【正文】 t difference in the mechanical properties of the fibres and matrix. As a result, a machined FRP posite usually contains various damages, such as fibre pullout, fibre fragmentation, matrix cracking, fibrematrix debonding and delamination . To 32 date, most experimental investigations on the machining of FRP posites are on the following issues: effect of fibre or matrix types , influence of fibre volume fraction and orientations , role of tool materials and geometries , contribution of the depth of cut , and selection of processing parameters . These studies, however, are limited to the traditional machining methods, such as turning,milling and drilling, and are still facing the poor surface integrity problems highlighted above. To acplish a high quality surface of FRP posites, the mon understanding is that grinding is more appropriate , because the instant depth of cut of a single cutting edge in grinding is much smaller than the diameter of a fibre . Nevertheless, grinding is inefficient in many cases. On the other hand, vibrationassisted cutting, which adds a displacement of microscale amplitude at an ultrasonic frequency to the tip motion of a cutting tool, has been experimentally evidenced to be an effective method to cut many single phase materials such as metals and ceramics . In order to machine FRP posites effectively, the authors have developed a vibrationassisted cutting technique . This technique applies ultrasonic vibrations to the tool tip and based on the directions of the vibrations, the tool tip trajectories can be controlled to follow, ., an elliptic path named as an elliptic vibrationassisted (EVA) cutting. Their investigation has shown that the EVA can significantly reduce cutting forces and subsurface damages in a workpiece even by using a simple cutting tool. The effects of vibrations in cutting and normal directions on machining characteristics have also been studied using the novel vibrator developed. They found that the vibration in the cutting direction is more effective in reducing the cutting force, but that normal to the cutting direction facilitates the chip removal. When the vibration is applied to both the directions in an EVA cutting, the cutting force can be greatly reduced, the surface integrity of an FRP workpiece can be much improved, and the tool life can be largely extended. However, the mechanics and mechanisms of the EVA in the material removal process are still unclear. This has significantly hindered the optimisation and practical application of the EVA technique. The objective of this paper is to remove the above barrier through a detailed mechanics analysis to understand the science behind the EVA cutting of unidirectional FRP posites and thus to establish he essential fundamentals . The most imp ortant factors, such as cutting forces, fibre deformation, fibre fragmentation, and fibrematrix debonding, will be prehensively integrated in experiments will be carried out to examine the model established. 33 2. Mechanics modelling . The principle Fig. 1 illustrates the principle of an EVA cutting process, in which the cutting tool feeds at a feed rate, v, while it vibrates elliptically at an ultrasonic frequency with a microscale amplitude in the xzplane. The feed rate is smaller than the maximum vibration speed in xdirection, such that an intermittent cutting is generated in each vibration cycle of the tool. In a cycle, cutting takes place only when the tip wedges into the workpiece at time instant tb, and finishes when the tangential cutting direction is parallel to the fibre orientation at time instant te. Thus, if a fibre/matrix breakage happens during this process, chips form and are pulled out by the tool. To facilitate the breakage of the fibres and matrix, the cutting distance within a cycle of the tool vibration, Δ, is set to be smaller than the fibre diameter, D, so as to improve the surface quality as explored in the previous work . Assume that a and b are the vibration amplitudes in x and zdirections, respectively, f is the vibration frequency, ψ is the phase difference,r e is the radius of the cutting edge, ap is the set depth of cut, and δ is the bouncing back of the workpiece in the contact zone of the tool with the finished surface. The relative elliptic motions of the tool in xdirection, x(t), and zdirection, z(t), can be described by the equations shown in Table 1 . Based on the motion of the tool vibration relative to the feed direction, one can define three types of vibrationassisted cutting: (1) cuttingdirectional Fig. 1. A schematic illustration of an elliptic vibrationassisted cutting of an FRP posite 34 vibrationassisted (CDVA) cutting where the tool vibrates in the cutting direction only (., a≠0 but b=0)。研究還揭示了主要的材料去除機理，針對纖維變形的影響，纖維斷裂和纖維與基體界面脫粘。結(jié)果表明，傳 統(tǒng)的切割需要最大切削力最大，其次是 NDVA 和 CDVA 切削， EVA 切削最小。因此，纖維上的斷裂點是不可預測的，導致一個不規(guī)則的破裂面。 當應用橢圓振動，如圖 5（ d）， EVA 切削融合了 CDVA 和 NDVA 的優(yōu)點。通常，纖維與基質(zhì)脫粘深度是用來描述損傷程度。增加后刀面與工件材料之間的摩擦力時，切削力在區(qū)域 2 是： ?? 222 c osmx PF ? 15 k’m= k’= )co ss i n1(22 ???mz PF ?? （ 21） 因此，總切削力 Fx 和 Fz 變?yōu)? ： XxAxx FFFF 21 ??? zzAzz FFFF 21 ??? （ 22） 由于刀尖的振動頻率遠遠超過切削系統(tǒng)的固有頻率，刀具 – 工件的相互作用是不連續(xù)的，但有很多微小的影響。 ?? )]()([)(2 )(2)]()([11 31241 24313 zFzFBzFB zFBzFzFBm mmm mmmdzdxk ??? ???? ??? ????? （ 7a） ?? )]()([)(2 )(2)]()([1 31645 28317 zFzFBzFB zFBzFzFBm mmm mmmk ??? ???? ??? ???? （ 7b） ? ?)]()(2)([)](2)()([ )]()(2)([)](2)()([3 32124311 432144313 zFzFzFCzFzFzFC zFzFzFCzFzFzFCmb mbmbmbmbmbmb mbmbmbmbmbmbK ?????? ??????? ????? ??????? （ 7c） ?? )()()( )]()()([22 121 42231 1442322 zFzFBzFB zFBzFzFBmffff mmm mmmIEdz xdIEM ??? ??