A variable-parameter groove grinding trajectory planning method considering kinematic fairing

Abstract

This invention discloses a method for planning the grinding trajectory of variable-parameter chip grooves considering kinematic smoothness, comprising the following steps: parametric geometric model; establishing a model of equivalent machining error for groove width and equivalent machining error for core thickness based on the principle of circular arc envelope projection; establishing a smoothness measurement index model based on the composite smoothness principle of grinding wheel posture geometric continuity and machine tool kinematic performance; constructing a multi-objective trajectory planning model with geometric error, posture smoothness error, and machine tool kinematic performance error as objectives; constructing the planning model as a multi-objective optimization problem that dynamically evolves along the axial section, and solving it according to the principle of dynamic optimization to obtain the Pareto optimal solution set of continuous grinding wheel posture; performing five-axis post-processing on the optimal grinding wheel posture sequence to generate a machine tool trajectory and CNC program that satisfy machining constraints. This invention can significantly improve the machining accuracy, posture smoothness, and machine tool motion stability during the chip groove grinding process of variable-parameter milling cutters.

Description

Technical Field

[0001] This invention relates to the fields of CNC tool manufacturing, five-axis linkage tool grinding and intelligent optimization control, and in particular to a variable parameter chip groove grinding trajectory planning method that takes kinematic smoothness into account. Background Technology

[0002] In high-end manufacturing, solid end mills, as a crucial component of cutting tools, are widely used in industries such as aerospace, automotive manufacturing, and precision mold making, especially in the machining of complex materials. Chip grooves are one of the key geometric features of solid end mills, and their design directly impacts the cutting performance, machining accuracy, and tool life. Traditional solid end mill designs often employ fixed-parameter structures, meaning that parameters such as groove width, core thickness, and rake angle remain constant throughout the entire tool. However, this design approach cannot adapt to different cutting requirements under complex working conditions, easily generating significant vibrations that affect machining stability and cannot guarantee high-precision machining.

[0003] To overcome the aforementioned shortcomings, variable parameter end mill designs have been proposed in recent years. By adjusting parameters such as the helix angle, rake angle, core thickness, and flute width angle, these parameters are varied along the tool's axis, thereby improving the tool's cutting performance. These variable parameter end mills can better adapt to complex working conditions, improve tool rigidity, vibration resistance, and chip removal capabilities, and thus enhance machining accuracy and efficiency.

[0004] However, the chip flute geometry of variable parameter milling cutters is quite complex, especially since precise control of its geometry is required during design and machining. Traditional grinding methods often focus on calculating the conjugate relationship between the grinding wheel and the tool contact point through geometric modeling and empirical formulas. However, this method is insufficient for the precise machining of complex variable parameter milling cutters, especially between multiple axial sections. The changes in the grinding wheel posture fail to take into account the kinematic performance and smoothness of the machine tool, thus affecting machining accuracy and stability.

[0005] The machining accuracy of the chip grooves in a solid milling cutter is primarily determined by the position and orientation of the grinding wheel. Traditional geometric error control methods are mainly based on the conjugate surface method (CAP), which treats the grinding wheel and the tool surface as conjugate surfaces and uses geometric analysis to ensure perfect contact between them. However, in the grinding process of variable parameter milling cutters, due to the complexity of the tool shape, this method struggles to handle geometric errors that vary along the axial cross-section.

[0006] To address this issue, a circular arc projection geometric modeling method has been proposed in recent years. This method projects the groove width curve and core thickness revolution surface of the tool chip flute onto the axial section of the grinding wheel, and calculates the machining errors of the groove width and core thickness using the geometric principles of circular arc projection (Ren Lei, A Method for Grinding Wheel Pose Planning in Overall Tool Chip Flute Grinding, Publication No. CN115982865A). By comparing the relative positional relationship between the projected curve and the grinding wheel cross-sectional profile, the geometric error can be accurately calculated, providing a reference for subsequent trajectory planning. Although the circular arc projection method simplifies the problem and provides intuitive error analysis, it can only locally control the geometric error of each discrete section and cannot consider the continuity of the grinding wheel pose during axial changes.

[0007] The motion control of a five-axis linkage tool grinder is accomplished by three linear axes and two rotary axes. The spatial attitude of the grinding wheel is controlled by the five-axis linkage. In actual machining, due to the kinematic limitations of the machine tool's servo system in terms of speed, acceleration, and position, if the attitude of the grinding wheel changes too drastically along the tool axis, it may lead to problems such as overspeeding and acceleration exceeding limits of the machine tool, thereby causing machining errors and machine tool vibration.

[0008] Existing trajectory planning methods typically generate the machine tool's motion trajectory through simple linear interpolation or tool axis vector interpolation after solving the grinding wheel pose. However, this method often neglects the dynamic performance of the machine tool in actual operation, fails to guarantee a smooth transition of the grinding wheel posture, and does not consider the smoothness of the machine tool's kinematic properties (such as the angular velocity and angular acceleration of the axis). Therefore, traditional trajectory planning methods have the following shortcomings in the variable parameter milling process: Insufficient geometric error control: Traditional methods fail to fully consider the geometric errors between multiple sections and the continuity of the grinding wheel posture; Poor grinding wheel posture smoothness: The grinding wheel pose may change abruptly between adjacent sections, affecting grinding accuracy; Lack of consideration for machine tool kinematic performance: The machine tool's kinematic performance is not incorporated into the optimization process, resulting in unstable machine tool movement and affecting machining quality.

[0009] Therefore, traditional methods cannot meet the high requirements for accuracy, stability and efficiency in modern variable parameter milling grinding. There is an urgent need for a new multi-objective optimization method that can optimize both the smoothness of the grinding wheel posture and the kinematic performance of the machine tool while ensuring geometric accuracy. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention proposes a multi-objective trajectory planning method for chip groove grinding of variable-parameter integral milling cutters such as tapered flat-end mills and barrel mills, along with corresponding devices, electronic equipment, and computer-readable storage media. This method primarily applies to five-axis linkage tool grinders, and through geometric modeling, machine tool kinematics modeling, and multi-objective evolutionary algorithms, it achieves comprehensive optimization of machining parameters such as geometric errors and attitude smoothness during the chip groove grinding process of variable-parameter milling cutters.

[0011] The present invention is achieved by at least one of the following technical solutions.

[0012] A method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness includes the following steps:

[0013] S1. Establish the three-coordinate system of the chip groove of the variable parameter milling cutter and the unified parameterized geometric model that varies with the axial parameter; S2. Based on the principle of circular arc envelope projection, establish a model of equivalent machining error for groove width and equivalent machining error for core thickness; S3. Establish a smoothness measurement index model based on the composite smoothness principle of grinding wheel attitude geometric continuity and machine tool kinematic performance; S4. Construct a multi-objective trajectory planning model with geometric error, attitude compliance error and machine tool kinematic performance error as objectives; S5. Discretize the milling cutter groove into multiple sections along the axial direction, construct the above multi-objective programming model into a multi-objective optimization problem that dynamically evolves along the axial section, and solve it according to the dynamic optimization principle to obtain the Pareto optimal solution set of continuous grinding wheel pose; S6. Perform five-axis post-processing on the optimal grinding wheel pose sequence and generate machine tool trajectory and CNC program that meet machining constraints.

[0014] Further, step S1 includes: S11. Establish the tool coordinate system, grinding wheel coordinate system, and machine tool fixed coordinate system; S12. Define the outer wheel of the tool using a p-order spline function. Outline radius:

[0015] in The outer radius of the tool. For p-order B-spline basis functions; Radius of the control point; is the tool axial parameter; n is the number of control points; S13, Generate a surface of revolution from the outer contour. Represented as:

[0016] in Circumferential angle; S14. The cutting edge curve is determined by the helix angle, rake angle, core thickness, and groove, and the cutting edge curvature and normal continuity constraints are added to improve the geometric manufacturability of the cutting edge shape. S15. The tip of the blade is constructed using independent spline segments to create a smooth transition in order to maintain overall continuity.

[0017] Further, step S2 includes: S21. Map the groove width curve and the core thickness rotation surface to the grinding wheel coordinate system through homogeneous coordinate transformation; S22. Obtain the equivalent projection of the groove width and the upper envelope of the core thickness by using circular arc envelope projection in the plane of the grinding wheel section. S23. Define the groove width and core thickness error by the maximum interference between the projection curve and the cross-sectional profile of the grinding wheel. S24. Calculate the sensitivity of the error to the grinding wheel attitude vector, which is used for subsequent optimization of direction guidance; S25. Dynamic error correction is performed using grinding wheel wear as a compensation variable. S26. Automatically adjust the projection resolution based on the local curvature to improve the accuracy of error resolution.

[0018] Further, step S3 includes: S31. Calculate joint angles, angular velocities, angular accelerations, and angular jerkes using the forward and inverse kinematics of a five-axis machine tool. S32. Construct a system including first-order attitude smoothness, grinding wheel axial unit vector attitude change angle, and second-order attitude continuity term. Attitude geometric compliance index; S33. Construct machine tool dynamic smoothness indicators, including servo torque change rate, joint dynamic load change, flexible vibration sensitivity and nonlinear interpolation error; S34, based on A five-axis singularity avoidance index is constructed by axis coupling, and the attitude continuity constraint weight is increased to automatically avoid singular points when the index approaches the singular region.

[0019] Further, step S4 includes: S41. Define decision variables: The grinding wheel pose sequence is the decision variable; S42. The geometric error target adopts a dynamic weighting mechanism that automatically adjusts with the axial direction:

[0020] in For error weights, For the first Equivalent machining error of the groove width of each axial section; For the first Equivalent machining error of core thickness for each axial section; The objective function for the geometric error of the chip groove parameters; Indicates the serial number of the axial discrete section; S43, Attitude compliance targets include , and attitude curvature smoothing term:

[0021] in For attitude increment; The angle between the normal vectors of the grinding wheel and the target vectors changes. It is a second-order smooth term; Let the attitude compliance objective function be; , , These are the weighting coefficients for the first-order attitude change, the rate of change of attitude angle, and the second sister's attitude continuity, respectively. The grinding wheel pose vector for the k-th cross-section S44. Machine tool kinematic performance targets are based on axis velocity, acceleration, and acceleration and interpolation error. :

[0022] in The objective function for the kinematic performance of the machine tool; , , These are the weighting coefficients for machine tool angular velocity, angular acceleration, and interpolation error, respectively. S45. Construct machine tool travel, speed, acceleration limits, machining accessibility constraints, and multi-body collision avoidance constraints.

[0023] Further, step S5 includes: (1) Discretize the tool axis into multiple optimized sections, and each section constitutes an optimized environment that dynamically evolves with geometric changes; (2) An environmental difference measurement index is constructed based on parameters such as outer contour, helix angle, core thickness, and groove width to characterize the cross-sectional variation range; (3) Solve for the local Pareto solution set for section k; (4) In section k+1, the representative solution with the highest similarity in the previous section is inherited, and the continuity and diversity are maintained by combining drift detection, two-layer solution library management and variable partitioning inheritance mechanism.

[0024] Furthermore, the optimization methods include genetic algorithms, differential evolution, particle swarm optimization, co-evolution, and multi-population parallel optimization methods.

[0025] Further, step S6 includes: S61. Perform inverse kinematics solution on the grinding wheel pose sequence and re-decompose the pose based on the singularity index to avoid the A / B axis singularity region. S62. Perform interpolation error detection and repair to avoid interpolation discontinuities caused by sudden attitude changes; S63. Perform multi-body collision detection of tool-grinding wheel-machine tool components and avoid collisions by attitude adjustment or degree of freedom redistribution; S64. Based on the machine tool travel, axial load and speed characteristics, perform redundancy optimization and load balancing on the A / B axis posture to generate an executable machining program.

[0026] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0027] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0028] Compared with the prior art, the present invention has the following significant advantages: 1. Unified handling of various variable parameter milling cutter types.

[0029] By establishing a universal rotary surface model and cutting edge parameter curves in the tool coordinate system, this invention is compatible with various variable parameter milling cutter types, such as tapered milling cutters, tapered barrel milling cutters, and barrel milling cutters, requiring only changes to the radius function and axial parameter definitions. This unified modeling approach facilitates software system implementation and subsequent expansion.

[0030] 2. The geometric error of circular arc projection is intuitive and concise.

[0031] Compared to directly calculating the geometric deviation of the three-dimensional envelope surface, this invention uses the arc projection within the cross-section of the grinding wheel shaft to define the groove width and core thickness errors. This method transforms the 3D contact problem into a 2D cross-section problem, simplifying the calculation process and facilitating its integration into optimization algorithms. Moreover, the error has a clear physical meaning in terms of geometry: when the projected curve is tangent to the profile of the grinding wheel cross-section, the error is zero, and the degree of over- or under-tangency can be directly reflected by the interference quantity.

[0032] 3. Coordinated measurement of attitude and machine tool kinematic performance.

[0033] In traditional work, the smoothness of the grinding wheel's posture and the kinematic performance of the machine tool are often considered separately, or simply rely on empirical rules. This invention starts from the machine tool kinematic chain, linking the spatial posture of the grinding wheel with the joint motion of the machine tool: calculating posture changes in the workpiece coordinate system and calculating angular velocity and angular acceleration in the machine tool joint space. This allows for prediction of the machine tool's motion trend during the optimization stage, helping to avoid overspeeding or impact phenomena later on.

[0034] 4. Dynamic multi-objective optimization and memory mechanism.

[0035] Since the variable-parameter chip flute changes continuously along the axial cross-section, simply aggregating all cross-sections into a large-scale static optimization problem would result in excessively high dimensionality, slow convergence, and an inability to utilize the similarity between cross-sections. This invention decomposes the problem into a dynamic environment that "slides" along the axial direction, and allows DNSGA-II to complete the evolution using a memory mechanism: the memory stores representative Pareto solutions from the previous cross-section, serving as excellent initial solutions in the next cross-section, which helps maintain the continuity of solutions along the axial direction and the richness of the Pareto set.

[0036] 5. Seamlessly integrates with the five-axis post-processor.

[0037] The kinematic index model of this invention shares the same machine tool kinematic model as the formal five-axis post-processing. Therefore, the speed, acceleration, and other indices used in the optimization stage are highly consistent with the actual CNC system execution trajectory. The optimized grinding wheel pose sequence only requires time allocation and fine-tuning during post-processing, without significant modification to the geometric trajectory, thus ensuring the consistency of the design-optimization-machining closed loop.

[0038] 6. The project is highly feasible.

[0039] All calculations in this invention are based on explicit geometric and kinematic models, without introducing implicit parameters that are difficult to measure. Circular arc projection error, attitude smoothness, and machine tool kinematic performance indicators all have clearly defined calculation steps, making them suitable for integration into CAM software or machine tool host computers. For existing five-axis tool grinders, only a set of pre-processing and post-processing modules needs to be added to apply this invention to actual production. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart illustrating a variable-parameter chip groove grinding trajectory planning method that considers kinematic smoothness, as an example.

[0042] Figure 2 This is a schematic diagram of the coordinate system of the cutting tool, grinding wheel, and machine tool in an embodiment.

[0043] Figure 3 This is a schematic diagram of the grinding wheel attitude parameters for an example.

[0044] Figure 4 This is a schematic diagram illustrating the calculation of attitude smoothness and machine tool dynamics parameters in an example.

[0045] Figure 5 This is a schematic diagram of a dynamic multi-objective optimization framework for an example.

[0046] Figure 6 The simulation results of the grinding toolpath for the drum-shaped tool generated for the example are shown. Detailed Implementation

[0047] The method and apparatus of the present invention will be described in detail below through several embodiments. These embodiments can be combined with each other to constitute different technical solutions of the present invention without conflict.

[0048] like Figure 1 As shown in the figure, a variable parameter chip flute grinding trajectory planning method considering kinematic smoothness in this embodiment includes the following steps: S1. Establish the three-coordinate system and the unified parametric geometric model of the chip groove of the variable parameter milling cutter, which varies with the axial parameter, including the following steps: S11. Establishment of the coordinate system for the cutting tool, grinding wheel, and machine tool: like Figure 2 As shown, this invention uses three coordinate systems: 1). Tool coordinate system : It is fixed to the tool.

[0049] 2). Grinding wheel coordinate system : Changes with the attitude of the grinding wheel.

[0050] 3). Machine tool coordinate system : Fixed to the grinding machine bed, serving as the reference coordinate system for kinematic solutions.

[0051] The coordinate systems follow the following homogeneous transformation relationship:

[0052] In the formula: This is the transformation matrix from the machine tool coordinate system to the grinding wheel coordinate system; This is the transformation matrix from the machine tool coordinate system to the tool coordinate system; This is the transformation matrix from the tool coordinate system to the grinding wheel coordinate system.

[0053] homogeneous transformation adopts Matrix form:

[0054] in: It is a 3×3 rotation matrix; It is a 3×1 translation vector. General homogeneous transformation matrix (including rotation matrix) Translation vector ), yes Specific application forms.

[0055] This unified homogeneous transformation form facilitates subsequent geometric projection and kinematic calculations.

[0056] S12, B-spline function modeling of the outer contour.

[0057] Traditional cutting tool outlines are often described using simple linear functions or polynomials, such as:

[0058] Its expressive power is severely limited, making it unsuitable for complex variable-parameter cutting tools. This invention uses a p-order B-spline curve to express the outer contour radius of the cutting tool. :

[0059] in For p-order B-spline basis functions; Radius of the control point; Here, n represents the axial parameter of the tool; n is the number of control points (and the number of control points). Correspondingly, the node vector determines the locality of the curve; the number of control points can be flexibly set according to the complexity of the tool. The spline outer contour has local adjustability, overall smoothness and C2 continuity, which makes the tool outer contour smooth and improves grinding. It is suitable for taper, barrel, complex curvature and end transition regions, and can describe various nonlinear shapes, such as barrel and taper; its differentiability allows it to participate in Jacobian matrix calculation and normal vector solution.

[0060] S13, Expression for the outer contour of the revolving surface.

[0061] In the tool coordinate system In the middle, the outer contour of the tool is random. Changing surface of revolution :

[0062] in The axial position of the tool (from 0 to the tool length L); Circumferential angle By replacing the traditional linear outer contour with a spline outer contour, the tool geometry model becomes more realistic and designable.

[0063] S14, Blade Curve Modeling. In tooling, the cutting edge curve determines the cutting boundary and is one of the most critical geometric elements. The cutting edge curve is mainly determined by the following parameters: helix angle. Front corner Core thickness ,groove And add the curvature of the cutting edge With normal continuity constraint This improves the manufacturability of the blade's geometry.

[0064] The blade curve satisfies:

[0065] This formula is derived from the differential geometric relationship of the helical surface, and the slope of the tool's outer contour. With helix angle Together, they determine the axial / circumferential advance speed of the cutting edge. The larger the value, the steeper the cutting edge, the more complex the outer contour (larger the derivative change), and the more drastic the geometric change of the cutting edge. Therefore, the cutting edge modeling of this invention is fully applicable to the complex outer contour of variable parameter cutting tools.

[0066] S15, Core Thickness Rotation Surface Modeling.

[0067] Core thickness Also represented using B-spline:

[0068] For the core thickness B-spline function order basis functions, These are the control points for the core thickness B spline; Core thickness of the rotating surface:

[0069] Let be the spatial coordinate expression of the core-thickness rotating surface.

[0070] This allows for smooth core thickness variations to meet the design requirements of high-strength tools, with the ends constructed using independent spline segments to create a smooth transition and maintain overall continuity.

[0071] The core task of this step is to establish a unified geometric model that can accurately describe the outer contour, cutting edge curve, core thickness revolution surface, and slot width curve of a variable-parameter milling cutter. In one embodiment, a multi-control point spline curve (B-spline / NURBS) is used to establish the outer contour of the cutter, which has the following advantages: local adjustability: changes in a certain segment of the outer contour will not affect the whole; C2 continuity: conducive to ensuring grinding smoothness; strong geometric expression capability: can accurately describe complex shapes such as barrel shape, taper changes, and transition sections; can directly participate in matrix transformation, projection calculation, and error calculation.

[0072] S2. Based on the principle of circular arc envelope projection, establish a model for the equivalent machining error of groove width and the equivalent machining error of core thickness, including the following steps: S21. Coordinate transformation from the tool curve to the grinding wheel coordinate system.

[0073] Tool coordinate system Points in :

[0074] The three-dimensional coordinates of a point in the tool coordinate system; Transform to grinding wheel coordinate system :

[0075] The coordinates of a point in the tool coordinate system after transformation to the grinding wheel coordinate system. Determined by the machine tool kinematic chain (as in step S6).

[0076] This step ensures that all subsequent error calculations are performed on the cross-section of the grinding wheel.

[0077] S22, Polar coordinate projection.

[0078] Since the cross-section of the grinding wheel is in the (x, y) plane, it is easier to define the envelope error using polar coordinates.

[0079] Let be the polar radius of a point in the grinding wheel coordinate system; Let (x, y) be the coordinates of the point in the (x, y) plane of the grinding wheel coordinate system; (x, y) is the plane of the grinding wheel cross-section, and... The coordinates are represented on the same plane.

[0080] Therefore, the projection of the slot width curve is obtained. The core thickness is obtained by the envelope. .

[0081] S23. Calculation of circular arc envelope error.

[0082] The cross-sectional profile of the grinding wheel is as follows .

[0083] (1) Equivalent error of groove width :

[0084] in For the cross-sectional profile of the grinding wheel ,like Exceeding the sand outline If the groove width increases, the error is zero when the two are tangent.

[0085] (2) Core thickness equivalent error :

[0086] like If too much is ground away by the grinding wheel, the core thickness will be reduced, and the error will be optimal when tangent.

[0087] S24. Sensitivity of error to grinding wheel posture (optimization direction).

[0088] Grinding wheel attitude parameters :

[0089] in These are the three-dimensional position parameters of the grinding wheel relative to the cutting tool; For the grinding wheel tilt angle Partial derivative with respect to the error:

[0090] It reflects the impact of changes in the grinding wheel's attitude on the error and is used to guide the search direction of the optimization algorithm.

[0091] S25, Grinding wheel wear compensation model.

[0092] Grinding wheel wear This will reduce the cross-section of the grinding wheel:

[0093] It can dynamically compensate for error models, making planning more practical. To take into account the cross-sectional profile of the grinding wheel after wear.

[0094] Groove width error and core thickness error are two key indicators in chip groove grinding. This invention proposes an equivalent machining error model based on circular arc envelope projection. Compared with the traditional minimum distance method, this method has advantages such as high robustness, insensitivity to high curvature of the cross-section, immunity to local concave surface interference, and computational stability. Detailed derivation is given below.

[0095] S3. A smoothness measurement index model is established based on the composite smoothness principle of the geometric continuity of grinding wheel posture and the kinematic performance of machine tool.

[0096] Smoothness indicators include not only the continuity of the grinding wheel's posture on the tool surface, but also the smoothness of the machine tool's five-axis motion. For example... Figure 4 As shown, the present invention constructs the following multiple indicators: S31, Mapping of grinding wheel attitude vector to machine tool joint angle.

[0097] Grinding wheel attitude vector :

[0098] in The three-dimensional position parameters of the grinding wheel relative to the tool at the k-th cross-section; Let be the grinding wheel swing angle at the k-th cross section.

[0099] The machine tool axis position is determined using inverse kinematics:

[0100] in This refers to the position of the machine tool's linear axes (X, Y, Z axes); The angle of the machine tool's rotary axes (A and B axes).

[0101] S32, First-order attitude compliance (coherence):

[0102] This indicates the magnitude of attitude change between adjacent tool contacts.

[0103] Angle of attitude change :

[0104] In the formula This is the axial normal vector of the tool. The normal vector of the grinding wheel axis at the k-th cross-section; the first-order attitude change. and attitude change angle used for Prevent sudden changes in posture.

[0105] S33, Second-order attitude compliance (curvature continuity):

[0106] This is used to prevent sharp points in the attitude, which is key to ensuring a smooth trajectory transition. This represents the second-order attitude change.

[0107] S34. Machine tool dynamic smoothness indicators include: machine tool angular velocity :

[0108] This represents the time interval between adjacent sections.

[0109] angular acceleration :

[0110] Angular jerk (servo shock index) :

[0111] interpolation error Estimated based on the rate of change of the tool axis direction.

[0112] S35, the five-axis singularity avoidance index includes the five-axis Jacobian matrix. :

[0113] when "Time" implies approaching the singular. It is the smallest singular value of the matrix; For the k-th cross-section, the joint angle of the machine tool The corresponding Jacobian matrix.

[0114] This invention increases the attitude penalty weight, enabling the optimization algorithm to automatically avoid singular regions.

[0115] S4. Calculation error affecting grinding wheel attitude vector sensitivity This is used to guide subsequent optimization efforts.

[0116] As a specific implementation, based on the geometric error model, attitude compliance index, and machine tool kinematics index, a comprehensive multi-objective trajectory planning model with strong coupling characteristics, incorporating three types of objectives, is established. This model uses the grinding wheel pose parameters... The decision variables aim to simultaneously satisfy the following three optimization objectives: 1. Minimize geometric errors (groove width and core thickness).

[0117] 2. The grinding wheel posture has the best smoothness (continuity, second-order continuity).

[0118] 3. The machine tool has optimal kinematic performance (angular velocity, acceleration, interpolation error, etc.).

[0119] These three objectives are in obvious conflict, thus constituting a typical multi-objective optimization problem (MOP).

[0120] For example: Improving geometric accuracy usually requires frequent adjustments to the grinding wheel posture, which reduces smoothness; - Emphasizing smoothness may lead to increased geometric errors; Ensuring the smoothness of machine tool movement limits the range of attitude adjustment.

[0121] Therefore, this invention employs the Pareto optimality principle to automatically find a balance among the three objectives, such as... Figure 5 As shown, it includes the following steps: S41. Definition of decision variables.

[0122] Grinding wheel pose vector:

[0123] in: These are the positional parameters of the grinding wheel relative to the cutting tool. This refers to the tilt angle of the grinding wheel.

[0124] Set of decision variables:

[0125] For the first N The grinding wheel pose vector of each axial section.

[0126] S42, Geometric error objective function.

[0127] Geometric errors include slot width errors. With core thickness error .

[0128] This invention adopts a weighted quadratic sum form:

[0129] in To adaptively adjust based on tool geometry complexity, error weights are increased in complex regions (such as the end face or high curvature regions), and the quadratic sum can smoothly reflect the error magnitude, which is beneficial for optimizing the gradient judgment of the algorithm. The circular envelope error model originates from S2, therefore, It can accurately measure the machining geometry deviation caused by the grinding wheel posture. For the first Equivalent machining error of the groove width of each axial section; For the first Equivalent machining error of core thickness for each axial section; Let be the objective function for the geometric error of the chip groove parameters.

[0130] S43, Attitude compliance objective function.

[0131] Postural compliance is measured from a three-layer structure: 1. First-order attitude change; 2. Rate of change of attitude angle; 3. Second-order attitude continuity (prevention of cusps).

[0132] The definition is as follows:

[0133] in For attitude increment; The angle between the normal vectors of the grinding wheel and the target vectors changes. It is a second-order smooth term; Let the attitude compliance objective function be; , , These are the weighting coefficients for the first-order attitude change, the attitude angle change rate, and the second sister's attitude continuity, respectively.

[0134] The objective function of attitude smoothness is to ensure that the wheel attitude changes smoothly across the entire tool surface, avoid sharp points in five-axis interpolation, and guarantee continuous attitude curvature. This objective makes the grinding process stable and vibration-free.

[0135] S44, Objective function for machine tool dynamics performance.

[0136] The machine tool motion parameters obtained from step S3 are as follows: Five-axis angular velocity angular acceleration Interpolation error ; Therefore, the objective function is:

[0137] The objective function for the kinematic performance of the machine tool; , , These are the weighting coefficients for machine tool angular velocity, angular acceleration, and interpolation error, respectively.

[0138] This can prevent the machine tool from rotating rapidly; This can prevent the servo system from being impacted; To ensure stable interpolation trajectory error, this objective is to ensure that the CNC machine tool can smoothly execute the planned trajectory.

[0139] S45. Constraints. The trajectory planning model must satisfy the following constraints: 1. Travel constraints:

[0140] The same applies to the A / B axes.

[0141] These are the travel limits of the X, Y, and Z axes of the machine tool; 2. Speed ​​Constraints:

[0142] This refers to the maximum angular velocity of the machine tool axis; 3. Acceleration constraints:

[0143] This is the maximum angular acceleration of the machine tool axis; 4. Grinding wheel-tool interference avoidance constraint: circular envelope error , Do not exceed the safety threshold.

[0144] 5. Collision detection constraints, including grinding wheels, tool holders, tool shanks, and machine tool structural components.

[0145] S5. Discretize the milling cutter groove into multiple sections along the axial direction, and construct the above multi-objective programming model into a dynamic multi-objective optimization problem that varies with the cross sections. Solve the problem using DNSGA-II + Memory.

[0146] The variable-parameter tool continuously changes along the axial parameter u, resulting in different trajectory planning problems for each cross-section. Therefore, this invention proposes a dynamic multi-objective optimization method based on cross-section dynamic evolution and historical solution inheritance to ensure that the solution space transitions smoothly with the change of u, the solution set does not jump, and the entire grinding wheel posture sequence is continuous and smooth. This method includes the following steps: S51. Construction of a Dynamic Optimization Environment Tool axial parameters u As an environment variable:

[0147] This corresponds to the k-th cross section. Let be the axial parameter of the tool at the k-th cross section; The total number of axially discrete cross sections, each It has an independent geometric model, so each cross section corresponds to different: slot width error surface, core thickness error surface, attitude compliance evaluation, and machine tool kinematics evaluation. Its optimization environment changes dynamically with k.

[0148] S52. Define the environmental difference measurement index ΔE:

[0149] The environmental differences between the k-th and k+1-th sections are known; Let G(u) be the geometric parameters of the k-th cross section. G(u) includes the outer contour r1(u), helix angle β(u), core thickness c(u), and groove width w(u). If ΔE is large, it indicates a sudden change in the cross section, requiring enhanced solution inheritance. If ΔE is small, the inheritance ratio can be reduced, enhancing the local search capability.

[0150] S53, Historical Solution Inheritance Mechanism The Pareto optimal solution set of the previous section is The initial population of the current section is composed of several individuals selected from the representative Pareto solution most similar to the current environment and based on the inheritance ratio calculated based on ΔE, as expressed by the formula:

[0151] M represents the number of individuals inherited from the historical solution; A historical solution selection function based on the environmental difference index; A function to randomly initialize individuals (generating NM new individuals). in This is the Pareto optimal solution set for the previous section, avoiding the optimization of the (k+1)th section from starting "from zero" again, improving the convergence speed, and ensuring the continuity of the grinding wheel pose across sections.

[0152] S54, Two-tier database management, including: 1. Global solution library G-Archive stores representative Pareto solutions across cross sections for long-term continuity maintenance.

[0153] 2. Local solution library L-Archive stores the optimal solution for the current cross section for short-term evolution.

[0154] S55, a general-purpose, scalable, and optimized framework.

[0155] This invention does not limit the optimization algorithm; it can employ parallel optimization algorithms such as Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), and Multi-Population Evolutionary Algorithm (MPEA). The algorithm only needs to satisfy the following requirements: it can handle multi-objective problems, it can inherit solutions to the next cross-section, and it allows for adjustable encoding strategies.

[0156] S6. The obtained Pareto solution set of the grinding wheel pose is converted into a machine tool five-axis interpolation trajectory and CNC program through five-axis kinematic post-processing, including the following steps: S61, Solving the inverse kinematics of the machine tool.

[0157] Once the optimized grinding wheel pose sequence is selected The grinding wheel pose corresponding to each cross section can be converted into the five-axis joint variables of the machine tool using the inverse kinematics model of a five-axis machine tool. The specific steps are as follows: Using inverse kinematics model This yields the joint angles of the machine tool; pose for each cross section Calculate the corresponding five-axis positions and angles. This ensures the consistency of the kinematic model.

[0158] S62, Interpolation and Time Parameterization.

[0159] Based on the obtained five-axis joint angles Standard time parameterization methods, such as S-curve interpolation or spline interpolation, are used to convert joint trajectories into machine tool execution trajectories.

[0160] Calculate the time parameters for each cross section And smoothly transition the motion between each section; Control the feed rate and acceleration to ensure that the machine tool does not exceed the limits of its servo system during operation.

[0161] S63, CNC program generation.

[0162] The obtained five-axis interpolation trajectory is converted into G-code to generate the CNC program for the machine tool. The generated G-code contains motion commands for each axis of the machine tool, feed rate commands, and other auxiliary commands (such as coolant switch, spindle speed control, etc.).

[0163] Figure 6 (a) is the chip groove model of the two-edged drum-shaped cutter and related components of the CNC grinding machine simulated by the CNC grinding machine simulation platform built by the domestic software ZW3D; (b) is the simulation model of the chip groove of the two-edged drum-shaped cutter exported after the simulation is completed, in the format of stl; (c) is the cross-sectional view of the chip groove obtained by cutting a plane perpendicular to the tool axis at a distance of 5mm from the end section of the two-edged drum-shaped cutter and the measurement results of related parameters; (d) is the cross-sectional view of the chip groove obtained by cutting a plane perpendicular to the tool axis at a distance of 10mm from the end section of the two-edged drum-shaped cutter and the measurement results of related parameters.

[0164] The above describes the complete embodiments and technical solutions of the present invention. In practical applications, the parameters of the algorithm can be appropriately adjusted according to different tool geometry parameters, process requirements, and machine tool performance to optimize the machining effect.

[0165] The preferred embodiments of this invention are merely illustrative of the invention. They do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the invention, enabling those skilled in the art to better understand and utilize it.

Claims

1. A method for planning the grinding trajectory of a chip flute considering kinematic smoothness, characterized in that, Includes the following steps: S1. Establish the three-coordinate system of the chip groove of the variable parameter milling cutter and the unified parameterized geometric model that varies with the axial parameter; S2. Based on the principle of circular arc envelope projection, establish a model of equivalent machining error for groove width and equivalent machining error for core thickness; S3. Establish a smoothness measurement index model based on the composite smoothness principle of grinding wheel attitude geometric continuity and machine tool kinematic performance; S4. Construct a multi-objective trajectory planning model with geometric error, attitude compliance error and machine tool kinematic performance error as objectives; S5. Discretize the milling cutter groove into multiple sections along the axial direction, construct the above multi-objective programming model into a multi-objective optimization problem that dynamically evolves along the axial section, and solve it according to the dynamic optimization principle to obtain the Pareto optimal solution set of continuous grinding wheel pose; S6. Perform five-axis post-processing on the optimal grinding wheel pose sequence and generate machine tool trajectory and CNC program that meet machining constraints.

2. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S1 includes: S11. Establish the tool coordinate system, grinding wheel coordinate system, and machine tool fixed coordinate system; S12. Define the outer contour radius of the tool using a p-order spline function: in The outer radius of the tool. For p-order B-spline basis functions; Radius of the control point; is the tool axial parameter; n is the number of control points; S13, Generate a surface of revolution from the outer contour. Represented as: in Circumferential angle; S14. The cutting edge curve is determined by the helix angle, rake angle, core thickness, and groove, and the cutting edge curvature and normal continuity constraints are added to improve the geometric manufacturability of the cutting edge shape. S15. The tip of the blade is constructed using independent spline segments to create a smooth transition in order to maintain overall continuity.

3. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S2 includes: S21. Map the groove width curve and the core thickness rotation surface to the grinding wheel coordinate system through homogeneous coordinate transformation; S22. Obtain the equivalent projection of the groove width and the upper envelope of the core thickness by using circular arc envelope projection in the plane of the grinding wheel section. S23. Define the groove width and core thickness error by the maximum interference between the projection curve and the cross-sectional profile of the grinding wheel. S24. Calculate the sensitivity of the error to the grinding wheel attitude vector, which is used for subsequent optimization of direction guidance; S25. Dynamic error correction is performed using grinding wheel wear as a compensation variable. S26. Automatically adjust the projection resolution based on the local curvature to improve the accuracy of error resolution.

4. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S3 includes: S31. Calculate joint angles, angular velocities, angular accelerations, and angular jerkes using the forward and inverse kinematics of a five-axis machine tool. S32. Construct a system including first-order attitude smoothness, grinding wheel axial unit vector attitude change angle, and second-order attitude continuity term. Attitude geometric compliance index; S33. Construct machine tool dynamic smoothness indicators, including servo torque change rate, joint dynamic load change, flexible vibration sensitivity and nonlinear interpolation error; S34, based on A five-axis singularity avoidance index is constructed by axis coupling, and the attitude continuity constraint weight is increased to automatically avoid singular points when the index approaches the singular region.

5. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S4 includes: S41. Define decision variables: The grinding wheel pose sequence is the decision variable; S42. The geometric error target adopts a dynamic weighting mechanism that automatically adjusts with the axial direction: in For error weights, For the first Equivalent machining error of the groove width of each axial section; For the first Equivalent machining error of core thickness for each axial section; The objective function for the geometric error of the chip groove parameters; Indicates the serial number of the axial discrete section; S43, Attitude compliance targets include , and attitude curvature smoothing term: in For attitude increment; The angle between the normal vectors of the grinding wheel and the target vectors changes. It is a second-order smooth term; Let the attitude compliance objective function be; , , These are the weighting coefficients for the first-order attitude change, the rate of change of attitude angle, and the second sister's attitude continuity, respectively. The grinding wheel pose vector for the k-th cross-section S44. Machine tool kinematic performance targets are based on axis velocity, acceleration, and acceleration and interpolation error. : in The objective function for the kinematic performance of the machine tool; , , These are the weighting coefficients for machine tool angular velocity, angular acceleration, and interpolation error, respectively. S45. Construct machine tool travel, speed, acceleration limits, machining accessibility constraints, and multi-body collision avoidance constraints.

6. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S5 includes: (1) Discretize the tool axis into multiple optimized sections, and each section constitutes an optimized environment that dynamically evolves with geometric changes; (2) An environmental difference measurement index is constructed based on parameters such as outer contour, helix angle, core thickness, and groove width to characterize the cross-sectional variation range; (3) Solve for the local Pareto solution set for section k; (4) In section k+1, the representative solution with the highest similarity in the previous section is inherited, and the continuity and diversity are maintained by combining drift detection, two-layer solution library management and variable partitioning inheritance mechanism.

7. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 6, characterized in that, The optimization methods include genetic algorithms, differential evolution, particle swarm optimization, co-evolution, and multi-population parallel optimization methods.

8. The method for planning the grinding trajectory of a variable-parameter chip flute considering kinematic smoothness according to claim 1, characterized in that, Step S6 includes: S61. Perform inverse kinematics solution on the grinding wheel pose sequence and re-decompose the pose based on the singularity index to avoid the A / B axis singularity region. S62. Perform interpolation error detection and repair to avoid interpolation discontinuities caused by sudden attitude changes; S63. Perform multi-body collision detection of tool-grinding wheel-machine tool components and avoid collisions by attitude adjustment or degree of freedom redistribution; S64. Based on the machine tool travel, axial load and speed characteristics, perform redundancy optimization and load balancing on the A / B axis posture to generate an executable machining program.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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