**1. Introduction**

92 Performance Evaluation of Bearings

III-104.

[24] Šooš, Ľ. New methodology calculations of radial stiffness nodal points spindle machine tool. In: International symposium on Advanced Engineering & Applied Management - 40th Anniversary in Higher Education: Romania /Hunedoara/ 4-5 November, 2010. - Hunedoara: Faculty of Engineering Hunedoara, 2010. - ISBN 978-973-0-09340-7. - III-99 -

> Rolling elements, such as ball bearings and races, contain surface imperfections known as asperities. The height of surface asperities may be quantified through surface roughness analyses, which assigns a Ra number related the characteristics of the surface and asperities. The depth and width of the valleys between asperities is one significant characteristic of a surface that influences wear, friction, and contact fatigue life of the rolling element.

> Surface lubrication may be divided into three categories: i) full film, ii) boundary layer, and iii) mixed film and boundary lubrication (Bhushan, 1999). With full film lubrication, the film is sufficiently thick so that surface asperities do not protrude through the film and will not contact the mating surface. Boundary lubrication describes the condition in which a film is present, but load is transferred between asperity peaks on the surfaces and not the film. Mixed lubrication conditions assume that both film and asperity transmit contact load, and therefore both must be considered in the analysis. A numerical approach capable of modeling all three types using fluid lubrication may be found in (Hu and Zhu, 2000). The proposed model is found to work well over a specific range of film-thickness-ratios and surface RMS roughness.

> The need to quickly determine the fatigue life of rolling elements has given rise to rolling contact fatigue test methods that enable fatigue testing at reduced cost. Historically, RCF tests have used petroleum-based liquid-lubricants, which restrict rotational speed of the test due to liquid-lubrication churning. In comparison, RCF testing using solid film lubricants in ultra-high vacuum enables higher rotational speeds leading to test results in less time. For example, a rod composed of a candidate bearing material may accumulate over 10 million stress cycles in a few days running at 130Hz in ultra-high vacuum. The exact number of stress cycles accumulated on the rotating elements will depend on the specifics of the test configuration, such as ball diameter, rod diameter, and the number of balls present. In contrast, RCF testing in air using oil based liquid-lubrication is speed limited, usually to 60 Hz or less, and is limited to a maximum of three ball-contact elements. RCF testing in air using liquid-lubrication requires more time to accumulate the same number of stress cycles.

© 2012 Danyluk and Dhingra, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Danyluk and Dhingra, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Rolling contact bearings may have multiple and diverse layers of gaseous molecules accumulated on their surface that can significantly influence friction and wear behavior. Physisorption and chemisorption of external molecules on to the substrate surface effect wear and friction, particularly for thin-films used in high vacuum conditions. Surface texture has a significant influence on wear and friction behavior as well since it determines the nature of contact. Physisorption layers of atoms involve weak Van dar Waals bonds. These layers can begin to detach from the substrate at pressures below 10-4 Pa in a process described as surface out-gassing. The energy to initiate physisorption outgassing is roughly 1-2 kCal/mol. Physisorbed layers of atoms do not share electrons with surface atoms and therefore may be easily removed when heat is applied in vacuum conditions. Chemisorbed layers however do share electrons with surface atoms and these bonds can be very strong with an associated energy of 10-100 kCal/mol. Physisoption occurs on all surfaces when exposed to air while chemisorption requires a chemical reaction with the substrate surface and is therefore heavily influenced by surface chemistry.

Rolling Contact Fatigue in Ultra High Vacuum 95

compliant layer to reduce subsurface stress, or, a hard and stiff layer to increase wear resistance. The effective hardness of a thin solid film system is influenced by the hardness of its layers and substrate along with the elastic-plastic behavior of the coating system. If the film is very thin then the effective hardness is mostly influenced by substrate hardness, leading to an optimized lubricant coating that is thin and soft, applied over a hard-stiff coating bonded to the substrate. The soft lubricant reduces subsurface stress and the hard

Solid to solid contact results in two broad categories of surface bonding: adhesive and cohesive. Cohesive bonding takes place in the bulk material and has chemical interactions with covalent bonding, metallic bonding, and ionic and electrostatic bonding. Adhesive bonding involves two dissimilar surfaces and includes physical interactions and Van der Waals bonding. Adhesion is a function of material combination, crystal structure, surface condition, ambient temperature, and crystallographic orientation. Indeed, good adhesion is desired between the solid film lubricant and the surface of the rolling element, and very

The technology of solid lubricants grew rapidly during the 1960s and 70s to meet the needs of the aerospace industry and for operation in ultra-high vacuum environment. Silver, gold, and lead along with compounds like MoS2 and graphite were needed for environments in which liquid oil-based and hydrocarbon out gassing could not be tolerated, such as, rotating devices within very high electrical potential or inside space satellite guidance equipment. Test equipment used to gather tribology data for solid lubrication systems were developed through NASA, and industry leaders such as Timken, Du Pont, and General Dynamics to name a few. Platforms were developed for high vacuum and high temperature applications that involved sliding-contact, rolling-contact ball bearings, metal disk and riders, and sliding contact of a sleeve on a cylindrical rod and may be found in (NASA SP-5059, 1972).

Solid lubricants find unique application in systems with an operating pressure range of 10-4 to 10-9 Pa and are also temperature resistant in high vacuum. Rotating anode x-ray tubes that use ball bearing elements are one example of a rolling contact configuration under high vacuum and at high temperature. Non-volatile thin-film lubrication is required due to operation in vacuum and in the presence of high electrical potential. Solid lubrication systems are greatly influenced by process history and operating conditions. It is strongly suggested that testing and evaluation involving any solid film be done using equipment known to correlate with the specific application for which the coating system is being considered. RCF testing of coating systems and ball-bearing materials is one example of a

Matthews et al. (2007) report that thin film coating survival is most dependent on adhesion and substrate subsurface bonding. Surface studies at the nano scale suggest that friction begins at the atomic level through mechanical vibrations within the lattice structure of the

little cohesion is desired within the solid lubricant itself to reduce friction.

Each of these test platforms was designed to test a specific load situation.

test method that closely simulates rolling element bearing systems.

**1.1. Current research** 

and stiff coating increases wear resistance.

Hertzian contact analysis considers the deformation of two elastic solid surfaces with the following assumptions: i) the surfaces are smooth, continuous, and nonconforming to each other, ii) the strains are small in the contact area, iii) each solid can be modeled as an elastic half space in the proximity of the contact, and iv) the surfaces are frictionless. The two contacting surfaces can be of general shape, but most often they are chosen to be convex. Maximum shear stress occurs below the surface in the location of the contact. The depth of maximum shear stress is related to the radius of curvature and Poisson ratio of the substrate material. For example, Hertzian contact analysis applied to a material with Poisson's ratio of 0.3 is calculated to have maximum shear stress at a depth of 0.48 times the radius of the contact. Maximum compressive stress occurs at the point of contact. Maximum tensile stress takes place just beyond the edge of the contact area on the surface. Considering RCF loading conditions, subsurface cracking that eventually leads to surface spall and flaking begins at the location of maximum shear stress below the surface of the ball. If a thin film is present, an interfacial spall may result at the location of either maximum compressive or tensile stress, while subsurface cracking will occur within the substrate below the contact zone.

Understanding wear and friction requires knowledge of the type of contact between the two solid bodies. Incipient sliding occurs when two contacting bodies are pressed together such that a stick-point exists within the contact area and materials from each body slide relative to each other about that point. There is no imposed relative motion between the bodies during incipient sliding condition, rather sliding occurs due to elastic deformation of each surface around the stick-point. Friction between rolling contact elements is proportional to the shear strength of the base materials. Stresses in the contact area greater than the yield stress of the material are possible due to compression at the point of contact.

One of the benefits of solid lubricant coatings such as silver, lead, gold, and MoS2 is their low shear strength to reduce subsurface stresses during incipient sliding. The compliant nature of these solid film lubricants helps to reduce subsurface stress by reducing shear loading in the substrate. However, if increased wear resistance is desired, then a hard and stiff layer is preferred which presents a trade-off when selecting a coating system: soft compliant layer to reduce subsurface stress, or, a hard and stiff layer to increase wear resistance. The effective hardness of a thin solid film system is influenced by the hardness of its layers and substrate along with the elastic-plastic behavior of the coating system. If the film is very thin then the effective hardness is mostly influenced by substrate hardness, leading to an optimized lubricant coating that is thin and soft, applied over a hard-stiff coating bonded to the substrate. The soft lubricant reduces subsurface stress and the hard and stiff coating increases wear resistance.

Solid to solid contact results in two broad categories of surface bonding: adhesive and cohesive. Cohesive bonding takes place in the bulk material and has chemical interactions with covalent bonding, metallic bonding, and ionic and electrostatic bonding. Adhesive bonding involves two dissimilar surfaces and includes physical interactions and Van der Waals bonding. Adhesion is a function of material combination, crystal structure, surface condition, ambient temperature, and crystallographic orientation. Indeed, good adhesion is desired between the solid film lubricant and the surface of the rolling element, and very little cohesion is desired within the solid lubricant itself to reduce friction.

The technology of solid lubricants grew rapidly during the 1960s and 70s to meet the needs of the aerospace industry and for operation in ultra-high vacuum environment. Silver, gold, and lead along with compounds like MoS2 and graphite were needed for environments in which liquid oil-based and hydrocarbon out gassing could not be tolerated, such as, rotating devices within very high electrical potential or inside space satellite guidance equipment. Test equipment used to gather tribology data for solid lubrication systems were developed through NASA, and industry leaders such as Timken, Du Pont, and General Dynamics to name a few. Platforms were developed for high vacuum and high temperature applications that involved sliding-contact, rolling-contact ball bearings, metal disk and riders, and sliding contact of a sleeve on a cylindrical rod and may be found in (NASA SP-5059, 1972). Each of these test platforms was designed to test a specific load situation.

Solid lubricants find unique application in systems with an operating pressure range of 10-4 to 10-9 Pa and are also temperature resistant in high vacuum. Rotating anode x-ray tubes that use ball bearing elements are one example of a rolling contact configuration under high vacuum and at high temperature. Non-volatile thin-film lubrication is required due to operation in vacuum and in the presence of high electrical potential. Solid lubrication systems are greatly influenced by process history and operating conditions. It is strongly suggested that testing and evaluation involving any solid film be done using equipment known to correlate with the specific application for which the coating system is being considered. RCF testing of coating systems and ball-bearing materials is one example of a test method that closely simulates rolling element bearing systems.

## **1.1. Current research**

94 Performance Evaluation of Bearings

and is therefore heavily influenced by surface chemistry.

Rolling contact bearings may have multiple and diverse layers of gaseous molecules accumulated on their surface that can significantly influence friction and wear behavior. Physisorption and chemisorption of external molecules on to the substrate surface effect wear and friction, particularly for thin-films used in high vacuum conditions. Surface texture has a significant influence on wear and friction behavior as well since it determines the nature of contact. Physisorption layers of atoms involve weak Van dar Waals bonds. These layers can begin to detach from the substrate at pressures below 10-4 Pa in a process described as surface out-gassing. The energy to initiate physisorption outgassing is roughly 1-2 kCal/mol. Physisorbed layers of atoms do not share electrons with surface atoms and therefore may be easily removed when heat is applied in vacuum conditions. Chemisorbed layers however do share electrons with surface atoms and these bonds can be very strong with an associated energy of 10-100 kCal/mol. Physisoption occurs on all surfaces when exposed to air while chemisorption requires a chemical reaction with the substrate surface

Hertzian contact analysis considers the deformation of two elastic solid surfaces with the following assumptions: i) the surfaces are smooth, continuous, and nonconforming to each other, ii) the strains are small in the contact area, iii) each solid can be modeled as an elastic half space in the proximity of the contact, and iv) the surfaces are frictionless. The two contacting surfaces can be of general shape, but most often they are chosen to be convex. Maximum shear stress occurs below the surface in the location of the contact. The depth of maximum shear stress is related to the radius of curvature and Poisson ratio of the substrate material. For example, Hertzian contact analysis applied to a material with Poisson's ratio of 0.3 is calculated to have maximum shear stress at a depth of 0.48 times the radius of the contact. Maximum compressive stress occurs at the point of contact. Maximum tensile stress takes place just beyond the edge of the contact area on the surface. Considering RCF loading conditions, subsurface cracking that eventually leads to surface spall and flaking begins at the location of maximum shear stress below the surface of the ball. If a thin film is present, an interfacial spall may result at the location of either maximum compressive or tensile stress,

while subsurface cracking will occur within the substrate below the contact zone.

stress of the material are possible due to compression at the point of contact.

Understanding wear and friction requires knowledge of the type of contact between the two solid bodies. Incipient sliding occurs when two contacting bodies are pressed together such that a stick-point exists within the contact area and materials from each body slide relative to each other about that point. There is no imposed relative motion between the bodies during incipient sliding condition, rather sliding occurs due to elastic deformation of each surface around the stick-point. Friction between rolling contact elements is proportional to the shear strength of the base materials. Stresses in the contact area greater than the yield

One of the benefits of solid lubricant coatings such as silver, lead, gold, and MoS2 is their low shear strength to reduce subsurface stresses during incipient sliding. The compliant nature of these solid film lubricants helps to reduce subsurface stress by reducing shear loading in the substrate. However, if increased wear resistance is desired, then a hard and stiff layer is preferred which presents a trade-off when selecting a coating system: soft

Matthews et al. (2007) report that thin film coating survival is most dependent on adhesion and substrate subsurface bonding. Surface studies at the nano scale suggest that friction begins at the atomic level through mechanical vibrations within the lattice structure of the substrate. Substrate material properties influence spall behavior and RCF life as well. Microtribology considers the mechanics of cracks and fracture in the material at the asperity level. Berthier et al. (1989) consider velocity differences between contact surfaces and suggests four mechanisms to accommodate these differences: elastic deformation, fracture, shear stress, and rolling contact. They report that although hard coatings are preferred for wear resistance, the addition of a thin compliant film that includes nano scale hard elements in the solid lubricant reduces friction as well.

Rolling Contact Fatigue in Ultra High Vacuum 97

A review of the current literature indicates that ball-on-rod RCF testing in high vacuum and at high speeds (approaching 130 Hz) has not received much attention; the work presented here is meant to fill that gap related to high speed RCF testing of tribology coatings. A thirdbody approximation that accounts for coating wear has been implemented as well for aid to predict test life based on contact stress. A Lundberg-Plamgren empirical model is also presented for comparison with the third-body approximation model. Surface and coating diagnostic tools are presented to show the relationship between coating composition and

The RCF test rig in Figure 1 was assembled using off the shelf components purchased from leading vacuum and mechanical equipment vendors (Danyluk and Dhingra, 2012a). For example, a KollmorgenTM servo motor (model number AKM21E) is used to rotate the rod. The drive motor is mounted underneath the chamber and motor torque is delivered to the test rod inside the vacuum chamber using a ferro-fluidic rotary feed-through device similar to Kurt J. Lesker VacuumTM part number FE121099. High vacuum is applied using a

VarianTM V-81M turbo pumping system as shown in the right panel of Figure 1.

**Figure 1.** Support hardware and UHV-RCF chamber: turbo pumping system, residual gas analyzer,

The RCF hardware inside the chamber is a modification of the three-ball-rod test rig of reference (Hoo 1982). The test-head hardware components were fabricated from 304L stainless steel and are positioned inside the UHV chamber as shown in Figure 2c. A component view of the test chamber is shown in Figure 2a, with emphasis on hardware type and assembly order. The RCF test elements: the balls, rods, and races, are shown in Figure 2b. The races are press fit into the test fixture and held stationary while the balls rotate between the fixed races and the rotating rod. A typical test consumes 5 or 6 balls depending on which ball size is used: 12.7 mm or 7.94 mm. For example, when testing with 12.7 mm diameter balls as shown in Figure 2c, five balls, two races and one rod will constitute a test.

servo motor drive, and ferro-fluidic rotary feed through.

**1.2. Chapter overview** 

**2. Experimental procedure** 

RCF life.

Sadeghi et al. (2009) report that subsurface failures usually occur during RCF testing due to fatigue. If a rolling element such as a ball-bearing is kept lubricated and clean, then the primary failure mode will be subsurface spall from fatigue. Fatigue failure beneath the substrate surface is thought to proceed as follows: i) work hardening, ii) elastic response, iii) material softening leading to yield. In a solid lubrication system that uses silver for example, work hardening of the substrate occurs within the run-in period in addition to silver transfer between the surfaces. If there is a sufficient amount of silver, the test will operate in the elastic response regime for as long as the silver is present. Material softening results in a larger volume of material that has yielded plastically. Plastic yielding begins the onset of subsurface cracking which then propagates to the surface resulting in a spall. Cracks and the onset of spall may also originate from inclusions or material defects, which, helps to explain the huge scatter in RCF life test data.

Polonsky et al. (1998) confirm two types of RCF failures related to composite coatings: subsurface-initiated spall and near-surface coating failure. They report coating-cohesive failure of 750 nm thick TiN running against softer 12.7 mm diameter ANSI M50 steel balls due to interface initiated spall in the TiN coating. Rosado et al. (2010) sought more understanding of the spall growth process once a spall has occurred and identify material parameters to optimize and improve spall growth resistance. For contact stress of 2.41 GPa, they report slower spall growth in ANSI M50 compared with either ANSI M50NiL or ANSI 52100 due to material composition and processing. Danyluk and Dhingra (2011) observe two types of failures related to RCF testing in ultra-high vacuum: coating depletion and surface spall. Solid film nickel-copper-silver lubrication was applied to ball bearings over a range of process voltage and pressure using a physical vapor deposition ion plating process. Coating depletion and surface spall failures were the two most common failure modes, and a unique spall-related non-precession type failure was also observed. The non-precession failure mode was associated with higher process voltages and with reduced RCF life.

Higgs and Wornyoh (2008) use conservation of mass to model an in-situ mechanism for self replenishing powder lubrication on sliding contacts. Application of Archard's wear law and a third-body concept are used to formulate the conservation mass equation. The controlvolume-fraction-coverage (CVFC) model concept is applied to set the bounds of their theoretical approach. Wornyoh and Higgs (2011) extend the work of (Higgs and Wornyoh, 2008) to an asperity-based fractional coverage (AFC) model derivation and analysis. The latter AFC model extends the surface applicability to tribo-surfaces using atomic force microscopy that enable inclusion of surface topology information in the film transfer model.
