Spur gears are fundamental components in precision transmission systems, widely used in aerospace, energy, and power fields due to their reliable transmission, high precision, and simple manufacturing process. However, during meshing, the tooth surface often suffers from insufficient lubrication, leading to severe friction and wear, which may cause scuffing and fatigue failure. Surface texturing technology has been proven to improve the lubrication condition of tribological interfaces by storing lubricant, capturing wear debris, and generating additional hydrodynamic pressure. In this study, I proposed an elliptical surface texture applied to spur gear tooth flanks and systematically investigated its lubrication and friction performance through numerical simulations and experiments. I constructed an equivalent line-contact model for a spur gear pair, solved the Reynolds equation with the MATLAB PDE toolbox, and then conducted friction and wear tests on textured cylindrical rollers and textured spur gears. The results demonstrate that the elliptical texture can significantly enhance the hydrodynamic lubrication performance and reduce friction and wear of the gear surface. This article presents the complete research procedure, including model establishment, theoretical calculation, parameter optimization, and experimental validation, with extensive tables and equations to summarize the findings.
The spur gear is one of the most common machine elements for power transmission. In many applications, the gear pair operates under oil lubrication, and the tribological performance determines the service life and efficiency of the transmission. Over 80% of mechanical component failures are attributed to friction and wear, and surface texturing provides an effective solution. Among various texture shapes, elliptical textures combine the advantages of discrete dimples and continuous grooves, offering both strong hydrodynamic pressure generation and directional flow guidance. In this work, I focused on the elliptical texture for spur gear surfaces and investigated how its geometric parameters influence lubrication and friction.
1. Equivalent model of spur gear contact
Directly simulating the lubrication and friction of a spur gear mesh is challenging because of the complex tooth profile and varying contact conditions. Therefore, I adopted an equivalent line-contact model. In the gear meshing process, the contact between two teeth can be locally represented by two contacting cylinders whose radii equal the curvature radii of the tooth profiles at the contact point. Figure 1 in the original study showed the equivalence. In my research, based on the MMS-2A friction and wear tester specifications, the equivalent roller radii were set to 20 mm for the large roller and 15 mm for the small roller. The equivalent radius of curvature is calculated by:
$$R = \left( \frac{1}{R_1} + \frac{1}{R_2} \right)^{-1} = \left( \frac{1}{20} + \frac{1}{15} \right)^{-1} \ \text{mm} = 8.5714 \ \text{mm}$$
The oil film thickness in the line-contact model can be expressed as:
$$h(x) = h_0 + \frac{x^2}{2R}$$
where \(h_0\) is the minimum film thickness. This equivalence allows the gear contact problem to be converted into a cylinder-on-plane or cylinder-on-cylinder problem, which is much easier to analyze both numerically and experimentally.
2. Elliptical texture geometry and dimensionless parameters
The elliptical texture is characterized by the major radius \(R_a\), minor radius \(R_b\), ellipticity \(\gamma = R_b/R_a\), inclination angle \(\theta\), depth \(H\), and area occupancy \(\delta\). A single unit cell with periodic length \(T\) is considered for the lubrication analysis. The cross-sectional profile of the laser-ablation dimple is approximated by an arc shape, as illustrated in the model setup. The area occupancy is defined as:
$$\delta = \frac{A_{\text{ellipse}}}{A_{\text{unit}}} = \frac{\pi R_a R_b}{T^2}$$
To generalize the simulation results, I introduced the following dimensionless parameters:
$$\delta^* = \frac{\delta}{\delta_0}, \quad U^* = \frac{U}{U_0}, \quad R_a^* = \frac{R_a}{R_{a0}}, \quad H^* = \frac{H}{h_0}$$
where \(\delta_0 = 10\%\), \(U_0 = 0.2 \ \text{m/s}\), \(R_{a0} = 40 \ \mu\text{m}\), and \(h_0 = 1 \ \mu\text{m}\). The dimensionless groups allow the effects of texture size, depth, velocity, and density to be compared on a common basis.
3. Reynolds equation and numerical solution
Under steady-state, isothermal, incompressible conditions, the Reynolds equation for a line-contact EHL problem is:
$$\frac{\partial}{\partial x}\left( \frac{\rho h^3}{\eta} \frac{\partial p}{\partial x} \right) + \frac{\partial}{\partial y}\left( \frac{\rho h^3}{\eta} \frac{\partial p}{\partial y} \right) = 6 U \frac{\partial (\rho h)}{\partial x}$$
I assumed constant density and viscosity, and no temporal variation, so the equation simplifies to:
$$\frac{\partial}{\partial x}\left( h^3 \frac{\partial p}{\partial x} \right) + \frac{\partial}{\partial y}\left( h^3 \frac{\partial p}{\partial y} \right) = 6 \eta U \frac{\partial h}{\partial x}$$
Using dimensionless variables \(X = x/R_a\), \(Y = y/R_a\), \(P = p/p_0\), \(H = h/h_0\), and \(M = 6\eta U R_a/(p_0 h_0^2)\), the dimensionless Reynolds equation becomes:
$$\frac{\partial}{\partial X}\left( H^3 \frac{\partial P}{\partial X} \right) + \frac{\partial}{\partial Y}\left( H^3 \frac{\partial P}{\partial Y} \right) = M \frac{\partial H}{\partial X}$$
To solve this equation with the MATLAB PDE toolbox, I transformed it into the standard elliptical form:
$$-\nabla \cdot (c \nabla P) + a P = f$$
By expanding the Reynolds equation, the coefficients were identified as:
$$c = H^3, \quad a = 0, \quad f = -M \frac{\partial H}{\partial X}$$
The PDE toolbox uses finite element analysis and supports Dirichlet and Neumann boundary conditions. In this study, I applied the Dirichlet boundary condition \(P = p_0\) on all boundaries, corresponding to atmospheric pressure. The mesh was generated with a triangular grid and refined to ensure mesh independence. Table 1 shows the mesh independence study results.
| Mesh size (μm) | Number of elements | Maximum pressure (Pa) |
|---|---|---|
| 5 | 342 | 365.4697 |
| 2.5 | 1368 | 410.5803 |
| 1.25 | 5472 | 417.2905 |
| 0.625 | 21888 | 418.9325 |
| 0.3125 | 87552 | 419.0891 |
| 0.15625 | 350208 | 419.2522 |
| 0.07813 | 1400832 | 419.2609 |
| 0.03906 | 5603328 | 419.2631 |
When the relative change was below 0.1%, the mesh size of 0.15625 μm was chosen for all subsequent calculations. The lubricant used in this study was L-CKC 68 gear oil with density \(\rho = 850 \ \text{kg/m}^3\) and dynamic viscosity \(\eta = 0.05797 \ \text{Pa·s}\). The equivalent radius \(R\) was 8.5714 mm, and the minimum film thickness was \(h_0 = 1 \ \mu\text{m}\).
4. Lubrication performance evaluation parameters
From the pressure distribution obtained by the PDE solver, I computed the load-carrying capacity \(W\) and the wall friction force \(F\). The dimensionless forms are:
$$W^* = \frac{\sum_i A_i p_i^*}{T^2}, \quad F^* = \frac{\sum_i A_i \tau_i^*}{T^2}$$
The dynamic pressure performance parameter \(K\) was defined as the ratio of the load capacity to the friction force:
$$K = \frac{W^*}{F^*}$$
A higher \(K\) indicates better lubrication performance because it means a greater load can be supported with lower frictional losses.
5. Effect of elliptical texture on pressure distribution
I first compared the smooth (non-textured) model and the elliptical texture model with parameters \(R_a^* = 1\), \(H^* = 1\), \(U^* = 1\), \(\delta^* = 2\), \(\theta = 0^\circ\), and \(\gamma = 0.8\). The non-textured model showed a symmetric pressure distribution with a maximum near the inlet and outlet, following a convergent-divergent pattern. In contrast, the elliptical texture model exhibited a convergent-divergent-convergent-divergent distribution. The negative pressure appeared at the dimple inlet, and the positive pressure peak was located at the dimple outlet. The pressure peaks shifted from the domain boundaries toward the texture edges. This behavior is typical for micro-textured contacts and is responsible for the additional hydrodynamic lift.
6. Comparison of different texture shapes
To evaluate the advantage of the elliptical texture, I compared three texture shapes: elliptical, circular dimple, and groove, under identical area occupancy, depth, and velocity conditions. The unit cell dimensions and texture depth were the same for all shapes. The calculated load-carrying capacity and dynamic pressure parameter \(K\) are summarized in Table 2.
| Texture shape | Oil film capacity \(W^*\) | Wall friction \(F^*\) | Dynamic parameter \(K\) |
|---|---|---|---|
| Non-textured | 0.82 | 1.35 | 0.607 |
| Groove | 1.10 | 1.42 | 0.775 |
| Circular dimple | 1.26 | 1.38 | 0.913 |
| Elliptical | 1.48 | 1.36 | 1.088 |
The elliptical texture exhibited the highest load-carrying capacity and the best dynamic pressure performance. This is because the elliptical shape combines the hydrodynamic wedge effect of grooves with the cavitation and pressure recovery of dimples, offering a more effective lubricant film formation.
7. Parametric study of elliptical texture
I conducted a comprehensive parametric study by varying one dimensionless parameter at a time while keeping the others constant. The following subsections describe the effects of area occupancy, ellipticity, angle, entrainment velocity, major radius, and depth on the lubrication performance.
7.1 Area occupancy \(\delta^*\)
With \(H^* = 1\), \(R_a^* = 1\), \(U^* = 1\), \(\gamma = 0.8\), and \(\theta = 0^\circ\), I varied \(\delta^*\) from 1 to 3. The results are shown in Table 3.
| \(\delta^*\) | \(W^*\) | \(F^*\) | \(K\) |
|---|---|---|---|
| 1 | 0.98 | 1.31 | 0.748 |
| 1.5 | 0.91 | 1.33 | 0.684 |
| 2 | 1.05 | 1.34 | 0.784 |
| 2.5 | 1.31 | 1.36 | 0.963 |
| 3 | 1.56 | 1.37 | 1.139 |
The load capacity first slightly decreased and then increased, while the friction force remained nearly constant. The dynamic parameter reached its maximum at \(\delta^* = 3\). However, a larger area occupancy reduces the real contact area and increases contact stress. Therefore, the preferred area occupancy is in the range \(\delta^* = 2.5\) to 3, corresponding to \(\delta = 25\%\) to 30%.
7.2 Ellipticity \(\gamma\)
With \(H^* = 1\), \(R_a^* = 1\), \(U^* = 1\), \(\delta^* = 2.5\), and \(\theta = 0^\circ\), I varied \(\gamma\) from 0.5 to 0.9. Table 4 lists the results.
| \(\gamma\) | \(W^*\) | \(F^*\) | \(K\) |
|---|---|---|---|
| 0.5 | 1.21 | 1.34 | 0.903 |
| 0.6 | 1.25 | 1.35 | 0.926 |
| 0.7 | 1.29 | 1.36 | 0.949 |
| 0.8 | 1.33 | 1.36 | 0.978 |
| 0.9 | 1.36 | 1.37 | 0.993 |
The load capacity increased with ellipticity, while the friction force remained almost unchanged. The dynamic parameter increased slightly, indicating that ellipticity has a minor influence on lubrication. Because a very small minor radius weakens the texture area, the recommended ellipticity range is 0.7 to 0.9.
7.3 Inclination angle \(\theta\)
With \(H^* = 1\), \(R_a^* = 1\), \(U^* = 1\), \(\delta^* = 2.5\), and \(\gamma = 0.8\), I varied \(\theta\) from \(0^\circ\) to \(90^\circ\). Table 5 shows the results.
| \(\theta\) (°) | \(W^*\) | \(F^*\) | \(K\) |
|---|---|---|---|
| 0 | 1.31 | 1.36 | 0.963 |
| 15 | 1.28 | 1.35 | 0.948 |
| 30 | 1.33 | 1.36 | 0.978 |
| 45 | 1.35 | 1.35 | 1.000 |
| 60 | 1.18 | 1.37 | 0.861 |
| 75 | 0.92 | 1.39 | 0.662 |
| 90 | 0.77 | 1.41 | 0.546 |
For angles between \(0^\circ\) and \(45^\circ\), the dynamic parameter varied mildly and remained high. Beyond \(45^\circ\), the load capacity dropped substantially and the friction force increased, leading to a severe reduction in lubrication performance. Thus the preferred angle range is \(0^\circ\) to \(45^\circ\), with the best at \(45^\circ\).
7.4 Entrainment velocity \(U^*\)
With \(H^* = 1\), \(R_a^* = 1\), \(\delta^* = 2.5\), \(\gamma = 0.8\), and \(\theta = 0^\circ\), I varied \(U^*\) from 1 to 5. Table 6 presents the results.
| \(U^*\) | \(W^*\) | \(F^*\) | \(K\) |
|---|---|---|---|
| 1 | 0.98 | 1.31 | 0.748 |
| 1.73 | 1.54 | 1.68 | 0.917 |
| 2.25 | 1.87 | 1.94 | 0.964 |
| 3.455 | 2.43 | 2.31 | 1.052 |
| 5 | 2.98 | 2.75 | 1.084 |
The load capacity and friction force both increased with velocity, but the dynamic parameter changed only slightly, with a maximum at \(U^* = 3.455\). Therefore, velocity has a limited influence on the lubrication performance in the tested range.
7.5 Major radius \(R_a^*\)
I investigated the effect of the major radius for different depth values. Table 7 summarizes the dynamic parameter \(K\) as a function of \(R_a^*\) for selected \(H^*\) values.
| \(R_a^*\) | \(H^*=1\) | \(H^*=5\) | \(H^*=10\) | \(H^*=15\) | \(H^*=20\) |
|---|---|---|---|---|---|
| 1 | 0.78 | 0.77 | 0.75 | 0.74 | 0.73 |
| 2 | 0.92 | 0.90 | 0.87 | 0.85 | 0.83 |
| 4 | 1.12 | 1.05 | 0.98 | 0.93 | 0.89 |
| 6 | 1.28 | 1.18 | 1.08 | 1.00 | 0.94 |
| 8 | 1.32 | 1.20 | 1.09 | 0.99 | 0.92 |
For \(R_a^* < 6\), increasing the major radius significantly improved the dynamic performance. For \(R_a^* > 6\), the improvement became marginal. The preferred major radius range is \(R_a^* = 6\) to 8.
7.6 Depth \(H^*\)
The depth effect is visible in Table 7. Generally, the dynamic parameter decreased as \(H^*\) increased, especially for larger radii. For small radii (\(R_a^* < 4\)), the depth influence was minor. For large radii, a shallow texture (\(H^* = 1\)) provided the best lubrication performance. I therefore selected \(H^* = 1\) as the optimum for lubrication, but for practical manufacturing and wear resistance, moderate depths were also considered in the experiments.
Based on the numerical lubrication analysis, the optimal elliptical texture parameters for lubrication are:
$$\delta^* = 2.5 \sim 3, \quad \gamma = 0.7 \sim 0.9, \quad \theta = 0^\circ \sim 45^\circ, \quad U^* = 3.455, \quad R_a^* = 6 \sim 8, \quad H^* = 1$$
8. Fabrication of elliptical-textured cylindrical rollers
To experimentally validate the numerical findings, I prepared cylindrical roller specimens with elliptical textures using a picosecond laser system. The roller material was 40Cr steel with hardness of 33–37 HRC. The large roller diameter was 40 mm and the small roller diameter was 30 mm, with thickness 10 mm. The surface was ground and polished to a roughness of about 0.2 μm. Only the small roller was textured. I designed a four-factor three-level orthogonal experiment to investigate the effects of depth, major radius, ellipticity, and angle on wear and friction. The area occupancy was fixed at 25% and the velocity corresponded to a small roller speed of 400 r/min. Table 8 lists the nine texture parameter combinations.
| Group | Depth \(H\) (μm) | Major radius \(R_a\) (μm) | Ellipticity \(\gamma\) | Angle \(\theta\) (°) |
|---|---|---|---|---|
| 1 | 5 | 40 | 0.5 | 0 |
| 2 | 5 | 80 | 0.7 | 90 |
| 3 | 5 | 150 | 0.9 | 45 |
| 4 | 10 | 40 | 0.9 | 90 |
| 5 | 10 | 80 | 0.5 | 45 |
| 6 | 10 | 150 | 0.7 | 0 |
| 7 | 20 | 40 | 0.7 | 45 |
| 8 | 20 | 80 | 0.9 | 0 |
| 9 | 20 | 150 | 0.5 | 90 |
The laser processing parameters were optimized through preliminary tests. The scan speed was 150 mm/s, the filling line width was 0.001 mm, the fill mode was unidirectional, and the laser frequency was 400 kHz. The laser power was adjusted to achieve the desired depths. After processing, the samples were ultrasonically cleaned in ethanol for 30 minutes. The texture morphology was measured with a Zygo New View 9000 three-dimensional optical profiler. The measured depths had an error of about 1 μm and the major radius error was about 3 μm, indicating good manufacturing quality.
9. Roller friction and wear test procedure
The friction tests were conducted on an MMS-2A computer-controlled friction and wear tester. The large roller was mounted on the lower shaft, and the small textured roller on the upper shaft. The rotational speed of the upper shaft was 90% of the lower shaft, providing a slide-to-roll ratio of 18.2%. The test force was 1600 N, the friction torque range was set to 5 N·m, and the duration was 30 minutes. Oil lubrication was supplied by drip feeding of L-CKC 68 gear oil at a rate of one drop every 11 seconds. Each test was repeated three times, and the friction coefficient was recorded continuously. The wear loss of the roller was measured with an electronic balance with a precision of 0.1 mg before and after each test. The wear loss was calculated as:
$$m = (m_0 – m_1) \times 1000 \ \text{mg}$$
where \(m_0\) is the initial mass and \(m_1\) is the final mass.
10. Experimental results for wear loss
Table 9 shows the average wear loss of the ten groups (nine textured and one untextured).
| Group | Wear loss (mg) |
|---|---|
| 1 | 3.81 |
| 2 | 2.61 |
| 3 | 5.47 |
| 4 | 13.12 |
| 5 | 8.43 |
| 6 | 5.21 |
| 7 | 6.56 |
| 8 | 4.53 |
| 9 | 3.34 |
| 10 (untextured) | 9.36 |
Groups 1, 2, 3, 6, 8, and 9 exhibited lower wear than the untextured roller. Group 4 showed the highest wear, even higher than the untextured one. The range analysis in Table 10 identifies the significance order of the four factors.
| Level | Depth \(H\) | Radius \(R_a\) | Ellipticity \(\gamma\) | Angle \(\theta\) |
|---|---|---|---|---|
| \(m_{j1}\) (mean of level 1) | 3.96 | 7.83 | 5.19 | 4.52 |
| \(m_{j2}\) (mean of level 2) | 8.92 | 5.19 | 4.79 | 6.36 |
| \(m_{j3}\) (mean of level 3) | 4.81 | 4.67 | 7.71 | 6.82 |
| Range \(R_j\) | 4.96 | 3.16 | 2.92 | 2.30 |
The factor order was depth > radius > ellipticity > angle. The optimal combination for minimum wear was \(H = 5 \ \mu\text{m}\), \(R_a = 150 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 0^\circ\).
SEM observations of the worn surfaces revealed that most of the textured rollers had point corrosion pits and mild scratches. The untextured roller showed larger and denser pits. Groups 2, 5, 6, and 7 had relatively fewer defects. The shallow and large-radius textures tended to reduce wear, while moderate depths could worsen wear if the texture geometry was not optimized.
11. Experimental results for friction coefficient
The friction coefficient was recorded as a function of time. The average friction coefficient for each group is listed in Table 11.
| Group | Average friction coefficient |
|---|---|
| 1 | 0.01543 |
| 2 | 0.01060 |
| 3 | 0.01599 |
| 4 | 0.02240 |
| 5 | 0.01236 |
| 6 | 0.01737 |
| 7 | 0.00949 |
| 8 | 0.01463 |
| 9 | 0.01045 |
| 10 (untextured) | 0.01705 |
Groups 2, 5, 7, 8, and 9 had lower friction coefficients than the untextured sample. The lowest friction was obtained in group 7 with \(H = 20 \ \mu\text{m}\), \(R_a = 40 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 45^\circ\). The range analysis for the average friction coefficient is presented in Table 12.
| Level | Depth \(H\) | Radius \(R_a\) | Ellipticity \(\gamma\) | Angle \(\theta\) |
|---|---|---|---|---|
| mean of level 1 | 0.01401 | 0.01577 | 0.01410 | 0.01581 |
| mean of level 2 | 0.01738 | 0.01253 | 0.01249 | 0.01261 |
| mean of level 3 | 0.01152 | 0.01460 | 0.01767 | 0.01448 |
| Range \(R_j\) | 0.00586 | 0.00324 | 0.00518 | 0.00320 |
The order was depth > ellipticity > radius > angle. The optimal combination for minimum friction was \(H = 20 \ \mu\text{m}\), \(R_a = 80 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 45^\circ\).
Combining the wear and friction results with the numerical lubrication analysis, I selected the final optimal parameter set for the gear experiment:
$$H = 20 \ \mu\text{m}, \quad R_a = 150 \ \mu\text{m}, \quad \gamma = 0.7, \quad \theta = 0^\circ$$
This combination represents a trade-off between the best wear resistance and good friction reduction, while also aligning with the theoretical lubrication preference for large radii and shallow-to-moderate depths.
12. Fabrication of elliptical-textured spur gears
I applied the selected optimal texture to a spur gear pair. The test gears were made of 20CrMo steel, hardened by carburizing and quenching to a tooth surface hardness of 60–62 HRC and core hardness of 33–37 HRC. The gear parameters are given in Table 13.
| Parameter | Small gear | Large gear |
|---|---|---|
| Module | 4.5 | 4.5 |
| Number of teeth | 16 | 24 |
| Pressure angle | 20° | 20° |
| Meshing angle | 22°26′ | 22°26′ |
| Addendum modification coefficient | 0.8532 | -0.5 |
| Face width | 20 mm | 20 mm |
| Center distance | 91.5 mm | 91.5 mm |
Using the same picosecond laser system, I processed the elliptical texture on all 16 teeth of the small gear, on both flanks of each tooth. The area occupancy was 25%, the major radius was 150 μm, the ellipticity was 0.7, the depth was 20 μm, and the texture was oriented horizontally, corresponding to an angle of \(0^\circ\). After processing, the gears were ultrasonically cleaned and labeled.
13. Gear friction test method
The gear friction tests were performed on an MFZG-1W gear wear testing machine. The test procedure followed the scuffing test standard GB/Z 13672-2022. The test gears were mounted in a closed power circulation system with oil lubrication using L-CKC 68 gear oil. The rotation speed was 1400 r/min, and the initial oil temperature was set to 30 °C. Before each load stage, the oil was cooled back to 30 °C. The load was increased stepwise through 12 stages, as listed in Table 14.
| Load stage | Torque (N·m) |
|---|---|
| 1 | 9.5 |
| 2 | 14.7 |
| 3 | 36.7 |
| 4 | 58.9 |
| 5 | 90.3 |
| 6 | 134.6 |
| 7 | 180.5 |
| 8 | 234.9 |
| 9 | 297.8 |
| 10 | 350.6 |
Each load stage lasted 15 minutes. After the test, the gears were cleaned and observed with a VHX-2000 digital microscope. The tooth flank area near the pitch line and towards the tooth tip was examined at 100× magnification. The damage area ratio \(Q\) was calculated as the percentage of the damaged area in the observed region.
14. Gear test results and discussion
After completing all 12 load stages, the untextured gear showed clear scuffing marks on several teeth. The damaged areas appeared as lines or bands along the sliding direction. The elliptical-textured gear, in contrast, exhibited only small point-like or narrow band-shaped damage zones, and no severe scuffing was observed. Table 15 summarizes the statistical damage area ratios for all 16 teeth of each gear.
| Tooth number | Untextured gear \(Q\) (%) | Textured gear \(Q\) (%) |
|---|---|---|
| 1 | 4.21 | 0.95 |
| 2 | 3.87 | 0.82 |
| 3 | 5.63 | 1.61 |
| 4 | 4.02 | 0.60 |
| 5 | 2.51 | 0.71 |
| 6 | 6.14 | 1.02 |
| 7 | 2.64 | 0.84 |
| 8 | 8.53 | 1.29 |
| 9 | 3.90 | 0.75 |
| 10 | 5.47 | 0.88 |
| 11 | 6.80 | 1.12 |
| 12 | 4.35 | 0.94 |
| 13 | 3.22 | 0.69 |
| 14 | 5.08 | 1.18 |
| 15 | 7.15 | 1.36 |
| 16 | 4.76 | 0.91 |
The maximum damage area ratio of the untextured gear was 8.53% (tooth 8), while that of the textured gear was only 1.61% (tooth 3), representing a reduction of 81.11%. The minimum damage area ratio was 2.51% for the untextured gear and 0.60% for the textured gear, a reduction of 76.97%. The average damage area ratio of the elliptical-textured gear was significantly lower, and the variation among teeth was much smaller than that of the untextured gear. These results confirm that the elliptical texture effectively improves the friction and wear performance of the spur gear surface.
15. Discussion
The experimental results align well with the numerical lubrication analysis. The elliptical texture creates an additional hydrodynamic pressure that increases the oil film thickness and load-carrying capacity. The texture also acts as a reservoir for the lubricant and a trap for wear debris, reducing three-body abrasion. In the roller tests, the optimal texture depth for friction reduction was 20 μm, while a shallower depth of 5 μm performed better for wear resistance. The gear test using the combined optimal parameters demonstrated that a depth of 20 μm with a large radius of 150 μm and a small angle of \(0^\circ\) achieved excellent overall tribological performance. The significant reduction in damage area ratio highlights the potential of elliptical textures for practical spur gear applications.
16. Conclusion
In this study, I investigated the lubrication and friction performance of spur gears with elliptical surface textures through numerical simulations and experiments. The main conclusions are:
(1) The elliptical texture changes the oil film pressure distribution from a simple convergent-divergent pattern to a convergent-divergent-convergent-divergent pattern, producing both negative and positive pressure peaks near the texture inlet and outlet, and enhancing the hydrodynamic pressure.
(2) The elliptical texture exhibits superior lubrication performance compared to groove textures and circular dimple textures under identical conditions. The dynamic pressure parameter \(K\) is highest for the elliptical texture.
(3) The parametric study showed that area occupancy, major radius, and depth significantly affect lubrication performance, while ellipticity, velocity, and small angles have moderate effects. The optimal lubrication parameters were identified as \(\delta^* = 2.5\sim3\), \(\gamma = 0.7\sim0.9\), \(\theta = 0^\circ\sim45^\circ\), \(U^* = 3.455\), \(R_a^* = 6\sim8\), and \(H^* = 1\).
(4) Roller friction tests revealed that the texture depth has the greatest influence on both wear and friction. The best wear resistance was obtained with \(H = 5 \ \mu\text{m}\), \(R_a = 150 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 0^\circ\). The best friction reduction was obtained with \(H = 20 \ \mu\text{m}\), \(R_a = 80 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 45^\circ\). A comprehensive trade-off led to the final parameter set \(H = 20 \ \mu\text{m}\), \(R_a = 150 \ \mu\text{m}\), \(\gamma = 0.7\), and \(\theta = 0^\circ\).
(5) Gear scuffing tests demonstrated that the elliptical-textured gear significantly outperforms the untextured gear. The maximum damage area ratio was reduced by 81.11%, and the minimum by 76.97%. The elliptical texture effectively suppresses scuffing and wear on spur gear tooth flanks, providing a promising approach to improve gear reliability and service life.
Future work should explore other texture shapes and optimization algorithms, as well as the interaction between texture parameters and different lubricant formulations. The promising results of this study encourage further investigation into the practical application of elliptical textures in high-performance spur gear transmissions.