A method and system for speed planning of multi-axis linkage CNC machining based on sequential linear programming

Abstract

This invention belongs to the field of CNC machining technology, specifically a multi-axis linkage CNC machining speed planning method and system based on sequential linear programming. Taking the minimization of machining time as the objective function, a kinematic constraint model is established based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis. This kinematic constraint model is transformed into N discrete points, and the objective function is linearized by approximating it with a continuous linear function, resulting in a discrete kinematic constraint model. Cubic uniform B-splines are used to establish the velocity along the interpolation guide stroke at the discrete points and the relationship between the interpolation guide stroke and the control points. The relationship between the acceleration and pseudo-shortness along the stroke and the control points is derived. Using the spline control points as independent variables, the linearization of each constraint is achieved. Then, the interpolation guide stroke velocity at each discrete point is obtained through iterative solution. This invention combines high machining efficiency with high computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of CNC machining technology, specifically relating to a multi-axis linkage CNC machining speed planning method and system based on sequential linear programming. Background Technology

[0002] Multi-axis CNC machining technology, with its high flexibility and adaptability in tool attitude control, has become a key manufacturing method for complex free-form surface parts in fields such as aerospace and energy equipment. In multi-axis CNC machining, feed rate planning is the core link connecting the tool geometry path and machine tool physical execution. Its core task is to generate a feed rate curve that maximizes machining efficiency while strictly adhering to multiple constraints constituted by machine tool dynamics and machining processes. However, due to the complexity of the high-order kinematics of multi-axis CNC machine tools, generating a time-optimal feed rate curve that satisfies both machine tool drive constraints and process constraints still faces significant challenges.

[0003] Existing research on this problem can be broadly categorized into two types: model-based methods and optimization-based methods. The main characteristic of model-based methods is the pre-designed acceleration / deceleration curve model, which considers geometric and kinematic constraints. Common acceleration / deceleration curve models include trapezoidal and S-shaped representations. Based on these models, research has implemented higher-order feed rate scheduling and axial drive constraints. However, these methods can only achieve higher-order kinematic constraints in certain locations, exhibiting inherent limitations in time optimization. When dealing with complex toolpaths, the pre-designed feed rate curve struggles to flexibly adapt to rapid changes in kinematic states, thus limiting the improvement of machining efficiency.

[0004] Optimization-based methods involve formulating the feed rate scheduling problem into an optimization problem, considering process constraints and driving constraints, constructing an objective function that minimizes processing time, and employing certain strategies to solve it. The main difficulty of these methods lies in certain nonlinear constraints, such as speed constraints. Some studies have proposed transforming the nonlinear optimization problem into a linear one, but this linearization process sacrifices some feasible space, limiting the optimality of the solution. Furthermore, most current research simply approximates the objective function in this optimization problem as a discrete sum of squares, which can easily lead to local abnormal speed drops and low processing efficiency. Other studies employ intelligent algorithms to handle complex nonlinear optimization problems. These methods have the potential to find solutions close to the global optimum, but they have limitations in terms of solution efficiency.

[0005] Therefore, it is necessary to provide an improved method for speed planning in multi-axis linkage CNC machining to solve the above problems. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-axis linkage CNC machining speed planning method and system based on sequential linear programming, which solves the problem that existing speed planning methods are difficult to achieve both high machining efficiency and high computational efficiency while satisfying machine tool drive constraints and process constraints.

[0007] To achieve the above objectives, the first aspect of the present invention provides a method for speed planning of multi-axis linkage CNC machining based on sequential linear programming, comprising the following steps: S1, establish the high-order spline relationship between the position of each motion axis of the machine tool and the interpolation guide stroke; S2, establish the relationship between the motion characteristic parameters of each motion axis and the motion characteristic parameters along the interpolation guide stroke and the higher-order spline; wherein, the motion characteristic parameters include velocity, acceleration and agility; S3, with the goal of minimizing processing time, a kinematic constraint model is established based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis; wherein, the process constraints include the speed, acceleration, and agility constraints of the interpolation guide stroke, and the kinematic constraints include the speed, acceleration, and agility constraints of each motion axis; S4, the kinematic constraint model is transformed into N discrete points, and the objective function is approximated by a continuous linear function to linearize the objective function. Combined with the objective function approximation constraint, the discrete kinematic constraint model is obtained. S5. Using cubic uniform B-splines, establish the velocity along the interpolation guide stroke at discrete points and the relationship between the interpolation guide stroke and the control point, and further derive the relationship between the acceleration along the interpolation guide stroke, the pseudo-shortness along the interpolation guide stroke, and the control point. S6. Based on the relationship between the control points obtained in step S5, and using the spline control points as independent variables, linearize the approximate constraints of the objective function, the velocity and acceleration constraints of the interpolated guide stroke, and the velocity and acceleration constraints of the motion axis in the discretized kinematic constraint model. S7, through Taylor expansion, linearizes the agility constraints of the interpolation guide stroke and the agility constraints of the motion axis, and obtains a linearized kinematic constraint model; S8. The linearized kinematic constraint model is iteratively solved using a sequential linear programming method until the convergence condition is met, and finally the interpolation guide stroke speed of each discrete point is obtained.

[0008] Furthermore, in step S1, the establishment of the higher-order spline relationship includes: obtaining n two-dimensional spaces with the positions Q of the n motion axes as the vertical axis and the interpolation guide stroke S as the horizontal axis; in the n two-dimensional spaces, interpolating the discrete interpolation guide stroke and the position points of each motion axis to obtain the QS curve of each motion axis; and performing first, second, and third derivatives on the QS curve to obtain the first derivative of the position of each motion axis relative to the interpolation guide stroke. Second derivative and third derivative The expression is as follows: .

[0009] Furthermore, in step S2, based on the derivative relationship of each motion axis relative to the interpolation guide stroke, the relationship between the velocity, acceleration, and agility of each motion axis and the velocity, acceleration, and agility of the interpolation guide path is established, as shown below:

[0010] in, , , These are the velocity, acceleration, and speed of the motion axis in the machine tool coordinate system, respectively. , , These are the speed, acceleration, and agility of the interpolation guide stroke, respectively. Define the ratio of interpolation guide path shortcut to speed as pseudo-shortcut, and convert the motion axis shortcut to:

[0011] in This is a pseudo-shortcut.

[0012] Furthermore, in step S3, the kinematic constraint model is as follows:

[0013] Where T is the processing time. The value at the end of the journey. The maximum value of the square of the process speed. This represents the maximum process acceleration. This represents the maximum process speed. The maximum value of the square of the single-axis velocity. This represents the maximum value of single-axis acceleration. This represents the maximum single-axis agility.

[0014] Furthermore, in step S4, linearizing the objective function specifically includes: Take the interpolation guide stroke S Equally spaced points As discrete points, Quantity at the point Simplified representation as Then, the processing time under the discretization parameters is approximately as follows:

[0015] in, These are the values ​​of equal spacing between discrete points; use A linear function, approximately a nonlinear function To obtain an approximate function The expression is as follows:

[0016] in, For a given piecewise linear function, the points of discontinuity are given. The objective function, after being approximated by processing time, is expressed as follows: .

[0017] Furthermore, by adding the objective function approximation constraint to the kinematic constraint model, the discrete kinematic constraint model is obtained as follows: .

[0018] Furthermore, step S5 specifically includes: S51, using cubic uniform B-spline interpolation, the interpolation guide stroke at discrete point i is represented by control points. and the square of the travel speed As shown below:

[0019] in, For travel control points; The control point is the square of the stroke speed; S52, combining the boundary conditions of cubic uniform B-spline interpolation, solves for all travel control points using a linear matrix. ; S53. Based on the interpolation characteristics of cubic uniform B-spline, the first and second derivatives of the interpolation guide stroke with respect to the spline parameters at each discrete point are obtained. S54, derives the square of the stroke speed on the interpolation guide stroke. acceleration Pseudo-shortcut The relationship between the two factors is then established; substituting the first and second derivatives from step S53, the interpolated guided stroke acceleration and pseudo-shortness at discrete points are transformed into expressions using control points, as shown below:

[0020] in, , These represent the first and second derivatives of the interpolation guide stroke with respect to the spline parameters, respectively. S55, the square of the travel speed at discrete point i. acceleration Pseudo-shortcut Write it in the following uniform format:

[0021] in, , , , All are constant horizontal quantities of length N+2.

[0022] Furthermore, in step S7, the speed of the interpolation guide stroke is... And the agility of the motion axis As about A multivariate function at a point By finding its first-order Taylor expansion, we obtain the agility constraints of the interpolation guide stroke and the agility constraints of the motion axis. This is a linearized expression of the independent variable.

[0023] Furthermore, in step S8, the iterative solution includes: S81, in the discrete nonlinear kinematic constraint model of step S3, the maximum value is constrained by the process speed. Nonlinear quantities of the speed constraint in the alternative model This yields an over-constrained linear programming model; solving this linear programming model yields the initial feasible solution for the over-constraints. ; S82, according to Calculate each discrete point Further calculate the linearization coefficients of the process agility constraints and motion axis agility constraints in the linear programming sub-model, thus obtaining the linear programming sub-model. S83, Solve this linear programming sub-model to obtain its optimal solution. ;if and If the difference is less than a set threshold, then That is, the optimal solution to the sequential linear programming problem; otherwise, let Reconstruct and solve the linear programming problem iteratively; S84 will provide the final optimal solution. Substituting the values ​​into the calculation, we obtain the interpolation-guided stroke speed planning for the isolation point i with the minimum processing time. .

[0024] A second aspect of the present invention provides a multi-axis linkage CNC machining speed planning system based on sequential linear programming, comprising: The high-order spline relation establishment module is used to establish the high-order spline relation of the position relative interpolation guide stroke of each motion axis of the machine tool; The motion characteristic parameter relationship establishment module is used to establish the relationship between the motion characteristic parameters of each motion axis and the motion characteristic parameters along the interpolation guide stroke and the higher-order splines; wherein, the motion characteristic parameters include velocity, acceleration and agility; The kinematic constraint model building module is used to build a kinematic constraint model based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis, with the objective function of minimizing the processing time; wherein, the process constraints include the speed, acceleration, and agility constraints of the interpolation guide stroke, and the kinematic constraints include the speed, acceleration, and agility constraints of each motion axis; The discrete module is used to transform the kinematic constraint model into N discrete points and approximate the objective function using a continuous linear function to linearize the objective function. Combined with the objective function approximation constraint, the discrete kinematic constraint model is obtained. The control point relationship establishment module is used to establish the velocity along the interpolation guide stroke at discrete points and the relationship between the interpolation guide stroke and the control points using cubic uniform B-splines, and further derives the relationship between the acceleration along the interpolation guide stroke and the pseudo-shortness along the interpolation guide stroke and the control points. The linearization module is used to linearize the approximate constraints of the objective function, the velocity and acceleration constraints of the interpolated guide stroke, and the velocity and acceleration constraints of the motion axis in the discretized kinematic constraint model based on the relationships between the obtained control points and with spline control points as independent variables; the linearization of the agility constraints of the interpolated guide stroke and the agility constraints of the motion axis is achieved through Taylor expansion, resulting in a linearized kinematic constraint model. The iterative solution module is used to iteratively solve the linearized kinematic constraint model using a sequential linear programming method until the convergence condition is met, and finally obtain the interpolated guide stroke speed at each discrete point.

[0025] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. The multi-axis linkage speed planning method used in this invention constructs a unified speed planning kinematic constraint model, and collaboratively optimizes and solves process parameter constraints and machine tool axis performance constraints, effectively avoiding the defect of traditional planning methods where process requirements and equipment capabilities are disconnected. The model considers speed constraints, which can significantly reduce vibration and impact during processing and improve processing quality.

[0026] 2. The multi-axis linkage speed planning method used in this invention employs an optimization-based approach, which fully utilizes the physical properties of the machine tool axes. The final planning result satisfies the "Bang-Bang" characteristic, resulting in high machining efficiency. During the planning process, by approximating the objective function, the abnormal speed reduction problem that is prone to occur in other speed planning methods is avoided, further improving machining efficiency.

[0027] 3. This invention reduces the number of independent variables in the optimization model by establishing the relationship between the control points of cubic uniform B-splines and the interpolation speed, acceleration, and pseudo-shortness of discrete points. At the same time, it makes full use of the locality characteristics of cubic uniform B-splines, simplifies the linear constraint matrix, and significantly reduces the complexity of solving linear programming problems, thus achieving high computational efficiency.

[0028] 4. The multi-axis linkage speed planning method used in this invention simplifies the originally complex nonlinear optimization problem into an iteration of linear programming subproblems through Taylor expansion and sequential linear programming. This improves computational efficiency while ensuring that the final result is as close as possible to the theoretical optimal solution.

[0029] 5. The multi-axis linkage speed planning method used in this invention has universality and can theoretically be applied to any multi-axis collaborative machining CNC machine tool. The method has strong scalability and strong engineering applicability. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the steps of the multi-axis linkage speed planning method based on sequential linear programming in an embodiment of the present invention; Figure 2 This is a schematic diagram of the relationship between shaft position Q and interpolation stroke S in an embodiment of the present invention; Figure 3 This is a schematic diagram of the approximation of the objective function by multiple continuous linear functions in an embodiment of the present invention; Figure 4 This is a schematic diagram of the process of solving the problem using the sequential linear programming algorithm in an embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0032] Example 1 Please see Figure 1 A multi-axis linkage CNC machining speed planning method based on sequential linear programming is described in detail below: S1: Establish the high-order spline relationship between each motion axis and the interpolation guide path, including its first, second and third derivatives.

[0033] In multi-axis motion planning, the key motion trajectory that determines the actual machining effect is typically defined as the interpolation guide path. The specific form of this path varies depending on the machining scenario. For example, in five-axis machining, the motion trajectory of the tool tip is usually used as the interpolation guide path; while in winding machining, the rotation axis of the mandrel is often used. During actual machining, each motion axis must follow this guide path for coordinated interpolation motion. The interpolation stroke refers to the curve length from the current position to the starting point of the path on the interpolation guide path.

[0034] Assuming there are n motion axes, with the interpolation guide stroke S as the horizontal axis and the positions Q of the n motion axes as the vertical axes, we obtain n two-dimensional spaces.

[0035] In n two-dimensional spaces, the QS curves of each motion axis are obtained by interpolating the discrete interpolation guide stroke and the position points of each motion axis, as follows: Figure 2 As shown, the relationship is:

[0036] The first derivative is obtained by taking the first derivative of the QS curve, the second derivative is obtained by taking the second derivative of the QS curve, and the third derivative is obtained by taking the third derivative of the QS curve, which can be expressed as follows:

[0037] S2: Establish the relationship between the velocity, acceleration, and speed of each motion axis and the velocity, acceleration, speed, and position-stroke high-order splines along the interpolation guide stroke.

[0038] Based on the derivative relationships of each motion axis relative to the interpolation guide path, the relationships between the velocity, acceleration, and agility of each motion axis and the velocity, acceleration, and agility of the interpolation guide path can be established as follows:

[0039] in , , These represent the velocity, acceleration, and speed of each motion axis in the machine tool coordinate system. , , Positions of each motion axis Relative to interpolation guide stroke The first, second, and third derivatives; , , These are the speed, acceleration, and slack of the interpolation guide stroke, respectively.

[0040] If we define the ratio of interpolation guide path agility to speed as pseudo-agility, then motion axis agility can be expressed as follows:

[0041] in This is called pseudo-shortness, where different axes of motion have different first, second, and third derivatives, which ultimately result in different calculated velocities, accelerations, and speeds of motion.

[0042] S3: With the optimization objective of optimal processing time, a kinematic constraint model is established based on the speed, acceleration, and agility limits of the process interpolation guide stroke, as well as the speed, acceleration, and agility limits of each motion axis.

[0043] The goal of time-optimal speed planning is to minimize processing time. The formula for calculating time is as follows:

[0044] in, This is the value at the end of the journey, i.e., the total journey length.

[0045] Considering process constraints, the speed, acceleration, and agility of the interpolation guide stroke cannot exceed given boundaries, namely:

[0046] Considering the kinematic constraints of each motion axis of the machine tool, the speed, acceleration, and speed of each motion axis cannot exceed the given boundaries, that is:

[0047] The above formulas are the general kinematic constraints for each motion axis. For example, when the number of motion axes n=5, there are five sets of the above kinematic constraint formulas.

[0048] In summary, the velocity planning kinematic constraint model used in this invention can be expressed as follows:

[0049] in, The maximum value of the square of the process speed. This represents the maximum process acceleration. This represents the maximum process speed. The maximum value of the square of the single-axis velocity. This represents the maximum value of single-axis acceleration. This represents the maximum single-axis agility.

[0050] S4: Discretize the above optimization model into a finite-dimensional problem and approximate the objective function to achieve linearization of the objective function.

[0051] Take throughout the entire journey Equally spaced points As discrete points. And for ease of representation, Quantity at the point Simplified representation as The processing time under the discretization parameters can then be approximated as follows:

[0052] in These are the values ​​for the equal spacing between discrete points.

[0053] The objective function is nonlinear, which poses challenges to optimization. Therefore, this invention proposes a method to linearize the objective function by approximating it with a continuous linear function. Figure 3 As shown, using A linear function, approximately a nonlinear function An approximate function can be obtained. The expression is as follows:

[0054] in Let be the points of discontinuity of a given piecewise linear function.

[0055] Therefore, the processing time of the objective function can be approximated as follows:

[0056] In summary, the discretized kinematic constraint model can be represented as follows:

[0057] S5: Establish the relationship between the velocity along the stroke and the interpolated guided stroke and the control point using cubic uniform B-splines, and further derive the relationship between the acceleration along the stroke and the pseudo-shortness along the stroke and the control point.

[0058] Note that in the above constraint model, the independent variable is Furthermore, since the relationship between travel speed, acceleration, and pseudo-shortness was not established, this step establishes a cubic uniform B-spline relationship to realize the relationship between travel speed, acceleration, and pseudo-shortness, and reduces the number of independent variables.

[0059] Using cubic uniform B-spline interpolation, the travel distance at discrete points is represented by control points. and the square of the travel speed as follows:

[0060] in For travel control points; The control point is the square of the travel speed.

[0061] The boundary conditions for supplementing the cubic uniform B-spline interpolation of the travel spline are as follows:

[0062] All travel control points can be solved using the following linear matrix, taking into account boundary conditions. : .

[0063] Based on the interpolation properties of cubic uniform B-spline, the first and second derivatives of the stroke at each discrete point with respect to the spline parameters can be obtained as follows:

[0064] The square of the stroke speed can be derived from the interpolation guide stroke. acceleration Pseudo-shortcut The relationships exist as follows:

[0065] Substituting the values, we can obtain the discrete point travel acceleration and pseudo-shortness, which can be represented by control points as follows:

[0066] set up Obviously, the travel speed at discrete points acceleration Pseudo-shortcut All about A linear function. Using As the independent variable, the number of independent variables starts from... Reduce to This reduces the size of the optimization problem. The square of the travel speed at discrete points... acceleration Pseudo-shortcut Write it in the following uniform format:

[0067] in , , All are constant horizontal quantities of length N+2.

[0068] S6: Based on the above relationships, control points are obtained using the squared spline of the travel speed. The independent variable is used to linearize the objective function approximation constraints, process speed constraints, process acceleration constraints, motion axis speed constraints, and motion axis acceleration constraints in the discrete optimization model.

[0069] The objective function approximation conditions and constraints are as follows: The independent variable is represented as follows:

[0070] Discrete point process speed and acceleration constraints The independent variable is represented as follows:

[0071] Discrete point motion axis velocity and acceleration constraints The independent variable is represented as follows:

[0072] S7: By using Taylor expansion, the process speed constraints and motion axis speed constraints are linearized, transforming the original nonlinear optimization problem into a linear programming subproblem.

[0073] The formulas for discrete point process agility and motion axis agility are as follows:

[0074] To linearize these two functions, a first-order Taylor expansion is needed. However, directly using... Finding the first-order Taylor expansion for the independent variable would result in an overly complex expression. Here we will... and As about multivariable functions, due to All are about A linear function, based on Perform first-order Taylor expansion and based on The result of performing a first-order Taylor expansion is the same. At the point... Finding its first-order Taylor expansion, we get:

[0075] in .

[0076] Then process speed constraints and motion axis speed constraints, in order to The linearized expression for the independent variable is as follows: .

[0077] In summary, after using the following... After reconstructing the independent variables and linearizing the constraints, the kinematic constraint model for time-optimal velocity programming is as follows: .

[0078] S8. The linear programming subproblem is solved iteratively using the sequential linear programming method until the convergence condition is met.

[0079] The solution process for sequential linear programming is as follows: Figure 4 As shown, the solution process starts from a feasible initial solution. Initially, this invention provides a feasible method for obtaining the initial solution, namely, constraining the maximum value using process speed in the original discrete nonlinear model. Nonlinear quantities of the speed constraint in the alternative model We can obtain an over-constrained linear programming model as follows:

[0080] in, .

[0081] Solving this linear programming model directly yields an over-constrained initial feasible solution. ; Obtain an initial feasible solution After that, it can be based on Calculate each discrete point Furthermore, the linearization coefficients of the process agility constraints and motion axis agility constraints in the linear programming sub-model can be calculated. This involves obtaining a linear programming sub-model, solving the linear programming subproblem, and obtaining its optimal solution. ;if and If the difference is less than a set threshold, then That is, the optimal solution to the sequential linear programming problem; otherwise, let The linear programming problem is reconstructed and solved iteratively.

[0082] The final optimal solution By substituting the values ​​into the calculation, we can obtain the isolation point speed planning method that minimizes the processing time. .

[0083] Example 2 A multi-axis linkage CNC machining speed planning system based on sequential linear programming includes: The high-order spline relation establishment module is used to establish the high-order spline relation of the position relative interpolation guide stroke of each motion axis of the machine tool; The motion characteristic parameter relationship establishment module is used to establish the relationship between the motion characteristic parameters of each motion axis and the motion characteristic parameters along the interpolation guide stroke and the higher-order splines; wherein, the motion characteristic parameters include velocity, acceleration and agility; The kinematic constraint model building module is used to build a kinematic constraint model based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis, with the objective function of minimizing the processing time; wherein, the process constraints include the speed, acceleration, and agility constraints of the interpolation guide stroke, and the kinematic constraints include the speed, acceleration, and agility constraints of each motion axis; The discrete module is used to transform the kinematic constraint model into N discrete points and approximate the objective function using a continuous linear function to linearize the objective function. Combined with the objective function approximation constraint, the discrete kinematic constraint model is obtained. The control point relationship establishment module is used to establish the velocity along the interpolation guide stroke at discrete points and the relationship between the interpolation guide stroke and the control points using cubic uniform B-splines, and further derives the relationship between the acceleration along the interpolation guide stroke and the pseudo-shortness along the interpolation guide stroke and the control points. The linearization module is used to linearize the approximate constraints of the objective function, the velocity and acceleration constraints of the interpolated guide stroke, and the velocity and acceleration constraints of the motion axis in the discretized kinematic constraint model based on the relationships between the obtained control points and with spline control points as independent variables; the linearization of the agility constraints of the interpolated guide stroke and the agility constraints of the motion axis is achieved through Taylor expansion, resulting in a linearized kinematic constraint model. The iterative solution module is used to iteratively solve the linearized kinematic constraint model using a sequential linear programming method until the convergence condition is met, and finally obtain the interpolated guide stroke speed at each discrete point.

[0084] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for speed planning in multi-axis linkage CNC machining based on sequential linear programming, characterized in that, Includes the following steps: S1, establish the high-order spline relationship between the position of each motion axis of the machine tool and the interpolation guide stroke; S2, establish the relationship between the motion characteristic parameters of each motion axis and the motion characteristic parameters along the interpolation guide stroke and the higher-order spline; wherein, the motion characteristic parameters include velocity, acceleration and agility; S3, with the goal of minimizing processing time, a kinematic constraint model is established based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis; wherein, the process constraints include the speed, acceleration, and agility constraints of the interpolation guide stroke, and the kinematic constraints include the speed, acceleration, and agility constraints of each motion axis; S4, the kinematic constraint model is transformed into N discrete points, and the objective function is approximated by a continuous linear function to linearize the objective function. Combined with the objective function approximation constraint, the discrete kinematic constraint model is obtained. S5. Using cubic uniform B-splines, establish the velocity along the interpolation guide stroke at discrete points and the relationship between the interpolation guide stroke and the control point, and further derive the relationship between the acceleration along the interpolation guide stroke, the pseudo-shortness along the interpolation guide stroke, and the control point. S6. Based on the relationship between the control points obtained in step S5, and using the spline control points as independent variables, linearize the approximate constraints of the objective function, the velocity and acceleration constraints of the interpolated guide stroke, and the velocity and acceleration constraints of the motion axis in the discretized kinematic constraint model. S7, through Taylor expansion, linearizes the agility constraints of the interpolation guide stroke and the agility constraints of the motion axis, and obtains a linearized kinematic constraint model; S8. The linearized kinematic constraint model is iteratively solved using a sequential linear programming method until the convergence condition is met, and finally the interpolation guide stroke speed of each discrete point is obtained.

2. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 1, characterized in that, In step S1, the establishment of the higher-order spline relationship includes: obtaining n two-dimensional spaces with the positions Q of the n motion axes as the vertical axis and the interpolation guide stroke S as the horizontal axis; in the n two-dimensional spaces, interpolating the discrete interpolation guide stroke and the position points of each motion axis to obtain the QS curve of each motion axis; and taking the first, second, and third derivatives of the QS curve to obtain the first derivative of the position of each motion axis relative to the interpolation guide stroke. Second derivative and third derivative The expression is as follows: 。 3. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 2, characterized in that, In step S2, based on the derivative relationship of each motion axis relative to the interpolation guide stroke, the relationship between the velocity, acceleration, and agility of each motion axis and the velocity, acceleration, and agility of the interpolation guide path is established, as shown below: in, , , These are the velocity, acceleration, and speed of the motion axis in the machine tool coordinate system, respectively. , , These are the speed, acceleration, and agility of the interpolation guide stroke, respectively. Define the ratio of interpolation guide path shortcut to speed as pseudo-shortcut, and convert the motion axis shortcut to: in This is a pseudo-shortcut.

4. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 3, characterized in that, In step S3, the kinematic constraint model is as follows: Where T is the processing time. The value at the end of the journey. The maximum value of the square of the process speed. This represents the maximum process acceleration. This represents the maximum process speed. The maximum value of the square of the single-axis velocity. This represents the maximum value of single-axis acceleration. This represents the maximum single-axis agility.

5. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 4, characterized in that, Step S4, linearizing the objective function specifically includes: Take the interpolation guide stroke S Equally spaced points As discrete points, Quantity at the point Simplified representation as Then, the processing time under the discretization parameters is approximately as follows: in, These are the values ​​of equal spacing between discrete points; use A linear function, approximately a nonlinear function To obtain an approximate function The expression is as follows: in, For a given piecewise linear function, the points of discontinuity are given. The objective function, after being approximated by processing time, is expressed as follows: 。 6. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 5, characterized in that, By adding the aforementioned objective function approximation constraint to the kinematic constraint model, the discrete kinematic constraint model is obtained as shown below: 。 7. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 6, characterized in that, Step S5 specifically includes: S51, using cubic uniform B-spline interpolation, the interpolation guide stroke at discrete point i is represented by control points. and the square of the travel speed As shown below: in, For travel control points; The control point is the square of the stroke speed; S52, combining the boundary conditions of cubic uniform B-spline interpolation, solves for all travel control points using a linear matrix. ; S53. Based on the interpolation characteristics of cubic uniform B-spline, the first and second derivatives of the interpolation guide stroke with respect to the spline parameters at each discrete point are obtained. S54, derives the square of the stroke speed on the interpolation guide stroke. acceleration Pseudo-shortcut The relationship between the two factors is then established; substituting the first and second derivatives from step S53, the interpolated guided stroke acceleration and pseudo-shortness at discrete points are transformed into expressions using control points, as shown below: in, , These represent the first and second derivatives of the interpolation guide stroke with respect to the spline parameters, respectively. S55, the square of the travel speed at discrete point i. acceleration Pseudo-shortcut Write it in the following uniform format: in, , , , All are constant horizontal quantities of length N+2.

8. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 7, characterized in that, In step S7, the speed of the interpolation guide stroke is adjusted. And the agility of the motion axis As about A multivariate function at a point By finding its first-order Taylor expansion, we obtain the agility constraints of the interpolation guide stroke and the agility constraints of the motion axis. This is a linearized expression of the independent variable.

9. The multi-axis linkage CNC machining speed planning method based on sequential linear programming according to claim 8, characterized in that, In step S8, the iterative solution includes: S81, in the discrete nonlinear kinematic constraint model of step S3, the maximum value is constrained by the process speed. Nonlinear quantities of the speed constraint in the alternative model This yields an over-constrained linear programming model; solving this linear programming model yields the initial feasible solution for the over-constraints. ; S82, according to Calculate each discrete point Further calculate the linearization coefficients of the process agility constraints and motion axis agility constraints in the linear programming sub-model, thus obtaining the linear programming sub-model. S83, Solve this linear programming sub-model to obtain its optimal solution. ;if and If the difference is less than a set threshold, then That is, the optimal solution to the sequential linear programming problem; otherwise, let Reconstruct and solve the linear programming problem iteratively; S84 will provide the final optimal solution. Substituting the values ​​into the calculation, we obtain the interpolation-guided stroke speed planning for the isolation point i with the minimum processing time. .

10. A multi-axis linkage CNC machining speed planning system based on sequential linear programming, characterized in that, include: The high-order spline relation establishment module is used to establish the high-order spline relation of the position relative interpolation guide stroke of each motion axis of the machine tool; The motion characteristic parameter relationship establishment module is used to establish the relationship between the motion characteristic parameters of each motion axis and the motion characteristic parameters along the interpolation guide stroke and the higher-order splines; wherein, the motion characteristic parameters include velocity, acceleration and agility; The kinematic constraint model building module is used to build a kinematic constraint model based on the process constraints of the interpolation guide stroke and the kinematic constraints of each motion axis, with the objective function of minimizing the processing time; wherein, the process constraints include the speed, acceleration, and agility constraints of the interpolation guide stroke, and the kinematic constraints include the speed, acceleration, and agility constraints of each motion axis; The discrete module is used to transform the kinematic constraint model into N discrete points and approximate the objective function using a continuous linear function to linearize the objective function. Combined with the objective function approximation constraint, the discrete kinematic constraint model is obtained. The control point relationship establishment module is used to establish the velocity along the interpolation guide stroke at discrete points and the relationship between the interpolation guide stroke and the control points using cubic uniform B-splines, and further derives the relationship between the acceleration along the interpolation guide stroke and the pseudo-shortness along the interpolation guide stroke and the control points. The linearization module is used to linearize the approximate constraints of the objective function, the velocity and acceleration constraints of the interpolated guide stroke, and the velocity and acceleration constraints of the motion axis in the discretized kinematic constraint model, based on the relationships between the obtained control points and with spline control points as independent variables; the linearization of the agility constraints of the interpolated guide stroke and the agility constraints of the motion axis is achieved through Taylor expansion, resulting in a linearized kinematic constraint model. The iterative solution module is used to iteratively solve the linearized kinematic constraint model using a sequential linear programming method until the convergence condition is met, and finally obtain the interpolated guide stroke speed at each discrete point.

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