Abstract
The study focuses on the impact of helical gear meshing moments on the transient lubrication performance of planetary gear journal bearings in wind turbine gearboxes. Planetary gear systems are commonly used in wind turbines due to their structural compactness, high power density, and ability to transmit large torques. However, helical gears in these systems generate meshing moments that can lead to misalignment between the planetary gears and pin shafts, resulting in edge contact risks and reduced operational life. This research investigates the dynamic effects of radial loads, bending moments, and rotational speeds on the journal bearings. A transient tribo-dynamic coupling model is established and validated through experimental tests. The results reveal that the dynamic meshing forces and generated bending moments significantly influence the oil film/solid contact pressures and misalignment moments. Additionally, reducing the journal bearing radial clearance effectively enhances its transient lubrication performance.
Introduction
Wind energy has emerged as a leading renewable energy source worldwide due to its environmental friendliness and sustainability. Wind turbine gearboxes play a crucial role in converting wind energy into mechanical energy that drives the generator. Planetary gear systems are extensively utilized in these gearboxes because of their advantages in structural compactness, high power density, and capability to transmit large torques.
Traditionally, rolling bearings have been used in gearboxes; however, with the trend towards larger wind turbines requiring higher torque density and lighter designs, sliding bearings are increasingly being adopted to support planetary gears. These bearings often use the inner holes of the planetary gears and pin shafts as the bearing sleeves and journals, respectively. However, the complex loading conditions and transmission configurations in wind turbines can lead to misalignment between the planetary gears and pin shafts, posing challenges for stable lubrication.
Helical gears are preferred in wind turbine gearboxes to improve transmission smoothness and gear load-bearing capacity. However, their meshing generates dynamic forces that can introduce additional bending moments, causing misalignment between the planetary gears and pin shafts. This misalignment, combined with the low-speed, high-load operating conditions and time-varying meshing stiffness, makes it difficult to maintain stable full-film lubrication, increasing the risk of edge contact and reducing operational life.
Literature Review
Previous studies have investigated the lubrication performance of journal bearings in various applications. Research on misaligned bearings has shown that misalignment moments can cause solid contact between the shaft and bearing, leading to increased local oil film pressures. Bouyer et al. analyzed the effect of misalignment on oil film pressures and found that the maximum film pressure in the central plane of misaligned bearings decreased by up to 20% compared to aligned bearings. Pierre et al. considered thermal effects and used a thermo-hydrodynamic lubrication model to analyze the impact of installation errors and thermal deformations on bearing performance. Lahmar et al. studied the influence of misalignment on the fluid dynamic performance of bearings with oil groove structures and found that misalignment increased bearing eccentricity and significantly reduced the minimum oil film thickness.
Several studies have specifically focused on the lubrication contact characteristics of journal bearings in wind turbine gearboxes. Hagemann et al. used finite element methods to establish a thermo-elastohydrodynamic coupling model for sliding bearings in wind turbine gearboxes and found that the radial clearance was sensitive to the maximum oil film pressure at the edge when using large helix angles. Lucassen et al. proposed a method to identify critical operating conditions for planetary gear journal bearings using simulation tools and analyzed bearing reliability under different steady-state conditions. Gong et al. discussed the effects of bearing modifications, gear helix angles, and radial clearances on the lubrication performance of bearings under steady-state conditions and found that the temperature rise in the bearings was only 2°C at rated conditions.
Time-varying load excitations can dynamically alter the lubrication state of journal bearings. Mokhtar et al. conducted starting tests on bearings under stable loads and observed that the shaft moved in a spiral pattern before reaching a stable position, with solid contact occurring during this phase. Cui et al. established a transient tribo-dynamic analysis model for bearing startup processes based on the average Reynolds equation and found that increasing the bearing design clearance shortened the solid contact time, allowing a faster transition from mixed to full-film lubrication.
Research Methodology
This study investigates the transient lubrication performance of planetary gear journal bearings in a 6 MW wind turbine gearbox, considering the dynamic effects of radial loads, bending moments, and rotational speeds. A transient tribo-dynamic coupling model is established and validated through experimental tests. The model inputs include dynamic meshing forces and time-varying speeds extracted from a SIMPACK dynamics model of the wind turbine drive chain.
Model Development
1. Planetary Gear-Pin Shaft Structure and Transmission Principle
The planetary gear system in the 6 MW wind turbine gearbox consists of three stages, with the low-speed and intermediate stages supported by sliding bearings and the third stage supported by rolling bearings. The low-speed planetary gear system primarily comprises a planetary carrier, sun gear, planetary gears, and ring gear. The input torque drives the carrier, which then rotates the planetary gears through the pin shafts, ultimately driving the sun gear .
The planetary gear journal bearings consist of planetary gears, pin shafts, and bushings. The oil film forms between the inner holes of the planetary gears and the outer surface of the bushings. Oil enters the film through holes in the pin shafts and exits at both ends, avoiding the film convergence zone . The meshing forces generated by the helical gears introduce time-varying bending moments, causing misalignment between the planetary gears and pin shafts .
2. Transient Lubrication Model
The transient lubrication model considers the dynamic changes in oil film thickness due to bearing eccentricity, misalignment, and surface modifications. The transient average flow Reynolds equation governs the oil film pressure distribution:
frac∂∂θ(ϕθh3η∂θ∂p)+∂z∂(ϕzh3η∂z∂p)=6usϕc∂θ∂h+12ϕc∂t∂h
where h is the oil film thickness, η is the lubricant viscosity, p is the oil film pressure, us is the oil film interface linear velocity, ϕθ and ϕz are the circumferential and axial flow factors, respectively, ϕc is the contact factor, θ and z are the circumferential and axial dimensionless positions, respectively, and t is time.
The oil film thickness h consists of the nominal thickness ho, the thickness variation due to bearing modifications hc, and the variation due to misalignment hm:
h(θ,z,t)=ho(θ,z,t)+hc(θ,z)+hm(θ,z,t)
The nominal oil film thickness ho is given by:
ho(θ,z,t)=c[1+ϵ(t)sin(θ−φ(t))]
where c is the radial clearance, ϵ(t) is the eccentricity ratio, and φ(t) is the misalignment angle.
The solid contact pressure pasp between the pin shaft and gear bore is calculated using the Greenwood-Williamson (G-W) model:
pasp=βD162π(βDσ)2E∗F2.5(σh)
where β and D are the asperity curvature radius and surface roughness density, respectively, E∗ is the composite elastic modulus, and F2.5 is a function of the film thickness ratio.
3. Planetary Gear Motion Analysis
The dynamic meshing forces and bending moments affect the oil film gap shape, influencing the oil film forces and bending moments acting on the planetary gears. Considering only the translational and rotational degrees of freedom in the xp and yp directions, the planetary gear equations of motion are derived based on Newton’s second law and angular momentum conservation:
M∗X¨∗=Fh∗+Fc∗−W∗
where M∗ is the planetary gear mass and inertia vector, X∗ is the displacement and rotation vector, Fh∗ and Fc∗ are the oil film and solid contact force vectors, respectively, and W∗ is the external meshing force and bending moment vector.
4. Load Boundary Conditions
The dynamic meshing forces and bending moments acting on the planetary gears are extracted from a SIMPACK dynamics model of the wind turbine drive chain . The model considers the time-varying speeds and meshing forces of the planetary gears as inputs for the journal bearing transient lubrication analysis.
Results and Discussion
Model Validation
The transient lubrication model is validated through comparisons with experimental data and simulation results from previous studies. The oil film pressure distributions obtained from the model with experimental results by Ferron et al. and simulation results by Mokhtar et al. under steady-state conditions.
The model accurately captures the overall trends and magnitudes of the oil film pressures, with maximum errors of 6.35% and 5.75% compared to the experimental data.
Influence of Helical Gear Meshing Moments
The dynamic meshing moments generated by the helical gears significantly affect the lubrication performance of the journal bearings. The impact of meshing moments on the oil film pressure distribution under fixed operating conditions.
The meshing moments cause misalignment, leading to a significant increase in edge oil film pressure from 54.96 MPa to 77.39 MPa, a 40.81% increase.
To further analyze the influence of varying loads, the transmission chain input torque is varied from 1300 kN·m to 6500 kN·m (20% to 100% of the rated torque). The changes in bearing eccentricity, misalignment angles, and oil film pressures under different load conditions.
As the load increases, the bearing eccentricity ratio increases, while the misalignment angles exhibit dynamic variations. The maximum oil film pressure increases, and the minimum oil film thickness decreases significantly.
Effect of Input Torque
Time-varying low-speed, heavy-load conditions make it challenging to maintain stable full-film lubrication in the low-speed stage of the planetary gear system. The time-varying trajectories of the journal bearing center under different input torques.
As the input torque increases, the bearing center trajectory becomes more eccentric, with increased solid contact risks under extreme conditions. The time-varying lubrication performance under varying input torques.
The misalignment angles and oil film/solid contact forces and moments vary dynamically with the input torque, with increased maximum oil film pressures and decreased minimum oil film thicknesses under heavier loads.
Influence of Radial Clearance
The radial clearance of the journal bearings significantly impacts their lubrication performance. The oil film pressure distributions under different clearances at a specific time instant.
As the clearance increases, the central region of the bearing gradually transitions from full film to line contact, with increased edge oil film pressures. The influence of varying clearances on bearing performance under time-varying meshing moments.
Larger clearances result in increased bearing eccentricities and reduced minimum oil film thicknesses, with the onset of solid contact at clearances greater than 130 μm.
Experimental Validation
To further validate the transient lubrication model, experiments were conducted on a full-scale test rig for wind turbine planetary gear journal bearings. The experimental setup, which includes a radial force loading unit, bending moment loading unit, bearing support unit, bearing test unit, and test rig base.
Table 1 summarizes the bearing parameters and experimental conditions. The experimental results were compared with numerical predictions, as shown in Figures 12 and 13.
Table 1: Journal bearing parameters and experimental conditions
| Parameter | Value |
|---|---|
| Radius (mm) | 205 |
| Radial clearance (μm) | 215 |
| Length (mm) | 460 |
| Lubricant viscosity (30°C, Pa·s) | 0.473 |
| Shaft elastic modulus (GPa) | 210 |
| Bearing material elastic modulus (GPa) | 105 |
| Shaft Poisson’s ratio | 0.3 |
| Bearing material Poisson’s ratio | 0.34 |
| Radial load (kN) | 590 |
| Bending moment load (kN·m) | 20 |
| Shaft speed (rpm) | 20 |
The numerical and experimental oil film pressure distributions show good agreement under both radial load-only and combined radial load and bending moment conditions .
Conclusions
This study investigated the transient lubrication performance of planetary gear journal bearings in a 6 MW wind turbine gearbox, considering the dynamic effects of radial loads, bending moments, and rotational speeds. A transient tribo-dynamic coupling model was developed and validated through experimental tests. The key findings are as follows:
- Influence of Meshing Moments: The dynamic meshing moments generated by helical gears significantly increase edge oil film pressures and reduce minimum oil film thicknesses, leading to increased solid contact risks.
- Effect of Input Torque: Under time-varying loads, the bearing misalignment angles and lubrication characteristics exhibit dynamic variations, with increased oil film/solid contact forces and moments under heavier loads.
- Radial Clearance: Increasing the radial clearance reduces the central bearing load-bearing capacity and increases the maximum oil film pressure and minimum oil film thickness variations, facilitating edge contact under heavier loads.
The results provide valuable insights into the lubrication performance of planetary gear journal bearings in wind turbine gearboxes and can guide bearing design and optimization to improve operational reliability and lifetime.