Contact ratio is average number of gear teeth in contact with one another as the gears are in operation. Gear tooth profiles must be dimensioned in such a way that more than one pair of gears must be in contact with one another. This insures smooth and quiet operation of the gear pair. The formula to find that ratio for an external spur gear pair is:
Where:
And:
You must take into account that none of these formulas take the backlash of the gears. Backlash will shorten the line of action by its vertical component. So I more accurate representation would be:
Where alpha is the pressure angle.
In its simplest form, contact ratio is the number of pairs of teeth in contact at one point in time. Some ways that contact ratio is changed is through the modification of the tooth profile, i.e. addendum modification, decreasing the pressure angle for a longer line-of-action, or increase the number of teeth. Reducing backlash is one of the most effective ways to increase the contact ratio. Another effective would be the increase of the diametral pitch of the gear pair. In most applications, a contact ratio of 1.2 or greater is desired. A ratio greater than 2 is not usually achieved in external spur gears, but can be accomplished by using internal, helical or nonstandard gears.
For a quote to manufacture your gears for an upcoming project or for a design review, contact Marples Gears through our website http://www.marplesgears.com/contact/custom-quote/ or give us a call at 626-570-1744.
Sources:
Jelaska, Damir. Gears and Gear Drives. Chichester, West Sussex ; Hoboken: John Wiley & Sons, 2012. Web.
Mosedale, Andrew. “Understanding the Contact Ratio for Spur Gears with Some Comments on Ways to Read a Textbook .” Www.myweb.ttu.edu/Amosedal/Documents/, Texas Tech University, 2019, www.myweb.ttu.edu/amosedal/documents/contactratio.pdf.Oberg, Erik, and Christopher J. McCauley. Machinery’s Handbook: a Reference Book for the Mechanical Engineer, Designer, Manufacturing Engineer, Draftsman, Toolmaker and Machinist. Industrial Press, 2000.
