A self-adaptive step interpolation method, system and medium for precision machining of a machine tool

Abstract

The application is a kind of self-adaptive step interpolation method, system and medium for precision machining of machine tool, belonging to the field of precision numerical control machine tool, comprising the following steps: S1, obtaining the parameterized curve set in the numerical control program, setting the corresponding initial parameters; S2, solving the initial interpolation step based on the feed speed; S3, calculating under the interpolation step T, if, jump to S5; if execute S4; S4, let T=, execute S3; S5, judge whether the interpolation is completed, when the interpolation is completed, calculate the trajectory based on the calculated curve parameters and output the curve function after difference compensation; otherwise, let i=i+1 and jump to S2. Through dynamic adjustment of the interpolation step, real-time balance of calculation accuracy and efficiency is realized, which can not only avoid redundant calculation of simple curve segments, but also ensure the machining accuracy of complex curve segments through step adaptive optimization.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of precision numerical control machine tools, and particularly relates to a self-adaptive step interpolation method, system and medium for precision machining of machine tools. BACKGROUND

[0002] The interpolation method of a numerical control machine tool is one of the core technologies for realizing high-precision machining. It generates smooth motion trajectories through mathematical calculation of the path set in the numerical control program, thereby significantly improving the quality and accuracy of the machined surface. With the continuous progress of computer technology and algorithms, interpolation methods are increasingly widely used in numerical control technology, becoming an important driving force for the development of manufacturing towards high precision and high efficiency. Interpolation technology not only optimizes the motion path of the tool, but also effectively reduces vibration and errors in the machining process, providing reliable technical support for the machining of complex parts.

[0003] With the continuous development of manufacturing, the requirements for machining precision and efficiency are increasingly high, and the traditional machining method has been difficult to meet the needs of modern production. In the prior art, in order to solve this problem, a parameter interpolation algorithm is used to realize interpolation technology. The parameter interpolation algorithm includes differential equation numerical method and iterative approximation method, etc. to perform parameter interpolation technology in numerical control machine tools. The differential equation numerical method determines the motion trajectory of the curve by solving the differential equation; the iterative approximation method gradually approximates the true curve shape through continuous iterative calculation.

[0004] However, there are still some problems in the parameter interpolation technology in the prior art. The parameter interpolation algorithm such as the differential equation numerical method and the iterative approximation method lacks adaptability, making it difficult to dynamically balance the calculation precision and efficiency. It uses fixed step size or pre-set iteration threshold and other rigid parameter settings, which cannot adjust the calculation strategy in real time according to the curve curvature change and the processing speed requirement, resulting in redundant calculation and resource waste in simple curve segments, and under-cut or over-cut defects caused by insufficient precision in complex curve segments. SUMMARY

[0005] The application proposes a numerical control machine tool interpolation method based on an adaptive parameter interpolation algorithm. The method can dynamically adjust the interpolation step size and the iteration threshold, and can optimize the calculation strategy in real time according to the curve curvature change and the processing speed requirement, thereby ensuring the precision while improving the calculation efficiency. In addition, the application also introduces an error control mechanism, which compares the deviation value with the precision parameter to dynamically adjust the interpolation step size, ensuring the stability and reliability of the machining process. Through the above technical solutions, the application can effectively solve the problem of balancing the precision and efficiency in the existing parameter interpolation algorithm, and provides comprehensive technical support for high-precision machining.

[0006] The technical scheme adopted by the application is as follows:

[0007] In a first aspect, the present application provides an adaptive step-size interpolation method for precision machining of machine tools, comprising the following steps:

[0008] Step S1, obtaining the parameterized curve S(u) set in the NC program and setting the corresponding initial parameters;

[0009] The initial parameters include curve parameter u, feed speed V, accuracy parameter and the initial interpolation step size T, where the curve parameter u is a function of time t;

[0010] Step S2: Set the curve parameter u at t= Perform the second-order Taylor expansion at the position, solve the initial interpolation step T based on the feed rate V, and calculate t= Curve parameters at time , the initial value of i is 1;

[0011] Step S3: Calculate the interpolation parameters and the truncation error of the interpolation step length T, and solve ,like , jump to step S5;

[0012] like Execute step S4;

[0013] Step S4: Set the curve parameter u at t= Perform the second-order Taylor expansion at the feed rate V, and let T= , execute step S3;

[0014] Step S5: Determine whether the interpolation is completed. If the interpolation is completed, perform trajectory calculation based on the calculated curve parameters and output the interpolated curve function; otherwise, set i=i+1 and jump to step S2.

[0015] Preferably, in step S2, The calculation formula is solved using the second-order Taylor expansion method:

[0016]

[0017] in is the curve parameter at t=ti+1; is the curve parameter at t=ti; is the feed rate at t=ti;

[0018] S(u)=(x(u),z(u)), where x(u) and z(u) are the horizontal and vertical coordinates corresponding to the curve parameter u respectively.

[0019] Preferably, The calculation formula includes the following process:

[0020] u at t = ti, a second order Taylor expansion gives:

[0021]

[0022] where HOT is the higher order term in the Taylor expansion;

[0023] The first derivative of the parametric curve S(u) with respect to the time parameter t gives:

[0024]

[0025] The first derivative of the parameter u with respect to the time parameter t is:

[0026]

[0027] Differentiating the above equation again with respect to the time parameter t gives the second derivative of the curve parameter u with respect to the time parameter t:

[0028]

[0029] In the above equation:

[0030]

[0031]

[0032] gives:

[0033]

[0034] Since the interpolation step T = ti+1- ti, we have:

[0035] .

[0036] Preferably, the derivative of the parametric curve S(u) with respect to the curve parameter u is:

[0037]

[0038]

[0039] and the feed step in the interpolation period ΔLi= ViT, we have:

[0040] .

[0041] Preferably, in step S3, let ui be the starting node, T be the interpolation step for solving the next curve parameter ui+1approximation, the truncation error of the second order Taylor expansion method is O(T3), which is expressed as:

[0042]

[0043] where for the Taylor expansion method, the truncation error of the n-th order Taylor method is O(Tn+1);

[0044] The step size T is halved and the next curve parameter ui+1 is calculated at the starting node ui in two steps with step size T / 2. The stage error of each step can be expressed as Thus:

[0045]

[0046] When the interpolation step size is halved, the error is reduced to about 1 / 4:

[0047]

[0048] The equation is modified equivalently to obtain

[0049]

[0050] The Δ between the calculation results is obtained as

[0051] where is the derivative of the curve parameter at t = ti+1, interpolation step size is the derivative of the curve parameter at t = ti, interpolation step size .

[0052] Preferably, in step S5, the parameter value in the parameter densification process is brought into the given curve parameterization equation to obtain the specific coordinate position of the next interpolation point, i.e.

[0053] ;

[0054] where P is the objective function, and Pi+1 is the objective point at i+1 step.

[0055] Preferably, in step S5, the difference between the specific coordinate position of the interpolation point and the coordinate position of the target end point is judged. If the difference is less than the precision parameter , the interpolation is completed and the objective function P is output; otherwise, i = i + 1 is given and the step S2 is jumped.

[0056] In a second aspect, the present application provides a self-adaptive step size interpolation system for precision machining of machine tools, comprising:

[0057] A data acquisition module is configured to acquire a parameterized curve and initial parameters set in a numerical control program.

[0058] ​A data processing module is configured to receive the data from the data acquisition module and calculate a target function based on the data.

[0059] Preferably, the data processing module comprises a calculation unit and a judgment unit.

[0060] The calculation unit is configured to calculate a deviation and an interpolation step length based on the data.

[0061] The judgment unit is configured to determine the size of the deviation and an accuracy parameter and determine whether the difference between the specific coordinate position of the interpolation point and the target end coordinate position is greater than the accuracy parameter.

[0062] In a third aspect, the present application provides a computer readable storage medium, characterized in that the computer readable storage medium comprises a stored program, wherein the program controls the device where the computer readable storage medium is located to execute the machine tool precision machining adaptive step interpolation method of the first aspect when the program is running.

[0063] From the above technical solutions, the present application has the following advantages:

[0064] 1. By dynamically adjusting the interpolation step length, the real-time balance of calculation accuracy and efficiency is achieved, which can avoid redundant calculation of simple curve segments and ensure the machining accuracy of complex curve segments through step adaptive optimization, effectively solve the overcut and undercut problems caused by traditional fixed step length methods, adapt to the needs of different machining scenes, and improve the overall performance of the numerical control machine tool.

[0065] 2. The second-order Taylor expansion method is used to calculate the parameter increment, which significantly reduces the algorithm complexity under the premise of retaining sufficient calculation accuracy, avoids the exponential growth of calculation amount caused by high-order Taylor expansion, balances the interpolation efficiency and accuracy, and reduces the intermediate conversion error through direct mapping of the parameterized curve coordinates.

[0066] 3. Through the complete derivation of the second-order Taylor expansion formula and the truncation of high-order terms, the calculation process is simplified, the trajectory dynamic prediction is realized by using the derivative relationship between the time parameter and the curve parameter, the calculation resource consumption is reduced, the real-time matching of the interpolation step length and the curvature change is ensured, and the trajectory smoothness of the complex curve is improved.

[0067] 4. By calculating the first derivative of the parameterized curve with respect to the curve parameter, the feed step length and the curve geometric characteristics are directly related, the dynamic coupling of the velocity and the curvature is realized, the trajectory deviation caused by the decoupling of the geometric characteristics and the motion parameters in the traditional method is avoided, and the continuity and stability of the machining trajectory are enhanced.

[0068] ​5、By step size halving method quantization truncation error and dynamic adjustment of step size, the mathematical mapping relationship between error and step size is established, which can quickly converge to the target accuracy, avoid the blindness of artificial preset step size, realize the optimal allocation of computing resources, and is especially suitable for precise interpolation of mutation curvature or high nonlinear curve.

[0069] 6、Through the parameter densification process, the interpolation point coordinates are directly output, the intermediate parameter conversion link is reduced, the cumulative error risk is reduced, and the direct solving of the parameterized equation is combined to ensure that the interpolation points strictly follow the mathematical definition of the curve and improve the theoretical consistency of the machining trajectory; the interpolation process is dynamically terminated by the difference value of the end point coordinates to prevent the end point deviation problem caused by excessive iteration or early termination, ensure that the machining path completely covers the target curve, and avoid the residual error of the path end point caused by the fixed step size in the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the present application, 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 application, and other drawings can be obtained by those skilled in the art without creative labor.

[0071] Figure 1 The flowchart of the adaptive step interpolation method for precise machining of machine tools in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0072] In the following detailed description, various embodiments of the present disclosure will be described more fully. 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 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 alternatives falling within the spirit and scope of various embodiments of the present disclosure.

[0073] The following are some explanations of terms in the present scheme to facilitate better understanding of the present scheme:

[0074] 1、Interpolation

[0075] Interpolation is a key technology in numerical control machine tools, which is used to generate smooth motion trajectories according to the path set in the numerical control program. Through mathematical calculation, interpolation technology connects discrete machining points into continuous curves or straight lines, so as to ensure the accuracy of the movement trajectory of the tool in the machining process. Interpolation method directly affects the quality and accuracy of the machining surface, and is one of the core technologies of modern high-precision machining. With the development of computer technology and algorithm, interpolation technology is continuously optimized, from traditional linear and circular interpolation to more complex parameterized interpolation, to meet the needs of manufacturing industry for high precision and high efficiency.

[0076] 2. Taylor's expansion method

[0077] Taylor's expansion method is a mathematical tool used to approximate complex functions as polynomials. In interpolation techniques, Taylor's expansion method can be used to locally approximate parameterized curves, simplifying the calculation process and improving interpolation accuracy. Through Taylor's expansion, a high-order approximation of a function can be obtained near a certain point on the curve, thereby optimizing the selection of interpolation steps.

[0078] 3. Parameterized curve

[0079] Parameterized curve is a curve described by a parameter equation, commonly used in numerical control machine tool interpolation techniques. Unlike traditional explicit or implicit equations, parameterized curves define the coordinates of each point on the curve by introducing a parameter variable (such as time or path length). This representation method has strong flexibility and wide applicability, and can accurately describe complex three-dimensional curves and surfaces. In interpolation techniques, parameterized curves provide a mathematical basis for smooth tool movement, allowing the machining trajectory to better adapt to complex geometric shapes.

[0080] 4. Interpolation step

[0081] Interpolation step refers to the distance or time interval that the tool moves from one machining point to the next during interpolation. The choice of interpolation step directly affects machining accuracy and efficiency: a large step size will result in rough machining surfaces, while a small step size will increase computational load and reduce machining efficiency. In parameter interpolation techniques, the optimization of interpolation step is a key issue, especially in 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.

[0082] 5. HOT (High-Order Term)

[0083] High-order term in Taylor's expansion refers to the terms of higher powers (such as cubic, quartic, and higher) in addition to low-order terms (such as constant, linear, and quadratic) during Taylor's expansion process. These high-order terms are used to more accurately describe the behavior of the function near that point, especially in areas where the function changes rapidly or has high curvature. The introduction of high-order terms can improve the approximation accuracy of Taylor's expansion, but as the order increases, the computational complexity will also significantly increase, so in practical applications, the appropriate expansion order needs to be selected according to the balance between accuracy requirements and computational efficiency.

[0084] The application provides a numerical control machine tool interpolation method based on an adaptive parameter interpolation algorithm.

[0085] Embodiment one:

[0086] The application provides an adaptive step interpolation method for precise machining of machine tools, as shown in Figure 1 The method comprises the following steps:

[0087] Step S1, obtaining a parameterized curve S(u) set in a numerical control program, and setting corresponding initial parameters;

[0088] In actual operation, when the parameterized curve S(u) is obtained, the mathematical expression of the curve is extracted in the G code of the numerical control program or the CAM software, for example, Bezier curve, B-spline curve or NURBS curve. These curves usually take parameter u as a variable.

[0089] The initial parameters include curve parameter u, time parameter t, feed speed V, accuracy parameter and interpolation step T;

[0090] Step S2, performing second-order Taylor expansion of the curve parameter u at t= , solving the initial interpolation step T based on the feed speed V, and calculating the curve parameter at t= , and i is an initial value of 1;

[0091] In step S2, the calculation formula of is solved by using the second-order Taylor expansion method:

[0092] The calculation formula of

[0093] The second-order Taylor expansion of u at t=ti can be obtained as follows:

[0094]

[0095] Wherein HOT is a high-order term in the Taylor expansion;

[0096] The first-order derivative of the parameterized curve S(u) with respect to the time parameter t can be obtained as follows:

[0097]

[0098] The first derivative of the parameter u with respect to the time parameter t is:

[0099]

[0100] Differentiating the above equation again with respect to the time parameter t, the second derivative of the curve parameter u with respect to the time parameter t is obtained:

[0101]

[0102] In the above equation:

[0103]

[0104]

[0105] Thus:

[0106]

[0107] Since the interpolation step T = ti+1-ti, it can be obtained that:

[0108] .

[0109] Differentiating the parameterized curve S(u) with respect to the curve parameter u:

[0110]

[0111]

[0112] And the feed step △Li=ViT in the interpolation period, it can be obtained that:

[0113] ;

[0114]

[0115] Wherein is the curve parameter at t = ti+1; is the curve parameter at t = ti; is the feed speed at t = ti;

[0116] S(u) = (x(u), z(u)). Wherein x(u), z(u) are the horizontal coordinate and vertical coordinate corresponding to the curve parameter u, respectively;

[0117] The second-order Taylor expansion method is used to calculate the parameter increment, which significantly reduces the algorithm complexity under the premise of sufficient calculation precision, avoids the exponential growth of calculation amount caused by high-order Taylor expansion, balances the interpolation efficiency and accuracy, and reduces the intermediate conversion error through direct mapping of the parameterized curve coordinates.

[0118] Meanwhile, the complete derivation of the second-order Taylor expansion formula and the truncation of high-order terms simplify the calculation process, and the derivative relationship between the time parameter and the curve parameter is used to realize trajectory dynamic prediction, which reduces the consumption of calculation resources while ensuring the real-time matching of interpolation step and curvature change and improving the trajectory smoothness of complex curves.

[0119] In step S3, the truncation error of the interpolation parameter and the interpolation step T when calculating the interpolation step T is calculated as follows: If , jump to step S5;

[0120] If , execute step S4;

[0121] In step S3, let ui be the starting node, T be the interpolation step for solving the next curve parameter ui+1 approximation, and the truncation error of the second-order Taylor expansion method be O(T3), which is expressed as follows:

[0122]

[0123] Wherein, for the Taylor expansion method, the truncation error of the n-order Taylor method is O(Tn+1);

[0124] The step length T is halved, and the step length T / 2 is used to calculate the next curve parameter ui+1 at the starting node ui in two steps, and the phase error of each step can be expressed as Therefore:

[0125]

[0126] When the interpolation step is halved, the error is reduced to about 1 / 4:

[0127]

[0128] The equation is modified equivalently to obtain:

[0129]

[0130] The deviation Δ between the calculation results is:

[0131] ;

[0132] Wherein is the interpolation step at t=ti+1 derivative of the curve parameter at t, derivative of the curve parameter at t, derivative of the curve parameter at t;

[0133] Step S4, performing a second-order Taylor expansion of the curve parameter u at t= based on the feed speed V, letting T= , executing step S3;

[0134] The first derivative calculation of the curve parameter through the parameterized curve directly links the feed step and the curve geometric characteristics, realizes the dynamic coupling of the speed and the curvature, avoids the trajectory deviation caused by the decoupling of the geometric characteristics and the motion parameters in the traditional method, and enhances the continuity and stability of the machining trajectory.

[0135] The step length is halved to quantify the truncation error and dynamically adjust the step length, and a mathematical mapping relationship between the error and the step length is established, which can quickly converge to the target accuracy and avoid the blindness of manually presetting the step length, realizes the optimal allocation of computing resources, and is especially suitable for precise interpolation of mutation curvature or high nonlinear curve.

[0136] Directly outputting the interpolation point coordinates through the parameterization process reduces the intermediate parameter conversion link and reduces the risk of cumulative error, and at the same time, combining the direct solution of the parameterized equation ensures that the interpolation points strictly follow the mathematical definition of the curve, and improves the theoretical consistency of the machining trajectory; dynamically terminating the interpolation process through the difference value of the end point coordinates prevents the end point deviation problem caused by excessive iteration or early termination, ensures that the machining path completely covers the target curve, and avoids the residual error at the end of the path caused by the fixed step length in the traditional method.

[0137] Step S5, judging whether the interpolation is completed, when the interpolation is completed, calculating the trajectory based on the calculated curve parameter and outputting the curve function after difference interpolation; otherwise, letting i=i+1 and jumping to step S2;

[0138] In step S5, the parameter value in the parameterization process is brought into the given curve parameterization equation, and the specific coordinate position of the next interpolation point can be obtained, that is:

[0139] ;

[0140] Wherein, P is the target function, and Pi+1 is the target point at i+1 step;

[0141] Judging the difference value between the specific coordinate position of the interpolation point and the target end point coordinate position, if the difference value is less than the accuracy parameter , the interpolation is completed and the target function P is output; otherwise, given i=i+1 and jump to step S2.

[0142] By dynamically adjusting the interpolation step, the real-time balance of calculation accuracy and efficiency is realized, which can avoid redundant calculation of simple curve segments and ensure the machining precision of complex curve segments through step adaptive optimization, effectively solve the overcut and undercut problems caused by traditional fixed step method, adapt to the needs of different machining scenes, and improve the overall performance of numerical control machine tools.

[0143] Embodiment two:

[0144] The application provides a self-adaptive step interpolation system for precision machining of machine tools, comprising:

[0145] The data acquisition module is configured to obtain a parameterized curve and initial parameters set in a numerical control program.

[0146] The data acquisition module extracts key information such as the type of parameterized curve, control points, and node vectors by analyzing the geometric instructions in the numerical control program, and obtains the parameter domain of the curve. The setting of initial parameters includes the starting point of the curve, the starting point of time, the feed speed, the accuracy requirement, and the interpolation step. These parameters are configured according to the specific needs of the machining task to provide basic data support for subsequent interpolation calculation.

[0147] This module ensures the accuracy and stability of the machining process through data extraction and parameter configuration, and can dynamically adjust the parameters according to the actual machining requirements to provide reliable technical support for the machining of complex curves.

[0148] The data processing module is configured to receive data from the data acquisition module and calculate a target function based on the data.

[0149] The data processing module receives the parameterized curve information and initial parameters provided by the data acquisition module, integrates and analyzes the data based on the specific needs of the machining task, and calculates the specific value of the target function. This module uses efficient calculation algorithms to ensure the accuracy and real-time performance of the data processing process, and can dynamically adjust the calculation strategy according to the curve curvature change and machining speed to provide reliable data support for subsequent interpolation control and achieve high-precision and high-efficiency machining goals.

[0150] The data processing module in this embodiment includes a calculation unit and a judgment unit:

[0151] The calculation unit is configured to calculate a deviation based on the data and the interpolation step;

[0152] The computing unit calculates the interpolation step and the deviation value by receiving the data provided by the data processing module, combining the curve geometric characteristics and the processing speed, and using the second-order Taylor expansion method; the unit reduces the calculation amount in the simple curve segment to improve the efficiency by dynamically adjusting the step, increases the calculation precision in the complex curve segment to avoid the under-cutting or over-cutting phenomenon, and at the same time, through the error control mechanism, ensures that the deviation value meets the preset precision requirement, provides accurate calculation results for the subsequent interpolation control, and realizes the processing goal of high precision and high efficiency.

[0153] The judging unit is used for judging the size of the deviation and the precision parameter , and judging the size of the difference between the specific coordinate position of the interpolation point and the target terminal coordinate position and the precision parameter .

[0154] The deviation is judged and the precision parameter , when the deviation is greater than the precision parameter , the calculation of the new deviation Δ is carried out; when the deviation is less than or equal to the precision parameter , the determination of the interpolation step is carried out.

[0155] The interpolation step is determined, and the is outputted to obtain the specific coordinate position of the next interpolation point.

[0156] The parameter value in the parameter densification process is brought into the given curve parameterization equation, and the specific coordinate position of the next interpolation point can be obtained, that is:

[0157]

[0158] The difference between the specific coordinate position of the interpolation point and the target terminal coordinate position is judged, if the difference is less than the precision parameter , the interpolation is completed and the target function P is outputted.

[0159] The judging unit receives the deviation value and the interpolation step data provided by the computing unit, compares the size of the deviation value and the precision parameter, if the deviation value is greater than the precision parameter, the interpolation step is dynamically adjusted through the iteration strategy until the deviation value meets the precision requirement; 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 terminal coordinate position, if the difference is less than the precision parameter, the target function is outputted to complete the interpolation, otherwise the iteration calculation is continued to ensure the high precision and high efficiency of the processing process.

[0160] Embodiment three:

[0161] The application provides a computer readable storage medium, which comprises a stored program, wherein the computer readable storage medium controls a device where the computer readable storage medium is located to execute the adaptive step interpolation method for precision machining of a machine tool according to the embodiment I when the program is running.

[0162] It can be understood that the systems, apparatuses, modules or units illustrated by 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 specific forms 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 of these devices.

[0163] The computer readable medium includes permanent and non-permanent, removable and non-removable media, which can be implemented by any method or technology to store information. The 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 technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, disk storage, quantum memory, graphene-based storage medium or other magnetic storage device, or any other non-transmission medium that can be used to store information accessible by a computing device. According to the definition herein, the computer readable medium does not include transitory computer readable media such as modulated data signals and carriers.

[0164] It should also be noted that the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusion, so that processes, methods, articles or devices including a series of elements not only include those elements, but also include other elements not explicitly listed, or other elements inherent in such processes, methods, articles or devices. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0165] The above-described embodiments of the application have been described in connection with what are presently considered to be the most practical and preferred implementations, but are not intended to be limited to the specific forms set forth. Rather, the scope of the application should be determined only by the claims that follow. Furthermore, it should be understood that where the application is identified or described herein as comprising certain features, such retention of the word "comprising" is intended to mean that 100% of the product "comprises" the

[0166] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of one or more embodiments of the disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0167] It will be understood that, although the terms first, second, third, etc. can be used herein to describe various information, the information should not be limited by these terms. These terms are only used to distinguish one piece of information from another. For example, a first information could be termed a second information, and, similarly, a second information could be termed a first information without departing from the scope of one or more embodiments. As used herein, the term "if' can be construed to mean "when" or "in response to determining" or "in response to a determination" depending on the context.

[0168] The foregoing is considered as illustrative only of the principles of the one or more embodiments. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the one or more embodiments to the exact one or more embodiments illustrated and described. Accordingly, all such variations are intended to be included within the scope of one or more embodiments of the present disclosure. The disclosure has been provided in connection with what are presently felt and considered to be the most practical and preferred embodiments. However, it is understood that no limitation of the scope of the one or more embodiments is actually intended or is to be inferred from any specific description herein. Accordingly, the one or more embodiments are intended to embrace all available alternatives, modifications, equivalents, and alternatives falling within the spirit and scope of the one or more embodiments.

Claims

1. An adaptive step-size interpolation method for precision machining of machine tools, characterized in that: The following steps are involved: Step S1, obtaining the parameterized curve S(u) set in the NC program and setting the corresponding initial parameters; The initial parameters include curve parameter u, feed speed V, accuracy parameter and the initial interpolation step size T, where the curve parameter u is a function of time t; Step S2: Set the curve parameter u at t= Perform the second-order Taylor expansion at the position, solve the initial interpolation step T based on the feed rate V, and calculate t= Curve parameters at time , the initial value of i is 1; u at t = t i In the second-order Taylor expansion, we can get: Where HOT is the higher-order term in Taylor expansion; Step S3: Calculate the interpolation parameters and the truncation error of the interpolation step length T, and solve ; Let u i is the starting node, T is the solution for the next curve parameter u i+1 The interpolation step size of the approximation value, the truncation error of the second-order Taylor expansion method is O(T 3 ), which is expressed as follows: For the Taylor expansion method, the truncation error of the n-order Taylor method is O(T n+1 ); Halve the step length T and use step length T / 2 to start at the starting node u in two steps. i Calculate the next curve parameter u i+1 , the truncation error at each step can be expressed as ,therefore: When the interpolation step size is halved, the error is reduced to about 1 / 4: For the equation Make equivalent modifications to obtain: The deviation Δ between the calculated results is obtained as: ； in For t=t i+1 , the interpolation step length is Time curve parameters, For t=t i+1 , the interpolation step length is Time curve parameters; like , jump to step S5; like Execute step S4; Step S4: Set the curve parameter u at t= Perform the second-order Taylor expansion at the feed rate V, and let T= , execute step S3; Step S5: determining whether the interpolation is completed. If the interpolation is completed, performing trajectory calculation based on the calculated curve parameters and outputting the interpolated curve function; Otherwise, set i=i+1 and jump to step S2.

2. The adaptive step-size interpolation method for precision machining of machine tools according to claim 1, characterized in that: In step S2, the interpolation step length T=t i+1 -t i , The calculation formula is solved using the second-order Taylor expansion method: in For t=t i+1 Curve parameters when ; For t=t i Curve parameters when ; For t=t i Feed rate at 1000 rpm; S(u)=(x(u),z(u)), where x(u) and z(u) are the horizontal and vertical coordinates corresponding to the curve parameter u respectively.

3. The adaptive step-size interpolation method for precision machining of machine tools according to claim 2, characterized in that: Find the derivative of the parameterized curve S(u) with respect to the curve parameter u: And the feed step length △L in the interpolation cycle i =V i T, we can get: 。 4. The adaptive step-size interpolation method for precision machining of machine tools according to claim 1, characterized in that: In step S5, the parameter values ​​in the parameter densification process are brought into the given curve parameterization equation to obtain the specific coordinate position of the next interpolation point, namely: ； Among them, P is the objective function, P i+1 For t=t i+1 The target point at the time.

5. The adaptive step-size interpolation method for precision machining of machine tools according to claim 4, characterized in that: In step S5, the difference between the specific coordinate position of the interpolation point and the coordinate position of the target end point is calculated and determined. If the difference is less than the accuracy parameter , then the interpolation is completed and the objective function P is output; otherwise, i=i+1 is given and the process jumps to step S2.

6. A computer-readable storage medium, characterized in that The computer-readable storage medium includes a stored program, wherein when the program is run, the device where the computer-readable storage medium is located is controlled to execute the adaptive step-size interpolation method for machine tool precision machining according to any one of claims 1 to 5.

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