Pitch bearings of wind turbines are large, grease-lubricated rolling bearings that connect the rotor blades with the rotor hub. They are used to turn the rotor blades to control the power output and/or structural loads of the turbine. Common actuators turning the blades are hydraulic cylinders or electrical motor–gearbox combinations. In order to design pitch actuator systems that are able to turn the blades reliably without imposing an excessive power demand, it is necessary to predict the friction torque of pitch bearings for different operating conditions. In this paper, the results of torque measurements under load are presented and compared to results obtained using different calculation models. The results of this comparison indicate the various sources of friction that should be taken into account for a reliable calculation model.
Pitch bearings (also called blade bearings) are subject to unfavorable operating conditions as they have to accommodate high bending moments while stationary or rotating at very low speeds. The connected parts, especially the rotor blades, provide limited stiffness. Usually, four-point contact ball bearings are used for this application, but for newer models of turbines, three-row bearing types have been chosen as well (Stammler and Reuter, 2015; Burton, 2011).
Pitch bearings are driven by combinations of electric motors and gearboxes
with a total ratio exceeding
Pitch-bearing test rig at Fraunhofer IWES and corresponding FE model.
In order to design pitch actuator systems that are able to turn the bearings reliably but do not require excessive power, it is necessary to predict the friction torque for pitch bearings under all operating conditions.
Several equations and numerical models are available to calculate the friction torque of rolling bearings. However, there are no publications which compare them with experimental results of pitch bearings. In this paper, experimental results obtained at the Fraunhofer IWES pitch bearing test rig in Bremerhaven are compared to the results of different calculation models. Torque values throughout this paper are normalized instead of absolute values. The models considered range from two bearing manufacturers' catalog equations (SKF, 2014; Rothe Erde, 2016), which are based on Palmgren's classical approach for friction prediction (Palmgren, 1957), to the numerical model developed by Wang (Wang, 2015). These four models represent the available types of approaches used for friction torque calculations, as such other bearing manufacturer models with comparable approaches were not taken into account.
The pitch-bearing test rig at Fraunhofer IWES (see Fig. 1) is designed for bearings of 3 MW class wind turbines. In order to reproduce the operating conditions of pitch bearings, all interfaces (hub, blade, pitch drive) are the same as in the actual wind turbine.
All loads are applied by hydraulic cylinders that are connected to ropes (see red rectangle in Fig. 1). The loads are measured by means of load cells. The rope is attached to a load frame, whose center point is 30 m from the blade root.
Optical position measurement.
The bending moment applied to the bearing is calculated with the force measured and the load vector, which is calculated with the aid of an optical measurement system. This optical measurement system consists of four cameras and several reflecting marks. Some of these marks are reference marks with known positions. These references are used to calculate the position of the camera and the coordinates of the marks of interest. At the rotor blade, three marks indicate the current deflection (see Fig. 2). Another mark is fixed to the lower end of the load rope.
The pitch drive is equipped with a strain-gauge torque measurement system at the pinion shaft on the low-speed side. A full bridge of strain gauges is mounted on the shaft (see Fig. 3), together with a rotary unit. Data transfer and power supply is performed telemetrically via a ring stator. The measurement system has been calibrated by applying known torques to the shaft.
Torque measurement strain gauges on shaft.
Oscillating rotations and torque measurements (example).
The bearing is a grease-lubricated two-row four-point bearing of a 3 MW class
turbine with an outer diameter of roughly 2.3 m. In addition to the tests
with a mounted rotor blade, tests without the blade were executed to obtain
data for zero load. The torque measurements were carried out under different
pitch speeds and different external forces. The oscillating rotations of the
bearings had a peak-to-peak amplitude of 10
To determine the load on the rolling elements of the bearing, a finite element (FE) model of the test rig was set up in ANSYS 15. For the bearing, this model uses the simplifications described in Daidie et al. (2008). These element loads are necessary for some of the friction calculation models. An example result of such FE calculations can be found in Schwack et al. (2016).
Simple bearing friction models use external influences (speed and load) to calculate the overall friction of a bearing. To obtain sound results with such an approach, it is necessary to actually measure the bearing friction under different external conditions. A change to the bearing system, e.g., a different lubricant or sealing, will require a new measurement to determine the bearing friction in order to obtain exact results.
To actually predict the friction behavior of a bearing without the need for
measurements, several friction mechanisms must be taken into account (Harris
and Kotzalas, 2007). These mechanisms may be categorized according to
influencing factors. For a given bearing, load, speed or both influence the
friction torque exerted by the different mechanisms.
Factors that are load and speed dependent:
Heathcote (conformity) slip due to differential velocities Sliding due to roller body spinning Rolling friction due to lubricant movements in the rolling contact Sliding of rolling bodies against cage/spacer Cage sliding against bearing rings Factors that are load dependent:
Sub-surface hysteresis due to load changes Sliding of the sealing(s) against the bearing rings Factors that are speed dependent:
Lubricant flow (churning) losses
In the following sections, two simple models (see Sect. 2.3 and 2.6) and two more detailed models (Sect. 2.4 and 2.5) are presented. In the literature, another model explicitly identified for blade-bearing friction evaluation was evaluated (González et al., 2008), but as this model is contained within the more detailed model described in Sect. 2.5, it was not used for the subsequent calculations.
In Palmgren's model (Palmgren, 1957), the friction torque of a
bearing is divided into a load-independent and a load-dependent part. The
load-independent part
The load-dependent part
The equivalent load
As the empirical values are not available for the pitch bearing used for this test, a minimum square deviation over all measured points is used to best fit the results obtained. Since the parameters have to be fitted to experimental data, the model is of little use to predict the friction of untested types of bearing.
The Palmgren model was further refined to take account of the various
components of the bearing that contribute to the total friction. One of these
models was developed by a bearing manufacturer (SKF, 2014). The following
Eq. (3) shows the different elements of the total friction
To calculate
The sealing friction
The last part of
Wang (Wang, 2015) considers enhanced
rheological fluid models and experimental results in his model for
calculating the friction torque. The model follows the assumptions of
Steinert (Steinert, 1995) and Zhou (Zhou and Hoeprich, 1991), who divide
the friction torque into different parts that can be calculated independently
from each other. For ball bearings, these parts are the friction torque,
which results from the irreversible deformation work on the bearing steel
Equation (8) shows the different parts in a mathematical relationship for a
better understanding. The parts
The friction moment of the deformation work
To calculate
Equation (11) takes into account the diameter of the rolling element
According to Zhou (Zhou and Hoeprich, 1991), the hydrodynamic force
As mentioned before, the physical effect which leads to a sliding moment
It must be borne in mind that it is difficult to apply this approach for
The friction from the differential slippage and Heathcote effect depends
on the energy balance and takes into account the frictional losses at the
inner (
All sliding losses in the contact lead to high shear rates within the contact areas and are thus dominated by the lubricant behavior. Empirical results are used to calculate the friction torque, which takes into account the limiting shear stress. These results are obtained using a two-disc machine (see Fig. 5).
Two-disc machine.
Measured friction torque at different speeds and loads.
The relationship between the medium shear stress
While the two aforementioned approaches try to split the friction torque
according to different friction causes, the following model is taken from a
manufacturer's current bearing catalog (Rothe Erde, 2016). This method has no
speed-dependent component and is adapted to different bearing types by the
friction coefficient
This model does not take into account any load-independent part. In practice, however, all bearings experience frictional losses even under unloaded conditions. Consequently, the bearing manufacturer states that the equation must not be used for unloaded conditions.
The results of the FE calculations have been compared to the results of the
optical measurement system described in Sect. 2.1. A bending moment of
5 MN
Deviations of deformations between FE model and test rig measurements.
While positions 5 and 3 show satisfactory agreement, position 6 shows a large relative deviation between FE analysis and test rig. The large relative deviation is partly caused by the low absolute deformation (less than 20 mm) near the blade root (small absolute values result in high relative values) and the longer distance to the camera positions, which result in higher uncertainty.
Figure 6 shows the results of friction torque measurements at different
rotating speeds of the pitch bearing. The measurements were executed with the
bending moment varied in steps of 1 MN
The values of the friction torque are normalized to the highest value of the
measurements obtained at 1.04 rpm and the 6 MN
In Fig. 7, the values are again normalized to the highest friction torque measured. The error bars refer to the standard deviation of the measured values.
In order to obtain results for the first manufacturer's and the Palmgren
calculations, previously unavailable empirical values had to be chosen to
match the curves with the measured values: for the Palmgren calculation, the
value
Measured and calculated friction torque at different loads.
Measured and calculated friction torque at different speeds and
a 5 MN
The aforementioned choices of empirical values come with some drawbacks:
currently, the Palmgren model cannot be used to predict the friction torque
of other pitch bearings as there are no available values for the empirical
factors
Overview of agreement between bearing friction models and experimental results.
Similar to the Palmgren model, the first manufacturer model contains only one
empirical factor, which can be adjusted (
The Wang and the second manufacturer model contain all necessary
empirical values. However, the results are not completely satisfactory: the
second manufacturer's equation is explicitly not intended for zero load; as
such this value is not displayed in the chart. The friction torque calculated
with this model deviates by 35 % from the measured values at a load of
2 MN
The model proposed by Wang does not take account of the sealing friction and shows the friction torque to have a rather high speed dependence that does not match the measured values. The model was originally intended for the calculation of friction under fully lubricated conditions and needs some further adjustments for mixed friction conditions.
Figure 8 shows the speed dependence of the different calculation methods and
the measurement results at a 5 MN
Only the models from Wang and from the second manufacturer can be used to predict the friction torque of pitch bearings without additional tests, as the other models need the adjustment of empirical values. The second manufacturer's model relies on empirical values as well, but in this case these values for different types of pitch bearings are available in the public domain.
In this paper, torque measurements of a loaded four-point ball-type pitch bearing on which realistic interfaces were mounted have been presented. The measurements were executed at a pitch-bearing test rig with realistic interfaces (hub, pitch actuator, blade). While the measurements show a clear load dependence, no systematic dependence on the rotational speed of the bearing is observed within the range of speeds tested.
The load dependence exhibits nearly linear behavior, with a positive value at zero load condition. This supports the assumption that the friction torque has a load-independent part that is present in all of the calculation methods except for the second manufacturer's model.
With the Palmgren model, empirical values were adapted to match the measurement results, but it is doubtful if these values match other load conditions and/or types of pitch bearing. The sealing friction part of the first manufacturer's model was adjusted to match the measured values at zero load. This led to a dominance of the sealing friction, which does not seem plausible. As such, it may be concluded that the other parts of the friction are underestimated by this model. The second manufacturer's model overestimates the load dependence of the friction. The Wang model overestimates the speed dependence of the total friction.
None of the models reviewed are able to predict all aspects of the friction torque behavior of the pitch bearing. With the Palmgren, Wang and first manufacturer's models, this may be due to the range of bearings taken into account to create the models. Both the bearing types and sizes underlying the models differ significantly from those of typical pitch bearings. Additionally, it can be assumed that most of the experiments leading to the creation of these models were conducted under close-to-ideal lubrication conditions with oil lubrication, fully flooded contacts, and a complete separation between raceway and rollers. In grease-lubricated pitch bearings, mixed lubrication is possible under normal operating conditions. As such, the results have only limited comparability to the models based on tests under better lubrication conditions.
With none of the models being able to reliably predict the friction torque of the pitch bearing in the test described, the only way to currently determine the friction torque is with the aid of measurements. In future work, the test rig will be used for further friction torque measurements with different bearings to support the development of models suitable for large grease-lubricated bearings like pitch bearings. Further development work on the models will take into account the influence of the sealing, the lubrication conditions within pitch bearings, and the characteristics of different types of pitch bearing.
The underlying data are not available due to confidentiality agreements in this commercial project.
The authors declare that they have no conflict of interest. Edited by: Lars Pilgaard Mikkelsen Reviewed by: two anonymous referees