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Contract No. DE-AC36-08GO28308

Gearbox Reliability 

Collaborative High Speed Shaft 

Tapered Roller Bearing 

Calibration

J. Keller and Y. Guo

National Renewable Energy Laboratory

B. McNiff

McNiff Light Industry

Technical Report

NREL/TP-5000-60319

October 2013
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Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

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Contract No. DE-AC36-08GO28308

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Technical Report

NREL/TP-5000-60319

October 2013

Gearbox Reliability 

Collaborative High Speed 

Shaft Tapered Roller Bearing 

Calibration

J. Keller and Y. Guo

National Renewable Energy Laboratory

B. McNiff

McNiff Light Industry

Prepared under Task No. WE11.0301
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
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Acknowledgments

This work was supported by the U.S. Department of Energy under contract number DE-AC36-

08GO28308 with the National Renewable Energy Laboratory. The authors would like to thank 

Dr. Donald Houser and Jason Austin of The Ohio State University for their finite element 

modeling support.
iv

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List of Acronyms

C Celsius

CRB cylindrical roller bearing

DAS data acquisition system

GB gearbox

GRC Gearbox Reliability Collaborative

HS high speed

HSS high speed shaft

Hz hertz

kN kiloNewtons

mm millimeter

με microstrain

μm micrometer

NI National Instruments

NREL National Renewable Energy Laboratory

NWTC National Wind Technology Center

R2 coefficient of determination

RCS remote control screen

RTD resistance temperature detector

SOP safe operating procedure

TRB tapered roller bearing

V Volt
v

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Table of Contents

Acknowledgments ...................................................................................................................................... 1

List of Acronyms........................................................................................................................................ iv

List of Figures ............................................................................................................................................ vi

List of Tables .............................................................................................................................................. vi

1 Introduction........................................................................................................................................... 1

2 Test Bearings........................................................................................................................................ 2

2.1 Description and Modifications......................................................................................................... 2

2.2 Instrumentation ................................................................................................................................ 3

2.3 Calibration Requirements ................................................................................................................ 9

2.3.1 No Calibration................................................................................................................... 9

2.3.2 Direct Calibration.............................................................................................................. 9

3 Test Environment ............................................................................................................................... 11

3.1 Load Frame .................................................................................................................................... 11

3.2 Bearing Calibration Fixture ........................................................................................................... 12

3.3 Calibration Fixture Assembly ........................................................................................................ 13

3.4 Data Acquisition System................................................................................................................ 13

4 Test Sequence .................................................................................................................................... 14

4.1 Temperature Sensitivity Tests........................................................................................................ 14

4.2 Load Calibration Tests................................................................................................................... 14

5 Data Analysis ...................................................................................................................................... 15

5.1 Temperature Sensitivity Analysis.................................................................................................. 15

5.2 Load Calibration Analysis ............................................................................................................. 15

5.2.1 Example Gage and Applied Load Responses ................................................................. 15

5.2.2 Gage and Applied Load Data Processing........................................................................ 17

5.2.3 Example Gage and Applied Load Regression Analysis.................................................. 18

5.2.4 Full Regression Analysis Results.................................................................................... 20

5.2.5 Final Calibration Coefficients......................................................................................... 23

6 Conclusions ........................................................................................................................................ 25

7 References .......................................................................................................................................... 27
vi

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List of Figures

Figure 1. Schematic of high-speed shaft installation in the gearbox.................................................... 3

Figure 2. Upwind tapered roller bearing strain ........................................................................................ 5

Figure 3. Downwind tapered roller bearing strain ................................................................................... 6

Figure 4. Strain gage data sheet................................................................................................................ 7

Figure 5. Bearing outer ring temperature................................................................................................. 8

Figure 6. Bearing instrumentation before protection.............................................................................. 9

Figure 7. Bearing instrumentation after protection................................................................................. 9

Figure 8. The 110-kip load frame (left) and test bearing (right)............................................................ 12

Figure 9. Bearing calibration fixture ....................................................................................................... 12

Figure 10. Completed calibration assembly........................................................................................... 13

Figure 11. Effect of temperature on measured strain ........................................................................... 15

Figure 12. Measured load and strain for upwind bearing at 0° groove in thin end at 25 kip (left) and 

50 kip (right) ........................................................................................................................................ 16

Figure 13. Rolling element positions at signal maximum and minimum ............................................ 17

Figure 14. Regression analysis for upwind bearing at 0° groove in thin end, for mean (left) and 

range (right)......................................................................................................................................... 18

Figure 15. Regression analysis for upwind bearing.............................................................................. 20

Figure 16. Regression analysis for downwind bearing......................................................................... 21

Figure 17. Calibration sensitivity comparison ....................................................................................... 22

Figure 18. Load components ................................................................................................................... 23

List of Tables

Table 1. TRB Calibration Instrumentation ................................................................................................ 4

Table 2. Load Frame Instrumentation..................................................................................................... 11

Table 3. Upwind Bearing Calibration Coefficients................................................................................. 24

Table 4. Downwind Bearing Calibration Coefficients............................................................................ 24
1

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1 Introduction

The National Renewable Energy Laboratory (NREL) Gearbox Reliability Collaborative (GRC) 

is a project investigating gearbox reliability primarily through testing and modeling. Previous 

dynamometer testing focused upon acquiring measurements in the planetary section of the test 

gearbox [1]. Prior to these tests, the strain gages installed on the planetary bearings were 

calibrated in a load frame [2].

Recent input from GRC participants has highlighted the need for measurements of gear and 

bearing response, including reactions, load distributions, and temperatures in the high speed (HS) 

section of the gearbox due to a high rate of failures in the locating bearings supporting the high 

speed shaft (HSS) [3]. Thus, instrumentation has been added to the HSS, pinion, and tapered 

roller bearing (TRB) pair of the GRC gearbox (GB) to measure loads and temperatures. A 

portion of the upcoming GRC dynamometer test program will then measure these loads in test 

conditions, including normal operation, generator radial misalignment, and simulated emergency 

stop conditions [4].

The new HSS instrumentation on the TRB pair was calibrated from May 22−24, 2013, prior to 

starting the planned dynamometer tests. The purpose of this document is to describe this 

calibration process for the TRB pair instrumentation and the test results.
2

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2 Test Bearings

2.1 Description and Modifications

The test articles are the instrumented TRB pair for GRC GB #2. Both bearings are type SKF

32222 J2 tapered roller bearings. The TRB is 200 millimeters (mm) in outer diameter, with a 

bore of 110 mm and a total length of 56 mm. It has 20 rolling elements at a 16° taper angle 

and weighs approximately 20 pounds. The radial static load capacity of the bearing is 570 

kiloNewtons (kN) (128 kip) [5].

In operation, the HSS is supported on its upwind end by a cylindrical roller bearing (CRB) and 

near its midpoint by the TRB pair. The TRB pair is mounted in an o-configuration, which 

provides greater tilt stiffness than the x-configuration, and the TRBs are separated by a pair of 

spacers. Each of these bearings is supported within parts of the housing casting, notably the 

“cone” supporting the TRB pair. A locknut on the shaft provides the clamping force to retain the 

preload in the TRBs. The bearing outer rings are retained by an end cap, which is bolted to the 

exterior of the housing. The end cap reacts the axial loads imparted at the pinion. The entire HSS 

assembly and gearbox housing are shown in Figure 1.

The HSS assembly was removed from GB #2 in November 2012. During the removal, the 

existing TRB pair was slightly damaged, preventing reuse. A new TRB pair was purchased and 

then machined in January 2013 to facilitate the installation of the instrumentation. Four equally 

spaced axial grooves were machined in the outer ring of each TRB. Each groove is cut at an 

angle that matches the taper angle of the outer ring, with a maximum depth of 10 mm at the thick 

end and a width of 15 mm. The axial grooves allow for the actual placement of the gages, but 

also serve the purpose of increasing the local strain field to improve gauge response. A 5 mm 

wide by 4.2 mm deep circumferential groove was also machined in the outer ring to allow for 

routing of the wiring to one location, which serves as the exit point from the bearing face and out 

through the gearbox housing. Finally, a small hole was machined in the thick end of each outer 

race such that a pin could be installed between each bearing, serving as a key.
3

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Figure 1. Schematic of high-speed shaft installation in the gearbox. Illustration by Powertrain 

Engineers Inc.

2.2 Instrumentation

The instrumentation, listed in Table 1, was installed on the TRBs in March 2013. Strain gages on 

the TRB outer rings measure radial loads, as shown in Figure 2 and Figure 3. The data sheet for 

the strain gages is shown in Figure 4. Gage pairs are located at two different axial locations in 

each of the four grooves for a total of eight gage pairs per bearing. They are wired in a Poisson 

half-bridge configuration. Additionally, a resistance temperature detector (RTD) measures the

outer ring temperature of each TRB, as shown in Figure 5. The instrumentation package installed 

on the topmost groove of the downwind TRB is shown in Figure 6. Finally, the gages and RTDs,

along with the wires in the circumferential grooves, were glued together and to the bearing for 

environmental protection, as shown in Figure 7.

The installed strain gages measure the strain in the remaining “bridge” of bearing race material 

as the rollers move underneath it and deflect it. Finite element modeling was employed to 

determine the groove dimensions to result in an appreciable strain field in the remaining bridge 

material [6]. The two axial locations provide an indication of the load distribution across the 

axial width of the ring. The axial locations were selected to be well within the contact area 

between the roller and ring, while still providing enough room for the wires between the ring and 

the gearbox housing. The four circumferential locations provide a coarse indication of the load 

distribution around the bearing outer ring. Instrumenting both the upwind and downwind TRBs, 

of course, gives an indication of the load share between bearings.

High 

Speed 

Shaft

End Cap

Pinion

Upwind 

TRB

Downwind 

TRB

Locknut

Housing 

Cone

CRB & 

Baffle Baffle
4

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Table 1. TRB Calibration Instrumentation

Part Derived Measurement Label Sensor

Upwind TRB Strain, 0°, thin end TRB_Up_00_A Vishay CEA-06-062UT-350

Upwind TRB Strain, 0°, thick end TRB_Up_00_B Vishay CEA-06-062UT-350

Upwind TRB Strain, 90°, thin end TRB_Up_90_A Vishay CEA-06-062UT-350

Upwind TRB Strain, 90°, thick end TRB_Up_90_B Vishay CEA-06-062UT-350

Upwind TRB Strain, 180°, thin end TRB_Up_180_A Vishay CEA-06-062UT-350

Upwind TRB Strain, 180°, thick end TRB_Up_180_B Vishay CEA-06-062UT-350

Upwind TRB Strain, 270°, thin end TRB_Up_270_A Vishay CEA-06-062UT-350

Upwind TRB Strain, 270°, thick end TRB_Up_270_B Vishay CEA-06-062UT-350

Upwind TRB Outer ring temperature TEMP_TRB_Up Omega SA1-RTD-120

Downwind TRB Strain, 0°, thin end TRB_Dwn_00_D Vishay CEA-06-062UT-350

Downwind TRB Strain, 0°, thick end TRB_Dwn_00_C Vishay CEA-06-062UT-350

Downwind TRB Strain, 90°, thin end TRB_Dwn_90_D Vishay CEA-06-062UT-350

Downwind TRB Strain, 90°, thick end TRB_Dwn_90_C Vishay CEA-06-062UT-350

Downwind TRB Strain, 180°, thin end TRB_Dwn_180_D Vishay CEA-06-062UT-350

Downwind TRB Strain, 180°, thick end TRB_Dwn_180_C Vishay CEA-06-062UT-350

Downwind TRB Strain, 270°, thin end TRB_Dwn_270_D Vishay CEA-06-062UT-350

Downwind TRB Strain, 270°, thick end TRB_Dwn_270_C Vishay CEA-06-062UT-350

Downwind TRB Outer ring temperature TEMP_TRB_Dwn Omega SA1-RTD-120
5

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Figure 2. Upwind tapered roller bearing strain

Source: McNiff Light Industry
6

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Figure 3. Downwind tapered roller bearing strain

Source: McNiff Light Industry
7

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Figure 4. Strain gage data sheet

Source: Vishay Precision Group (http://www.vishaypg.com/docs/11125/062ut.pdf)
8

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Figure 5. Bearing outer ring temperature

Source: McNiff Light Industry
9

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Figure 6. Bearing instrumentation before protection. Photo by Scott Naucler, NREL 26259

Figure 7. Bearing instrumentation after protection. Photo by Jonathan Keller, NREL 26257

2.3 Calibration Requirements

Calibration requirements are different for the different sensors. The strain gages require direct 

signal-to-force calibration, necessitating a special test rig. The RTDs do not require calibration.

2.3.1 No Calibration

The RTDs installed on the TRB outer rings do not require calibration because they meet the 

RT100 specification. These devices are connected to special RTD specific modules in the data 

acquisition system (DAS), and they are recorded in units of degrees Celsius.

2.3.2 Direct Calibration

In the case of these strain gages, the data of interest is the absolute magnitude of load at each 

gage location. This measured load can then be compared to predictions in commercial modeling
10

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software. Differences in the load distribution around the circumference, across the bearing face, 

and between the upwind and downwind TRBs are all of interest. In the ideal design and 

operational scenario, the loads would be shared equally in all of these areas. However, the 

combination of axial and radial loads from the pinion gear mesh, and the close spacing of the 

TRB pair results in unequal load sharing. Additionally, manufacturing tolerances and external 

loads from the brake disk or generator misalignment can further disrupt load sharing and result in 

a reduction in bearing life. Lastly, transient loads from the generator, such as a generator speed 

change or grid fault, are likely to disrupt load sharing and also result in a reduction in bearing 

life.

The desire for a measure of the absolute magnitude of load at each bearing gage location, along 

with the unique geometry of the bearing and groove necessitate direct calibration. The objective 

of this direct calibration is to measure the correlation between the load applied to the bearing and 

the strain gage response. The best method for calibration of the TRBs is to apply loads separately 

to each TRB while they are installed on a representative shaft. In-situ calibration of the TRBs 

was not possible, because there is no easy way to apply loads to the TRBs individually when the 

shaft is installed in the housing bore. Therefore, construction of a special test rig was required,

which would facilitate application of loads individually to each TRB.

Furthermore, the test rig and loading mechanism must apply the load to the bearings in the axial 

direction rather than the radial direction. Either method would result in measurable strain on the 

TRB outer rings. However, applying a radial load would result in an unequal strain distribution 

around the circumference of the TRB. With only four measurement locations spaced around the 

circumference, translation of this unequal strain distribution to an equivalent load distribution 

would be problematic, if not impossible. Application of an axial load results in a nearly constant 

strain distribution around the circumference of the TRB. In this case, the axial load is transmitted 

through the bearing taper angle to the outer rings, resulting in an expansion of the outer ring,

which is resisted by the housing (or test fixture). Only a portion of the axial load results in a 

radial load because of the taper angle; the majority of the axial load is reacted by the contact 

between the outer ring, spacer, and housing (or test fixture). A special test fixture was developed 

for that purpose and is described in the next section.

In operation in the GRC GB, the TRB pair reacts the axial and radial forces from the gear mesh 

and the shaft bending moments created by them. Modeling of the GRC GB predicts that at rated 

torque the bearing pair is loaded by axial and radial forces of 22 kN (5 kip) and 60 kN (13.5 kip), 

respectively. However, the bearings are not loaded equally around their circumference, nor are 

they loaded equally between the upwind and downwind rows [6]. A worst-case scenario would 

have only a portion of one bearing carrying all of these loads. In the course of this test, up to 50 

kip of axial force was applied to each bearing. Through the 16° taper angle, this equates to a 

radial load of 61 kN (13.8 kip) distributed evenly around the bearing circumference. Thus, this 

test resulted in a radial load approximately equivalent to a worst case loading condition at rated 

torque in the gearbox.
11

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3 Test Environment

The following sections describe the test equipment and setup.

3.1 Load Frame

The load frame used to calibrate the HSS TRBs was previously used to calibrate the GRC planet 

bearings [2] and is shown in Figure 8. It is located in the high bay of building 251 at the NWTC. 

It consists of a steel frame holding a 110 kip (444.8 kN) hydraulic actuator. The actuator is 

mounted on a crosshead assembly, which can be moved vertically through jackscrews. Once in 

the desired position, the crosshead is manually locked into position by tightening bolts around 

the load frame. In this manner, loads can be applied vertically downward to the test article from a 

variable height. The loads are then transmitted through the test article to a baseplate. The entire 

load frame is mounted to a large steel base with standard “t-slots.” The base and t-slots are 

useful for mounting the required ancillary equipment, such as hydraulic pumps.

Control of the load frame is through an MTS Systems-designed controller using either a 

handheld remote control screen (RCS) device at the load frame itself or through a software 

program on a dedicated computer in a separate control room. In either case, the load frame can 

be operated in either load or displacement control modes. In load control, a load is commanded,

and the actuator displaces as much as required to achieve the desired load—up to a total of 6 

inches of travel. In displacement control, a displacement is commanded, and the actuator applies 

as much force as required to achieve the desired displacement—up to 110 kip. Various safety 

settings can be configured on the dedicated computer, which range from notifying the operator 

that a limit has been exceeded to completely shutting down the load frame. In this test, very 

small displacement limits were configured along with a maximum compressive force of 55 kip.

Installed on the load frame are a calibrated load cell and a proximity sensor, which measure the 

applied load and resulting displacement of the actuator, as listed in Table 2. Calibration of these 

devices and the control system was performed by MTS in advance of testing.

Table 2. Load Frame Instrumentation

Instrument Derived Measurement Label Sensor

Proximity probe Axial displacement Displacement MTS 244-41

Load cell Applied axial load Force MTS 661.23E-01
12

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Figure 8. The 110-kip load frame (left) and test bearing (right). Photos by (left) Jonathan Keller, 

NREL 26258 and (right) Mark McDade, NREL 26260

3.2 Bearing Calibration Fixture

A special calibration fixture, shown in Figure 9, was designed to support the instrumented TRB. 

An end cap is located at the top of the fixture. The end cap houses a Timken T200A thrust 

bearing, which allows for rotation of the TRB while under axial load. This permits the rolling

elements to rotate directly under each individual groove in the outer ring. The thrust bearing 

mates with a shaft plug, which simulates the HSS. The shaft plug has a shoulder in it, which 

transfers loads to the TRB inner ring. The plug also has a radial through-hole, which allows a rod 

to be inserted into the plug to turn it under load. The TRB itself is retained in a collar that 

simulates the gearbox housing and retains the bearing circumferentially and axially. The collar 

design specifies 20 to 47 μm of diametrical clearance with the TRB outer ring, identical to the 

specified range of diametrical clearance between the downwind TRB outer ring and the end cap 

which retains it in the gearbox itself (P/N 251347). The collar produced was reported to have a 

clearance of just over 20 micrometers (μm). The collar is recessed into the baseplate, which in 

turn is bolted to the load frame base plate. The sensor wires from the TRB exit a slot machined in 

the collar.

Figure 9. Bearing calibration fixture

Source: Illustrations by Ed Overly, NREL

Applied

Load
13

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3.3 Calibration Fixture Assembly

A schematic assembly of the complete fixture in the load frame is shown in Figure 10.

Figure 10. Completed calibration assembly

Source: McNiff Light Industry

3.4 Data Acquisition System

The DAS is based on the National Instruments (NI) deterministic Ethernet platform. Two NI 

9237 signal-conditioning modules collected the eight strain gage half bridges and a NI 9217 

signal-conditioning module collected the RTD signal. Additionally, the outputs of the load cell 

and axial displacement sensor on the load frame were brought into the DAS via Ethernet 

exchange with the MTS load frame controller. These signals were then sent through a NI PXI1041Q chassis into the DAS computer. The data was displayed on screen for all channels. The

strain gage channels were displayed and recorded in the native units of Volts per Volt (V/V) and 

also με, using a conversion factor of 366,300 derived from the gage factor and the Poisson 

arrangement. Temperature, actuator displacement, and force were displayed and recorded in 

units of degrees Celsius (C), inches, and kips, respectively.

The data files were named using the convention “TRB_UW_” or “TRB_DW_” and appended 

with “XX_YYYY_MM_DD_HH_SS_ZZZHz.tdms,” where XX is the load in kips as measured 

by the load cell; YYYY, MM, DD, HH, and SS are the year, month, date, hour, and second of 

the data acquisition; and ZZZ is the data acquisition rate in hertz (Hz).
14

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4 Test Sequence

This section describes the calibration process. Each TRB was calibrated separately.

4.1 Temperature Sensitivity Tests

Pretest measurements were acquired while the bearing outer ring was separated from the inner 

ring and rollers, and completely unloaded. The outer ring was heated to assess the effect of 

temperature on the measured strain value. The bearing was wrapped in an electric “barrel” heater 

and strain values were measured with the temperature ranging from ambient to 45°C. Data was 

acquired for a total of 60 seconds at 10 Hz, yielding data records of 600 points.

4.2 Load Calibration Tests

This section describes the set of tests to determine the correlation between radial load and 

measured strain. Setup and routine operation of the load frame was in accordance with an 

existing safe operating procedure (SOP) [7].

The actuator was placed in displacement control to slowly lower it until it came in contact with 

the end cap. At that point, the actuator was placed in force control for the remainder of the test. 

Loads were then applied in five kip increments up to 50 kip. At each increment, the bearing inner 

ring was rotated 180° in approximately five seconds to ensure that a minimum of three rollers 

pass under each groove. Data was acquired for a total of 20 seconds at 500 Hz, yielding data 

records of 10,000 points. Two acquisitions were acquired at each load level to assess 

repeatability. Upon reaching the maximum load, the process was reversed again, performing two 

acquisitions at each load level—yielding a total of four acquisitions at each load level.
15

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5 Data Analysis

5.1 Temperature Sensitivity Analysis

The effect of temperature on the static output of all gages for the downwind bearing is shown in 

Figure 11. Ambient temperature the day of the test was 24°C. The maximum temperature the 

bearing was heated to by the “barrel” heater was 45°C. Over this range, the strain increased by 

approximately 5 μV/V, or 2 με, for each gage pair. This change in strain is small compared to 

the strains experienced under the axial loading tests representative of operational loads described 

in the following sections.

Figure 11. Effect of temperature on measured strain

5.2 Load Calibration Analysis

Gage calibration is determined from the measured data by regression analysis of the gage

response to the applied load. The analysis process and final results are discussed in the following 

subsections.

5.2.1 Example Gage and Applied Load Responses

Figure 12 shows example acquisitions for the TRB_Up_00_A channel (upwind bearing, 0° 

groove, thin end) at applied loads of 25 and 50 kip. Only the first 10 seconds of the acquisition 

are shown for clarity. The strain gage response has been displayed in units of μV/V for ease of 

interpretation. True strain values are also given throughout the text for reference; however, for 

the purpose of future dynamometer testing, the relationship of interest is really between the 

applied load (kip) and strain gage response (V/V). The intermediate step of converting strain 

gage response (V/V) to true strain (με) is not necessary.

Both signals are composed of three regions. The first is an initial, steady level. Then at 

approximately t = 2 seconds, the bearing was rotated 180° by hand over a period of 3 to 5 

seconds, resulting in a sinusoidal behavior in the measured strain gage response. During this 
16

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period, the load fluctuates only slightly, but the strain gage response changes dramatically. The 

strain gage response is composed of three to four approximate sine waves, which correspond to 

three or four rollers passing underneath the gage pair. At the conclusion of the rotation, the strain 

gage response returns to a final, steady level.

There are several interesting characteristics of the responses. Firstly, the applied load in each 

case is relatively constant as desired. During the rotation, it varies less than ± 0.2 kip, which is 

less than 1% of the applied load. Turning to the strain gage response, note that the initial and 

final strain gage response values are highly dependent upon the roller position relative to the 

strain gage pair. The initial strain gage response is approximately -1000 μV/V for both of these 

cases, although the applied load has been doubled. Thus, the mean must be assessed from the 

sinusoid itself, rather than the initial or final responses, which have little intrinsic value. At 25 

kip, the mean strain gage response is approximately -950 μV/V (348 με); at 50 kip, the mean 

strain gage response is approximately -1250 μV/V (458 με). This mean strain gage response can 

be thought of as a result of the hoop stress within the bearing due to the applied axial force and 

the bearing taper angle.

Figure 12. Measured load and strain for upwind bearing at 0° groove in thin end at 25 kip (left) and 

50 kip (right)

Within the sinusoidal region during the rotation of the bearing, the peaks occur when two rolling 

elements are equally spaced away from the gage pair as shown in Figure 13. The valleys in the 

response occur when a rolling element is located directly under the groove and gage pair axis. 

This behavior was visually confirmed during the course of the test and can be thought of as a 

result of the flexure of the remaining ‘bridge” of material in the bearing groove where the strain 

gage pair is located. The flexure of the bridge is highly dependent upon the location of the rollers 

beneath it, as illustrated in Figure 13. When the rollers are equidistant from the groove, the 

bearing radial forces bend the bridge of material downward, resulting in a compressive bending 

condition measured by the gage, which reduces the total stress. When the roller is directly under 

the groove, the bearing radial force bends the bridge of material upward, resulting in a tensile 

bending condition measured by the gage, which is additive to the mean hoop stress.

At 25 kip, the range (peak-to-valley) of the sinusoid is approximately 300 μV/V (110 με); at 50 

kip, the range is approximately 600 μV/V (220 με). Note that strains of this magnitude, 100 to 
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200 με, can be measured very accurately by the strain gages. Thus, the grooves function as 

intended, resulting in measurable strain values as predicted by finite element modeling.

Figure 13. Rolling element positions at signal maximum and minimum

As seen in the responses, there are some variations in the magnitudes of the individual peaks and 

valleys for each roller, especially at the lower applied load level. Thus, when reducing the data, it 

is best to define a mean and a range by averaging the peaks and valleys for each acquisition as 

discussed in the following section.

5.2.2 Gage and Applied Load Data Processing

The data for each gage pair at each load level was post-processed to calculate the mean and 

range. In this process, additional steps were required to de-noise the data and are outlined as 

follows.

1. A 10 Hz, a low-pass filter is applied to de-noise the data originally acquired at 500 Hz.

2. The individual valleys (time index from start of data set) are then located using first and 

second derivatives and accounting for slip, duplicated valleys, and half periods. Using the 

individual valleys allows the identification of each sinusoid in the response.

3. For each sinusoidal period identified:

• The mean applied load for the period is the mathematical average of the load cell 

output in the period.

• The mean of the strain gage response for the period is the mathematical average of 

strain gage response in the period.

• The range of the strain gage response for the period is determined by subtracting the 

maximum strain response from the minimum strain response within the period.

4. For each acquisition containing multiple sinusoidal periods:

• The mean applied load for the acquisition is the mathematical average of the mean 

applied load for each period.
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• The mean of the strain gage response for the acquisition is the mathematical average 

of the mean of the strain gage response for each period.

• The range of the strain gage response for the acquisition is the mathematical average 

of the range of the strain gage response for each period.

5.2.3 Example Gage and Applied Load Regression Analysis

Once the mean applied load, mean of the strain gage response, and range of the strain gage 

response were calculated for each acquisition, a regression analysis was completed as outlined in 

the following sections. The desired outcome of the regression analysis is a linear correlation 

between the applied load and some strain gage response characteristic. For previous GRC 

calibration of planet bearings, the range of the strain gage response provided the best correlation 

with applied load [2]. For this activity, regression analyses were performed for both the mean 

and the range.

Figure 14 shows the results of the regression analysis for just the TRB_Up_00_A channel 

(upwind bearing, 0° groove, thin end). Regression analyses were performed for all channels on 

both bearings, but the results shown below are typical. For both the mean and the range, the 

strain gage response increases monotonically with applied load. However, the mean exhibits a 

bilinear response, whereas the range exhibits a linear response.

Figure 14. Regression analysis for upwind bearing at 0° groove in thin end, for mean (left) and 

range (right)

Up to an applied load of approximately 25 kip, the mean increases significantly with applied 

load, but after this point the mean increases much more slowly. Remember that the collar 

retaining the bearing was produced with just over 20 μm of diametrical clearance with the TRB 

outer ring. It is hypothesized that below 25 kip of applied load, the bearing outer ring has not yet 

been stretched diametrically enough to fill up this clearance; thus, the system stiffness is simply 

comprised of the outer ring stiffness. At 25 kip, the bearing outer ring becomes fully engaged 

with the steel collar. At this point, the system stiffness is now composed of both the outer ring 

stiffness and the steel collar stiffness. This relatively simple explanation describes the bilinear 

behavior in the mean strain.
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There can be small differences in diametrical tolerances of the steel collar, the gearbox end cap 

(P/N 251347) that retains the downwind bearing, the gearbox bore that retains the upwind 

bearing, and any individual bearing. These tolerance differences would result in a difference in 

the diametrical clearance in each situation from 20 to 47 μm, and thus, a difference in the 

inflection point in the mean strain. Therefore, this bilinear behavior is undesirable for purposes 

of translating measured strain gage response to operating load in the planned gearbox tests.

Turning to the range of the strain gage response, note that it is not affected by this hypothesized 

change in system stiffness at 25 kip. It exhibits a linear response over its entire range. There are 

single data points at the 40, 45, and 50 kip applied loads that have lower range values than the 

other three data points; however, they are not representative of the overall trend. In general, the 

measured range at each applied load is relatively consistent. Using a linear curve fitting approach 

yields a coefficient of determination (R2) value of 0.96 for this data set.
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5.2.4 Full Regression Analysis Results

The regression analysis results for the range for the upwind bearing are shown in Figure 15.

Figure 15. Regression analysis for upwind bearing
21

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The regression analysis results for the range for the downwind bearing are shown in Figure 16.

Figure 16. Regression analysis for downwind bearing
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The results are more consistent for the downwind bearing, with a minimum R2 value of 0.97, 

than the upwind bearing, with a minimum R2 value of 0.92. For the upwind bearing, there are 

single acquisitions at the 40, 45, and 50 kip applied loads, which have lower range values than 

the other three acquisitions. The downwind bearing tests did not exhibit this behavior.

The sensitivity of each gage pair to applied load—that is, the slope of the linear correlation of 

range of the strain gage response—is also given in Figure 15 and Figure 16. For convenience, 

these sensitivities are shown all together in Figure 17. There are several trends that are of note. 

For any given axial position (A to D), it is expected the sensitivity around the circumference (0° 

to 270°) should be very similar given the grooves are machined with the same dimensions rather 

accurately, the gages are installed in the same location and orientation within the groove as 

closely as possible, and the load distribution around the circumference should be nearly circular. 

This expectation largely bears out. The best example of similarity is the gages on the downwind 

bearing, thin end (axial position D). Here, the average sensitivity is 11.2 μV/V/kip with the 

maximum being 8% greater than the average. The gages on the upwind bearing, thin end (axial 

position B) show the least similarity, where the average sensitivity is 7.4 μV/V/kip with the 

maximum being 22% greater than the average.

Figure 17. Calibration sensitivity comparison

The average sensitivities are 11.2, 8.3, 7.4, and 10.1 μV/V/kip for positions D, C, B, and A 

respectively. As expected, the sensitivities for the thin-end gages (D and A) should be similar 

and also greater than the thick-end gages (C and B). Regarding the differences in sensitivities 

around the circumference and between similar positions, referring back to Figure 6 shows that 

the strain gage occupies a sizeable portion of the groove in the bearing race. It is hypothesized 

that small differences in the gage position within the groove and orientation to the shaft axis

result in slightly varying stiffness and response characteristics at the strain gages.
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5.2.5 Final Calibration Coefficients

The calibration results discussed herein have thus far been in terms of applied axial load and 

resulting strain gage response. For the purposes of dynamometer testing, the range of the strain 

gage response will be measured for each gage pair. These measured ranges will then be used to 

calculate the radial, not axial, load at each position. Thus, the desired final result from this 

calibration exercise is the sensitivity of the range of the strain gage response in units of radial 

load per volt output of the Wheatstone bridge (kip/V/V). These final sensitivities are calculated 

in the following subsections. First, however, it is required to determine the component of the 

applied load acting at the gage axis.

5.2.5.1 Determining Applied Load

Although the load was applied to the test article along its axial (rotation) axis, as shown in Figure 

18, the calibration objective is to determine the signal response proportional to radial load. The 

radial load, Fradial, is proportional to the load applied axially to the inner ring, Fapplied, and the 

tangent of the taper angle (θ = 16°):

F F tan radial applied = θ . (1)

Figure 18. Load components

Source: McNiff Light Industry

The load at one roller, Froller, as it goes over the gage axis, is the radial load divided by the 

number of rollers (Nroller = 20), assuming a circular load distribution. This roller load is the load 

the gage is responding to sinsusoidally:

radial

roller

roller

F F

N = . (2)

In this situation, with only an axial load, this assumption is well justified within normal bearing 

manufacturing tolerances, and the proper alignment of the load frame and bearing. Regarding the 

influence of the grooves on the circular load distribution, finite element modeling also showed 

this assumption to be fairly well justified. Compared to a bearing without grooves, the rollers 

experienced a radial force of only 10% to 15% less than when directly under a groove in the 

modified bearing [6].
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5.2.5.2 Calculated Calibration Coefficients

Table 3 and Table 4 list the final calibration coefficients, in terms of the measured sensitivity of 

the range of the strain gage response to the axial load from this test, in units of μV/V/kip, and the 

radial load sensitivity to range of the strain gage response to be used in the upcoming 

dynamometer test, in units of kip/V/V).

Table 3. Upwind Bearing Calibration Coefficients

A B

Circumferential 

Position

Range 

Sensitivity to

Axial Load

(μV/V/kip)

Radial Load

Sensitivity to

Range

(kip/V/V)

Range 

Sensitivity to 

Axial Load

(μV/V/kip)

Radial Load

Sensitivity to

Range

(kip/V/V)

0° 10.61 2.70 x 104 7.14 4.02 x 104

90° 8.95 3.20 x 104 9.02 3.18 x 104

180° 10.89 2.63 x 104 7.44 3.85 x 104

270° 10.10 2.84 x 104 5.95 4.82 x 104

Table 4. Downwind Bearing Calibration Coefficients

C D

Circumferential 

Position

Range 

Sensitivity to 

Axial Load

(μV/V/kip)

Radial Load

Sensitivity to

Range

(kip/V/V)

Range 

Sensitivity to 

Axial Load

(μV/V/kip)

Radial Load

Sensitivity to

Range

(kip/V/V)

0° 7.60 3.77 x 104 10.84 2.65 x 104

90° 7.14 4.02 x 104 10.81 2.65 x 104

180° 8.43 3.40 x 104 12.08 2.37 x 104

270° 9.88 2.90 x 104 10.96 2.62 x 104
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6 Conclusions

An instrumentation package was designed, installed, and calibrated for the tapered roller bearing 

pair supporting the GRC gearbox HSS assembly. The instrumentation consists of eight strain 

gage pairs and one RTD installed in axial grooves machined in the outer ring of each bearing. 

The gages are installed at two axial locations in each of the four equally spaced axial grooves. 

The gages are wired in a Poisson half-bridge configuration and measure the strain response when 

a roller passes underneath them, while the RTD simply measures the temperature of the outer 

ring.

The strain gages underwent calibration testing from May 22−24, 2013, in a 110-kip load frame 

located at the National Wind Technology Center. The load frame applied up to 50 kip of axial 

load to the bearing, which was housed in a steel collar representative of the GRC gearbox 

housing. The maximum applied axial load corresponds to a worst-case radial condition for the 

bearing in operation in the gearbox. At each load condition, the inner ring of the bearing was 

rotated 180° manually, resulting in up to four rollers passing underneath each axial groove, and 

the resulting strain response was measured. In addition, the sensitivity of the strain response to 

temperature was also measured.

The strain gage response during the bearing rotation was then post-processed to extract the mean 

and range. A linear regression analysis was used to correlate each measured output with the 

applied load. It was found that:

• The mean of the strain gage response exhibited a bilinear correlation with applied axial 

load, with an inflection point of approximately 25 kip. Above this point, the mean was 

less sensitive to increases in applied load. It is hypothesized this inflection point 

corresponds to the point at which the diametrical clearance between the outer ring and 

restraining steel collar was filled. Below this point, the system stiffness is composed of 

the outer ring alone, and above this point the system stiffness is composed of the outer 

ring and steel collar.

• The range of the strain gage response exhibited a linear correlation with applied axial 

load. That is, its response is governed by the local stiffness of the groove in the outer 

ring, and it is insensitive to the diametrical clearance between the outer ring and steel 

collar.

• The range of the strain gage response calibration factors varied from 8% to 22% around 

the circumference of the bearing. Because of the relative size of the strain gage within the 

groove and subsequent challenge of locating the strain gage pair in the exact center of the 

groove, it was considered important to calibrate each gage pair individually for both 

bearings.

• The absolute strain magnitudes (over 450 με) and the strain range (over 200 με) are well 

within the strain gage pair measurement accuracy. Finite element modeling of the groove 

geometry under expected operating conditions was valuable in determining the axial 

groove dimensions to yield these measureable strain values.
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• The measured strain gage response was insensitive to temperature. Strain response values 

changed less than 1% over the range of 24°C to 45°C. This measured strain would only 

affect test results if the mean strain was used as the metric to determine the applied load. 

The strain range, which is to be measured over a very short time duration (on the order of 

seconds), would be unaffected by longer-term changes in temperature.

• In the course of running the tests, the proportional and integral gain factors of the MTS 

controller for the load frame required adjustment in order to maintain consistent values of 

applied load while rotating the bearing by hand. It is suspected that because the bearing 

and load fixture are very stiff systems with very little compliance, small changes in 

displacement or force while rotating the bearing resulted in the controller applying large 

loads to compensate. If the test were to be run again, a rubber mat would be added 

between either the collar and baseplate, or the baseplate and load frame itself. Such a 

rubber mat would add some compliance and reduce the amount of controller tuning 

required to maintain consistent applied loads.
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7 References

1. Link, H.; LaCava, W.; van Dam, J.; McNiff, B.; Sheng, S.; Wallen, R.; McDade, M.; 

Lambert, S.; Butterfield, S.; Oyague, F. Gearbox Reliability Collaborative Project Report: 

Findings from Phase 1 and Phase 2 Testing. NREL/TP-5000-51885. Golden, CO: National 

Renewable Energy Laboratory, 2011.

2. van Dam, J. Gearbox Reliability Collaborative Bearing Calibration. NREL/TP-5000-47852. 

Golden, CO: National Renewable Energy Laboratory, 2011.

3. Sheng, S. “Report on Wind Turbine Subsystem Reliability—A Survey of Various 

Databases.” NREL/PR-5000-59111. Golden, CO: National Renewable Energy Laboratory,

2013.

4. Link, H.; Keller, J.; Guo, Y.; McNiff, B. Gearbox Reliability Collaborative Phase 3 Gearbox 

2 Test Plan, NREL/TP-5000-58190. Golden, CO: National Renewable Energy Laboratory,

2013.

5. SKF Group. Specification SKF 32222 J2: Tapered roller bearings, single row. 

http://www.skf.com/group/products/bearings-units-housings/roller-bearings/tapered-rollerbearings/single-row/index.html?prodid=1310002222&nfp=NFP-1310002222#.

6. Austin, J.L. A Multi-Component Analysis of a Wind Turbine Gearbox using a High Fidelity 

Finite Element Model, M.S. Thesis, The Ohio State University, 2013.

7. Jenks, M. Safe Operating Procedure for Conducting Structural Tests at the NREL NWTC. 

SOP-0515. Golden, CO: National Renewable Energy Laboratory, 2013.