In the first of this two-part series, we explored how new computer-based modeling of geared systems is allowing the design of gear microgeometry for durability and lower noise, vibration, and harshness, or NVH. No two gears are manufactured the same, but addressing variability with optimized gear microgeometry boosts durability and NVH.

Here we continue our explanation of an automated approach to optimize microgeometry, and Monte Carlo simulation for investigating microgeometry designs.

Automated optimization

Two things are critical to good gear design: Consideration of misalignment variation with load, and knowledge of detailed gear contact behavior. Now, understand that no design transmits only one load — so additional data and variables must be considered when analyzing a range of loads for optimization. Here, automated optimization allows engineers to effectively process large amounts of data and drastically reduce the time required to create a design.

Some design software includes automated optimization tools to assist in microgeometry design. It resolves potentially conflicting demands of different targets such as durability, NVH, and so on. This is done through a designerselected cost function that defines the balance between NVH and durability requirements.

Know that optimization can be very sensitive to the relative weighting of these factors, so automated optimization should not be considered a black box that produces the perfect design at the click of a button. Instead, it is a tool that provides a starting-point design — one that requires further refinement.

Let us assume that for our example third gear pair, we increase cost function within the software with a low transmission error, or TE. Note that TE under higher load is given slightly lower weighting, as gear whine noise is often perceived to be less of a problem at high load. As for edge, tip, and root contact: Maximum contact load close to the tooth perimeter greatly reduces score.

The results of this optimization are shown in Figs. 8 and 9: TE is very low across the whole torque range, indicating that this design’s NVH quality is good. The contact load distributions show that the optimizer has avoided edge contact by introducing end relief, and the load is distributed over a wide area of the tooth — thus reducing overall peak load. In turn, contact damage for the full duty cycle is considerably reduced (pinion by 33% and wheel by 26%) compared with the manually optimized design. However, the optimizer converges on a solution with almost zero crowning, so contact is not well centered at the lowest and highest load. While this is not in itself a problem, it does mean that our design is likely to be sensitive to manufacturing variations in lead slope.

Refined Optimization

Treating these results as a starting point, further re nements can be made to improve the design. The cost function can be adjusted by including a factor that biases the result so that maximum contact load is close to the tooth center. This is likely to force the optimizer to increase the amount of crowning which may in turn degrade TE. However, as TE is already very low for a transmission of this type, it is acceptable to sacri-  ce some NVH performance for an overall improved design.

With this adjusted optimization, more crowning is included as predicted. The amount of crowning is still only 2 μm, which is small compared to crowning manufacturing tolerances possible in mass production. For the final design, crowning is thus manually increased to 5 μm.

The results of this refined optimization are shown in Figs. 10 and 11. Contact load distribution shows improvement over the previous design in that contact is more centralized across the load range, and peak load is reduced at the highest torques. On the other hand, there is slight increase in peak load at lower torques due to the reduction in contact area caused by additional crowning. The effect of this can be seen in the full duty-cycle contact damage, which increases to 48% and 38% for the pinion and wheel respectively.

A secondary effect of crowning is that it tends to increase TE at low loads due to the deviation of the gear surface from the ideal involute. At high loads the increase in TE is small as the higher contact forces deform the tooth surface back towards the involute shape. This is confirmed by TE results, which show a proportionally larger increase in TE below 100 Nm than at higher torques when compared with the previous optimization results. However, the TE is still low and falls well within what would is considered a quiet range.