During generating cutting, sometimes engineer would cut a part of the involute profile of the root of the machi-ned gear, that is what people called undercutting.
The undercut phenomenon occurs as the tool tip line (rack type tool) or the tip circle (gear insert) exceeds the limit mesh point. Root cutting will weaken the strength, and may even reduces the transmission coincidence and affects the transmission quality, which should be avoided possibly.
Influence: After cutting, the thickness of the root would be thinned, the bending resistance of the gear and the degree of coincidence would be also reduced, which affects the stability of the transmission, we must be avoid such problem. In order to prevent the undercut from cutting the involute in the root of the gear when machining the gear, or to use a displacement gear. When the gear ratio and modulus are fixed, if the smaller pinion number z1 selected, the number of teeth of the large gear z2 and the number of teeth and (z1+z2) will be reduced, then the size and weight of the gear mechanism would be also reduced, the number of teeth z1 become smaller.
However, when gears manufactured by generating cutting, the involute that outside the base of the tooth root will be cut off by the tip of the tool if there is a small number of teeth of gear, that is what we call undercutting. Obviously, the undercutting weakens the bending strength of the gear teeth which may also affects the smoothn-ess of the transmission.
To avoid that, the number of teeth of the designed gear should be greater than zmin. When cutting a normal-tooth standard spur gear with a hob, the minimum number of teeth is taken as zmin = 17. However, to satisfy the bending strength of the teeth, when the root portion is allowed to have a slight undercut, the number of gear teeth can be made less than the above, for example, for a normal tooth standard spur gear, zmin can be 14. In order to avoid undercutting, modified gears can be adopted.
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