Using profile shift in gearing

Understanding the process of increasing and decreasing tooth thickness to check out potential failure modes of gear pairs.

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We all pretty much know that profile shifting is used to create gears with tooth thicknesses that are different from standard gears. By making the tooth thickness of involute gears thicker or thinner, you can change gear strength and / or the center distance of gear pair. Profile Shift or “addendum modification” or “correction” is simply the displacement of the basic rack datum line from the reference diameter of the gear. A positive profile shift increases tooth thickness, which in turn makes the tooth more resistant to bending and the curvature of the profile decreases so that the contact stress is also reduced. A negative profile shift decreases tooth thickness; however, this has an opposite effect on tooth bending stress.

One way to think about profile shifting is that it’s similar to increasing the number of teeth in a gear. If we look at Figure 1 (and many of you have seen this before), we can note that as the number of teeth is increased from 10 to 200, the undercut reduces and then is almost completely eliminated. The curvature of the tooth increases; it still an involute, but one with an ever-increasing instantaneous radius of curvature.

The two main reasons or benefits of shifting the profile of a tooth is to balance the predicted service life between bending fatigue compared to surface compressive stress, or to adjust the center distance of a given gear pair as a means to use standard or existing tooling. There are limits in profile shifting for both positive correction and negative correction. A positive correction (a positive profile shift or coefficient) generates a tooth profile with increased bending strength (lower root tensile stress) due to the thickening of the root (as shown as increasing tooth count, “z,” in Figure 1). Conversely, a negative profile shift (or coefficient) essentially makes the tooth taller, thus increasing the potential for undercut. These are examples of an equal profile shift — meaning that the amount of positive profile shift used on one gear is applied in the opposite direction (negative profile shift or coefficient).

Figure 1.

Profile shift has no influence on the shape of the tooth flank. All profile-shifted gears use the same involute for the tooth shape compared to their corresponding standard gears. The only difference is that the region of the tooth profile that contacts its mate shifts either up or down the tooth form. For gears that have a non-zero profile shift, the same involute forms the shape of the tooth flank. The base circle therefore does not change with a profile shift since the base circle is determined solely by the flank angle of the cutting tool.

The distance between the production pitch circle and the tool reference line is called the profile shift. To create a positive profile shift, the tool is not plunged as deep into the gear blank, creating a tooth that is thicker at the root and narrower at the tip. A negative profile shift is defined as plunging the cutting tool deeper into the gear blank, with the result that the tooth root is narrower and undercutting may occur sooner as a function of total number of teeth. In addition to the effect on tooth thickness, the sliding velocities will also be affected by the profile shift. As a function of a positive profile shift (or coefficient) the radius of curvature of the involute increases with increasing length — meaning the greater the diameter (above the base circle), the larger the instantaneous radius of curvature is. This translates into a “flatter” tooth surface. Remember that contact stress is a function of both the normal load applied to the tooth surface (flank) as well as the required amount of localized elastic deflection (reduced Hertzian contact stress) required as a function of material properties. Stated another way, the lower the effective pressure angle, the larger the contact patch that can be generated as an elastic deformation.

Also, profile shift has no effect on the flank angle of the tool or on the base circle of the gear. Thus, even with either a positive or negative profile shift, the line of action and thus the pitch point always remain unchanged. The unchanging position of the pitch point is apparent from its meaning. The pitch point describes the point at which there is only rolling action between the gear teeth (sliding velocity is zero). A shift of the tool profile in a radial direction, however, does not change the speed ratios and thus the position of the pitch point.

There is a difference between “profile shift,” “profile shift coefficient,” and “profile correction factor.” Profile Shift is the actual amount you intend to move the cutter (e.g. shaper or hob) relative to the “textbook” position. Profile shift coefficient is calculated as the actual profile shift amount or distance as a function of the module (profile shift distance multiplied by the module of the gear design). Finally, Profile correction factor is the radial displacement of the tooth-generating profile. A positive profile correction factor (an increase in the radial distance of the cutter relative to the gear blank) is a ratio of the actual tool movement divided by the base diameter.

Fixed sum of profile shift coefficients: The center distance is calculated on the basis of a predefined profile shift sum. The sum of profile shift influences the profile shift coefficients of both gears as well as the operating pitch circle and the operating pressure angle.

A fixed profile shift coefficient is intended to balance specific sliding of the two gears in mesh. This is done in conjunction with optimizing the center distance with respect to balanced sliding. This methodology calculates the center distance in such a way as to balance gear pair specific sliding (for cylindrical gears) for a specified profile shift. Generally, you should also perform this calculation considering tip alteration recommendations as specified in DIN 3960. You will also find more information regarding this in DIN 3992 recommendations for well-balanced tooth geometry.

Finally, all of the above can be done to balance predicted service life, or to balance sliding velocities, or flank strength / fatigue, or root stress; basically, all the various ways we look at potential failure modes of any gear pair. This manufacturing technique can be used to apply an equal profile shift or a non-equal profile shift. Use of equal profile shift is usually done to maintain a fixed center distance while attempting to better balance any of the aforementioned failure modes. Non-equal profile shift is used to adjust center distance and may be used in conjunction with an attempt to balance the gear design. The amount of profile shift is generally limited by the onset or excessive undercut in one direction and the limit of tooth tip width in the other. As mentioned, there are recommended or suggested starting values for profile shift. Your final design will likely be a combination of the recommended starting profile shift amount and the constraint imposed by either undercut and / or tooth tip width limit. Shift away!

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Dr. William Mark McVea, P.E., is President and Principal Engineer of KBE+, Inc. which develops complete powertrains for automotive and off-highway vehicles. He is the Principal Engineer with Kinatech, a joint venture with Gear Motions / Nixon Gear. He has published extensively and holds or is listed as co-inventor on numerous patents related to mechanical power transmissions. Mark, a licensed Professional Engineer, has a B.S. in Mechanical Engineering from the Rochester Institute of Technology, a Ph.D. in Design Engineering from Purdue University.