Critical Transition Relations for Fatigue Failure of PEEK Gear under Oil-Jet Lubrication
Abstract:
Polyetheretherketone (PEEK) gears are high-performance polymer gears widely used in automobiles, drones, robots, and other fields. However, the complex failure mechanism of PEEK gears and the lack of basic data on loading capacity lead to a shortage of a reasonable design basis in power transmission applications. To address the unclear failure mechanism and the lack of fundamental durability data of PEEK gears, fatigue performance tests of PEEK helical gear pairs under oil-jet lubrication were carried out, and the contact stress and bending stress were calculated. The failure mechanisms were investigated by using scanning electron microscopy and other equipment. Experimental results show that the primary failure modes of PEEK gears under oil-jet lubrication were tooth surface pitting failure and tooth root fatigue fracture. The critical transition relationship between PEEK gear contact fatigue failure and bending fatigue failure was identified, and an evaluation method for the failure form of PEEK gears was proposed. When the ratio of contact stress to bending stress of the PEEK gear was smaller than 1.02, the PEEK gear mainly suffered from root fatigue fracture; when the ratio of contact stress to bending stress was larger than 1.10, the PEEK gear mainly suffered from tooth surface pitting failure. When the ratio was in the range from 1.02 to 1.10, there was a critical failure threshold between tooth surface contact fatigue and root bending fatigue.
Keywords: polyetheretherketone (PEEK) gear; loading capacity; gear temperature; failure modes
Introduction
Compared with metal gears, polymer gears have advantages such as light weight, low noise, and low cost. Over the past few decades, they have gradually replaced metal gears in motion transmission applications such as automobiles, home appliances, and office equipment [1-3]. With the advancement of new polymer materials and gear manufacturing technologies, the load-carrying capacity of polymer gears has continuously improved, with the transmitted power increasing from less than 10 kW in the past to nearly 30 kW [4], meeting the power transmission needs of new energy vehicle wheel-side reducers, unmanned aerial vehicle transmission systems, etc. [5], and is expected to promote "replacing steel with plastic" in gear transmissions. However, in the power transmission process, the failure behavior of polymer gears is comprehensively influenced by factors such as load conditions, ambient temperature, and lubrication methods, and its failure mechanism is still unclear, limiting the application of polymer gears in power transmission scenarios.
In recent decades, researchers have conducted extensive studies on the failure behavior of polymer gears. Due to the self-lubricating properties of polymer gears, they are often used in dry contact scenarios. Mao et al. [6-7] and Li et al. [8] explored the effects of material type, processing method, output torque, and other factors on the wear performance of polymer gears under dry contact based on self-developed polymer gear wear test rigs, finding that output torque plays a dominant role in the failure behavior of polymer gears under dry contact. Under dry contact, polymer gears mainly experience wear failure and have short lifespans, making it difficult to meet the load-carrying capacity and service life requirements in power transmission scenarios. Therefore, improving lubrication conditions and enhancing the load-carrying capacity of polymer gears has gradually become the focus of polymer gear research. Zorko et al. [9] conducted operation tests of steel-PEEK gear pairs under different lubrication conditions and found that, compared with dry contact under the same load, grease lubrication can reduce the body temperature of PEEK gears and extend the average lifespan of gears by 1.23 times. Zhong et al. [10] conducted load-carrying capacity tests of polyoxymethylene (POM) gears under oil lubrication and found that cracks initiate and propagate in the subsurface layer of the gear tooth surface under contact stress and shear stress, ultimately developing into contact fatigue failure in the form of surface fatigue cracks and pitting. Lu Zehua et al. [11] studied the effects of lubrication and load conditions on the service performance of POM gears and found that POM gears mainly experience wear failure under dry contact and fatigue failure under oil lubrication, with the operating temperature of POM gears significantly reduced and the load-carrying capacity significantly improved under oil lubrication. Yu et al. [12] compared the differences in wear behavior of POM gear pairs under dry friction and oil lubrication conditions and found that under dry friction conditions, bulges form in the pitch line area of the gear tooth surface as wear accumulates, while under oil lubrication, there is no severe damage to the tooth surface, and oil lubrication greatly improves the load-carrying capacity of POM gears. Obviously, oil lubrication improves the load-carrying capacity and extends the service life of polymer gears by reducing friction and enhancing heat dissipation, becoming the preferred lubrication method for polymer gears in power transmission scenarios.
Oil lubrication reduces the probability of wear failure on the tooth surface of polymer gears, making fatigue failure the dominant failure mode [13-14]. Illenberger et al. [15] studied the stress conditions affecting the tooth surface damage behavior of oil-lubricated PEEK gears and found that under sufficient oil lubrication and adequate root load-carrying capacity, the gear failure mode is mainly pitting damage. Illenberger et al. [16] conducted tooth surface load-carrying capacity tests of gears made of different materials (pure PEEK and 30% carbon fiber reinforced PEEK) using a power-closed gear test rig and found that both 30% carbon fiber reinforced PEEK gears and PEEK gears experience pitting failure at an output torque of 43 N·m. Blais et al. [17] conducted bending fatigue tests on polymer gears, and the tests showed that gear cracks propagate very rapidly after initiation, so the crack initiation life of gears is more suitable for evaluating the bending fatigue life of gears. Lu et al. [18] conducted operation tests of steel-PEEK gears under oil lubrication and found that oil-lubricated PEEK gears exhibit pitting and pitting-induced tooth surface fracture under light and medium loads, and tooth root fatigue fracture under heavy loads. Compared with research on polymer gear wear, research on polymer gear fatigue is less, and it is concentrated on the study of single fatigue failure modes. However, in the application of polymer gears in power transmission scenarios, there are many factors affecting fatigue failure, and the failure process is influenced by the competition between different fatigue failure modes such as contact fatigue and bending fatigue. Currently, there is little research on the competition and transition of fatigue failure in polymer gears under oil lubrication, and the anti-fatigue design of power transmission polymer gears is still at the empirical rough design stage, leading to frequent fatigue failure accidents of polymer gears in engineering practice.
To address the unclear correlation between fatigue failure modes of polymer gears under oil lubrication and load conditions in the field of power transmission, the authors conducted operational fatigue tests on PEEK-PEEK gear pairs under oil lubrication, analyzed the evolution of PEEK gear operating temperature and fatigue failure behavior, and identified the relationship between PEEK gear contact stress, bending stress, and fatigue failure behavior to support the prediction of failure modes in power transmission polymer gears.
1 Fatigue Performance Operation Test of PEEK-PEEK Gears under Oil-Jet Lubrication
1.1 Test Gear Parameters
The test gear materials are all PEEK, with the material grade HPG 140GRA, which has high temperature resistance, high wear resistance, and corrosion resistance, and can maintain high mechanical strength and dimensional stability under harsh conditions. Its mechanical properties are shown in Table 1.
Table 2 shows the geometric parameters of the PEEK-PEEK gear pair, representing typical power transmission application scenarios in automobile engines. The test gears are involute cylindrical helical gears, injection molded, with the driving gear left-handed and the driven gear right-handed.
1.2 Gear Fatigue Performance Operation Test Rig and Detection
The multi-purpose transmission performance test rig used for PEEK gear fatigue tests is shown in Figure 1. The test rig consists of two spindle boxes, two drive motors, guide rails, and a monitoring system. The driving wheel spindle box can move along the guide rail to adjust the gear center distance, with a movement accuracy of up to 1 μm. By monitoring vibration signals, automatic shutdown function can be achieved.
The lubricating oil used in the PEEK gear fatigue test process is engine extreme pressure lubricating oil with the grade HX7 PIUS 5W-40, and its basic performance parameters are shown in Table 3. The test uses oil-jet lubrication. To ensure good lubrication between the gear pairs, the oil-jet volume is controlled at 0.6±0.2 L/min, and oil is supplied continuously directly to the meshing area.
**Table 1 The material properties of the test gear**
| Property | Value |
|---|---|
| Elastic modulus (40 ℃) E/MPa | 3 600 |
| Density ρ/(g·cm⁻³) | 1.3 |
| Tensile strength (23 ℃) R_m/MPa | 95 |
| Glass transition temperature T/℃ | 143 |
Table 2 Main geometric parameters of the PEEK-PEEK gear pair
| Parameter | Value |
|---|---|
| Normal module m_n/mm | 1.898 |
| Number of teeth | 28 |
| Normal pressure angle α_n/(°) | 13.796 |
| Center distance a/mm | 54 |
| Face width b/mm | 15 |
| Gear ratio | 1 |
[Figure 1: Multipurpose transmission performance test rig]
Table 3 The basic parameters of test lubricating oil
| Property | Value |
|---|---|
| Kinematic viscosity (100 ℃)/(mm²·s⁻¹) | 14.7 |
| Kinematic viscosity (40 ℃)/(mm²·s⁻¹) | 89.5 |
| Dynamic viscosity μ/(mPa·s) | 5 471 |
| Density ρ/(g·cm⁻³) | 0.841 |
The PEEK gear fatigue test process is shown in Figure 2. The test set up 6 load levels, with output torque T₂ of 15, 20, 25, 30, 35, 40 N·m respectively. Before the test, the PEEK gears were placed in a 95% ethanol solution for ultrasonic cleaning, dried with nitrogen, and then placed in a standard environment (temperature 23±2 ℃, humidity 50%±5%) for 88 h. The gear accuracy was measured using a Klingelnberg P26 precision gear profile comprehensive measuring instrument, and the average accuracy of the test gears met the level 10 accuracy requirements in GB/T 10095. At the same time, the gear roughness was detected using a German Mahr M series portable roughness meter M300C. Three measurements were taken on the tooth surface of one tooth randomly selected from the gear, and the average arithmetic mean deviation Ra of the tooth surface profile was 0.279 μm. After the formal test, an infrared thermal imager (Fotric, 238) was used to monitor the operating temperature of the test gear pair, recording the gear body temperature and oil outlet lubricating oil temperature every 10⁵ cycles, with 3 temperature values recorded each time, and the average value taken as the stable temperature at that moment. After gear failure, scanning electron microscopy (SEM) was used to analyze the microscopic features of tooth surface fatigue damage.
1.3 PEEK Gear Strength Calculation Method
Load is one of the key factors affecting the failure mode of polymer gears. Under light and medium load conditions, PEEK gears mainly fail by pitting, while under heavy load conditions, PEEK gears are more prone to tooth root fatigue fracture [18]. According to the German polymer gear strength calculation manual VDI 2736-2 [19], which is widely used in the international polymer gear industry, the tooth surface contact stress, root bending stress, and related coefficients under different output torques are calculated.
The maximum tooth surface contact stress calculation formula for PEEK gears is:
σ_H = Z_E Z_H Z_ε Z_β √[(2T₂ K_H (u + 1)) / (b d₁² u)] (1)
Where: Z_E is the elastic influence coefficient; Z_H is the zone coefficient; Z_ε is the contact ratio coefficient; Z_β is the helix angle coefficient; T₂ is the output torque, N·mm; K_H is the tooth surface load coefficient; u is the gear ratio; b is the face width, mm; d₁ is the pitch circle diameter, mm.
The elastic influence coefficient Z_E considers the influence of the elastic modulus E and Poisson's ratio μ of the material properties on the contact stress, and the calculation formula is:
Z_E = 1 / √[π ((1 - μ₁²)/E₁ + (1 - μ₂²)/E₂)] (2)
Where: E₁, E₂ are the elastic moduli of the paired gear materials, MPa; μ₁, μ₂ are the Poisson's ratios of the paired gear materials.
The related coefficients in the contact stress calculation calculated based on gear material parameters, geometric parameters, and VDI 2736 are shown in Table 4. Compared to steel-PEEK gears [18], the elastic influence coefficient Z_E of PEEK-PEEK gear pairs is lower, and the contact load-carrying capacity is higher under the same load.
The maximum tooth root bending stress calculation formula for PEEK gears is:
σ_F = K_F Y_Fa Y_Sa Y_ε Y_β (2T₂) / (b d₁ m_n) (3)
Where: K_F is the tooth root load coefficient; Y_Fa is the form factor for helical gears; Y_Sa is the stress correction coefficient; Y_ε is the contact ratio coefficient; Y_β is the helix angle coefficient; m_n is the normal module, mm.
The related coefficients in the bending stress calculation calculated based on gear material parameters, geometric parameters, and VDI 2736 are shown in Table 5.
2 Test Results and Discussion
Lubricating oil reduces the operating temperature of polymer gears by carrying away the heat generated during the meshing process of polymer gears and forming an oil film on the tooth surface to reduce tooth surface friction [11], thereby improving the load-carrying capacity of polymer gears. This section describes the operating temperature of the PEEK gear body, lubricating oil temperature, and gear failure modes during the test process, and analyzes the impact of load under oil lubrication on the load-carrying capacity and service performance of PEEK gears.
2.1 Temperature and Stress State Analysis
The infrared thermal imager was used to measure the gear body temperature during gear operation at each load level, with the emissivity of the thermal imager set to ε = 0.95 [9].
The gear pair operation images and thermal imaging images are shown in Figure 3. The temperature of the gear and spindle box connection disk is significantly higher than that of the gear pair, mainly because the lubricating oil only lubricates and cools the gear pair, while the connection disk relies on air convection for cooling. The driving and driven gear body temperatures of the PEEK gear pair have good consistency.
During the test, the PEEK gear body temperature and lubricating oil temperature were recorded separately. When the output torque T₂ was 30 N·m, the variation trend of gear body temperature and lubricating oil temperature with the number of cycles N is shown in Figure 4(a). After the test started, the gear body temperature and lubricating oil temperature rose rapidly, stabilizing near N = 1×10⁶, and the gear body temperature and lubricating oil temperature basically did not change until fatigue failure, thus determining the selection range of steady-state temperature for gear body and lubricating oil under different load levels. Figure 4(b) shows the steady-state temperatures of lubricating oil and gear body under each load level. It can be seen that the oil temperature remains basically unchanged under different load levels, stable at 32±2 ℃, and the gear body temperature is basically stable at 42±2 ℃. Under oil lubrication, the influence of load on the PEEK gear body temperature can be ignored.
Table 4 Values of correlation coefficients of contact stress on the tooth surface of test gear
| Coefficient | Value |
|---|---|
| Load coefficient K_H | 1.1 |
| Zone coefficient Z_H | 2.898 |
| Elastic influence coefficient Z_E | 26.12 |
| Contact ratio coefficient Z_ε | 0.855 |
| Helix angle coefficient Z_β | 0.998 |
Table 5 Test gear root bending stress correlation coefficient values
| Coefficient | Value |
|---|---|
| Load coefficient K_F | 1.1 |
| Form factor Y_Fa | 3.16 |
| Stress correction coefficient Y_Sa | 1.41 |
| Contact ratio coefficient Y_ε | 0.554 |
| Helix angle coefficient Y_β | 0.964 |
**[Figure 3: Gear operating and thermal images]**
[Figure 4: Temperatures of lubricating oil and gear wheel]**
(a) Variation of lubricating oil temperature and gear body temperature with cycle number
(b) Steady-state temperatures of lubricating oil and gear body under different load levels
2.2 PEEK Gear Failure Modes
During the PEEK gear test process, the test was stopped when the test gear cycle number exceeded 10⁷ or met the failure criteria. The PEEK gears exhibited two failure modes: tooth surface pitting and tooth root fatigue fracture, as shown in Figure 5. When the output torque T₂ was 30 N·m, the gear experienced contact fatigue failure, manifested as pitting damage near the pitch line; when the output torque T₂ was 40 N·m, the gear experienced bending fatigue failure, manifested as tooth root fatigue fracture damage.
Figure 6 shows the microscopic morphology of PEEK gear tooth surface pitting under scanning electron microscope when the output torque T₂ was 30 N·m. It can be seen that the tooth surface pitting is mainly concentrated near the pitch line of the gear tooth surface, with basically no pitting in the root and tip areas, but slight scratches exist. According to the research by Zhong et al. [10], the meshing gear pair only has rolling at the pitch line, while relative sliding exists in both the root and tip areas, which is the possible reason for the slight scratches in the tip and root areas. During gear operation, the Hertz contact stress near the pitch line on the tooth surface is higher than in the root and tip areas, thus leading to pitting damage in the pitch line area of the PEEK gear tooth surface. The pitting area at the pitch line of the gear tooth surface is distributed with a large number of fatigue cracks and pitting pits. Fatigue cracks mainly initiate in the subsurface layer of the gear, and under the cyclic stress on the gear surface, the initial cracks in the subsurface layer gradually expand and extend in all directions. When multiple cracks converge and extend to the tooth surface, pitting pits are formed [20-21].
Figure 7 shows the typical tooth root fatigue fracture characteristics of PEEK gears. When the output torque T₂ was 35 N·m, the final failure mode of the PEEK gear was tooth root fatigue fracture, as shown in Figure 7(a). Under heavy load conditions, the root bending stress exceeds the local bending fatigue strength, cracks appear at the root fillet, and the cracks propagate from the loaded tooth surface root surface to the inside of the tooth root, leading to tooth root fatigue fracture. The dangerous position of crack initiation is consistent with the 30° tangent position [22]. When the output torque T₂ was 40 N·m, the gear ultimately experienced complete tooth fracture at the root. The restored broken tooth profile is shown in Figure 7(b), and it is found that the tooth root fatigue fracture location has good consistency with the crack position in Figure 7(a).
**[Figure 5: PEEK gear fatigue failure]**
**[Figure 6: PEEK gear pitting surface micromorphology]**
**[Figure 7: Macro and micro features of PEEK gear root fracture]**
(a) PEEK gear root fatigue fracture macro morphology
(b) PEEK gear root fatigue fracture micro morphology
**[Figure 8: Contact stress and root bending stress of PEEK gear under different load levels]**
To better reflect the impact of the variation trend of tooth surface contact stress and tooth root bending stress of PEEK gears with output torque on gear fatigue failure modes, the PEEK gear failure transition point k is proposed, defined as the ratio of tooth surface contact stress to tooth root bending stress of PEEK gears:
k = σ_H / σ_F (4)
Figure 9 shows the variation trend of the PEEK gear failure transition point k under different output torques. As the output torque increases, the k value decreases continuously, and the variation amplitude of k decreases with the increase of output torque. When k > 1.10, the gear mainly fails by tooth surface pitting; when k < 1.02, the gear mainly fails by tooth root fatigue fracture. Therefore, there is a critical failure transition point for PEEK gear tooth surface pitting and tooth root fatigue fracture within the range of k from 1.02 to 1.10.
The service life of polymer gears largely depends on their tooth root load-carrying capacity. If the load exceeds the local bending fatigue strength, cracks appear in the root fillet area, ultimately leading to tooth root fatigue fracture [15], and the number of cycles required for tooth root fatigue fracture failure from root fillet crack initiation to final tooth fracture is fewer than the number of cycles required for subsurface crack initiation to final tooth surface pitting failure. Tooth root fatigue fracture failure occurs faster. Tooth root fatigue fracture of polymer gears significantly affects the transmission performance of the transmission system, even leading to complete failure of the transmission system, damaging equipment and even endangering personal safety. By estimating the critical transition point for tooth surface pitting and tooth root fatigue fracture of PEEK gears through tests, it can provide support for predicting the failure modes of PEEK gears.
### 2.3 PEEK Gear Fatigue Life
Figure 10 shows the fatigue life of 16 PEEK gear pairs under different output torques. When the output torque is below 30 N·m, PEEK gears mainly experience contact fatigue failure, with life run-out points at output torques of 15 N·m and 25 N·m; when the output torque is above 35 N·m, all PEEK gears experience bending fatigue failure, especially at an output torque of 40 N·m, where the bending fatigue life of PEEK gears drops sharply, with an average life of only 1.8×10⁵ cycles, reduced by about one order of magnitude compared to 30 N·m.
Based on the fatigue test data of 16 groups of PEEK gears, the contact fatigue S-N curve and bending fatigue S-N curve of PEEK gears are drawn, as shown in Figure 11. There is a clear boundary between the contact fatigue failure test points and bending fatigue failure test points, and the contact fatigue failure test points are relatively concentrated, while the bending fatigue failure test points are relatively dispersed, indicating that the bending fatigue life of PEEK gears changes significantly with the increase of output torque. When the maximum tooth root bending stress of PEEK gears is below 102.22 MPa, the gear tooth root fatigue strength is sufficient, and at this time, contact fatigue failure dominated by the maximum tooth surface contact stress mainly occurs; when the tooth root maximum bending stress is above 119.26 MPa, all gears experience bending fatigue failure, indicating that the bending fatigue strength limit range of PEEK gears is between 102.22~119.26 MPa. In Figure 11, when the maximum tooth surface contact stress of PEEK gears is 79.50 MPa and 102.63 MPa, the gear cycle number exceeds 10⁷, and there is gear life run-out; however, when the tooth surface contact stress is 91.80 MPa, the average fatigue life of the gear is about 8.86×10⁶, so the contact fatigue strength limit range of PEEK gears is between 79.50~91.80 MPa. When the tooth root bending stress increases by 20 MPa, the gear fatigue life decreases by about one order of magnitude; when the gear tooth surface contact stress is below 112.43 MPa, the contact fatigue life of PEEK gears is basically stable at the same order of magnitude. From Figure 10, it can be seen that when the output torque exceeds 35 N·m, all PEEK gears experience bending fatigue failure, and their bending fatigue life is almost all below 3×10⁶ cycles, consistent with the cycle base set when obtaining the bending fatigue strength limit for metal gears.
Since the test gears were not designed according to the test gear parameters recommended for basic data measurement in the standards GB/T 14229-2021 "Gear Contact Fatigue Strength Test Method" and GB/T 14230-2021 "Gear Bending Fatigue Strength Test Method", the fatigue S-N curve of this PEEK gear has certain limitations. For PEEK gears with different structural parameters, the fatigue S-N curve obtained in this paper can be used as a reference, and accurate gear fatigue S-N curves still need to be obtained through new tests.
3 Conclusions
To address the unclear correlation between fatigue failure modes of polymer gears under oil lubrication and operating load in the field of power transmission, fatigue tests on PEEK-PEEK gear pairs under oil lubrication were conducted. It was found that the fatigue failure modes of PEEK gears under oil lubrication change with increasing load, and thus the PEEK gear failure transition point k (the ratio of gear tooth surface contact stress to tooth root bending stress) was proposed, and the range of the critical transition point k for PEEK gear tooth surface pitting and tooth root fatigue fracture failure was determined, providing theoretical basis for the reliable design and failure analysis of high-load polymer gears. The main conclusions are as follows:
1) Under light and medium loads, oil-lubricated PEEK gears mainly experience contact fatigue failure, while under heavy loads, bending fatigue failure occurs. Oil-lubricated PEEK test gears experience tooth surface pitting at output torques below 30 N·m, and tooth root fatigue fracture at output torques above 35 N·m.
2) The critical transition point for tooth surface pitting and tooth root fatigue fracture failure of PEEK gears is in the range of k from 1.02 to 1.10. When k is below 1.02, PEEK gears experience tooth root fatigue fracture; when k is above 1.10, tooth surface pitting occurs.
3) When the cycle base is 10⁷, the contact fatigue strength limit range of PEEK gears under oil lubrication is between 79.50~91.80 MPa; the cycle base for the bending fatigue limit of PEEK gears under oil lubrication is approximately 3×10⁶, with the bending fatigue strength limit range between 102.22~119.26 MPa.
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