Rolling contact fatigue tests on pre-damaged slewing bearings

Abstract

Blade bearings of wind turbines are grease-lubricated rolling bearings which are operated in an oscillating manner. They can be subjected to both rolling contact fatigue and wear, in particular standstill marks and false brinelling. Rolling contact fatigue arises from alternating stresses due to the passage of rolling elements under high loads, standstill marks and false brinelling occur during cyclic motion and are often exacerbated by inadequate lubrication. In this paper, we want to understand fatigue and the influence of false brinelling on fatigue better and to investigate whether it is advantageous to avoid false brinelling. We performed fatigue tests with four blade bearings. Three of them had existing false brinelling damage. In addition, we repeated tests on much smaller angular contact ball bearings. To contextualize the results, we calculated the fatigue life of a pitch bearing from a reference turbine matching our test bearing design and compared the calculation to the test results. Although the stochastic fatigue behavior in combination with the low number of tests makes it difficult to draw general conclusions, the results indicate that false brinelling shortens fatigue life, even if the blade bearings pass the fatigue test.

Introduction

Blade bearings (also called pitch bearings) of wind turbines are typically large (double-row) four-point bearings or roller bearings.^1,2 They allow rotation of the blades along their longitudinal axes in order to adapt the blade alignment to the wind. ² This adaptation is called pitching. With a changing pitch angle, the acting loads, caused by the wind, change as well. Thus, power and load control of the turbine are possible. ³ In operation, pitch bearings with modern control mechanisms typically perform small, oscillatory movements, which can increase the likelihood of standstill marks and false brinelling. ⁴ Furthermore, turning at least two of the blades to the feather position results in stopping of the turbine. ² This is done in case of an emergency to stop the turbine. Accordingly, the blade bearings play a key role for the operation of the turbine and in its safety system. If a blade bearing fails, its replacement is unavoidable, even if it is expensive and time-consuming. The costs for this consist of the cost for the new bearing, working hours, the downtime of the turbine, and the equipment costs, which also include the fee for a crane. Consequently, it makes sense to use a blade bearing for as long as possible, even if it is damaged. From a technical perspective, doing so appears unproblematic, as damage does not mean that the pitch actuator cannot rotate the blade anymore. Even if damage is identified, it makes sense to keep the bearing in use. However, the presence of damage is probably associated with continuous further degradation of the bearing. Other damage modes can be triggered and occur as well. Ultimately, the friction torque of the damaged bearing may reach a level where a pitch actuator cannot turn it anymore. Blade bearings need to withstand combinations of radial, thrust and moment loads, but their main load is a bending moment caused by an eccentrical thrust load, making blade bearings thrust-type bearings.^1,2

Understanding the different damage modes of rolling bearings is essential for preventing failures. Some research is related to blade bearings of wind turbines and takes their characteristic operating parameters into account. Stammler ⁵ offers an overview of possible blade bearing damage and its origin. Standstill marks, false brinelling, and rolling contact fatigue (RCF) are all types of damage which occur on the bearing's raceways. They are explained in Section 2. For RCF, it is possible to calculate the probability of the first spall, but the calculation comes with a lot of questions and uncertainties. A review by Menck and Stammler ⁶ discusses the available literature on RCF calculation in oscillating bearings. It notes that most available calculation models are based on the ISO standards^7–9 and that these ISO-related methods are currently the ones with the most experimental validation, although all models discussed in the review could benefit from better validation. The most applicable ISO-based method for general oscillating bearings according to Menck and Stammler ⁶ is the Finite Segment Method by Menck, ¹⁰ but a number of simplified ISO-approaches exist for simple operating cases, including some by Houpert ¹¹ and Rumbarger. Some non-ISO-related models available in the literature are those by Hwang and Poll, ¹² who analyze the stress cycles at different depths in a bearing, or by Leupold et al., ¹³ who employ a reduced finite element model in a multi-body simulation to determine the stresses in a segmented bearing simulation, or by Escalero et al., ¹⁴ who use a three-dimensionally discretized model of a bearing for stress cycle analysis. All of these approaches focus only on the initiation of the first spall. After this first spall has occurred, it is mostly unknown how long the bearing can endure to the end of usability.

In contrast to fatigue, to the best of the authors’ knowledge, there are no established methods for calculating standstill marks or false brinelling in oscillating bearings. Tetora et al., Wandel and Bartschat, and Behnke and Schleich showed that false brinelling can develop within a short time with a low number of repeated oscillation cycles, but what that means for the end of life of the bearings remains unclear.^15–17 De la Presilla et al. ¹⁸ recently published a review of the available literature on tribotesting and analysis approaches in oscillating bearings, noting that standstill marks and false brinelling negatively affect fatigue life, and that the oscillation amplitude and its relation to contact size (commonly called x/2b) as well as the lubricant play a significant role in potential development of damages such as standstill marks or false brinelling. ¹⁹ Because there are no established methods to calculate these damages modes in oscillating bearings, the review cites a number of experimental references, which are common for publications on standstill marks and false brinelling. One attempt to calculate rolling contact starvation and potentially resulting false brinelling occurrence is given by Wandel et al. ²⁰ who vary the oscillation amplitude and the oscillation frequency, and propose an extension of a method originally proposed by Damiens et al. (“starvation degree”) to calculate starvation in oil-lubricated bearings. However, they note that this approach currently disregards a number of parameters and only serves to visualize observed effects in their studies.

Standstill marks or false brinelling and RCF can both occur independently, but it is highly likely that they influence the RCF life, ¹⁸ as they significantly affect the raceway surface, which leads to local stress concentrations and diminished lubrication at the points where standstill marks or false brinelling are present. ²¹ Experiments by Schadow et al. ²² and Tetora et al. ²³ indicated that false brinelling pre-damage accelerates fatigue onset. With this paper, we aim to shed further light on the effect of false brinelling on RCF, with a particular focus on slewing bearings such as pitch bearings in wind turbines. To this end, we performed tests on real blade bearings and on smaller bearings with the objective of investigating whether false brinelling reduces fatigue life.

Definitions of damage

End of life and calculated lifetime

As stated in the introduction, the occurrence of damage does not mean that the blade bearing has failed. In this paper, the term “end of life” is used to describe the state in which the torque of the bearing reaches a level where the actuator cannot turn the bearing anymore. One example could be that the raceways display heavy damage, which has also caused other damage like cage fracture or damaged rolling elements, and that the sum of these damages triggers an increase in the torque. The term “end of life” is not completely precise, as it is possible that changing load conditions allow the actuator to turn the bearing again or that the actuator is simply replaced by a stronger one. However, for simplicity's sake, we shall assume that the end of life has been reached once the actuator is not able to turn the bearing anymore in any regular operating condition. The next term which must be defined is the “calculated life”. In terms of rolling bearings, the common approach is to work with the RCF calculation, since it is the only damage that can be calculated in an acknowledged way. When doing so, it is important to note that the fatigue initiation is stochastic, since the damage starts at randomly distributed material imperfections, e.g. inclusions. ²⁴ In conclusion, it implies that any calculation can give merely the probability of damage. The calculated life is the probability of the first occurrence of a spall or pitting on the raceway. In this condition, the bearing is usually still able to rotate. It could be possible for the bearing to block, but it would be a very unlikely coincidence.

Fatigue

Rolling contact fatigue, in this paper simply called “fatigue”, is damage to the bearing raceway caused by repeated stress cycles due to rolling elements moving over the raceway. Rolling contact fatigue can initiate on or very close to the surface as well as beneath it. These two separate phenomena are commonly referred to as “surface-initiated fatigue” and “subsurface-initiated fatigue” respectively.

Subsurface-initiated fatigue is caused by a change in the subsurface shear stress. The rolling elements transfer the loads and thus cause pressure on the raceway, which, in turn, creates subsurface shear stress. Since this shear stress originates due to the normal load of the roller, it can occur even in well-lubricated bearings with negligible surface friction. Any time a roller moves over the contact, the shear stress changes, which can eventually cause a spall to originate under the surface and move towards it. Subsurface-initiated fatigue is the phenomenon which has been studied for longer, with the first well-accepted calculation method dating back to 1947 ²⁵ and continuing to be the basis for ISO 281. ⁹

Surface-initiated fatigue is caused by high surface shear stresses due to poor lubrication conditions. Much like with subsurface-initiated fatigue, repeated rollovers cause stress cycles, which, in turn, produce spalls on the surface. Surface-initiated fatigue is highly dependent on the lubrication conditions and surface roughness in the contact. Corresponding calculation methods were developed later than for subsurface-initiated fatigue, as it took more time for the lubrication conditions on a bearing to be well understood. ISO 281 includes a factor a_ISO that is based on research by Ioannides et al. ²¹ As surface damage significantly increases local roughness and stress and degrades the lubricant cleanliness, it is generally accepted to accelerate the onset of surface-initiated fatigue significantly.

False brinelling

False brinelling is surface-induced damage and can occur on the raceways of a rolling bearing. ²⁶ In contrast to fatigue, false brinelling does not happen after a certain number of load cycles, but rather under cyclic movements under load with poor lubrication conditions.^20,27 False brinelling in oscillating bearings is commonly characterized by the so-called x/2b-ratio, where x is the travel of the rolling element, and 2b the width of its contact ellipse. This paper defines false brinelling as observable macroscopic wear damage in rolling element bearings that results from operation with x/2b ≥ 1, following the definition by La Presilla et al. ¹⁸ Depending on the application, greases or oils are commonly used for lubrication and to prevent or mitigate false brinelling and other wear phenomena. ²⁴ They separate the contact partners with an oil film and, if present, their additives form a protective layer. Alternatively, contact partners can also be separated by solid lubricants. These mechanisms generally prevent false brinelling, but the lubrication can fail under challenging circumstances. Cyclic movements under high loads can lead to displacement of the lubricant.^20,28 As a result, wear mechanisms like abrasion, adhesion, and tribo-corrosion can take hold and lead to surface damage. ²⁶

In rolling bearings, a distinction is made between “standstill marks” and “false brinelling”. Standstill marks have an undamaged inner area and are typically caused by vibrations or oscillations with a small amplitude (corresponding to x/2b < 1). ¹⁸ Oscillations with larger amplitudes tend to cause false brinelling (corresponding to x/2b ≥ 1), which can be identified in an early stage by its brown or red corrosion products. Abrasion of these oxide products leads to polished dents in a later stage. All damages shown in this paper are false brinelling marks since x/2b > 1.

Blade bearings of wind turbines perform cyclic movements under high loads, which is why they are at risk of standstill marks and false brinelling. ⁵ Wandel et al. showed that false brinelling can be created within several hours. ¹⁶ Behnke and Schleich reported similar findings. ¹⁷ However, the authors are not aware of any evidence that a blade bearing has failed due to false brinelling alone. This statement comes with two problems. First, public data are rare, and second, a failed bearing usually shows high degradation, and it is unclear whether false brinelling was the root cause.

False brinelling-fatigue interaction

Schadow et al. produced false brinelling damage on 60 mm-diameter bearings and exposed them to subsequent fatigue testing. They produced false brinelling in the bearings by oscillating them while using grease lubrication. Once the damage had been produced, the bearings were then tested by rotating them in an oil-lubricated environment. The authors also intended to carry out fatigue tests with undamaged bearings for comparison but were unable to produce fatigue in the previously undamaged bearings within the possible test time. Most of the pre-damaged bearings failed in the possible test time but still endured longer than ISO 281 predicts for a bearing in factory new condition. Tetora et al. continued Schadow et al.'s tests but used grease lubrication for the subsequent fatigue tests and did not clean the bearings after false brinelling had been produced. As in the previous project, false brinelling pre-damage accelerated fatigue spalling onset in the rotating bearings tested for fatigue. The authors did not perform comparisons against ISO 281 calculations.

Test bearings and test rigs

We tested two different types of rolling bearings: real blade bearings and smaller standard bearings. The blade bearings are serial bearings from a wind turbine with a rated power of 3 MW. They have two rows filled with balls in four-point (4P) contact. Their outer diameter is 2.6 m, which is almost 15 times larger than the small ones. The small bearings are angular contact ball bearings (ACBB) of the type 7220. They have a similar contact geometry to the 4P blade bearings (both have an initial contact angle of 40°). In contrast to the 4P bearings, they have a two-point contact and are designed to carry axial loads in just one direction. Table 1 lists the mean values of both bearings.

Table 1.

Properties of the tested bearing types.

Property	Symbol	4P	ACBB	Unit
Bearing type		Four-point contact ball bearing	Angular contact ball bearing	-
Inner diameter	di	2070	100.0	mm
Outer diameter	do	2600	180.0	mm
Pitch diameter	dm	2310	139.8	mm
Number of rows	k	2	1	-
Rolling elements per row	n	98	15	-
Rolling element diameter	d	65	25.4	mm
Initial contact angle	α	40	40	°
Inner and outer groove conformity	osc	∼0.53	∼0.52	-
Rotating ring		outer	for tests: inner	-

For comparison of the sizes, Figure 1 shows both bearings.

Figure 1.

Blade bearing (left) and ACBB on top of blade bearing (right).

All bearings are grease-lubricated with a commercial grease for pitch bearings. The grease has a base oil viscosity of 50 cSt at 40 °C and an NLGI class of 2. The thickener is based on lithium. The grease also contains additives and solid lubricants. The bearings were not relubricated at any point during the tests.

All four-point contact bearings came from one manufacturer of slewing bearings who also manufactures blade bearings for actual wind turbines. All of the ACBB came from a single different manufacturer.

Test rig BEAT 0.1

The second test rig is the BEAT0.1. It is identical to the BEAT0.2 which is shown in Figure 2. Both angular contact ball bearings are vertically mounted on the shaft. A hydraulic cylinder is located inside the housing and applies an adjustable static axial load to the outer ring of the right side bearing in Figure 2. The maximum possible load is 227 kN. The inner ring then transmits the load to the shaft, which in turn transmits it to the left side bearing, which finally transmits it to the housing. A servo motor (“drive”) turns the shaft and allows for accurate position control of the inner bearing rings. The torque meter measures the torque that is required to move the inner rings of the bearings. It can measure up to 50 Nm and has a linearity error (including hysteresis) of ±0.3%. The torque of 50 Nm corresponds to the rated output torque of the motor.

Figure 2.

Left: functional principle of BEAT0.1 shown on identical BEAT0.2 ²⁹ ; right: exploded CAD view of BEAT0.1 shown on identical BEAT0.2.

Test rig BEAT2.2

The BEAT2.2 (Bearing Endurance and Acceptance Test rig) tests the original blade bearings. Figure 3 shows the test rig with a visualization of the inner design. The bearings (positions 1 and 2 in the Figure) are horizontally oriented on top of each other. A third outer ring in between connects both bearings at the outer ring (position 4 in the Figure). This makes it possible to rotate both outer rings at the same time with one electric motor (blue component in the Figure) which actuates the bearings on their gears on the outer ring. A hydraulic system applies a static axial load (position 3 in the Figure). It acts between the inner rings, which are consequently pushed apart. The force is thus transmitted above or below the bearings. The test rig has a load capacity of 10 MN, which leads to a maximum contact stress of 2.7 GPa.

Figure 3.

Test rig BEAT2.2. ¹⁷

Test setup

In a previous study, Menck et al. explained uncertainties for an RCF life calculation and concluded that this also affects the certification guidelines. ³⁰ They pointed out that there are no uniform calculation requirements. However, it can be assumed that the turbine manufacturers design their bearings to withstand several years of operation in order to prevent failure. Accordingly, failure within a short time should be unlikely. In contrast, false brinelling can develop in a very short time, as mentioned above. Therefore, it makes sense to start with the false brinelling tests followed by the fatigue tests. The false brinelling tests introduce a pre-damage to the bearing for the subsequent fatigue test. To analyze whether false brinelling influences fatigue, different bearings with different degrees of false brinelling damage were chosen. In total, four blade bearings and six ACBB were tested.

Contact pressures were chosen to replicate actual pressures that can occur in a wind turbine. For the rolling contact fatigue test, rotational speed was intentionally accelerated in order to produce fatigue in a reasonable amount of time, therefore reducing L₁₀ significantly as compared to operation on a real turbine.

Initial false brinelling test

The initial false brinelling tests on the 4P (Bearing 103 to 108) are tests which lead to different false brinelling characteristics. This false brinelling characteristic will be referred to as “pre-damage” in the following, since it acts as a pre-damage for the subsequent fatigue tests. The aim of these tests was to test different severities of false brinelling damage caused by varying x/2b ratios and contact pressures. Table 2 lists the test parameters. All test profiles except for that of bearing 151 consist of sine movements. This means that the bearings are repeatedly oscillated back and forth, following a sine movement pattern, by the double amplitude and with the oscillation frequency given in the table. This movement results in an entrainment speed for the lubricant in the ball-raceway contact, and an x/2b ratio (see Figure 4) as given in Table 2. Assuming a static equilibrium of forces, the force F applied to the bearing resulted in a ball contact force Q of

$$Q=F/(Z\cdot l\cdot sin(\alpha ))$$

where Z is the number of balls, l the number of rows, and α the contact angle. This corresponds to a Hertzian contact pressure in the center of the contact ellipse of each rolling element as shown in Table 2. Bearing 110 was tested with an additional cycle with a double amplitude of 1.8° every 50 cycles.

Figure 4.

Movement of a contact ellipse of width 2b during an oscillation with contact track x.

Table 2.

Test parameters of the initial false brinelling test for the blade bearings.

Bearing ID	x/2b	Double amplitude in °	Contact pressure in GPa	Maximum speed in °/s	Oscillation frequency in Hz	Entrainment speed in mm/s	Number of cycles
103	Undamaged
110	3.6	0.8	2.05	0.8	0.32	7.72	40,800
151			2.55	Test with varying oscillation angles and speeds
108	18.4	5	2.55	5	0.32	48,25	40,000

Table 3.

Test parameters of the initial false brinelling test for the ACBB.

Bearing ID	x/2b	Double amplitude in °	Contact pressure in GPa	Maximum speed in °/s	Oscillation frequency in Hz	Entrainment speed in mm/s	Number of cycles
301	Factory new and undamaged
300	3.6	4.5	2.05	12.9	0.91	7.72	40,800
319	3.6	4.5	2.4	12.9	0.91	7.72	40,800
320	3.6	4.5	2.4	12.9	0.91	7.72	40,800
333	3.6	4.5	2.4	12.9	0.91	7.72	40,800
334	3.6	4.5	2.4	12.9	0.91	7.72	40,800

Bearing 103 has an undamaged raceway. It serves as a reference and helps to range the results of the other bearings. Bearing 110 has the highest degradation, which is shown in Figure 5. Bearings 151 and 108 have less severe damage. Figure 6 shows their damage marks. Further information on Bearings 110 and 108 can be found in the study by Behnke and Schleich. ¹⁷ They were tested with a continuous oscillating movement as described above. The underlying test of Bearing 151 is described by Bartschat et al. ²⁹ The key difference is that the motion profile is based on a realistic pitch movement of a wind turbine. As such, the oscillations change in their amplitude and frequency.

Figure 5.

False brinelling damage of Bearing 110. ¹⁷

Figure 6.

False brinelling damage of Bearings 151 (left) and 108 (right). ³¹

The tests with the ACBB are intended to confirm the results of the blade bearing tests. The test parameters are shown in Table 3. First, one undamaged bearing (Bearing 301) and a second bearing with false brinelling damage (Bearing 300) are tested. This false brinelling test was designed to produce damage comparable to Bearing 110. Therefore, the parameters are scaled from the 4P size to the ACBB size. The x/2b ratio is the first scaling parameter. It relates the travel of the ball x with the width of the Hertzian contact ellipse 2b as shown in Figure 4. Second, the contact pressure for the ACBB was kept the same as for the 4P bearing 110. Together with the x/2b ratio, it is then possible to calculate the required oscillation angle for the ACBB tests that retains the same contact pressure and x/2b ratio as for 4P bearing 110. Finally, the frequency and the speed information of the ACBB tests must be chosen. The entrainment speed was used to determine these values. It has been chosen to replicate the behavior of 4P bearing 110. If it is the same for both bearing sizes, the speed and frequency can be calculated.

Figure 7 shows the false brinelling mark of Bearing 300. It has a similar shape to the mark on Bearing 110, shown in Figure 5, which indicates that the scaling described above worked as intended.

Figure 7.

False brinelling damage of Bearing 300.

Bearings 319 and 320, as well as 333 and 334, are both pre-damaged in a false brinelling test with the same parameters as 300 but using higher pressure. The bearings were not disassembled, but the authors infer that false brinelling damage has occurred due to the reproducibility of these tests and because a higher pressure was used than for Bearings 301 and 300. Moreover, measurement signals, specifically spikes in the torque signal, indicated that damage had occurred. Disassembly after the subsequent fatigue test showed evidence of false brinelling damage.

Subsequent fatigue tests

Table 4 lists the test parameters for the subsequent fatigue tests. As previously, the x/2b ratio refers to the ratio of the movement of the contact ellipse (x) to the width of the contact ellipse (2b), see Figure 4. Similar to the false brinelling tests, the bearing is moved in a sine movement pattern. However, the double amplitude of this movement is now chosen to be significantly wider, in order to prevent false brinelling damage from occurring due to this oscillation. Since false brinelling is prevented by the wide double amplitude of the movement, fatigue damage can be induced instead. The double amplitude results in a maximum and mean speed of the bearing as shown in Table 4. This speed is faster than in the false brinelling tests in order to accelerate the onset of fatigue damage in the bearing. It also causes a lubricant entrainment speed as shown in the table. Furthermore, an axial load as given in Table 4 was applied to the bearing and caused contact pressure in the center of each ball's contact ellipse as shown.

Table 4.

Test setup for tests I to IV.

Test ID	Bearing ID	x/2b	Double ampli-tude in °	Axial load in kN	Contact pressure in GPa	Max. speed in °/s	Mean speed in °/s	Max. entrain-ment speed in mm/s	Number of cycles
I	103 + 110	220.6	60	8100	2.5	6.00	5.45	57.9	420,563
II	151 + 108	424.3	120	9000	2.6	6.00	5.71	57.9	193,903
III	301 + 300	220.6	338.97	100	2.5	100.75	62.99	57.9	436,127
IV	319 + 320	220.6	338.97	90	2.4	100.75	62.99	57.9	351,547
V	333 + 334	220.6	338.97	90	2.4	100.75	62.99	57.9	451,916

The contact pressure from Test ID I was slightly increased in Test ID II. Furthermore, the amplitude was increased to reduce the number of movement reversals, which again increases the mean speed. Both measures shorten the test time, which was necessary to finish the test within the project. The bearings for tests I and II were combined randomly. For both tests, the number of cycles was a result, not an input parameter, i.e. the test ran until damage was presumed to have taken place. The intention was to stop the tests after the first fatigue damage but before the bearing reached its end of life. This makes it possible to identify the influence of false brinelling on fatigue, with the intention that degradation is not too severe to identify different fatigue origins. The respective test end and its reason are described in Section 6.

For the ACBB (Test ID III), the number of rollovers per oscillation for a damage mark on the raceway was chosen to be identical to that of Test ID I, and the contact pressure was chosen to be very similar to it. For Test ID IV and V, the number of cycles was not fixed. Instead, the bearing ran until the authors assumed damage to have occurred based on measurement data, specifically spikes in the torque signal. The load was reduced slightly, everything else was kept the same as in Test ID III.

Fatigue calculation

In order to compare the results of the 4P test to the operational loads during the service life of a turbine on a turbine, two fatigue calculations were conducted: one for a reference turbine and one for the test rig tests. For the CWD3.5 reference turbine, which has an individual pitch controller (IPC), ¹³ 20 years of operation were considered and the life of the bearing under the collective of operating conditions according to DCL1.2 was determined. In contrast, the tested bearings saw one continuous operating condition over the entirety of the test.

The test rig calculation was performed using ISO-based approaches, even though all bearings except for 103 and 301 were pre-damaged. The life calculation is thus intended more to give a reference than to provide an actual estimate of the expected life. Factor a_ISO was not included in all calculations. This is due to the fact that the bearings were pre-damaged and that the bearings were grease-lubricated with additives, which makes a_ISO an unreliable parameter. ISO 281 ⁹ states that for “proven effective EP additives”, viscosity ratio κ may be set to 1 – it is probable that the additives are effective, but we did not perform strict validation of this in advance. Moreover, the calculation here serves primarily to compare the life of the bearing in the test to that in the turbine. This means that as long as the lubrication conditions in the test resemble those in the turbine, a_ISO may be neglected, because it would be identical for both the test and the turbine and cancel out in the comparison.

Fatigue calculation of the blade bearing

The life of the blade bearing of the reference turbine was determined according to the procedure laid out by Menck et al. ³⁰ In order to circumvent the need for a large amount of finite element simulations, the equivalent load was calculated according to

$$P=0.75F_r+F_a+k\cdot M/d_{\mathrm{m}},$$

where F_r is the radial force, F_a is the axial force, and M the resulting bending moment acting on the bearing. Variable d_m is the pitch diameter and factor k was determined according to a finite element simulation at a bending moment of 7.3 MNm to be k = 2.35 for this particular turbine. The life in each bin of the simulation data can be calculated according to

$$L_{10}=(C_a/P{)}^3.$$

Individual bins are combined into a total bearing life using the Palmgren-Miner hypothesis. With a dynamic rating of C_a = 2.27 MN, the calculation results in a life of L₁₀ = 2.09 ⋅ 10³ revolutions or 4.03 years based on the DLC1.2 timeseries that have been used.

Fatigue calculation of the reference test

Two tests (Test ID I and II) with two bearings each (103 and 110, then 151 and 108) were carried out. The test rig was simulated for both tests, with an axial load of 8.1 MN and 9.0 MN, see Table 4.

Simulations were carried out using the finite segment method, with each raceway being separated into 1800 segments. ¹⁰ This means that the actual movement profile in combination with the finite element simulated loads was used to determine the damage from rollovers if a ball passed a segment on the raceway. This allows for visualization of the damage on the individual bearing rings. As the method is based on ISO 281 and ISO 16281, it can be used to compare the life with the turbine calculation. Figure 8 shows ln(1/S_m), a measure of the damage, of Bearings 151 and 108 after 100 cycles. The metric ln(1/S_m) gives information about the damage incurred to a segment m. A higher value corresponds to a lower survival probability S_m. It is based on the Lundberg-Palmgren theory which is the basis of ISO 281 and 16281. The raceway closer to the load application in the center (not displayed in the figure, in the empty space between the rings) is loaded higher and therefore experiences more fatigue damage. The same applies for Bearings 103 and 110, where 103 is the lower bearing and 110 the upper one.

Figure 8.

Calculated inner ring damage for Bearings 151 and 108 after 100 oscillation cycles.

For the ACBB 301 and 300, the test rig is relatively stiff, and therefore the equivalent load can be calculated according to approaches such as those used by ISO. Oscillation cycles were large and thus resembled rotational movement. Thus, the life has been calculated according to ISO 281 with the Harris factor used for adjustments (cf. Houpert and Menck ³² ). Based on ISO 281, the bearings have a load rating of C_a = 199.8 kN and were exposed to an axial load of 100 kN. At an average speed of 62.99 °/s (see Table 4), this gives a fatigue life of L₁₀ = 527.6 days.

Since L₁₀ is the life at which 10% of bearings are expected to have failed according to ISO 281, L₅₀ was calculated, too. This was done assuming a two-parametric Weibull distribution with a Weibull slope of e = 10/9 according to DIN SPEC 1281-1. ³³ Using these assumptions, L₅₀ = 5.45 ⋅ L₁₀.

Test results

Blade bearings

The four blade bearings were tested in two test runs, since the test rig demands two bearings per test (see Section 3). This means that the test end is the same for both, even if one bearing does not show damage. Despite having no visible damage on the raceways prior to testing, Bearing 103 incurred significant rolling contact fatigue damage. Figure 9 shows photos taken after the bearing had been disassembled and cleaned. It is worth noting that even with large chunks of the raceways missing, the bearing as shown was still able to operate. The test was stopped when significant and steep peaks in the friction torque were present. They may have been caused by cage fracture, see the broken cage in Figure 10, which could be observed in addition to the raceway damage shown in Figure 9.

Figure 9.

Fatigue damage on Bearing 103.

Figure 10.

Cage fracture on Bearing 103. ³¹

Bearing 110 displayed eight instances of fatigue damage in total. Figure 11 shows three examples with the damage progress increasing from left to right. The damage in an early stage, in particular, can be assigned to the false brinelling marks (see Figure 5) from the previous test. The brown oxide layer or the changed surface roughness make it possible to identify their position. The origin of the damage marks which show higher degradation, like the right one in Figure 11, could also be assigned to a false brinelling mark. The distance between damage on the raceway matches the distance of the balls, so it is possible to conclude that the fatigue damage originates from the false brinelling damage.

Figure 11.

Fatigue damage on Bearing 110, earlier false brinelling damage marked pink. ³¹

Figure 12 shows the raceway of Bearing 151 after the fatigue test. Although the reddish-brown false brinelling marks are no longer visible, residual gray discoloration indicates their position. This bearing is the only one of the 4P which does not display fatigue damage on the hardened raceways, however, there was spalling damage in the soft spot. This indicates that the soft spot was unintentionally loaded.

Figure 12.

Polished false brinelling marks on Bearing 151. ³¹

In contrast to Bearing 151, Bearing 108 had plenty of different fatigue damages on the raceways. Some incidences grew to the size of several centimeters, whereas others were in an early stage. Figure 13 shows one example of each.

Figure 13.

Large area of fatigue damage (left) and smaller example of developing fatigue (right) on Bearing 108.

The raceways of this bearing (108) were in bad condition. Indentations from the fatigue flakes or from large spalls make it hard to identify the previous false brinelling marks. Nonetheless, we were able to identify three different incidences of fatigue damage, which started at the left end of a false brinelling mark. Figure 14 shows one of these. However, Bearing 108 also showed significant damage near the soft spot, starting at the transition between soft spot and hardened raceway.

Figure 14.

Fatigue damage initiated at a false brinelling mark on Bearing 108. ³¹

Figure 8 indicates that the raceway that is closer to the load application in the test rig center has a much higher probability of failure because the loads in that raceway are higher than in the one further away from the load application. In other words, for the upper bearing, the lower raceway has a higher probability of failure, and, for the lower bearing, the upper raceway has a higher probability of failure. For Bearings 103 and 108, the results corresponded to this prediction, whereas for Bearing 110, the upper raceway was damaged more, despite the bearing being in the top position on the test rig.

ACBB test results

The undamaged angular contact ball bearing (Bearing 301) does not show any signs of fatigue or any other damage. According to Table 5, it is an expected result, since less than 55 test days is too short a period for a significant fatigue probability. In contrast, the pre-damaged bearing (Bearing 300) has several incidences of fatigue damage, despite being subjected to the same load and cycles. In total, seven spalls could be observed. Four of them were on the outer ring and three on the inner ring. Figure 15 shows some examples.

Figure 15.

Bearings 300 (left) and 334 (right) with fatigue damages; former false brinelling mark on Bearing 319 highlighted pink and fatigue damage (middle).

Table 5.

Life L₁₀ and test results for the tested bearings.

Bearing ID	Type	Life L10 in days	Life L50 in days	Tested time in days	False brinelling pre-damage before fatigue test	Fatigue damage after test
103	4P	23.7	129.3	107.1	-	x
110	4P	25.3	137.8	107.1	x	x
151	4P	16.6	90.4	94.3	x	-
108	4P	17.1	93.3	94.3	x	x
301	ACBB	527.6	2875.4	54.3	-	-
300	ACBB	527.6	2875.4	54.3	x	x
319	ACBB	723.7	3944.1	43.8	x	x
320	ACBB	723.7	3944.1	43.8	x	-
333	ACBB	723.7	3944.1	56.3	x	-
334	ACBB	723.7	3944.1	56.3	x	x

The depth of the damages in Figure 15 has been measured with a laser microscope. A line through the center of the damage mark was drawn and its depth is given in Figure 16. The deepest damage in Figure 15 is, from left to right, approximately 400 µm, 200 µm and 600 µm. The theoretical value of z₀ at which the highest orthogonal shear stress occurs on the inner ring at the load given in Table 4 is 233 µm, indicating that these damages might be subsurface-induced; though a surface-induction is more likely due to the significant false brinelling pre-damage in the bearing. High shear stresses on the raceway are also known to modify and increase the subsurface stress field ¹⁰ such that the damage may have been initiated below the surface but still accelerated due to the higher surface stress.

Figure 16.

Damage profile laser scan results of spalls from Figure 15.

The false brinelling marks from the previous test are difficult to identify, since the high number of rollovers led to a polished surface. Furthermore, chips from the spalls have caused indentations on the raceways. Nevertheless, some remnants of the corrosion on the lower or upper edge are still visible (see Figure 15). This makes it possible to estimate the position of the false brinelling marks, and thus it is possible to conclude that all fatigue damage initiated at a false brinelling mark.

For Bearings 319 and 320, the false brinelling marks of the previous test have also been somewhat removed by polishing. Note that 319 and 320 were not disassembled after the false brinelling test, but the authors infer from experience and the reproducibility of false brinelling tests that the damage was most likely more severe directly after the false brinelling test than at the time of disassembly, once the bearing had been tested for fatigue for several days. Bearing 319 showed fatigue damage, while Bearing 320 did not.

Comparison to fatigue calculations

Despite the pre-existing damage, Bearings 103 and 110 survived for 107.1 days and thus came very close to the theoretical L₅₀ value for a bearing in factory new condition (129.3 and 137.8 days, respectively). Bearings 151 and 108 survived 94.3 days of testing and thus even surpassed their theoretical L₅₀ value by 4 and 1 day(s), respectively. Since Bearing 151 did not incur damage on the hardened raceways, it is considered undamaged for this comparison, as the calculation applies to the hardened raceways only.

Bearing 300, on the other hand, failed significantly earlier than expected from a pre-damaged bearing, reaching only about 2% of its theoretical L₅₀ value; Bearing 319 failed even quicker in comparison, lasting 10 days less.

Blade bearing life and tested life

The calculated life of the blade bearings can be compared to the results achieved on the test rig. To this end, the Miner sum of field operation was determined using the design life of 20 years of the CWD3.5 turbine according to

$$D_{\mathrm{field}}={\displaystyle \frac{20\mathrm{years}}{L_{10,\mathrm{field}}}.}$$

The Miner sum of test rig operation was then determined as per

$$D_{\mathrm{test}}={\displaystyle \frac{T_{\mathrm{test}}}{L_{10,\mathrm{test}}},}$$

where T_test is the tested time according to Table 5 and the respective L₁₀ lives are taken from the same table. It is possible to determine that the test represented D_test/D_field of the turbine lifetime operation, i.e. 90.9% for Bearing 103, 85.4% for Bearing 110, 114.5% for Bearing 151, and 111.0% for Bearing 108, without consideration of statistical uncertainty. Despite the pre-existing damage on Bearings 110, 151, and 108, all bearings came very close to the Miner sum of 20 years of turbine operation, and, in the case of 151 and 108, they even exceeded it.

Conclusions

In this work, we tested four blade bearings with an outer diameter of 2.6 m on a sandwich-type test rig and four smaller serial bearings to investigate the influence of false brinelling on fatigue in oscillating, grease-lubricated rolling bearings. Both the blade bearings and the ACBB included three pre-damaged bearings that had visible false brinelling damage on their surfaces and one without such damage.

The smaller bearings behaved very much as expected in that the false brinelling damage seemed to accelerate the onset of fatigue significantly in two of the three damaged bearings. Both of these bearings did not even reach 2% of their calculated L₅₀ according to ISO 281. Though the bearings were still operational at the time of disassembly, it is reasonable to assume that they would have failed soon after.

The results for the blade bearings are far more surprising. All tested blade bearings came very close to or even exceeded their theoretical value of L₅₀. This is despite the fact that three of the bearings had visible false brinelling pre-damage on their raceways. One of the pre-damaged bearings (151) even reached the end of the test without having visible fatigue damage on the hardened raceways, while one bearing (103) without false brinelling pre-damage developed fatigue damage within the same duration of the test at the same external load. The reasons for this are difficult to ascertain. The two bearings may have been of different quality and Bearing 103, despite having no visible pre-damage, may have had more material inclusions or other defects in the raceway that accelerated fatigue onset, whereas Bearing 110, despite having been damaged from the start of the fatigue test, may have had a higher material quality. Nevertheless, the results show that if fatigue was present on the hardened raceways, it initiated at false brinelling marks, though it may also have initiated near the soft spot for 108. Similar results were found by Schadow et al. ²² on rotating, pre-damaged angular contact ball bearings, where the fatigue damage initiated at false brinelling damage locations. The logical conclusion to be drawn is that avoiding false brinelling, and avoiding loading of the soft spot, contributes to protecting a blade bearing.

Despite these uncertainties, it is worth noting that the blade bearings all came close to or even exceeded the design life of the CWD3.5 reference turbine and their theoretical L₅₀ value during the test despite being pre-damaged. This may imply that blade bearings, even in a pre-damaged state, are much more robust than small bearings regarding damage propagation, that is to say that damage may take a long time to spread until the bearing becomes truly dysfunctional. It may also take longer to initiate for some reason. Alternatively, it is possible that the bearings tested were not representative of a larger batch due to the relatively small number tested. Nonetheless, it is surprising that the blade bearings held out for so long.

In further investigations it may be useful to increase the number of tests to minimize uncertainties. Furthermore, we want to investigate the behavior of roller bearings, since they become more prominent as pitch bearings.