## 1 Introduction  
Low-cost precision machining presents a bottleneck when fabricating parts with ruled surfaces like the fir-tree slots in a turbine disc [1]. They are commonly made of difficult-to-cut materials such as nickel-based alloys and titanium alloys, and require strict surface integrity, allowing no recast layers nor microcracks. Wire electrochemical machining (WECM) uses a metal wire as the tool cathode and removes material by anodic electrochemical dissolution, and the part is formed with the relative motion between the wire electrode and the workpiece. WECM has great advantages and well surface integrity such as no dependence on mechanical properties of the material being machined, no tool wear, no residual stress, no recast layers, or heat-affected zones. Hence, it is a potential method for processing parts with ruled surfaces made of difficult-to-cut materials [2; 3]. In WECM, the machining gap is usually tens of microns down to only a few microns, making it very difficult to rapid remove electrolytic products entirely from such a small gap. To expedite the elimination of electrolytic products, [PERSON] et al. [4] utilized a tungsten wire with vibration and fabricated a micro-blade structure on a 100 \(\upmu\)m-thick nickel plate. [PERSON] et al. [5] applied ultrashort voltage pulses to machine micro grooves and gears on 100-\(\upmu\)m-thick stainless steel plates. However, when the workpiece thickness reaches millimeter level, the amount of electrolytic products in WECM increasessharply. They will accumulate continuously in the gap, thereby leading to an uneven distribution of electrolyte conductivity, inhomogeneous material dissolution, as well as deteriorated machining accuracy. In severe cases, the material can no longer dissolve, whereupon the continuous feeding of the wire electrode results in short circuits and processing failure. The aforementioned micro-amplitude vibration has little effect on machining macro structures. Much research has been conducted to improve the outcome of WECM on thick workpieces, and they can be divided into two categories according to the electrolyte flow status. In the first category, the workpiece is immersed in electrolyte, and the electrolyte in machining gap flows following the electrode movement. [PERSON] et al. [6] used the oscillating-wire method to machine 20-mm-thick Monel 400 alloys. [PERSON] et al. [7] carried out research on WECM, adopting a ribbed wire electrode with large-amplitude vibration, and [PERSON] et al. [8] used an edge-cutting electrode; they were able to manufacture a 5-mm-thick fir-tree slit. [PERSON] et al. [9] and [PERSON] et al. [10] proposed the methods of using a rotating helical electrode and electrodes with non-circular cross sections, respectively, to enhance the electrolyte refreshment. The second category is axial electrolyte flushing. The electrolyte with a certain pressure is ejected from the nozzle, and flows into the machining gap along the electrode, which brings the electrolyte products out of the machining gap from top to bottom. High-speed flushing is the most commonly used method to promote electrolyte renewal and replenishment. [PERSON] et al. [11] studied the influence of wire and voltage parameters, nozzle diameter, and velocity of the electrolyte flow on the feed rate in WECM with axial electrolyte flushing. [PERSON] et al. [12] machined 1.8 mm thick titanium alloy with wire electrode of 0.1 mm diameter, and the feed rate could achieve 1.8 mm/min. [PERSON] et al. [13] performed experiments on TiAl alloy of thickness 10 mm, and the feed rate was 0.18 mm/min. [PERSON] et al. [14] machined 6-mm-thick mild steel using axial electrolyte flushing, and the maximum feed rate was 2.5 mm/min. [PERSON] et al. [15] combined axial electrolyte flushing with rotating two twisted wires to optimize the electrolyte flushing, and machined Inconel 718 of thickness 40 mm with the cutting rate up to 20 mm\({}^{2}\)/min. However, the maximum feed rates decrease significantly with the increase of workpiece thickness.