Vibration Machining (2 nd Report)

Maching Energy and Collision Velocity

Abstract

Basing on the tool's collision velocity υ₀ obtained theoretically in the 1 st report, the present paper considered the machining energy E that is the energy consumed for machining, and also the repulsion coefficient α which is related to the machining energy. The paper, furthermore, discussed the machining energy which may be influenced by the exciting force F₀, the frequency f and also the amplitude ratio γ respectively. The main results obtained in this paper are as follows :
(1) When the collision velocity becomes a definite magnitude, the repulsion coefficient becomes the minimum and the machining energy the maximum simultaneously. The collision velocity giving this maximum machining energy is called by the name of Limit Collision Velocity in this paper.
(2) The machining energy is given theoretically by the following expressions : When |υ₀|≤|υ_L|, E= (η/8)·F₀²·(1-γ²) / (mf), and when |υ₀|≥|υ_L|, E= (η/2)·mfυ_L², in which υ_L is the limit collision velocity.
(3) There exists the optimum frequency that makes the machining energy the maximum. Even if the machining condition may vary, it is necessary, however, to maintain the ratio of the exciting force to the frequency to be a definite value for machining at the condition of limit collision velocity.