Multiple papers have been written about micropitting, its description, and its causes [1] [2].  Micropitting can lead to significant surface damage, macropitting, and catastrophic failure.  Alternatively, it may appear in patches and arrest its growth as tribological conditions improve during run-in.  If one is designing gearing for critical applications, it is desirable to be able to calculate the risk of micropitting in an effort to avoid it.

The presence or absence of micropitting is not easy to determine with an analytical model because micropitting occurs on the asperity level, The engineer needs to determine what percentage of the asperities will come into contact through the lubricant film thickness, the asperity plasticity, the number of cycles the asperities see as they travel through the contact zone, the fatigue limit of the asperities, and the pressure applied to the asperities.  In 3-dimensional calculations, this is dependent on loads, local tooth geometry, and roughness along the direction of tooth motion, lubricant selection, and the metallurgy of the gear.  As a result, there is no comprehensive model to predict micropitting risk.

ISO/TS 6336-22 (Calculation of load capacity of spur and helical gears — Part 22: Calculation of micropitting load capacity) is the ISO technical specification containing a proposal for a calculation of risk of micropitting in gear sets. [3] This document was originally published in 2010 as ISO/TR 14179-1 and added to the ISO 6336 suite of documents in 2018.  It was developed based on testing an observations of many gear sets with normal modules between 3 mm and 11 mm and pitch line velocities between 8 m/s and 60 m/s,  The analytical calculation in ISO/TS 6336-22  focuses on film thickness as a determinant for when micropitting will occur.  This paper uses the document to calculate the risk of micropitting for gear sets in three different operating conditions and compares that to field experience.  The simplified computation in Method B is utilized in order to simulate how the average gear engineer will use the method.  For these examples, micropitting is not predicted to occur and this points out some limitations in the method.

Overview of the ISO/TS 6336-22 Calculation

ISO/TS 6336-22 contains a calculation of the micropitting load capacity of external gear sets that is based on testing.  It assumes that micropitting occurs when the minimum specific film thickness of a gear set in application falls below a permissible value for specific film thickness.  The ratio of the minimum specific lubricant film thickness to the permissible specific lubricant film thickness is the safety factor against micropitting.  

“Specific film thickness” is also called “lambda ratio” in some industries and is expressed as the ratio of the film thickness to the arithmetic mean roughness.

In other sections of ISO 6336, safety factors are used to calculate the risk of macropitting and bending fatigue.  Advice about the acceptable minimum value of the factor can be found in a general rating calculation, an application rating specification, or a user specification for equipment design.  ISO/TS 6336-22 does not contain advice for a minimum safety factor.  Instead, it provides this guidance:  

“An appropriate probability of failure and corresponding safety factor shall be carefully chosen to meet the required reliability at a justifiable cost. Depending on the reliability of the assumptions on which the calculations are based (for example, load assumptions) and according to the reliability requirements (consequences of occurrence), a corresponding safety factor is selected.”

Minimum Specific Film Thickness

The calculations for minimum specific film thickness are performed at multiple contact points in the tooth mesh region, with the minimum selected as the lowest value in the results array.  This allows for the prediction of both the risk of micropitting and the region on the tooth flank that will experience damage.

In the document, the minimum specific lubricant film thickness can be determined using two different methods.  Method A allows the engineer to calculate the value with a gear computing program that models the complete contact area of the mesh.  The results appear as a map of pressures and film thicknesses across the face of the pinion and gear flanks.

Method B starts with the assumption that the minimum specific film thickness will be on the tooth flank in the region of negative sliding.  The lubricant film thickness is calculated with a modified Dowson/Higginson analysis along the line of action.  It deviates from the norm, though, with the addition of a local sliding parameter.  This parameter accounts for the influence of sliding on temperature, which affects film thickness.  This changes the pressure-viscosity coefficient and dynamic viscosity, thus adjusting the film thickness in the regions of negative specific sliding.

(1)

(2)

where

is the local specific film thickness 

is the local lubricant film thickness 

is the effective arithmetic mean roughness value (averaged between pinion and gear roughnesses), μm

Y indicates the local contact point along the line of action

is the normal radius of relative curvature at point Y along the path of contact, mm

is the material parameter

is the local velocity parameter

is the local load parameter

is the local sliding parameter

The contact points along the line of action are determined with the familiar calculations for the lower point of active profile, lower point of single tooth contact, pitch point, upper point of single tooth contact, and upper point of active profile.  Figure 2 shows this in a gear mesh.  ISO/TS 6336-22 also considers mid-points between the lower and upper points of active profile and single tooth contacts.

 

Permissible Specific Film Thickness

The permissible specific film thickness can be determined using several different procedures.  All procedures require some level of experimental investigations, whether that be conducted with the actual gear set or with representative gear sets.  Ideally, testing is conducted with the actual gear sets, lubrication, and inlet temperatures that match the operating conditions that the gearing will see.  Method A recommends that this testing be conducted until micropitting just occurs.  The permissible specific film thickness is then calculated per the Method A calculation for minimum specific film thickness using the conditions of the final load stage.

Method B uses two different options to set the permissible specific film thickness.  One option is to conduct studies with gearing that is similar in geometry, quality, and material of the gearing being designed.  Using standardized tests, the gearing is run until the micropitting failure limit is reached.  The critical specific film thickness for the test gearing is then calculated using the data from the failure stage.  This is the permissible specific film thickness.  

If comparative testing cannot be performed (due to cost, timeline, test rig availability, etc.), the permissible specific film thickness can be generally determined from a simplified set of curves based on the lubricant’s performance in FVA-FZG micropitting tests [4] and its viscosity.  These curves are derived from mineral oils and are shown in Figure 3.

1 ISO VG 460

2 ISO VG 220

3 ISO VG 100

4 ISO VG 32

Figure 3 – ISO/TS 6336-22 Figure A.1 – Minimum permissible specific film thickness for mineral oils as a function of nominal lubricant viscosity and failure load stage in FVA-FZG micropitting tests.

ISO/TS 6336-22 also contains alternative curves that can be used to determine a value of the permissible specific film thickness based on the results of FVA-FZG micropitting testing of mineral oils at oil temperatures of 60°C, 90°C, and 120°C.  These curves account for the additives in the oil by accounting for its “quality”.  High-quality oils are specifically formulated with base oils, additives, and thickeners to prevent micropitting. These are used when the costs of failure are high and maintenance is challenging.  Mid-quality oils have some micropitting-preventing additives and are used in industrial gear lubrication when reliability is important and maintenance is scheduled.  Low-quality oils have not been adjusted to prevent micropitting and are used in basic applications.  In application, the choice of lubricant is recommended by the gear manufacturer and executed by the equipment owner.  It can result in micropitting if the lubricant is not formulated to minimize the phenomenon.

Clearly, testing is a prominent theme in the determination of the permissible specific film thickness!  ISO/TS 6336-22 is careful to point out that testing should be carefully conducted and well-documented.  Testing variability is a risk to the accuracy of the results.  Practically, three to five tests are conducted with comparable load stage results and either the average or (more conservatively) the minimum value is used for the calculation.

In summary, the uncertainty in the permissible specific film thickness value increases as one moves further from Method A.  Figure 4 illustrates the options for methods in ISO/TS 6336-22.

 

Case Study – Using the Calculation

Case studies using ISO/TS 6336-22 or its predecessor document, ISO/TR 15144-1, have been performed in previous papers [5] [6].  Many of those focus on using the Method A calculations for calculating tooth pressure and the specific film thickness.  

Of particular interest is a paper by Pinnekamp and Heider [7] that contains ISO/TR 15144-1 calculations with practical examples from industry.  The FVA-FZG software RIKOR was used to determine the specific film thickness per Method A.  Method B was used for the permissible specific film thickness.  The resulting safety factors ranged between 1.0 and just over 3.0.  Micropitting was observed on examples with safety factors over 2.0.  The authors created a zoned diagram to predict the risk of micropitting based on quality of the calculation, knowledge of operating conditions, and calculated safety factor. 

This paper tests the behavior of the calculation using the analytical calculations in Method B to calculate specific film thicknesses.  In two of the cases, it was not practical to calculate the permissible specific film thickness with comparative testing.  The simplified curves based on viscosity and failure load stage of the lubricant were used for these.  As much as possible, the paper simulates the path that the average gear engineer would take to evaluate an existing gear set that experienced micropitting in operation or to assess a new design for the risk of micropitting. 

The input data for each calculation consists of the gear geometry and arrangement, the lubrication, and the gear loads.  The results are presented as the minimum specific film thickness, the permissible specific film thickness, and the safety factor that is calculated.  When available, pictures of micropitting damage are also included.

Case 1 – High-Speed Gear Set

The first case is a speed increasing gear set from a centrifugal compressor.  Micropitting was found on the pinion on the dedendum extending through the pitch line to the addendum, favoring the drive end.  Macropitting was also present.  Micropitting was also found on the gear around the pitch line.  The gear set had run for approximately 120,000 hours (54.6 x 10⁹ cycles).  Pictures of the damage can be seen in Figures 5 through 7.