The influence of journal bearings on the gearbox dynamics of a 5 MW wind turbine drivetrain

In recent years, journal bearings have been replacing roller bearings in wind turbine gearboxes, as they are believed to provide higher reliability compared with roller bearings. However, replacing roller bearings with journal bearings can drastically change the gearbox dynamics. Journal bearings have complex dynamics at different operating speeds, and, as a wind turbine operates at various speeds, it is vital to analyze the gearbox dynamics for the entire speed range. This contribution presents the dynamic response of a wind turbine gearbox when the roller bearings of the high-speed shaft are replaced with journal bearings. This is done by performing a comparative case study using a detailed multibody simulation (MBS) model of a 5 MW reference wind turbine drivetrain. A dynamic model of the journal bearings, developed in Simulink, is dynamically coupled with the 5 MW drivetrain MBS model using co-simulation. The simulation results for the gearbox vibration as well as gear forces are compared with the simulation results of the drivetrain model with roller bearings. The findings from this work will help in clarifying the advantages (or disadvantages) of using journal bearings instead of roller bearings in wind turbine gearboxes.


Introduction
The conventional wind turbine gearbox designs are equipped with roller bearings, which have shown a high rate of failures in the past [1].Such failures lead to unwanted downtimes, which directly affect the operation and maintenance costs as well as the energy yield.Consequently, continued efforts are required for developing reliable wind turbine drivetrain systems to reduce unscheduled downtimes.In recent years, wind turbine drivetrains have witnessed the application of journal bearings instead of roller bearings in the gearbox.The implementation of journal bearings in wind turbine gearboxes has several drivers, such as [2]: • reliability (theoretically infinite bearing life when correctly designed); • torque density increase (journal bearings require less space than roller bearings); and • noise reduction (due to the higher damping characteristics).
Although journal bearings have a long track record in other heavy-duty applications such as industrial gearboxes, ship propulsion systems, and turbomachines, their utilization in the wind industry is relatively new.Consequently, there is only limited information available in the state of the art regarding the use of journal bearings in wind turbine gearboxes.The experimental tests conducted in [1], [3], [4], and [5] showed the benefits of using journal bearings inside a gearbox in terms of lower frictional losses, minimal bearing wear, and significant noise reduction compared with the gearbox with roller bearings.
Studies such as [6], [7], and [8] have shown the influence of gear design parameters and movements on the wear and lifetime of the journal bearings in the gearbox planetary stage.
Since journal bearings have complex dynamics at different operating speeds, replacing roller bearings with journal bearings in a gearbox changes the dynamic response of the system [9].The trajectory of the gear shaft supported by the journal bearings can have significantly larger orbits (depending on the hydrodynamic clearance) and stronger coupled stiffness compared with roller bearings [10].The findings from [11] and [12] for the case of a marine propulsion gearbox showed that the journal bearings influenced the gear meshing forces.There are only a few publications available regarding the influence on the gear forces of a wind turbine gearbox when roller bearings are replaced with journal bearings.Some studies have been conducted for the planetary gear stage using journal bearings in planet gears.In the simulation-based investigation in [13], it was found that the changing clearance in the journal bearings affects the gear backlash and teeth forces.The investigations in [14] concluded that the load-sharing characteristics of planetary gears are related to the parameters of the journal bearing.Furthermore, a conventional wind turbine gearbox often has multiple gear stages with a parallel gear pair at the high-speed end.It is also important to investigate the dynamics of journal bearings for the high-speed gear stage, and it is critical to ensure that the introduction of journal bearings does not compromise the design life of gears.
This contribution addresses this concern for the case of a geared wind turbine drivetrain system with journal bearings replacing the roller bearings at the high-speed shaft (HSS).The primary aim is to analyze the dynamic response of the HSS gear stage for the entire operating speed range of the wind turbine drivetrain.Furthermore, this contribution also describes a co-simulation approach which allows full coupling of a detailed drivetrain model with an analytical journal bearing model.The drivetrain is modeled using multibody simulation (MBS) in Adams with detailed gear contact definitions.The dynamic model of the journal bearing is developed in Simulink using an analytical approach which includes the relevant dynamics of a journal bearing.This model is fully coupled to the HSS bearings of the drivetrain MBS model via co-simulation.Section 2 describes these models and the co-simulation framework of the coupled models.Section 3 describes the case study conducted to investigate the dynamic response of the high-speed gear stage.The results are shown in Section 4. Section 5 concludes the paper with key findings and areas of investigation for future work.

Drivetrain model
The 5 MW reference model described in [15] is selected, which is designed for the NREL offshore 5 MW baseline wind turbine [16] and includes a gearbox configuration most common in megawatt-scale wind turbines.It has a 4-point suspension configuration with two main bearings and a multi-stage gearbox having two planetary and one parallel stage gears.Spur gears are used in the planetary gear stages and the high-speed side contains a parallel helical gear stage.The MBS model of the drivetrain is developed in Adams software as shown in Figure 1 using the parameters provided in [15].All the gears in the reference gearbox are modeled as rigid bodies with detailed 3D gear teeth contact definition which considers the gear out-of-plane movement.The bearings are modeled using force elements with defined stiffness corresponding to each type of bearing used.

Journal bearing model
Detailed approaches such as the elastohydrodynamic (EHD) method [17] and computational fluid dynamics (CFD) [18] are used for modeling the detailed physics of a journal bearing.However, these methods usually require very high computation times for performing time domain analysis of journal bearings in complex systems, such as a wind turbine drivetrain.In this work, the analytical approach for deriving the fluid film forces from the Reynolds equation as described in [19] is used for modeling journal bearings as it is computationally fast and includes the required dynamics needed for the objectives of this paper.In this approach, the dynamic nonlinear forces due to pressure distributions in the oil film of the journal bearing are described by taking the following assumptions into consideration: • The rotor bearing system has a rigid rotor and rigid supports.
• The thin film approximation holds.
• The theory of lubrication is applicable.
• The assumption of short journal bearings with laminar and isothermal flow.Considering the nonlinear oil film force model according to the short bearing theory, the nondimensional form of the Reynolds equation describing the pressure generation within the lubrication film is given by where R is the radius of the bearing, L is the length of bearing, ℎ = ℎ ̅ / represents the normalized thickness of the oil film,  = ̅ / is the normalized axial displacement of the journal center,  =  ̅/ and  = ̅ / are the normalized eccentricity of the journal center, dimensionless velocity components are  ′ = ̇ ⁄ and  ′ = ̇ ⁄ ,  = ̅ 6(/) 2 ⁄ represents the normalized pressure, and C is the radial clearance of the bearing.In the short bearings, the cavitation model neglects the predicted negative pressures and equates them to zero.As such, the positive pressure filed in the oil film has an extent region of [α, α+π] over the angular coordinate θ and the angle α.By integrating the Reynolds equation with respect to x, the nondimensional pressure of the oil film is obtained as Integrating the pressure along the lubricated arc of bearing, the non-dimensional components of the fluid force are obtained as where P is half the weight of the rotor and σ is a modified Sommerfeld number.
Based on the mathematical transformations given in [17], the following expression for fy and fz can be obtained: where This allows solution of the equations of motion of the journal center Q ̅ ̈=   (, ,  ̇,  ̇) +  2 cos   ̅ ̈=   (, ,  ̇,  ̇) +  2 sin  −  (6) where ω is the angular velocity of rotor, E is the static unbalance of the rotor, and t is time.The nondimensional forces fy and fz can be given by: This approach leads to the following equations of motion of the journal center ̅ ̈=   (, ,  ′ ,  ′ ) +  2 cos   ̅ ̈=   (, ,  ′ ,  ′ ) +  2 sin  − The generally accepted guideline for diametrical journal bearing clearance is 1.5 mils per inch of journal diameter.Clearance values are usually specified as a range, and the limit proposed here for the minimum permissible clearance is 1.0 mil per inch of shaft diameter plus one mil.The maximum permissible clearance is 2.0 mils per inch [20].The desired viscosity grade is determined by the bearing rotational speed, oil temperature, and load.

Co-simulation framework
The

Case study
To understand the impact of introducing the journal bearing into the gearbox dynamics, a comparative case study is performed using two variations of the drivetrain MBS model for the same load case.A speed ramp is given at the main shaft with a counter torque applied at the high-speed shaft.The input speed profile of the main shaft ramps up from 0 to 12 rpm in the first 40 s.After that, the gearbox runs at a rated speed of 12 rpm until 50 s.The nominal generator shaft torque is applied at the high-speed shaft.With these settings, two simulations are performed.In the first one, the HSS shaft is supported by a cylindrical roller bearing (CRB) at the front end, and tapered roller bearings (TRB) at the rear end.In the second one, these bearings are replaced with journal bearings via co-simulation.Since the journal bearing model only generates the radial forces, an additional axial force element is added at the front bearing location to handle the axial forces with the same stiffness as the CRB.As a result, both model variations have the same axial stiffness for the HSS bearings but different radial stiffnesses.

Vibrations of the high-speed shaft
The HSS vibrations have been extracted from the shaft center marking for the three translational directions.As shown in Figure 5, the model with journal bearings significantly damped the HSS vibrations in lateral directions.Figure 6 shows the vibration spectrum of the HSS supported by roller bearings, where multiple resonances occurring at gear mesh frequencies and their harmonics can be observed.In Figure 7, it can be observed that the journal bearings significantly reduced these vibrations in the lateral direction.This observation is consistent with the findings of the existing studies in literature.The vibrations associated with the excitation of eigenfrequencies around the 200 Hz and 350 Hz regions are completely diminished in the model containing journal bearings.

Conclusions
This work has investigated the dynamic behavior of a wind turbine gearbox, when replacing the roller bearing of the high-speed shaft with a journal bearing.The fluid forces of the journal bearing have been fed into a detailed drivetrain model via co-simulation.A comparative case study has been performed between the drivetrain models with roller bearings and journal bearings supporting the high-speed shaft (HSS) to analyze the vibrations of the HSS and the gear forces of the third gear stage.It has been observed that the HSS vibrations are significantly damped in the journal bearing based gearbox model.Furthermore, the gear meshing frequency of the third gear stage and its harmonics in the yaw and pitch axis vibrations show lower amplitude in the case with the journal bearing model.For the gear force components of the high-speed gear stage, however, it has been observed that the journal bearing model leads to a higher amplitude in the sub-rated speed region.At rated speed, the gear force in both models has similar average values.The fluid forces have been found to influence the gear force directly and their increase around the resonance region cause the gear forces to increase.Further case studies should be performed by replacing all the roller bearings in the gearbox with journal bearings to analyze the system response.The gearbox housing flexibility and gear shaft flexibility are also important modeling aspects to study the interaction of journal bearing dynamics and the eigenmodes of the flexible components of the wind turbine gearbox.Furthermore, additional studies are required to investigate the coupled dynamics of the gearbox and journal bearings in combination with a high-fidelity wind turbine model that can simulate and incorporate the effects of external interactions, such as wind and wave motions and generator side excitations.

Figure 1 :
Figure 1: MBS model of the 5 MW drivetrain

Figure 2 :
Figure 2: Schematic drawing of the fluid film in a journal bearing and reference frame (, , ) + cos  ⋅ (, , ) − 2 sin  ⋅ (, , ) 3 ⋅ (, , ) − sin  ⋅ (, , ) − 2 cos  ⋅ (, , ) } journal bearing model is fully coupled with the MBS model of the drivetrain via co-simulation.Simulink provides the platform for the co-simulation between the journal bearing dynamic model and the MBS model of the 5 MW gearbox.The positions, velocity, speed of the HSS shaft, and radial contact force of the third gear stage are the output parameters of the MBS model delivered to the journal bearing model for calculating the fluid force.The journal bearing model provides components of fluid force to the MBS model at the bearing locations supporting the HSS via a force element.Both models communicate by passing the input and output variables back and forth in time intervals that correspond to the simulation step size.The MBS model in Adams uses the HHT (I3) integrator with a step size of 10 -4 s.The fixed-step Runge-Kutta solver (ode4) is used in Simulink.The co-simulation framework between Simulink and Adams is shown in Figure 3.

Figure 3 :
Figure 3: Co-simulation framework for journal bearing model

Figure 4 :
Figure 4: Model variations for the case study

Figure 6 :
Figure 6: HSS vibration spectrum for model with roller bearings along the axial (a), vertical (b), and lateral directions (c)

Figure 7 :Figure 8 :Figure 9 :
Figure 7: HSS vibration spectrum for model with journal bearings along the axial (a), vertical (b), and lateral directions (c) 4.2.High-speed stage gear forces While the model with journal bearings has clearly shown a significant reduction of shaft vibrations along the lateral directions, it is also important to analyze the influence of journal bearings on the forces acting upon the gear teeth.The teeth forces of the HSS gear pair are plotted in Figure8for comparison.Two observations can be made: First, in the sub-rated speed region, the forces on the gear teeth are significantly higher in the model containing journal bearings.Second, in the rated speed region, the magnitude of such forces is comparable in both models.By comparing these results with the fluid forces delivered by the journal bearing model, a direct correlation can be observed in Figure9.The peak of fluid forces in the Y and Z directions occurs in the same speed range (denoted as D) where high gear forces were observed.The fluid forces are highly dependent on the loads and speed.Since the wind turbine operates in the sub-rated speed range for a significant amount of time during its operating life, it is vital to ensure that the gear teeth forces remain within the design envelope.Increased gear forces in the sub-rated speed range can influence the remaining life of the gearbox.In the presented case study, while switching to journal bearings can lead to better vibration damping performance, it has the tendency to influence the corresponding gear stage teeth forces adversely.The co-simulation approach presented