关键字：involute gear; interference and undercutting; number of teeth; tip pointing

摘要：The smaller number of teeth can achieve a more reliable gear transmission when the center distance is fixed. But small number of teeth will produce the problem of undercutting. Undercutting is a serious problem in designing involute gears with small numbers of teeth. We have successfully developed a tooth profile which absorbs the advantages of both involute and double circumlar-arc gears. The tooth shape of the gear consists of two involute curves which are linked by a transitional curve and form the ladder shape of the tooth. Such gear is called "Double Involute Gear". At first, the interference and undercutting are analyzed. Afterwards, a general method is presented for the determination of the minimum number of teeth that can be cut in a double involute helical gear without undercutting by a rounded-tooth rack-cutter. The analysis is completed according to the cutting engagement of the rack-cutter and a helical gear in the transverse plane. In this paper, based on avoid undercutting and pointing, the study is completed about the minimum number of teeth. An example is included to illustrate that the pointing and undercutting of the double involute gear can,be avoided at the same time.

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