# Theoretical length of hob for cutting metal in gear slot

In Figure 1, at the cutting end of the hob, although the hob teeth beyond the meshing length LM do not participate in the work of enveloping the tooth profile, they cut the metal from the tooth groove of the gear blank. This part must have enough length, otherwise it will overload the cutter teeth and even damage the cutter teeth. Therefore, the length of hob should include not only the length needed for enveloping tooth profile, but also the length of cutter teeth needed for cutting metal.

For the length of hob needed to cut metal, it can be considered that the hob cuts into the blank from point E as shown in Fig. 1. Therefore, the hob should have EF length in the cutting part

Where: RA is the top circle radius of the gear to be machined; h is the full tooth height of the gear to be machined.

The EF is reflected in the direction of hob axis, and its length is LC,

When hobbing spur gear and helical gear with the same or different rotation direction as hob, there are 12 ways of forward or reverse milling, and the total length of hob is still LC + LM; when LC > LM, the length of groove is LC LM, so the minimum theoretical length of hob is asymmetric during hobbing. It can be seen from Fig. 1 that the theoretical length of hob required for cutting the metal in the gear slot includes half of the theoretical length of hob required for enveloping the gear tooth profile, and it is symmetrically distributed with the center line of the gear blank. The length required for cutting the metal in the gear slot is at the end of the gear blank that first prevents the hob from “meshing” from turning in or out.

It can be seen from the above analysis that the length of the effective meshing lines on both sides of the hob is 2lm in the direction of the hob axis, which is the length of the involutes and groove bottom on both sides of the hobbing tooth profile. Therefore, the length LM of the two enveloping tooth profiles must be strictly controlled, or there will be residual teeth on one or both sides of the non involute tooth profile. For example, according to the above requirements, two enveloping tooth profiles should be taken as the length LM When the hob of LM is precision rolling, if the cutting load of side teeth is light, the cutting length Lc LM can be shorter, but the cutting load of side teeth is heavy. In a word, the two lengths LM of the enveloping tooth profile on both sides of the hob must be ensured, and the groove length Lc LM can be conditionally shorter, so the cutting edge length of the hob should not be less than LC + LM.

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