Abstract
A fine mechanical machining treated in this paper may be called by the name of Vibration Machining, through which hard and brittle materials are able to be rapidly machined, as in the case of ultrasonic mechanical machining, by the energy of free abrasive grains given through the action of an elastically suspended tool vibrated by electro-magnetic force of time with sonorous frequency of about from 10 to 104 c/s.
Concerning to the sonorous vibration system of the present vibration machining apparatus, is studied elementarily under some assumption the tool motion occured in its vibration states, in which the tool end collides with the material to be worked before the vibration displacement of the tool becomes its maximum amplitude.
Some of the theoretical results thus obtained are as follows, and they are also confirmed by experimental study in the paper.
1) The tool motion becomes more stable at its resonance condition than non-resonance, in which it keeps almost harmonic displacement vibration expressed by x=a0 cos nt
where a0 shows the distance between neutral position of tool vibration and contact point of tool and work. Therefore, we can see that it is advantageous to excercise the Vibration Machining at the resonance condition of tool vibration.
2) The velocity υ0 at which the tool comes into collision with the material to be worked is given by
υ0=-1/1+α F0√1-r2/2mf
3) The relation between amplitude ratio r and machining force Fw is expressed by
Fw/F0=1/2√1-r2
