Designing High Contact-Ratio Gears

While there are many ways to design high contact-ratio gears, the following explains one design method that could be used.


High contact-ratio (HCR) gears are gears defined with a contact ratio greater than 2.0. Standard gears have a typical contact ratio of 1.2 to 1.6. In their most basic form, gears are designed to transmit power, and HCR gears perform especially well. They are stronger, quieter, and smoother, and they have significantly lower stresses. Also, they normally have lower pressure angles and a greater number of teeth than standard gears.

HCR gears always have two or three gear teeth in contact at any one time. They never have only one set of teeth in contact; since there are more teeth in contact, the load is spread across more teeth and is therefore reduced. These gears are approximately one-third stronger than standard gears because of the extra sets of gear teeth in contact.

Because of the non-standard nature of HCR gears, AGMA cannot and does not calculate the gear tooth stresses nor does it recognize HCR gears in any of its standards. And few programs can calculate these gear tooth stresses. Even so, because HCR gears have so many advantages as previously stated, they are still a viable design option in many different applications.

HCR gears necessitate higher quality levels due to the required accuracy of the multiple sets of teeth in contact. They are typically more sensitive to manufacturing errors and gear tooth profile modifications.

Quieter spur gears — a sign of design excellence as defined by the evolving needs of the manufacturing industry — were discussed in an article, “Higher Contact Ratios for Quieter Gears,” by Dr. Gonzalo González Rey in the January 2009 issue of Gear Solutions.

Many gears have standard gear tooth proportions. The addendum is one divided by the diametral pitch, and the outside diameter is the pitch diameter plus two addendums.

The following describes a method I use for designing HCR gears. In my method, the addendum is 1.25 to 1.35 divided by the diametral pitch, or 25 to 35 percent larger than a standard addendum. Use the lower value if possible. Therefore, the outside diameter is also larger.

This is not a long/short addendum system where the addendum changes and the tooth thickness also changes proportionately. In my method, the tooth thicknesses stay the same.

I usually start by using a pressure angle of 20 degrees. The actual finished pressure angle might be greater or lesser than this amount. The whole depth will now be equal to between 2.5 and 2.6 divided by the diametral pitch.

Typically, I use a minimum of 25 teeth for the pinion. Often, this is a trial-and-error method requiring a number of design iterations. For a good design, the items to look for are: a top land that is not too narrow (less than 0.25/DP), or the gear teeth do not contact each other below the base circle diameter. If either one of these occur, then add teeth to the gear set or reduce the pressure angle.

Regarding the manufacturing of HCR gear teeth, special tools are typically required such as hobs or shaper cutters with a deeper whole depth. They typically use the same manufacturing processes as standard gear teeth; therefore, they are normally no more expensive to produce.

Because of their many advantages previously mentioned, HCR gears have become more commonly designed and used in the industry. They are worth consideration when you want strong, quiet, and high-strength gears. The method presented here is just one way, among others, to design HCR gears.

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is president/sole member of Innovative Drive Solutions LLC, which provides gear design engineering services for optimizing gears, gearboxes, and other geared devices. Miller has created over 300 original gearbox system designs. He is a member of AGMA, SAE, and ASME, and he holds three patents. He is vice chair of the AGMA Vehicle Gearing Committee. For more information, visit