A case study demonstrates the benefits of advanced mesh analysis, including design and application of optimized microgeometry through precision tooth form grinding. Recommendations can be applied at the design phase to optimize gearing performance or, reactively, to identify root cause of failures.

Through a case study involving pinion failures on plastic extruder drives, this paper covers failure analysis, gear rating review, application of advanced mesh analysis to define component deflections causing loaded mesh misalignment, and reduced tooth contact/high stress concentration resulting in tooth macropitting. The paper demonstrates the capability and benefits of advanced mesh analysis, including design and application of optimized microgeometry through precision tooth form grinding, with recommendations on types of microgeometry that are most effective and easiest to apply, inspect, and document in a production gear manufacturing environment.

Figure 1: Photographs of shifted contact

The summary will review tools that are commercially available to perform advanced mesh analysis and design, manufacture, and inspect optimized microgeometry, which compensates for tooth deflection, shaft bending, torsional windup, and bearing deformation in order to improve gearing mesh alignment and tooth contact under load for quiet running and longer-life gearing.


AGMA gear rating standards like 2001 and 6123, for example, consider how mesh contact affects gear tooth strength and durability by developing a load distribution factor Km.

Figure 2: Involute and lead inspection of returned pinion suggests that the original quality was in tolerance per AGMA 2000 Q12 as specified; the wear on the right flank measures 0.0013″ with a distinct step at the end face

These standards offer an empirical method to estimate Km; however, without extensive application experience, caution should be taken and advanced analysis should be considered. Km is found in the denominator of the allowable power rating equations, is greater than 1.0, and is a derating factor. The subject application carries a 1.6 service factor on both bending and contact strengths based on Km of 1.37 per AGMA 2001. A typical design goal is to apply modified leads and involutes to precision-ground tooth gearing, which compensate for deflections under a known load condition, and achieve Km defined in the rating calculations. This tool was developed in the 1990s to better understand numerous and various wind turbine gearing failures where gear drives were put on a weight diet, increasing deflections, and designed to operate for 20-plus years in unknown wind conditions with poor electronics for load feedback and control.

Figure 3: 3D model of the gear mesh, bearings, and shaft configuration


An application from a helical speed reducer is presented, and the subject pinion has macropitting failure as shown in Figure 1. Note the heavy contact on the left side of the active face width by the heavy contact pattern, wear step at the mating gear face edge, and macropitting.

Figure 4: LVR load intensity factor (similar to AGMA Km) of 4.57


The bending and durability strengths of both pinion and gear were checked using AGMA 2001 gear rating software. The gear set design is optimized for balanced ratings with a minimum 1.8 service factor at the 200-hp application and 513 rpm on the pinion. The metallurgy and heat treatment of the returned pinion was evaluated and found to be within print specifications. Experience suggests that a service factor of 1.2 minimum would be sufficient for this electric motor-driven application with low torsionals and shock loads. The calculated minimum service factor indicates that the design, materials, and heat treatment are conservative and not the root cause for the failures.

Figure 5: Plot of shaft bending deflection under load

The shifted, concentrated contact pattern is visually evident, resulting in a much higher Km than the 1.2 assumed in the rating calculations based on ground tooth accuracy. Previous photographs show how the contact intensity increases across the face, as evidenced first by polishing, then micropitting, and finally macropitting/tooth durability failure on the left side of the face width. The shifted contact with good gear geometry (see Figure 2) prompted a mesh modeling analysis, which considers torsional windup, tooth deflection, and shaft bending to develop a 3D load intensity plot across the active tooth flank area. See Figure 3 and Figure 4.

Figure 6: Optimized lead modifications (values in micrometers); gear 1: 50 mm crown; gear 2: 10 mm crown plus 130 mm helix slope correction

The software predicts extremely heavy loads on the left (long shaft) side of the pinion, which correlates with the visual evaluation of the failed pinion and the contact shift caused by pinion bending with the tooth section not centrally located between the bearings. See Figure 5.

The software recommends optimum involute modifications (tip relief). A combination of lead taper/crown was identified, which optimized the load intensity plot across the active tooth flank area after several iterations of varying lead modifications (crown, end relief, and taper). See Figure 6, Figure 7, and Figure 8.

Figure 7: Optimized profile modifications (values in micrometers); gear 1 and gear 2: 30.3 mm circular tip relief starting 5.37 mm along line of action below OD

Additional Example of Advanced Mesh Analysis

The following example of a cantilever-mounted pinion driving a gear mounted to a rigid bogie wheel is provided to present the capability of advanced mesh analysis software. See Figure 9, Figure 10, Figure 11, and Figure 12.

Figure 9: Gearing model, cantilever-mounted pinion driving straddle-mounted gear


Corrective microgeometry was applied through precision tooth form grinding — verified by inspection — and the field failures of the pinion were eliminated.

Figure 9: Gearing model, cantilever-mounted pinion driving straddle-mounted gear

Many resources are available for advanced mesh analysis:

  • AGMA consultants
  • LVR software supported by MDesign
  • Contact analysis in KISSsoft software
  • Romax software
  • Dontyne software
Figure 8: Optimized predicted contact with load intensity factor (AGMA Km) improved from 4.570 to 1.145

Advanced mesh analysis software is precise, sensitive, and relative to how changes in microgeometry can affect contact — especially under light loads, which do not spread contact across non-conforming surfaces. Optimized microgeometry is developed through several iterations by watching how the predicted load intensity changes, and it is tempting to fall into a trap of changing microgeometry by 0.000050″ and seeing significant changes in load intensity. Keep it real, and limit microgeometry values to those that can be manufactured and measured.

Figure 10: Predicted bending deflection of pinion shaft and gear

It is also possible to apply complex parabolic modification forms or compound curves (suggested for high contact ratio spur gears), which forces form grind operators to use modification tables. The author prefers to use modifications of 0.0002″ or greater and simple, circular forms with direct form grinding machine input of two parameters (amount and start point), which can be adjusted on the fly if necessary. If more complex forms are required, be sure to verify understanding and capability of the manufacturer. Lead, involute, slope, and form tolerances are based on specified accuracy. RMS values of these tolerances should be applied in both plus and minus directions to the calculated modifications and mean modification values adjusted to optimize performance. Circular tooth tip chamfers or linear chamfers with transition radius should be considered when necessary.

Figure 11: Predicted mesh contact with no lead or involute modifications

Verification and Inspection of Optimized Microgeometry

AGMA 2015, which is now obsolete and was replaced by ISO 1328-1 B14, was developed to improve accuracy and control of gear accuracy, eliminating “K” chart interpretation, and to provide analytical analysis of slope, form, and total error in the unmodified lead and involute zones. The wording of AGMA 2015 avoided the details related to inspection of microgeometry modifications, as it was not well-defined while the standard was being developed. Gear manufacturers and users have agreed to verify the location of one point of a modification within 2015. The updated ISO 1328 accuracy standard will facilitate and require verification of the total modification form rather than a single point — making the assumption that the rest of the form is correct.

Figure 12: Predicted mesh contact with modified lead and involute 0.0015″ lead crown and 0.0026″ taper per flank with 0.002″ tip relief


This paper covered the application of advanced mesh analysis tools as a reaction to failures and, proactively, to optimize gearing performance. The key steps are:

  • Procuring a resource, either a consultant or commercially available software
  • Understanding application loads
  • Modeling the gearing, shafting, and bearings
  • Designing optimized microgeometry
  • Applying modifications through precision tooth grinding
  • Verifying that the applied modifications are true to form and amount


  1. MDesign User’s Manual for LVR 2012 Software
* 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. 15FTM28.
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has been with Milwaukee Gear since 2000. He is the chief engineer of the Mechanical Components Group within Regal Beloit America Inc.’s Power Transmission Solutions business segment — a family of product brands, including Milwaukee Gear, that supply power transmission components. Klaves received his bachelor’s and master’s degrees in engineering from the University of Wisconsin — Milwaukee, and he specializes in gear design and optimization. He started his career in 1972 with Falk Corporation, now owned by Rexnord. Klaves can be reached at tklaves@milwgear.com.