High-speed and high-precision NURBS curve interpolation parameter calculation method and system

Abstract

The invention discloses a high-speed and high-precision NURBS curve interpolation parameter calculation method and system, and relates to the technical field of numerical control machining, and the method comprises the steps: adaptively adjusting the feeding speed of an interpolation point based on a machining precision requirement and a normal acceleration; a Runge-Kutta method is adopted to accurately calculate the parameter value of each interpolation point of the NURBS curve; calculating the deviation between the actual value and the expected value of the feeding speed; and carrying out accurate real-time spline interpolation by using a harmonic mean value Newton iteration method. The feeding speed needs to be used in the fourth-order Runge-Kutta method during interpolation, the speed is restrained by the bow height error, the parameter correction link is carried out in the subsequent interpolation parameter accurate calculation process, the interpolation precision is further improved according to the speed fluctuation rate error, meanwhile, the interpolation parameter calculation adopts the fourth-order Runge-Kutta method for calculation, and the interpolation precision is further improved. According to the method, high-order derivation does not need to be carried out on an NURBS curve, and when the feeding speed is corrected, the harmonic mean Newton iteration method is adopted, and the three-bound convergence characteristic of the harmonic mean Newton iteration method is utilized, so that the calculation efficiency is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical control machining, and in particular to a high-speed and high-precision NURBS curve interpolation parameter calculation method and system. Background Art

[0002] CNC interpolation is the intensive refinement of the interpolation of the tool machining trajectory, and outputs real-time control information of the machine tool motion during the interpolation cycle. In ordinary motion control systems, there are only basic functions such as linear interpolation, circular interpolation, and spiral interpolation. Although various functions can be basically realized, the performance is greatly reduced. For more complex path planning problems, the commonly used algorithm is to process the complex path as a continuous line segment for approximation or to fit the complex path using a parametric curve method. Among them, the continuous line segment approximation problem is often handled by acceleration and deceleration control and speed look-ahead; and in the parametric curve fitting problem, the NURBS curve is favored because of its powerful modeling ability and unified mathematical description. Compared with the complex processing of the continuous line segment approximation problem, the use of NURBS curves for curve fitting has great advantages.

[0003] However, in the field of machining, the traditional method is to divide the NURBS curve into a large number of tiny straight line segments or circular arc segments, and then perform linear interpolation. This will cause the machining speed to be subject to more constraints, and even produce violent fluctuations, which seriously affects the machining efficiency and machining accuracy. In order to overcome the above problems, it is necessary to develop a NURBS direct interpolation function to avoid decomposing complex curves into micro-segments. Its NC code can directly express the NURBS curve by controlling parameters such as vertices, node vectors and weight factors. Compared with traditional CNC machining methods, the amount of NC code is greatly reduced. Since the approximation processing of micro-segments is avoided, the machining accuracy and efficiency are improved. However, the mathematical expression of the NURBS curve is very complex, and there is no fixed expression relationship between the arc length and the parameter value, which has become the primary obstacle to direct interpolation of CNC machine tools.

[0004] In recent years, domestic and foreign researchers have done a lot of research on NURBS interpolation algorithms and have achieved certain research results. At present, the most commonly used real-time spline interpolation methods are Taylor expansion method, Newton iteration method, bisection method, etc. Since the high-order terms are ignored in the actual calculation, the Taylor expansion approximation method will inevitably cause truncation errors and further aggravate the interpolation speed fluctuations. Although the Newton iteration method and the bisection method greatly improve the interpolation accuracy, the excessive number of iterations reduces the real-time performance of the interpolation. Summary of the invention

[0005] Based on the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide a high-speed and high-precision NURBS curve interpolation parameter calculation method and system to solve the above-mentioned technical problems.

[0006] To achieve the above object, the present invention provides the following technical solution: a high-speed and high-precision NURBS curve interpolation parameter calculation method, comprising:

[0007] Adaptively adjust the feed speed of the interpolation point based on machining accuracy requirements and normal acceleration;

[0008] The Runge-Kutta method is used to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve;

[0009] Calculate the deviation between the actual value and the expected value of the feed speed;

[0010] Accurate real-time spline interpolation using harmonic mean Newton iteration method.

[0011] The present invention is further configured that the machining accuracy requirement includes a bow height error limit; and the feed speed of the interpolation point is adaptively adjusted based on the machining accuracy requirement and the normal acceleration, including:

[0012] Calculate the parameter u at the interpolation point i The feed speed based on the bow height error limit is calculated as follows: Among them, V e (u i ) is the feed speed based on the bow height error limit, T S is the interpolation period, ρ i is the curvature radius of the interpolation point, h max is the maximum allowable bow height error;

[0013] Calculate the parameter u at the interpolation point i The feed rate is based on the normal acceleration limit, and the calculation logic is: Among them, V n (u i ) is the feed rate based on normal acceleration limitation, A n,max is the maximum allowable normal acceleration of the machine tool;

[0014] The logic of adaptive regulation is: V(u i )=min{V m ,V e (u i ),V n (u i )}, where V(u i ) is the feed speed of the interpolation point adjusted adaptively, V m Give the machine a maximum feed rate.

[0015] The present invention is further configured to use the Runge-Kutta method to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve, and the calculation logic is: Among them, u i is the interpolation point C(u i ) corresponding interpolation parameters, T s is the interpolation cycle, K1, K2, K3 and K4 are the intermediate variables in the Runge-Kutta method, V(u) is the feed rate, C(u) is the k-th NURBS expression, Where u is the parameter variable of the NURBS curve; k is the degree of the NURBS curve; d i (i=0,1,…,n) is the control point; ω i is the control point d i The corresponding weight factor is used to reflect the degree to which the control point affects the shape of the curve, and ω0, ω n >0, except ω0, ω n Other than i ≥0; N i,k (u) is the k-order B-spline basis function defined on the knot vector U, which is defined as: U = [u0, u1, ..., u k ,u k+1 ,…,u n ,u n+1 ,…,u n+k+1 ],N i,k (u) is defined and calculated by the deBoor-Cox recursive formula:

[0016] The present invention is further configured to calculate the deviation between the actual value and the expected value of the feed speed, including: the parameter value u obtained by the fourth-order Runge-Kutta calculation i With expected parameter value If the error is not consistent within the allowable range, it means the corresponding feed step length ΔL i Not exactly equal to the expected feed step length That is, the absolute value of the speed fluctuation rate is greater than the maximum speed fluctuation rate, and the interpolation parameter u is adjusted. i , until the error requirement is met; the calculation logic of the deviation between the actual value and the expected value of the feed speed is: Where δ is the deviation between the actual value and the expected value of the feed speed, V r (u i ) is the actual value of feed speed, V(u i ) is the expected feed speed.

[0017] The present invention is further configured such that the calculation logic of the deviation between the actual value and the expected value of the feed speed is equivalently expressed as: Among them, C(u i ) is a k-order NURBS expression, ||C(u i+1 )-C(u i)|| is the actual feed chord length of the tool, V(u i ) is the feed speed of the interpolation point adjusted adaptively, T S is the interpolation period. In order to reduce the difference between the actual feed chord length and the theoretical feed chord length, let ||C(u i+1 )-C(u i )||-V(u i )T S = 0, F(x) = || C(x) - C(u i )||-V(u i )T, that is, the actual feed chord length is used to approximate the theoretical feed chord length, and the next interpolation parameter u is accurately calculated by the above formula i+1 , there is no fluctuation in feed speed, and the real-time interpolation problem is transformed into: Find u i+1 A solution that makes the above equation true. The solution logic includes: estimating interpolation parameters through the harmonic mean Newton method, calculating the initial value of iteration through the RK method, and solving the parameter u that satisfies the allowable velocity fluctuation rate through the harmonic mean Newton method. i+1 , the calculation logic is: Among them, F(u i ) is the parameter u at the interpolation point i The function value at F'(u i ) is the parameter u at the interpolation point i F(u i ), v i is an intermediate variable used for auxiliary calculation, The termination conditions of the iteration include: Among them, condition I is the speed fluctuation rate control condition, δ k represents the feed speed fluctuation rate after k iterations, Δ represents the upper limit of the speed fluctuation rate set by the user or required by the system, condition II is used to ensure the real-time performance of the spline interpolation algorithm, and the maximum number of iterations K of the algorithm is set t .

[0018] The present invention also provides a high-speed and high-precision NURBS curve interpolation parameter calculation system, the system comprising:

[0019] Adaptive adjustment module: Adaptively adjust the feed speed of the interpolation point based on the machining accuracy requirements and normal acceleration;

[0020] The first calculation module: uses the Runge-Kutta method to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve;

[0021] The second calculation module: calculates the deviation between the actual value and the expected value of the feed speed;

[0022] Spline interpolation module: Use the harmonic mean Newton iteration method to perform accurate real-time spline interpolation.

[0023] The present invention provides a high-speed and high-precision NURBS curve interpolation parameter calculation method and system. The method adaptively adjusts the feed speed of the interpolation point based on the machining accuracy requirement and the normal acceleration; uses the Runge-Kutta method to accurately calculate the parameter value of each interpolation point of the NURBS curve; calculates the deviation between the actual value and the expected value of the feed speed; and uses the harmonic mean Newton iteration method to perform accurate real-time spline interpolation. The beneficial effects produced include:

[0024] 1. High processing accuracy: The present invention uses the fourth-order Runge-Kutta method during interpolation, which requires a feed speed that is constrained by the bow height error. In the subsequent precise calculation of interpolation parameters, a parameter correction link is performed, and the interpolation accuracy is further improved according to the speed fluctuation rate error.

[0025] 2. High computational efficiency: The fourth-order Runge-Kutta method is used to calculate the interpolation parameters, and there is no need to perform high-order derivatives on the NURBS curve. When correcting the feed speed, the harmonic mean Newton iteration method is used, which greatly speeds up the computational efficiency by taking advantage of its three-bound convergence characteristics.

[0026] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0028] Figure 1 A flowchart of a high-speed and high-precision NURBS curve interpolation parameter calculation method is shown as an exemplary embodiment of the present invention;

[0029] Figure 2 An algorithm flow chart showing a high-speed and high-precision NURBS curve interpolation parameter calculation method according to an exemplary embodiment of the present invention

[0030] Figure 3 A parameter curve to be processed is shown as an exemplary embodiment of the present invention;

[0031] Figure 4The number of iterations of the parameter u in each interpolation cycle using the fourth-order Runge-Kutta method is shown as an exemplary embodiment of the present invention;

[0032] Figure 5 A bow height error diagram of an interpolation algorithm shown as an exemplary embodiment of the present invention;

[0033] Figure 6 A speed fluctuation diagram of an interpolation algorithm shown as an exemplary embodiment of the present invention;

[0034] Figure 7 The present invention is a schematic structural diagram of a high-speed and high-precision NURBS curve interpolation parameter calculation system according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0035] The following will describe the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention, not for limiting the scope of protection of the present invention.

[0036] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0037] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0038] Embodiment 1

[0039] See also Figure 3 , Figure 3The figure shows a parameter curve to be processed in an exemplary embodiment of the present invention. The dashed line in the figure represents the NURBS curve, showing the shape of the NURBS (non-uniform rational B-spline) curve. The NURBS curve is a commonly used mathematical representation used to accurately describe complex free curves and surfaces. The solid line in the figure represents the control polygon, which represents the polygon of the control points. The control points and weights determine the shape of the NURBS curve, and the NURBS curve is interpolated or approximated through these control points.

[0040] A high-speed and high-precision NURBS curve interpolation parameter calculation method, such as Figure 1 As shown, including:

[0041] Adaptively adjust the feed speed of the interpolation point based on machining accuracy requirements and normal acceleration;

[0042] The Runge-Kutta method is used to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve;

[0043] Calculate the deviation between the actual value and the expected value of the feed speed;

[0044] The harmonic mean Newton iteration method is used for precise real-time spline interpolation. Precise real-time spline interpolation means that in practical applications, the position and parameters of the interpolation points are accurately calculated to generate smooth spline curves in real time to meet the needs of processing or control.

[0045] For details, please refer to Figure 2 , Figure 5 and Figure 6 , Figure 2 An algorithm flow chart of a high-speed and high-precision NURBS curve interpolation parameter calculation method shown as an exemplary embodiment of the present invention; Figure 5 This is a graph of the bow height error of the interpolation algorithm shown in an exemplary embodiment of the present invention. The bow height error reflects the deviation between the actual position of the curve and the expected position during the interpolation process. When the bow height error is large, it means that the position of the interpolation point deviates greatly from the expected position and needs to be adjusted; Figure 6 The speed fluctuation diagram of the interpolation algorithm is shown as an exemplary embodiment of the present invention. The speed fluctuation rate indicates the relative deviation between the actual feed speed and the expected feed speed. The smaller the speed fluctuation rate, the more stable the feed speed is, which meets the expected value. The feed speed of the interpolation point is adaptively adjusted based on the machining accuracy requirement and the normal acceleration. In a feasible embodiment of the present invention, the machining accuracy requirement includes the bow height error limit. The feed speed of the interpolation point will be adaptively adjusted based on the normal acceleration and the maximum bow height error of the point as the constraint conditions. The interpolation point parameter u is calculated. i The feed speed based on the bow height error limit is calculated as follows: Among them, V e (u i ) is the feed speed based on the bow height error limit, T S is the interpolation period, ρ i is the curvature radius of the interpolation point, h max is the maximum allowable bow height error; calculate the interpolation point parameter u i The feed rate is based on the normal acceleration limit, and the calculation logic is: Among them, V n (u i ) is the feed rate based on normal acceleration limitation, A n,max is the maximum allowable normal acceleration of the machine tool; the logic of adaptive adjustment is: V(u i )=min{V m ,V e (u i ),V u (u i )}, where V(u i ) is the feed speed of the interpolation point adjusted adaptively, V m Give the machine a maximum feed rate.

[0046] The present invention is further configured to use the Runge-Kutta method to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve, and the calculation logic is: Among them, u i is the interpolation point C(u i ) corresponding interpolation parameters, T s is the interpolation cycle, K1, K2, K3 and K4 are the intermediate variables in the Runge-Kutta method, V(u) is the feed rate, C(u) is the k-th NURBS expression, Where u is the parameter variable of the NURBS curve; k is the degree of the NURBS curve; d i (i=0,1,…,n) is the control point; ω i is the control point d i The corresponding weight factor is used to reflect the degree to which the control point affects the shape of the curve, and ω0, ω n >0, except ω0, ω n Other than i ≥0, further, the derivative of a section of the NURBS expression is: N i,k (u) is the k-order B-spline basis function defined on the knot vector U, which is defined as: U = [u0, u1, ..., u k ,u k+1 ,…,u n,u n+1 ,…,u n+k+1 ], in a feasible embodiment of the present invention, take u0=u1=…=u k =0,u n+1 =…=u n+k+1 =1, the rest of the elements are between (0,1), the number of repetitions of the first and last identical elements 0 and 1 is k+1, N i,k (u) is defined and calculated by the deBoor-Cox recursive formula:

[0047] The present invention is further configured to calculate the deviation between the actual value and the expected value of the feed speed, including: the parameter value u obtained by the fourth-order Runge-Kutta calculation i With expected parameter value If the error is not consistent within the allowable range, it means the corresponding feed step length ΔL i Not exactly equal to the expected feed step length That is, the absolute value of the speed fluctuation rate is greater than the maximum speed fluctuation rate, and the interpolation parameter u is adjusted. i , until the error requirement is met. The error requirement is set according to specific needs and is not restricted here. The calculation logic of the deviation between the actual value and the expected value of the feed speed is: Where δ is the deviation between the actual value and the expected value of the feed speed, V r (u i ) is the actual value of feed speed, V(u i ) is the expected feed speed.

[0048] The present invention is further configured such that the calculation logic of the deviation between the actual value and the expected value of the feed speed is equivalently expressed as: Among them, C(u i ) is a k-order NURBS expression, ||C(u i+1 )-C(u i )|| is the actual feed chord length of the tool, V(u i ) is the feed speed of the interpolation point adjusted adaptively, T S is the interpolation period. In order to reduce the difference between the actual feed chord length and the theoretical feed chord length, let ||C(u i+1 )-C(u i )||-V(u i )T S = 0, F(x) = || C(x) - C(u i )||-V(u i )T, that is, the actual feed chord length is used to approximate the theoretical feed chord length, and the next interpolation parameter u is accurately calculated by the above formula i+1 , there is no fluctuation in feed speed, and the real-time interpolation problem is transformed into: Find u i+1A solution that makes the above equation true. Specifically, in terms of solving parametric equations, the most commonly used and simplest is the Newton iteration method. However, the Newton iteration method is not efficient. The mean Newton law attempts to improve this situation by introducing the concept of harmonic mean, and its convergence speed is three bounds, and the iteration speed is faster. The Newton method iteration formula is: The iterative formula of the harmonic mean Newton method is: The iterative initial value calculation and derivation of the harmonic mean Newton method are the same as those of the Newton iteration method. The interpolation parameters are estimated by the harmonic mean Newton method, the initial value of the iteration is calculated by the RK method, and the parameter u that satisfies the allowable velocity fluctuation rate is solved by the harmonic mean Newton method. i+1 , the calculation logic is: Among them, F(u i ) is the parameter u at the interpolation point i The function value at F'(u i ) is the parameter u at the interpolation point i F(u i ), v i is an intermediate variable used for auxiliary calculation, The termination conditions of the iteration include: Among them, condition I is the speed fluctuation rate control condition, δ k represents the feed speed fluctuation rate after k iterations, Δ represents the upper limit of the speed fluctuation rate set by the user or required by the system, condition II is used to ensure the real-time performance of the spline interpolation algorithm, and the maximum number of iterations K of the algorithm is set t .

[0049] See also Figure 4 , an exemplary embodiment of the present invention shows the number of iterations of the parameter u in each interpolation cycle using the fourth-order Runge-Kutta method, the x-axis represents the interpolation step number, ranging from 0 to 400, the interpolation step number represents the number of steps performed during the interpolation process, each step corresponds to the calculation of an interpolation point, and the y-axis represents the number of times the parameter is modified in each interpolation cycle, ranging from 0 to 3. This indicates the number of times the interpolation parameter is modified in each interpolation cycle to meet the feed speed requirement. The image provides intuitive information about the parameter modification behavior during the NURBS curve interpolation process, showing the frequency of parameter modification at different interpolation steps to meet the feed speed and accuracy requirements.

[0050] Based on the above interpolation parameter calculation method, the present invention adopts the Runge-Kutta method to calculate the interpolation parameters, avoiding the high-order derivation of the NURBS curve, reducing the calculation complexity, and improving the real-time performance of the algorithm. At the same time, the third-order convergence characteristics of the harmonic mean Newton iteration method are used to quickly find the next interpolation point, greatly improving the calculation efficiency.

[0051] Embodiment 2

[0052] See also Figure 7 , the exemplary high-speed and high-precision NURBS curve interpolation parameter calculation system comprises:

[0053] Adaptive adjustment module: Adaptively adjust the feed speed of the interpolation point based on the machining accuracy requirements and normal acceleration;

[0054] The first calculation module: uses the Runge-Kutta method to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve;

[0055] The second calculation module: calculates the deviation between the actual value and the expected value of the feed speed;

[0056] Spline interpolation module: Use the harmonic mean Newton iteration method to perform accurate real-time spline interpolation.

[0057] It should be noted that the high-speed and high-precision NURBS curve interpolation parameter calculation system provided in the above embodiment and the high-speed and high-precision NURBS curve interpolation parameter calculation method provided in the above embodiment belong to the same concept, wherein the specific manner in which each module and unit performs the operation has been described in detail in the method embodiment, and will not be repeated here. In actual applications, the high-speed and high-precision NURBS curve interpolation parameter calculation system provided in the above embodiment can allocate the above functions to different functional modules as needed, that is, divide the internal structure of the system into different functional modules to complete all or part of the functions described above, and this is not limited here.

[0058] The above embodiments can be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that contains one or more available media sets. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state hard disk.

[0059] It should be understood that the term "and / or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. A and B can be singular or plural. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship, but it may also indicate an "and / or" relationship. Please refer to the context for specific understanding.

[0060] In this application, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0061] It should be understood that in the various embodiments of the present application, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0062] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0063] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0064] In the several embodiments provided in the present application, it should be understood that the disclosed system can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0065] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0066] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0067] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage media include: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks or optical disks.

[0068] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A high-speed and high-precision NURBS curve interpolation parameter calculation method, characterized in that: include: Adaptively adjust the feed speed of the interpolation point based on machining accuracy requirements and normal acceleration; The Runge-Kutta method is used to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve; Calculate the deviation between the actual value and the expected value of the feed speed; Accurate real-time spline interpolation using harmonic mean Newton iteration method.

2. A high-speed and high-precision NURBS curve interpolation parameter calculation method according to claim 1, characterized in that: Machining accuracy requirements include bow height error limits; Adaptively adjust the feed rate of the interpolation point based on machining accuracy requirements and normal acceleration, including: Calculate the parameter u at the interpolation point i The feed speed based on the bow height error limit is calculated as follows: Among them, V e (u i ) is the feed speed based on the bow height error limit, T S is the interpolation period, ρ i is the curvature radius of the interpolation point, h max is the maximum allowable bow height error; Calculate the parameter u at the interpolation point i The feed rate is based on the normal acceleration limit, and the calculation logic is: Among them, V n (u i ) is the feed rate based on normal acceleration limitation, A n,max is the maximum allowable normal acceleration of the machine tool; The logic of adaptive regulation is: V(u i )=min{V m ,V e (u i ),V n (u i )}, where V(u i ) is the feed speed of the interpolation point adjusted adaptively, V m Give the machine a maximum feed rate.

3. A high-speed and high-precision NURBS curve interpolation parameter calculation method according to claim 1, characterized in that: The Runge-Kutta method is used to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve. The calculation logic is: Among them, u i is the interpolation point C(u i ) corresponding interpolation parameters, T s is the interpolation cycle, K1, K2, K3 and K4 are the intermediate variables in the Runge-Kutta method, V(u) is the feed rate, C(u) is the k-th NURBS expression, Where u is the parameter variable of the NURBS curve; k is the degree of the NURBS curve; d i (i=0,1,…,n) is the control point; ω i is the control point d i The corresponding weight factor is used to reflect the degree to which the control point affects the shape of the curve, and ω0, ω n >0, except ω0, ω n Other than i ≥0; N i,k (u) is the k-order B-spline basis function defined on the knot vector U, which is defined as: U = [u0, u1, ..., u k ,u k+1 ,…,u n ,u n+1 ,…,u n+k+1 ],N i,k (u) is defined and calculated by the deBoor-Cox recursive formula:

4. A high-speed and high-precision NURBS curve interpolation parameter calculation method according to claim 1, characterized in that: Calculate the deviation between the actual value and the expected value of the feed rate, including: the parameter value u obtained by the fourth-order Runge-Kutta calculation i With expected parameter value If the error is not consistent within the allowable range, it means the corresponding feed step length ΔL i Not exactly equal to the expected feed step length That is, the absolute value of the speed fluctuation rate is greater than the maximum speed fluctuation rate, and the interpolation parameter u is adjusted. i , until the error requirement is met; the calculation logic of the deviation between the actual value and the expected value of the feed speed is: Where δ is the deviation between the actual value and the expected value of the feed speed, V r (u i ) is the actual value of feed speed, V(u i ) is the expected feed speed.

5. A high-speed and high-precision NURBS curve interpolation parameter calculation method according to claim 4, characterized in that: The calculation logic of the deviation between the actual value and the expected value of the feed speed is equivalent to: Among them, C(u i ) is a k-order NURBS expression, ||C(u i+1 )-C(u i )|| is the actual feed chord length of the tool, V(u i ) is the feed speed of the interpolation point adjusted adaptively, TS is the interpolation period, and in order to reduce the difference between the actual feed chord length and the theoretical feed chord length, let ||C(u i+1 )-C(u i )||-V(u i )T S = 0, F(x) = || C(x) - C(u i )||-V(u i )T, that is, the actual feed chord length is used to approximate the theoretical feed chord length, and the next interpolation parameter u is accurately calculated by the above formula i+1 , there is no fluctuation in feed speed, and the real-time interpolation problem is transformed into: Find u i+1 A solution that makes the above equation true. The solution logic includes: estimating interpolation parameters through the harmonic mean Newton method, calculating the initial value of iteration through the RK method, and solving the parameter u that satisfies the allowable velocity fluctuation rate through the harmonic mean Newton method. i+1 , the calculation logic is: Among them, F(u i ) is the parameter u at the interpolation point i The function value at F'(u i ) is the parameter u at the interpolation point i F(u i ), v i is an intermediate variable used for auxiliary calculation, The termination conditions of the iteration include: Among them, condition I is the speed fluctuation rate control condition, δ k represents the feed speed fluctuation rate after k iterations, Δ represents the upper limit of the speed fluctuation rate set by the user or required by the system, condition II is used to ensure the real-time performance of the spline interpolation algorithm, and the maximum number of iterations K of the algorithm is set t .

6. A high-speed and high-precision NURBS curve interpolation parameter calculation system, characterized in that: include: Adaptive adjustment module: Adaptively adjust the feed speed of the interpolation point based on the machining accuracy requirements and normal acceleration; The first calculation module: uses the Runge-Kutta method to accurately calculate the parameter values ​​of each interpolation point of the NURBS curve; The second calculation module: calculates the deviation between the actual value and the expected value of the feed speed; Spline interpolation module: Use the harmonic mean Newton iteration method to perform accurate real-time spline interpolation.

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