# The Zen of Gear Design

Exploring the ‘hows and whys’ of choosing the proper center distance for your gearing requirements.

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The feeling of Zen is one that we all can aspire to. Through practice and self-reflection, we can work toward being centered and grounded. Unfortunately for gears, too many designers overlook the need for gears to be properly centered.

When set at the proper center distance, gears will mesh at the pitch point. In doing so, they will perform as designed. The proper center distance allows for the tooth of one gear to engage with the mating gear at the optimal intersection point; it allows for the proper flow of lubricant into the mesh; it allows for the gears to operate with the designed backlash allowance, and it minimizes gear noise.

The formula for calculating the center distance of two parallel axis gears is:

Center Distance = (Pitch Diameter of Gear A + Pitch Diameter of Gear B) / 2

This formula calculates the nominal value of the center distance. (Figure 1)

It does not reflect the tolerance of that value. For most parallel axis gear applications, a tolerance of ±25~30 µm is ideal.

This range reflects the inherent variations in pitch through one rotation of each gear.

Table 1 shows the center distance tolerance for parallel axis gears.

The tolerance values in this table are quoted from JGMA1101-01 (2000), and are applicable for involute spur and helical gears made of iron and steel.

When designing a gear pair, the consideration of center distance is often one of the last values calculated. In some instances, the center distance between the parallel shafts is different than the optimum center distance of the gears.

This situation can arise if you replace diametral pitch gearing with metric gearing. As these two systems are not 100-percent interchangeable, the center distance of standard metric gears would not fit an inch dimensioned shaft center distance. For example, a 10DP, 20-tooth spur gear mated with a 25-tooth spur gear would have a designed center distance of 2.25 inches. If these gears are replaced with a Module 2.5, 20-tooth spur gear mated with a 25-tooth spur gear, its design center distance is 56.25 mm (2.2146 inches).

One of the ways in which these metric gears can be adjusted in order to match the shaft center distance is to design the pinion with an enlarged addendum. A modification factor, known as the coefficient of profile shift, can be applied to a gear during manufacture, which will increase the pitch point of the pinion such that its effective pitch diameter is larger than the nominal pitch diameter. By selecting a positive profile shift coefficient that increases the effective pitch diameter of the pinion by 1.8 mm, these gears would now fit the 2.25-inch center distance.

The second way for these gears to meet this center distance requirement would be to introduce a helix angle. Since the pitch diameter of a helical gear is calculated as:

Pitch Diameter = {(Module * Number of Teeth) / cos β}, where β is the helix angle, the pitch diameter increases as the helix angle increases.

For this example, if you make the pinion a left-hand gear with a helix angle of 10° 10’ 54” and make the mating gear a right-hand gear with a helix angle of 10° 10’ 54”, then these gears will have a center distance of 2.25 inches. (Figure 2) 