Comparison of transfer path characteristics for different wind turbine drivetrain variations

An increase in energy from renewable sources is crucial for a successful transition from fossil fuels to less CO2 emissions. Wind energy takes on a leading role, showing a trend towards larger and more efficient Wind Turbines (WT) over the last decades.

With the development of ever-larger turbines, various turbine configurations have also been developed, each of which is intended to achieve the optimum in terms of performance and costs. Generally speaking, wind turbines can be divided into direct drive turbines and turbines with a gearbox. Direct Drive Turbines are built without a main gearbox, the Torque is directly applied to a generator. The generator for Direct Drive Turbines tends to be very large. Adding a gearbox between the rotor and generator allows for a much smaller generator but adds an additional component to the turbine. Gearbox systems can be further categorized by the drive train’s arrangement and the number of bearing points.

Most WTGs have a so-called 3‑point (3P) or 4‑point (4P) bearing arrangement (Fig. 1). In a 3P variant, the drive train is supported by a main bearing near the hub and by two torque arms of the gearbox. In this case, the generator is separated from the rest of the drive train by a coupling and mounted separately. In the 4P arrangement, an additional main bearing is inserted on the shaft near the gearbox.

A different design, which is applied in some newer wind turbine models, is an integrated drivetrain concept. This is characterized by a medium-speed generator that is directly coupled to the gearbox housing. The gearbox housing, in turn, is directly connected to the bearing unit of the main bearings and is not mounted separately. This allows a very compact design of the entire drive train, which positively affects weight, costs, and transport. On the other hand, this results in a very stiff connection between all turbine parts.

Aside from the development of larger and more efficient turbines, regulations for new turbine sites significantly reduce this technology’s expansion. Such strict regulations are intended to reduce the negative impact of acoustic emissions from WT on residents nearby. To increase the number of potential areas for wind energy, the acoustic emissions of new turbines must be reduced. To achieve this reduction, developers aim to simulate the acoustic emissions of a WT early in the development process and optimize the WT accordingly. To reduce acoustic emissions of a WT, the source of the vibrations (e.g. blades, gearbox), the emitting surfaces (e.g. blades, tower, and nacelle cover) and the transmission between source and surface have to be studied. The Transfer Path Analysis (TPA) can be used to determine the relevant acoustic transfer paths between an active and passive part of an exited structure and so be able to optimize the structure accordingly.

The focus of this paper lies in the identification of relevant transfer paths between the WT drivetrain and the mainframe. It will compare the transfer path for the 3P, 4P, and an integrated drivetrain design variation. The identified transfer paths can be used to improve turbine acoustics, especially by identifying problematic transmission areas [1].

The TPA aims to study the transmission of vibrations from an active source to a passive structure. This can be a point of Interest, a surface of radiation, or an acoustic measurement point. The transfer paths are the coupling points between the active and passive sides (Fig. 2). To describe the transfer characteristics, the excitation and transfer characteristics are described separately. The excitation is measured with the interface forces at the transfer path (F_i) from the dynamic simulation, while the transfer characteristic is described by separately measuring the Frequency Response Function (FRF) or determining the transmissibility matrix of the structure [1].

In the literature, different types of transfer path analysis are distinguished [1]. There is the classical TPA, the component-based TPA, and the operational TPA. In classical TPA, the FRF is determined on the entire system, and the forces are measured during operation or determined via a mount stiffness or Matix Inversion Method. In component-based TPA, the forces are measured only on the active side, and the FRF is measured only on the passive side. This allows easy calculation of different variants with changing components. In Operational TPA (OTPA), the transfer properties are determined only by measurements from the operation, thus eliminating the need for separate measurements of the FRF. For the transfer properties, the transmissibility matrix is calculated from measurement data [1, 4].

The individual path contributions are calculated by multiplying the FRF and the Interface Force. The sum of the path contributions can be compared here with the measurements at the reference point.

The OTPA is based on the determination of a transfer matrix H_yu from the relationship between the input signal (x^(m) (f)) and output signal (y^(k) (f)). The input signals are usually the acceleration or forces at the transfer paths (a_ai or F_i), and the output signals are the accelerations or sound pressures at the reference point (u_q, p_q). The transfer matrix is based on the consideration of the machine structure at different load conditions e.g. depending on the speed range or torque (Indize r).

Thus, the determination of the transmission matrix is done by the least square (LS) calculation, which resolves Eq. 2 to H. The number of measurement blocks must be larger than the number of measured nodes u_q and the calculation of the transmission matrix must be performed for each frequency in the spectrum of the signal [2, 3].

The solution can be done either by H1-calculation (Eq. 3) or by H2-calculation (Eq. 4). Both variants differ in the weighting of noise in the input or output signal. As a shorthand notation, in Eq. 3 and 4 the variables X and Y stand for matrices in complex form, X^T and Y^T are the complex conjugate matrices, G_yy and G_xx stand for the spectral power density and G_xy and G_yx for the cross-power spectrum (CPS) [3]. It has been shown that the H2 method produces better results when applied from simulation data.

The path contribution is finally determined using Eq. 5. For the calculation of the path contributions, a measurement of the FRF is therefore no longer necessary.

The graphical representation of the path contributions is done using a Partial Path Contribution Plot (PPCP). This allows the amplitude of the path contributions for each path to be plotted on top of each other depending on the speed, and frequency at an operating point or order.

The structure of the reference model and the variations are described below. A turbine model with a 3P-bearing arrangement is selected as the reference model. This model was subsequently extended to include components to be able to represent the 4P-bearing arrangement and the integrated drivetrain design.

In the following, the results of the system variations are presented. First, the waterfall plot of the accelerations at the reference point at the tower head in the horizontal direction is shown here as an overview, then the PPCPs for the nominal speed and at the first and third tooth mesh frequency of the IMS (Order 4.73 and Order 14.19). These have proved to be particularly relevant in the analysis of system behavior.

In this paper, the method of TPA was first explained and OTPA was specifically discussed. The advantage of OTPA is that no separate measurement of the FRF is necessary and therefore it can be easily applied to measurements of a WT in operation. The method was applied to the results of a simulation model of a WT with a 3P bearing. It is shown that for a WT drivetrain the transfer paths via the gearbox bearing in the horizontal and vertical direction and via the main bearing in the radial direction show the largest path contribution. Furthermore, the path contributions were also investigated depending on the speed or order.

The design of the wind turbine was varied based on the reference model to be able to represent other turbine configurations. Thus, a 4P bearing and an integrated drive train design were simulated and compared with the reference model. It was shown that the total vibrations decreased for the 4P bearing, but the transfer path via the rotor-side main bearing was still more relevant than via the new gearbox-side bearing. For the integrated drive train concept, the total vibrations were significantly higher than for the 3P or 4P bearing, and the transfer path via the direct coupling between the gearbox housing and mainframe is now also significantly more relevant.