Sample load distribution analyses and ISO predictions are presented for several experimental results from testing both FVA standard micropitting test gears and the AGMA tribology gears to calculate the safety factor for micropitting.

Recently, ISO 15144 [1] has been approved by ISO as a technical report that presents an analysis procedure, which is designed to predict whether micropitting will occur in a given gear design. The procedure is based on results from many testing programs performed at FZG in Munich [2, 3]. However, little of their testing program data is available in the literature. This paper’s main goal is to share the results of a series of tests on a newly refurbished FZG tester, in which the testing of both FVA standard micropitting test gears (C type gears) and the AGMA tribology gears [4] was performed. The current testing has been performed in such a manner that the procedures of the ISO report could be assessed. Baseline tribology data was first created with standard FVA C micropitting test gears using the FVA 54/7 [5] procedure. The AGMA tribology gears were then subjected to a series of 130- to 160-hour constant load tests in an effort to find the location of the threshold load for micropitting failures.

The first portion of this study that was reported in the master’s thesis by Pickens [6, 7] outlines the refurbishment of a 91.5 mm FZG tester and the writing of a MATLAB program for performing a three-dimensional full tooth surface evaluation of micropitting safety factors using ISO 15144. The thesis also presents results of an experimental dynamics study of the FZG tester and presents results of some initial testing of the AGMA tribology gears.

Figure 1: Diameters used in safety factor calculations


Micropitting is a phenomenon that occurs predominantly on case-hardened gears and manifests itself as a gray appearance that eventually results in tooth wearing and profile degradation. It has been studied extensively, and a review of micropitting literature and a discussion of the micropitting phenomenon have been presented by Errichello [8, 9]. A search of the Ohio State GearLab literature database of over 20,000 papers on gearing has found over 200 papers on micropitting. Olver [10] briefly defined micropitting as occurring in regions of the tooth where it is simultaneously sliding, being subjected to high contact stresses, and operating in a partial or reduced elastohydrodynamic lubrication (EHL) regime (partial metal-to-metal contact). Olver described micropitting as a form of surface damage in rolling contacts, consisting of numerous pits and associated cracks on a scale smaller than that of the Hertz semi-width, and it is distinguished from macropitting by the small size of the individual pits. In addition, micropits are commonly present in large numbers.

Houser et al. [11] developed a modified FVA 54 type staged testing procedure for the testing of micropitting using the AGMA tribology test gears [4]. Adjustments to the applied torques needed to be made so that the testing of the AGMA gears was at the same stress levels as those used in the FVA procedure. It is interesting to note that the loads that caused wear (usually a form of polishing wear) were about 20 percent of those used in the AGMA macropitting testing [4]. Buzdygon and Cardis [12] also developed an alternative micropitting testing procedure using the AGMA tribology gears. Analyses of Buzdygon and Cardis’ results are included in this paper. Prior to developing the authors’ final experimental design, many papers containing micropitting data —Olver et al. [13], Hohn et al. [14], Brechot et al. [15], Cardis and Webster [16], Ueno et al. [17], and Pinnekamp et al. [18], to name a few — were reviewed in detail to try to ascertain data on run-in procedures that minimize micropitting as well as lubricant and surface texture combinations that also minimize micropitting. The ISO 15144 procedure has been discussed by both Hohn [2] and Tobie [3]. Tobie reported on many experimental studies performed at FZG in Munich that formed the basis of the ISO 15144 technical report, but due to confidentially, little specific supporting data was shared. The ISO technical report does, however, present several examples of the computation of safety factors of gears that have been known to micropit [19].

Table 1: AGMA tribology gear geometry [4]

ISO 15144 Modeling Overview

One of the concepts of ISO/TR 15144-1:2009E is that the EHL equation for calculating film thickness and the lambda ratio (ratio of lube film thickness to roughness) is only a slight modification of the classic Dowson and Higginson film thickness equation [20]. Dowson’s equation assumes steady state rolling, a constant radius of curvature, and no sliding. Yet gears are only in contact for a fraction of a second, and radii of curvature and relative sliding velocities both change during the meshing process.

The basic premise of ISO 15144 is to calculate a micropitting safety factor, Sl, which, when greater than 1.0, states that there is less chance of micropitting than for values less than 1.0. It is implied that a value of 1.0 should be at the torque threshold value for micropitting. There is likely to be much room for uncertainty because of statistical variations of parameters as well as practical reliability issues. This safety factor is defined as:

where Hohn [2] gives recommendations for its minimum value as:

Slmin < 1 : high risk of micropitting

1 < Slmin < 2 : moderate risk of micropitting

Slmin > 2 : low risk of micropitting

Table 2: Evaluation of earlier micropitting tests performed using the AGMA tribology gears

The specific lubricant film thickness, lGF,min, is calculated from the ratio, hmin / Ra, where hmin is the film thickness calculated with Equation 1 and Ra is the arithmetic mean roughness of the gear tooth surfaces. The denominator term, lGFP, is the permissible specific lubricant film thickness that is discussed by Hohn [2] and is obtained either from experience with the specific design or, more likely, by using a standardized testing procedure such as the FVA 54 micropitting evaluation procedure. This latter approach tests a standard gear pair using the application lubricant under conditions similar to those of the application. It uses the modified Dowson and Higginson EHD equation to calculate the film thickness at the load at which test gears micropit to calculate the permissible film thickness, thus “calibrating” the lubricant without testing it in the actual application.

The standard Dowson and Higginson film thickness equation is:

626.pngEquation 1


ρe is the local normal radius of relative curvature

Gm is a material factor

Ug is a velocity factor

WΥ is a loading factor

ISO 15144 adds an additional factor, called a sliding factor, that attempts to account for the higher likelihood of micropitting at the regions of higher flash temperature. The sliding factor is the ratio of the product of the local contact temperature pressure viscosity coefficient and dynamic viscosity coefficient to the same product evaluated at the bulk temperature. The modified Dowson and Higginson equation then becomes:

616.pngEquation 2


S is the sliding factor

The entire ISO 15144 technical report was programmed into a spreadsheet using predicted contact stresses from a load distribution prediction program [20], viscosity and temperature data on the lubricant, permissible lambda factor, lGFP, from FVA 54 testing, and numerous other factors that are contained or calculated in the ISO report. Contact stresses are calculated at seven contact points along the tooth profile from A at the start of active profile (SAP) to E at the tip. Locations AB and DE are located midway between points A and B and midway between points D and E (see Figure 1). In this paper’s evaluations, locations AB and DE are placed at the locations of maximum flash temperature — locations that tend to correlate well with the locations of the initial micropitting.

Figure 2: Micropitting images of test pinion after (a) Stage 7 and (b) Stage 10

Use Of ISO 15144 With Data From The Literature

Prior to performing the testing, a literature search was performed in an effort to find existing micropitting data that could be used to exercise the ISO procedure. Unfortunately, few of the studies had sufficient data to assess the permissible specific film thickness. The exception to this was the data of Buzdygon and Cardis [12], who provided FVA 54 failure stage data that could be used for this purpose. Buzdygon and Cardis tested the AGMA tribology gears that were also used in this study. The gears are designed to operate in a 91.5 mm center distance FZG tester, with the gear pair geometries given in Table 2. The gears have tip relief and lead crown values that are typical of industrial gears designed to operate at torques in the range of 300 Nm. Buzdygon and Cardis’ tests were single-load tests at 370 Nm, and a summary of the five tests that had FVA 54 failure stage data is shown in Table 2.

Figure 3: Profile traces at 16 face-width locations (a) after wear-in and (b) after the completion of Stage 10 (Tooth 13, 265 Nm)

How To Define A Micropitting Failure

Throughout this study, one of the major subjects of debate has been how to define a failure level. Three levels of safety factors were defined earlier, but when running a durability test for a finite number of hours that is often much less than the duration of operation of the running gearbox, one has to decide when the gear pair is at failure. In terms of safety factor, one assumes this would be what is predicted for a value under 1, with values between 1 and 2 showing some micropitting that is not seen as life-threatening for the gear set and values above 2.0 being in a safe region where micropitting wear is not expected to proceed to a level that will put the gearbox out of service, either by large profile wear or the development of macropitting.

Figure 4: Wear progression of FZG C gear as loading stages increase

FVA 54 identifies several means of measuring micropitting — namely, measuring the area of micropitting coverage, weight loss, or amplitude of profile deviation due to wear. For the purpose of creating a measure of wear, FVA 54 identifies levels of failure for the C gear used in the standard. Yet, the AGMA tribology gears are tip-relieved gears with significant lead crown so that, initially, the area of coverage would need to be altered, as would the weight factor, due to the contact area changing with each test load. Although initial durations of testing at each level in FVA 54 are only in 16-hour increments at a given level, Buzdygon and Cardis identified that for their case A test, after 48 hours, the pinion micropitting area was very low with little weight loss. However, at 168 hours, the same gears had the largest micropitting area and weight loss of all of the parts tested and, in this case, could be deemed a failure. This occurrence places in doubt the validity of short-term tests for assessing micropitting. From the perspective of identifying failures, the Buzdygon and Cardis’ gears illustrate the earlier discussed quandary. Their case A and case B tests have led to macropitting, so it is obvious that these are micropitting failures that one would expect to have predicted with safety factors of less than one. Test cases C–D all have some micropitting, with the area of micropitting getting less as one progresses in order from C to D, but the question is, which are true failures?

Table 3: Results of sensitivity test of input variables when adjusted one variable at a time

Table 3 presents safety factor prediction results for the five results of Buzdygon and Cardis. One of the statements made in ISO 15144 is that when performing FVA 54 tests for evaluating the permissible specific film thickness, the temperature of type C gear testing should be the same as used in the gear application. In this case, the test gears were operated at 60°C, and it is suspicioned that the FVA 54 load stage data were evaluated at 90°C, since this is the temperature recommended in the FVA 54 document. For the sake of comparison, a set of safety factors that result from using a 60-degree evaluation temperature in assessing the specific film thickness is also shown in the table.

For test case A, which is the one that had little micropitting wear after 48 hours and the greatest amount after 168 hours, the predicted safety factor is 1.26, which, since this gear pair can be assessed as a failure, seems to be a bit high. For test case B, which also could be designated a failure, the predicted factor of safety is 1.01, closer to being under 1.0 than the earlier case. Since this case had less wear than case A, it is interesting to note that its predicted safety factor is less than that for case A. The reason for this lower value, even though it has a higher fail stage, is that the case A lubricant is a mineral oil and the case B lubricant is a synthetic oil, and the procedure has a factor within it that penalizes synthetic oils.

Figure 5: Average and maximum tooth wear of four teeth across the loading stages

Cases B through E had much lower levels of micropitting with fewer areas of micropitting and less than 10 percent of the weight loss of case A. Ranking the gears by weight loss, case B had the next largest weight loss, case D was next, followed by C, and then E, which by far had the lowest amounts of wear. By rank, the data compares quite well with the predicted safety factors that are 1.01 for B, 1.52 for both C and D, and 2.07 for case E. The safety factor numbers, taken using the earlier evaluation, show that cases C and D fall between 1 and 2, so they are in the in-between region. They do have micropitting, but it is debatable whether, with more hours, it will progress to a harmful situation. Case E has a safety factor just above 2.0, and its micropitting does not appear to be causing much wear, so it may well indeed not “fail” after running for a longer duration. It is interesting to note that when the lower temperature of FVA 54 evaluation is used, the safety factors become much smaller with all cases except case E, being less than 1.0.

To summarize this section, the ISO 15144 analysis seems to be in the ballpark in its prediction of micropitting, other than case A, but it must be placed against the gearbox user’s assessment of when a failure is a failure and what will happen as additional hours are placed on the gear set, since for most gearboxes, 168 hours would be a very short life.

Figure 6: Micropitting area from the beginning of the staged load testing

ISO 15144 Sensitivity Assessment

The case A gear pair’s operating temperature was adjusted slightly so its safety factor prediction was 1.0. Then, each input parameter that would have some effect on the safety factor was adjusted by about 10 percent for one variable at a time to show how much the safety factor would shift for that single variable change. Table 3 shows these results. Since comparing these variables is like comparing apples and oranges, conclusions are difficult to make, but in terms of making realistic changes to variables, both surface finish and oil sump temperature seem to have a large influence on the safety factor.

Figure 7: Photo of the wear on the mating gear

Current Testing Philosophy

The current tests were set up to start from scratch using an existing FZG tester that needed extensive rebuilding [6]. This experimental effort was designed to educate the authors with regard to the nuances of ISO 15144, and at the same time, familiarize them with many of the test procedures required to perform a complete micropitting safety factor analysis. This included preparing a spreadsheet program to evaluate ISO 15144, using FVA 54 to assess the permissible lambda value, and then running durability tests on the AGMA tribology gears that were provided by the AGMA Foundation. As previously mentioned, these gears are meant to mimic application gears, since they have traditional tip relief for avoiding tip-root interference and are lead crowned to compensate for misalignment. The lubricant chosen for the study was Dexron 6, an automatic transmission fluid for which little data on micropitting has been published. The FZG tester being used does not have lubrication jets and only has lubricant cooling, so the upper temperature available for testing is regulated by the power level of the test. Hence, the temperature of 40°C was realizable for the broad range of loads that are needed to run the FVA 54 testing procedure. Quite often, it seems a single load is used to evaluate a gear set. This is true of the examples used in ISO 15144 Part 2 [19] and in the tests by Buzdygon and Cardis. A challenge with this procedure is that there is a possibility that little is learned about threshold load level for the harmful micropitting region to exist. In theory, this region would be predicted by ISO 15144 at safety factors between 1.0 and 2.0. Therefore, in this testing, a broad range of torques were planned for the same gear geometry in an effort to identify this threshold of micropitting.

Figure 8: Measured effective topography deviation from a perfect involute.

FVA 54 Testing For The Evaluation Of Specific Lubricant Film Thickness

Most tribology-related design/rating procedures, because of the unknown effect of chemical interactions between the lubricant and the gear surface, require some sort of calibration or reference data on the lubricant. This is true for wear models like the one done by Ding and Kahraman [22], and it is also true for the ISO 15144 procedure. The ISO method B, which is used in this study, recommends using FVA Information Sheet 54/7 [5] to determine the specific lubricant film thickness that goes in the denominator of the equation to calculate the safety factor, Sl. This is done by running a staged loading test (16 hours per stage) of the perfect involute FVA C gear and then using one of the micropitting assessment metrics — either wear amplitude, weight loss, or micropitting area — to determine a pass/fail load level. In this study, topography measurements of the tooth profiles were used to measure when the wear amplitude exceeded 7.5 microns in any of the 16-hour stage tests from Stage 5 (70 Nm) to Stage 10 (265 Nm). The percentage area of micropitting was also measured, but no measurement of gear weight loss was performed.

The test rig limitations discussed earlier (dip lubrication and lack of lubricant heating) would not make testing possible at the 90°C level required for the test, but an option in the standard allows for testing at 40°C, which seems reasonable here since it was decided to also run the specimen testing at the same temperature. This follows a suggestion in 15144 that strongly encourages using the same temperature in FVA 54 testing as is used in the practical application. A topography measurement that encompasses 16 profiles and a single lead was performed on four teeth of each of the FVA C gears following each stage of loading. The four-tooth average surface roughness of Ra = 0.34 for the pinion and Ra = 0.33 for the gear were obtained. It should be noted that these surface finish values are quite a bit less than the 0.5 values called out on the gear prints, so in the FVA 54 document, there is a recommendation to reduce the failure stage level by one or two stages in order to compensate for the fact that one is using reference gears that are much less likely to micropit due to their surface roughness being much less than the recommended value. In subsequent analyses, results using both the measured values and the print values are provided. One slight difference from the test protocol of FVA 54 is that a torque strain gage bridge on one of the gear shafts has been calibrated such that its reading is used in setting the testing torque [11].

Figure 9: Predicted load distribution and surface temperatures for a test pinion tooth surface when loaded at 215 Nm

Figure 2 shows photos of pinion tooth 13 following Stage 7 (132.5 Nm) and Stage 10 (265 Nm), respectively. Micropits typically start by breaking off machining mark high spots along the profile and at regions of tooth interference, such as the pinion dedendum corner contact that is evident near the bottom of the dedendum area in the figure. On this tooth, the micropitting progresses to roughly 25 percent of the total tooth area that is shown in the Stage 10 photo. Figure 3 shows the 16 profile tooth topography that was measured on the pinion tooth, first after wear-in and then after Stage 10. The micropitting wear is indicated by the slight dip near the SAP and then the gradual rise to near the pitch point at mid-tooth. Another perspective of the wear is shown in Figure 4, by superimposing the profiles taken following each of the load stages. The maximum wear appears to be about 8 microns, but in reality, one must subtract out the slight dip in the original profile of about 1 micron, so for this tooth, the maximum wear following the Stage 10 test becomes 7 microns. It is interesting to note that the wear varied quite a bit for the different face-width positions and varied a great deal from tooth to tooth.

Based upon these results, the next step is to assess the stage pass/fail level. The FVA 54 stage failure threshold is for wear to be less than 7.5 microns. Figure 5 shows that the average wear of four teeth at Stage 4 is a bit above 5 microns, and the tooth with the most wear had roughly 7.5 microns of wear. Depending upon whether one uses average values or maximum values would determine whether the judgment is fail Stage 10 or pass Stage 10. Continuing testing for the additional 400 hours could lead to fail Stage 10 judgment if the wear exceeded 20 microns. Since this subsequent testing has not been completed, it was assumed for the remainder of the analyses presented here that the lubricant achieves a fail Stage 10 or 265 Nm torque capacity. However, because the roughness of the type C gears was considerably lower than the specified 0.5 micron, according to %%0416-OSU-T9%% of FVA 54 [5], one must apply a two-stage reduction, so a Stage 8 (171.6 Nm) would be a more appropriate failure stage. Figure 6 shows the relationship between load level and micropitting wear area that shows a similar trend to the wear amplitude plot of Figure 5. The wear area would seem to be of sufficient magnitude to have a failure stage that is one or two levels from that ascertained in the profile wear measurements, but due to ambiguity of the wear area, the fail Stage 8 will continue to be used. Although the wear on the mating gear was always much less than that on the pinion, the photo of the gear shown in Figure 7 shows that there is micropitting in the gear dedendum.

Figure 10: Predicted safety factors based on load distribution calculated using the average measured topography

The next step is to reverse calculate, using the ISO 15144 equations, the permissible lambda value. Example 1 of ISO 15144 Part 2 [19] outlines this procedure that essentially iterates on the permissible lambda value such that a safety factor of 1/1.4 = 0.714 is achieved, with the value of 1.4 being a conservative multiplication factor. For the FVA C gear, the peak micropitting wear almost always looks like the dedendum wear pattern of Figure 4 where the peak wear occurs near the SAP (it is actually slightly up the flank where corner contact occurs), so the evaluation point is at point A where the contact stress used in the ISO 15144 examples [19] is 1333 MPa at 215 Nm torque. It should be noted that this calculation does not in any way include the much higher contact stresses that occur in the corner contact region where the wear initiates. Doing this for Stage 8 failure and a corrected surface finish of 0.5 micron results in a permissible lambda value of 0.226. Had the real surface finish of 0.34 micron been used, the permissible would have been 0.357.

When using the calculated stresses of the FVA 54 C gears with a load distribution program, the method assumes that load distribution values (KH) are at unity so that the calculated contact stresses should only be weighted by the application factor (KA) and the dynamic factor (KV). This assumes that in the stress calculation, the production gears match the print profiles and leads, that all teeth have identical topographies, and that there are no spacing errors. The method also does not include tip interference (corner contact) in the stress calculation, which would significantly change the contact stress at entering contact. This is essentially verified by the fact that maximum wear does not occur at the tip but occurs up the flank where the corner of the driven gear intersects with the dedendum of the driving gear.

Figure 11: Tooth surfaces for a pinion operated at (a) 215 Nm after 40 hours and (b) 215 Nm after 160 hours

AGMA Tribology Gear Micropitting Testing

The specifications for the AGMA test gears are given in Table 1. As mentioned earlier, the testing temperature would be 40°C, and the average respective surface finishes are Ra = 0.4 micron for the pinion and 0.28 micron for the gear. Unlike in FVA 54, where a precise definition is given in terms of amplitude of wear over a prescribed testing period, in gear applications, such numbers and definitions do not exist, so the final conclusion will be subject to interpretation. Looking at the examples of ISO 15144 Part 2 [19], the wear values ranged from 10 to 15 microns, indicating that significant levels of wear are required to be designated a failure, which may be contrary to earlier wording in the report that states that safety factors between 1 and 2 indicate the existence of micropitting. Also, the description of the examples does not provide the number or hours of testing nor photos of the worn gears, so it is difficult to place the tests reported in this study alongside the examples.

After running several tests of various loads and durations, it was decided to perform single-load tests similar to those done by Buzdygon and Cardis [12], who ran tests for 168 hours’ duration. Here, the gear set was first measured to get tooth topographies and surface finish, and then measurements and photos were repeated after 40-hour run intervals until a total of 160 hours of run time was achieved. Load levels for the tests were chosen to match the torques used in FVA 54, so tests were run at four levels from 132.5 Nm to 265 Nm, with multiple runs being made at two of the loads.

Figure 12: A further magnification showing three distinctly different surface appearances within the tooth contact zone

Load Distribution Analysis And Safety Factor Calculation For The Test Loads

Figure 8 shows the measured effective topography that was created by adding the profiles of the pinion and gear to one of the AGMA test gear pairs. The tip relief of the pinion and gear are about the same in shape and amplitude, but the lead crown tapers from one end of contact to the other. This topography was then used with a load distribution program [21] to predict the contact stresses that are shown in Figure 9. Also shown in Figure 9 is a prediction of the surface temperature, the sum of flash temperature, and sump temperature. The locations of the peaks of the flash temperature were used for the calculation of contact stresses at points AB and DE in the ISO calculation. The same ISO 15144 spreadsheet that was used for the calculation of the permissible lambda value was used to calculate the safety factor of the AGMA gears. The surface finishes of 0.40 micron for the pinion and 0.28 micron for the gear were an average of surface finishes measured on five different test gears. Since there was some debate as to which FVA stage to use in the calculation, safety factors for Stages 7 through 10 are given, as well as factors for two sets of permissible lambdas corresponding to type C gear pair roughness of 0.5 micron and 0.335 micron, respectively.

Figure 13: Measurement of wear near the center of pinion face (FW=6.44) for a 215 Nm test

Testing Results

As previously mentioned, testing at different torques was done in an effort to identify the threshold of micropitting, i.e., identify the torque beneath which there is little or no micropitting and torques for which micropitting continues to progress or turns into macropitting. After a few tests were used to see if micropitting would occur for the AGMA tribology gears using the Dexron lubricant, it was found that the upper range of the torque range of Figure 10 did result in micropitting.

One interesting observation of the testing is that the pinion surfaces not only micropitted as shown in the dedendum of the pinion of Figure 11 and Figure 12, but also had what appears to be a smearing of the surface in the addendum. This smearing may be what is sometimes called polishing wear that was observed in the AGMA tribology tests [4]. The photos of Buzdygon and Cardis [12] also show both types of wear that were observed in these tests. The surface distress due to this smearing tends to remove material starting at point DE, and in the more severe cases, removes material extending beyond the pitch point. Figure 13 shows such a case where the profile is slowly disappearing across the total profile. However, it does appear that in the dedendum where there is micropitting, the wear tends to be increasing with time, while in the addendum where there is smearing, the wear seems to be tailing off. The mating gear had the reverse happening, with the smearing occurring in the dedendum and the micropitting occurring in the addendum, with levels of wear being a bit less than those observed for the pinion.

Figure 14 shows a summary of the average wear of four teeth for each of the tests that were run. It certainly appears that the threshold of micropitting has been identified in the range between 133 and 172 Nm and that the wear at loads of 215 Nm and higher seems to be continually growing and showing some signs of the creation of larger pits. The next step is to refer back to Figure 10a that shows that in the 133 to 172 Nm range, the safety factor is about 1.5 for the Stage 8 failure level. This range is in the moderate micropitting range, which seems reasonable. The Figure 10 graphs do seem quite flat, in that no matter what is done with this lubricant, it would appear that operation cannot get to a safety factor of greater than 2 or less than 1.0 without using loads that would be impractical for this gear set.

Figure 14: Load effect on micropitting wear for all tests — most of them after 160 hours

Superfinished Gear

One pair of the AGMA tribology gears was superfinished to a level of 0.2 μm. An ISO 15144 evaluation shows the safety factor to be 6.7 at 265 Nm torque. When operating at this torque, no visual micropitting was observed after 160 hours, and profile measurements showed little wear. This affirms the calculated safety factor in the statements of many authors.

Analysis Of A Worn Gear

A load distribution analysis following completion of one of the 215 Nm tests is shown in Figure 15. The peak contact stresses, although about the same amplitude as that for gears prior to running (Figure 9a), are shifted in location from near the center of the pinion tooth face width toward the edges. In essence, the wear occurs at the original high stress region, hence reducing stresses in this region, reducing wear there, and moving the wear to the new higher-stress regions. This brings up the possibility that the wear might eventually arrest the micropitting as cycles accumulate. Tests were resumed to 240 hours for one of the 215 Nm tests, and new wear was still occurring.


The methodology of ISO 15144 has been shown to be realizable but with several parts of the procedure being subject to user interpretation or questioning.

Evaluation of permissible specific film thickness (permissible lambda): Only the FVA 54 approach was attempted, and even though other procedures are referred to in ISO 15144, the FVA 54 method is the most mature method and is the only procedure that has any significant details for its application in the example cases of ISO 15144. FVA 54 assumes wear occurring at point A, even though the wear in the examples typically occurs a bit up the flank. Certain factors, such as the load distribution factor, are assumed to be 1.0, which assumes the gears have perfect leads and there are no housing misalignments.

Figure 15: Contact stresses for a worn tooth

It would be possible to use the current data to test out the method A procedure for determining the permissible lambda. The main issue would be to try to establish the criterion for failure, including duration of the test and a measurement that would predict whether failure would occur. For instance, in this testing, after 40 hours, there is little wear at a given load, yet at later durations of testing, the wear becomes significant. This type of behavior would lead to false conclusions.

Comparison of safety factors to test results: In the literature evaluation, FVA 54 stage levels are reported without mention of lubricant temperature, so it was assumed that the testing of C gears was at the same temperature as that of the test gears. If the temperatures were different, there is no correction procedure for determining a proper permissible lambda. Nonetheless, the safety factors rank in the same order of the areas of micropitting for the Buzdygon data.

Experimental tests: In the current testing, the safety factors are somewhat in doubt since a conclusive pass/fail level for calculating the permissible lambda was not established. The test results do present a range of loads at the threshold of micropitting. The safety factor for this load range falls in an appropriate safety factor range. However, the range of wear as a function of torque in the measurements does not seem as flat as the predicted safety factors across the torque range of testing. For instance, for the Stage 8 failure analysis, at 133 Nm, where little or no wear was observed, the safety factor is just above 1.5, while at 265 Nm, where some macropitting was starting, the safety factor is about 1.2. One would expect values above 2.0 for the 133 Nm result and beneath 1.0 for the 265 Nm result.


The authors would like to thank the AGMA Foundation for donating the test gears and providing partial funding for this project. They would also like to thank the sponsors of the Gear and Power Transmission Research Laboratory for the remainder of the funding for this research. Several students are to be thanked for their assistance in the durability testing and gear measurements: M.D. Fahad, Tiffany Lim, Isaac Hong, and Joshua Balser.


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  15. Brechot, P., Cardis, A. B., Murphy, W. R., and Theissen, J., “Micropitting resistant industrial gear oils with balanced performance,” Ind. Lubr. Tribol. Vol. 52, No. 3, 2000, pp. 125–136.
  16. Cardis, A.B., Webster, M.N., “Gear Oil Micropitting Evaluation,” AGMA Fall Technical Meeting, Paper 99FTM4, 1999.
  17. Ueno, T., Ariura, Y., Nakanishi, T., “Surface durability of case-carburized gears – On a phenomenon of “gray-staining” of tooth surface,” ASME paper 80-C2/DET27, ASME Design Engineering Technical Conference, 1980.
  18. Pinnekamp, B., Weiss, T., Steinberger, G., ‘Micropitting – A serious damage? Testing, standards and practical experience,” AGMA Fall Technical Meeting, AGMA Paper 11FTM15, 2011.
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  21. Houser, D. R. “User’s guide for using the OSU Load Distribution Program (LDP), Shaft Analysis Program, and RMC,” The Ohio State University Gear and Power Transmission Research Laboratory, 2011.
  22. Ding, H., Kahraman, A. “Interactions between nonlinear spur gear dynamics and surface wear,” J. Sound and Vibration, Vol. 303, No. 3, 2007, pp. 662–672.
Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association (AGMA). This paper was presented October 2015 at the AGMA Fall Technical Meeting in Detroit, Michigan. 15FTM25.


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received his B.S. and M.S. degrees from The Ohio State University. For over 10 years, he has been a research engineer with the Gear and Power Transmission Research Laboratory, an industrial research consortium that currently has over 70 sponsor companies. Shon has worked on gear projects ranging from durability to efficiency for both aerospace and ground vehicle companies.
professor emeritus, received his B.S., M.S., and Ph.D. from the University of Wisconsin in Madison. He is retired from the faculty of the Department of Mechanical Engineering at Ohio State, where he taught for 35 years. Dr. Houser is the founder of the Gear Dynamics and Gear Noise Research Laboratory that has been renamed the Gear and Power Transmission Research Laboratory, an industrial research consortium that currently has over 70 sponsor companies. He is a recipient of the Darle Dudley award from ASME, and he has supervised over 120 graduate theses and has consulted on gear problems with over 50 companies.