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 (Ref. 1). ISO/TS 6336-22 calculates a safety factor against micropitting by comparing the minimum specific lubricant film thickness to the permissible lubricant film thickness. Unfortunately, ISO/TS 6336-22 does not recommend a minimum safety factor. Rather, it is left to the engineer to compare the calculated results to a similar gear application.

The approach has been published since 2010 and the “technical specification” designation of the document means that it contains calculations that are still subject to further development. The next systematic review of the document will require that it either be converted to an international standard or withdrawn. For this reason, it is important to verify that the calculations in ISO/TS 6336-22 reliably predict the risk of micropitting.

As is typical of gear calculation standards, two different methods are presented in ISO/TS 6336-22. The first, Method A, allows the engineer to calculate lubricant film thicknesses using a gear computing program that models the complete contact area of the mesh. In contrast, Method B starts with the assumption that micropitting will start in the region of negative sliding and evaluates the film thickness at specific points along the line of action. ISO/TS 6336-22 recommends both methods should be validated against experience with gear sets in similar application conditions for the calculation of the permissible specific film thickness.

A previous paper, “Case Study of ISO/TS 6336-22 Micropitting Calculation” (Ref. 2), evaluates three cases using the Method B calculations. The first example is an increasing gear set for a compressor, the second is a wind turbine gear set, and the last is the American Gear Manufacturers Association (AGMA) Tribology Test gear set. These examples cover a range of gearing sizes and application conditions. All the gear sets experienced micropitting, providing good examples to verify the computation results. Using Method B, only the AGMA Tribology Test gearing resulted in safety factors that aligned with expectations predicting micropitting.

The results for all three cases were reviewed with members of ISO Working Group 6, who were central to the development of ISO/TS 6336-22. They expressed concern about the use of Method B for Cases 1 and 2. With a pitch line velocity above 80 m/s, Case 1 requires the use of Method A according to the scope of ISO/TS 6336-22. For Case 2, ISO/IEC 61400-4 for wind turbines requires the use of Method A to calculate the minimum specific film thickness. The operating sump temperature for this drive was also scrutinized as wind turbine gearing can run at higher temperatures.

Consequently, the operating conditions and calculation parameters for all three cases were investigated further. That information has been modified for this paper. The results from the previous paper have been updated and are presented here along with the results from Method A. The results from both methods are compared in order to point out the differences. They are also compared to the field results to determine whether ISO/TS 6336-22 Method A reliably indicates micropitting will occur.

Description of ISO/TS 6336-22

The previous paper contained a detailed description of the methods in ISO/TS 6336-22. A brief refresher is presented here.

In ISO/TS 6336-22, two different methods are presented for the calculations of the minimum specific lubricant film thickness and the permissible specific film thickness. Like other ISO gear calculations, Method A involves the use of testing or detailed calculations to determine critical parameters. Method B is a simplified, analytical method for each. Method B was used in the previous paper.

It is possible to calculate the minimum specific film thickness in the numerator of the safety factor using one method and the permissible specific film thickness in the denominator of the safety factor using the opposite method.

Method B

Method B calculations were conducted using a Mathcad worksheet to follow the equations found in ISO/TS 6336-22.

Minimum specific film thickness

A calculation of the minimum specific film thickness using Method B begins by calculating the film thickness with a Dowson/Higginson analysis along the line of action. This value is modified by a local sliding factor that accounts for regions of negative sliding. The minimum of the specific film thicknesses along the line of action is used to calculate the safety factor.

Permissible specific film thickness

The permissible specific film thickness is determined by conducting standardized testing with gearing that is similar in geometry, quality, and material of the gearing being designed. The gearing is run until the micropitting failure limit is reached. The critical specific film thickness for the test gearing is then calculated with ISO/TS 6336-22 using the load data from the failure stage. This is the permissible specific film thickness. If it is not possible to test with real gears, one may use the failure load stage of the lubricant in standardized tests, such as FVA 54 (Ref. 3), and calculate the minimum specific film thickness using the test gearing.

Method A

Minimum specific film thickness

To determine the minimum specific lubricant film thickness using Method A, the engineer calculates the value with a gear computing program that models the complete contact area of the mesh. The load distribution, sliding velocities, and actual service conditions are considered in this analysis. The results appear as maps of pressures and film thicknesses across the face of the pinion and gear flanks. These are used to calculate the specific lubricant film thickness at each point in the contact zone. It is important to note that the minimum value is used for the safety factor against micropitting.

Permissible specific film thickness

The permissible specific film thickness is determined through testing of real gears in conditions like the application until micropitting just occurs. The test loads and the gear computing program are then used to calculate the film thickness. These tests can also be performed for gear designs and service conditions very similar to the gear set of interest. However, testing such as this can be very costly and may not always be practical if the applications are high load, low speed, with varying operating conditions, and low production volume, or noncritical service. If that is the case, there are options to approximate the permissible specific film thickness from reference gears and FZG lubricant tests. However, each approximation reduces the accuracy of the resulting safety factor.

As recommended in ISO/TS 6336-22, it is important to interpret the micropitting safety factor by comparing it to the performance of similar gearing used in the field under similar operating conditions.

Application of Method A in This Paper

As can be seen in the preceding clauses, a true Method A calculation of the permissible specific film thickness requires that real gearing be tested in a controlled test until micropitting occurs. In Cases 1 and 2, this was not possible given their applications, size, and load conditions. The calculations here were done using Method A for the minimum specific film thickness in the numerator and Method B for the permissible value in the denominator of the safety factor calculation.

Method A Gear Computation Program–WindowsLDP

There are several gear computing programs capable of calculating the Hertzian stresses in the contact zone of a gear tooth mesh. This paper uses the WindowsLDP (Load Distribution Program) from The Ohio State University to determine the stresses. The remainder of the factors follows the methods of ISO/TS 6336-22 to calculate the minimum specific film thickness.

WindowsLDP is a quasistatic gear design and analysis tool for external and internal spur and helical gear pairs. It employs computationally efficient and accurate semianalytical formulations to compute the load distribution between multiple mating teeth of gears.

The contact pressure distribution is calculated using a parallel-axis gear pair load distribution model (Ref. 4). This model combines:

• The unloaded tooth contact analysis proposed by Singh and Houser (Ref. 5),
• Sources of compliance including tooth bending and shear (Ref. 6),
• Tooth base rotation (Ref. 7) and contact deformation (Ref. 8),
• An initial separation vector including any deviations of the surfaces from perfect involutes (i.e., microgeometry modification).

The load distribution is computed by implementing the modified simplex algorithm proposed by Conry and Seireg (Ref. 9).

WindowsLDP has been validated against testing throughout its development.

Using the predicted load distribution, WindowsLDP computes the loaded transmission error, root and contact stress distributions, mesh stiffness functions, and tooth forces. Other design evaluation parameters such as lubricant film thickness and surface temperature can also be computed. Tooth modifications of various forms can be entered interactively or can be read from the tooth surface measurements. The results are presented by an interactive graphical user interface that provides the user the flexibility to process and present them in desired formats.

Case Studies Using Method A

Cases of operating gear sets that experienced micropitting were selected to exercise the ISO/TR 6336-22 document. Because there was concern over the influence of operations and maintenance on micropitting, the authors reviewed lubrication tests, load cases, and operating conditions for each, particularly for Cases 1 and 2. The details of the calculations of these case studies are quite lengthy. The drawings and details of the profile and lead modifications are also proprietary. The authors can provide specific details upon request.

Case 1—High-Speed Compressor Gear Set

Case 1 is a high-speed gear set driving a centrifugal compressor. This set had micropitting on the pinion starting in the dedendum, extending through the pitch line and to the addendum. The micropitting is localized to the drive end of the face width. From experience, this result is predictable due to an increase in tooth contact temperature as the gear mesh load travels through the helical contact pattern.

This gearbox operated for approximately 120,000 hours or 54.6 x 109 cycles. The installation was not located near an area of salt water, high humidity, or subject to significant climatic temperature fluctuations. It operated continuously for four- to five-year periods of time under constant load and speed in an environmentally controlled room. This continuous operation prohibited the absorption of water into the lubricant. After every four to five years of operation, the gearbox was shut down, inspected, and routinely maintained. It was not until approximately 13.5 years of operation that micropitting was detected. At this point, the gear set was exchanged. Prior to this, there was no significant maintenance required.

A picture of the micropitting damage can be seen in Figure 1, with more detail in the previous paper. Other than micropitting, the rest of the gear tooth surface is in very good condition and there are no indications of contact distress or scuffing.

Figure 1—Micropitting on the flank of the pinion teeth. The red zone is closest to the compressor (drive end). The black zone is the motor side. (Photo courtesy of Artec Machine Systems.)

The geometry, loads, and lubricant for this case are summarized in Table 1. The gear teeth have adequate profile and lead modifications for the operating loads.

Dimension	Units	Pinion	Gear
Number of teeth	-	37	163
Ratio	-	4.405
Center distance	mm	600
Normal module	mm	5.90
Face width	mm	280
Outside diameter	mm	236.30	987.29
Pressure angle	degrees	20.00
Helix angle	degrees	10.00
Addendum modification coefficient	-	0.2407	-0.0876
Surface roughness	μ m	0.41	0.40
ISO accuracy grade	-	4	4
Material surface hardness	HRC	58-64	58-64
Pinion speed	rpm	7,582.0
Pinion torque	N-m	12,209.3
KA Kv KHα KHβ product	-	1.4170
Lubricant	-	Mobil Teresstic AC ISO VG 32
Inlet lubricant temperature (estimated)	°C	5
Bulk temperature (for calculations)	°C	82.93/100

Table 1—Input data for Case 1.

Lubricant Condition

The lubricant used in this gear drive was Mobil Teresstic AC 32. This is an ISO VG 32 rust and oxidation oil. Light lubricants such as this are typically used in compressor-duty gear drives wherein there is a long history of successful use.

After detection of micropitting, a sample of this lubricant was analyzed compositionally using ferrography and comparing it to a sample of new lubricant. The analyses showed:

• No significant deterioration of the lubricant chemical composition,
• No significant water content,
• Improved particle content compared to the new sample indicating excellent filtration.

See Figure 2 for “used” ferrography analysis of the lubricant indicating acceptable operating conditions.

Figure 2—Analytical ferrography of used lubricant. (Photo courtesy of Artec Machine Systems.)

This case is of interest because micropitting has been sporadically seen in similar gear drives operating at pitch line speeds between 73 m/s and 175 m/s. In most cases, micropitting was observed after long years of operation. This gear set was only inspected approximately every four to five years, so it is not certain exactly when the micropitting first occurred.

The gear drives are installed indoors in a heated building. They run at steady loads in continuous operation. The manufacturer reviewed the history of sump temperature and oil analysis for the drives that micropitted. There is no evidence of high temperatures, contaminated lubricant, or nonuniform contact in the gear mesh.

It is interesting to note that Martinaglia’s (Ref. 10) testing demonstrates that the zone of highest temperature is located toward the exit end of the tooth face designed with spray ports symmetrically spaced along the spray bars. This result corresponds to the offset pattern in the micropitting seen on this gear set where the tooth flank experienced the highest operating temperatures. We can conclude that the rise in temperature across the face contributed to the onset of micropitting.

In summary, the lubricant and lubrication system for Case 1 performed well throughout the gear set’s operation based on the previously mentioned analyses. All data associated with this case’s lubricant condition are available upon request.

Calculation Methods for Bulk Temperature and Film Thicknesses

The formulas in ISO/TS 6336-22 were validated with gearing with pitch line velocities between 8 m/s and 60 m/s. Case 1 has a pitch line velocity of 88 m/s. In the previous paper, the Method B calculations arrived at a minimum specific film thickness of 2. While reviewing this example with members of ISO Working Group 6, it was pointed out that the equation for the bulk temperature, θM, is not applicable for pitch line velocities above 80 m/s because of significant heat generation from churning and windage that occur at high velocities. Method A is recommended for calculations at pitch line speeds greater than 80 m/s.

A thorough calculation using Method A would model both the contact pressure and bulk temperature across the face of the gear teeth. Unfortunately, WindowsLDP does not calculate friction or heat generation within the mesh and creating a model to do so is beyond the time frame for this paper. Instead, we turned to the work of Amendola (Ref. 11) to evaluate the bulk temperature for high-speed gears for scuffing calculations. This work is based on tests conducted by Akazawa (Ref. 12) and Martinaglia (Ref. 10). The result is an equation for bulk temperature that depends on the pitch line velocity for gear sets running at greater than 35 m/s. This equation has been incorporated into AGMA 925-B22 (Ref. 13). Using this equation from AGMA 925, a bulk temperature of 82.93⁰C resulted and was used in our Method A calculations.

Amendola’s previous work (Ref. 14) to correlate MAAG gear predictions to AGMA 925-A03 (Ref. 15) and AGMA 6011-J14 (Ref. 16) uses 100⁰C for the bulk temperature. To observe the change in the predicted film thickness, 100⁰C was used for a second set of Method A calculations.

The permissible specific film thickness for Mobil Teresstic AC 32 was calculated using Method B with the geometry of FVA 54 test gears. Unfortunately, no FVA 54 micropitting testing could be found for this lubricant. However, the manufacturer of this gearbox reported that a similar lubricant (Mobil DTE Light, VG 32) used in a similar gearbox was tested and performed to Load Stage 8. Both lubricants have been proven satisfactory in similar applications. Thus, FVA 54 failure Load Stage 8 with 60⁰C test temperature was used.

Calculation Results

Method A Results

The results using Method A are shown in Table 2.

			θ M Method
Name	Symbol	Units	Amendola High PLV Calculation	MAAG Approx.
Bulk temperature	θM	°C	82.93	100.00
Minimum specific film thickness	λ GFmin	-	1.574	1.149
Permissible specific film thickness	λ GFP	-	0.127	0.127
Safety factor	Sλ	-	12.39	9.04

Table 2—Results using ISO/TS 6336-22, Method A for Case 1.

The pressure distribution and specific film thickness across the contact zone can be seen in Figure 3. The zone of highest pressure and lowest film thickness occurs in the dedendum of the pinion, which corresponds to the location of micropitting. The variation of bulk temperature across the face of the high-speed pinion could not be modeled by WindowsLDP, so it does not predict that micropitting will be predominant on the drive end of the face.

Figure 3—Pressure distribution (left) and specific film thickness (right) across the contact zone for Case 1.

Method B Updated Results

In Table 3, we recalculated the example from the previous paper using Method B for the minimum specific film thickness and bulk temperatures of 82.93⁰C and 100⁰C in order to have a closer comparison to the WindowsLDP results.

			θ M Method
Name	Symbol	Units	ISO/TS 6336-22 Method B (previous paper)	Amendola High PLV Calculation	MAAG Approx.
Bulk temperature	θM	°C	60.00	82.93	100.00
Minimum specific film thickness	λ GFmin	-	2.12	1.29	0.95
Permissible specific film thickness	λ GFP	-	0.157	0.127	0.127
Safety factor	Sλ	-	13.48	10.18	7.50

Table 3—Recalculated results using ISO/TS 6336-22, Method B for Case 1.

The Safety Factors

The safety factors that result from all of the calculations—whether using Method A or Method B—are very high. This result occurs when the specific film thickness is much larger than the permissible specific film thickness. However, there are two areas of concern in these calculations:

• The minimum specific film thickness is heavily dependent on the bulk temperature. We did not have a program that can accurately calculate this value. It is also not possible to measure this during the actual operation of the gear drive. We assumed fairly high values for the bulk temperature, but a complete model would contain measured values along the tooth contact, thereby requiring testing with real gears in operating conditions.
  
  
• The permissible specific film thickness is based on the assumed performance of Teresstic VG 32 in FVA 54 tests. A more exact value would be derived from standard testing with similar gears. As the permissible value becomes less accurate, the safety factors calculated with ISO/TS 6336-22 are less reliable.
  
  
• This gear set operated for billions of stress cycles before surface distress was noted. In such a long life, other applications may be subject to transient torsional, start-up, and shutdown loads that contribute to momentary reductions of film thickness. This gear set was run at even loads without stopping for years. Based on photos of the gear teeth, operational data, and observations, this example appears to have operated under full elastohydrodynamic lubrication (EHL). As such, a lambda greater than one is not a good initial basis for predicting micropitting. Rather, this example suggests that asperity interaction was not a factor in micropitting. Instead, it suggests that micropitting can emerge as a microsurface Hertzian fatigue phenomenon under full EHL. Only sufficient accumulated stress cycles appear to be needed. Development of a predictive model that incorporates this unique micropitting mechanism is important as gear drive life cycle expectations continue to grow.

Case 2—Wind Turbine Gear Set

Case 2 is a gear set from a 1.5-MW wind turbine at the National Renewable Energy Laboratory (NREL) Flatirons Campus in Colorado. This example is representative of minor micropitting in wind turbine gearing that has operated for five years or more. Micropitting was found in the start of active profile (SAP) of all of the sun pinion teeth. Micropitting and some abrasions were also found higher on the flanks of the sun pinion teeth. The gear set had been installed for just over 8 years. It had produced approximately 6-million kWh of energy in 14,170 hours of grid operation time, representing approximately 8 percent of its minimum design life. Micropitting was noted after just over 6 years of operation, which represents a relatively low number of stress cycles.

Pictures of the micropitting can be seen in Figure 4. The previous paper also contains pictures of the micropitting and details about the gear drive as documented in (Ref. 17). For this paper, all maintenance records were reviewed. In addition, extensive operational data were acquired and analyzed from the turbine’s supervisory control and data acquisition (SCADA) system. Reference [18] is publicly available and contains the full documentation for this information.

Figure 4—Micropitting on the sun pinion teeth. (Photos by Scott Eatherton, Wind Driven, NREL 61193 and 61194.)

The geometry and lubricant for this case are summarized in Table 4. The gear teeth have adequate profile and lead modifications for the operating loads.

Dimension	Units	Pinion	Gear
Number of teeth	-	27	88
Ratio	-	3.2593
Center distance	mm	487.51
Normal module	mm	8.0609
Face width	mm	200.9
Outside diameter	mm	247.955	759.079
Pressure angle	degrees	22.5
Helix angle	degrees	17.584
Addendum modification coefficient	-	0.0804	0.0804
Surface roughness	μ m	0.22	0.55
ISO accuracy grade	-	6	6
Material surface hardness	HRC	59-63	58-62
KA Kv KHα KHβ product	-	1.478
Lubricant	-	Castrol Optigear A320
Inlet lubricant temperature	°C	50 and 70 (see measured data in Figure 3)

Table 4—Input data for Case 2.

SCADA Data and Lubricant Analysis

In reviewing the details of the Method B results from the previous paper, questions were raised regarding the gear drive operating temperature and lubricant condition. This gear drive was well-monitored during its operation. To better understand the influence of its application conditions on the presence of micropitting, three different factors were reviewed:

• Operating temperatures. Data were available for the temperature of the oil sump for approximately 7.5 years of the 8 years of operation. Oil sump temperatures ranged from 20⁰C to 66⁰C, with the densest cluster being between 40⁰C and 60⁰C, as shown in Figure 5 [16]. Later measurements on a replacement gearbox showed the temperature of the outer race of the high-speed-shaft bearing, one of the highest operating temperatures in the gearbox, did not exceed 70⁰C [19]. Based on this, calculations for the sun pinion were performed with a normal oil temperature of 50⁰C and a worst-case temperature of 70⁰C.
  
  

  Figure 5—Oil sump temperatures (Ref. 18).
  
  

• Load cases. Wind turbines operate under varying load conditions. The previous paper applied the mean load condition to calculate the micropitting safety factor. In order to gain an understanding of the running loads that affected the gearing, the operational torque and speed data were mined in both one-second and 10-minute intervals (Ref. 18). The largest amount of time the turbine spent was actually in idle mode, in which the rotor speed is 0–1 rpm and there is no load of the grid operating time, there were high numbers of data points at rotor speeds of 11 rpm (cut-in speed) with loads under 20 percent and 18 rpm (rated speed) at loads ranging from 40 percent to just over 100 percent. An additional collection of points was seen at 13 rpm and relatively light loads under 25 percent. Based on this, it was decided to run calculations at these three load cases summarized in Table 5.
  
  

  	Units	Original Paper	Cut-In Speed	Intermediate Speed	Rated Speed and Load
  Rotor Speed	rpm	18.3	10.91	12.73	18.3
  Sun Pinion Speed	rpm	254.17	140.62	164.08	254.17
  Sun Pinion Torque	N-m	20,880	3,840	4,080	20,880

  
  Table 5—Load cases for Case 2 calculations.
  
  
• Oil condition. The NREL report on the gear drive condition [17] mentions that sludge was found in the filter during a late 2017 inspection just prior to removal of the gearbox. In order to determine whether the oil condition influenced the onset of micropitting, especially with respect to water content, the gear drive maintenance records were reviewed. Other than an unexplained brief spike in the water content in 2012, the lubricant condition is normal until the late 2017 inspection. The oil viscosity, particle counts, and water content were otherwise within recommended parameters [18]. From this, it was concluded that the lubricant was well-maintained, resulting in relatively cool, clean, and dry conditions and did not contribute to the micropitting.
  
  
• Castrol Optigear A320 lubricant. The lubricant supplier was contacted for information related to the lubricant’s micropitting resistance. Castrol Optigear A320 has a FVA 54 failure load stage greater than 10 at 60⁰C and 90⁰C test temperatures. The permissible specific film thickness of this lubricant was calculated at an oil temperature of 60⁰C because that provided a more conservative calculation and was representative of the operational data for the wind turbine.

Calculation Results

Method A Results

The results using Method A are shown in Table 6.

			Load Case
Name	Symbol	Units	Cut-in Speed		Intermediate Speed		Rated Speed and Load
Oil temperature	θ oil	⁰C	50	70	50	70	50	70
Bulk temperature	θ M	⁰C	50.00	70.00	50.00	70.00	50.00	70.00
Minimum specific film thickness	λ GFmin	-	1.742	0.921	1.829	0.964	1.516	0.769
Permissible specific film thickness	λ GFP	-	0.338	0.338	0.338	0.338	0.338	0.33

Table 6—Results using ISO/TS 6336-22, Method A for Case 2.

At the rated speed and load and an oil temperature of 70⁰C, the pressure distribution and specific film thickness across the contact zone can be seen in Figure 6. The tooth microgeometry can be seen in the pressure distribution, where low pressure zones are at the root and tip of the pinion tooth. The region of lowest film thickness is located in the dedendum of the pinion between the root clearance and the pitch diameter.