum pressure on the microtextured oil film’s upper surface remains below 5%. Considering both computational cost and convergence rate, a final tolerance value of 1 × 10⁻⁵ is selected.

In this simulation, the upper wall of the micro-texture simulation model was set with slip conditions; the lower wall was set with stationary boundary conditions; the front and rear walls were set with symmetric boundary conditions; and the pressure inlet and outlet boundary conditions are illustrated in Figure 3c. The lubricating medium utilized was shale oil with a density of 870 kg/m³ and a viscosity of 0.08 Pa·s, which flows along the negative x-axis direction at 1 m/s. The outlet and inlet pressures were maintained at 101.325 kPa. The three-dimensional steady-state challenge within the computational domain was analyzed using a pressure solver combined with PISO coupling to solve the pressure and velocity fields.

The texture simulation model includes warhead-type, concentric circle-type, and multilayer rectangular-type textures. The texture dimensions are as follows: sizes of 2.5 mm, 3 mm, and 3.5 mm; groove widths of 0.1 mm and 0.2 mm; and depths ranging from 0.05 mm to 0.5 mm. Ultimately, the maximum pressure on the oil film surface served as the final evaluation criterion for texture performance, guiding the selection of surface texture for the rubber stator.

3.2. Influence of Texture Morphology on the Lubricating Properties of Stator Rubber Surfaces

Figure 4a–c depict the pressure distribution of the oil film on the stator rubber surface with different texture morphologies. Shale oil transits from a small convergence wedge to a large convergence wedge. With the increase in wedge angle, the volume of the fluid channel increases, and the volume of shale oil decreases instantaneously in the transition zone. In this process, the relative volume of shale oil changes, resulting in the emergence of negative pressure. The alternating converging and diverging wedges created an irregularly symmetric pressure distribution on the oil film, thereby enhancing the net load-bearing capacity. Thus, with varying texture morphology, the positive and negative pressure areas on the oil film wall exhibited changes. Upon comparing Figure 4a–c, it was observed that the maximum pressure and positive pressure areas of the asymmetric warhead-type micro-texture exceeded those of the symmetric concentric circle-type and multilayer rectangular-type textures. In Figure 4d, the grooves on the stator rubber surface formed a wedge gap, exhibiting a dynamic pressure effect, leading to fluctuations in the pressure field. Figure 4e illustrates the net pressure distribution curve of the warhead-type texture oil film. The grooves exhibited distinct pressure peaks, with the positive pressure region exceeding those of the negative pressure region. At this point, the dynamic pressure effect dominated the flow field. The asymmetry effectively prevented the positive and negative pressures from canceling each other out, enhancing the texture fluid dynamic effect, improving the load-bearing capacity of the film, and augmenting the friction and drag reduction effects.

Figure 4f illustrates the maximum pressure on the oil film surface of the textured surface under working conditions with groove widths of 0.1 mm and 0.2 mm for three different texture shapes. The oil film of the warhead-type texture exhibited a higher maximum pressure under the same groove width, indicating that irregularly symmetric textures exhibited superior dynamic pressure lubrication compared with concentric circle-type and multilayer rectangular-type textures.

The upper wall of the oil film exhibited a higher maximum pressure for a groove width of 0.2 mm compared with a groove width of 0.1 mm. At a groove width of 0.2 mm, the texture convergence interval increased, and the stator–rotor mutual sliding process enhanced the hydrodynamic pressure, indicating dynamic pressure lubrication performance. Initially, as the texture size increased, the maximum pressure tended to increase and then decrease, peaking at an outer texture size of 3 mm. Subsequently, as the texture size increased, the maximum pressure on the oil film wall decreased. This resulted in a reduced net bearing capacity, diminished friction, and drag reduction effects.

3.3. Influence of Texture Depth on the Lubricating Properties of the Stator Rubber Surface

To analyze the influence of the texture groove depth on the lubrication performance of the rubber surface, three types of textures with varying morphologies were selected and simulated across groove depths from 50 μm to 500 μm. The fluid domains for groove depths of 100 μm, 300 μm, and 500 μm are shown in Figure 5a. The pressure distribution across the cross-section of the microtextured grooves was analyzed, showing distinct variations as shale oil flows through the grooves. The gradual lightening of pressure color from the outer to the inner grooves indicates an enhancement in hydrodynamic lubrication. In regions with darker pressure color, an increase in additional load-bearing capacity is observed, leading to improved lubrication performance.

The maximum pressure on the upper wall of the textured oil film versus the groove depth for different textured morphologies and groove width is shown in Figure 5b. The curve code initials represent different textured morphologies: W for warhead-type textures, C for concentric circle-type textures, and R for multilayer rectangular textures. As the groove depth increased, the maximum pressure on the oil film surface of the three textures initially increased and then decreased. The pressure on the upper surface of the oil film within the unit area was integrated across various depth conditions to assess the variation in average pressure. As illustrated in Figure 5c, the trend of average pressure aligns closely with that of the maximum pressure. The threshold groove depth was 100 μm. Beyond this threshold, the vortex volume inside the texture expanded. Thus, when the groove depth reached 500 μm, a new vortex formed inside the texture, consuming part of the fluid dynamic pressure energy. Thus, energy loss increased. Under different depth conditions, when the micro-texture groove width was 0.2 mm for the three different texture morphologies, the maximum positive pressure on the upper wall of the oil film was greater, resulting in a higher net bearing capacity and enhancing friction and drag reduction effects.

Figure 5d shows the dynamic pressure lubrication field distribution at the stator rubber textured groove depths of 100 μm, 300 μm, and 500 μm for the warhead-type textured groove with a width of 0.2 mm condition. Furthermore, when the groove depth was 100 μm, the vortex did not fully form, the distribution of flow traces was dense, and the dynamic pressure lubrication effect inside the groove was dominant. As the groove depth increased, the flow state of the internal flow field inside the groove changed dramatically, accompanied by varying degrees of reflux and vortex phenomena as well as energy changes. Groove depth increased vortex volume and intensity, increasing the maximum pressure on the oil film wall. However, the vortex also led to energy loss, inhibiting the increase in the oil film-carrying capacity. As vortex energy consumption increased, the flow trace line distribution became sparse, reducing the impact of the fluid dynamic pressure lubrication effect. Therefore, the groove depth was selected such that the vortex was not fully formed, preventing excessive vortex intensity.

3.4. Influence of Irregular Symmetry on the Lubrication Performance of Stator Rubber Surface

The irregular symmetrical properties of the warhead-type microstructure led to differences in the direction of lubricant flow direction and different dynamic pressure lubrication effects on the stator rubber surface. To investigate this influence, the positive direction along the positive x-axis and the negative direction along the negative x-axis were defined. Simulations were conducted for both positive and negative directional textures.

Furthermore, when shale oil flows from the positive and negative directions toward the warhead-type texture, the pressure distribution on the upper wall of the oil film is depicted in Figure 6a,b. When shale oil flows in the positive direction of the x-axis, the texture head exhibits a negative pressure area, and the tail exhibits a positive pressure area. Conversely, when shale oil flows in the negative direction of the x-axis, the texture head exhibited positive pressure, and the tail exhibited negative pressure. Upon comparing Figure 6a,b, it was observed that when the shale oil flows along the negative direction of the x-axis, the maximum pressure on the upper wall of the stator rubber surface texture oil film was higher, and the positive pressure region was larger. This was attributable to the front of the warhead-type texture, which exhibited exceptional convergence compared to the tail, enhancing the dynamic pressure effect. The irregular symmetry of the warhead-type texture inhibited positive pressure loss and enhanced the additional net load capacity obtained at the wall on the oil film compared with the regular symmetrical texture.

Figure 6c illustrates the influence of shale oil flow along the x-axis in both the positive and negative directions on the maximum pressure on the upper wall of the oil film at the different groove depths. As the groove depth increased, the maximum pressure on the upper wall of the oil film decreased in both directions. When the groove depth was 100 μm, the maximum pressure on the upper wall of the oil film increased by 4.10% compared with the positive direction. As the groove depth increased, the rate of the maximum pressure increases on the upper wall of the oil film decreased. At a groove depth of 500 μm, the maximum pressure increases by 1.64%. At each depth, the maximum pressure on the upper wall of the oil film increased by an average of 2.64%, indicating that under reasonable depth conditions, the dynamic pressure effect dominated. Thus, the irregular symmetry significantly affected the texture lubrication performance. As the depth increased, the volume and number of vortices increased, the vortex effect dominated, and the influence of the irregular symmetry texture on the lubrication performance was weakened. Therefore, given the irregular symmetry characteristics, designing the texture with a reasonable depth effectively enhanced the hydrodynamic lubrication effect.

4. Screw Pump Textured Stator Rubber Friction Test

4.1. Preparation of the Textured Rubber Surface

High acrylonitrile rubber was selected as the test material, and a cuboid with dimensions of 60 mm × 20 mm × 3 mm was prepared. The stator rubber was textured using IPG nanosecond laser equipment. As shown in Figure 7, the texture laser processing parameters were as follows: speed of 800 mm/s, power of 10%, frequency of 200 kHz, and five engraving passes. After processing, the sample was cleaned using an ultrasonic cleaner combined with anhydrous ethanol. After drying, the surface texture morphology of the rubber sample was observed using three-dimensional confocal microscope (VK-X1050), KEYENCE, Osaka, Japan.

Figure 8a shows the surface morphology of three textures after preparation under Olympus 3D confocal microscope: the warhead type, concentric circle type, and multilayer rectangle type. A slight laser ablation phenomenon was observed at the starting point of the adjacent groove. This was attributable to the energy retention of the initial laser pulse during processing, prolonging the laser retention time within the unit pulse time, and resulting in unavoidable slight thermal damage at the starting point. The overall morphology of the texture was a layered groove array. The texture was uniform, and there were no micro-convex peaks. Figure 8b shows the change in hardness value of screw pump stator rubber under the condition of 70 °C shale oil immersion for 7 days. Under this working condition, the hardness of the rubber sample was tested every 24 h, and the average hardness of the rubber sample was recorded. As the number of soaking days increased, the hardness of the rubber sample decreased first and then eased, and the original hardness decreased from 75.8 HA to 72.4 HA. Figure 8c shows how the tensile sample of the soaked rubber sample was subjected to tensile test. As the tensile stress increased, the rubber sample broke at 85.7 mm, and the elongation at break reached 285.7%.

4.2. Actual Complex Well Fluid Textured Rubber Friction Test

The friction and wear tests on the surface of texturized rubber were carried out on the UMT-3 reciprocating friction and wear tester based on the actual operating conditions of screw pumps in shale oil wells. Using the UMT-3 reciprocating friction and wear testing machine, the experimental study on the surface of texturized rubber is carried out, and the schematic diagram of the friction and wear testing machine is given, as shown in Figure 9a,b. A GCr15-bearing steel ball served as the upper sample, sliding relative to the lower sample at a constant speed. The test was conducted in an oil-rich state to simulate the real-time operating conditions of the screw pump, ensuring the accuracy and effectiveness of the test results. The actual complex well-conditioned fluid of a shale oil well served as the lubricating medium upon fluid addition through dripping. The test environment temperature was 18 °C, the friction frequency was 3 Hz, the reciprocating distance was 6 mm, the loads were 5 N, 10 N, and 15 N, the test duration was 1200 s.

Figure 9c illustrates the tribological characteristics of textured stator rubbers in screw pumps under actual well conditions with liquid lubrication at applied loads of 5 N, 10 N, and 15 N. As the load increases, the friction coefficients of warhead-type, concentric-circle type, and multilayer-rectangular type textured stator rubbers exhibit an upward trend. Among these, the warhead-type shows enhanced adaptability across varying load conditions and demonstrates superior lubrication performance. Under a 10 N applied load, the friction coefficient of the warhead-type and multilayer rectangular-type textured stator rubber decreased significantly within 200 s and gradually stabilized thereafter. Furthermore, during the test, the upper sample continued to reciprocate, leading to the actual well-conditioned fluid in the reciprocating interval, exhibiting a certain degree of temperature increase. This temperature increase led to a decrease in the fluid viscosity, thereby promoting a reduction in the friction coefficient. In the initial stage of the running-in period, the concentric circular micro-texture does not immediately form a complete lubricant film, leaving numerous contact points on the friction surface and resulting in a higher friction coefficient. Over time, as the lubricant fluid gradually accumulates and diffuses within the texture, the lubricating effect improves, causing the friction coefficient to initially increase, then decrease, and eventually stabilize. After 800 s, the friction coefficients of the warhead-type and concentric circular textures became similar within a small range. Additionally, due to the extrusion effect, the lubricating oil at the groove of the warhead-type texture exhibited side leakage, resulting in a slight overlap of the friction coefficients of the two textures. The geometric properties possessed by the rectangular micro-texture make the micro-texture edges and sharp corners produce stress concentrations during friction, making it difficult for the lubricant to maintain a uniform distribution in these areas. At the same time, the edges of the multilayer rectangular-type micro-texture restrict the recirculation and distribution of the lubricant, making it more difficult for the lubricant to return to the friction surface. This restriction leads to a higher coefficient of friction in the friction test results for the multilayer rectangular-type micro-texture. The results indicated that under loads of 5 N, 10 N and 15 N, the rubber surface with a warhead-type texture exhibited the smallest friction coefficient. Consequently, the warhead-type texture exhibited enhanced lubrication and friction reduction effect, which was followed by the concentric circular-type and the multilayer rectangular-type texture.

5. Conclusions

• The friction performance of the warhead-type micro-texture was superior compared with the concentric circle and multilayer rectangular micro-textures. The head of the warhead-type texture featured a sharp converging wedge along the flow direction, with its irregular symmetry enhancing the hydrodynamic lubrication effect within the texture groove. This improvement significantly enhanced the lubrication characteristics between the stator rubber and the rotor of the screw pumps.
• The hydrodynamic lubrication performance of the textured stator rubber surface was highly influenced by the groove width. As the groove width increased, the pressure distribution on the upper wall of the oil film changed significantly, leading to an increase in additional net bearing capacity. This effectively enhanced the film pressure between the stator and rotor friction pairs.
• Under different textured morphology conditions, the maximum pressure on the wall surface of the textured stator rubber oil film initially increased with depth, followed by a decrease. As depth increased, the vortex volume within the grooves increased, which was accompanied by energy changes that further diminished the effect of dynamic pressure lubrication.
• Friction tests on the textured stator rubber of a progressive cavity pump show that under a load of 5 N, 10 N and 15 N, a friction frequency of 3 Hz, and an oil-rich condition, the average friction coefficient of the three types of textured stator rubber initially decreased and then gradually stabilized over time. The warhead texture exhibited an enhanced lubrication effect. Given all texture parameters, the optimal combination included a warhead-type texture size of 3 mm, a groove width of 0.2 mm, and a depth of 0.1 mm, resulting in an excellent dynamic pressure lubrication effect.