ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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After continued running, some of the cracks may propagate further into the surface. The exact mechanism that

allows some cracks to propagate, while most remain arrested, is probably related to nonmetallic inclusions

providing stress risers, but it could also be related to more severe interaction of the surfaces in localized areas

(scuffing) or the action of the lubricant. As cracks progress further into the surface, larger chunks of material

can break away, leaving larger cavities. When cavities have grown from the size of exfoliation up to about 100

μm (0.004 in.) deep, the condition is termed micropitting. The term frosting sometimes is applied to this

condition as well. For critical applications, the occurrence of micropitting over a significant area is considered

failure. A gear in this condition is shown in Fig. 3.

Fig. 3 Specimen gear with micropitting (frosting) failure

As cracks progress further into the surface, the rate of propagation increases. This increase is related in part to

lubricant (under contact pressure) being forced into the crack and wedging it further open, but it mostly is due

to the higher shear stresses produced by the contact load. At some point below the surface, in the region of 100

to 500 μm (0.004 to 0.020 in.) or deeper, depending on contact geometry, shear stresses produced by the contact

loading become high enough to promote rapid crack propagation. Progressively larger pieces break away from

the surface, leaving yet larger cavities. This condition is termed pitting or macropitting. The material is torn

away from the damaged area by the relative motion of the contacting part; thus, the cavity becomes wider and

deeper in the direction opposite to sliding, leading to an arrow shape. Figure 4 illustrates a gear with an arrow-

shaped surface origin pit at this stage. As pits become larger, they eventually cause a readily detectable increase

in dynamic loads. A loss of material that reaches this level is frequently termed spalling and is considered

failure.

Fig. 4 Specimen gear with arrow-shaped surface origin pit

Subsurface origin pitting typically occurs only in cases where the elastohydrodynamic lubricant film thickness

is great enough to prevent significant asperity interaction. This pitting occurs in high-speed power gearing and

in aerospace power drives. It is also typical in antifriction bearings (which operate with pure rolling as at the

pitch diameter on spur gears). The origin is typically a nonmetallic inclusion or discontinuity in the structure, in

the area of highest shear stress (about 100 to 500 μm, or 0.004 to 0.020 in.) below the surface. Crack

propagation is initially quite slow, until a crack penetrates the surface, allowing lubricant to enter. It can be

difficult to tell the difference between surface and subsurface origin pits, although subsurface origin pits often

do not have the arrow shape typical of surface origin pits. As with surface origin pits, when the pit becomes

large enough to cause a readily detectable increase in noise and vibration, it is considered a failure. Because

most pits start small and progressively grow large, some critical high-speed drives incorporate a chip detector in

the lubrication system to provide advance warning of imminent failure.

Failure Modes in Root Fillets

Failure of the gear tooth also can occur in the root fillet. This failure is primarily due to bending fatigue but can

be precipitated by sudden overloading (impact). Sudden overloads can be caused by a large foreign object (e.g.,

a broken tooth) being drawn through the mesh, the driving or driven shafts suddenly stopping, or sudden loss of

alignment (failure of an adjacent bearing).

Bending Fatigue. The origins of bending fatigue failures typically are imperfections in the surface of the root

fillet (e.g., tooling “witness” marks) or nonmetallic inclusions near the surface. Cracks slowly propagate around

the origin until they reach the critical size for the case material at the prevailing stress level. For hardened high-

carbon material typically used for gears, when the crack reaches this critical size, it “pops” through the case

(i.e., the entire case fractures). At this point, the rigidity of the tooth is reduced (compliance increases), and

dynamic load increases significantly. This produces a readily detectable increase in noise and vibration and

represents failure.

In many rig tests it is impossible to stop the rig quickly enough, once cracking is detected, to prevent complete

fracture of the tooth and potential jamming of the test rig. This limitation causes some reluctance to conduct

bending fatigue tests in high-speed power-circulating gear test rigs. However, with some transmission designs

there is enough time between the onset of increased vibration and catastrophic failure for a vibration monitoring

system to give sufficient warning to permit an orderly shutdown of the equipment. The mechanism that allows

this shutdown is the reduced compliance of the cracked tooth, which transfers some of the load to adjacent

teeth. The lower load and the lower hardness of the core results in slower crack propagation, allowing a brief

interval between the occurrence of detectable cracking and fracture of the tooth. This feature notwithstanding,

tooth fracture is a potential catastrophic form of gear failure, and a substantial portion of gear test programs are

dedicated to obtaining sufficient data to minimize its occurrence in service. In some gear designs (such as thin

rims), cracks can propagate into the rim area. Rim fracture is the most catastrophic form of gear failure and

should always be avoided.

Impact fracture of a gear tooth occurs in one loading cycle. The impetus for studying impact properties of gear

steels is to ensure that steels used in gears have enough impact resistance to prevent failure when gears are

subjected to normal spike loads.

References cited in this section

1. E.E. Shipley, “Failure Modes in Gears,” presented at Forum on Gear Manufacture and Performance, 19

Oct 1973 (Detroit), American Society of Mechanical Engineers

2. D.W. Dudley, Gear Wear, Wear Control Handbook, M. Peterson and W. Winer, Ed., American Society

of Mechanical Engineers, 1980

3. G. Niemann and H. Winter, Getriebeschäden und Abhilfe, Entwicklungstendenzen, Maschinen-

elemente, Vol 2, 2nd ed., Springer-Verlag (Berlin), 1983

4. “Appearance of Gear Teeth—Terminology of Wear and Failure,” ANSI/AGMA 1010-E95, American

National Standards Institute/American Gear Manufacturers Association

5. R. Errichello, Friction, Lubrication, and Wear of Gears, Friction, Lubrication, and Wear Technology,

Vol 18, ASM Handbook, ASM International, 1992, p 535–545

6. L. Alban, Systematic Analysis of Gear Failures, American Society for Metals, 1985

Mechanical Testing of Gears

Douglas R. McPherson and Suren B. Rao, Applied Research Laboratory, The Pennsylvania State University

Stress Calculations for Test Parameters

Gear-rating standards, such as American National Standards Institute (ANSI)/American Gear Manufacturers

Association (AGMA) 2001-C95 (“Fundamental Rating Factors and Calculation Methods for Involute Spur and

Helical Gear Teeth”) and International Organization for Standardization (ISO) 6336, base gear performance on

contact and bending stresses. Nominal stresses are determined from first principles and are then modified to

allow for the realities of manufactured gears running in actual gearboxes. This modification approximates a

reasonable upper limit for the range of stress variation.

ANSI/AGMA 2001-C95 contains factors in the fundamental stress formulas for contact and bending to address

overload, gear dynamics, size, load distribution, surface condition (contact only), and rim thickness (bending

only). Design-allowable stress numbers are modified by further factors that address intended life, operating

temperature, reliability, safety factor, and hardness ratio (contact only). It is normal practice in determining

stresses to be reported with rig test results to take all of these factors as unity. The intent of rig testing is to

compare the effect of various attributes or characteristics on performance. Thus, it is reasonable to determine

the actual stress based on a value of unity for each factor, then determine suitable values for the factors based

on test results.

The factors that are in essence being ignored by this approach represent real phenomena that occur as gears

operate. It is critical to address this fact in the design of test rigs and in their day-to-day operation. For example,

it is important to conduct tests in a manner that precludes overloading; in a set of tests intended to evaluate the

effect of overloading, only controlled overloads can be permitted. Most of the other factors can be handled in

the same manner. However, gear dynamics and load distribution need to be addressed in a more direct fashion

because they both can introduce uncontrolled variation in a set of test results.

Gear dynamics present a problem in determining the proper stress to be related to performance. Rating

standards provide guidance on dynamic load variations in normal gearboxes. Gear test rigs, as described here,

load one gearbox against another to keep power requirements to a minimum. Thus, there are two or more sets

of dynamic variations, plus their interactions, to be considered. If the shafts connecting the gearboxes are quite

rigid, the dynamic loading can be greater than the applied loading, even when precision gears are tested. Owing

to the complexity of the situation, stresses for rig tests are computed making no allowance for dynamics. The

fact that the dynamics of gear test rigs are not the same as real machines that use gears is a principal reason that

bench testing and full-scale testing are required before a given gear design is adopted for critical applications.

The load distribution factor accounts for variations in alignment due to deflections of teeth, gearbox, and so on

for variations in axial alignment of gear teeth, and for variations in load sharing between teeth. Much of the

variation in load distribution can be minimized by straddle mounting test gears between bearings so their axes

remain parallel under loading, modifying the profiles of test gears to optimize load sharing and so on. However,

concentration of contact load at one end of a gear tooth (due to a small variation in axial alignment) produces a

bending stress concentration. To avoid this condition, one or both test gears can be crowned to keep the load at

the center of the face width. In this condition, the load-distribution factor is taken as unity for bending stress,

and a suitable factor is estimated as shown in the following section for contact stress. However, crowning adds

an additional variable that could affect test repeatability. It may be more expensive to accurately crown (and

measure for verification) these test gears. Many times it may be more feasible to use high-accuracy standard

test gears and very stiff (lateral) mounting to ensure uniform load distribution.

Contact Stress Computations for Gear Tooth Flank. Contact stresses on the surfaces of gear teeth are

determined using Hertz's solution for the stress between contacting cylinders. The equation for contact stress

taken from this solution, reduced to the simplest form applicable to spur gear teeth, is:

Contact stress = (P′ × B)

1/2

× EF

(Eq 1)

where the contact force per unit width, P′, is:

(Eq 2)

and

(Eq 3)

where B is the geometry factor, R

is the radius of the pinion contact surface at the point of interest, and R

the radius of the gear contact surface at the point of interest.

(Eq 4)

where EF is the elasticity factor, E

is the pinion modulus of elasticity, ν

is the pinion Poisson's ratio, E

is the

gear modulus of elasticity, and ν

is the gear Poisson's ratio. For pinion and gear (both steel), the EF is 2290 in

U.S. customary units (P′ in lb/in., B in in.

-1

, and stress in psi), and EF is 190.2 in Système International d'Unités

(SI) units (P′ in N/mm, B in mm

-1

, and stress in MPa).

The most critical combination of contact load and sliding in spur gears occurs on the flank of the driving gear at

the lowest point of contact with one pair of teeth in mesh (the location labeled “lowest single tooth contact” in

Fig. 1). The radii of the contact surfaces at this point can be determined from the corresponding roll angles for

the gear and pinion. The radius of curvature is the roll angle (in radians) times the base radius. The radii used in

determining the geometry factor are thus:

(Eq 5)

(Eq 6)

where OR

is the pinion outside the radius, BR

is the pinion base radius, N

is the number of pinion teeth, OCD

is the operating center distance, BR

is the gear base radius, N

is the number of gear teeth, and OPA is the

operating pressure angle, equal to cos

-1

(BR

+ BR

)/OCD.

The contact stress returned by Eq 1 is a nominal stress and assumes uniform distribution of load. With crowned

gears this uniform distribution will not be the case. The contact area becomes an ellipse, or in most cases, the

center portion of an ellipse, with the highest contact stress at the center of the face width and progressively

lower contact stress toward the ends. The proportions of the ellipse can be determined from a more complex

form of Hertz's solution to the contact stress problem. A second geometry factor, A, related to the radius of

curvature along the lead of the gears is needed:

(Eq 7)

where R′

is the radius of curvature along the pinion lead, R′

is the radius of curvature along the gear lead, and

R′ is the radius of curvature along the lead (only one gear crowned).

The amount of crown is usually a very small proportion of the face width; thus, the radius of curvature is large,

and the section that can be measured represents an infinitesimal angular segment of the circle. This geometry

makes it difficult for coordinate measuring machines (CMMs) to determine the crown radius. A useable crown

radius can be determined from lead traces and Eq 8:

(Eq 8)

The following equations regarding the contact ellipse are empirical in nature and assume that the ratio B/A is

appreciably greater than 20, which will be the case with most crowned gears. If this is not the case, a thorough

presentation of Hertz's contact solution, such as Ref 7, should be consulted.

(Eq 9)

where k is the ratio of ellipse minor to major axis.

(Eq 10)

If the crown radii are small enough in proportion to the contact load and effective face width, the contact area

will be an ellipse narrower than the effective face width. The width of the elliptical contact area and the

corresponding contact stress for this case can be determined from Eq 11, 12, and 13.

(Eq 11)

Width of contact ellipse, EW, is determined by:

(Eq 12)

(Eq 13)

These formulas can compute contact stresses for rig test specimen gears far higher than would be predicted by

the load distribution factors presented in gear-rating standards. The formulas are presented here to permit

comparison of performance on a stress basis between gears with differing crown. Stresses determined in this

manner should be reduced by a typical load distribution factor before being used to develop allowable design

stresses.

In most cases, there will be variation in contact stress between specimen gears in the same lot (and from tooth

to tooth on each gear) tested at the same load. The edge break at the ends of teeth is frequently applied in a

manual operation; thus, the effective face width can vary. Crown can vary from tooth to tooth on each gear.

Center distance can vary due to radial runout in shafts and bearings. The outside diameter of gears can vary (as

required for manufacturing tolerance). It is important, therefore, to determine the mean contact stress and the

probable range of variance.

Bending stress computations for root fillets are computed based on the assumption that the gear tooth is a

cantilever beam with a stress concentration at its supported end. AGMA rating standards determine the form of

the cantilever beam from the solution presented by Lewis and use a corresponding stress concentration factor.

ISO and Deutsche Industrie-Normen (German Industrial Standards) (DIN) use different proportions for the

beam and determine the stress concentration factor in a different manner. Only the AGMA approach is

discussed here.

Figure 5 shows a spur gear tooth with a point load applied at the highest point of single-tooth contact. This

point of loading corresponds to the highest bending stress when there is effective load sharing between gear

teeth. Specimen gears used in rig tests should have effective load sharing, so this is the appropriate point of

loading for determining bending stress in rig tests. For gears tested in single-tooth bending fatigue, the actual

point of loading established by the test fixture should be used in calculating bending stresses.

Fig. 5 Layout of Lewis parabola for tooth-bending stress calculation

The Lewis parabola is drawn from the point at which the load line intersects the center of the gear tooth and is

tangent to the root fillet. Methods used to lay out this parabola depend on how the root form is generated, the

particulars of which are presented in detail elsewhere (Ref 8). The critical height and width are determined from

the Lewis parabola as shown in Fig. 5. The angle between the load line and a normal-to-the-tooth center is

termed the load angle (it differs from the pressure angle at the point of loading because of the thickness of the

tooth). The bending stress is thus:

(Eq 14)

where s is the critical width from the Lewis Parabola, h is the critical height from the Lewis Parabola, and K

the stress concentration factor:

(Eq 15)

where r is the minimum fillet radius, H is equal to 0.331 - 0.436 × (nominal pressure angle, in radians), L is

equal to 0.324 - 0.492 × (nominal pressure angle, in radians), and M is equal to 0.261 + 0.545 × (nominal

pressure angle, in radians).

Equation 14 is derived from first principles but also can be derived from AGMA standards by taking the forms

of relevant formulas pertinent to spur gears and setting all design factors at unity. While a similar formula could

be developed for helical gears, testing them usually represents a step between rig testing and bench testing, and

such tests are negotiated between the client and the testing laboratory.

References cited in this section

7. A.P. Boresi and O.M. Sidebottom, Advanced Mechanics of Materials, 4th ed., John Wiley & Sons, 1985

8. “Information Sheet: Geometry Factors for Determining the Pitting Resistance and Bending Strength of

Spur, Helical, and Herringbone Gear Teeth,” AGMA 908-B89 (R1995), American Gear Manufacturers

Association, 1995

Mechanical Testing of Gears

Douglas R. McPherson and Suren B. Rao, Applied Research Laboratory, The Pennsylvania State University

Specimen Characterization

Specimen characterization is a critical part of any fatigue test program because it enables meaningful

interpretation of the results. It is important to know that the specimens to be tested meet specifications, where

key parameters fall in the specified range, and what the variations are. Characterizations fall into four areas:

dimensional, surface finish/texture, metallurgical, and residual stress.

Dimensional Characterization. Basic dimensional checks include size and alignment of mounting surfaces, size

and alignment of test surfaces relative to mounting surfaces, and size and uniformity of edge breaks at the edges

of test surfaces. These checks ensure that the specimens will fit into the test rig and either ensures that stresses

will be consistent or provides data to determine variations.

The important dimensions to check on rolling contact fatigue (RCF) specimens are diameters of mounting

trunnions and test surface, total indicator reading (TIR) test surface-to-mounting trunnions, and overall length.

The important dimensions to check on the mating load rollers are inside and outside diameters, TIR inside to

outside, crown radius and location of high point of crown, and thickness. In the case of nonstandard specimens

where the entire width of the test surface is intended to make contact, the size and uniformity of the edge break

needs to be checked.

The important dimensions to check on gear specimens fall into the areas of mounting surfaces, gear functional

charts, and other specific features impacting stress. All of the gear specimens described in the following

sections are mounted on their inside diameter. Thus, inside diameter, length between end faces, and

perpendicularity of end faces to inside diameter need to be checked. For specimens with a splined bore, the

pitch diameter, or inside diameter if so specified, counts as the inside diameter for alignment checks. The gear

functional charts are developed with the gear mounted on the test mounting surfaces. Typical measurements

include lead, profile, spacing, index, and runout. Other specific items to check include diameter over wires, root

diameter, and size and uniformity of edge break at tooth ends and along the tip.

Surface Finish/Texture Characterization. It has been standard practice to specify surface finish and texture in

terms of arithmetic average surface roughness (R

). Because it is possible to manufacture surfaces with widely

varying load capacity, all with the same R

, more information than R

is needed to interpret data. At a minimum,

(a measure of “average” peak roughness) should also be measured. A preferable method would be to

examine surfaces with an optical interference system that maps the contour of an area rather than the traditional

line contact. Test surfaces to be subject to contact fatigue should also be examined at 10× to ensure they are

free of corrosion, dings, scratches, and so on.

Metallurgical Characterization. Both surface hardness and hardness gradients are to meet specification. For gear

specimens, hardness should be checked at the tooth half height and at the root fillet. Details of the

microstructure should be characterized at the same locations as hardness. Typical practice has been to prepare

and document photomicrographs of the etched structure at 400× to 600×.

Residual Stress Measurement. Residual stresses vary among a lot of parts; therefore, enough measurements

should be made to permit a statistical analysis. Residual stress gradients provide more useful information than

surface measurements but at a much higher price. A complete study should include some residual stress

gradient data. Typical practice is to measure surface residual stress at six points per variant and measure the

residual stress gradient at one or two of these points. Contact fatigue specimens should be measured at the

center of the contact surface. Gear specimens should be measured at the tooth half height (or lowest point of

single-tooth contact) for surface durability tests and at the midpoint of the root fillet for bending strength tests.

Mechanical Testing of Gears

Douglas R. McPherson and Suren B. Rao, Applied Research Laboratory, The Pennsylvania State University

Tests Simulating Gear Action

Tests that simulate gear action are the RCF test, the single-tooth fatigue test, the single-tooth single-overload

test, and the single-tooth impact test.

Rolling Contact Fatigue (RCF) Test

The RCF test simulates the rolling/sliding action that occurs in a gear mesh, and depending on the test

parameters employed, it can simulate the most severe condition in the mesh. Because the specimens are

cylindrical, this test is the least expensive to run in both cost and time. Hence, it is frequently used as a

screening test, and its results are used to plan further gear testing.

Test Equipment. Figure 6 shows a schematic of the rolling/sliding contact fatigue test. The specimen and load

rollers are cylindrical. The outside diameter of the load roller is crowned to concentrate the load at the center of

contact and eliminate the possibility of concentrated loading at the edge of contact due to misalignment. A

normal load is applied by air pressure. Phasing gears, attached to the shafts on which the specimen and load

rollers are mounted, control the extent of sliding at the specimen/load roller interface. The amount of sliding is

determined by the gear ratio and can be fixed at any value (21 and 43% are commonly selected), simulating the

rolling/sliding action at any desired location on gear teeth. This test is primarily intended to evaluate the

resistance of candidate material systems to surface origin pitting, but other modes of surface failure can be

studied. The surfaces of the specimen and load roller are sliding against each other, with lubrication, under high

load. Therefore, some indication of the lubricated wear resistance of the material being tested can be obtained.

In addition, the resistance of the material/surface finish/lubricant system to scuffing can be studied. Tests are

conducted at very high overload to promote failure in real time; thus, it is possible to introduce plastic

deformation (rippling) on the contact surface. With specially adapted equipment, these tests can be conducted at

different temperatures up to 400 °F. Specimens and load rollers can be designed for a variety of testing

requirements, depending on the exact material and objective of the test.

Fig. 6 Schematic of a rolling/sliding contact fatigue (RCF) test

Test Procedure. The lubricant stream to the specimen/load roller interface is aimed at the discharge side of the

mesh (to cool the surfaces after contact). The lubricant flow rate is adjusted (typically to about 2 L/min, or as

specified for the project), with the lubricant at test temperature.

Alignment of the specimen and load roller is checked as each test is set up. One method often used is to coat the

surface of the load roller with a thin layer of layout blue and ensure that contact occurs uniformly at the center

of the load roller. Before the start of testing at load, a break-in run is typically conducted. This procedure is

accomplished by running the machine for 10 min at each of a series of increasing loads up to the full test load.

The intent of the break-in run is to gently polish away asperities on the contacting surfaces that might cause

scuffing (i.e., localized scoring), burnishing, or wear to occur under full load.

Tests are stopped periodically, and the contacting surfaces of the specimen and load roller are inspected for

signs of surface distress. The diameter at the center of the specimen is also measured to provide an indication of

wear. The formation of large, progressing pits produces a strong vibration signal, which, in turn, shuts down the

test. Lubricant temperature, lubricant pressure, and air pressure (to apply the contact load) are also monitored,

and the test is stopped if irregularities are detected.

The results of contact fatigue tests exhibit more scatter than is typical with other fatigue tests. One gage of

scatter is the Weibull slope, a measure of the increase in rate of failure with increasing life. For many fatigue

tests, a Weibull slope of six or more is typical. A Weibull slope of six can be roughly translated into practical

terms as follows. If 20 samples were randomly selected from a large group of theoretically identical parts and

tested to failure under identical conditions, the longest test would, on the average, last about twice as long as the

shortest. For contact fatigue testing with current ultraclean steels, a Weibull slope of 1.5 is typical. In this

example, if the Weibull slope were 1.5, the longest of the 20 tests would last approximately 20 times as long as

the shortest. The impact on test programs is that many tests have to be conducted to develop enough data to

make statistically meaningful comparisons. The minimum number of tests with each variant (at each load) to

enable reasonable comparisons has typically been considered to be six. With six tests for each of two variants

and Weibull slopes of 1.5, the G50 life of one variant would have to be twice that of the other to conclude that

it is better. If the comparison were made on the basis of G10 life, the ratio would have to be 5 to 1.

Specimen Results. An example set of data, representative of the results of rolling/sliding contact fatigue testing,

is shown in Table 1. In addition to specimen identification, load, and life to failure, other information is

reported to aid in the interpretation of results. Several test parameters can be varied as needed; thus, the actual

values are reported with the results. These parameters include lubricant, lubricant bulk temperature, nominal

filter size, test speed, and phasing gear set/slide ratio. Also reported for each test are data regarding surface

roughness, ratio of elastohydrodynamic lubricant film thickness to composite roughness, wear, and wear rate. A

Weibull statistical analysis of this set of results is shown graphically in Fig. 7. Comparisons between variants

are made on either a G10 life or a G50 life basis.

Table 1 Example of rolling/sliding contact fatigue test data

Lubricant, automatic transmission fluid. Bulk temperature, 90 °C (194 °F). Filter, 10 μm (nominal). Test speed,

1330 rpm. Phasing gear set, 16 tooth/56 tooth. Slide/roll ratio, 43%. Contact stress, 400 ksi. Load, 3000 lb.

Test

duration

(a)

Test

No.

Specimen

No.

cycles

h Specimen

Load

roller

(b)

Wear

(c)

in.

Wear

rate

(d)

Comments

1.173 14.7

13.5 3.8

3 10-9/LR 1 1.603 20.2

8.5 … 0.58

0.0002 12

Surface origin pitting

8 10-11/LR

7.332 92.3

9.3 … 0.56

0.0001 1.4

Surface origin pitting

12 10-4/LR

7.565 95.3

… 5.0 0.57

0.0008 12

Surface origin pitting.

Severe exfoliation and

wear at center of wear

track

18 10-2/LR

5.267 66.3

9.0 6.8 0.51

0.0002 3.8

Surface origin pitting

22 10-3/LR

6.322 79.7

… 5.0 0.56

0.0003 4.7 Surface origin pitting

(a) R

, arithmetic average surface roughness measured in axial direction, μin.

(b) λ, ratio of elastohydrodynamic film thickness to composite surface roughness. In cases where surface

roughness was not measured for a particular specimen or load roller, λ is based on average surface roughness

for group.

(d) Change in diameter, in. × 10

-5

/cycles × 10