Manufacturing Variability

The optimization process described requires thousands of gear contact analyses. For this reason, the analysis algorithm must be very fast to make this a practical tool for the engineer: The computer code to perform this analysis is highly streamlined, and the optimization routines we describe here are performed in a couple hours. It is possible to leverage these fast solution times to carry out other parametric studies that require several evaluations of gear contact analysis.

One particularly useful application is the simulation of microgeometry manufacturing variability effects on gear performance. The optimization process produces a design, which is nominally the best, but it takes no account of the A design with very good performance, when made to exact optimization specifications, may give poor performance when even very small changes are made to microgeometry parameters.

Microgeometry parameters such as lead and involute slope, crowning, barreling, and tip and end relief cannot be varied individually to assess the sensitivity of the durability and NVH performance. There is too much interaction between these parameters for such an approach to provide any useful information on robustness. A better method is to vary each parameter simultaneously using Monte Carlo simulation — which randomly varies parameters within a normal distribution to examine the effect on some outcome. (We explore TE in the example that follows.) When sufficient random variations are analyzed, an outcome distribution can be generated and valuable information gained.

Let us consider some variation in the lead slope, involute slope, and crowning. The amount of variation is based on the tolerances for an ISO Quality Grade 7 gear. The values are chosen randomly with a probability determined by a normal distribution; the mean is the nominal value from the optimization and the standard deviation is 1/6th of the tolerance range for that parameter. Crowning cannot have a negative value; therefore, the mean value must be great enough to ensure that the lower limit is greater than zero.

Let us explore Monte Carlo simulation on 200 variants of our automated and re ned microgeometry designs at low (14 Nm), medium (82 Nm), and high (177 Nm) loads. Histograms of the resulting TE distributions are shown in Fig. 12.

At 14 Nm, the automated design has a distribution with a lower mode and narrower peak than the refined design. This indicates that the automated design is better at this low torque level. However, at 82 and 177 Nm the refined design is better, as the mode is lower and the distribution widths are approximately the same. In this example it is difficult to say which design is ‘best’ overall, as no specific targets are defined — but this information is very useful in a real design situation.

Where targets are de ned, it is possible to set them based on a percentage failure rate rather than a nominal value. These distributions could be used to indicate where manufacturing tolerances need to be tightened or where they can be relaxed. The ability to relax tolerances with con dence can lead to signi - cant production cost savings through the use of cheaper manufacturing processes.

Coming soon

The development of fast algorithms for analyzing gear contact behavior is allowing other parametric study types. Here, we examine Monte Carlo simulation to verify predictions of production variability on NVH performance. Beyond this, more sophisticated design-ofexperiments methods can be used to identify the sensitivity of individual parameters. The next development based on the approaches we explore here is to include manufacturing variability as a factor in the optimization cost function. Currently, run times for this (which grow by a factor of several hundred) make this impractical. That said, the continuous exponential improvement in computing performance means that a one-week task last year is an ‘overnight task’ this year, and will become a ‘coffee-break’ task next year.

By making use of such computer- based analysis techniques, gear designers can create robust designs faster and with greater confidence than before. Enabling engineers to carry out such detailed analysis upfront in the design process reduces the need for redesign, repeated prototyping, and later testing — and decreases development time and cost.

For more information, visit www.romaxtech.com.

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