Timothy Krantz and Christopher DellaCorte

Glenn Research Center, Cleveland, Ohio

Michael Dube

Goddard Space Flight Center, Greenbelt, Maryland

Experimental Investigation of Forces Produced

by Misaligned Steel Rollers

NASA/TM—2010-216741

July 2010
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Timothy Krantz and Christopher DellaCorte

Glenn Research Center, Cleveland, Ohio

Michael Dube

Goddard Space Flight Center, Greenbelt, Maryland

Experimental Investigation of Forces Produced

by Misaligned Steel Rollers

NASA/TM—2010-216741

July 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

40th Aerospace Mechanisms Symposium

cosponsored by the NASA Kennedy Space Center and Lockheed Martin Space Systems Company

Cocoa Beach, Florida, May 12–14, 2010
Acknowledgments

This research was supported by the NASA Engineering Safety Center. The experimental work was done with assistance from 

Mr. Justin Elchert of Case Western Reserve University as part of the NASA GRC LeRCIP Summer Student Program.

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7115 Standard Drive

Hanover, MD 21076–1320

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Available electronically at http://gltrs.grc.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216741 1

Experimental Investigation of Forces Produced 

by Misaligned Steel Rollers 

Timothy Krantz and Christopher DellaCorte 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Michael Dube 

National Aeronautics and Space Administration 

Goddard Space Flight Center 

Greenbelt, Maryland 20771 

Abstract 

The International Space Station (ISS) Solar Alpha Rotary Joint (SARJ) uses a roller-based 

mechanism for positioning of the solar arrays. The forces and moments that develop at the roller 

interfaces are influenced by the design including the kinematic constraints and the lubrication 

condition. To help understand the SARJ operation, a set of dedicated experiments were 

completed using roller pairs. Of primary interest was to measure the axial force directed along the 

axis of rotation of the roller as a function of shaft misalignment. The conditions studied included 

dry and clean surfaces; one surface plated by a gold film, and greased surfaces. For the case of a 

bare 440C roller against a nitrided 15-5 roller without lubrication, the axial force can be as great as 

0.4 times the normal load for a shaft angle of 0.5°. Such a magnitude of force on a roller in the 

SARJ mechanism would cause roller tipping and contact pressures much greater than anticipated 

by the designers. For the case of a bare 440C roller against a nitrided 15-5 roller with grease 

lubrication, the axial force does not exceed about 0.15 times the normal load even for the largest 

misalignment angles tested. Gold films provided good lubrication for the short duration testing 

reported herein. Grease lubrication limited the magnitude of the axial force to even smaller 

magnitudes than was achieved with the gold films. The experiments demonstrate the critical role 

of good lubrication for the SARJ mechanism. 

Introduction 

The International Space Station (ISS) makes use of a roller-based mechanism for positioning of 

the solar arrays. The fundamental concept of the roller-based mechanism of the ISS Solar Alpha 

Rotary Joint (SARJ) is described by Loewenthal and Schuller (Ref. 1). A careful study of the SARJ 

system reveals an interesting and significant interplay of forces at the interface where the rollers of 

the rotary joint mechanism touches the large rotating ring. It is well established in the literature that 

forces and moments can develop at the interacting surfaces in rolling and sliding contact (Refs. 2 

and 3). The forces and moments that develop are influenced by the details of the design including 

the kinematic constraints. Proper understanding of the influence of roller misalignment has proven to 

be important in the development of a roller mechanism used for positioning of a radio astronomy 

antenna (Refs. 4 to 6). The influence of roller misalignment is likewise important for the operation of 

the SARJ mechanism. 

The roller and ring of the SARJ mechanism and the meaning of the term “shaft misalignment” is 

depicted in schematic form in Figure 1. The SARJ rollers are constrained to rotate about shaft axes 

that nominally intersect the rotational axis of the ring (Figs. 1(a) and (b)). Any deviation from perfect 

alignment of a roller axis and ring axis (Fig. 1(c)) will give rise to a force at the contact interface in 

the direction of the roller shaft axis (termed herein the axial force). The magnitude of the axial force 
NASA/TM—2010-216741 2

Figure 1.—SARJ ring and roller schematic, top view. (a) Overall view, roller axis 

aligned with ring axis; (b) close-up view near roller, aligned axis; (c) close-up 

view near roller, roller axis misaligned (misalignment magnitude greatly 

exaggerated). 

Figure 2.—Schematic of the SARJ roller and ring in contact, front 

view. Illustrated are the forces imposed by the ring on the roller 

and the reaction forces at the pivot point in the roller housing. 

will depend on the magnitude of misalignment, the normal load on the roller, the stiffness of the 

system, the torque transmitted by the roller, and frictional condition of the contacting surfaces. 

The SARJ mechanism was built to high precision, and the installed roller shaft angle 

(misalignment) was within a fraction of a degree to perfect alignment. As will be evident from 

this study, misalignments of even such small magnitude can produce significant forces that 

influence the performance of the mechanism. 

The axial force that develops in response to the misalignment of the axes can have a 

significant influence on the operating conditions of the SARJ hardware. The axial force and the 

associated moment that arise from misaligned axes are carried by a pair of tapered roller 

bearings via the roller shaft to the roller housing. The axial force interacts through a pivot point 

in the roller housing (Fig. 2). In the absence of misalignment, the pivot point allows for uniform 

contact of the nominally flat roller profile contacting the nominally flat raceway surface. But for 

the case of misaligned axes, the axial force acts via the pivot point and produces a non-uniform 

contact pressure across the roller profile. Note from Figure 2 the moments created by the 

normal load and axial force acting via the pivot point must be balanced for static equilibrium. 

Thereby, the axial force acts to shift the position of the resultant normal load along the face of 

the ring and roller contact. The axial force arising from misaligned axes can, if of sufficient 

magnitude, cause tipping of the roller. Also note that the axial force acting on a roller is carried 

to the roller shaft via a pair of lightly-preloaded tapered roller bearings. The magnitude of the 

axial force influences the drag torque of the bearings and thereby influences the torque required 

to rotate the mechanism. 

(a) (b) (c)

normal load

roller

pivot axis of

roller housing

reaction forces

at pivot point

ring

rotational axis

of the roller axial force

normal load

roller

pivot axis of

roller housing

reaction forces

at pivot point

ring

rotational axis

of the roller axial force
NASA/TM—2010-216741 3

To help understand the SARJ mechanism operation, a set of dedicated experiments were 

completed using roller pairs. The purpose of the experiments was to quantify the relationship of 

the misalignment of roller axes to the resulting forces that develop. The relationship of shaft axis 

misalignment magnitude to axial force magnitude was determined for the material combination 

used in the SARJ mechanism for a variety of surface and environment conditions as can 

influence the friction and, thereby, the behavior of the mechanism. 

Apparatus, Specimens, and Procedures 

Test Apparatus for Roller Pairs 

Testing was done using the NASA Glenn Research Center Vacuum Roller Rig (Fig. 3). The 

rig allows for application and measurement of a load pressing the rollers together while having a 

purposely misaligned and adjustable shaft angle. The rig is depicted in schematic form in 

Figure 4. A drive motor provides motion to the driving roller. A magnetic-particle brake attached 

to the output shaft imposes torque on the driven roller. The rig can be operated with the brake 

not energized. For such a condition the torque transmitted through the roller pair is only the drag 

torque of the output shaft (drag of the seals and support bearings). The normal load pressing 

the rollers together is provided by an air cylinder. The cylinder acts through a gimbal point to 

rotate the plate that mounts the driving shaft and drive motor. The rotation of the drive motor 

plate displaces the driving roller toward the driven roller shaft. The pressure to the cylinder, and 

thereby the load between the contacting rollers, is adjusted by a hand-operated valve (openloop control). Testing can be done in vacuum or ambient air. Vacuum is provided by a diffusion 

pump with a liquid nitrogen cold trap. The diffusion pump is assisted by a mechanical vacuum 

pump. Figure 5 provides a simplified schematic labeled with some of the nomenclature used 

herein. 

A set of sensors on the test apparatus monitors the test conditions. The outputs of the 

analog sensors were digitized and stored via a data collection unit at a rate of 0.66 Hz. Each of 

the sensors and the methods of calibration will be described in turn. 

The misalignment of the driving roller shaft and driven roller shaft is depicted in an 

exaggerated manner in Figure 4(b). The misalignment is measured via a linear variable 

differential transformer (LVDT). The transducer housing is attached to the bedplate, and the 

translating, spring-loaded transducer tip contacts against a mechanical stop on the turntable. 

The mechanical stop is mounted at a known radial distance and tangential orientation from the 

center of the turntable. Calibrated gage blocks were used to displace the transducer by known

amounts, and using the rig geometry the equivalent angular rotation of the turntable was 

calculated. The preceding steps established the relationship of change in transducer output to 

the change in relative shaft angle. To establish the aligned condition, a special tooling block was 

Figure 3.—Vacuum roller rig. 
NASA/TM—2010-216741 4

(a)

(b)

Figure 4.—Schematic views of the vacuum roller rig. (a) Schematic, side view. 

(b) Schematic, overhead view with shaft misalignment depicted and exaggerated. 

Figure 5.—Simplified schematic view including some of the important sensed data. 

(a) Schematic, front view. (b) Schematic, side view. 

drive motor

ferrofluid seals

and bearings

“axial” force/thrust sensor

brake

pivot point for drive motor 

plate relative to turntable

bedplate

air piston

“normal load”

force sensor

vac chamber

turntable

bedplate

bellows drive motor

ferrofluid seals

and bearings

“axial” force/thrust sensor

brake

pivot point for drive motor 

plate relative to turntable

bedplate

air piston

“normal load”

force sensor

vac chamber

turntable

bedplate

bellows

ferrofluid seal and bearing

“axial” force/thrust sensor

brake

drive motor

bedplate

turntable on bearing

load cell for “tangential” force,

mounted to turntable

ferrofluid seal and bearing

“axial” force/thrust sensor

brake

drive motor

bedplate

turntable on bearing

load cell for “tangential” force,

mounted to turntable

pivot point for drive motor 

plate relative to turntable

normal load

braking torque

tangential force

normal load

normal load

axial force

normal load

input shaft

output shaft output shaft

(a) (b)

normal load

braking torque

tangential force

normal load

normal load

axial force

normal load

input shaft

output shaft output shaft

(a) (b)
NASA/TM—2010-216741 5

machined to locate the roller-mounting surfaces of the two shafts as parallel. With the shafts 

aligned by the tooling block, the transducer circuit balance was adjusted to provide an output of 

zero. The precision of this method for aligning the shafts was limited by the dimensions of the 

roller mounting surfaces used as the reference planes. From the test rig drawing tolerances and 

geometry, the alignment procedure using the tooling block to define the zero-degree position 

has an accuracy of no better than 0.11°. 

The torque on the output shaft is monitored by a strain-gage type torquemeter of 22 N-m 

(200 in.-lb) torque capacity. Calibration was done in place using deadweights acting on a torque 

arm of known length. 

The load that presses the rollers together is termed herein the “normal load” (Fig. 5). The 

normal load is applied via an air-pressure actuated piston. The air piston acts through a load cell 

against the drive motor plate that is gimbal-mounted relative to the test chamber (Fig. 4(a)). In 

this way the air cylinder moves the roller on the input shaft in an arc motion toward the test 

roller. Once the rollers are in contact, additional force commanded from the air cylinder 

increases the normal load between the test rollers. The force sensed by the load cell located 

between the gimbaled motor plate and the air piston is a linear combination of two sources, the 

unbalanced mass relative to the gimbal point and the normal load on the test roller. 

The following calibration procedure was used so that the two sources influencing the load 

cell output during testing could be separated. First the load cell was removed from the rig, 

calibrated using deadweights, and reinstalled on the test apparatus. Next, a LVDT was used to 

monitor the displacement of the motor plate. With no test roller installed on the output shaft, the 

air piston was used to move the motor plate through the full range of motion while recording the 

output of the calibrated load cell. In this manner the force as sensed at the load cell due to the 

unbalanced mass of the gimbaled motor plate was determined as a function of the motor plate 

position. Next, the end of the input shaft where the test roller is mounted was attached by a 

highly-rigid link to the apparatus frame. The rigid link included a calibrated reference load cell in 

the load path. The rigid link was carefully positioned to be oriented in the position and direction 

of the normal load created between the contacting test rollers. By increasing the pressure on the 

air-piston actuator, load was created on the rigid link and measured on the reference load cell. 

This procedure established the relationship of the normal load on the test roller acting through 

the gimbal point and resulting in a force imparted on the load cell located at the air piston. 

During testing both the motor table position and load cell force was recorded. From the table 

position data and calibration data, the force attributed to the unbalanced mass on the gimbaled 

motor plate could be subtracted from the force value recorded by the load cell. The value 

remaining from the load cell (after the subtraction operation) is due to the normal force between 

the test rollers, and via the calibration curve the load on the test roller is determined. 

When rollers operate in a misaligned condition a force will develop in the direction of the 

shaft axis (Refs. 2 to 6). In such a condition points on the two rollers in intimate contact and 

within a “stick” zone of the contact patch are constrained to move in unison. If the points were 

not in contact the kinematic constraints would provide a slightly different path of motion. The 

difference in the actual path of motion and that defined by the motion if the points were not in 

contact gives rise to surface strains and a resultant axial force. A sensor to measure this force is 

labeled as the “axial force” sensor in Figure 4. The axial force sensor is co-located on the output 

shaft with the torquemeter sensor. The configuration of the rig did not allow for direct 

deadweight calibration in place. To calibrate the sensor in place, the following procedure was 

used. First, a load cell was calibrated via deadweights and then was placed on the free end of 

the output shaft to act as a reference load cell. A threaded jackscrew acted against the 

reference load cell and a hard stop in the vacuum chamber. Adjusting the jackscrew length 

allowed for changing the force imparted on both the reference load cell and, the rig’s axial load 

cell and to the machine frame. In this manner the same force was applied to both load cells, and 

the reference cell output used to calibrate the axial load cell sensor in place. 
NASA/TM—2010-216741 6

The preceding two paragraphs describe the sensors (and sensor calibrations) to determine 

two mutually perpendicular forces acting on the driven test roller. A force also acts along a third 

axis. This is the force directed tangential to the roller diameter and is termed here as the 

“tangential” force. The tangential force on the input shaft roller acts through a gimbal point 

(Fig. 4(b)). The rotational motion about the gimbal point is restrained by a mechanical link to the 

turntable structure. There is a load cell load in the load path from said mechanical link to the 

turntable structure. This sensor was calibrated in place by using a pulley-cable system and dead 

weights to relate the tangential force applied at the test roller position to the sensor output. 

During testing, this sensor is also affected by spin moments (Ref. 2) that can develop in roller 

contacts. The data from the tangential force sensor was recorded for possible future use, but 

such data were not of immediate interest and are not reported herein. 

Shaft speeds and total number of shaft revolutions were measured using encoders on each 

shaft. The encoder pulses were counted and recorded via a digital pulse counter. The encoder 

pulses were also monitored by a frequency converter to provide a convenient shaft speed 

display to the test operator. The encoders provide 6,000 pulses for each shaft revolution. 

The pressure in the chamber was monitored by an ionization gauge at the top of the main 

test chamber. The typical pressure in the testing chamber during vacuum testing was 

5x10–6 torr. Vacuum is provided by a diffusion pump with a liquid nitrogen cold trap. The 

diffusion pump is assisted by a mechanical vacuum pump. The diffusion pump and cold trap 

arrangement prevents oil vapors from the mechanical vacuum pump to enter the test chamber 

so as to maintain the desired tribological test condition. 

Test Specimens 

The test specimens used for this research had a nominal geometry of 35.6 mm (1.4 in.) 

outer diameter and a 12.7 mm (0.5 in.) width. The roller on the drive motor (input) shaft was 

made from 15-5 alloy (matching the SARJ raceway material). The roller on the brake (output) 

shaft was 440C alloy, matching the SARJ roller material. A set of nitrided 15-5 rollers were 

manufactured to match the processing parameters of the SARJ ring. An additional set of 15-5 

rollers without nitriding were manufactured for research purposes. In the remainder of this 

document we use the term “un-nitrided” to refer to a 15-5 roller that does not have the nitride 

surface layer. The profile across the roller width for the 15-5 rollers was nominally flat. The 

mating 440C rollers used for this project had a crown radius profile across the roller width. For 

the test apparatus used, at least one of the two rollers must be crowned to have a controlled 

contact condition. The nominal crown radius of the 440C test rollers for this project was 

approximately 42 mm (1.65 in.). The 440C rollers had a measured surface hardness via a 

Rockwell tester of typically 56 HRC. The SARJ mechanism makes use of gold-plated rollers. A 

subset of the 440C rollers were provided with gold plating. All of the gold-plated test rollers were 

done in a single batch process. The plating vendor reported the applied gold layer thickness as 

2300 angstroms. 

A photograph of a pair of rollers installed and undergoing test is provided in Figure 6. The 

upper roller is a 15-5 roller with a nominally flat profile. The bottom roller is the 440C roller 

having a crown radius. The localized contact provided by the crowned roller is evident in 

Figure 6. 

To document the surface condition of the new rollers, rollers were inspected via a stylus 

profilometer using a diamond-tipped stylus. The data were processed to assess the roughness 

features. The roughness of a 440C roller was typically 0.14 m roughness-average. The 

roughness of a nitrided 15-5 roller was typically 0.62 m roughness-average. Plots of the 

roughness profile for a typical 440C and nitrided 15-5 roller are provided in Figures 7 to 8 

(note the differing automatic scaling used in these two figures). 
NASA/TM—2010-216741 7

Figure 6.—View of tested rollers in the test apparatus showing 

localization of the roller contact and crowned profile of the 

lower roller. 

Figure 7.—Typical roughness of a 440C roller. 

Figure 8.—Typical roughness of a nitrided roller. 
NASA/TM—2010-216741 8

Procedure to Install Test Rollers 

Test specimens were cleaned and installed using careful procedures to provide a clean test 

surface. The 15-5 test rollers were cleaned just prior to installation into the rig using de-ionized 

water and 0.05 m alumina powder. After appropriate hand scrubbing, the cleaning powder was 

rinsed with deionized water making sure that the entire roller surface wetted uniformly to confirm 

complete cleaning of surface oils. The water was removed from the roller using dried 

pressurized nitrogen. Bare (without gold-plating) 440C specimens were cleaned in the same 

manner as the 15-5 specimens. The 440C test rollers with gold-plating were vacuum-sealed in 

plastic bags by the plating vendor, and so cleaning with alumina powder was not needed. The 

bags remained closed until ready for installation. Test rollers and mounting hardware were 

handled only with gloved hands and clean tools to complete installation into the test apparatus. 

Procedure for Testing Rollers 

The first step for testing after installation of the test rollers was to immediately isolate the 

testing chamber and provide a vacuum, using the mechanical roughing pump, to approximately 

50x10–3 torr chamber pressure. This isolation step was done even if test scheduling required 

some delay between the time of installation of rollers and the time for testing to minimize 

exposure of the cleaned surfaces to any contaminants that might be present in the atmosphere. 

Just prior to testing the diffusion pump was energized and the pressure in the testing chamber 

established to approximately 5x10–6 torr. 

Some tests were done to investigate the influence of grease lubrication of the performance 

of the contacting rollers. For these tests the roller surfaces were lubricated using a spacequalified grease. The base oil of the grease is a stable perfluorinated polyether. The gelling 

agent is a tetrafluoroethylene telomer. The grease contains molybdenum disulfide. The grease 

was applied using a syringe. The difference in the mass of the syringe before and after applying 

the grease was 0.34 g. The grease was distributed on the rollers by positioning the rollers with 

only a small gap between them and the shafts were rotated. As the grease became distributed 

by the shaft rotation the gap between the rollers was slowly reduced in increments. This action 

proved effective to distribute the grease about the roller circumference, and by visual inspection 

the distribution of the grease about the roller circumference appeared uniform. 

Once rollers were installed and the chamber pressure test condition was established, the 

next step of the test procedure was to “run-in” the roller surfaces. In general contacting surfaces 

will quickly “run-in” via wear and deformation of asperity features. The test rig shaft 

misalignment angle was set to 1.5° and the rollers were brought into contact with approximately 

667 N (150 lb) normal force between the rollers. The test rig was operated for at least 1000 

shaft revolutions to run-in the test surfaces. 

The third step of the test procedure was to smoothly and continuously change the 

misalignment angle while recording data to investigate the traction capability of the contact. This 

step was done to establish the relationship of the misalignment angle to the developed axial 

force. The misalignment angle was changed by hand-turning of a threaded rod to rotate the 

turntable relative to the rig bedplate. The misalignment angle was swept from a position of 

approximately 1.5° to a position of –1.5°, and after a short pause the direction reversed and the 

angle adjusted again in a smooth fashion back to the starting angle of 1.5°. The angle 

adjustment occurred over a time of approximately 3 min. During these sweeps of the 

misalignment angle the magnetic-particle brake on the output shaft was not energized, and the 

recorded torque on the output shaft was in the range 0.8~1.2 N-m (7~11 in.-lb). The procedure 

to adjust the misalignment angle was repeated for 3 values of the normal load, approximately 

445, 667, and 890 N (100, 150, and 200 lb). 
NASA/TM—2010-216741 9

The preceding paragraphs described the procedure to investigate the behavior of the 

contact with small torque transmitted buy the roller pair. Next, a test was completed to assess 

the relationship of axial force as a function of the torque transmitted by the rollers for a condition 

of shaft misalignment of 1.5°. The rollers were the same roller pair as described in the preceding 

paragraph. The rig was operated at a speed of approximately 15 rpm. The test was done in 

vacuum of 5x10–6 torr. The normal load between the rollers was 436 N (98) lb. With the test 

operating, the braking torque on the output shaft was adjusted until the output shaft was at a 

near stall condition because of the high braking torque. The data was processed to determine 

the measured axial force as a function of the torque transmitted by the roller pair. 

Test Results 

Axial Force as a Function of Shaft Misalignment Angle 

Data were recorded and processed to determine the axial force created in the direction of the 

rotational axis of the output shaft as a function of the operating condition. The array of testing that 

was performed is documented in Table I. Each of the test conditions of Table I were repeated for 

3 levels of applied normal load, the targeted loads being 445, 667, and 890 N (100, 150, and 

200 lb). A Hertz contact analysis was completed for each of the three targeted load using the 

calculation method of Hamrock and Brewe (Ref. 7). The maximum calculated contact pressures 

for these loads are 1.55, 1.79, and 1.97 GPa (225,000, 260,000, and 285,000 psi), respectively. 

The measured loads (as opposed to the targeted test loads) were used for the processing and 

reporting of data and results. 

TABLE I.—TEST CONDITIONS 

Roller on input shaft Roller on output shaft Grease lubrication? Chamber condition 

un-nitrided 15-5 440C – no plating no vacuum 

un-nitrided 15-5 440C – no plating yes vacuum 

nitrided 15-5 440C – no plating no vacuum 

nitrided 15-5 440C – gold plating no vacuum 

nitrided 15-5 440C – no plating yes vacuum 

nitrided 15-5 440C – no plating no ambient air 

The axial force that developed in the contact was measured and plotted as a function of the 

misalignment angle. Figure 9 is a plot of data for the case of un-nitrided 15-5 roller with a 440C roller 

in a vacuum environment for three levels of normal load. The data has been plotted as a ratio of the 

measured axial force to the measured normal load as a function of shaft misalignment angle. The 

data shows that, for practical engineering purposes of this investigation, the functional relationship of 

the axial force/normal load ratio to shaft misalignment angle is not strongly influenced by changes in 

the normal load. To simplify the plotting and discussion of data, the results for the three levels of 

normal load were treated as a single dataset for the remainder of this report. 

The results of testing at three levels of normal load for the case of a 440C roller mated with a 

nitrided 15-5 roller and operated in a vacuum are provided in Figure 10. For the case of a bare 

(un-plated) 440C roller against a nitrided 15-5 roller and without lubrication, the axial force can be 

as great as 0.4 times the normal load for a shaft angle of 0.5°. Experiments and analysis done by 

others have shown that such a magnitude of force on a SARJ roller would cause roller tipping and 

contact pressures much greater than anticipated by the designers. However, for the same base 

materials but provided lubrication via a solid gold film or via grease, the axial force does not 

exceed about 0.2 times the normal load even for the largest misalignment angles tested. For 

practical purposes, for the case of lubricated rollers the maximum attainable axial force develops 

for shaft angles of about 0.5°. These test results highlight the critical role of lubrication for the 

SARJ mechanism. 
NASA/TM—2010-216741 10

Figure 9.—Ratio of axial load to normal load for three levels of normal load. Test conditions were 

nitrided 15-5 roller versus bare 440C (no plating) roller, no grease, in vacuum. 

Figure 10.—Axial force as a ratio of the normal load as a function of the shaft misalignment 

angle when testing nitrided rollers. The data were recorded as three levels of normal load 

(445, 667, and 890 N) {100, 150, and 200 lb}. 

misalignment angle (degrees)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

axial force / normal load

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

99 lb preload

149 lb preload

202 lb preload

440 N normal load

663 N normal load

899 N normal load

misalignment angle (degrees)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

axial force / normal load 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

gold plated 440C vs nitrided 15-5

bare 440C vs nitrided 15-5

bare 440C vs nitrided 15-5 with grease
NASA/TM—2010-216741 11

Figure 11.—Axial force as a ratio of the normal load as a function of the shaft misalignment 

angle when testing un-nitrided rollers. The data were recorded as three levels of normal load 

(445, 667, and 890 N) {100, 150, and 200 lb}. Data for nitrided rollers from Figure 10 are 

included for comparison. 

If the raceway of the SARJ mechanism becomes damaged, it is possible that the un-nitrided 

substrate will be exposed and will interact with the hardened 440C roller surface. Therefore, it 

was desired to study the case of un-nitrided material mating with 440C rollers in a vacuum 

environment. The results of these tests with the un-nitrided material are provided in Figure 11. 

The data for nitrided roller is also provided on the chart for comparison. The axial force that 

develops for the case of un-nitrided versus 440C with no lubrication is somewhat less than can 

be obtained for the nitrided surfaces. Still, with no lubrication the axial force can be high, an 

undesirable condition for the SARJ mechanism. Providing grease lubrication to the un-nitrided 

15-5 material greatly reduces the maximum attainable axial force with the value limited to about 

10 percent of the applied normal load. Comparing the data for testing with grease (Figs. 10 and 

11), regardless of the nitrided or un-nitrided condition the functional relationship of axial load to 

shaft angle is approximately the same, and the axial force is limited to about 15 percent of the 

normal load. 

Certain testing of the full-scale SARJ mechanism was done in an air environment. To 

provide some insight about the relative behavior of rollers operating in vacuum or air, a set of 

tests were conducted in air using a bare 440C roller and a nitrided 15-5 roller with no lubrication. 

The testing was done for 3 levels of normal load (445, 667, and 890 N), {100, 150, and 200 lb}. 

The results of the testing are provided in Figure 12. The maximum attainable axial force is 

slightly less when testing in air as opposed to testing in vacuum. The test was conducted using 

a pair of rollers that was first exposed to vacuum for testing and then exposed to air for 

approximately 20 min before starting the testing. It is recognized that this lab procedure does 

not necessarily recreate the surface condition of the SARJ mechanism during full-scale testing. 

The test data show that high magnitudes of axial force can be created when operating 440C 

rollers against nitrided 15-5 rollers in air. 

misalignment angle (degrees)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

axial force / normal load 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

bare 440C vs nitrided 15-5

bare 440C vs un-nitrided 15-5

bare 440C vs un-nitrided 15-5 with grease
NASA/TM—2010-216741 12

Figure 12.—Axial force as a ratio of the normal load as a function of the shaft misalignment 

angle when testing nitrided rollers in vacuum and in air. The data were recorded as three 

levels of normal load (445, 667, and 890 N) {100, 150, and 200 lb}. 

The data of Figures 9 to 12 provide insight about the operation of the SARJ mechanism. 

Large axial forces can develop even for small magnitudes of shaft misalignment. These axial 

forces in the case of the SARJ mechanism act via a pivot point in the housing to produce nonuniform contact pressures across the roller width, and if the forces are of sufficient magnitude 

can cause roller tipping. The experiments and data demonstrate the critical role of good 

lubrication. The gold films provided good lubrication for the short duration testing done and 

reported herein. It was noted that the gold did wear away during testing, and by cursory visual 

inspection the gold appeared to have been removed for the contact path. However, the axial 

forces remained low indicating good lubrication. Close inspection of the rollers after removal 

from the rig with the aid of magnification revealed that the gold, while depleted in depth and 

coverage, was not completely worn away during these tests. The grease lubrication limited the 

magnitude of the axial forces that could develop to even smaller magnitudes than was achieved 

with the gold-film lubrication. 

Axial Force as a Function of Braking Torque With Shaft Misalignment 

The data results presented in the previous section was for the condition of a small amount of 

torque transmitted by the rollers. To gain additional insight about the behavior of rollers in 

contact with shaft misalignment, a test was completed to assess the relationship of axial force 

as a function of the torque transmitted by the rollers for a condition of shaft misalignment of 

1.5°. The rollers used for this test were a bare 440C roller and a previously run nitrided 15-5 

roller. The rig was operated at a speed of approximately 15 rpm. The test was done in vacuum 

of 5x10–6 torr. The normal load between the rollers was 434 N (98 lb). With the test operating, 

the braking toque on the output shaft was steadily increased. The axial force (normalized to the 

normal load) as a function of the braking torque applied to the output shaft is provided in 

Figure 13. As the braking torque increased, the axial force decreased as should be expected 

and will be explained in discussion to follow. The axial force changes in a non-linear fashion 

with respect to the braking torque on the output shaft. The contacting region between the rollers 

includes both a stick and slip zones. The transition from stick to slip depends on the total 

misalignment angle (degrees)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

axial force / normal load 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

bare 440C vs nitrided 15-5 in vacuum

bare 440C vs nitrided 15-5 in air
NASA/TM—2010-216741 13

Figure 13.—Axial force as a ratio of the normal load as a function of braking torque applied 

to the output shaft for a bare 440C roller and a nitrided 15-5 roller operating in vacuum at 

15 rpm. 

traction force comprised of two orthogonal components, the axial and tangential forces. The 

application of additional braking torque increase the tangential component of the traction force 

and thereby alters the contact conditions, with the stick zones decreasing in size and the slip 

zones increasing in size. This test highlights that the axial force that develops when shafts are 

misaligned at small angles is largely the result of strains that develop in the stick region of the 

contact. The total traction force that can be supported by the contact is limited by the frictional 

condition of the mating surfaces. As was highlighted in the previous section, lubrication limits 

the total traction capability of the contact and thereby limits the magnitude of the axial force in 

response to shaft misalignment. 

The trends of the data of Figure 13 demonstrate that the axial force to normal load ratio 

investigated herein, although having a mathematical form matching that of coefficient of friction, 

is not a direct measure of the coefficient of friction of the contacting surfaces. The friction 

condition indeed plays a primary role influencing the behavior of the contact. The axial force to 

normal load ratio is also influenced by the design details and by the operating conditions 

including the torque transferred by the roller. 

Summary 

A set of experiments were done using roller pairs to understand and quantify the forces that 

can develop for a variety of test conditions. The materials and test conditions were selected to 

help understand the behavior of the SARJ mechanism. Tests were done using hardened 440C 

rollers mated with 15-5 rollers, the 15-5 rollers being both in nitrided and bare (not nitrided) 

condition. Tests were done with no lubrication, solid gold-film lubrication, and grease lubrication. 

Of great significance to the operation of the SARJ mechanism is the magnitude of the axial 

force that will develop because of shaft misalignment. The experiments demonstrate the critical 

role of good lubrication for the SARJ mechanism. The following specific results were obtained: 

braking torque (N-m) 

0123456

axial force / normal load

0.0

0.1

0.2

0.3

0.4

0.5

0.6
NASA/TM—2010-216741 14

1. For the case of a bare (un-plated) 440C roller against a nitrided 15-5 roller without 

lubrication, the axial force can be as great as 0.4 times the normal load for a shaft angle 

of 0.5°. Experiments and analysis done by others have shown that such a magnitude of 

force on a SARJ roller would cause roller tipping and contact pressures much greater 

than anticipated by the designers. 

2. The axial force for the case of bare (un-plated) 440C versus un- nitrided 15-5 with no 

grease is somewhat less than can be obtained using the nitrided 15-5 surfaces. Still, 

with no lubrication the axial force can be high, an undesirable condition for the SARJ 

mechanism. 

3. For the case of a gold-plated 440C roller against a nitrided 15-5 roller without grease, 

the axial force does not exceed about 0.2 times the normal load even for the largest 

misalignment angles tested. 

4. For the case of a bare (un-plated) 440C roller against a nitrided 15-5 roller with grease 

lubrication, the axial force does not exceed about 0.15 times the normal load even for 

the largest misalignment angles tested. 

5. The experiments and data demonstrate the critical role of good lubrication. The gold 

films provided good lubrication for the short duration testing done and reported herein. 

Grease lubrication limited the magnitude of the axial force to even smaller magnitudes 

than was achieved with the gold-film lubrication. 

6. For the case of a bare (un-plated) 440C roller against a nitrided 15-5 roller without 

lubrication, the maximum attainable axial force was slightly less when testing in air as 

opposed to testing in vacuum.

References 

1. Loewenthal, S. and Schuller, F., “Feasibility study of a discrete bearing/roller drive rotary 

joint for the Space Station,” NASA Technical Memorandum 88800, 1986. 

2. Johnson, K.L., Contact Mechanics, Cambridge University Press, 1985. 

3. Kalker, J.J., “Rolling contact phenomena: linear elasticity,” Rolling Contact Phenomena 

CISM Courses and Lectures, Issue: 411, Springer-Verlag, 2000. 

4. Woody, D. and Lamb, W., “A design for a precision 10-m sub-millimeter antenna,” ALMA 

Memo 241, Mar 1999. http://www.mma.nrao.edu/memos/html-memos/alma241/ 

memo241a.pdf, accessed Feb. 26, 2009. 

5. McGinness, H., “Antenna azimuth bearing model experiment,” DSN Progress Report 

42–53, July and August 1979, Jet Propulsion Laboratory, Pasadena, Calif., 1979. 

6. McGinness, H., “Lateral forces induced by a misaligned roller,” DSN Progress Report 

42–45, March and April 1978, Jet Propulsion Laboratory, Pasadena, Calif., 1978. 

7. Hamrock, B., and Brewe, D., “Simplified Equation for Stresses and Deformations,” 

ASME J. Lubr. Technol., 105, pp. 171–177, 1983. 
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Experimental Investigation of Forces Produced by Misaligned Steel Rollers 

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Krantz, Timothy; DellaCorte, Christopher; Dube, Michael 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The International Space Station (ISS) Solar Alpha Rotary Joint (SARJ) uses a roller-based mechanism for positioning of the solar arrays. 

The forces and moments that develop at the roller interfaces are influenced by the design including the kinematic constraints and the 

lubrication condition. To help understand the SARJ operation, a set of dedicated experiments were completed using roller pairs. Of primary 

interest was to measure the axial force directed along the axis of rotation of the roller as a function of shaft misalignment. The conditions 

studied included dry and clean surfaces; one surface plated by a gold film, and greased surfaces. For the case of a bare 440C roller against a 

nitrided 15-5 roller without lubrication, the axial force can be as great as 0.4 times the normal load for a shaft angle of 0.5°. Such a 

magnitude of force on a roller in the SARJ mechanism would cause roller tipping and contact pressures much greater than anticipated by the 

designers. For the case of a bare 440C roller against a nitrided 15-5 roller with grease lubrication, the axial force does not exceed about 0.15 

times the normal load even for the largest misalignment angles tested. Gold films provided good lubrication for the short duration testing 

reported herein. Grease lubrication limited the magnitude of the axial force to even smaller magnitudes than was achieved with the gold 

films. The experiments demonstrate the critical role of good lubrication for the SARJ mechanism.

15. SUBJECT TERMS

Rollers; Lubrication; Kinematics 

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