Runout and Helix Accuracy—Ask the Expert
This question and answer also appeared in the June/July 2012 issue of Gear Technology (download PDF).
Regarding inspection: Why does DIN 3962 specify F beta tolerances, taking into consideration only the gear face width? Should not consideration also be given to the influence of gear diameter due to the runout?
Durval Baroca, gear process specialist, ZF do Brasil
Effects of Radial Runout
All standards for accuracy of gears, such as DIN 3962, ISO 1328 and AGMA 2015, provide a series of classes, or grades, that assign different levels of tolerances for aspects of gear quality. These relate to analytical parameters such as involute, helix (or lead), pitch variation, accumulated pitch variation and runout.
These different levels of tolerance have been developed over time, by experience gained with different manufacturing methods such as cutting, shaving and grinding. Function in final applications has also been considered.
You mention F beta, which is the symbol for helix. You are indeed correct in recognizing that runout (Fr) has an influence on helix accuracy. However, it doesn’t matter what causes the error; the only concern is that it doesn’t exceed the tolerance—regardless of cause. The design engineer presumably determined which level of accuracy would meet his requirements for transmission error or functional life, and picked an appropriate accuracy grade.
When looking at the analytical gear inspection charts, the shape of the traces for helix—as well as the amplitude—can be very informative as a diagnostic tool. Typically, four teeth—approximately 90° apart—are inspected on both sides.
If all of the traces have a slope error and are parallel, your problem is from the cutting or grinding machine set-up.
If they all vary in slope direction from one trace to another, the problem is probably from runout.
An AGMA technical paper (93FTM6), "Effect of Radial Runout on Element Measurements," by Irvin Laskin, Robert Smith and Edward Lawson, explains this in detail (available at www.agma.org). To illustrate the effects, a gear was made of master gear quality ("Table 3"). It also was made with a 3.5-inch-long face width in order to show the resulting sinusoidal-type helix traces when .0034" run-out was introduced in the inspection. Continuing with the same referenced paper, "Figure 13" shows the theoretical result and "Figure 14" shows the actual, measured results. "Figure 13" also shows what the tooth alignment would look like if it had a narrow face width; only short pieces of the sinusoidal wave would show, looking like typical helix error—but at different angles for each tooth.
This gear, as checked with runout of 88.9 micrometers, would meet a DIN Class 11. The tolerance for helix for this DIN Class–11 gear would be 100 micrometers; the measured maximum F beta equals 73.6 micrometers.
In conclusion, it only matters whether the traces fall within the allowable limit for any prescribed grade or class. Looking at the characteristic of the traces can be useful when determining what to fix in bringing the gear within tolerance. The above remarks also apply to involute traces that are either parallel or have varying slopes.