Internal ring gears – design and considerations 

When using internal ring gears, you can develop a gear system with a high reduction ratio in a compact space — but there are considerations regarding the reduction ratio, interference possibilities, and design window dimensions. 

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When one is under a great deal of stress, they have a choice to either internalize the stress or to express it. Some express it through exercise, some drown their sorrows at the neighborhood pub, and some choose to berate others. In gearing, there are situations when internalizing the gear mesh is desirable. For these applications, we specify ring gears.

Internal gears, ring gears, and internal ring gears are interchangeable terms for the same type of gear. These gears are composed of a cylindrical shape having teeth inside a circular ring. The gear teeth of an internal gear typically mesh with the teeth of a spur gear. Spur gears have a convex-shaped tooth profile and internal gears have reentrant shaped tooth profile; this characteristic is opposite of internal gears. The formulas for calculating the dimensions of internal gears and their interferences are quite different than those of other gearing.

Figure 1: The meshing of internal gear and external gear.

Figure 1 presents the mesh of an internal gear and external gear.  Of vital importance are the working pitch diameters (dw) and working pressure angle (αw). They can be derived from center distance (a) and equations detailed below.

Table 1 shows the formulas for calculating the geometry of a profile shifted internal gear and a non-shifted external gear. In this type of gear system, it is common for one or both members to be profile shifted in order to overcome the various interference fits.

Table 1: The calculations of a profile shifted internal gear and external gear where the module of the gears is 3, the number of teeth on the spur gear is 16, the number of teeth on the internal gear is 24, and the internal gear is profile shifted.

If the center distance (a) is known, then x1 and x2 can be obtained from the inverse calculations of items 4 thru 8 of Table 1. These inverse formulas are detailed in Table 2.

Table 2: The calculations of the profile shift of an internal gear and external gear when the center distance is known.

There are three different types of interference can occur with internal gears: involute interference, trochoid interference, and trimming interference.

Figure 2: Involute interference.

1. Involute interference (Figure 2) occurs when the distance between the dedendum of the external gear and the addendum of the internal gear is too narrow and the gears cannot mesh properly. It is prevalent when the number of teeth of the external gear is small. Involute interference can be avoided by observing the following cited conditions:

Equation 2 is true only if the tip diameter of the internal gear is bigger than the base circle:

For a standard internal gear, where α = 20°, Equation 4 is valid only if the number of teeth is z2 > 34.

2. Trochoid interference refers to an interference occurring at the addendum of the external gear and at the dedendum of the internal gear during recess tooth action. This interference is due to the distance between the teeth being too shallow. It tends to happen when the difference between the numbers of teeth of the two gears is small. Equation 5 presents the condition for avoiding trochoidal interference.

where αa1 is the pressure angle of the spur gear tooth tip:

In the meshing of an external gear and a standard internal gear where the pressure angle α = 20°, trochoid interference is avoided if the difference of the number of teeth, z2 – z1, is larger than 9. (Figure 3)

Figure 3: Trochoid interference.

3. Trimming interference occurs in the radial direction in that it prevents the pulling of the gears apart. Thus, the mesh must be assembled by sliding the gears together with an axial motion. It tends to happen when the numbers of teeth of the two gears are very close. Equation 8 indicates how to prevent this type of interference.

This type of interference can occur in the process of cutting an internal gear with a pinion cutter. Should that happen, there is danger of breaking the tooling.

Table 3 shows the limit for the pinion cutter to prevent trimming interference when cutting a standard internal gear, with pressure angle α0 = 20°, and no profile shift, i.e., x0 = 0.

Table 3: The limit to prevent an internal gear from trimming interference.

There will be an involute interference between the internal gear and the pinion cutter if the number of teeth of the pinion cutter ranges from 15 to 22 (z0 = 15 to 22) .

Figure 4: Trimming interference.

Table 4 shows the limit for a profile shifted pinion cutter to prevent trimming interference while cutting a standard internal gear. The correction (x0) is the magnitude of shift, which was assumed to be: x0 = 0.0075 z0 + 0.05.

Table 4: The limit to prevent an internal gear from trimming interference.

There will be an involute interference between the internal gear and the pinion cutter if the number of teeth of the pinion cutter ranges from 15 to 19 (z0 = 15 to 19).

When using internal ring gears, you can develop a gear system with a high reduction ratio in a compact space. However, there are many considerations regarding the reduction ratio, interference possibilities, and design window dimensions. 

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Brian Dengel
is general manager of KHK USA Inc, a subsidiary of Kohara Gear Industry with a 24-year history of working in the industrial automation industry. He is skilled in assisting engineers with the selection of power-transmission components for use in industrial equipment and automation. Dengel is a member of PTDA and designated as an intern engineer by the state of New York. He is a graduate of Hofstra University with a Bachelor’s of Science in Structural Engineering.