A fine mechanical machining treated in this paper may be called by the name of Vibration Lapping, those tool vibrates tangentially along the work operating like the ordinary lapping machining.
In the present report, is related the experimental apparatus and some experimental and theoretical results on the machining speed of the Vibration Lapping for glass.
The main results are as follows :
1) The machining speed of the Vibration Lapping for glass is proportional to about v^1.5 with respect to the mean velocity of the tool v (machining amplitude a×frequency f×4).
2) Similarly, it is proportional to about p^1.2 with respect to the lapping pressure p, but when the lapping pressure exceeds the limit lapping pressure p_l, it becomes to show the saturating tendency and has no relation to the lapping pressure.
3) The relation between the lapping pressure p and the amplitude ratio r is expressed by
p=πF₀/4μS√1-r².
4) Assumed the machining speed W is expressed in the form W=Kp^αa^β, the optimum amplitude ratio r₀ is theoretically given by
r₀=√β/α+β_??_0.75,
and it is also confirmed to have a good agreement with the experimental result.
Then the optimum lapping pressure p₀, is given by
p₀=πF₀/4μS√α/α+β.
5) In the case that the lapping pressure is extremely high, the machining speed takes the maximum, when p_l>p₀, at the optimum amplitude ratio r₀ and, when p_l<p₀, at the amplitude ratio corresponding to the limit lapping pressure p_l.