## Case Study of ISO/TS 6336-22 Micropitting Calculation

By : Mark Michaud ,

By : Mark Michaud ,

**Introduction**

Micropitting is a form of Hertzian fatigue damage that occurs on gear teeth. It appears as ultrafine cracks on the surface of the flank, with the resulting loss of material looking like grey staining. Although the cause of micropitting is not fully understood, it appears to be caused by cyclic stresses and plastic deformation on the asperity scale. In addition, sliding between gear teeth causes traction forces that subject asperities to shear stress. Micropitting is influenced by a number of factors including loads, temperatures, gear tooth macro- and micro-geometry, flank surface finish, heat treat, and lubricant properties.

Micropitting predominantly occurs on case-hardened gear teeth when it occurs. Figure 1 illustrates the appearance of micropitting.

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.