**By Prokop Sroda University of Mining and Metallurgy Krakow, Poland **

Edited by Victoria Reitz

The most common failures in high-performance gears are gear-tooth fractures. They often stem from fatigue cracks that start at the root of the tooth. Repeated bending loads widen the crack across the base until the tooth breaks away from the gear.Fortunately, gear profiles can be modified to reduce these failures. The key is to find a profile that does not compromise other performance variables. For example, if profile modifications increase the radius of curvature, contact stresses and wear will decrease. However, excessive profile modification can decrease the contact ratio and thus increase root stresses. Slight changes in profile can also significantly change both root and contact stresses. Hence trade-offs need to be made to get the most from profile modifications.

**BENDING STRESS**There are several methods for calculating break strength for teeth. According to ISO standards, bending stress at a tooth root calculated in section A-A is:

where the stress correction factor is:

Allowable tooth root stress is defined as:

The actual bending stress must be equal to or less than the allowable tooth root stress

Substituting equations for bending stress and allowable bending stress into the above relationship results in:

This equation lets designers determine maximum unit load *Q** _{F}*.

**PROFILE MODIFICATION**The stress correction factor of the pinion, Y

*FS1*, depends on a modification coefficient,

*x*

*. The stress correction factor of the wheel,*

_{1}*Y*

*, depends on modification coefficient,*

_{FS2}*x*

*. Therefore, optimal*

_{2}`) x`

*1*and

`) x`

*2*can be found such that:

An example illustrates the effect of correction on permissible unit loads. Consider a set of gears with *z*_{1 }= 17, *z*_{2 }= 42, *m** _{n }*= 3.0, = 0B, tooth rim widths

*b*

_{w}_{1 }= 32,

*b*

_{w}_{2 }= 30. Both wheels are 18H2N8 grade steel, carburized and hardened to 52 HRC, and manufactured to Grade 7 accuracy. The pinion gear operates at 1,500 rpm.

The *Permissible unit loads *graph shows loadlimit results for various gear parameters with a factor of safety of 1.4. Line "a" in the figure represents the contact ratio = 1.2, "b" are measures of the tip relief, "c" are measures of tooth undercut, and "e" and "f" are measure of tooth interference.

The graph is separated into two areas, the upper part Q*F*1 where gear load is defined by pinion teeth strength; and the second area *Q*_{F}_{2}, where gear load is defined by wheel teeth strength. These two areas are separated by a dashed line that represents equal values of pinion teeth strength and wheel teeth strength. Position of the line depends on the following ratio:

In the example, wheel materials are the same and *w *= 1. For *w *greater than 1 the dashed line moves to the left and for *w *less than 1 to the right. The optimum correction coefficients are determined by point "B" located on line "a" where *x** _{1 }*= 1.03 and

*x*

*= 0.2. This permits a 49.5% increase in permissible specific load in relation to uncorrected gears.*

_{2 }