Effects and optimization of bionic texture parameters on the tribological behavior of line contacts under starved lubrication conditions

Gears are critical components in mechanical transmission systems, widely used in mechanical equipment, aerospace and other engineering fields. Modern machinery and equipment require higher safety and service life to meet regular operation under various working conditions. Studying the tribological performance of gears is conducive to improving the transmission performance of gears. Insufficient lubricating oil during gear meshing will reduce the thickness of the lubricating oil film, the contact gap on the surface of the gear cannot be filled with lubricating oil and the gear transmission system is in a state of lack of oil lubrication (Cooley et al., 2011). Even a momentary operation error or mechanical failure may lead to starvation lubrication, leading to gear failure. Therefore, it is significant to study the tribological performance of gear under starved lubrication conditions.

Trapping of wear debris and lubricant by micro-textures such as micro dimples and generating micro hydrodynamic lift were identified as key mechanisms contributing to enhancing the tribological performance of textured surfaces (Zhang et al., 2014, 2018). Etsion (2005) reviewed the state of the art in laser surface texturing and explored its potential applications in various lubricated systems, such as mechanical seals, piston rings and thrust bearings. Gropper et al. (2016) outline the research effort on surface texturing worldwide and provide a comparative summary of different modeling techniques for fluid flow, cavitation and micro-hydrodynamic effects. Gruetzmacher et al. (2019) elucidated numerical approaches to predict the behavior of multi-scale surface texturing under lubricated conditions and summarized the existing knowledge and hypotheses about the underlying driven mechanisms responsible for the improved tribological performance of multi-scale textures. Huang et al. (2021) designed a bionic micro-texture combined with solid lubrication SnAgCu to improve the tribological performance of AISI 4140 steel, and the optimized bionic texture parameters were obtained by the response surface method (RSM). Saeidi et al. (2016) investigated the effect of laser surface texturing on the friction behavior and the lifetime of grey cast iron reciprocating under starved lubrication conditions; the results indicated that with the following texture parameters: depth of 50 μm, diameter of 100 μm, length of 500 μm, area fraction of 5% and a sliding direction perpendicular to the micro-textures, the friction coefficient reached its minimum value. Wang et al. (2020) investigated the influences of texture on the anti-wear characteristics of valve pairs under natural seawater lubrication. The results indicated that the reasonable nonsmooth unit produces a hydrodynamic lubrication effect. Galda et al. (2016) found that the presence of dimples improved the tribological characteristics under starved lubrication conditions at low sliding speeds through sliding friction tests of steel-steel materials. Zheng et al. (2018) elucidate the size effect (groove width, unit length and area density) of the hexagonal texture on tribological performance under lubrication. Niu et al. (2021) found that the depth of the dimple is the main factor that significantly affects the friction and wears performance of the steel surface in nonconformal contact under starved lubricated conditions by the friction and wears tests. Gupta et al. (2020) explored the tribological and vibrational behaviors of conventional and textured spur gear pairs under different operating conditions. The results revealed texture could improve the tribological and dynamic performance of the gear pair.

Marian et al. (2022) carried out numerical design and optimization of micro-textures for specific conditions and then customized micro-textures to reduce friction and wear, thus improving energy efficiency and sustainability. Shen et al. (2021) proposed a new surface texture design to improve the tribological performance of bioimplants, optimized the texture parameters based on orthogonal experiments and numerical analysis and verified its tribological performance through experiments. Qiu et al. (2013) evaluated the friction coefficient and stiffness of gas-lubricated textured parallel slider bearings as a function of six different texture shapes and optimized texture geometry and density in terms of minimum friction coefficient and maximum bearing stiffness, and the ellipsoidal shape is found to yield the minimum friction coefficient and the highest bearing stiffness. Greiner and Schaefer (2015) textured 100Cr6 bearing steel pins with snake and sandfish skin-inspired scale-like morphologies, resulting in a 40% reduction in friction forces under dry conditions. Rosenkranz et al. (2019) summarized the state of the art of surface texturing applied to machine elements, with a special emphasis on piston rings, seals, roller bearings and gears, and provided more general design guidelines for surface texturing in machine elements.

The surface texture has been widely studied and applied in many fields. However, the design of gear surface texture has not formed a systematic study, especially in extreme working conditions (starvation lubrication or dry friction) for the parameter design of gear surface texture. The types of gear meshing are numerous (gear and rack meshing, spur gear meshing, helical gear meshing, bevel gear meshing, etc.) and the operating conditions are complex, making the design and optimization of gear surface textures intricate. This paper focuses on the design and optimization of surface textures during the line contact process of gear–rack mechanisms under starved lubrication conditions. The influence of bionic texture parameters (width, depth and spacing) on the tribological performance (average friction coefficient and average wear amount) of tested samples under line contact and starved lubrication conditions was analyzed by using a quadratic rotation orthogonal combination test. This study provides a theoretical basis for optimizing the line contact motion pairs surface tribological performance.

The C45E4 steel was a relatively common gear matrix material, and this paper used C45E4 steel as the material of tested samples and counterparts. The tested sample is a 31 × 7 × 6 mm cuboid with a surface roughness (R_a) of 0.4 µm. The counterpart is a disc with a diameter of 40 mm and a thickness of 10 mm, and the surface roughness (R_a) is 0.4 µm. The tested sample and counterpart are quenched and the surface hardness is HRC40. During the test, the lubricating oil was L-CKC220 medium load gear oil (density is 0.85 g/cm³, kinematic viscosity at 40°C is 198∼242 mm²·s⁻¹).

Inspired by the fact that sharks could swim at high speeds under the pressure of the deep sea by relying on the orderly arrangement of tiny, scaly protrusions on the surface of their skin, this paper simulated the texture of shark skin surface to design biomimetic textures. According to the relevant literature (Philip, 1999; Dean et al., 2013), the bionic texture was determined to be a diamond-shaped grid-like structure and the interlaced grid line angle was 115° [as shown in Figure 1(d)]. FemtoYL-IR-40W^® femtosecond laser was used to process the bionic texture on the surface of the tested sample (detailed structural parameters are given in Section 2.3). The femtosecond laser processing system used was LR-Fem1030-40, featuring a laser center wavelength of 1030 nm, a pulse width of 500 fs, a grating scanning frequency of 100 kHz, a grating scanning speed of 100 mm/s, a pulse energy ≤ 80 μJ, a focal length of 160 mm for the focusing field lens and a focused spot diameter of 35 μm. After processing, the tested sample was polished and cleaned, as shown in Figure 1(a). The 3D topography of the tested sample surface was measured by using a VK-X250 3D laser measuring microscope, as shown in Figure 1(b) and (c).

The test apparatus is the M200 friction testing machine, which can simulate the linear contact process of gear meshing (Chang et al., 2023; Li et al., 2018), and its structural schematic is shown in Figure 2(a). Tested samples were numbered before the start of the test. To ensure the test conditions for starvation lubrication, the lubricating oil was evenly applied to the surface of the tested sample and counterpart before the test and the lubricating oil was no longer added dropwise during the test. During the test, the tested sample was mounted on the upper clamp; the counterpart was mounted on the lower clamp. The physical drawing of the tested sample clamping is shown in Figure 2(b). The load of the friction testing machine was set to 500 N (contact stress is 362 MPa), the speed of the grinding part was set to 200 r/min and the test time was 70 min. Owing to the inability of the M200 friction testing machine to continuously record the friction coefficient during operation, we recorded the friction coefficient every 10 min during the testing process, taking the average value as the test data. After the test, the tested sample was placed in absolute ethanol and ultrasonically cleaned for 20 min, dried at room temperature. Then the wear mark width of the specimen was measured using a VK-X250 3D laser measurement microscope.

The model used in this paper is implemented based on the methods presented in the papers by Huang et al. (2021) and Saeidi et al. (2016). We perform experiments on tested samples with different texture parameters through a quadratic rotation orthogonal combination test. Subsequently, we used the RSM to obtain a regression equation between the friction coefficient and texture parameters. Finally, with the minimum friction coefficient as the target, we solved the regression equation to obtain the optimal texture parameters.

According to the Principle of Central Composite design (Huang et al., 2021), this experiment adopted the quadratic rotational orthogonal combination test scheme. Taking width, depth and spacing as the test factors and taking average friction coefficient and average wear mark width as the response indexes, the friction test was carried out to study the primary and secondary effects of each factor as well as the interactions between factors. Through the preliminary pretest, the variation range of test factors was determined as follows: width 40 ∼ 200 µm, depth 10 ∼ 100 µm, spacing 400 ∼ 1,000 µm. The test is arranged according to the three-factor five-level, and the test factor and level coding table are shown in Table 1. According to the factor level coding table, the quadratic rotation orthogonal combination test scheme was formulated and 19 groups of tests were arranged. Each sample was tested three times under the same experimental conditions and the results reported were average. The test scheme and results are shown in Table 2. Table 3 presents the friction coefficient data and uncertainties during the testing process for some tested samples (No.1 and No.19). As shown in Table 3, the uncertainties are significantly smaller than the measured values of the friction coefficients, indicating the validity of the measurement results. The surface topography of all tested samples is shown in Figure 3.

The surface wear morphology of one group of test samples (No.1–No.19) is shown in Figure 4. The 3D wear topography of some representative tested samples (No.12–No.14) is shown in Figure 5. When tested samples come into contact with counterparts, the texture groove of the tested samples’ surface traps the wear debris. Subject to the pressure on the counterpart, the particles of grinding chips in the texture groove cannot flow out, which will block the texture groove and eventually make the texture groove disappear, as shown in Figure 5(a). In addition, in combination with Figure 4, we find that the texture width of the worn areas is smaller relative to the nonworn areas. There are two main reasons for this phenomenon; on the one hand, owing to the processing error, the texture groove section is approximately trapezoidal rather than rectangular [as shown in Figure 1(c)]; on the other hand, owing to the pressure and frictional heat, plastic deformation is generated at the texture groove [as shown in Figure 5(b)]. In addition, compared with the tested samples with small texture spacing, some tested samples with large texture spacing have deeper scratches on the surface [as shown in Figure 5(c)]. This may be because the texture spacing is relatively large and the texture groove cannot easily catch the wear debris of large particles.

The variance analysis was performed on the experimental data above, and the results of the quadratic polynomial regression equation are shown in Table 4. The results in Table 3 reveal that the level of fitting of the regression models for the coefficient of friction (μ) and the wear mark width (W_m) were both extremely significant (P <0.01), whereas the lack of fit for the regression equation was not significant, indicating a good fit with the actual situation. For the regression equation of the coefficient of friction (μ), the regression terms D, S, WD, DS and D² all had significant effects (P <0.01), whereas the effects of W, WS, W² and S² were not significant (P >0.05). The lack of fit term was not significant (P >0.05), suggesting that no other major factors were affecting the response index, and the model was reasonable. For the regression equation of wear mark width (W_m), the regression terms S, WD and DS all had significant effects (P <0.01), whereas the effects of W, D and WS were not significant (P >0.05). The lack of fit term was not significant (P >0.05), suggesting that no other major factors were affecting the response index, and the model was reasonable.

The data processing software Design-Expert was used to perform multiple regression fitting on the experimental data and two quadratic polynomial regression equations were established, which took the coefficient of friction (μ) and the wear mark width (W_m) as response functions, whereas the width (W), depth (D) and spacing (S) were taken as independent variables. The nonsignificant regression terms were removed. The regression equations are expressed as follows:

The findings of the variance analysis in Table 3 show that the interaction of width and depth significantly influence on the regression equation of friction coefficient and wear mark width. The response surface and contour plot are plotted, as shown in Figure 6. As shown in Figure 6(a) and (c), the friction coefficient increased with increasing depth when the width was at a low level (40 μm) and decreased with increasing depth when the width was at a high level (200 μm). In addition, the friction coefficient increased with increasing width when the depth was at a low level (10 μm) and decreased with increasing width when the depth was at a high level (100 μm). As shown in Figure 6(b), the friction coefficient was minimal when the width and depth satisfied the one-time function relationship (D = 0.356W + 3.75). As shown in Figure 6(d), the wear mark width was minimal when the width and depth satisfied the one-time function relationship (D = 0.567W-18.5).

The findings of the variance analysis in Table 3 show that the interaction of depth and spacing significantly influence the regression equation of friction coefficient and wear mark width. The response surface and contour plot are plotted, as shown in Figure 7. As shown in Figure 7(a) and (c), the friction coefficient decreased with increasing spacing when the depth was at a low level (10 μm) and the friction coefficient increased with increasing spacing when the depth was at a high level (100 μm). In addition, the friction coefficient decreased with increasing depth when the spacing was at a low level (400 μm) and the friction coefficient increased with increasing width when the spacing was at a high level (1,200 μm). As shown in Figure 7(b), the friction coefficient was minimal when the depth and spacing satisfied the one-time function relationship (S = −22.857D + 2000). As shown in Figure 7(d), the wear mark width was minimal when the depth and spacing satisfied the one-time function relationship (S = −8.6D + 1500).

Under starved lubrication conditions, micro-textured primarily reduce the friction coefficient through two mechanisms. The first mechanism is that the grooves in the micro-textured can store lubricating oil. As wear progresses, the depth of the micro-textured gradually decreases and the lubricating oil stored in the micro-textured groove slowly overflows, providing lubrication. In addition, the compression of the counterpart on the micro-textured surface during the wear process also causes the lubricating oil to overflow from the grooves and lubricate the surrounding surface, demonstrating the “secondary lubrication” phenomenon. The second mechanism is that the grooves in the micro-textured can capture and store abrasive particles, preventing their accumulation on the sliding surface, reducing the plowing effect and adhesive friction and thus improving surface friction and wear performance. The specific combination of texture parameters can efficiently retain lubricating oil, thereby maximizing lubrication during wear on contact surfaces. Simultaneously, it promptly captures debris through textured grooves during the generation of abrasion between contact surfaces, preventing the accumulation of debris on the contact surfaces. Furthermore, this specific combination of texture parameters ensures the strength of the contact surfaces, preventing plastic deformation and, consequently, reducing wear caused by insufficient strength. In addition, it can be seen from Figures 6 and 7 that the overall trend of the influence of the interaction of texture parameters on the friction coefficient and wear mark width is the same but there are slight differences.

The optimal regression equation was solved by Design-Expert software with the minimum friction coefficient as the goal. The objective function and constraints are shown in equation (3). The optimal solution of the parameters is that the width is 68.94 µm, the depth is 24 µm, the spacing is 1,162.44 µm and the predicted friction coefficient is 0.1292, the predicted wear mark width is 1,540.93 µm. Rounding the above weaving parameters results in an optimized combination of width 69 µm, depth 24 µm and spacing 1,162 µm:

We processed samples with optimized texture (optimal texture) and without texture (nontexture) and conducted tribological tests. The friction coefficients and wear mark widths of the optimal texture and nontexture are shown in Table 5, and the 3D wear morphology of a set of samples is shown in Figure 8. Comparing the optimal texture and the nontexture, we found that the friction coefficients and wear mark widths of the optimal texture are smaller than the nontexture. Comparing the optimal texture with other samples (No.1–No.19), we found that the friction coefficients and wear mark widths of the optimal texture are at a low level among all samples, which proves that the optimized texture parameters can effectively reduce the friction coefficient. Of course, there are differences between the predicted and experimental results, but they still have guiding significance.

Inspired by the microstructure of the shark skin surface, this paper designed a diamond-shaped biomimetic texture to improve the tribological performance of gear–rack mechanism under starved lubrication conditions. The line contact meshing process of gear–rack mechanisms under lubrication-deficient conditions was simulated by using a block-on-ring test. Using the response surface method, this paper analyzed the effects of bionic texture parameters on the tribological performance of tested samples under line contact and starved lubrication conditions, and the following conclusions were obtained:

• Two quadratic regression rotation-orthogonal models of the coefficient of friction (μ) and the wear mark width (W_m) were established. For the regression equation of the coefficient of friction (μ), the regression terms D, S, WD, DS and D² had significant effects (P <0.01). For the regression equation of the wear mark width (W_m), the regression terms S, WD and DS all had significant effects (P <0.01).

• There was an optimal proportional relationship between the texture parameters, which made the tribological performance of the tested sample the best. And the bionic texture parameters were optimized by the main objective function method, and the preferred combination of parameters was that the width was 69 µm, the depth was 24 µm and the spacing was 1,162 µm.

This work was supported by the National Natural Science Foundation of China (51775158) and Anhui Provincial Key Research and Development Plan (JZ2022AKKG0093).