1. The undercut phenomenon of the involute tooth profile When machining the gear by the forming method, if the intersection of the tip line of the tool and the meshing line exceeds the limit point of the cut gear, the tooth tip of the tool will be the tooth of the cut gear. The involute tooth profile of the root cuts off part of the root to form the undercut phenomenon, as shown in the following figure: The undercut tooth profile will greatly weaken the bending strength of the gear teeth, reduce the coincidence degree, destroy the fixed transmission ratio transmission, and affect the stability of the transmission.
Second, the proof of the undercut phenomenon is now illustrated by the rack cutter as shown below:
The center line of the rack tool and the indexing circle of the cut gear are cut at the node P, and the intersection point B2 of the tool tip line and the mesh line has exceeded the limit point N of the cut gear.
Point B1 in the figure is the intersection of the tooth top circle of the cut gear and the meshing line. When the tool profile is fed from point B1 to the right to its position through point N, the NF section of the tool profile cuts out the involute profile NE of the wheel blank. During this section of the cutting process, the tool tip There is no involute profile that cuts into the root of the wheel blank. However, the machine will force the tool and the wheel blank to continue to expand according to the constant gear ratio, that is, when the tool continues to move to the right, the undercut phenomenon begins to occur until point B2 is reached. If the tool movement distance is r, the angle of the wheel blank is changed because the center line of the tool and the index circle of the wheel blank are pure. At this time, the tooth profiles of the wheel blank and the tool are respectively located at the position sum. The tooth profile and the meshing line intersect perpendicularly to the point K, so NK=rcos=rb, then the arc length of the N point on the wheel blank is NN=rb, so the vertical distance of the point N to the linear tooth profile is obtained due to NK. NN is an arc, so the point N must be to the left of the tooth profile. Since N is the starting point of the tooth profile g on the base circle, the tooth tip of the tool must be cut into the tooth root of the wheel blank, not only the tooth profile in the base circle is cut off, but also the involute tooth profile outside the base circle. A part of the cut is cut off.
3. The minimum number of teeth when the involute standard gear does not undergo root cutting. As described above, when the gear is machined by the forming method, if the tip line of the tool exceeds the meshing limit point N, the undercut phenomenon will occur. Therefore, to avoid it, the top line of the tool must not exceed the limit point N. As shown in the figure: When the standard gear is cut with a standard rack tool, the center line of the tool is tangent to the indexing circle of the gear to be cut. In order to avoid undercutting, the tip line of the tool must not exceed the limit point N, ie h amNM but NM=PNsin=rsin2=mz2sin2z 2h
Asin2 is substituted into the above formula and the result is =20ha=1. Substituting into the above formula is: Z17.09726441 It can be seen from the above formula: When the number of teeth Z is 17 teeth, there is still a very small undercut. Therefore, the minimum number of teeth when the involute standard gear does not undercut is 18 teeth, that is, Zmin=18
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