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. 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. 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.
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.
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.
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.
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.
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.
Corrective microgeometry was applied through precision tooth form grinding — verified by inspection — and the field failures of the pinion were eliminated.
Many resources are available for advanced mesh analysis:
- AGMA consultants
- LVR software supported by MDesign
- Contact analysis in KISSsoft software
- Romax software
- Dontyne software
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.
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.
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.
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
- MDesign User’s Manual for LVR 2012 Software