A method for turning free-form surfaces based on B-axis control of uniform tool wear

Abstract

A method for turning free-form surfaces based on B-axis control of uniform tool wear includes: (1) preparation stage: setting tool parameters, surface quality requirements and effective cutting edge discretization model; (2) offline path planning stage: generating tool contact points based on Archimedes spiral, combining surface normal angle and virtual wear accumulation array, dynamically selecting the cutting edge with the least wear, calculating the corresponding B-axis rotation angle and updating the wear state; (3) online machining stage: performing tool center coordinate compensation, generating X, Z, C, B four-axis linkage NC code, driving the machine tool to complete the machining; This invention actively controls the B-axis posture, transforming tool wear from local concentration to uniform distribution across the entire cutting edge, significantly extending tool life, improving the machining accuracy and consistency of free-form surfaces, and is particularly suitable for single-point diamond turning of optical components such as off-axis parabolic surfaces.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ultra-precision machining, and particularly relates to a free-form surface turning machining method based on B-axis control tool uniform wear. BACKGROUND

[0002] Free-form optical elements play an increasingly important role in the fields of aerospace, lithography equipment, laser nuclear fusion, and precision medical devices, due to their strong aberration correction ability, lightweight system, and functional integration. Multi-axis ultra-precision single-point diamond turning is one of the main technical means for manufacturing high-precision free-form surface elements. In this machining process, tool wear is a fundamental constraint factor that determines the final surface quality (including surface roughness and shape accuracy) and machining efficiency of the parts.

[0003] The physical nature of tool wear lies in the fact that during cutting, the tool edge and the workpiece material undergo intense friction, high temperature and high pressure, causing the tool material to gradually fall off in the form of tiny particles. For a single-point diamond turning tool, its cutting edge is a precisely polished circular arc, and any change in micro-geometric shape will be directly "reproduced" and magnified on the rotating workpiece surface, thereby seriously affecting the final performance of the part.

[0004] In existing multi-axis linkage free-form surface turning machining, in order to ensure that the tool is always tangent to the theoretical surface, the contact point between the tool and the workpiece (tool contact point) will move along the circular arc edge of the tool. However, this movement is passive, and its position is completely determined by the local geometry of the machined surface (i.e., the surface normal direction). For most free-form surfaces, there are large areas of gentle curvature variation on the surface, which means that when machining these areas, the tool contact point will be concentrated in a very narrow area on the circular arc edge of the tool for a long time.

[0005] The "passive concentration of tool contact point" phenomenon in existing technology directly leads to local concentrated wear of the circular arc edge of the tool, causing a series of serious technical problems: Tool life is dramatically shortened, and production costs are high. Local concentrated wear will quickly form a narrow and deep crescent depression or relief wear band in the commonly used area of the tool edge. When the wear amount of this local area exceeds the tolerance, the entire tool must be replaced, while the other parts of the tool circular arc edge are still sharp and perfect. This causes a great waste of expensive super-hard tool material and significantly increases production costs.

[0006] Inconsistent surface quality, low yield. Local wear of the tool changes its micro cutting geometry in real time. This means that the state of the tool is dynamically changing at different stages of machining the same part. In the early stages of machining, the tool is sharp, and the surface quality is good; as the machining progresses, the local wear of the tool intensifies, and the cutting state deteriorates, resulting in a significant deterioration of the surface roughness in the later stages of machining. This inconsistency is fatal for optical elements that require overall high quality, and seriously affects the yield of the product.

[0007] Limited machining efficiency. In order to slow down tool wear, operators are often forced to use more conservative cutting parameters (such as lower feed rates). More importantly, frequent stoppages, tool changes, and auxiliary operations such as tool setting seriously disrupt the continuity of machining, greatly reducing the effective utilization of expensive CNC equipment and overall production efficiency.

[0008] To solve the problem of uniform tool wear in a broad sense, there have been relevant explorations in other machining fields. For example, Chinese patent CN109093447B discloses a tool path design method applied in five-axis milling machining, which realizes uniform wear by controlling the reciprocating swing of the tool shaft posture of a ball-end mill. However, this prior art has the following fundamental defects and deficiencies, which cannot be applied to the turning field targeted by the present invention: The technical field is not applicable, and the scheme cannot be directly transplanted. Milling and turning have essential differences in kinematics and cutting mechanism (tool rotation, workpiece rotation). Therefore, the tool shaft swing compensation model for a ball-end mill is completely unsuitable for B-axis rotation compensation of a single-point turning tool. Applying this scheme to turning field has insurmountable technical barriers.

[0009] Introducing new process instability. The technical scheme of this patent requires dynamic adjustment of spindle speed according to tool shaft swing angle. In ultra-precision turning that pursues nanoscale surface quality, frequent changes in spindle speed will introduce vibration and thermal instability, which is extremely harmful to the final surface quality.

[0010] Limitations of control strategy. This patent uses a preset, open-loop swing strategy that lacks feedback on the actual wear state of the tool. It cannot adaptively adjust the wear strategy based on the machining history.

[0011] In summary, the existing free-form surface turning technology generally has the problem of local tool wear caused by passive concentration of tool contact points, while the uniform wear schemes in other fields (such as milling) cannot be applied due to fundamental differences in technical principles and application scenarios, and there are defects of introducing new process instability. SUMMARY

[0012] To overcome the shortcomings of the prior art, the present invention aims to propose a free-form surface turning method based on B-axis control for uniform tool wear. Without introducing additional process instability factors, this method actively plans the rotation angle of the B-axis to change the arc-shaped cutting edge of the tool, and eliminates the resulting geometric deviations through real-time coordinate compensation on the X and Z axes. This method uses the tool wear amount throughout the machining process as the optimization target, and solves the motion law of the B-axis through an algorithm, thereby uniformly distributing concentrated wear across the entire effective cutting edge. This significantly extends tool life, improves surface quality consistency, and enhances machining efficiency while ensuring machining accuracy.

[0013] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for turning free-form surfaces based on B-axis controlled uniform tool wear includes the following steps: Step 1: Preparation Stage 1.1 Select a circular arc-cut diamond turning tool and obtain its tip radius r_e; set the target residual height h according to the workpiece surface quality requirements; 1.2 Determine the angle range [θ_min, θ_max] of the effective cutting edge region of the tool, and discretize it into N independent cutting edge segments, each cutting edge segment i corresponding to the center angle θ_i; 1.3 Create a one-dimensional floating-point array of length N, denoted as wear accumulation array W_acc[N]. Initialize the wear accumulation array W_acc[N] by setting all elements W_acc[i] to zero, which is used to record the cumulative cutting distance of each cutting edge. Step 1: Preparation Stage 1.1 Select a circular arc-cut diamond turning tool and obtain its tip radius r_e; set the target residual height h according to the workpiece surface quality requirements; 1.2 Determine the angle range [θ_min, θ_max] of the effective cutting edge region of the tool, and discretize it into N independent cutting edge segments, each cutting edge segment i corresponding to the center angle θ_i; 1.3 Create a one-dimensional floating-point array of length N, denoted as wear accumulation array W_acc[N]. Initialize the wear accumulation array W_acc[N] by setting all elements W_acc[i] to zero, which is used to record the cumulative cutting distance of each cutting edge. Step 2: Offline route planning and optimization stage: 2.1 Based on the target residual height h and the tool tip radius r_e, the spiral step s is calculated using the formula s ≈ sqrt(8*r_e*h); an Archimedean spiral covering the entire machining area is constructed in the XY plane and discretized into M path points (x_j, y_j) with high density; 2.2 Project each path point onto the free surface defined by the mathematical model z=f(x,y) to obtain the three-dimensional knife contact point coordinates P_contact_=(x_j, y_j, z_j), and calculate the corresponding C-axis angle c_j and the small distance ΔL_j between adjacent points; 2.3 Perform iterative optimization for each path point j: i) Calculate the angle between the projection of the workpiece surface normal vector at this point onto the XZ plane of the machine tool and the Z-axis to obtain the normal angle α_normal_j at this point; ii) Find the element with the smallest current value in the wear accumulation array W_acc, with index i_min, which corresponds to the optimal cutting edge segment θ_{i_min}; iii) Calculate the required B-axis rotation angle based on the geometric relationship: β_j = α_normal_j - θ_{i_min}, and store this β_j in Beta[j]; iv) Accumulate ΔL_j to W_acc[i_min] = W_acc[i_min]+ΔL_j, and update the wear accumulation value of this cutting edge; 2.4 Output the complete B-axis angle sequence Beta[M]; Step 3: Online processing execution phase: 3.1 For each path point j, based on the known theoretical tool contact point coordinates P_contact_j = (x_j, y_j, z_j), normal angle α_normal_j, and B-axis rotation angle β_j, the actual coordinates of the tool center are calculated using the coordinate compensation formula: P_center_j = (x_center_j, y_center_j, z_center_j). x_center_j = x_j - r_e* sin(α_normal_j) y_center_j = y_j z_center_j = z_j + r_e* cos(α_normal_j) 3.2 Generate NC code containing four-axis linkage instructions from the compensated coordinates (x_center_j, z_center_j), C-axis angle c_j, and B-axis angle β_j according to the G-code format supported by the machine tool; 3.3 Load the NC program into the CNC system to drive the synchronous motion of the four axes X, Z, C, and B to complete the precision turning of free-form surfaces and achieve uniform distribution of tool wear on the effective cutting edge.

[0014] The effective cutting edge region [θ_min, θ_max] is... The number of discretizations N≥180, such that each blade segment represents an arc of no more than 0.5°.

[0015] The freeform surfaces include off-axis parabolic surfaces, off-axis aspherical surfaces, complex surfaces, XY polynomial freeform surfaces, Zernike polynomial freeform surfaces, Q polynomial freeform surfaces, and NURBS freeform surfaces.

[0016] The value of the B-axis rotation angle β_j is constrained by the maximum rotational stroke of the machine tool's B-axis [β_min, β_max]. When deciding on the optimal cutting edge segment, it is necessary to ensure that β_j ∈ [β_min, β_max].

[0017] The wear accumulation array W_acc accumulates the cutting distance ΔL_j of each cutting edge in real time, and constructs a digital mapping model of tool wear; during the path planning process, the usage intensity of each cutting edge is dynamically tracked, and this is used as the basis for optimizing the B-axis rotation, thereby transforming concentrated wear into uniform wear.

[0018] Step 2.2 Calculate the corresponding C-axis angle c_j and the small distance ΔL_j between adjacent points using the formula: c_j = -atan2(y_j, x_j) ΔL_j = sqrt((x_j - x_(j-1))^2 + (y_j - y_(j-1))^2 + (z_j - z_(j-1))^2).

[0019] The calculation formula for step 2.3 (i) is: α_normal_j=atan(-(z_j-z_(j-1)) / (x_j-x_(j-1))).

[0020] Step 2.3, step iii), the calculation formula is: β_j = α_normal_j - θ_{i_min}, where θ_{i_min} is the element with the smallest current value found in the wear accumulation array W_acc, and its index is i_min, corresponding to the optimal cutting edge angle θ_{i_min}.

[0021] A free-form surface turning method based on B-axis controlled uniform tool wear is applied to a four-axis CNC turning machine with X and Z translational axes, C rotary spindle, and controllable rotating tool axis B-axis.

[0022] Compared with the prior art, the present invention has the following advantages: 1. To achieve uniform wear on the effective cutting edge of the tool and avoid excessive local wear. By establishing a wear accumulation array W_acc[N] during the offline path planning stage, the effective cutting edge area of ​​the tool (such as...) is... Discretized modeling is performed, and the cutting edge segment with the minimum cumulative cutting distance is dynamically selected at each machining path point as the actual cutting position, so that the usage intensity of different cutting edges tends to be balanced. This mechanism fundamentally changes the traditional mode in which only a local cutting edge continuously participates in cutting under a fixed tool posture, effectively preventing premature tool failure caused by concentrated wear.

[0023] 2. Improve the surface quality stability and shape accuracy of freeform surface workpieces. Tool wear is a fundamental limiting factor determining the final surface quality of parts (including surface roughness and shape accuracy). This invention significantly reduces the fluctuation of cutting geometry error caused by changes in tool edge morphology during machining by homogenizing wear distribution, thereby ensuring the consistency of surface morphology across the entire freeform surface region and avoiding local surface distortion or texture abnormalities.

[0024] 3. Extends the service life of diamond tools and reduces processing costs. Because the effective cutting edge resources of the tool are fully utilized, rather than relying on a single area to bear the entire cutting load, the overall wear rate of the tool is reduced and its service life is extended while completing the same machining task. This reduces the frequency of tool changes, tool setting and adjustment time, and tool consumption costs, thereby improving the economy of ultra-precision machining.

[0025] 4. Suitable for the high-precision manufacturing requirements of off-axis freeform surface optical components This method takes free-form surfaces such as off-axis parabolic surfaces, which are cut from rotationally symmetric parent surfaces, as typical processing objects. By combining C-axis rotation with X / Z / B-axis linkage and B-axis attitude optimization based on the surface normal angle in real time, it can accurately track the geometric features of complex surfaces and meet the stringent requirements of such optical components for high surface accuracy and low surface defects.

[0026] 5. The method of this invention can be integrated into existing four-axis CNC turning systems, making it highly feasible for engineering implementation. The method only requires the machine tool to have a controllable B-axis (tool tilt axis) and C-axis (workpiece rotation axis). Path planning is completed offline, generating standard four-axis linkage NC code. There is no need to modify the hardware of existing ultra-precision lathes or increase the complexity of real-time control, which makes it easy to promote and apply in industrial environments.

[0027] In summary, this invention not only solves the long-standing problem of uneven tool wear in ultra-precision turning, but also improves the intelligence level and process robustness of the entire machining system through an integrated path planning framework of "perception-decision-execution", which has significant technological advancement and industrialization value. Attached Figure Description

[0028] Figure 1This is a schematic diagram of the overall process of the method described in this invention.

[0029] Figure 2 shows a comparison between localized concentrated wear and uniform wear on the cutting tool. Figure 2(a) is a schematic diagram of localized concentrated wear on the cutting tool, and Figure 2(b) is a schematic diagram of uniform wear on the cutting tool.

[0030] Figure 3 This is a schematic diagram illustrating the principle of actively controlling the cutting area of ​​the tool through B-axis rotation in this invention.

[0031] Figure 4 A schematic diagram of the final turning path generated for machining an off-axis parabolic surface.

[0032] Figure 5 This is a block diagram illustrating the principle of the real-time coordinate compensation module in this invention. Detailed Implementation

[0033] The following will be combined with the appendix Figures 1 to 5 This paper takes the precision turning of a specific free-form surface—an off-axis parabola—as an example to provide a comprehensive and detailed description of the specific embodiments of the present invention. This embodiment aims to clearly and completely explain the technical solution of the present invention so that those skilled in the art can implement it accordingly, but it does not constitute any limitation on the scope of protection of the present invention.

[0034] This invention provides a free-form surface turning method based on B-axis controlled uniform tool wear. In a preferred embodiment, it is implemented on a four-axis CNC turning center with X and Z translational axes, a C rotary spindle, and a B-axis (i.e., a controllable rotating tool axis) capable of driving the cutting tool to rotate in a controlled manner. In this embodiment, we define a machine coordinate system {M}, with its Z-axis along the spindle direction and its X-axis along the radial direction; a workpiece coordinate system {W} is fixed to the workpiece, with its origin located on the workpiece's rotation center surface; and a tool coordinate system {T} is fixed to the tool, with its origin located at the center of the tool tip arc.

[0035] The objective of this embodiment is to machine an off-axis parabolic surface. The parent body of this parabolic surface is a paraboloid of revolution, and its surface equation can be expressed in the workpiece coordinate system {W} as follows: z = f(x, y) = (x² + y²) / (2R) Where R is the radius of curvature at the vertex of the parabola. In this embodiment, a region on the parent body that is offset from the axis of rotation D and has a diameter of A is being processed.

[0036] Reference Figure 1 The flowchart shown illustrates the specific implementation steps of the method of the present invention as follows: Step S101: Delineation of the effective cutting edge area and establishment of the wear model The purpose of this step is to establish a calculable and optimizable mathematical description of tool wear, providing a quantitative basis for subsequent B-axis rotation strategy planning.

[0037] Parametric description of the cutting edge of the tool: This embodiment uses a standard diamond circular arc cutting tool with a tip radius of r_e. In the tool coordinate system {T}, the circular cutting edge of the tool can be precisely parameterized. A two-dimensional plane is established with the center of the tip arc as the origin and the tool axis as the Z-axis. Then, the coordinates of any point P on the circular arc cutting edge can be expressed as a function of angle θ:

[0038] The radius of curvature within which the cutting tool can be used, for example, θ from -45° to +45°, is discretized in the software into N sufficiently small independent cutting segments. Each cutting segment i (i = 1, 2, ..., N) is represented by its center angle θ_i. A larger value for N results in a more accurate model, but also increases the computational load. Typically, N = 180, meaning each 0.5 degrees is considered an independent cutting segment. The determination of this effective cutting edge region [θ_min, θ_max] is based on factors including the machine tool's B-axis travel limitations, tool installation interference checks, and cutting performance analysis.

[0039] Quantification and recording model of wear accumulation: According to the classic Archard wear theory, under precision machining conditions where the three cutting elements (speed, feed, and depth of cut) are relatively stable, the wear volume is proportional to the normal load and the sliding distance. Simultaneously, the wear weight coefficient can be adjusted according to the workpiece material characteristics; for example, the cumulative wear value per unit distance can be increased for high-hardness materials. To enable effective prediction and control during the path planning stage, this embodiment simplifies the model, using the cumulative cutting distance L as the core indicator for measuring the wear degree of each cutting edge segment. Therefore, in the offline path planning software, a one-dimensional floating-point array of length N is created, denoted as the wear accumulation array W_acc[N]. All elements W_acc[i] of this array are initialized to 0, used to simulate and accumulate the total cutting distance completed by each cutting edge segment i throughout the entire toolpath planning process. The optimization objective of this invention is to minimize the variance Var(W_acc) of the W_acc array after machining, so that the cumulative cutting distance L_i of each cutting edge segment tends to be equal.

[0040] Step S102: Planning the B-axis rotation strategy based on uniform wear theory Generate the initial three-axis toolpath (baseline path): First, disregarding B-axis rotation, we need to generate a high-quality initial three-axis (X, Z, C) toolpath for the off-axis paraboloid. Here, we use the constant residual height spiral method.

[0041] Determining the helical pitch: To ensure uniform surface roughness after machining, a strategy of equal residual height is adopted. The relationship between the residual height h, tool radius r_e, and helical pitch s is approximately s = sqrt(8 * r_e * h). Based on the machining requirements, set the target residual height h and calculate the required helical pitch s.

[0042] Constructing the helix: Using the center of the off-axis parabola (D_off, 0) as the planning center, construct an Archimedean helix on the XY plane of the workpiece. First, generate a helix (x_local, y_local) centered at the origin with a maximum radius of A / 2. Then, translate it entirely by D_off to obtain the XY coordinates of the tool contact point: x_contact = x_local + D_off, y_contact = y_local Generating a 3D toolpath by projecting onto a freeform surface: Discrete points (x_j, y_j) on the 2D helix are mapped to 3D space. For each point (x_j, y_j) on the helix, its corresponding tool position Z-coordinate z_j is directly calculated by substituting into the parabolic equation: z_j = f(x_j, y_j). Simultaneously, the workpiece needs to rotate by an angle c_j equal to... atan2(y_j , x_j ).

[0043] Generate the knife contact point sequence: Through the above steps, an initial three-dimensional knife contact point trajectory sequence P_contact_path={x_j , y_j , z_j} consisting of a large number of knife contact points is obtained, and the small segment path ΔL_j between each two adjacent knife contact points is calculated.

[0044] Solving the law of rotational motion along axis B: The goal of this step is to find an optimal B-axis rotation angle β_j for each point j on the initial toolpath. Its core principle and process are as follows: Figure 3 As shown.

[0045] The top left frame, "Tool Position," illustrates the core action of this invention. As the tool moves along the "tool trajectory" (dashed line), the method of this invention actively controls the rotation of the B-axis, dynamically adjusting the tool position. The figure shows the tool position at four different moments, demonstrating that the tangent point of the tool relative to the trajectory is constantly changing. This means that different areas on the tool's arc-shaped cutting edge are sequentially used for cutting.

[0046] The upper right frame, titled "Tool Wear at Different Angles," illustrates the direct effects of the aforementioned pose adjustments. In each individual pose, wear is concentrated in the tiny area in contact with the workpiece. By continuously changing the pose, the wear point moves along the tool's arc-shaped cutting edge.

[0047] The bottom right frame shows "Cumulative Tool Wear": Over the entire machining process, countless independent and tiny wear points accumulate, eventually forming a wide and continuous wear area on the cutting edge of the tool.

[0048] The lower left frame, "Uniform Wear," represents the final ideal result of "Cumulative Tool Wear." Because the wear is evenly distributed across a large arc-shaped cutting edge, the wear depth at each point is very shallow, achieving uniform tool wear as shown in Figure 2(b) and avoiding the localized concentrated wear shown in Figure 2(a).

[0049] This principle is implemented through the following iterative algorithm: For each path point j, firstly, based on its surface normal α_normal_j=atan(-(z_j-z_(j-1)) / (x_j-x_(j-1))), then a greedy algorithm is used to find the cutting edge i_min with the minimum current cumulative wear in the W_acc array as the target cutting edge segment, and then the required B-axis rotation angle β_j=α_normal_j for this step is calculated. θ_i_min, and finally update the cumulative wear of the corresponding blade segment in the W_acc array.

[0050] Step S103: Real-time coordinate compensation and machining execution Mathematical model and implementation of coordinate compensation: like Figure 5 As shown, this is a block diagram illustrating the principle of real-time coordinate compensation. When the B-axis rotates, the tool center position must be compensated to ensure that the correct cutting edge accurately contacts the theoretical machining point.

[0051] Let the theoretical tool contact point coordinates be P_contact = (x_contact, y_contact, z_contact). At this point, the angle between the projection of the workpiece surface normal onto the XZ plane and the Z-axis is α_normal. To ensure the tool's circular cutting edge is tangent to this point, the tool center P_center must be located along the normal direction, at a distance of one tool tip radius r_tool from the tool contact point. Therefore, the compensated tool center coordinates P_center = (x_center, y_center, z_center) are calculated as follows:

[0052] y_center= y_center

[0053] This calculation can be completed in the post-processing stage of CAM software, directly generating the compensated NC code; or, in a more advanced CNC system, it can be dynamically completed by a real-time motion controller within each interpolation cycle based on the input theoretical tool contact trajectory and B-axis angle command.

[0054] Generate and execute the final NC code: The compensated tool center coordinates (x_center_j, y_center_j, z_center_j), the corresponding C-axis angle c_j, and the B-axis angle β_j are integrated to generate the final four-axis simultaneous NC code. For example... Figure 4 As shown in the figure, this diagram illustrates the final turning path generated for machining an off-axis parabola. This path not only precisely conforms to the complex contour of the part in three-dimensional space, but more importantly, it implies the continuous and smooth rotational motion of the B-axis during the machining process, thereby ensuring uniform tool wear.

Claims

1. A method for turning free-form surfaces based on B-axis controlled uniform tool wear, characterized by comprising the following steps: Step 1: Preparation Stage 1.1 Select a circular arc-cut diamond turning tool and obtain its tip radius r_e; set the target residual height h according to the workpiece surface quality requirements; 1.2 Determine the angle range [θ_min, θ_max] of the effective cutting edge region of the tool, and discretize it into N independent cutting edge segments, each cutting edge segment i corresponding to the center angle θ_i; 1.3 Create a one-dimensional floating-point array of length N, denoted as wear accumulation array W_acc[N]. Initialize the wear accumulation array W_acc[N] by setting all elements W_acc[i] to zero, which is used to record the cumulative cutting distance of each cutting edge. Step 2: Offline Path Planning and Optimization Stage 2.1 Based on the target residual height h and the tool tip radius r_e, the spiral step s is calculated using the formula s ≈ sqrt(8*r_e*h); an Archimedean spiral covering the entire machining area is constructed in the XY plane and discretized into M path points (x_j, y_j) with high density; 2.2 Project each path point onto the free surface defined by the mathematical model z=f(x,y) to obtain the three-dimensional knife contact point coordinates P_contact_=(x_j, y_j, z_j), and calculate the corresponding C-axis angle c_j and the small distance ΔL_j between adjacent points; 2.3 Perform iterative optimization for each path point j: i) Calculate the angle between the projection of the workpiece surface normal vector at this point onto the XZ plane of the machine tool and the Z-axis to obtain the normal angle α_normal_j at this point; ii) Find the element with the smallest current value in the wear accumulation array W_acc, with index i_min, which corresponds to the optimal cutting edge segment θ_{i_min}; iii) Calculate the required B-axis rotation angle based on the geometric relationship: β_j = α_normal_j - θ_{i_min}, and store this β_j in Beta[j]; iv) Accumulate ΔL_j to W_acc[i_min] = W_acc[i_min]+ΔL_j, and update the wear accumulation value of this cutting edge; 2.4 Output the complete B-axis angle sequence Beta[M]; Step 3: Online processing execution phase: 3.1 For each path point j, based on the known theoretical tool contact point coordinates P_contact_j = (x_j, y_j, z_j), normal angle α_normal_j, and B-axis rotation angle β_j, the actual coordinates of the tool center are calculated using the coordinate compensation formula: P_center_j = (x_center_j, y_center_j, z_center_j). x_center_j = x_j - r_e* sin(α_normal_j) y_center_j = y_j z_center_j = z_j + r_e * cos(α_normal_j) 3.2 Generate NC code containing four-axis linkage instructions from the compensated coordinates (x_center_j, z_center_j), C-axis angle c_j, and B-axis angle β_j according to the G-code format supported by the machine tool; 3.3 Load the NC program into the CNC system to drive the synchronous motion of the four axes X, Z, C, and B to complete the precision turning of free-form surfaces and achieve uniform distribution of tool wear on the effective cutting edge.

2. The free-form surface turning method as described in claim 1, characterized in that, The effective cutting edge region [θ_min, θ_max] is... The number of discretizations N≥180, such that each blade segment represents an arc of no more than 0.5°.

3. The free-form surface turning method as described in claim 1, characterized in that, The freeform surfaces include off-axis parabolic surfaces, off-axis aspherical surfaces, complex surfaces, XY polynomial freeform surfaces, Zernike polynomial freeform surfaces, Q polynomial freeform surfaces, and NURBS freeform surfaces.

4. The free-form surface turning method as described in claim 1, characterized in that, The value of the B-axis rotation angle β_j is constrained by the maximum rotation stroke of the machine tool's B-axis [β_min, β_max]. When deciding on the optimal cutting edge segment, it is necessary to ensure that β_j∈[β_min, β_max].

5. The free-form surface turning method as described in claim 1, characterized in that, The wear accumulation array W_acc accumulates the cutting distance ΔL_j of each cutting edge in real time, and constructs a digital mapping model of tool wear; during the path planning process, the usage intensity of each cutting edge is dynamically tracked, and this is used as the basis for optimizing the B-axis rotation, thereby transforming concentrated wear into uniform wear.

6. The free-form surface turning method as described in claim 1, characterized in that, Step 2.2 The formula for calculating the corresponding C-axis angle c_j and the small distance ΔL_j between adjacent points is: c_j = -atan2(y_j, x_j) ΔL_j = sqrt((x_j - x_(j-1))^2 + (y_j - y_(j-1))^2 + (z_j - z_(j-1))^2).

7. The free-form surface turning method as described in claim 1, characterized in that, The calculation formula for step 2.3 (i) is: α_normal_j=atan(-(z_j-z_(j-1)) / (x_j-x_(j-1))).

8. The free-form surface turning method as described in claim 1, characterized in that, Step 2.3, step iii), the calculation formula is: β_j = α_normal_j - θ_{i_min}, where θ_{i_min} is the element with the smallest current value found in the wear accumulation array W_acc, and its index is i_min, corresponding to the optimal cutting edge angle θ_{i_min}.

9. A free-form surface turning method based on B-axis controlled uniform tool wear as described in any one of claims 1 to 8, applied to a four-axis CNC turning machine having X and Z translational axes, a C rotary spindle, and a controllable rotating tool axis B-axis.

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