With the emergence of various difficult-to-machine materials and their application in aerospace, precision instruments, die manufacturing, and other fields, more stringent requirements are being imposed on the efficiency and accuracy of mechanical processing. Consequently, appropriate processing and manufacturing techniques have become hot topics in current research . Among precision machining techniques, electrochemical machining (ECM) has gained favor. ECM involves the local corrosion and removal of material from a metal workpiece in an electrolyte based on the principle of electrochemical anodic dissolution . This enables a variety of metallic conductive materials to be processed without regard to the strength or hardness of the material itself, because the workpiece material is dissolved and removed in ionic form . During processing, the cathode tool is always located away from the anode workpiece, and so no machining stress is generated. In addition, the tool cathode does not wear out, because it does not dissolve and only hydrogen bubbles are produced on its surface. The machined surface quality is good, and there is no recasting layer or thermal deformation because this is a cold machining method . ECM has been applied in the manufacture of aero-engine blisks, casings, microprecision parts, and other key components [5, 6].
Wire electrochemical machining (WECM) is based on conventional ECM and uses a metal wire to cut the workpiece in a 2D plane . This method not only inherits the advantages of conventional ECM, but also has its own unique benefits. A linear cathode with a simple structure is used, thus avoiding the complex shaped cathode designs employed in conventional ECM, and thereby improving machining flexibility. WECM is suitable for the processing of high-precision 2.5-dimensional parts.
The limitation of mass transfer in narrow slits is a decisive factor that restricts the improvement of machining efficiency and accuracy [8, 9]. This is because the electrolytic products that remain in the machining gap change the electrolyte conductivity and negatively affect the distribution of the electric field in the machining gap, thus degrading the efficiency and accuracy of WECM. This problem becomes worse as the depth of the cutting slit increases, i.e., with increasing workpiece thickness. In recent years, a large number of studies have attempted to accelerate the removal of electrolytic products and refresh the electrolyte in the machining gap, thereby improving the machining efficiency and accuracy. For wire electrochemical micro-machining, the axial reciprocating vibration of a wire electrode has been proposed . This uses the reciprocating vibration of the wire electrode to drag the electrolyte, promoting the removal of electrolytic products and the renewal of the electrolyte. A microscale square column tool array with a surface roughness of 0.058 µm was fabricated on an 80-µm-thick cobalt-based superalloy at a feed rate of 0.5 µm/s. Upward and downward reciprocating movement of the workpiece was found to induce a fluid flow in the electrolyte that aids the removal of electrolytic products. With this technique, a micro-gear structure was fabricated on an amorphous material, namely nickel-based metallic glass, at a feed rate of 0.5 µm/s . The intermittent vibration of the electrode in the feed direction was observed to induce electrolyte flow in the machining gap, accelerating the removal of electrolytic products. This method has been proved to be effective in both simulations and experiments .
For the electrochemical cutting of thick workpieces, Volgin et al.  performed simulations that examined whether rotation or reciprocating movement of the cathode assisted electrochemical cutting and improved machining efficiency, especially if an electrode with a noncircular (e.g., square or triangular) cross-section was adopted. It has also been found  that using a ring of metal wire under unidirectional movement as the cathode drags the electrolyte, facilitating the rapid removal of electrolytic products and the refreshment of the electrolyte. Using this technique, groove and micro-star structures were fabricated on 5-mm-thick 304 stainless steel. Additionally, the use of a high-speed reciprocating traveling wire to accelerate the removal of electrolytic products from the machining gap enabled a curved slit structure to be fabricated on 20-mm-thick 304 stainless steel . Zou et al.  processed a bar code on 5-mm-thick 304 stainless steel by WECM using vibrating ribbed wire tools, and achieved a feed rate of up to 1.5 µm/s. High-speed rotation of the electrode also induces the flow of electrolyte in the machining gap and promotes diffusion of the electrolytic products. A hollow structure of 3 mm thickness has been fabricated on 304 stainless steel using a high-speed rotary helical electrode at a feed rate of 6 µm/s . In addition, a fir tree slot was fabricated using a cutting edge electrode at a feed rate of 6 µm/s on 5-mm-thick 304 stainless steel .
The auxiliary measures in the above research have improved the machining efficiency and machining ability of thick workpieces, but there is still room for improvement. Thus, ECM methods assisted by electrolyte flushing have been proposed. The high-velocity flow of electrolyte into the machining gap can flush electrolytic products rapidly from the gap and refresh the electrolyte . Using two twisted metal wires as cathodes, machining tests were carried out on 40-mm-thick direct-aged (DA) Inconel 718 with axial electrolyte flushing and a rotating cathode . However, the top and bottom sides of the slit have quite different widths. In another approach, a linear metal tube with array holes replaces the conventional metal wire as the tool cathode, with electrolyte being injected directly into the machining gap through these holes to wash out electrolytic products . A feed rate of 5 µm/s for a 10-mm-thick 304 stainless steel workpiece can be achieved with this technique. Yang et al. studied the effect of the holes spacing and inclination angle on the machining results. Through simulations and experiments, they found that the machining efficiency improved when the tube electrode with inclined holes was used for inner-jet electrochemical cutting. However, the problem of differences between the upper and lower slit widths persisted .
To improve the machining efficiency and reduce the difference between the upper and lower slit widths, a method of workpiece vibration in feed direction assisted electrochemical cutting using tube electrode with inclined jet-flow holes is proposed. Workpiece vibration along the feed direction rapidly and periodically changes the machining gap. The near-instantaneous increases in the machining gap promotes the waste electrolyte containing electrolytic products to flow down the machining gap. At the same time, the electrolytic reaction time under the non-uniform flow field caused by the inclined downward injection of electrolyte is reduced. The flow field simulation of electrolyte in machining gap indicates that the near-instantaneous increases in the machining gap can improve the flow velocity of electrolyte. Experiment demonstrates that the average feed rate can be increased by 50% and the machining efficiency is superior to that of electrochemical cutting assisted by workpiece non-vibration in feed direction. The difference between the upper and lower slit widths is reduced and the machining accuracy is improved. The effect of the vibrational amplitude and frequency on the machining result is also investigated. Finally, an array slice structure is fabricated on a stainless steel block with a cross-section of 10 mm × 10 mm at average feed rate of 6 µm/s using a vibrational amplitude and frequency of 0.1 mm and 1.5 Hz, respectively.