When /i:=l, a=20, when the upper type can be used to obtain the standard gear, the minimum number of teeth without the undercut phenomenon can be known from the above. The standard gear is used to machine the standard gear, as long as the given tooth The minimum number of teeth in which the angular a and the height of the crest are not rooted are also determined. However, the situation is different when a spur gear is used to machine a spur gear. Because the top line of the rack-shaped cutter is a straight line, and the top line of the disc-shaped cutter tool is a circle, under the other conditions, the intersection point of the tooth top circle of the disc-shaped cutter tool and the meshing line B It is lower than the rack-shaped tool, so the minimum number of not-cut teeth is related to the number of teeth of the file cutter. When =13, W=l, a=20, the minimum number of not-cutting teeth is Zmn=13. Although the number of teeth of the gear-shaped serrated knife is at least not less than the number of teeth processed by the rack-toothed cutter, One of the biggest drawbacks of the gears produced by the disc-shaped knives is that the number of gears that mesh with them is limited by the number of teeth of the disc-shaped knives. When the number of teeth meshing with the gear is greater than the number of teeth of the tooth cutter, the radius of the tip of the tooth must be larger than the radius of the top of the pinion, which inevitably causes interference.
To sum up: (1) The external gear processed by the rack cutter can be machined with any external gear with a minimum number of teeth without teeth at a distance of 20 and =1. Engage. (2) When the outer gear of the disc-shaped boring tool is processed at a=20, /=1, the minimum number of non-cutting teeth is related to the number of teeth of the knives, but it is definitely less than the 17 teeth (for example, the boring cutter is 13) In the case of teeth, the minimum number of teeth not to be cut is 13 teeth), however, the machined gears cannot be meshed with gears larger than the number of teeth of the teeth in the case of standard meshing. Otherwise, it will inevitably cause interference. Incidentally, the above discussion is all about the case where the disc cutter is used to machine the external gear. When the machined gear is meshed with other gears, the number of teeth of the outer gear must also be smaller than the number of teeth of the tooth cutter. Otherwise, interference will also occur during meshing. Of course, the amount of thinning and the tolerance of the actual machining of the gear have a great influence on the number of teeth of the meshing gear, which will not be discussed herein.
I personally experimented with a pair of meshing gears 21=14, 72=44 (both external gears) with a disc-shaped serrated knife with modulus m = 2 and Z-knife = 38.
Since the Z-knife = 38, it is obvious that the Z-turn can only cause interference when the Z-knife is engaged with the gear of the 38. However, 厶=44, which is larger than 38 teeth, theoretically interferes, but actually interferes and cannot be properly meshed, which proves the limitations of the disc-shaped knives processing external gears. In the actual production process, things such as not paying attention to this are very likely to happen. Such results are not elaborated in today's textbooks such as the mechanical design basis, the 'mechanical principles,' and so on. I think this is the shortcoming of the current textbook.
For a long time, because there is no such information available, it is generally believed that the gears produced by the disc cutter are no different from the gears produced by the rack knife (or hobbing cutter). In particular, students who have just graduated from school do not have practical experience in this area, so this problem is likely to occur in practical work. Therefore, I think that in today's textbooks, the principle of the undercut and interference of the gear-shaped knives should be explained in order to be applied in future work. At the same time, it can also correct the gear industry in the mechanical industry. It is widely believed that there is no difference in the gears produced by the rack knife and the disc cutter.
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