## 1 Introduction
[27] developed and analyzed the flow path of the gap flow field geometry model based on a CFD simulation of electrolyte flow state, and determined the influence of the flow field on the accuracy and stability of the cooling hole manufacturing process. [PERSON] et al. [28] used COMSOL simulation software to optimize the cathode shape in the electrochemical machining process of square deep holes and optimized the combination of processing parameters through gray relational analysis, which successfully solved the technical problem of electrochemical machining of square deep holes. The intersecting hole was a typically shaped hole, and the electrochemical machining of the inner intersecting hole could be generally divided into two categories: one is deburring, the other is shape machining. [PERSON] et al. [29] inserted a cylindrical cathode into a small hole intersecting with a large hole, and proposed an automatic electrolytic deburring method based on current detection, to deburr the intersecting hole with a diameter of 5 mm, and reducing the burr height of 0.9 mm to 0.15 mm. [PERSON] et al. [30] analyzed the deburring effect of different shapes of cathodes using a finite element method, and thickened the spherical and cylindrical tangent parts of hemispherical cathodes, to remove burrs in the intersecting holes with a diameter of 5 mm, which improved the machining efficiency and quality. [PERSON] et al. [31] proposed a localized electrochemical deburring process using gel electrolytes, to reduce the burr height from 473.832 \(\upmu\)m to 178.643 \(\upmu\)m, effectively solving the problem of stray corrosion during electrochemical deburring. [PERSON] [32] proposed a nested circle fitting method for the centering of micro-holes, aiming at the accuracy and stability of centering during the secondary processing of micro-holes, which could effectively remove the edge and surface burrs of micro-holes. Deburring can effectively improve the flow field characteristics of intersecting holes, but for some parts with special requirements, it cannot fully meet the requirements of use. Thus, it is necessary to round the intersection line of the intersecting holes. The processing of a fillet requires the cathode to form a special shape to meet the electric field distribution required for fillet formation. [PERSON] et al. [33] used a cathode with an intersecting structure to study the deburring and arc modification of the intersecting line of the intersecting hole in a fuel injector. The radius of the transition arc was controlled to be 2 mm, and the radius error of the arc contour was about 10%. At present, theoretical and experimental research on the electrochemical machining of intersecting lines of small intersecting holes has carried out beneficial explorations of deburring and formation, and some research has great application value. However, it remains a challenge to achieve accurate control of the fillet shape. The difficulties include the following: (1) In order to ensure the fillet shape, it is necessary to design a cathode with a special shape, to ensure a uniform and stable flow field in a small space. (2) The diameter of the intersecting hole restricts the size of the cathode. The current processing method is to insert the cathode from the small hole, and it is difficult to make a small-sized cathode with a special shape. (3) The gap state changes in real time during the machining process, and there is a linkage relationship between the machining gap, current density, and current efficiency. How to accurately consider the electric field distribution law is also a difficult problem. In order to solve the above problems, this paper proposes a built-in fixed cathode electrochemical rounding technical scheme. By arranging the cathode opposite to the outside of the small intersecting hole, restriction of the diameter of the small intersecting hole on the shape of the cathode is removed from the processing method, and this is also conducive to the formation of a uniform and stable electrolyte flow field.