1. Introduction
The valve plate is an important component of an axial piston pump, which is a widely used hydraulic power component. Modern hydraulic transmission technology generally aims to achieve improvements at high-speed and high-pressure, with strict conditions on the working performance and service life of the valve plate. Numerical analysis has previously been carried out in order to express the mixed lubrication characteristics between the valve plate and cylinder block in the swash-plate type piston pump and motor [
1,
2].
Surface texturing is the design of a specific shape, size, and arrangement of the surface of a friction pair by means of physical and chemical methods. The surface texturing acts as a micro fluid hydrodynamic lubrication bearing under different conditions, enhances the hydrodynamic effect and improves the bearing capacity [
3,
4]. The lubricant reservoir provides continuous lubrication, and captures the wear particles to reduce the furrows [
5]. Surface texturing is a widely used approach to improve the load capacity, wear resistance, and friction coefficient of tribological mechanical components [
6,
7,
8], including sliding surfaces [
9,
10]. Surface texture can also improve the running-in process, to smooth contact surfaces, resulting in low friction [
11,
12]. A significant improvement in performance can also be obtained by creating a regular micro-surface structure in the form of micro-dimples [
13,
14]. Compared with plane surfaces, dimples will help to lower the coefficient of friction between surfaces [
15]. The optimal geometric and distributive ranges of the micro-pits are known, and the load-carrying capacity can be increased compared to untextured surfaces [
16,
17].
Surface texturing to control friction and wear has been the focus of numerous studies in the last few decades [
18]. Understanding the influence of surface properties on the performance of hydrodynamically lubricated contacts has been the aim of numerous studies [
19]. Surface microtexturing of the valve plate is a new topic. In 2003, Pettersson studied the friction and wear behavior of boundary-lubricated sliding surfaces and found that they are influenced by the surface texture. Lubricant can be supplied even inside the contact by small reservoirs, resulting in a reduced friction and a prolonged lifetime where there is tribological contact [
20]. In 2004, Pettersson again investigated the friction and wear properties of boundary-lubricated textured surfaces and found that the well-defined surface textures of square depressions or parallel grooves of different widths and distributions can be produced by lithography and anisotropic etching of silicon wafers [
21]. In 2000, Etsion presented that the tribological performance of mechanical can be improved seals by laser surface texturing [
22,
23]. In 2006, Etsion presented an experimental study to evaluate the effect of partial laser surface texturing (LST) on friction reduction in piston rings and found that the partial LST piston rings exhibited about one quarter of lower friction [
24]. The beneficial effects of laser surface texturing are more pronounced at higher speeds and loads and with higher viscosity oil [
25]. In 2016, Etsion used the finite element analysis to investigate the elastic contact of a sphere with a thin hard coating compressed by a rigid flat and also introduced a new approach for calculating the limit of elasticity in the coated system [
26,
27]. In 2008, Ivantysynova proposed that a surface micro-wave texture can be added to the design of the axial piston pump in order to increase the load-carrying properties of port plate pairs. The wave-like microtexture can generate an additional hydrodynamic effect and reduce the power loss of the piston pump and motor [
28]. In 2009, a mathematical model of the wave-like microtexture was established and solved. It demonstrated that a wave-like micro-surface shape variation applied to the valve plate gap surface reduces power loss in the cylinder block–valve plate interface. The effect of the waved surface is most significant at low operating pressures. The power loss in the cylinder block–valve plate interface could be reduced when using the waved surface, compared to the standard cylinder block–valve plate interface design [
29]. In 2014, Shin investigated the effect of surface non-flatness on the lubrication characteristics of the bearing/sealing parts between the cylinder barrel and valve plate in a hydrostatic axial piston pump. They found that the circumferentially wavy surface would allow for better performance of motion stability and power efficiency than a radially wedged land surface [
30].
A large part of the lubricant on the surface of the non-texture specimen is thrown out due to the fast operation speed of the friction pair, and the generated abrasive particles will aggravate the wear of the surface. The surface microtexture can store lubricating oil. The lubricating oil stored in the texture will overflow when the surface is partially worn out, and will be replenished to a certain extent, which can provide continuous lubrication to the friction pair. The surface texture can also play the role of containing the wear debris [
31], thereby improving the wear caused by the abrasive particles. Common texture patterns include columns, pits, grooves, and the like. The presence of a local cavity (texture) increases the lubricant film thickness and decreases the friction force. Partial texturing can generate a hydrodynamic lift when the texture is located in the declining part of the contact pressure field [
32]. The convergence gap formed between the edge of the microtexture and the surface of the friction pair can produce a hydrodynamic effect along the direction of the lubricant velocity under hydrodynamic lubrication conditions [
33].
Formerly, research has mainly focused on the effects of single shape microtexture parameters, such as the depth, diameter, and area ratio, on the lubrication characteristics of the motor. Part of the literature has examined the different shapes of the micro-dimple surface texture [
34,
35]. This paper focuses on the research of the surface texture field and optimize the parameters of microtexture. Three different microtexture shapes and parameters were selected to study their effects on lubrication characteristics. A finite differential method was used to solve the Reynolds equation for the oil film thickness and pressure, which were simulated under different microtextures. The influence of microtexture shape and structure on performance was studied and optimal parameters sought. It was found that the processing of a certain regular texture on the surface of the friction pair can improve the friction characteristics and lubrication effect between the friction pairs, in which the shape of the texture geometrical parameters is one of the key factors, and only in the appropriate range will have excellent lubrication effect; otherwise, it is counterproductive. There is an optimal parameter combination when adding microtexture with three shapes and the optimal dimensionless oil film pressure lubrication characteristics can be obtained.
4. Oil Film Thickness and Pressure Distribution of a Microtextured Valve Plate
The number of microtextures on the surface of the valve plate are shown in
Table 2. The pressure in the high- and low-pressure zone was set to 101,325 Pa, while the external pressure was set to 101,325 Pa.
4.1. Oil Film Thickness and Pressure Distribution of Valve Plate with Micro-Hemispherical Texture
Figure 7 shows the oil film thickness distribution of the valve plate with micro-hemispherical texture.
Figure 7a is the three-dimensional distribution graph of the oil film thickness,
Figure 7b is the two-dimensional distribution graph and
Figure 7c is a local magnification graph of 7a.
Figure 8 shows the oil film pressure distribution of a valve plate with micro-hemispherical texture. The local high pressure was produced by machining the micro-hemispherical texture.
Figure 8a is the three-dimensional distribution graph,
Figure 8b is the two-dimensional distribution graph and
Figure 8c is a locally magnified view of 8a. The micro-hemispherical texture was arranged on the surface of the valve plate.
4.2. Oil Film Thickness and Pressure Distribution of a Valve Plate with Micro-Cylindrical Texture
Figure 9 shows the oil film thickness distribution of a valve plate with micro-cylindrical texture.
Figure 9a is the three-dimensional distribution graph;
Figure 9b is the two-dimensional distribution graph; and
Figure 9c is the local magnification graph.
Figure 10 shows the distribution of oil film pressure for the valve plate with micro-cylindrical texturing.
Figure 10a is the three-dimensional distribution graph;
Figure 10b is the two-dimensional distribution graph; and
Figure 10c is a locally magnified view of
Figure 10a.
4.3. Oil Film Thickness and Pressure Distribution of a Valve Plate with a Micro-Square Texture
Figure 11 shows the oil film thickness distribution of a valve plate with a micro-square texture.
Figure 11a is the three-dimensional distribution graph;
Figure 11b is the two-dimensional distribution graph; and
Figure 11c is a locally magnified view. The micro-square texture was arranged regularly along the radial and circumferential directions in the Top Dead Center (TDC) and Bottom Dead Center (BDC) of the valve plate.
Figure 12 shows the oil film pressure distribution of a valve plate with a micro-square texture.
Figure 12a is the three-dimensional distribution graph;
Figure 12b is the two-dimensional distribution graph; and
Figure 12c is a locally magnified view.
4.4. Comparison of the Oil Film Pressure Lubrication Characteristics of Different Microtexture
Figure 7,
Figure 8,
Figure 9,
Figure 10,
Figure 11 and
Figure 12 show the distributions of pressure and oil film thickness for three types of microtextures: hemispherical, cylindrical, and square. For each parameter and shape, we show a three-dimensional and two-dimensional result, and there is also a locally magnified image. The figures were generated using (Fortran Algorithm Description) and (Matlab Plotting Software Description).
With a hemispherical microtexture. The oil film thickness increased locally as the hydraulic oil was entered and stored inside the micro-hemispherical texture region. The oil film thickness changed due to the internal depth variation of the microtexture. The micro-hemispherical texture is arranged regularly along the radial and circumferential directions in the BDC and TDC of the valve plate. There are changes in oil film thickness and gaps when the hydraulic oil flowed into and out of the micro-hemispherical texture region. Positive pressure was generated when the hydraulic oil flowed along the region of convergence formed by the hemispherical structure, resulting in elevation of the local oil film pressure in the hemispherical regions. It is not straightforward to generate positive or negative pressure when the hydraulic oil flows along a region of divergence and thus, it is difficult to generate hydrodynamic effects.
With a cylindrical microtexture. The oil film thickness increased locally as the hydraulic oil entered and was stored inside the micro-cylindrical textured region. The internal depth of the micro-cylindrical texture did not change, unlike for the micro-hemispherical texture. The oil film region had locally high pressure after machining of the micro-cylindrical texture. Furthermore, the oil film pressure formed by the micro-cylindrical texture was higher near the outer sealing belt of the valve plate.
Finally, with a square microtexture. The oil film thickness increased locally as the hydraulic oil entered and was stored inside the micro-square texture region. The internal depth of the micro-square texture did not change, unlike for the micro-hemispherical texture. The oil film region produced local high pressure, which was similar to that of the micro-hemispherical texture. The oil film pressure formed by the micro-square texture was higher in the TDC of the microtexture, while the oil film pressure was lower in the BDC of the microtexture. It was different from the influence of the micro-hemispherical texture and micro-cylindrical texture on the pressure of valve plate.
5. The Influence of Microtexture Radius on the Performance of the Valve Plate
Different microtexture shapes and parameters were selected for the simulation study in order to optimize the oil film carrying capacity, friction coefficient, friction force, and the offset load torque. The microtexture shapes selected were spherical, cylindrical, and square. The radius (half side length) of the micro-hemispherical texture, micro-cylindrical texture and micro-square texture varies from 0.2 to 1.0 mm, while the depth of microtexture varies from 0.02 to 0.07 mm.
5.1. The Influence of Micro-Hemispherical Texture Radius on the Performance of the Valve Plate
Figure 13 shows the influence of the micro-hemispherical texture’s radius on the performance of the valve plate.
Table 3 shows the oil film lubrication characteristic parameter value of micro-hemispherical texture. The radius of micro-hemispherical texture varies from 0.2 to 1.0 mm. Δ(Max − Min) represents the value of maximum minus minimum. There was no change for the dimensionless oil film pressure lubrication characteristics when the radius was 0.2 mm. This indicated that the micro-hemispherical texture had little or no effect on the valve plate. The oil film pressure lubrication characteristics varied differently when depth was kept constant and the radius was increased. This indicated that the oil film pressure lubrication characteristics are affected by the micro-hemispherical radius.
The oil film carrying capacity was 5.36 (minimum) when the radius was 0.2 mm, while the oil film carrying capacity was 19.72 (maximum) when the radius was 0.7 mm and the depth was 0.04 mm. Thus, the value could be increased by 14.36 compared to the minimum carrying capacity.
The oil film friction coefficient was 1.0117 (maximum) when the radius was 0.2 mm, while the oil film friction coefficient was 0.2571 (minimum) when the radius was 0.7 mm and the depth was 0.04 mm. The value thus increased by 0.7546 compared to the minimum oil film friction coefficient.
The oil film friction force was 5.4252 (maximum) when the radius was 0.2 mm, and 5.0701 (manimum) when the radius was 0.7 mm and the depth was 0.07 mm. The value thus increased by 0.3551 compared to the minimum oil film friction coefficient.
The oil film offset load torque was 0.001433 (minimum) when the radius of micro-hemispherical texture was 0.2 mm, and 110.41 (maximum) when the radius was 0.7 mm and the depth was 0.04 mm. The optimal value thus increased by 110.4086 compared with the minimum oil film offset load torque.
A different convergence gap was formed by different microtexture radius, which produced different hydrodynamic effects. The hydrodynamic effects of the micro-hemispherical texture increased with an increase in radius, within a certain range, however beyond that the hydrodynamic effects decreased due to the interactions within the texture. The optimal oil film lubrication characteristics can thus be obtained by optimizing the micro-hemispherical texture radius.
5.2. The Influence of Micro-Cylindrical Texture’s Radius on the Performance of Valve Plate
Figure 14 shows the influence of the micro-cylindrical texture’s radius on the performance of valve plate.
Table 4 shows the oil film lubrication characteristic parameter value of micro-cylindrical texture. The radius of the micro-cylindrical texture ranged from 0.2 to 1.0 mm. Δ(Max − Min) represents the value of maximum minus minimum.
The oil film carrying capacity was 5.36 (minimum) when the radius was 0.2 mm, and 10.37 (maximum) when the radius was 0.7 mm and the depth was 0.04 mm. Thus, the value could be increased by 5.01 compared with the minimum oil carrying capacity.
The oil film friction coefficient is 1.0106 (maximum) when the radius was 0.2 mm, and 0.4821 (minimum) when the radius was 0.7 mm and the depth was 0.04 mm. The value thus increased by 0.5285 compared with the minimum friction coefficient.
The oil film friction force was 5.4193 (maximum) when the radius was 0.2 mm, and 4.9517 (minimum) when the radius was 0.7 mm and the depth was 0.06 mm. The value could thus be increased by 0.4676 compared with the minimum friction force.
The oil film offset load torque reached a minimum of 0.001436 when the radius was 0.2 mm, and a maximum of 45.748 when the radius was 0.7 mm and the depth was 0.04 mm. The maximum value was thus 45.7466 greater than the minimum.
5.3. The Influence of Micro-Square Texture’s Half Side Length on the Performance of Valve Plate
Figure 15 shows the influence of the micro-square texture’s radius on the performance of the valve plate.
Table 5 shows the oil film lubrication characteristic parameter value of micro-square texture. The half side length of the micro-square texture was varied from 0.2 to 1.0 mm. Δ(Max − Min) represents the value of maximum minus minimum.
The oil film carrying capacity was 5.43 (minimum) when the half-side length is 0.2 mm, and 6.50 (maximum) when the half-side length was 0.5 mm and the depth was 0.04 mm. The maximum value was thus 1.07 higher than the minimum carrying capacity.
The oil film friction coefficient was 0.9069 (maximum) when the half-side length is 0.2 mm, and 0.6848 (minimum) when the half-side length was 0.7 mm and the depth was 0.04 mm. The value could thus be increased by 0.2221 compared to the minimum.
The oil film friction force was 4.9876 (maximum) when the half-side length was 0.2 mm, and 4.2649 (minimum) when the half-side length was 0.7 mm and the depth was 0.07 mm. The maximum value was thus 0.7227 more than the minimum.
The oil film offset load torque was 0.0596 (minimum) when the half-side length is 0.2 mm, and 15.273 (maximum) when the half-side length was 0.4 mm and the depth was 0.04 mm. The maximum value was thus 15.2134 higher than the minimum.
7. Comparison of the Optimum Oil Film Pressure Lubrication Characteristics
The oil film lubrication characteristics of valve plates under pressure are better when a microtexture is used, compared to no microtexture. The study of tribological performance for three types of microtexture surface found that:
For a fixed microtexture radius, an increase in depth tends to lead to an initial increase then decrease in the dimensionless oil film carrying capacity, friction force, and offset load torque. The oil film friction coefficient has the tendency to decrease first and then increase. Furthermore, at a fixed microtexture depth, an increase in the microtexture radius or side length leads to the dimensionless oil film carrying capacity, friction force, and offset load torque first increasing first then decreasing. The oil film friction coefficient tends to decrease first and then to increase. This indicated that the optimal oil film lubrication characteristics could be obtained by optimizing micro-hemispherical texture depth.
Figure 19 shows the oil film pressure lubrication characteristic curves at the optimal parameters.
Table 6 shows the optimal oil film lubrication characteristic values.
- (1)
The dimensionless oil film carrying capacity was 19.71, 10.27 and 6.5, when the radius (half-side length) was 0.7 mm and the depth 0.04 mm for the micro-hemispherical texture, micro-cylindrical texture, and micro-square texture. At this point, the dimensionless friction coefficient reached its minimum.
- (2)
The dimensionless oil film friction coefficient was 0.2571, 0.4821 and 0.6848 when the radius (half-side length) was 0.7 mm and the depth was 0.04 mm for the micro-hemispherical texture, micro-cylindrical texture, and micro-square texture respectively. At this point, the friction coefficient reached a minimum.