Definitions and Description of Waviness

On the left side of Figure 9, the waviness is shown as a three-dimensional image. The vertical axis shows the deviation of the manufactured and measured geometry from the designed geometry. Note the waviness in one direction. Note that the plane is twisted due to the natural twist from manufacturing. Note that this waviness is concerning one flank. In a mesh, several flanks are in contact at one point in time, and the waviness in one contact and the waviness in the next contact (for contact ratio above unity) overlap. On the right side of Figure 9, the definition of waviness on the flank, inclined by an angle, is shown. The amplitude, wavelength, inclination angle and phase shift are needed to define the waviness where the shape is a sinusoidal form. If the angle is set to zero, a waviness in profile direction results; if set to 180 degrees, a waviness in lead direction results.

Several such waviness definitions may be superimposed. On the left of Figure 10, waviness patterns in lead and profile direction are superimposed, creating a “rough” gear flank. Depending on the amplitude of this “roughness”, different maximum peak stresses result. Such an approach may be helpful to explain the formation of micropitting in a pattern resembling grinding marks. In the right of Figure 10, several waviness definitions having different phase shift, amplitude and wavelength are superimposed in the profile direction. This results in a composite waviness in profile direction that is not intuitively recognized as a superposition of sinusoidal shapes but looks realistic.

To represent the measured waviness, e.g., in profile direction, the user must come up with several sinusoidal curves and superimpose them. By adjusting phase shift, amplitude and wavelength for each sinusoidal curve, different patterns for the resulting waviness are achieved. With this approach, by increasing the amplitude, wear of a tool and an increase in waviness in production between dressing of the tool may be considered. Currently, the software lacks the functionality to create the individual sinusoidal shapes, again, a function to be added.