Self-adaptive step interpolation method and system for precision machining of machine tool and medium

Abstract

The invention relates to a self-adaptive step interpolation method and system for machine tool precision machining and a medium, and belongs to the field of precision numerical control machine tools, and the method comprises the following steps: S1, obtaining a parameterized curve set in a numerical control program, and setting corresponding initial parameters; s2, solving an initial interpolation step length based on the feeding speed; s3, calculating # imgabs0 # under the interpolation step length T, and if # imgabs1 #, skipping to S5; if # imgabs2, executing S4; s4, enabling T to be equal to # imgabs3 #, and executing S3; s5, judging whether interpolation is completed or not, and when interpolation is completed, performing trajectory calculation based on the calculated curve parameters and outputting a curvilinear function after difference compensation; otherwise, i is made to be equal to i + 1, and the step S2 is executed. By dynamically adjusting the interpolation step length, real-time balance of calculation precision and efficiency is achieved, redundant calculation of a simple curve segment can be avoided, and the machining precision of a complex curve segment can be ensured through step length self-adaptive optimization.

Description

Technical Field

[0001] The present invention belongs to the field of precision CNC machine tools, and particularly relates to an adaptive step interpolation method, system and medium for precision machining of machine tools. Background Technique

[0002] The interpolation method of CNC machine tools is one of the core technologies for achieving high-precision machining. It generates a smooth motion trajectory by performing mathematical calculations on the path set in the NC program, thereby significantly improving the quality of the machined surface and the accuracy of dimensions. With the continuous progress of computer technology and algorithms, the application of interpolation methods in NC technology is becoming increasingly widespread, becoming an important driving force for promoting the development of the manufacturing industry towards high precision and high efficiency. The interpolation technology can not only optimize the motion path of the tool, but also effectively reduce vibrations and errors during the machining process, providing reliable technical support for the machining of complex parts.

[0003] With the continuous development of the manufacturing industry, the requirements for machining accuracy and efficiency are increasing day by day. Traditional machining methods are difficult to meet the needs of modern production. In the prior art, to address this problem, parametric interpolation algorithms are used to implement interpolation technology. Parametric interpolation algorithms include numerical methods for differential equations, iterative approximation methods, etc., for parametric interpolation technology in CNC machine tools. Among them, the numerical method for differential equations determines the motion trajectory of the curve by solving differential equations; the iterative approximation method gradually approximates the true curve shape through continuous iterative calculations.

[0004] However, there are still certain problems in the parametric interpolation technology in the prior art: Parametric interpolation algorithms such as the numerical method for differential equations and the iterative approximation method lack adaptability, resulting in difficulties in dynamically balancing calculation accuracy and efficiency. Their rigid parameter settings such as fixed step size or preset iteration thresholds cannot adjust the calculation strategy in real time according to curve curvature changes, machining speed requirements, etc., which not only generates redundant calculations and wastes resources in simple curve segments, but also causes undercutting or overcutting defects due to insufficient accuracy in complex curve segments. Summary of the Invention

[0005] The present invention proposes an interpolation method for CNC machine tools based on an adaptive parameter interpolation algorithm. This method can dynamically adjust the interpolation step size and iteration threshold, and can optimize the calculation strategy in real time according to curve curvature changes and machining speed requirements, thereby improving the calculation efficiency while ensuring accuracy. In addition, the present invention also introduces an error control mechanism, which dynamically adjusts the interpolation step size by comparing the deviation value with the precision parameter to ensure the stability and reliability of the machining process. Through the above technical solutions, the present invention can effectively solve the problem of difficulty in balancing accuracy and efficiency existing in the existing parametric interpolation algorithms, and provide comprehensive technical support for high-precision machining.

[0006] The technical solution adopted by the present invention is as follows: In a first aspect, the present application provides an adaptive step interpolation method for precision machining of machine tools, including the following steps: Step S1: Obtain the parametric curve S(u) set in the numerical control program and set the corresponding initial parameters; The initial parameters include the curve parameter u, the feed speed V, the precision parameter and the initial interpolation step T, where the curve parameter u is a function of time t; Step S2: Perform a second-order Taylor expansion of the curve parameter u at t = , solve the initial interpolation step T based on the feed speed V, and calculate the curve parameter at the moment of t = , and the initial value of i is 1; Step S3: Calculate the truncation error between the interpolation parameter and the interpolation step T when calculating the interpolation step T, and solve . If , jump to step S5; If , execute step S4; Step S4: Perform a second-order Taylor expansion of the curve parameter u at t = , based on the feed speed V, let T = , and execute step S3; Step S5: Determine whether the interpolation is completed. When the interpolation is completed, perform trajectory calculation based on the calculated curve parameters and output the interpolated curve function; otherwise, let i = i + 1 and jump to step S2.

[0007] Preferably, in step S2, The calculation formula of

[0008] is solved by using the second-order Taylor expansion method: is the curve parameter at t = ti + 1; is the curve parameter at t = ti; is the feed speed at t = ti; S(u)=(x(u),z(u)), where x(u) and z(u) are the abscissa and ordinate corresponding to the curve parameter u respectively.

[0009] Preferably, The calculation formula of The second-order Taylor expansion of u at t = ti gives:

[0010] where HOT is the high-order term in the Taylor expansion; Taking the first derivative of the parametric curve S(u) with respect to the time parameter t, we can obtain:

[0011] The first derivative of the parameter u with respect to the time parameter t is:

[0012] Differentiating the above equation with respect to the time parameter t again, the second derivative of the curve parameter u with respect to the time parameter t is obtained:

[0013] In the above equation:

[0014]

[0015] We get:

[0016] Since the interpolation step size T = ti+1 - ti, we can obtain: .

[0017] Preferably, the parameterized curve S(u) is differentiated with respect to the curve parameter u:

[0018]

[0019] And since the feed step size △Li = ViT in the interpolation period, we can obtain: .

[0020] Preferably, in step S3, let ui be the starting node, T be the interpolation step size for solving the approximate value of the next curve parameter ui+1, and the truncation error of the second-order Taylor expansion method is O(T3), which is expressed as follows:

[0021] For the Taylor expansion method, the truncation error of the nth-order Taylor method is O(Tn+1); Halve the step size T and use the step size T / 2 to calculate the next curve parameter ui+1 in two steps at the starting node ui. The stage error of each step can be expressed as , so:

[0022] When the interpolation step size is halved, the error is reduced to approximately 1 / 4:

[0023] Perform an equivalent modification on the equation to obtain:

[0024] The Δ between the obtained calculation results is: , where is the derivative of the curve parameter at t = ti+1 and the interpolation step size is , is the derivative of the curve parameter at t = ti and the interpolation step size is .

[0025] Preferably, in step S5, substituting the parameter values in the parameter densification process into the given curve parameterization equation, the specific coordinate position of the next interpolation point can be obtained, that is: ; where P is the objective function and Pi+1 is the target point at the (i + 1)-th step.

[0026] Preferably, in step S5, judging the difference between the specific coordinate position of the interpolation point and the target end coordinate position. If the difference is less than the precision parameter , the interpolation is completed and the objective function P is output; otherwise, set i = i + 1 and jump to step S2.

[0027] In a second aspect, the present application provides an adaptive step interpolation system for precision machining of a machine tool, including: A data acquisition module for obtaining the parameterized curve and initial parameters set in the numerical control program; A data processing module for receiving the data from the data acquisition module and calculating the objective function according to the data.

[0028] Preferably, the data processing module includes a calculation unit and a judgment unit: The calculation unit is used to calculate the deviation and the interpolation step size according to the data; The judgment unit is used to compare the deviation with the precision parameter , and is used to judge the difference between the specific coordinate position of the interpolation point and the target end coordinate position and the precision parameter .

[0029] In a third aspect, the present application provides a computer-readable storage medium, characterized in that the computer-readable storage medium includes a stored program, wherein when the program runs, it controls the device where the computer-readable storage medium is located to execute the adaptive step interpolation method for precision machining of a machine tool described in the first aspect.

[0030] From the above technical solutions, it can be seen that the present invention has the following advantages: 1. By dynamically adjusting the interpolation step size, a real-time balance between calculation accuracy and efficiency is achieved. It can not only avoid redundant calculations for simple curve segments but also ensure the machining accuracy of complex curve segments through step size self-adaptation optimization, effectively solving the over-cutting and under-cutting problems caused by traditional fixed step size methods. At the same time, it adapts to the requirements of different machining scenarios and improves the overall performance of CNC machine tools.

[0031] 2. The second-order Taylor expansion method is used to calculate the parameter increment, significantly reducing the algorithm complexity while retaining sufficient calculation accuracy, avoiding the exponential growth of computational complexity brought by high-order Taylor expansion, taking into account both interpolation efficiency and accuracy. At the same time, through the direct mapping of parametric curve coordinates, the intermediate conversion error is reduced.

[0032] 3. Through the complete derivation of the second-order Taylor expansion formula and the truncation of high-order terms, the calculation process is simplified. Using the derivative relationship between time parameters and curve parameters to achieve dynamic trajectory prediction, while reducing the consumption of computing resources, ensuring the real-time matching of interpolation step size and curvature change, and improving the trajectory smoothness of complex curves.

[0033] 4. Through the calculation of the first-order derivative of curve parameters by parametric curves, the feed step size is directly related to the geometric characteristics of the curve, realizing the dynamic coupling of speed and curvature, avoiding trajectory deviation caused by the decoupling of geometric characteristics and motion parameters in traditional methods, and enhancing the continuity and stability of the machining trajectory.

[0034] 5. By the step size halving method to quantify the truncation error and dynamically adjust the step size, a mathematical mapping relationship between error and step size is established. It can not only quickly converge to the target accuracy but also avoid the blindness of manually presetting the step size, realizing the optimal allocation of computing resources, especially suitable for accurate interpolation of curves with sudden curvature or high nonlinearity.

[0035] 6. The interpolation point coordinates are directly output through the parameter densification process, reducing the intermediate parameter conversion link and the risk of cumulative error. At the same time, combined with the direct solution of the parametric equation, it ensures that the interpolation points strictly follow the mathematical definition of the curve, improving the theoretical consistency of the machining trajectory; the interpolation process is dynamically terminated through the difference of end point coordinates, preventing the end point deviation problem caused by over-iteration or premature termination, ensuring that the machining path completely covers the target curve, and avoiding the path end residual error caused by fixed step size in traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the present invention, the drawings required to be used in the description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0037] Figure 1It is a schematic flow chart of the adaptive step interpolation method for precision machining of machine tools in the specific implementation embodiments of the present invention. Specific implementation manners

[0038] In the following detailed description, various embodiments of the present disclosure will be described more comprehensively. The present disclosure can have various embodiments, and adjustments and changes can be made therein. However, it should be understood that there is no intention to limit the various embodiments of the present disclosure to the specific embodiments disclosed herein, but the present disclosure should be understood to cover all adjustments, equivalents, and / or alternative solutions falling within the spirit and scope of the various embodiments of the present disclosure.

[0039] The following are some noun explanations in this solution for better understanding of this solution: 1. Interpolation Interpolation is a key technology in numerical control machine tools, which is used to generate a smooth motion trajectory according to the path set in the numerical control program. Through mathematical calculations, interpolation technology connects discrete machining points into continuous curves or straight lines, thereby ensuring the accuracy of the tool's moving trajectory during the machining process. The interpolation method directly affects the quality of the machined surface and the accuracy of dimensions, and is one of the core technologies of modern high-precision machining. With the development of computer technology and algorithms, interpolation technology has been continuously optimized, evolving from traditional linear and circular interpolation to more complex parametric interpolation to meet the requirements of high precision and high efficiency in the manufacturing industry.

[0040] 2. Taylor expansion method The Taylor expansion method is a mathematical tool used to approximate complex functions as polynomial forms. In interpolation technology, the Taylor expansion method can be used for local approximation of parametric curves, thereby simplifying the calculation process and improving the interpolation accuracy. Through Taylor expansion, high-order approximate values of the function can be obtained near a certain point on the curve, and then the selection of the interpolation step size can be optimized.

[0041] 3. Parametric curve A parametric curve is a curve described by a parametric equation and is commonly used in the interpolation technology of numerical control machine tools. Different from traditional explicit or implicit equations, a parametric curve defines the coordinates of each point on the curve by introducing parametric variables (such as time or path length). This representation method has the characteristics of strong flexibility and wide applicability, and can accurately describe complex three-dimensional curves and surfaces. In interpolation technology, the parametric curve provides a mathematical basis for the smooth movement of the tool, enabling the machining trajectory to better adapt to complex geometric shapes.

[0042] 4. Interpolation step size The interpolation step size refers to the distance or time interval by which the tool moves from one machining point to the next during interpolation. The choice of interpolation step size directly affects machining accuracy and efficiency: a too large step size will result in a rough machining surface, while a too small step size will increase the computational amount and reduce machining efficiency. In parametric interpolation technology, the optimization of the interpolation step size is a key issue, especially for complex curve segments, where the step size needs to be dynamically adjusted according to the curve curvature and machining speed to achieve the best balance between accuracy and efficiency.

[0043] 5. HOT (Higher-Order Terms) The higher-order terms in the Taylor expansion refer to the terms with higher powers, such as cubic terms, quartic terms, and higher-order terms, in addition to the lower-order terms (such as constant terms, linear terms, quadratic terms, etc.) when the function is expanded near a certain point during the Taylor expansion process. These higher-order terms are used to more precisely describe the behavior of the function near that point, especially in regions where the function changes rapidly or has a large curvature. The introduction of higher-order terms can improve the approximation accuracy of the Taylor expansion, but as the order increases, the computational complexity will also increase significantly. Therefore, in practical applications, an appropriate expansion order needs to be selected based on the balance between accuracy requirements and computational efficiency.

[0044] The present invention proposes a numerical control machine tool interpolation method based on an adaptive parameter interpolation algorithm. By dynamically adjusting the interpolation step size and iteration threshold, this method can optimize the calculation strategy in real time according to the curve curvature change and machining speed requirements, thereby improving the computational efficiency while ensuring accuracy. In addition, the present invention also introduces an error control mechanism. By comparing the deviation value with the accuracy parameter, the interpolation step size is dynamically adjusted to ensure the stability and reliability of the machining process. Through the above technical solutions, the present invention can effectively solve the problem of difficulty in balancing accuracy and efficiency existing in the existing parameter interpolation algorithms, providing comprehensive technical support for high-precision machining.

[0045] Embodiment 1: The present invention provides an adaptive step size interpolation method for precision machining of machine tools in view of the problems in the prior art, as Figure 1 shown, which includes the following steps: Step S1: Obtain the parameterized curve S(u) set in the numerical control program and set the corresponding initial parameters; In actual operation, when obtaining the parameterized curve S(u), the mathematical expression of the curve is extracted from the G-code of the numerical control program or the CAM software, such as Bezier curve, B-spline curve, or NURBS curve. These curves usually take the parameter u as a variable.

[0046] The initial parameters include the curve parameter u, the time parameter t, the feed speed V, the accuracy parameter and the interpolation step size T; Step S2: Set the curve parameter u at t = Perform a second-order Taylor expansion at this point, solve the initial interpolation step size T based on the feed rate V, and calculate t = The curve parameters at the moment , the initial value of i is 1; In step S2, The calculation formula of is solved by the second-order Taylor expansion method: The calculation formula of includes the following process: Perform a second-order Taylor expansion of u at t = ti, and we can get:

[0047] where HOT is the high-order term in the Taylor expansion; Taking the first derivative of the parametric curve S(u) with respect to the time parameter t, we can get:

[0048] The first derivative of the parameter u with respect to the time parameter t is:

[0049] Taking the derivative of the above formula with respect to the time parameter t again, we get the second derivative of the curve parameter u with respect to the time parameter t:

[0050] In the above formula:

[0051]

[0052] We get:

[0053] Since the interpolation step size T = ti+1 - ti, we can get: .

[0054] Take the derivative of the parametric curve S(u) with respect to the curve parameter u:

[0055]

[0056] And the feed step size △Li = ViT in the interpolation period, we can get: ;

[0057] where is the curve parameter at t = ti+1; is the curve parameter at t = ti; is the feed rate at t = ti; S(u) = (x(u), z(u)), where x(u) and z(u) are the abscissa and ordinate corresponding to the curve parameter u respectively; The second-order Taylor expansion method is used to calculate the parameter increment, which significantly reduces the algorithm complexity on the premise of retaining sufficient calculation accuracy, avoids the exponential growth of the calculation amount brought by the high-order Taylor expansion, takes into account both the interpolation efficiency and accuracy, and at the same time reduces the intermediate conversion error through the direct mapping of the parametric curve coordinates.

[0058] At the same time, through the complete derivation of the second-order Taylor expansion formula and the truncation of the high-order terms, the calculation process is simplified, and the trajectory dynamic prediction is realized by using the derivative relationship between the time parameter and the curve parameter. While reducing the consumption of computing resources, it ensures the real-time matching of the interpolation step size and the curvature change, and improves the trajectory smoothness of complex curves.

[0059] Step S3, calculate the truncation error between the interpolation parameter and the interpolation step size T when calculating the interpolation step size T, and solve , if , jump to step S5; If Execute step S4; In step S3, let ui be the starting node, T be the interpolation step size for solving the approximate value of the next curve parameter ui + 1, and the truncation error of the second-order Taylor expansion method is O(T3), which is expressed as follows:

[0060] For the Taylor expansion method, the truncation error of the nth-order Taylor method is O(Tn + 1); Halve the step size T and calculate the next curve parameter ui + 1 at the starting node ui in two steps with the step size T / 2. The stage error of each step can be expressed as , so:

[0061] When the interpolation step size is halved, the error is reduced to about 1 / 4:

[0062] For the equation make an equivalent modification to obtain:

[0063] The deviation Δ between the calculation results is: ; where is the derivative of the curve parameter at t = ti + 1 with the interpolation step size of , At \(t = t_i\) and with an interpolation step size of is the derivative of the curve parameter; Step S4: Perform a second-order Taylor expansion of the curve parameter \(u\) at \(t =\) , based on the feed rate \(V\), let \(T =\) , and execute Step S3; By calculating the first derivative of the curve parameter through the parametric curve, directly associate the feed step with the curve geometric features, realize the dynamic coupling of speed and curvature, avoid the trajectory deviation caused by the decoupling of geometric characteristics and motion parameters in traditional methods, and enhance the continuity and stability of the machining trajectory.

[0064] Quantify the truncation error and dynamically adjust the step size through the step halving method, establish the mathematical mapping relationship between the error and the step size, which can not only quickly converge to the target accuracy, but also avoid the blindness of artificially presetting the step size, realize the optimal allocation of computing resources, and is especially suitable for the precise interpolation of curves with sudden curvature or high nonlinearity.

[0065] Directly output the interpolation point coordinates through the parameter densification process, reduce the intermediate parameter conversion link, reduce the risk of cumulative error, and at the same time combine the direct solution of the parametric equation to ensure that the interpolation points strictly follow the curve mathematical definition, improving the theoretical consistency of the machining trajectory; Dynamically terminate the interpolation process through the difference of the end point coordinates, prevent the end point deviation problem caused by over-iteration or premature termination, ensure that the machining path completely covers the target curve, and avoid the path end residual error caused by the fixed step size in traditional methods.

[0066] Step S5: Judge whether the interpolation is completed. When the interpolation is completed, perform trajectory calculation based on the calculated curve parameter and output the interpolated curve function; Otherwise, let \(i = i + 1\) and jump to Step S2; In Step S5, substitute the parameter value in the parameter densification process into the given curve parametric equation, and the specific coordinate position of the next interpolation point can be obtained, that is: ; where \(P\) is the objective function and \(P_{i + 1}\) is the target point at the \((i + 1)\)-th step; Judge the difference between the specific coordinate position of the interpolation point and the target end coordinate position. If the difference is less than the precision parameter , then complete the interpolation and output the objective function \(P\); Otherwise, let \(i = i + 1\) and jump to Step S2.

[0067] By dynamically adjusting the interpolation step size, realize the real-time balance of computing accuracy and efficiency, which can not only avoid the redundant calculation of simple curve segments, but also ensure the machining accuracy of complex curve segments through step size adaptive optimization, effectively solve the over-cutting and under-cutting problems caused by traditional fixed step size methods, and at the same time meet the requirements of different machining scenarios, improving the overall performance of the CNC machine tool.

[0068] Embodiment 2: This application provides an adaptive step interpolation system for precision machining of machine tools, including: A data acquisition module, which is used to obtain the parametric curve and initial parameters set in the numerical control program; The data acquisition module extracts key information such as the type, control points, and knot vectors of the parametric curve by parsing the geometric instructions in the numerical control program, and at the same time obtains the parameter domain of the curve; the setting of the initial parameters includes the curve starting point, time starting point, feed speed, accuracy requirement, and interpolation step. These parameters are configured according to the specific requirements of the machining task, providing basic data support for subsequent interpolation calculations.

[0069] Through data extraction and parameter configuration, this module ensures the accuracy and stability of the machining process, and can dynamically adjust parameters according to actual machining requirements, providing reliable technical support for the machining of complex curves.

[0070] A data processing module, which is used to receive the data from the data acquisition module and calculate the objective function according to the data.

[0071] The data processing module integrates and analyzes the data by receiving the parametric curve information and initial parameters provided by the data acquisition module, and combines the specific requirements of the machining task to calculate the specific value of the objective function; this module adopts an efficient calculation algorithm to ensure the accuracy and real-time of the data processing process, and can dynamically adjust the calculation strategy according to the curve curvature change and machining speed, providing reliable data support for subsequent interpolation control, and achieving the machining goals of high precision and high efficiency.

[0072] In this embodiment, the data processing module includes a calculation unit and a judgment unit: A calculation unit, which is used to calculate the deviation and the interpolation step; The calculation unit calculates the interpolation step and deviation value by receiving the data provided by the data processing module, and combines the curve geometric characteristics and machining speed, using the second-order Taylor expansion method; this unit dynamically adjusts the step, reducing the calculation amount to improve efficiency in simple curve segments, increasing the calculation accuracy in complex curve segments to avoid undercutting or overcutting phenomena, and at the same time ensuring that the deviation value meets the preset accuracy requirements through an error control mechanism, providing accurate calculation results for subsequent interpolation control, and achieving the machining goals of high precision and high efficiency.

[0073] A judgment unit, which is used to perform deviation and precision parameter comparisons, and is used to judge the difference between the specific coordinate position of the interpolation point and the target end coordinate position and the precision parameter comparisons; Judge the deviation With the precision parameter in size, when the deviation is greater than the precision parameter , calculate a new deviation Δ; when the deviation is less than or equal to the precision parameter , determine the interpolation step size; Determine the interpolation step size and output to obtain the specific coordinate position of the next interpolation point; Substitute the parameter value in the parameter densification process into the given curve parameterization equation to obtain the specific coordinate position of the next interpolation point, that is: ; Judge the difference between the specific coordinate position of the interpolation point and the target end coordinate position. If the difference is less than the precision parameter , complete the interpolation and output the objective function P; The judgment unit receives the deviation value and interpolation step size data provided by the calculation unit, combines the preset precision parameter, and compares the size of the deviation value with the precision parameter. If the deviation value is greater than the precision parameter, the interpolation step size is dynamically adjusted through the iterative strategy until the deviation value meets the precision requirements; at the same time, the unit judges whether the interpolation is completed by comparing the difference between the specific coordinate position of the interpolation point and the target end coordinate position. If the difference is less than the precision parameter, it outputs the objective function to complete the interpolation, otherwise it continues the iterative calculation to ensure the high precision and high efficiency of the processing process.

[0074] Embodiment 3: The present application provides a computer-readable storage medium. The computer-readable storage medium includes a stored program. Among them, when the program runs, it controls the device where the computer-readable storage medium is located to execute the adaptive step interpolation method for machine tool precision machining described in Embodiment 1.

[0075] It can be understood that the systems, devices, modules or units described in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer, and the specific form of the computer can be a personal computer, a laptop computer, a personal digital assistant, a tablet computer, a wearable device, or a combination of any several of these devices.

[0076] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be used to store information by any method or technology. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include temporary computer-readable media (transitory media), such as modulated data signals and carrier waves.

[0077] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0078] The above is a description of a specific embodiment of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0079] The terms used in one or more embodiments of this specification are only for the purpose of describing specific embodiments, and are not intended to limit one or more embodiments of this specification. The singular forms of "a", "said" and "the" used in one or more embodiments of this specification and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0080] It should be understood that although the terms first, second, third, etc. may be used in one or more embodiments of this specification to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from each other. For example, without departing from the scope of one or more embodiments of this specification, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "when" or "while" or "in response to determining".

[0081] The foregoing are only preferred embodiments of one or more embodiments of this specification and are not intended to limit one or more embodiments of this specification. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of one or more embodiments of this specification shall be included within the scope protected by one or more embodiments of this specification.

Claims

1. An adaptive step interpolation method for precision machining of machine tools, characterized in that, It includes the following steps: Step S1: Obtain the parametric curve S(u) set in the numerical control program and set the corresponding initial parameters; The initial parameters include the curve parameter u, the feed rate V, and the precision parameter and the initial interpolation step T, where the curve parameter u is a function of time t; Step S2: Perform a second-order Taylor expansion on the curve parameter u at t = to solve for the initial interpolation step T based on the feed rate V, and calculate the curve parameter at t = . The initial value of i is 1; ​ Step S3: Calculate the truncation error between the interpolation parameter and the interpolation step T when calculating the interpolation step T, and solve If , jump to step S5; If Execute step S4; Step S4: Perform a second-order Taylor expansion on the curve parameter u at t = . Based on the feed rate V, let T = , and execute Step S3; Step S5: Determine whether the interpolation is completed. When the interpolation is completed, perform trajectory calculation based on the calculated curve parameters and output the interpolated curve function; Otherwise, let i = i + 1 and jump to Step S2.

2. The adaptive step interpolation method for precision machining of machine tools according to claim 1, characterized in that In Step S2, perform second-order Taylor expansion of u at t = ti, and we can get: where HOT is the high-order term in the Taylor expansion.

3. The adaptive step interpolation method for precision machining of machine tools according to claim 2, wherein In step S2, the interpolation step size T = ti+1 - ti, and its calculation formula is solved by the second-order Taylor expansion method: wherein is the curve parameter at t = ti + 1; is the curve parameter at t = ti; is the feed rate at t = ti; S(u) = (x(u), z(u)), where x(u) and z(u) are the abscissa and ordinate corresponding to the curve parameter u respectively.

4. The adaptive step interpolation method for precision machining of machine tools according to claim 3, wherein, Derive the parametric curve S(u) with respect to the curve parameter u: And the feed step size △Li in the interpolation period = ViT, and we can get: 。 5. The adaptive step interpolation method for precision machining of machine tools according to claim 1, wherein In step S3, , where is the derivative of the curve parameter at t = ti+1 with an interpolation step size of , and is the derivative of the curve parameter at t = ti with an interpolation step size of .

6. The adaptive step interpolation method for precision machining of machine tools according to claim 1, characterized in that, In Step S5, substitute the parameter values in the parameter densification process into the given curve parametric equation to obtain the specific coordinate position of the next interpolation point, that is: ； where P is the objective function and Pi+1 is the target point at t = ti+1.

7. The adaptive step interpolation method for precision machining of machine tools according to claim 6, wherein In step S5, calculate and determine the difference between the specific coordinate position of the interpolation point and the target end coordinate position. If the difference is less than the precision parameter , then complete the interpolation and output the objective function P; otherwise, set i = i + 1 and jump to step S2.

8. An adaptive step interpolation system for precision machining of machine tools, characterized in that, It includes: A data acquisition module for obtaining the parametric curve and initial parameters set in the numerical control program; A data processing module for receiving the data from the data acquisition module and calculating the objective function according to the data.

9. The adaptive step size interpolation system for precision machining of machine tools according to claim 8, characterized in that The data processing module includes a calculation unit and a judgment unit: A calculation unit for calculating according to data and interpolation step size; A judgment unit for performing comparisons with a precision parameter and for judging the difference between the specific coordinate position of an interpolation point and the target end coordinate position and the precision parameter in terms of magnitude.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein when the program runs, it controls the device where the computer-readable storage medium is located to execute the adaptive step size interpolation method for precision machining of machine tools according to any one of claims 1-7.

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