Friction and wear are primary causes of mechanical equipment failure, particularly in motion pairs such as gear shafts. In differential assemblies, planetary gear shafts often experience rapid wear and scuffing due to inadequate lubrication. This study investigates the potential of fullerene C60 nano-carbon spheres as a lubricant additive to enhance anti-wear and friction-reduction properties for gear shafts. The unique spherical structure of C60, characterized by high symmetry and superior compressive strength, suggests its promise as a super-lubricant. Through ball-on-disc friction tests and planetary gear shaft fatigue life experiments, we evaluate the performance of C60-enriched lubricants under varying concentrations and operational conditions.
The fundamental mechanism of friction in gear shafts can be described by the coefficient of friction, defined as:
$$ \mu = \frac{F_f}{F_n} $$
where \( \mu \) is the friction coefficient, \( F_f \) is the frictional force, and \( F_n \) is the normal load. Wear volume, according to Archard’s wear equation, is expressed as:
$$ V = k \frac{F_n s}{H} $$
where \( V \) is the wear volume, \( k \) is the wear coefficient, \( s \) is the sliding distance, and \( H \) is the material hardness. Introducing nano-additives like fullerene C60 can alter these parameters by forming protective layers or acting as rolling elements between surfaces.
In this study, we prepared lubricant mixtures by dispersing fullerene C60 nano-carbon spheres into a base lubricant (Castrol BOT 805C) using electromagnetic stirring and ultrasonic oscillation. The dispersion process involved 45 minutes of electromagnetic stirring followed by 2 hours of ultrasonic vibration to ensure homogeneity. Six experimental groups were established: one with the base lubricant only, and five with C60 concentrations of 100, 200, 300, 400, and 500 ppm. The ball-on-disc tests were conducted on a friction wear tester, with a disc made of 20CrMnTi (simulating the gear shaft material) and a ball made of GCr15 bearing steel. Tests were performed under a load of 50 N, rotational speed of 200 rpm, and duration of 10 minutes at room temperature. The average friction coefficients were recorded, and wear scar morphology was analyzed using scanning electron microscopy (SEM).
The results from the ball-on-disc tests are summarized in Table 1. The average friction coefficient decreased significantly with the addition of C60, reaching a minimum of 0.0801 at 400 ppm concentration—a 71.1% reduction compared to the base lubricant. However, at 500 ppm, the friction coefficient increased, likely due to nanoparticle agglomeration. This demonstrates that an optimal concentration of C60 is critical for maximizing lubricity in gear shaft applications.
| Group | C60 Concentration (ppm) | Average Friction Coefficient | Reduction (%) |
|---|---|---|---|
| 1 | 0 | 0.2769 | – |
| 2 | 100 | 0.0917 | 66.9 |
| 3 | 200 | 0.1008 | 63.6 |
| 4 | 300 | 0.0992 | 64.2 |
| 5 | 400 | 0.0801 | 71.1 |
| 6 | 500 | 0.1064 | 61.6 |
SEM analysis of the wear scars revealed that surfaces lubricated with C60-enriched oil exhibited shallower and smaller wear tracks compared to those with the base lubricant. This indicates that C60 nano-spheres form a protective film, reducing direct metal-to-metal contact and minimizing wear on the gear shaft. The “rolling bearing” effect of C60 particles can be modeled by considering the reduction in shear stress:
$$ \tau = \mu \sigma $$
where \( \tau \) is the shear stress and \( \sigma \) is the normal stress. With C60 additives, the effective \( \mu \) decreases, leading to lower \( \tau \) and thus less wear.
To validate these findings in a real-world scenario, fatigue wear tests were conducted on planetary gear shafts using a transmission assembly fatigue life test bench. The planetary gear shaft, made of 20CrMnTi, was subjected to break-in and gear-shifting cycles under controlled conditions. Two sets of tests were performed: one with the base lubricant and another with C60-enriched lubricant (400 ppm). The break-in conditions included forward and reverse rotation with an input torque of ±182.5 N·m, input speed of ±9000 rpm, and output speed of ±749.3 rpm over 1.5 hours. Gear-shifting tests involved multiple cycles at specific torques and speeds, as detailed in Table 2.
| Gear | Input Torque (N·m) | Input Speed (rpm) | Output Speed (rpm) | Total Time (h) | Cycle Time |
|---|---|---|---|---|---|
| 1 | 365 | 5939 | 494.4 | 3.1 | 18 min 36 s |
| 2 | 365 | -5939 | -494.4 | 6.3 | 37 min 48 s |
After 10 cycles totaling 9.5 hours, wear depth on the planetary gear shaft was measured at both ends. The results, shown in Table 3, indicate that the C60-enriched lubricant reduced wear by approximately 60% compared to the base lubricant. This significant improvement underscores the effectiveness of C60 in protecting gear shafts under dynamic loading conditions.
| Gear Shaft Location | Wear Depth with Base Lubricant (mm) | Wear Depth with C60 Lubricant (mm) | Reduction (%) |
|---|---|---|---|
| Left End | 0.013 | 0.005 | 61.5 |
| Right End | 0.010 | 0.004 | 60.0 |
The anti-wear mechanism of fullerene C60 in gear shaft lubrication can be attributed to several factors. First, the spherical nanoparticles act as micro-bearings, converting sliding friction into rolling friction, which inherently has a lower coefficient. This effect can be described by the relationship:
$$ \mu_{\text{eff}} = \mu_s – \Delta \mu_r $$
where \( \mu_{\text{eff}} \) is the effective friction coefficient, \( \mu_s \) is the sliding friction coefficient, and \( \Delta \mu_r \) is the reduction due to rolling. Second, C60 particles fill micro-asperities on the gear shaft surface, forming a protective film that reduces direct contact. The film’s durability can be modeled using the concept of load-bearing capacity:
$$ W = \frac{F_n}{A_c} $$
where \( W \) is the load per unit area and \( A_c \) is the real contact area. With C60, \( A_c \) increases, distributing load more evenly and reducing stress concentrations.
Furthermore, the dispersion stability of C60 in lubricants is crucial for long-term performance. Agglomeration at high concentrations (e.g., 500 ppm) can lead to increased friction, as observed in our tests. The critical concentration for optimal dispersion can be derived from the DLVO theory, considering van der Waals forces and electrostatic repulsion:
$$ V_T = V_A + V_R $$
where \( V_T \) is the total interaction energy, \( V_A \) is the attractive potential, and \( V_R \) is the repulsive potential. At optimal concentrations, \( V_R \) dominates, preventing agglomeration and maintaining lubricity.
In practical applications, such as automotive differentials, the planetary gear shaft is subjected to cyclic stresses and varying speeds. The integration of C60 additives can extend the service life of these components by minimizing wear and friction. For instance, the wear rate of a gear shaft under lubricated conditions can be expressed as:
$$ \frac{dV}{dt} = k’ \frac{F_n v}{H} $$
where \( v \) is the sliding velocity. With C60, the wear coefficient \( k’ \) decreases, leading to a lower wear rate. This is particularly beneficial in high-speed gear shafts, where thermal effects and surface degradation are concerns.
Our findings align with previous research on nano-lubricants, highlighting the importance of nanoparticle morphology and concentration. The spherical shape of C60 facilitates easy rolling, while its high strength resists deformation under load. Compared to other additives like graphite or metal nanoparticles, C60 offers a unique combination of low friction and environmental friendliness, making it suitable for advanced gear shaft systems in aerospace, automotive, and industrial machinery.
In conclusion, fullerene C60 nano-carbon spheres significantly enhance the anti-wear and friction-reduction properties of lubricants for planetary gear shafts. The ball-on-disc tests demonstrated a friction coefficient reduction of up to 71.1% at 400 ppm concentration, while fatigue wear tests showed a 60% decrease in wear depth. These results validate the potential of C60 as a high-performance lubricant additive, contributing to improved efficiency and durability of gear shafts in mechanical transmissions. Future work will focus on optimizing dispersion techniques and exploring synergistic effects with other nanomaterials to further advance lubricant technology.