超音波加工用圓板型切斷工具の設計
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概要
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There are some troubles in cutting work by the ultrasonic machining, namely in such work the cutting tool can not be formed so thin, because such tool breaks down by the buckling action of cutting force and the cutting clearance becomes large due to the increasing lateral vibration. On the other hand, the usual cutting work by the rotating cutting wheel (diamond charged phosphor bronze circular plate wheel or elastic bonded abrasive cutting wheel) has some merits in machining narrow cutting clearance by the rigid thin plate effect due to its own rotation, but there are fundamental defects of large heat generation and violent tool wear. So we have designed a new tool which has usual circular cutting wheel form, rotates around its own axis and vibrates radially at the ultrasonic frequency. Accordingly we expect that this tool shall have the binary action of ultrasonic machining and rigid thin plate effect. In this paper, as preliminary considerations for the designing of this tool, the theory of axisymmetric extensional vibration of a disc of variable thickness having a central hole and some numerical results of them are given. An example of actual design of the tool based on these is also added. The shape of the treated disc in the theory is such that its thickness decreases as radius increases by following hyperbolic law : h=h_0(r/b)^<-2α>, where b=inner radius of the disc, 2h_0=thickness of the disc at the inner edge, 2h=thickness of the disc at radius r, 2α=thickness reduction index. The natural frequency f_n of the n-th mode of vibration can be calculated from the equation : [numerical formula] where E=Young's modulus, ρ=density, υ=Poisson's ratio of the material respectively and the coefficient z_n is given by the n-th roots of the equation [numerical formula] n=a/b, being the ratio of the outer radius to the inner radius, and p being the order of Bessel functions determined by p=√<1+2αυ+α^2>.
- 山梨大学の論文
- 1957-07-10
山梨大学 | 論文
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