Results of ISO/TS 633622 Evaluating Full Contact Zone
ISO/TS 633622 (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 633622 calculates a safety factor against micropitting by comparing the minimum specific lubricant film thickness to the permissible lubricant film thickness. Unfortunately, ISO/TS 633622 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 The next systematic review of the document will require that it either be converted to an international standard or withdrawn.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 633622 reliably predict the risk of micropitting.
As is typical of gear calculation standards, two different methods are presented in ISO/TS 633622. 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 633622 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 633622 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 633622. 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 633622. For Case 2, ISO/IEC 614004 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 633622 Method A reliably indicates micropitting will occur.
Description of ISO/TS 633622
The previous paper contained a detailed description of the methods in ISO/TS 633622. A brief refresher is presented here.
In ISO/TS 633622, 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 633622.
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 633622 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 633622, 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 633622 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 parallelaxis 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 633622 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—HighSpeed Compressor Gear Set
Case 1 is a highspeed 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 fiveyear 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  5864  5864 
Pinion speed  rpm  7,582.0  
Pinion torque  Nm  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 compressorduty 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 633622 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 highspeed 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 925B22 (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 925A03 (Ref. 15) and AGMA 6011J14 (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 633622, 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 highspeed 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 633622 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 633622, 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 633622 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, startup, 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 1.5MW 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 6million 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  5963  5862 
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 wellmonitored 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 highspeedshaft 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 worstcase 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 onesecond and 10minute 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 (cutin 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
CutIn 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
Nm
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 wellmaintained, 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  Cutin 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 633622, 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.
Figure 6—Pressure distribution (left) and specific film thickness (right) across the contact zone for Case 2.
Method B Updated Results
For comparison, Method B calculations were also run using the additional load cases and temperatures. The results are shown in Table 7.
Load Case  
Name  Symbol  Units  Cutin Speed  Intermediate Speed  Rated Speed and Load  
Oil temperature  θ oil  ⁰C  50  70  50  70  50  70 
Bulk temperature  θ M  ⁰C  50.31  70.32  50.35  70.37  51.70  71.75 
Minimum specific film thickness  λ GFmin    1.283  0.669  1.412  0.738  1.287  0.695 
Permissible specific film thickness  λ GFP    0.338  0.338  0.338  0.338  0.338  0.338 
Safety factor  Sλ    3.80  1.98  4.178  2.18  3.81  2.06 
Table 7—Results using ISO/TS 633622, Method B for Case 2.
The Safety Factors
The highest load condition for this gear set is at the rated speed. This is also the load case where the lowest safety factors are found. Using Method A, the safety factor is 2.28 with a 70⁰C oil temperature. However, the gear drive rarely ran with that sump temperature and we would expect the operating safety factor to be closer to 4.48. It is expected that an ISO calculation using Method B will be more conservative than one using Method A. That remains true in this case, with a safety factor of 2.06 when calculated using the 70⁰C oil temperature.
Guidance in IEC 614004
In the last several years, the IEC/ISO joint working group has been revising IEC 614004 “Wind turbines  Part 4: Design requires for wind turbine gearboxes” (Ref. 20) to include guidance on the use of ISO/TS 633622 for wind turbine gear drives. The calculations in this paper agree with the requirement to use Method A for the calculation of minimum specific film thickness and Method B for the permissible specific film thickness. There is an additional recommendation in IEC 614004 to balance the roughness of the pinion and gear teeth for critical gear stages that are not in ISO/TS 633622. This gear set does not adhere to that, but neither will many older wind turbine designs.
The draft wind turbine design document also recommends that the safety factor against micropitting should be greater than 2.0 to avoid damage. However, it strongly encourages the engineer to verify the results of the calculation to field experience with similar gear sets and establish a minimum safety factor based on that with values between 1.5 and 2.0. The safety factors calculated for Case 2 approach 2.0 as the oil temperature is raised toward 70⁰C. However, the gear drive never operated at this temperature. As can be seen in Figure 5, the maximum temperature was 66⁰C and was between 40⁰C and 60⁰C for the majority of the operating time. This is a case where the calculated safety factors should be validated against field experience.
As was noted in “Calculation Results,” the gear drive operated at several different load cases based on the wind speed. The load spectra are used to perform a cumulative fatigue damage calculation when wind turbine gearing is evaluated for gear tooth pitting and bending damage. This approach is not possible with micropitting because an SN curve for micropitting has not yet been established. A calculation in accordance with IEC 614004 would be made at the rated speed of the rotor.
Case 3—AGMA Tribology Gear Set
Case 3 is the gearing used in the AGMA Tribology Test Program (Ref. 21). This gearing is similar to FZG “C” gears, but more representative of industrial gears, as they have finer pitch, different tooth counts, and incorporate tip relief and profile modifications to remove interference. They also have axial crowning to increase compressive stress near the center of the face width.
In the previous paper, the micropitting safety factor was calculated with the lubricants that were used in the original tribology test. For this paper, the study performed by Houser (Ref. 22) is referenced. That study was run to test the ISO/TS 633622 method by testing with Dexron VI ATF to determine its micropitting load stage. Photos of the micropitted pinion appear in Figure 7.
Figure 7—Tooth surfaces of a pinion operated at (left) SKS 9 after 40 hours and (right) SKS 9 after 160 hours. (Photos courtesy of Gearlab at The Ohio State University.)
The calculations with Method B in the last paper resulted in safety factors that were between 1.10 and 1.80, with values decreasing as the load increased. This result is comparable to other calculations of micropitting safety factors that have been reported when micropitting was seen. This paper will compare Method A and Method B calculations with the test results from Houser’s study. The calculations were made using the loads for FVA 54 Load Stages 7, 8, 9, and 10 in order to simulate the testing that was performed on the gear set. The geometry and lubricant for this case are summarized in Table 8. The loads appear in Table 9.
Dimension  Units  Pinion  Gear 
Number of teeth    20  30 
Ratio    1.50  
Center distance  mm  91.50  
Normal module  mm  3.629  
Face width  mm  13.97  
Outside diameter  mm  82.042  116.716 
Pressure angle  degrees  20.00  
Helix angle  degrees  0  
Addendum modification coefficient    0.2533  0.0296 
Surface roughness  μ m  0.34  0.22 
ISO accuracy grade    4  5 
Material surface hardness  HRC  5961  5961 
KA Kv KHα KHβ product    1.0826  
Lubricant    Dexron VI ATF  
Inlet lubricant temperature  °C  40 (Measured) 
Table 8—Input data for Case 3.
SKS  Pinion Speed (rpm)  Pinion Torque (Nm)  Nominal Hertzian Contact Stress at Point A (N/mm2) 
7  2,250  132.5  1,048 
8  2,250  171.6  1,191 
9  2,250  215.6  1,333 
10  2,250  265.1  1,476 
Table 9—Load cases for Case 3 calculations.
Additional Details/Discussions on This Gear Set
The geometry of this example is very close to the FVA 54 test gears and the loads are those used in the load stages for the FVA 54 test. The permissible specific film thickness that is calculated for the lubricant will be representative of the test gearing. It is expected that the safety factors calculated for this case will be predictive of the micropitting found during the testing.
Calculations
Method A Calculation Results
The results using Method A are shown in Table 10.
SKS Load Stage  
Name  Symbol  Units  7  8  9  10 
Bulk temperature  θ M  ⁰C  53.28  56.58  60.19  64.09 
Minimum specific film thickness  λ GFmin    0.256  0.224  0.196  0.171 
Permissible specific film thickness  λ GFP    0.189  0.189  0.189  0.189 
Safety factor  Sλ    1.35  1.18  1.04  0.90 
Table 10—Results using ISO/TS 633622, Method A for Case 3.
The pressure distribution and the specific film thickness across the contact zone can be seen for the failure Load Stage 8 loads in Figure 8. The effect of the tooth crowning is clear with the loads centered on the tooth. The influence of the sliding factor on the film thickness is evident in the higher values near the pitch line and lower values near the tooth root.
Figure 8—Pressure distribution (left) and specific film thickness (right) across the contact zone for Case 3.
Method B Updated Results
The results of Method B calculations are shown in Table 11.
SKS Load Stage  
Name  Symbol  Units  7  8  9  10 
Bulk temperature  θ M  ⁰C  53.58  56.91  60.52  64.47 
Minimum specific film thickness  λ GFmin    0.319  0.273  0.233  0.200 
Permissible specific film thickness  λ GFP    0.189  0.189  0.189  0.189 
Safety factor  Sλ    1.69  1.44  1.23  1.06 
The Safety Factors
Using both Method A and Method B, the calculated safety factors are wellaligned to the micropitting seen on the test gears. Significant micropitting was seen between Load Stages 8 and 9 with low values of safety factors at these stages.
Conclusions
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. As a result, the authors can provide specific details upon request.
This investigation has reviewed calculations using ISO/TS 633622 Method A and Method B, comparing the results against field results. In the process of writing both papers, extensive reviews have been made of geometry, surface roughness, load conditions, and lubricant conditions. These reviews were done to best understand the influences of micropitting on each example and the applicability of the calculations to the results. The following conclusions about the methods can be made.
 The safety factors calculated using Method A and Method B did not predict micropitting for Cases 1 and 2. Both cases have high safety factors, but experienced micropitting in application.
 Permissible specific film thickness. The permissible specific film thickness is a significant factor in the calculation of a micropitting safety factor. It is important to use a value that is representative of the gear set being evaluated.
 This value is best when measured from testing of real gear sets in application conditions until they micropit. This is not always practical or possible.
 If testing with real gears is not possible, a calculation using the results of FVA 54 testing can be used. However, FVA 54 testing is a test of the micropitting resistance of a lubricant using gearing that is designed to micropit. The resulting permissible film thickness will have a degree of uncertainty based on how different the gearing and operating conditions are from the FVA 54 test.
 This value is best when measured from testing of real gear sets in application conditions until they micropit. This is not always practical or possible.
 Fatigue limits for micropitting. Case 1 ran at steady load and speed for much longer than what would be the endurance limit for the classic bending or pitting failures. In addition, the condition of the nondamaged flank areas indicates that the gearing operated in a full EHL regime throughout its life. The WindowsLDP analysis shows that the entire face of each tooth carried the contact. Despite these good operating conditions, the teeth experienced micropitting after billions of cycles. This outcome leads one to question whether micropitting is solely predicted by film thickness, or whether additional fatigue considerations play a role.
 Minimum specific film thickness. Method B is a general calculation model for the minimum specific film thickness. The engineer is advised that a more thorough analysis uses Method A. However, the engineer is left to decide how to determine the pressures and temperatures within the contact zone when using Method A.
 Influence of surface roughness method. ISO/TS 633622 uses the arithmetic mean roughness value (Ra) to assess the influence of the surface finish on the specific film thicknesses. Recent tribological work has utilized the rootmeansquare roughness (Rq) or maximum height of profile (Rz). In order to test whether the use of these parameters would change the results of the calculations, measured values of Rz from the gearing in Case 2 were used to calculate the specific film thickness. Measured values of FVA 54 test gearing were used to calculate the permissible specific film thickness. Specific film thickness decreased when using Rz. The resulting safety factor also decreased, but it is hard to say whether it is more predictive of micropitting. More review is needed on this topic.
Roughness Method
Name
Symbol
Units
Ra
Rz
Effective roughness1
Ra, Rz
μ m
0.385
4.315
Minimum specific film thickness
λ GFmin

0.653
0.058
Permissible specific film thickness
λ GFP

0.338
0.048
Safety factor
Sλ

1.932
1.212
1 Effective roughness using Ra is the arithmetic mean value. Effective roughness using Rz is the rootmeansquare value.
Table 12—Results of using alternate roughness parameters, Case 2, Method B.
In general, the methods in ISO/TS 633622 work best when the engineer has complete knowledge of the design, manufacturing, operating conditions, and service life of the gear set and its lubricant. Pinnekamp (Ref. 23) noted that confidence in the safety factor against micropitting relies on the engineer’s knowledge of the operating conditions and the quality of their calculations. The safety factor must be compared to the results of the tests with similar gears when there is low confidence in the methods.
Future Work
As the science behind predicting micropitting continues to evolve, some future work is needed for ISO/TS 633622. Future development should arrive at safety factors that do not require comparison to similar gearing for interpretation. Additional recommendations are to:
 Continue to develop a method to establish the permissible specific film thickness of the lubricant when testing of real gears is not possible. If results from FVA 54 lubricant tests must be used, it would be helpful to have a method to scale the data to the application geometry and loads.
 Improve the guidance to lead the engineer in the complete use of Method A, including all factors for consideration (e.g., load, temperature, surface topography, etc.).
 Develop a test procedure to evaluate the SN relationship for micropitting so the impact of accumulated stress cycles can be established when evaluating for the risk of micropitting. Further, developing a predictive model that incorporates this unique micropitting mechanism is important as gear drive life cycle expectations continue to grow.
Acknowledgments
Many thanks to the contributors to this paper:
 WindowsLDP data was provided by The Ohio State University.
 Artec Machine Systems provided the geometry and application data for the compressor gear set in Case 1.
 NREL and General Electric Renewables provided geometry and application data for the wind turbine gear set in Case 2.
 REM Surface Engineering provided the surface roughness analyses for all three cases.
 Regal Rexnord provided all support for the Method B calculations and analysis.
This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under Contract No. DEAC3608GO28308. Funding was provided by the US Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paidup, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.
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