Numerical control machine tool motion error diagnosis method based on three-dimensional phase space reconstruction

Abstract

The invention belongs to the field of numerical control machine tool motion error identification, and particularly relates to a numerical control machine tool motion error diagnosis method based on three-dimensional phase space reconstruction, which comprises the following steps: S0, establishing an error component mathematical model; the method comprises the following steps: S1, for each type of errors, generating a one-dimensional standard motion error time sequence only containing the single type of errors; s2, calculating phase space reconstruction parameters and performing phase space reconstruction to obtain a high-dimensional reconstruction track; drawing and generating a standard three-dimensional phase space reconstruction diagram of each type of errors according to a preset method; s3, controlling a motion axis of the numerical control machine tool to be diagnosed, and forming a one-dimensional actual motion error time sequence; s4, generating an actually measured three-dimensional phase space reconstruction diagram of the machine tool to be diagnosed by using the same method in S2; and S5, comparing the actually measured three-dimensional phase space reconstruction diagram with each standard three-dimensional phase space reconstruction diagram in the S2. According to the method, rapid and accurate diagnosis of motion errors of various numerical control machine tools can be realized under the condition that extra cost is not increased.

Description

Technical Field

[0001] This invention belongs to the field of motion error identification of CNC machine tools, and particularly relates to a method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction. Background Technology

[0002] As core equipment in the equipment manufacturing industry, CNC machine tools directly reflect a country's manufacturing development level. During the manufacturing process, motion errors, including geometric and control errors of the CNC machine tool, have a crucial impact on machining accuracy. Therefore, quickly and effectively identifying the motion errors of CNC machine tools is of paramount importance for improving machine tool precision.

[0003] Currently, methods for identifying motion errors in CNC machine tools mainly include techniques such as ballbars, laser interferometers, and R-tests. However, each of these methods has certain limitations: on the one hand, they often rely on specific types of CNC machine tools, which limits their versatility and application scope; on the other hand, these measurement methods usually require a long time to complete, which is not ideal for modern manufacturing industries that pursue high-efficiency production. Furthermore, due to the nonlinear interactions between various components during the operation of CNC machine tools, the motion errors exhibit complex nonlinear behavior, further increasing the difficulty of error diagnosis.

[0004] The problems with the aforementioned existing technologies stem primarily from two factors. First, traditional methods are ill-suited for different models and specifications of CNC machine tools, meaning each machine tool may require a customized solution, increasing cost and complexity. Second, traditional detection methods cannot effectively capture and analyze complex motion error patterns caused by nonlinear interactions, making accurate diagnosis exceptionally difficult. As CNC machine tools evolve towards higher speed and precision, achieving effective monitoring and accurate diagnosis of machine tool motion errors without impacting production efficiency has become an extremely challenging task.

[0005] Therefore, how to achieve rapid and accurate diagnosis of motion errors in various CNC machine tools without increasing additional costs has become an urgent problem to be solved. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the existing technology, the purpose of this invention is to provide a method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction, which can achieve rapid and accurate diagnosis of motion errors of various CNC machine tools without increasing additional costs.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A method for diagnosing motion errors in CNC machine tools based on three-dimensional phase space reconstruction includes the following steps:

[0009] S0. Based on the ideal circular motion performed by the CNC machine tool on the plane, establish corresponding mathematical models of error components for various error types of the CNC machine tool, which are used to calculate the position deviation caused by the corresponding type of error under an ideal circular trajectory of arbitrary radius.

[0010] S1. Set a sequence containing 2N equally spaced angle values ​​to represent a complete diagnostic cycle, where the first N angle values ​​correspond to clockwise circular motion and the last N angle values ​​correspond to counterclockwise circular motion; Based on the mathematical models of various error components established in S0, for each type of error, take the 2N angle values ​​as input and calculate the theoretical position deviation value generated under ideal circular motion conditions, thereby generating a one-dimensional standard motion error time series containing only this single type of error;

[0011] S2. For each type of error in the one-dimensional standard motion error time series obtained in S1, the phase space reconstruction parameters are calculated using a preset algorithm and the phase space is reconstructed to obtain the high-dimensional reconstruction trajectory. Based on the high-dimensional reconstruction trajectory, a standard three-dimensional phase space reconstruction diagram of each type of error is generated according to a preset method. The phase space reconstruction parameters include the optimal delay time and the embedding dimension.

[0012] S3. Control the motion axes of the CNC machine tool to be diagnosed to perform one clockwise circular motion and one counterclockwise circular motion in sequence on the plane; during the motion, synchronously collect the actual position coordinates of the machine tool, and calculate the actual motion error value according to the geometric relationship between the actual position coordinates and the corresponding ideal circular trajectory; arrange the actual motion error values ​​in the motion sequence to form a one-dimensional actual motion error time series of length 2N, where the first N data points correspond to the clockwise motion stage and the last N data points correspond to the counterclockwise motion stage;

[0013] S4. For the one-dimensional actual motion error time series obtained in S3, calculate its optimal delay time and embedding dimension using the same method as in S2, and generate the measured three-dimensional phase space reconstruction map of the machine tool to be diagnosed using the same method as in S2.

[0014] S5. Compare the measured three-dimensional phase space reconstruction image generated in S4 with the standard three-dimensional phase space reconstruction images obtained in S2. If it matches one of the standard three-dimensional phase space reconstruction images, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] 1. Enhance the universality and adaptability of diagnosis. This method constructs an error model based on ideal circular motion and compares the results using unified chaotic attractor features, without relying on specific machine tool structures or models. Compared to traditional methods that rely on ballbars, laser interferometers, etc., which require dedicated fixtures or calibration procedures for different machine tools, this solution has stronger universality and cross-platform applicability.

[0017] 2. Effectively captures nonlinear error characteristics. Utilizing phase space reconstruction and chaotic attractor visualization techniques, the complex and nonlinear evolution process of motion errors can be transformed into a recognizable geometric form. Compared to existing technologies that primarily focus on linear or static error indicators, this method can reveal the nonlinear error behavior caused by multi-source coupling and dynamic interaction, significantly enhancing the ability to identify latent faults.

[0018] 3. Simplified measurement process and improved diagnostic efficiency. Diagnosis can be completed simply by controlling the machine tool to complete one clockwise and one counterclockwise circular motion while simultaneously acquiring position data. No downtime is required to install high-precision external sensors or perform cumbersome calibration operations. Compared to traditional methods that often take tens of minutes or even longer, this method significantly shortens the diagnostic cycle and is more suitable for integration into routine maintenance or online monitoring systems.

[0019] 4. Achieve accurate identification of error types. By constructing a standard phase space reconstruction library corresponding to various typical errors and using morphological matching for identification, the actual source of error can be determined intuitively and accurately. This approach avoids the difficulty of decoupling in the case of multiple coupled errors in traditional methods, thus improving the reliability and interpretability of diagnostic results.

[0020] Therefore, this method can achieve rapid and accurate diagnosis of motion errors in various CNC machine tools without incurring additional costs.

[0021] Preferably, in S0, the process of establishing mathematical models for error components corresponding to various error types includes:

[0022] S01, Based on the target position when the CNC machine tool spindle end is used as the center and R is the radius for circular motion. With actual location The basic circular motion error trajectory model of the machine tool is constructed as follows:

[0023] ;in, The actual radius;

[0024] S02. Simplify the basic circular motion error trajectory model to obtain the simplified circular motion error trajectory model:

[0025] ;

[0026] S03. For a certain type of error, based on the range of physical parameters in practice, set corresponding typical error parameter values ​​and establish an analytical function relationship between the error parameter and the ideal coordinates and actual coordinates; substitute the analytical function relationship into the simplified circular motion error trajectory model and perform algebraic simplification to generate a mathematical model of the error components of this type of error.

[0027] This approach achieves both systematicity and scalability in error modeling. It transforms complex spatial errors into computable mathematical expressions and establishes a mapping relationship between error parameters and coordinate deviations through analytical functions, giving the error model clear physical meaning and adjustable parameters. Compared to traditional empirical modeling or black-box fitting methods, this approach has stronger theoretical support and versatility, facilitating modular modeling and expansion for different error sources (such as geometric errors and thermal deformation). Furthermore, by introducing the value ranges of typical error parameters and performing algebraic simplification, the error model retains the geometric essence of the original spatial error while possessing good computational efficiency and engineering applicability. This provides high-fidelity theoretical input for subsequent phase space reconstruction and chaotic attractor diagnosis, significantly enhancing the reliability of diagnostic results.

[0028] Preferably, the calculation of its phase space reconstruction parameters using a preset algorithm includes:

[0029] Calculate the following statistics using the CC algorithm:

[0030] ;

[0031] In the formula, Represents the radius of the b-th pair of phase points in the reconstructed phase space; This represents the number of disjoint subsequences into which the motion error sequence is decomposed; Used to reflect the autocorrelation characteristics of a sequence; Used for measurement The maximum deviation; , , for and Statistical measure;

[0032] The phase space reconstruction parameters are calculated based on the relevant statistics.

[0033] This setup achieves two key advantages: 1) Automated and scientific selection of phase space reconstruction parameters. Traditional methods often rely on experience or trial-and-error to select delay times and embedding dimensions, which can easily introduce subjective biases or lead to reconstruction failures. This scheme uses the CC algorithm combined with multidimensional statistical analysis, which can objectively reflect the intrinsic dynamic structure of the time series, thereby automatically identifying the reconstruction parameters that best restore the dynamic characteristics of the system, significantly improving the accuracy and robustness of phase space reconstruction.

[0034] 2. Enhanced reliability and comparability of chaotic attractor phase diagram generation. Accurate phase space reconstruction is a prerequisite for generating identifiable 3D chaotic attractors. The parameters obtained through this algorithm ensure that standard phase diagrams and measured phase diagrams with different error types are generated under the same reconstruction conditions, avoiding the risk of misjudgment due to parameter differences and providing a solid foundation for accurate matching of subsequent error types.

[0035] Preferably, the process of calculating phase space reconstruction parameters based on relevant statistics includes:

[0036] Determine the optimal delay time: Select The time corresponding to the first minimum value is the optimal delay time for the g-th type of error. ;

[0037] Determine the embedding dimension: The minimum value is the embedding box width of the time series. According to the embedded window and optimal delay time The embedding dimension is calculated according to the following formula. :

[0038] .

[0039] This setup achieves: 1. Efficient and quantifiable determination of phase space reconstruction parameters. The method determines the optimal delay time and embedding dimension through explicit mathematical criteria (minimum points), avoiding the uncertainties introduced by traditional trial-and-error methods or subjective experience. Specifically, it... The minimum value is related to the stationarity of the system's dynamic changes, and can effectively capture the maximum time interval of independent information in the error sequence, thereby improving the non-redundancy and information integrity of the reconstructed trajectory.

[0040] 2. This solution ensures the comparability of standard and measured phase diagrams for different error types under unified parameters. Due to the significant differences in the motion characteristics of various errors, failure to employ a consistent and scientific method for parameter determination may result in topological incomparability between standard and measured phase diagrams. This solution provides a standardized process to ensure that the phase space reconstruction for each type of error is optimized based on its own dynamic characteristics, while maintaining the consistency of the algorithm logic, thus providing a reliable foundation for subsequent chaotic attractor matching.

[0041] Preferably, in S2, for the one-dimensional standard motion error time series of the g-th type of error... Where i = 1, 2, ..., n, n = 2N, the phase space is reconstructed according to the following formula:

[0042] ;

[0043] In the formula, ; For the first The embedding dimension of each motion error; For the first The optimal delay time for each motion error;

[0044] The reconstructed trajectory constitutes a A dimensional matrix, whose t-th row is:

[0045] .

[0046] This setup achieves two key advantages: 1) High-dimensional topological representation of error dynamics. By transforming a one-dimensional time series into a multi-dimensional phase space trajectory, the hidden nonlinear dynamic characteristics within the error signal can be fully revealed. This reconstruction method preserves the internal temporal dependencies and dynamic evolution patterns of the system, allowing complex error patterns that were previously difficult to identify (such as periodic fluctuations and chaotic trends) to be explicitly presented in high-dimensional space, providing a structured data foundation for the subsequent generation of chaotic attractors.

[0047] 2. Improved the comparability and matching accuracy between the standard error model and measured data. This is because the reconstruction process strictly follows unified embedding parameters (…). , This ensures that the standard phase diagrams for each type of error are generated on the same dimension and time scale. This gives the standard phase diagrams the same geometric semantics as the reconstructed trajectories obtained from actual measurements, thus significantly enhancing the reliability and discriminative ability of both in morphological comparison.

[0048] Preferably, in S2, for the g-th type of error, the method for generating its standard three-dimensional phase space reconstruction diagram includes:

[0049] The embedding dimension determined by the CC algorithm Used for phase space reconstruction to obtain high-dimensional reconstructed trajectories;

[0050] Select the first three components of the reconstructed trajectory , , The X, Y, and Z axes are respectively used as the rectangular coordinate system of the phase space trajectory to construct a three-dimensional phase space reconstruction diagram.

[0051] This setup achieves two key advantages: 1) Visualization and structured representation of the dynamic characteristics of errors. By projecting the high-dimensional reconstructed trajectory into three-dimensional space, the nonlinear behaviors such as periodicity, convergence, or chaos in the error evolution process can be intuitively displayed. This visualization method not only preserves the core information of the system dynamics but also presents complex error patterns in a geometric form, facilitating subsequent manual identification or pattern matching analysis.

[0052] 2. Enhanced topological consistency and comparability between standard phase diagrams and measured phase diagrams. Since all standard phase diagrams employ a unified projection rule (i.e., the first three delay components constitute the XYZ axes), it ensures that different error types are generated in the same dimension and coordinate system, avoiding the risk of misjudgment due to differences in coordinate selection. This provides a reliable foundation for accurate comparison with the three-dimensional chaotic attractors generated from measured data.

[0053] Preferably, the error types include servo mismatch error, backflip error, backlash error, and periodic error.

[0054] This setup selects error types derived from common fault sources in CNC machine tool operation, such as servo mismatch errors caused by inconsistent servo system responses, backlash and reverse overshoot errors generated during commutation, and periodic errors caused by periodic fluctuations in mechanical structure or control parameters. Modeling these typical problems makes the diagnostic method more closely aligned with real-world application scenarios, significantly enhancing its applicability in industrial environments.

[0055] Preferably, the value of N is 360; the complete diagnostic cycle includes one clockwise circular motion and one counterclockwise circular motion executed sequentially, corresponding to a total of 720 equally spaced angle values, wherein the clockwise circular motion corresponds to the first 360 angle values ​​and the counterclockwise circular motion corresponds to the last 360 angle values, with an angle interval of 1°.

[0056] This setup, employing a combination of clockwise and counterclockwise bidirectional circular motion, effectively captures asymmetric behavior caused by direction-dependent errors such as backlash and overshoot. Simultaneously, the high angular resolution of 1° allows for fine-grained trajectory sampling, which is beneficial for revealing minute but crucial dynamic error characteristics, enhancing the accuracy of subsequent phase space reconstruction and chaotic attractor generation.

[0057] Preferably, in S5, the comparison includes identifying whether the measured three-dimensional phase space reconstruction image exhibits the same feature pattern as a certain standard three-dimensional phase space reconstruction image; wherein, the feature pattern includes: the overall outline of the geometric shape, the topological connection mode of the trajectory in the phase space, the local concentrated region of the distribution density, and the attractor dimension characteristics determined by the embedding dimension and the optimal delay time; if the measured three-dimensional phase space reconstruction image exhibits the same feature pattern as a certain standard three-dimensional phase space reconstruction image, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

[0058] This setup improves the accuracy and robustness of error identification. Relying solely on a single geometric feature (such as trajectory shape) is susceptible to noise or sampling bias, while this scheme comprehensively considers information from multiple aspects such as overall contour, topological connectivity, density distribution, and dimensional characteristics. It can more comprehensively reflect the dynamic nature of the error, significantly reduce the risk of misjudgment, and improve the reliability of the identification results.

[0059] 2. Enhanced ability to identify complex coupled errors. Different error types may exhibit similar behavior locally, but their global topology and attractor dimensions differ. By introducing the attractor dimension characteristics determined by the embedding parameters for comparison, error patterns with similar appearances but different underlying dynamic mechanisms can be effectively distinguished, thereby improving the ability to distinguish complex or hybrid errors.

[0060] Preferably, in S3, the actual position coordinates are acquired in real time by a laser interferometer, ballbar, or machine tool built-in position feedback system, and the radial deviation between the actual motion trajectory and the ideal circular trajectory is fitted by the least squares method as the actual motion error value.

[0061] This setup, employing high-precision measuring equipment such as laser interferometers and ballbars, or a machine tool closed-loop feedback system for position acquisition, can effectively obtain micron-level or even sub-micron-level position information, significantly improving the measurement accuracy of error data. Simultaneously, least squares fitting can eliminate the influence of random noise and sampling bias, obtaining a more stable and smooth radial deviation sequence, providing high-quality input for subsequent phase space reconstruction. Attached Figure Description

[0062] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0063] Figure 1 This is a flowchart of the method;

[0064] Figure 2 This is a diagram of the circular motion trajectory of the CNC machine tool in Example 1;

[0065] Figure 3This is a standard three-dimensional phase space reconstruction diagram from Example 1;

[0066] Figure 4 This is the error diagnosis diagram for the CNC milling machine XK-L540 in Example 2. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0069] Example 1

[0070] like Figure 1 As shown, this invention provides a method for diagnosing motion errors in CNC machine tools based on three-dimensional phase space reconstruction, comprising the following steps:

[0071] S0. Based on the ideal circular motion performed by the CNC machine tool on the plane, establish corresponding mathematical models of error components for each type of error of the CNC machine tool, which are used to calculate the position deviation caused by the corresponding type of error under the ideal circular trajectory of any radius.

[0072] The error types include servo mismatch error, backflip error, backlash error, and periodic error. The selected error types all originate from common fault sources in CNC machine tool operation, such as servo mismatch error caused by inconsistent servo system response, backflip and backlash errors generated during commutation, and periodic errors caused by periodic fluctuations in mechanical structure or control parameters. Models are established for these typical problems, making the diagnostic method more closely aligned with real-world application scenarios and significantly enhancing its applicability in industrial environments.

[0073] In practice, the process of establishing mathematical models for error components corresponding to various error types includes:

[0074] S01, Based on the target position when the CNC machine tool spindle end is used as the center and R is the radius for circular motion. With actual location The basic circular motion error trajectory model of the machine tool is constructed as follows:

[0075] ;

[0076] in, The actual radius; such as Figure 2 This is a diagram of the circular motion trajectory of a CNC machine tool.

[0077] S02. Simplify the basic circular motion error trajectory model to obtain the simplified circular motion error trajectory model:

[0078] ;

[0079] S03. For a certain type of error, based on the range of physical parameters in practice, set corresponding typical error parameter values ​​and establish an analytical function relationship between the error parameter and the ideal coordinates and actual coordinates; substitute the analytical function relationship into the simplified circular motion error trajectory model and perform algebraic simplification to generate a mathematical model of the error components of this type of error.

[0080] To facilitate a better understanding by those skilled in the art, the following example is provided.

[0081] Assuming machine tool The axis has periodic errors caused by linear gratings, etc., at this time:

[0082] ;

[0083] in, (um) represents the amplitude. For phase, (mm) represents the pitch. At this point, Therefore, the circular motion error trajectory is:

[0084] ;

[0085] If verticality error exists The error trajectory corresponding to the circular motion at this time is:

[0086] .

[0087] This method transforms complex spatial errors into computable mathematical expressions and establishes a mapping relationship between error parameters and coordinate deviations through analytical functions, giving the error model clear physical meaning and adjustable parameters. Compared to traditional empirical modeling or black-box fitting methods, this method has stronger theoretical support and versatility, facilitating modular modeling and expansion for different error sources (such as geometric errors, thermal deformation, etc.). Furthermore, by introducing the value ranges of typical error parameters and performing algebraic simplification, the error model retains the geometric essence of the original spatial error while possessing good computational efficiency and engineering applicability. This provides high-fidelity theoretical input for subsequent phase space reconstruction and chaotic attractor diagnosis, significantly enhancing the reliability of diagnostic results.

[0088] S1. Set a sequence containing 2N equally spaced angle values ​​to represent a complete diagnostic cycle, where the first N angle values ​​correspond to clockwise circular motion and the last N angle values ​​correspond to counterclockwise circular motion. Based on the mathematical models of various error components established in S0, for each type of error, take the 2N angle values ​​as input and calculate the theoretical position deviation value generated under ideal circular motion conditions, thereby generating a one-dimensional standard motion error time series containing only that single type of error.

[0089] In specific implementation, the value of N is 360; the complete diagnostic cycle includes one clockwise circular motion and one counterclockwise circular motion executed sequentially, corresponding to a total of 720 equally spaced angle values. The clockwise circular motion corresponds to the first 360 angle values, and the counterclockwise circular motion corresponds to the last 360 angle values, with an angle interval of 1°. Thus, by combining clockwise and counterclockwise bidirectional circular motions, asymmetric behavior caused by direction-dependent errors such as backlash and overshoot can be effectively captured. Simultaneously, the high angular resolution of 1° allows for fine sampling of the motion trajectory, which is beneficial for revealing minute but crucial dynamic error characteristics, enhancing the accuracy of subsequent phase space reconstruction and chaotic attractor generation.

[0090] S2. For each type of error in the one-dimensional standard motion error time series obtained in S1, the phase space reconstruction parameters are calculated using a preset algorithm and the phase space is reconstructed to obtain the high-dimensional reconstruction trajectory. Based on the high-dimensional reconstruction trajectory, a standard three-dimensional phase space reconstruction map of each type of error is generated according to a preset method. The phase space reconstruction parameters include the optimal delay time and the embedding dimension.

[0091] In specific implementation, the calculation of its phase space reconstruction parameters using a preset algorithm includes:

[0092] Calculate the following statistics using the CC algorithm:

[0093] ;

[0094] In the formula, Represents the radius of the b-th pair of phase points in the reconstructed phase space; This represents the number of disjoint subsequences into which the motion error sequence is decomposed; Used to reflect the autocorrelation characteristics of a sequence; Used for measurement The maximum deviation; , , for and Statistical measure;

[0095] The phase space reconstruction parameters are calculated based on the relevant statistics.

[0096] Traditional methods often rely on experience or trial-and-error to select delay times and embedding dimensions, which can easily introduce subjective biases or lead to reconstruction failures. This scheme employs the CC algorithm combined with multidimensional statistical analysis, which can objectively reflect the intrinsic dynamic structure of the time series, thereby automatically identifying the reconstruction parameters that best restore the system's dynamic characteristics, significantly improving the accuracy and robustness of phase space reconstruction. Furthermore, accurate phase space reconstruction is a prerequisite for generating a recognizable three-dimensional chaotic attractor. The parameters obtained through this algorithm ensure that standard phase diagrams and measured phase diagrams of different error types are generated under the same reconstruction conditions, avoiding the risk of misjudgment due to parameter differences and providing a solid foundation for accurate matching of subsequent error types.

[0097] In practice, the process of calculating phase space reconstruction parameters based on relevant statistics includes:

[0098] Determine the optimal delay time: Select The time corresponding to the first minimum value is the optimal delay time for the g-th type of error. ;

[0099] Determine the embedding dimension: The minimum value is the embedding box width of the time series. According to the embedded window and optimal delay time The embedding dimension is calculated according to the following formula. :

[0100] .

[0101] This method determines the optimal delay time and embedding dimension through explicit mathematical criteria (minimum points), avoiding the uncertainty brought about by traditional trial-and-error methods or subjective experience. In particular, it... The minimum value is related to the stationarity of the system's dynamic changes, effectively capturing the maximum time interval of independent information in the error sequence, thereby improving the non-redundancy and information integrity of the reconstructed trajectory. Furthermore, due to the significant differences in the motion characteristics of various errors, without a consistent and scientific parameter determination method, the standard phase diagram and the measured phase diagram may be incomparable in topological structure. This scheme provides a standardized process to ensure that the phase space reconstruction of each type of error is optimized based on its own dynamic characteristics, while maintaining the consistency of the algorithm logic, providing a reliable foundation for subsequent chaotic attractor matching.

[0102] In practice, for the one-dimensional standard motion error time series of the g-th type of error... Where i = 1, 2, ..., n, n = 2N, the phase space is reconstructed according to the following formula:

[0103] ;

[0104] In the formula, ; For the first The embedding dimension of each motion error; For the first The optimal delay time for each motion error;

[0105] The reconstructed trajectory constitutes a A dimensional matrix, whose t-th row is:

[0106] .

[0107] By transforming one-dimensional time series into multi-dimensional phase space trajectories, the hidden nonlinear dynamic characteristics in error signals can be fully revealed. This reconstruction method preserves the temporal dependencies and dynamic evolution laws within the system, allowing complex error patterns that were previously difficult to identify (such as periodic fluctuations and chaotic trends) to be explicitly presented in high-dimensional space, providing a structured data foundation for the subsequent generation of chaotic attractors. Furthermore, because the reconstruction process strictly follows unified embedding parameters (…),… , This ensures that the standard phase diagrams for each type of error are generated on the same dimension and time scale. This gives the standard phase diagrams the same geometric semantics as the reconstructed trajectories obtained from actual measurements, thus significantly enhancing the reliability and discriminative ability of both in morphological comparison.

[0108] In specific implementation, for the g-th type of error, the methods for generating its standard three-dimensional phase space reconstruction diagram include:

[0109] The embedding dimension determined by the CC algorithm Used for phase space reconstruction to obtain high-dimensional reconstructed trajectories;

[0110] Select the first three components of the reconstructed trajectory , , The X, Y, and Z axes are respectively used as the rectangular coordinate system of the phase space trajectory to construct a three-dimensional phase space reconstruction diagram.

[0111] Figure 3 This is a standard three-dimensional phase space reconstruction diagram of the four typical motion errors obtained during specific implementation: servo mismatch error, backflip error, backlash error, and periodic error.

[0112] By projecting the high-dimensional reconstructed trajectory into three-dimensional space, the nonlinear behaviors such as periodicity, convergence, or chaos in the error evolution process can be intuitively displayed. This visualization method not only preserves the core information of the system dynamics but also presents complex error patterns in geometric form, facilitating subsequent manual identification or pattern matching analysis. Furthermore, since all standard phase diagrams adopt a unified projection rule (i.e., the first three delay components constitute the XYZ axes), it ensures that different error types are generated in the same dimension and coordinate system, avoiding the risk of misjudgment due to differences in coordinate selection. This provides a reliable foundation for accurate comparison with the three-dimensional chaotic attractors generated from measured data.

[0113] S3. Control the motion axes of the CNC machine tool to be diagnosed to perform one clockwise circular motion and one counterclockwise circular motion in sequence on the plane; during the motion, synchronously collect the actual position coordinates of the machine tool, and calculate the actual motion error value according to the geometric relationship between the actual position coordinates and the corresponding ideal circular trajectory; arrange the actual motion error values ​​in the motion sequence to form a one-dimensional actual motion error time series of length 2N, where the first N data points correspond to the clockwise motion stage and the last N data points correspond to the counterclockwise motion stage;

[0114] In practice, the actual position coordinates are acquired in real time using a laser interferometer, ballbar, or the machine tool's built-in position feedback system. The radial deviation between the actual motion trajectory and the ideal circular trajectory is fitted using the least squares method, and this deviation is used as the actual motion error value. Thus, using high-precision measuring equipment such as laser interferometers and ballbars, or a machine tool's closed-loop feedback system for position acquisition, can effectively obtain micron-level or even sub-micron-level position information, significantly improving the measurement accuracy of error data. Simultaneously, the least squares fitting method can eliminate the influence of random noise and sampling bias, obtaining a more stable and smoother radial deviation sequence, providing high-quality input for subsequent phase space reconstruction.

[0115] S4. For the one-dimensional actual motion error time series obtained in S3, calculate its optimal delay time and embedding dimension using the same method as in S2, and generate the measured three-dimensional phase space reconstruction map of the machine tool to be diagnosed using the same method as in S2.

[0116] S5. Compare the measured three-dimensional phase space reconstruction image generated in S4 with the standard three-dimensional phase space reconstruction images obtained in S2. If it matches one of the standard three-dimensional phase space reconstruction images, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

[0117] In specific implementation, the comparison includes identifying whether the measured three-dimensional phase space reconstruction image exhibits the same characteristic pattern as a certain standard three-dimensional phase space reconstruction image; wherein, the characteristic pattern includes: the overall outline of the geometric shape, the topological connection mode of the trajectory in the phase space, the local concentrated region of the distribution density, and the attractor dimension characteristics determined by the embedding dimension and the optimal delay time; if the measured three-dimensional phase space reconstruction image exhibits the same characteristic pattern as a certain standard three-dimensional phase space reconstruction image, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

[0118] Relying solely on a single geometric feature (such as trajectory shape) is susceptible to noise or sampling bias. This approach, however, comprehensively considers information from multiple aspects, including the overall contour, topological connectivity, density distribution, and dimensional characteristics. This allows for a more complete reflection of the dynamic nature of the error, significantly reducing the risk of misjudgment and improving the reliability of the recognition results. Furthermore, different error types may exhibit similar behavior locally, but their global topological structure and attractor dimensions differ. By introducing attractor dimensional characteristics determined by the embedding parameters for comparison, error patterns with similar appearances but different underlying dynamic mechanisms can be effectively distinguished, thereby improving the ability to differentiate complex or hybrid errors.

[0119] Compared to existing technologies, this method constructs an error model based on ideal circular motion and compares it using unified chaotic attractor features, independent of specific machine tool structures or models. Compared to traditional methods that rely on ballbars, laser interferometers, or other specialized fixtures or calibration procedures for different machine tools, this solution offers greater versatility and cross-platform applicability. Furthermore, by utilizing phase space reconstruction and chaotic attractor visualization techniques, the complex and nonlinear evolution of motion errors can be transformed into a recognizable geometric form. Compared to existing technologies that primarily focus on linear or static error indicators, this method can reveal nonlinear error behavior caused by multi-source coupling and dynamic interaction, significantly enhancing the ability to identify latent faults. Moreover, diagnosis can be completed by controlling the machine tool to complete one clockwise and one counterclockwise circular motion while simultaneously acquiring position data, eliminating the need for downtime to install high-precision external sensors or perform cumbersome calibration operations. Compared to traditional methods that often involve measurement processes lasting tens of minutes or even longer, this method significantly shortens the diagnostic cycle, making it more suitable for integration into routine maintenance or online monitoring systems. In addition, by constructing a standard phase space reconstruction library corresponding to various typical errors and using morphological matching for identification, the actual source of error can be determined intuitively and accurately. This approach avoids the difficulty of decoupling in the case of multiple coupled errors in traditional methods, thus improving the reliability and interpretability of diagnostic results.

[0120] This method can achieve rapid and accurate diagnosis of motion errors in various CNC machine tools without incurring additional costs.

[0121] Example 2

[0122] To better illustrate the effectiveness of this method, the following experiment was conducted.

[0123] This experiment used an XK-L540 CNC milling machine as the object and a Renishaw QC20 ballbar for data acquisition. The CNC machine spindle was controlled by NC programming to perform circular motion in the xoy plane, with a feed rate of 1500 mm / min, a radius of 100 mm, and a ballbar length of 100 mm. To reduce the influence of random factors, three sets of data were collected each time, continuously for three days, to obtain the original sequence of motion accuracy.

[0124] The optimal delay time and embedding dimension were determined using the CC algorithm, and the results are shown in Table 1.

[0125] Table 1

[0126]

[0127] After denoising the first batch of actual motion error sequences, error identification based on chaotic attractor characterization is performed. Figure 4 This is a motion error identification diagram for the XK-L540 CNC milling machine.

[0128] Depend on Figure 4 It can be seen that this method can clearly identify the periodic error and reverse overshoot error of the milling machine.

[0129] in conclusion

[0130] (1) The chaotic attractor model reconstructed through phase space can be used to identify motion errors of CNC machine tools;

[0131] (2) By establishing mathematical models of motion errors of different machine tools through the circular motion of the machine tool, a mapping relationship model between motion errors of CNC machine tools and chaotic attractors is established based on phase space reconstruction. This invention can easily distinguish various types of motion errors and is independent of the specific type of machine tool, thus having strong versatility.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for diagnosing motion errors in CNC machine tools based on three-dimensional phase space reconstruction, characterized in that, Includes the following steps: S0. Based on the ideal circular motion performed by the CNC machine tool on the plane, establish corresponding mathematical models of error components for various error types of the CNC machine tool, which are used to calculate the position deviation caused by the corresponding type of error under an ideal circular trajectory of arbitrary radius. S1. Set a sequence containing 2N equally spaced angle values ​​to represent a complete diagnostic cycle, where the first N angle values ​​correspond to clockwise circular motion and the last N angle values ​​correspond to counterclockwise circular motion; Based on the mathematical models of various error components established in S0, for each type of error, take the 2N angle values ​​as input and calculate the theoretical position deviation value generated under ideal circular motion conditions, thereby generating a one-dimensional standard motion error time series containing only this single type of error; S2. For each type of error in the one-dimensional standard motion error time series obtained in S1, the phase space reconstruction parameters are calculated using a preset algorithm and the phase space is reconstructed to obtain the high-dimensional reconstruction trajectory. Based on the high-dimensional reconstruction trajectory, a standard three-dimensional phase space reconstruction diagram of each type of error is generated according to a preset method. The phase space reconstruction parameters include the optimal delay time and the embedding dimension. S3. Control the motion axes of the CNC machine tool to be diagnosed to perform one clockwise circular motion and one counterclockwise circular motion in sequence on the plane; during the motion, synchronously collect the actual position coordinates of the machine tool, and calculate the actual motion error value based on the geometric relationship between the actual position coordinates and the corresponding ideal circular trajectory. The actual motion error values ​​are arranged in the motion sequence to form a one-dimensional actual motion error time series of length 2N, where the first N data points correspond to the clockwise motion stage and the last N data points correspond to the counterclockwise motion stage. S4. For the one-dimensional actual motion error time series obtained in S3, calculate its optimal delay time and embedding dimension using the same method as in S2, and generate the measured three-dimensional phase space reconstruction map of the machine tool to be diagnosed using the same method as in S2. S5. Compare the measured three-dimensional phase space reconstruction image generated in S4 with the standard three-dimensional phase space reconstruction images obtained in S2. If it matches one of the standard three-dimensional phase space reconstruction images, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

2. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that: In S0, the process of establishing mathematical models for error components corresponding to various error types includes: S01, Based on the target position when the CNC machine tool spindle end is used as the center and R is the radius during circular motion. With actual location The basic circular motion error trajectory model of the machine tool is constructed as follows: ;in, The actual radius; S02. Simplify the basic circular motion error trajectory model to obtain a simplified circular motion error trajectory model: ； S03. For a certain type of error, based on the range of physical parameters in practice, set corresponding typical error parameter values ​​and establish an analytical function relationship between the error parameter and the ideal coordinates and actual coordinates; substitute the analytical function relationship into the simplified circular motion error trajectory model and perform algebraic simplification to generate a mathematical model of the error components of this type of error.

3. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that, In S2, the calculation of its phase space reconstruction parameters using a preset algorithm includes: Calculate the following statistics using the CC algorithm: ； In the formula, Represents the radius of the b-th pair of phase points in the reconstructed phase space; This represents the number of disjoint subsequences into which the motion error sequence is decomposed; Used to reflect the autocorrelation characteristics of a sequence; Used for measurement The maximum deviation; , , for and Statistical measure; The phase space reconstruction parameters are calculated based on the relevant statistics.

4. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 3, characterized in that, The process of calculating phase space reconstruction parameters based on relevant statistics includes: Determine the optimal delay time: Select The time corresponding to the first minimum value is the optimal delay time for the g-th type of error. ; Determine the embedding dimension: The minimum value is the embedding box width of the time series. According to the embedded window and optimal delay time The embedding dimension is calculated according to the following formula. : 。 5. The method for diagnosing motion errors in CNC machine tools based on three-dimensional phase space reconstruction as described in claim 4, characterized in that, In S2, for the one-dimensional standard motion error time series of the g-th type of error Where i = 1, 2, ..., n, n = 2N, the phase space is reconstructed according to the following formula: ； In the formula, ; For the first The embedding dimension of each motion error; For the first The optimal delay time for each motion error; The reconstructed trajectory constitutes a A dimensional matrix, whose t-th row is: 。 6. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 5, characterized in that: In S2, for the g-th type of error, the methods for generating its standard three-dimensional phase space reconstruction diagram include: The embedding dimension determined by the CC algorithm Used for phase space reconstruction to obtain high-dimensional reconstructed trajectories; Select the first three components of the reconstructed trajectory , , The X, Y, and Z axes are respectively used as the rectangular coordinate system of the phase space trajectory to construct a three-dimensional phase space reconstruction diagram.

7. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that: The error types include servo mismatch error, backflip error, backlash error, and cycle error.

8. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that: The value of N is 360; the complete diagnostic cycle includes one clockwise circular motion and one counterclockwise circular motion executed sequentially, corresponding to a total of 720 equally spaced angle values, of which the clockwise circular motion corresponds to the first 360 angle values ​​and the counterclockwise circular motion corresponds to the last 360 angle values, with an angle interval of 1°.

9. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that: In S5, the comparison includes identifying whether the measured three-dimensional phase space reconstruction image exhibits the same feature pattern as a certain standard three-dimensional phase space reconstruction image; wherein, the feature pattern includes: the overall outline of the geometric shape, the topological connection mode of the trajectory in the phase space, the local concentrated region of the distribution density, and the attractor dimension characteristics determined by the embedding dimension and the optimal delay time; if the measured three-dimensional phase space reconstruction image exhibits the same feature pattern as a certain standard three-dimensional phase space reconstruction image, it is determined that the CNC machine tool to be diagnosed has the motion error type corresponding to the standard three-dimensional phase space reconstruction image.

10. The method for diagnosing motion errors of CNC machine tools based on three-dimensional phase space reconstruction as described in claim 1, characterized in that: In S3, the actual position coordinates are acquired in real time by a laser interferometer, ballbar, or machine tool built-in position feedback system, and the radial deviation between the actual motion trajectory and the ideal circular trajectory is fitted by the least squares method as the actual motion error value.

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