Conjugate pendulum type precision subtractive electrochemical machining method

Abstract

The present application relates to a kind of conjugate swing precision subtractive electrochemical machining method, belong to electrochemical machining technical field.Its characteristics are, in subtractive electrochemical machining process, a certain fixed angle orientation on workpiece always with one or several fixed angle orientation on tool electrode keep corresponding coincidence rule.Through workpiece and tool electrode make reciprocating swing motion around respective axis, while tool electrode make continuous feeding motion relative to workpiece realize;Or through tool electrode make reciprocating linear motion, workpiece make reciprocating swing motion and make continuous feeding motion relative to tool electrode realize.The present application can reduce the machining idle stroke and motion mechanism space of arc sector-containing workpiece, workpiece and tool electrode are immersed in working fluid and cooperate with conjugate swing motion, can improve the chip removal and exhaust condition of machining interelectrode, obtain stable and uniform interelectrode state, improve workpiece machining precision and surface integrity, be applicable to arc sector-containing complex concave, convex surface difficult-to-cut material high-efficiency precision forming, expand the applicable scope of electrochemical machining technology.

Description

Technical Field

[0001] This invention relates to a swing-type precision subtractive electrical discharge machining method, belonging to the field of electrical discharge machining technology. Background Technology

[0002] For machining workpieces with complex concave and convex surfaces containing arc-shaped segments, especially those with large radii in the arc-shaped segments, current methods primarily utilize machining techniques for workpieces with complex concave and convex surfaces involving full-circumference rotation. Based on energy type, these machining methods are divided into two main categories: mechanical machining methods and subtractive electrical discharge machining (EDM) methods.

[0003] Existing machining methods utilize mechanical and thermal energy, relying on the contact between the cutting tool and the workpiece to remove material. These methods employ multi-axis machine tools with specialized tools for machining complex curved surfaces, moving according to a planned trajectory. The decision to continue with CNC grinding for finishing depends on the workpiece's required machining accuracy. (See Patent 1, "A Five-Axis Vertical Turning and Milling Composite Machining Method for Aero-Engine Casings," application number CN108262591A, applicants Li Bin, Yuan Wenyang, et al.; see Patent 2, "A Tool Trajectory Planning Method for Curved Surface Machining Constrained by Cutting Force Fluctuations," authorization number CN106125666B, inventors Ma Jianwei, Gao Ai'ai, et al.). Existing machining methods suffer from complex processes, long programming and calculation preparation times, high tool wear, high costs, and significant influences from force and heat, leading to residual tensile stress and excessive plastic deformation on the workpiece surface. Furthermore, auxiliary processes such as heat treatment are also required.

[0004] Subtractive electrical discharge machining (EDM) is a special machining method that uses electrical, thermal, and chemical energy to remove material from a workpiece. This non-contact machining method can process any conductive material and is suitable for precision machining of various cavities and surfaces. Among these, electrical discharge machining (EDM) and electrolytic machining (ECM) are suitable for machining workpieces with complex concave and convex surfaces that are difficult to machine.

[0005] For electrical discharge machining of workpieces with complex concave and convex surfaces that are difficult to machine, the existing method is to control the relative movement of the tool electrode and the workpiece through numerical control to achieve the forming. However, due to the electrode wear of the tool electrode, tool electrode wear compensation is required, which affects the machining accuracy.

[0006] For electrochemical machining of workpieces with complex concave and convex surfaces that are difficult to machine, there are three main categories of existing methods: "segmented" electrochemical machining, rotary scanning photoelectric electrochemical machining, and rotary printing electrochemical machining. (See Patent 1, "Method for Electrolytic Machining of Complex Chassis Surfaces", Application No. CN101733491A, Applicants: Xu Bin, Zhu Hainan, et al.; See Article 1, "Development and Application of Photographic Electrolytic Machining Technology", Authors: Li Hongying, Zhang Mingqi, et al., *Aeronautical Manufacturing Technology*, 2014, No. 23; See Patent 2, "Metal Photographic Electrolytic Machining Process", Application No. CN1073219A, Applicant: Liu Jiafu; See Patent 3, "Method and System for Electrolytic Machining of Complex Concave and Convex Surfaces", Authorization No. CN102179579A, Inventors: Zhu Di, Zhu Zengwei, et al.; See Patent 4, "Multi-speed Electrolytic Machining System and Method for Concave and Convex Array Structure on Rotary Body Surface", Application No. 202011336134.2, Applicants: Zhu Zengwei, Wang Dengyong, et al.). Among the above electrolytic machining methods, the spin-printing electrolytic method has the best precision and surface integrity in machining chassis, and can achieve integral forming of the workpiece.

[0007] However, the existing subtractive electrical discharge machining (EDM) methods require both the tool electrode and the workpiece to rotate a full circle during machining. For workpieces with larger diameters, simultaneous or double-angle rotation is difficult to achieve. The corresponding circumferential rotation range is small, resulting in a large idle angle during the full rotation, meaning the effective machining stroke is minimal, leading to low overall machining efficiency. Furthermore, as the radius of the workpiece's arc segment increases, from an equipment perspective, the corresponding rotary mechanism must also increase in size, causing space loss, operational difficulties, and increased costs. From a tooling perspective, the diameter of the tool electrode may also need to increase, increasing the difficulty of tool electrode manufacturing.

[0008] From the perspective of improving processing efficiency, processing quality, and surface integrity, there is currently a lack of suitable processing methods for difficult-to-machine material workpieces with complex concave and convex surfaces containing arc-shaped sections, especially for precision subtractive EDM methods for workpieces with large arc-shaped section radii. Therefore, there is an urgent need to find a subtractive EDM method for such workpieces with short machining idle strokes, high processing efficiency, low difficulty in electrode design, manufacturing, and finishing, and more uniform and stable machining gap distribution. Summary of the Invention

[0009] Purpose of the invention:

[0010] The purpose of this invention is to address the problem of low machining efficiency and large equipment size in machining workpieces with complex concave and convex surfaces containing arc-shaped segments, particularly those with large arc-shaped segments. This is because the turning angle range corresponding to the workpiece machining area is small, and existing technologies require a machining time-space travel many times greater than the effective working stroke. The invention provides a conjugate swing-type precision subtractive electrical discharge machining (EDM) method. This method involves the tool electrode and workpiece reciprocating around their respective axes while the tool electrode continuously feeds relative to the workpiece, or the tool electrode reciprocating linearly while the workpiece reciprocates and swings while continuously feeding relative to the tool electrode. This reduces the machining time-space travel, improves the machining gap, and facilitates the efficient and precise forming of workpieces with complex concave and convex surfaces containing arc-shaped segments.

[0011] Technical solution:

[0012] A conjugate swing-type precision subtractive electrical discharge machining (EDM) method is applicable to the forming of workpieces with complex concave and convex surfaces containing arc-shaped segments. The method is characterized by: a first axis and a second axis located in the same plane in space, intersecting at a fixed angle; the workpiece surface to be machined is an arc-shaped segment with a small circumferential angle; the tool electrode is a rotating structure; the workpiece is mounted on the first axis, and the tool electrode is mounted on the second axis; the workpiece and tool electrode are supplied with a fluid completely immersed in the working fluid; during the subtractive EDM process, a fixed angular position on the workpiece always maintains a corresponding coincidence with one or more fixed angular positions on the tool electrode: the tool electrode swings back and forth around the second axis at a certain angular velocity and continuously feeds relative to the workpiece, while the workpiece swings back and forth around the first axis at another angular velocity. The ratio K of the tool electrode oscillation angular velocity to the workpiece oscillation angular velocity is constant and can be adjusted according to machining needs. The distance between the workpiece and the tool electrode can be continuously adjusted to achieve radial feed machining motion. When the workpiece and the tool electrode swing back and forth, there is no relative axial movement between them. In the typical process of subtractive EDM of complex concave and convex surfaces with arc-segment sections—threaded surfaces or tooth profiles with arc-segment sections—before changing the EDM standard, the tool electrode first exits the workpiece and moves axially by a pitch or tooth thickness multiple of the workpiece thickness to compensate for the wear of the tool electrode. Then, the above characteristics are repeated to continue machining. By the reciprocating swing motion between the tool electrode and the workpiece according to the fixed angular orientation correspondence, the arc-segment surface of the workpiece is etched away from the outer surface of the tool electrode using the principle of subtractive EDM.

[0013] In subtractive EDM, the included angle between the first and second axes can be any value between 0° and 90°. During subtractive EDM, the ratio K of the tool electrode oscillation angular velocity to the workpiece oscillation angular velocity is equal to the ratio of the tool electrode oscillation angle to the workpiece oscillation angle. When machining threaded surfaces and tooth profiles containing arc segments, the ratio K of the tool electrode oscillation angular velocity to the workpiece oscillation angular velocity can be either n or... n is a positive integer. Using a single-specification tool electrode on the same device, by adjusting the ratio K of the tool electrode's oscillation angular velocity to the workpiece's oscillation angular velocity, precision subtractive electrical discharge machining (EDM) of workpieces with complex concave and convex surfaces containing arc-shaped segments can be achieved. During the subtractive EDM of a concave surface, the direction of the tool electrode's oscillation angular velocity is the same as the workpiece's oscillation angular velocity at any given time. During the subtractive EDM of a convex surface, the direction of the tool electrode's oscillation angular velocity is opposite to the workpiece's oscillation angular velocity at any given time. The surface to be machined on the workpiece is either its outer or inner surface. The tool electrode is always an outer surface electrode, and the outer surface of the tool electrode forms the surface to be machined on the workpiece. The material of the tool electrode can be any one of graphite, pure copper, stainless steel, aluminum alloy, tungsten alloy, and copper-carbon composite materials. The subtractive EDM method is any one of electrical discharge machining (EDM), electrolytic machining (ECM), electrolytic-EDM hybrid machining (ECM), or a hybrid machining and EDM process.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] 1. This invention targets workpieces with complex concave and convex surfaces containing arc-shaped segments that are difficult to machine. By using the conjugate swing motion between the workpiece and the tool electrode, subtractive electrical discharge machining of workpieces with complex concave and convex surfaces containing arc-shaped segments can be achieved.

[0016] 2. This invention uses a rotating tool electrode with an external surface that is easy to manufacture and ensures machining accuracy, thus reducing the difficulty of tool electrode manufacturing and testing;

[0017] 3. This invention enables the subtractive electrical discharge machining of various sizes of workpieces with complex concave and convex surfaces containing arc fan segments, using a single rotary tool electrode on the same device;

[0018] 4. In the electrical discharge machining process, the present invention causes disturbance of the working fluid flow through conjugate swing motion and feed motion, so that the narrow machining area has sufficient and good chip removal and air venting space, eliminating the high-pressure fluid supply method in traditional subtractive electrical discharge machining, reducing the number of electrical discharge machining devices, and achieving a better inter-electrode fluid supply effect when combined with simple immersion machining, obtaining a stable and uniform machining gap, which helps to improve the machining accuracy and surface integrity of the workpiece.

[0019] 5. This invention reduces the proportion of idle stroke in traditional subtractive EDM by using conjugate swing motion, thereby improving processing efficiency and reducing the space required for the motion mechanism and the size of the equipment. Attached Figure Description

[0020] Figure 1 Schematic diagram of the forming principle of conjugate swing-type precision subtractive EDM arc fan segment convex surface workpiece.

[0021] Figure 2 Schematic diagram of the forming principle of concave surface workpiece of arc fan segment by precision subtractive EDM.

[0022] Figure 3 Simulation model of a conjugate pendulum-type precision subtractive EDM forming method for arc-shaped convex surfaces (K=8)

[0023] Figure 4 Simulation model of conjugate swing-type precision subtractive EDM arc fan segment convex surface forming embodiment, flow field analysis, mesh generation

[0024] Figure 5 Simulation model of a conjugate pendulum precision subtractive EDM arc fan segment convex surface forming embodiment, position of a point T1 in the fluid region.

[0025] Figure 6 The statistical velocity curve of a point T1 in the fluid region of a simulation model of a conjugate pendulum precision subtractive EDM arc fan segment convex surface forming embodiment.

[0026] Figure 7 A simulation model of a conjugate pendulum precision subtractive EDM arc fan segment convex surface forming implementation case study: statistical pressure curve of T1 at a certain point in the fluid region.

[0027] Figure 8 Example of a large pitch diameter external gear block using a conjugate swing-type precision subtractive EDM for external gear electrodes.

[0028] Figure 9 Example of an external thread electrode conjugate swing-type precision subtractive EDM large-diameter internal thread arc fan-shaped thread rolling die (K=2)

[0029] Figure 10 Example of an external radial linear contour electrode conjugate cycloidal tooth template tool for precision subtractive EDM.

[0030] Figure 11 Example of an external toothed bar block electrode conjugate swing-type precision subtractive EDM involute tooth profile template tool

[0031] The labels in the diagram are as follows: 1. First axis, 2. Second axis, 3. Workpiece, 4. Tool electrode, 5. Working fluid circulation supply system, 6. Machining power supply. Detailed Implementation

[0032] The present invention will be further described below with reference to embodiments and accompanying drawings. The following description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

[0033] Figure 1 The diagram shows the forming principle of a conjugate swing-type precision subtractive EDM workpiece with an arc-shaped fan-shaped surface. The workpiece and tool electrode are immersed in the working fluid. The arc-shaped fan-shaped workpiece (3) swings back and forth around its axis O1 at a constant angular velocity ω1. The tool electrode (4) swings back and forth around its axis O2 at a constant angular velocity ω2 in the opposite direction of rotation. Simultaneously, the tool electrode (4) continuously feeds radially towards the arc-shaped fan-shaped workpiece (3) at a velocity v along the line connecting O1 and O2. Initially, P on the tool electrode (4)... 21 Point P on workpiece (3) l1 Point-to-point electrical discharge machining is performed, followed by P on the tool electrode (4). 22 Point P on workpiece (3) 12 Points correspond. When P on the tool electrode (4) 23 Point P on workpiece (3) 13 When making point contact, connect O1P 14 The included angle is θ1, and O2P is connected. 24 The included angle is θ2, which means that during the subsequent rotation of the tool electrode (4) by θ2, it corresponds to the conjugate rotation of the workpiece (3) by θ1, ensuring that P on the tool electrode (4) 24 Point P on workpiece (3) 14 Point-to-point contact. Similarly, P on the tool electrode (4) 25 Point P on the uppermost edge of workpiece (3) 15 Point-to-point contact, then the tool electrode (4) and the workpiece (3) simultaneously change their rotation direction to ensure that each relative point corresponds to the reciprocating oscillating electrical discharge machining (EDM). Figure 1 The double-dotted line indicates the two extreme positions of the workpiece (3), meaning that the relative motion between the tool electrode (4) and the workpiece (3) conforms to the motion law of a certain type of pair of conjugate bodies. In the above electrical discharge machining process, the formula for calculating the ratio K of the oscillation angular velocity of the tool electrode (4) to the oscillation angular velocity of the workpiece (3) is:

[0034]

[0035] Figure 2The diagram shows the forming principle of the concave surface of the arc fan segment in the precision subtractive EDM. The workpiece and the tool electrode are immersed in the working fluid. Similar to the forming principle of the arc fan segment of the concave subtractive EDM, each point on the tool electrode (4) always maintains the rule of coinciding with the corresponding angular phase point on the arc-shaped inner surface of the workpiece (3) to carry out concave swing continuous feed subtractive EDM.

[0036] Figure 3 The simulation model of the conjugate swing-type precision subtractive EDM arc sector convex surface forming embodiment shown (K=8) defines a point P on the whole circle O2 at a certain moment. 24 P 24 O2 and the horizontal centerline are θ2, and point P is on the arc sector. 14 P 14 O1 and the horizontal centerline are θ1. In this embodiment, θ2 = 8θ1, that is, at this time... The tool electrode has a solid boundary of φ7.13mm in the outer surface of a complete circle O2. It oscillates back and forth around the center O2 at a speed of 16r / s. Its upper and lower extreme oscillation positions P 21 O2 and P 25 The absolute value of the angle between O2 and the horizontal centerline O1O2 is 96°. The solid boundary of the workpiece is an arc-shaped sector composed of R24.93mm and R21.29mm (the center radius of the arc-shaped sector is R23.11mm), and this arc-shaped sector is along the horizontal centerline O. I O2 oscillates back and forth around the center O1 at a speed of 2 r / s, and the absolute value of the angle between its upper and lower extreme oscillation positions and the horizontal centerline O1O2 is 24°. The machining electrode gap between the tool electrode and the arc sector is defined as 0.5 mm. The above flow field model was established in ANSYS 2022R1 Workbench Design Modeler.

[0037] Figure 4 The simulation model of the conjugate swing-type precision subtractive EDM arc fan segment convex surface forming embodiment shown is used for flow field analysis and mesh generation. The flow field model was imported into the ANSYS 2022R1 Workbench Mesh component, and a triangular mesh was used for mesh generation. The boundary of the contact area was refined to ensure the accuracy of the fluid dynamics calculation. The final mesh generation diagram is shown below. Figure 4As shown, calculations show that the mesh element indices of this mesh model are all above 0.63, which meets the requirements for computational fluid dynamics simulation. The generated mesh model is imported into ANSYS 2022R1 Fluent for solving. Based on the actual processing conditions, the main solver parameters are set as follows: pressure-based transient solver, absolute velocity equations, standard Ke-squared two-equations for turbulence, standard near-wall treatment; deionized water as the fluid phase; dynamic mesh defined using a UDF program; SIMPLEC algorithm selected; transient calculations performed with a time step of 2000, a time step size of 0.0005s, and a maximum number of iterations of 10.

[0038] Figure 5 The simulation model of the conjugate pendulum precision subtractive EDM arc fan segment convex surface forming embodiment shows the position of a point T1 in the fluid region, which is located at the midpoint of the gap between machining electrodes. The midpoint T1 of the gap in the fluid region is measured using the ANSYS 2022 R1 Workbench post-processing component. Figure 4 The curves showing the changes in speed and pressure over time.

[0039] Figure 6 The simulation model of the conjugate swing-type precision subtractive EDM arc fan segment convex surface forming embodiment shows the statistical velocity curve of a certain point T1 in the fluid region. When point T1 is located at the minimum gap between the poles within one cycle, the point has an extreme velocity, and the velocity increase is significant compared to other times.

[0040] Figure 7 The simulation model of the conjugate pendulum precision subtractive EDM arc sector convex surface forming embodiment shows the statistical pressure curve at a point T1 in the fluid region. The statistical pressure curve at this point tends to be stable. Analysis Figure 6 and Figure 7 The two curves show that the conjugate oscillation motion between the tool electrode and the workpiece can create a better flow field in the gap between the machining electrodes, which can improve the chip removal and venting state of the gap, thus improving the machining efficiency and quality of subtractive EDM.

[0041] Figure 8 The example shown is an embodiment of a large-pitch-diameter external gear block produced by precision subtractive EDM using a conjugate swing-type external gear electrode. The workpiece and tool electrode are immersed in the working fluid. The external gear electrode (4) and the difficult-to-machine material gear block (3) satisfy the conjugate swing motion condition. The angular velocity of the reciprocating swing of the external gear electrode (4) is equal to the angular velocity of the reciprocating swing of the workpiece gear block (3) (K = 1). Simultaneously, the external gear electrode (4) performs continuous radial feed machining on the workpiece to obtain the external gear block (3). By increasing the angular velocity ratio K, using a small-diameter external gear electrode that easily achieves high dimensional and shape position accuracy, a similar conjugate swing-type precision subtractive EDM method can be used to machine large-pitch-diameter arc-shaped external gear blocks and internal gear blocks.

[0042] Figure 9 This embodiment illustrates a large-diameter internal thread arc-shaped thread rolling plate using a conjugate oscillating precision subtractive EDM method with an external thread electrode. The workpiece and tool electrode are immersed in the working fluid. The reciprocating angular velocity of the single-start external thread electrode is twice the reciprocating angular velocity of the large-diameter workpiece (K=2). In addition to reciprocating oscillation, the external thread electrode also feeds radially towards the workpiece. A large-diameter double-start internal thread arc-shaped thread rolling plate is obtained through this conjugate oscillating subtractive EDM method. A similar method can be used to process large-diameter multi-start external and internal thread blocks.

[0043] Figure 10 The example shown is an embodiment of a cycloidal tooth template tool for precision subtractive EDM of an outer radial straight contour electrode. The workpiece and the tool electrode are immersed in the working fluid. The cycloidal tooth template tool contour on the workpiece (3) is formed by the oscillating motion of a pair of radial straight contours on the tool electrode (4) in conjunction with the reciprocating oscillating motion and continuous feed motion of the workpiece (3). Compared with the mechanical point-by-point machining method for this type of template tool, the template tool obtained by the conjugate oscillating precision subtractive EDM method has a smoother transition of the linear surface, higher dimensional accuracy, and is more convenient to process.

[0044] Figure 11 The diagram shows an embodiment of a precision subtractive EDM template tool for involute tooth profiles using an external rack block electrode. The workpiece and tool electrode are immersed in the working fluid. The rack block tool electrode (4) reciprocates linearly at a speed v1, considered as a special case where the reciprocating swing radius is infinite. The workpiece (3) reciprocates at a constant angular velocity ω1, while simultaneously undergoing continuous feed motion relative to the tool electrode (4) at a speed v2. At the final machining position, the distance between the pitch line of the rack block tool electrode (4) and the swing axis of the workpiece (3) is equal to the pitch radius of the imaginary gear containing the involute tooth profile of the template tool. Using a linear profile electrode with easily controllable machining accuracy, a highly precise cycloidal tooth profile template tool is obtained.

Claims

1. A conjugate pendulum precision subtractive electrochemical machining method, which is suitable for forming machining of complex concave and convex surface difficult-to-machine material workpieces containing arc sector segments, characterized in that The process comprises the following steps: The first shaft (1) and the second shaft (2) are located in the same plane in space and intersect at a fixed angle; The surface to be machined of the workpiece (3) is an arc sector surface, and the circumferential angle of the arc sector surface is small; The tool electrode (4) is a rotary body structure; The workpiece (3) is installed on the first shaft (1), and the tool electrode (4) is installed on the second shaft (2); The workpiece (3) and the tool electrode (4) are supplied with liquid by being completely immersed in the working liquid; During the subtractive electrochemical machining process, a certain fixed angle position on the workpiece (3) always corresponds to and overlaps with one or more fixed angle positions on the tool electrode (4); The tool electrode (4) performs reciprocating swing motion around the second shaft (2) at a swing angular velocity and continuously feeds relative to the workpiece (3), and the workpiece (3) performs reciprocating swing motion around the first shaft (1) at another swing angular velocity; The ratio K of the swing angular velocity of the tool electrode (4) to the swing angular velocity of the workpiece (3) is constant, and the value can be adjusted according to the machining requirements; The distance between the workpiece (3) and the tool electrode (4) can be continuously adjusted to realize radial feeding machining motion; When the workpiece (3) and the tool electrode (4) perform swing motion, there is no relative axial motion between them; In the subtractive electrochemical machining process of a typical representative of a complex concave and convex surface with an arc sector, i.e., a thread surface or a tooth surface with an arc sector, the tool electrode (4) first exits the workpiece, moves axially by an integer multiple of a pitch or a tooth thickness corresponding to the thickness of the workpiece (3) to compensate for the loss of the tool electrode (3), and then repeats the above characteristics for continuous machining; Through the reciprocating swing motion between the tool electrode (4) and the workpiece (3) according to the fixed angle position corresponding overlap rule, the arc sector surface of the workpiece (3) is machined by using the subtractive electrochemical machining principle of eroding the outer surface of the tool electrode (4).

2. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: During the subtractive electrochemical machining process, the included angle between the first shaft (1) and the second shaft (2) can be any value between 0° and 90°.

3. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: In the subtractive electro-discharge machining process, the ratio K of the swing angular velocity of the tool electrode (4) to the swing angular velocity of the workpiece (3) is equal to the ratio of the swing angle of the tool electrode (4) to the swing angle of the workpiece (3). When machining a thread surface and a tooth profile containing an arc sector, the ratio K of the swing angular velocity of the tool electrode (4) to the swing angular velocity of the workpiece (3) is taken as n or n is a positive integer.

4. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: On the same device, a single specification tool electrode (4) is used, and by adjusting the ratio K of the swing angular velocity of the tool electrode (4) to the swing angular velocity of the workpiece (3), the precision subtractive electrochemical machining of workpieces with various specifications of complex concave and convex surfaces with arc sectors can be realized.

5. The conjugate traverse electrochemical subtractive material removal machining method of claim 1, wherein: During the subtractive electrochemical machining of the concave surface of the workpiece, the swing angular velocity direction of the tool electrode (4) is the same as that of the workpiece (3) at any time, and during the subtractive electrochemical machining of the convex surface of the workpiece, the swing angular velocity direction of the tool electrode (4) is opposite to that of the workpiece (3) at any time.

6. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: The surface to be machined of the workpiece (3) is its outer surface or inner surface, the tool electrode (4) is an outer surface electrode, and the outer surface of the tool electrode (4) and the surface to be machined of the workpiece (3) are formed.

7. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: The material of the tool electrode (4) is any one of graphite, pure copper, stainless steel, aluminum alloy, tungsten alloy, and copper-carbon composite material.

8. The conjugate traverse electro-subtractive machining method according to claim 1, characterized in that: The subtractive electrochemical machining method is any one of electric discharge machining, electrolytic machining, electrochemical discharge combined machining, and mechanical machining combined with electrochemical machining.

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