A mechanism-data fusion driven milling chatter stability prediction method and system
By employing a mechanism-data fusion approach, combining a milling dynamic parameter function model and Bayesian inference, the accuracy and cost issues of milling chatter stability prediction are resolved. This approach achieves efficient and reliable chatter stability domain prediction, applicable to various machining conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-19
Smart Images
Figure CN122241067A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of milling chatter stability prediction technology, specifically involving a mechanism-data fusion driven method and system for predicting milling chatter stability. Background Technology
[0002] Milling, a key cutting process in modern manufacturing, has wide applications in aerospace, mold making, and precision equipment. With the widespread use of high-performance CNC machine tools and the increasing demand for efficient machining, ensuring workpiece surface quality and dimensional accuracy while improving machining efficiency has become a core technical problem urgently needing to be solved in the manufacturing field. During milling, chatter, a self-excited vibration phenomenon caused by regenerative effects, severely restricts machining quality and production efficiency. Chatter not only leads to increased workpiece surface roughness, decreased dimensional accuracy, and accelerated tool wear, but may also cause tool breakage or damage to machine tool components, thus limiting the selection of cutting parameters (such as depth of cut and spindle speed), significantly reducing production efficiency and increasing manufacturing costs. Therefore, research on the prediction and control of chatter stability in the milling process has significant theoretical and engineering value.
[0003] In milling stability prediction, the main research methods can be divided into analytical methods (such as the zero-order approximation method) and discretization methods (including fully discretized methods and semi-discrete methods). These methods can solve the chatter stability domain lobe diagram based on the system dynamic parameters obtained from modal testing, thus providing guidance for the selection of process parameters. However, in actual machining, due to the influence of nonlinear time-varying factors on the milling system, its dynamic parameters often change with the spindle speed, and the system parameters under actual machining conditions are difficult to accurately obtain through offline modal testing. This leads to the stability domain solved based on traditional methods often failing to truly reflect the chatter stability of the actual machining system.
[0004] To obtain the true boundary of the stability region, researchers typically conduct numerous milling experiments and fit the stability region based on the experimental data. The boundary obtained by this method most directly reflects the actual chatter stability, but it has limitations such as high experimental costs and weak versatility; once the machine tool, cutting tool, or workpiece material is changed, the experiment must be recalibrated. With the development of computer technology, machine learning methods have been introduced into stability region prediction. This method does not require experiments for every rotational speed and avoids complex physical modeling processes, achieving stability region inference through a data-driven black-box model. However, machine learning methods require high accuracy and scale of training data, and the models often lack physical interpretability, so their reliability and generalization ability in practical industrial applications still face challenges. The existing patent publication number CN116484533A discloses a milling stability analysis method based on Bernoulli distribution and hybrid driving method. It judges chatter stability by establishing a milling dynamics model and the spectral radius of the state transition matrix, and corrects experimental parameters through Bernoulli distribution to construct a correction function to optimize the stability lobe diagram. This solves the problem that in high-speed milling, aerospace integral structural parts are prone to deformation and vibration due to their large size, high material removal rate, many thin-walled parts, and poor rigidity, making it difficult to control machining accuracy and surface quality. Existing methods lack the comprehensive use of physical models and data-driven methods for milling stability analysis. Patent CN117520767A discloses a Bayesian optimization-based method for predicting machining chatter. This method uses a Bayesian optimization approach to identify the optimal input parameters in the machining chatter prediction mechanism model through a cutting machining dataset. It then optimizes the objective function using a Gaussian process and entropy search function, and combines this with a stability discrimination method to solve for the stability lobe diagram. This addresses the problems of existing machining chatter prediction methods, such as severe uncertainty in input parameters leading to poor prediction accuracy, and the lack of physical interpretation and poor generalization of data-driven methods.
[0005] In summary, existing methods for predicting the stability domain of chatter have limitations in terms of accuracy, cost, and universality. While analytical and discretization methods based on mechanistic models provide theoretical guidance, their accuracy is limited by the difficulty in accurately obtaining actual time-varying system parameters. Empirical methods relying on numerous cutting experiments can directly reflect true stability, but they are costly and lack universality. Data-driven machine learning methods, while reducing experimental dependence, have strict requirements on data quality and scale, and their lack of physical interpretability affects their engineering credibility and generalization ability. Therefore, to promote the effective application of chatter stability prediction in practical machining, it is urgent to develop a novel prediction method that balances prediction accuracy, reduces experimental costs, and possesses good physical interpretability, enabling the rapid and reliable acquisition of the stability domain of real machining systems under limited experimental conditions. Summary of the Invention
[0006] To overcome the limitations of existing flutter stability prediction methods, this invention proposes a Bayesian flutter stability prediction method and system based on parameter variation laws. The method first establishes a functional model of the system's dynamic parameters as a function of the spindle speed, based on experimental and theoretical analysis. Then, using a fully discrete method, it calculates the spectral radius at each discrete point in the speed-depth parameter space and uses this as training samples to construct a Gaussian process regression model, thereby establishing the mapping relationship between the function model coefficients and the spectral radius. Subsequently, it constructs a flutter probability model using Floquet stability theory and establishes a Bernoulli likelihood function using measured flutter label data. Based on this, physical constraints are introduced, and a maximum a posteriori probability optimization algorithm is used for Bayesian inference to obtain the posterior mean estimate of the function coefficients. Finally, it determines the explicit functional relationship between system parameters and speed variation and outputs the probability distribution of the flutter stability domain. This method significantly reduces the amount of experimental data required while ensuring prediction accuracy and improving prediction efficiency.
[0007] To achieve the above objectives, in a first aspect, the present invention provides a mechanism-data fusion-driven method for predicting the stability of milling chatter, comprising the following steps: Milling dynamics system parameters and chatter label data were obtained through modal parameter identification and trial cutting experiments; Based on the physical laws governing the variation of milling dynamics system parameters with rotational speed, a parameterized function model of modal frequency and equivalent damping ratio with respect to spindle speed is constructed. Construct a Gaussian process regression model, and establish the mapping relationship between the coefficients of the parameterized function model and the spectral radius through the Gaussian process regression model; A flutter probability model is constructed based on Floquet theory, and a Bernoulli likelihood function is constructed based on flutter label data. By introducing physical constraints, Bayesian inference is performed based on the MAP optimization algorithm to obtain the posterior mean estimate of the model coefficients. Determine the specific functional expressions of the parameters of the milling dynamics system to obtain the probability distribution of the chatter stability domain.
[0008] Furthermore, the parameterized functional models for the modal frequencies and equivalent damping ratio with respect to the spindle speed are as follows:
[0009]
[0010] in, and These are the modal parameters measured when the system is at rest, i.e., the prior means; , , , Let be the undetermined coefficients of the function. The main spindle speed.
[0011] Furthermore, based on the fully discrete method, the spectral radius at each rotational speed-depth grid point is solved, and a Gaussian regression model is trained to obtain the relationship between the system parameters and the spectral radius, specifically expressed as follows:
[0012] in, The relationship between the coefficients of the parameterized function model and the spectral radius, representing the maximum spectral radius of the system's transfer function matrix, is expressed as:
[0013] in, , , , , , , , These are all undetermined coefficients of the model. This parameterized function model is used to calculate the spectral radius under corresponding cutting conditions, given the function coefficients.
[0014] Furthermore, the flutter probability model based on Floquet theory is as follows:
[0015] in, These are hyperparameters used to control model accuracy. flutter probability at location P =0.5; The flutter probability should follow Increase rapidly; The flutter probability should follow The increase was followed by a rapid decrease.
[0016] Furthermore, the Bernoulli likelihood function is:
[0017] Bernoulli likelihood represents the expression in the parameter vector The experimental results were observed below. The probability of; where, For experimental data points The flutter label.
[0018] Furthermore, physical constraints are introduced, and Bayesian inference is performed based on the MAP optimization algorithm to obtain the posterior mean estimate of the model coefficients. This includes introducing physical constraints with the objective of minimizing the negative log-posterior, and the objective function is expressed as:
[0019] in, The penalty function is applied to the objective function when the predicted result deviates from the milling experimental data. The penalty intensity increases with the increase of the prediction error. The specific expression of the penalty function is as follows:
[0020] in, This is the penalty coefficient, used to adjust the intensity of the penalty.
[0021] Furthermore, determining the specific functional expressions of the milling dynamics system parameters and obtaining the probability distribution of the chatter stability domain includes: using the posterior estimates of the function coefficients of the system parameters as a function of rotational speed obtained by Bayesian inference; solving the system parameters at each target rotational speed based on the parameterized function model; solving the spectral radius at all nodes in the rotational speed-depth discrete grid based on the Gaussian regression model; and solving the probability distribution of the chatter stability boundary based on the chatter probability model.
[0022] In a second aspect, the present invention provides a mechanism-data fusion driven milling chatter stability prediction system, including a data acquisition module, a parameterized function model construction module, a mapping relationship construction module, a chatter probability model construction module, a Bayesian inference module, and a probability distribution calculation module; The data acquisition module is used to obtain milling dynamics system parameters and chatter label data through modal parameter identification and trial cutting experiments; The parameterized function model building module is based on the physical law of the change of milling dynamic system parameters with rotational speed, and constructs a parameterized function model of modal frequency and equivalent damping ratio with respect to spindle speed; The mapping relationship construction module is used to construct a Gaussian process regression model, and establishes a mapping relationship between the coefficients of the parameterized function model and the spectral radius through the Gaussian process regression model; The flutter probability model construction module constructs a flutter probability model based on Floquet theory and builds a Bernoulli likelihood function based on flutter label data; The Bayesian inference module is used to introduce physical constraints, perform Bayesian inference based on the MAP optimization algorithm, and obtain the posterior mean estimate of the model coefficients. The probability distribution calculation module is used to determine the specific functional expressions of the milling dynamics system parameters and obtain the probability distribution of the chatter stability domain.
[0023] Thirdly, the present invention provides a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and the processor can realize the above-mentioned mechanism-data fusion driven milling chatter stability prediction method when executing part or all of the computer executable program.
[0024] Simultaneously, a computer-readable storage medium is provided, in which a computer program is stored. When the computer program is executed by a processor, it can realize the above-mentioned mechanism-data fusion driven milling chatter stability prediction method.
[0025] Compared with the prior art, the present invention has at least the following beneficial effects: Compared to traditional mechanistic models, experimental calibration methods, and purely data-driven prediction approaches, this invention significantly improves the prediction accuracy and physical interpretability of the flutter stability domain by integrating function modeling based on parameter variation patterns with a Bayesian inference framework, while inheriting the physical mechanism of the fully discrete method. Furthermore, this method requires only a small amount of experimental data to achieve probabilistic inference of time-varying system parameters, overcoming the dependence of traditional methods on large-scale calibration experiments or high-quality datasets, and greatly reducing experimental costs and data requirements. In addition, the established parameterized model exhibits good adaptability and generalization ability, providing a transferable solution for efficient stability prediction under different machine tool-tool-workpiece combinations. Attached Figure Description
[0026] Figure 1 This is a flowchart of the present invention.
[0027] Figure 2 This is the dynamic model of the milling system, the subject of study in this embodiment of the invention.
[0028] Figure 3 To predict the flutter stability domain lobe diagram using the method proposed in this invention under given system parameters and flutter tag data, the prediction accuracy was verified using experimental data points. Detailed implementation method: The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.
[0029] refer to Figure 1 and Figure 2 The present invention provides a mechanism-data fusion driven method for predicting the stability of milling chatter, which includes the following steps: Step 1: Obtain milling dynamics system parameters and chatter label data through modal parameter identification and trial cutting experiments; specifically, this includes obtaining the natural frequencies and equivalent damping ratios of the machine tool-cutting tool system in two orthogonal directions under static conditions using the hammer excitation method. Considering the error of the modal testing experiment, assuming that the prior parameters follow a normal distribution, it can be expressed as:
[0030] in, Let be the prior mean vector. Let be the covariance matrix. Taking a typical two-degree-of-freedom milling system as an example, the system includes... , Two orthogonal directions, containing a total of =4 independent parameters. In this case, each vector can be specifically represented as:
[0031]
[0032]
[0033] in, , , , All of these are system dynamic parameters; , , , This represents the average value of the test results for the dynamic parameters; , , , The variance of the test results, modal parameters (Natural frequency) and The damping ratio can be obtained through a hammer impact test. Prior mean. The elements corresponding to the modal parameters are the average of the results obtained from multiple repeated hammer impact experiments, and their variance is... Based on The data from each independent experiment were calculated using the following formula:
[0034] In the formula, Indicates the first The parameter estimates obtained from the hammer impact experiment For this parameter The mean of the measurement results.
[0035] Next, a series of discrete speed points were selected within the target speed range to conduct milling experiments on wedge-shaped workpieces. Chatter tests were performed sequentially. Once chatter was detected at a certain speed point, its critical depth of cut was recorded, and the experiment was continued at the next speed point.
[0036] Step 1 uses a hammer impact excitation method to obtain modal parameters of the machine tool-tool system in two orthogonal directions under static conditions. The aim is to identify modal parameters such as the structure's natural frequencies, damping ratios, and mode shapes by applying transient impact forces to the structure and measuring its response. Performing the experiment in a static state eliminates interference from dynamic factors such as cutting forces, allowing for the acquisition of the system's most fundamental dynamic characteristics. Performing the experiment in two orthogonal directions comprehensively captures the dynamic response of the machine tool-tool system within the working plane. This method involves using a hammer to impact the spindle or tool while simultaneously using an accelerometer to measure the vibration response of the tool or spindle. The data is then processed using Fourier transform and modal analysis software to extract the modal parameters.
[0037] A series of discrete speed points are selected within the target speed range to systematically explore the flutter characteristics of the system at different speeds and provide sufficient data support for the subsequent construction of a parameterized function model. The entire target speed range can be divided into several speed points, either uniformly or non-uniformly, based on actual processing requirements or experience. Alternatively, an adaptive strategy can be adopted: after preliminary experiments, the speed points are denser in areas where the flutter boundary changes rapidly, and sparser in areas where the change is gradual.
[0038] Conducting milling experiments on wedge-shaped workpieces is an effective method for chatter testing. By gradually increasing the cutting width or depth of cut, critical cutting parameters can be easily found, thus determining the chatter boundary. Wedge-shaped workpieces can be designed with gradually varying widths or depths. Trial cutting experiments are performed sequentially according to preset spindle speeds and cutting parameters to ensure the systematic nature and repeatability of the experimental process, avoiding data deviations caused by disordered experimental order. Accurately recording the critical depth of cut is fundamental to constructing chatter labeling data. Chatter detection can be performed in various ways, such as monitoring the vibration signal of the tool or workpiece using an accelerometer. When the vibration amplitude exceeds a preset threshold or a specific frequency component appears, it is identified as chatter. The strategy of moving to the next spindle speed point ensures that chatter information is obtained at each selected spindle speed point and efficiently covers the entire target spindle speed range, providing comprehensive data for subsequent model training. After determining the critical depth of cut at one spindle speed point, the spindle speed is immediately adjusted to the next preset discrete spindle speed point, and the trial cutting experiment process is repeated.
[0039] This application utilizes a systematic experimental data acquisition process and the hammer excitation method to obtain the modal parameters of the machine tool-cutting tool system in two orthogonal directions under static conditions. This provides a fundamental, unaffected, inherent dynamic characteristic of the system for subsequently constructing a parameterized function model of modal frequencies and equivalent damping ratios. The static modal parameters, as prior information, help constrain and guide the establishment of the parameterized function model. To comprehensively capture the performance of milling chatter under different working conditions, a series of discrete speed points are selected within the target speed range. At each selected speed point, wedge-shaped workpiece milling experiments are conducted, and trial cuts are performed sequentially. This allows the depth of cut to gradually increase in a single pass or a series of consecutive passes, thereby enabling precise identification of the critical conditions for chatter occurrence.
[0040] Step 2: Based on the physical laws governing the variation of milling dynamics system parameters with rotational speed, construct parameterized function models of modal frequencies and equivalent damping ratio with respect to spindle speed. Specifically, based on existing research and experimental observations, the parameterized function models describing modal frequencies and equivalent damping ratio have the following characteristics: The function model describing the modal frequencies should monotonically decrease with increasing rotational speed, and the rate of decrease should gradually slow down, exhibiting concave function characteristics; the function model describing the equivalent damping ratio should monotonically increase with increasing rotational speed; the rates of change of both decrease with increasing rotational speed, and the rate of increase should gradually slow down, exhibiting convex function characteristics. The parameterized function models of modal frequencies and equivalent damping ratio with respect to spindle speed are expressed as follows:
[0041]
[0042] in, and These are the modal parameters measured when the system is at rest, i.e., the prior means; , , , Let be the undetermined coefficients of the function. The main spindle speed.
[0043] By explicitly introducing the physical characteristics of modal frequency and equivalent damping ratio as they change with rotational speed when constructing the parameterized functional model, the modal frequency monotonically decreases with increasing rotational speed, exhibiting concave function characteristics; the equivalent damping ratio monotonically increases with increasing rotational speed, with the rate of increase gradually slowing down, exhibiting convex function characteristics. This accurate description of the physical laws ensures that the constructed functional model is not merely a simple curve fit, but a model with clear physical meaning and trend constraints. This is achieved by using modal parameters measured under static conditions of the system. and The prior mean is introduced into the model as the coefficients to be determined. , , , The determination of the parameters provides a physical benchmark, ensuring the model's rationality in the low-speed range. The undetermined coefficients will be optimized in subsequent Bayesian inference processes using trial-cut experimental data, enabling the model to more accurately reflect the system's dynamic characteristics across the entire speed range. This combination of prior physical knowledge and data-driven optimization allows the constructed parameterized function model to more accurately and stably describe the changes in milling dynamics system parameters with speed, providing more reliable input for subsequent chatter probability models and stability domain predictions. This addresses the problem of insufficient prediction accuracy in traditional models due to a lack of physical constraints.
[0044] Step 3: Based on the milling dynamics system parameters and chatter label data obtained in Step 1, and the simulated parameter vector satisfying a normal distribution, calculate the spectral radius at each rotational speed-depth grid point using the fully discrete method. A discrete grid is established in the rotational speed-depth parameter space, and the spectral radius at each grid point is calculated using the fully discrete method, serving as the training dataset. A Gaussian process regression model is trained separately for each rotational speed-depth grid point. This model is fast and differentiable, replacing the complex calculation process of the fully discrete method, thus improving efficiency. This model can be expressed as:
[0045] in, Let be the maximum spectral radius of the system's transfer function matrix.
[0046] Based on the parameterized function model obtained in step 2, the mapping relationship between the coefficients of the parameterized function model and the spectral radius can be expressed as:
[0047] in, , , , , , , , These are all undetermined coefficients of the model. This parameterized function model is used to calculate the spectral radius under corresponding cutting conditions, given the function coefficients.
[0048] Simulated data generated using the fully discrete method is used as input to optimize the internal parameters of a Gaussian process regression model, enabling it to learn and generalize the mapping between function coefficients and spectral radii. The Gaussian regression model provides the mean and variance of predictions, thus quantifying the uncertainty of the prediction. During training, the function coefficients from the simulated data can be used as input features of the model, and the corresponding spectral radii as the model's output target. Optimization algorithms such as maximum likelihood estimation or Bayesian inference are used to adjust the kernel function parameters and noise variance of the Gaussian process, allowing the model to best fit the training data. Once trained, the Gaussian regression model becomes a predictive tool that can accept new function coefficients as input and quickly output the corresponding predicted spectral radii, overcoming the limitations of training a Gaussian regression model purely on limited experimental data.
[0049] Step 4: Based on the obtained spectral radius mapping relationship, a flutter probability model is constructed based on Floquet stability theory. Combined with experimentally obtained flutter tag data, a Bernoulli likelihood function is constructed to describe the statistical relationship between the flutter probability and the spectral radius under the observed data. The system is considered stable when the modulus of all eigenvalues of the system's transfer matrix is less than 1. Therefore, the designed flutter probability model should satisfy the following characteristics: flutter probability at location P =0.5; The flutter probability should follow Increase rapidly; The flutter probability should follow The increase is followed by a rapid decrease. The specific model is as follows:
[0050] in, These are hyperparameters used to control model accuracy.
[0051] Assuming each experiment result is independent, the Bernoulli likelihood function is constructed based on the flutter label data as follows:
[0052] in, For experimental data points Flutter label, It indicates flutter.
[0053] By explicitly defining the Bernoulli likelihood function, which represents the probability of observing an experimental result under a parameter vector, a clear and mathematically rigorous connection is established between the mechanistic model and the experimental data. This function allows the model to quantify the likelihood of observing flutter label data under a specific parameter set. Specifically, for each experimental data point, if the observed flutter label is 1 (representing flutter), the likelihood function will evaluate the probability that the model predicts flutter under that cutting condition; if the observed flutter label is 0 (representing no flutter), the likelihood function will evaluate the probability that the model predicts no flutter (i.e., 1 minus the flutter probability). This provides a clear optimization objective for the MAP optimization algorithm, enabling it to effectively update and refine model parameters based on experimental data, and to integrate data-driven flutter label information into the Floquet-based mechanistic model, ensuring the robustness and reliability of system parameter estimation.
[0054] Step 5: Perform Bayesian inference based on Bayes' theorem. Bayes' theorem is stated as follows:
[0055] in, This represents the vector of unknown parameters to be estimated. Represents the observed data; This is called the prior distribution; It is the likelihood function; As evidence or marginal likelihood, it is a normalized constant that is usually difficult to calculate directly; It is a posterior distribution.
[0056] Therefore, Bayes' theorem can be simply understood as:
[0057] Based on the Bayesian inference framework, this paper adopts maximizing the posterior probability as the optimization objective to find the parameter vector that best reflects the true situation. The optimization objective is:
[0058] In practice, minimizing the negative logarithm posterior is used as the optimization objective. Based on Bayes' theorem, the optimization function can be expressed as:
[0059] To improve the physical consistency of the predictions, a regularization penalty term is introduced into the optimization objective. The strength of the penalty is proportional to the degree of deviation of the prediction results from the physical laws, thereby achieving posterior mean estimation of the function coefficients.
[0060] The optimization function is then finally expressed as:
[0061] The function coefficient vector that minimizes the optimal function value is used as the posterior distribution estimate.
[0062] The MAP optimization algorithm is a method for estimating model parameters within a Bayesian framework, finding the optimal parameter estimates by maximizing the posterior probability. In optimization problems, maximizing a function is equivalent to minimizing its negative value. In Bayesian inference, maximizing the posterior probability is equivalent to minimizing the negative log-posterior. Introducing physical constraints refers to imposing restrictions on model parameters based on the inherent physical laws or engineering experience of the system. Physical constraints ensure that the changing trends of parameters such as modal frequencies and damping ratios conform to actual physical phenomena. Ensuring the reasonableness of posterior parameters means that the parameter estimates are not only mathematically optimal but also physically acceptable and consistent with reality. By introducing physical constraints, the optimization process can guide the parameter estimates to fall within a reasonable physical range. A penalty function is a method that transforms constraints into part of the objective function. When the model's predictions deviate from actual milling experimental data, the penalty function increases the value of the objective function, thus penalizing parameter combinations that do not conform to the experimental data. The penalty intensity increases with the increase of prediction error, prompting the model to better fit the data.
[0063] This application combines Bayesian inference with the MAP optimization algorithm and introduces physical constraints and a penalty function to form a robust parameter estimation framework. In step 5, to obtain the posterior mean estimate of the function coefficients, the MAP optimization algorithm is used to minimize a specific objective function, which is a negative logarithmic posterior probability, including not only data likelihood terms and parameter prior terms but also a penalty function. When the chatter stability result predicted based on the currently estimated function coefficients deviates from the actual milling experimental data (chatter labels), the penalty function increases the value of the objective function according to the magnitude of the deviation. This prompts the optimization algorithm to not only maximize the posterior probability when searching for the optimal function coefficients but also ensure that the model prediction is highly consistent with the experimental data. At the same time, physical constraints are introduced to ensure that the estimated function coefficients can generate system parameters that conform to physical laws, thereby guaranteeing the rationality of the posterior parameters. In this way, the MAP optimization algorithm continuously adjusts the function coefficients during the iteration process until it finds a set of parameters that both fits the experimental data well, satisfies the physical constraints, and has the maximum posterior probability.
[0064] Step 6: Determine the specific functional expressions for the system parameters to obtain the probability distribution of the flutter stability domain. Specifically, this includes: obtaining the functional expressions for the modal frequency and equivalent damping ratio as a function of rotational speed based on the obtained posterior distribution estimates. Inputting the predicted system parameters into a Gaussian process regression model and calculating the spectral radius at each grid point allows the probability distribution of the flutter stability boundary to be obtained through the flutter probability model.
[0065] refer to Figure 3 The results shown are the flutter stability domain lobe diagrams predicted using the method proposed in this invention, given system parameters and flutter tag data. The prediction accuracy was verified using experimental data points.
[0066] The present invention also provides a mechanism-data fusion driven milling chatter stability prediction system, including a data acquisition module, a parameterized function model construction module, a mapping relationship construction module, a chatter probability model construction module, a Bayesian inference module, and a probability distribution calculation module; The data acquisition module is used to obtain milling dynamics system parameters and chatter label data through modal parameter identification and trial cutting experiments; The parameterized function model building module is based on the physical law of the change of milling dynamic system parameters with rotational speed, and constructs a parameterized function model of modal frequency and equivalent damping ratio with respect to spindle speed; The mapping relationship construction module is used to construct a Gaussian process regression model, and establishes a mapping relationship between the coefficients of the parameterized function model and the spectral radius through the Gaussian process regression model; The flutter probability model construction module constructs a flutter probability model based on Floquet theory and builds a Bernoulli likelihood function based on flutter label data; The Bayesian inference module is used to introduce physical constraints, perform Bayesian inference based on the MAP optimization algorithm, and obtain the posterior mean estimate of the model coefficients. The probability distribution calculation module is used to determine the specific functional expressions of the milling dynamics system parameters and obtain the probability distribution of the chatter stability domain.
[0067] On the other hand, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the implementation of a mechanism-data fusion-driven milling chatter stability prediction method as described in the present invention.
[0068] The present invention can also provide a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and the processor can implement the mechanism-data fusion driven milling chatter stability prediction method described in the present invention when executing the computer executable program.
[0069] The computer device may be a laptop, a desktop computer, or a workstation.
[0070] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).
[0071] The memory described in this invention can be an internal storage unit of a laptop, desktop computer, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.
[0072] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).
[0073] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.
Claims
1. A mechanism-data fusion-driven method for predicting the stability of milling chatter, characterized in that, Includes the following steps: Milling dynamics system parameters and chatter label data were obtained through modal parameter identification and trial cutting experiments; Based on the physical laws governing the variation of milling dynamics system parameters with rotational speed, a parameterized function model of modal frequency and equivalent damping ratio with respect to spindle speed is constructed. Construct a Gaussian process regression model, and establish the mapping relationship between the coefficients of the parameterized function model and the spectral radius through the Gaussian process regression model; A flutter probability model is constructed based on Floquet theory, and a Bernoulli likelihood function is constructed based on flutter label data. By introducing physical constraints, Bayesian inference is performed based on the MAP optimization algorithm to obtain the posterior mean estimate of the model coefficients. Determine the specific functional expressions of the parameters of the milling dynamics system to obtain the probability distribution of the chatter stability domain.
2. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, The parameterized functional models for modal frequencies and equivalent damping ratio with respect to spindle speed are as follows: in, and These are the modal parameters measured when the system is at rest, i.e., the prior means; , , , Let be the undetermined coefficients of the function. The main spindle speed.
3. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, The spectral radius at each rotational speed-depth grid point is solved using the fully discrete method. A Gaussian regression model is then trained to obtain the relationship between the system parameters and the spectral radius, specifically expressed as follows: in, The relationship between the coefficients of the parameterized function model and the spectral radius, representing the maximum spectral radius of the system's transfer function matrix, is expressed as: in, , , , , , , , All of these are undetermined coefficients of the model. The parameterized function model is used to calculate the spectral radius under the corresponding cutting conditions given the function coefficients.
4. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, The flutter probability model based on Floquet theory is as follows: in, These are hyperparameters used to control model accuracy. flutter probability at location P =0.5; The flutter probability should follow Increase rapidly; The flutter probability should follow The increase was followed by a rapid decrease.
5. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, Bernoulli likelihood function is: Bernoulli likelihood represents the expression in the parameter vector The experimental results were observed below. The probability of; where, For experimental data points The flutter label.
6. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, Introducing physical constraints and performing Bayesian inference based on the MAP optimization algorithm to obtain the posterior mean estimate of the model coefficients includes: introducing physical constraints with the objective of minimizing the negative log-posterior, the objective function of which is expressed as: in, The penalty function is applied to the objective function when the predicted result deviates from the milling experimental data. The penalty intensity increases with the increase of the prediction error. The specific expression of the penalty function is as follows: in, This is the penalty coefficient, used to adjust the intensity of the penalty.
7. The mechanism-data fusion driven milling chatter stability prediction method according to claim 1, characterized in that, Determining the specific functional expressions of the milling dynamics system parameters and obtaining the probability distribution of the chatter stability domain includes: using the posterior estimates of the function coefficients of the system parameters as a function of rotational speed obtained by Bayesian inference; solving the system parameters at each target rotational speed based on the parameterized function model; solving the spectral radius at all nodes in the rotational speed-depth discrete grid based on the Gaussian regression model; and solving the probability distribution of the chatter stability boundary based on the chatter probability model.
8. A mechanism-data fusion driven milling chatter stability prediction system, characterized in that, It includes a data acquisition module, a parameterized function model construction module, a mapping relationship construction module, a flutter probability model construction module, a Bayesian inference module, and a probability distribution calculation module; The data acquisition module is used to obtain milling dynamics system parameters and chatter label data through modal parameter identification and trial cutting experiments; The parameterized function model building module is based on the physical law of the change of milling dynamic system parameters with rotational speed, and constructs a parameterized function model of modal frequency and equivalent damping ratio with respect to spindle speed; The mapping relationship construction module is used to construct a Gaussian process regression model, and establishes a mapping relationship between the coefficients of the parameterized function model and the spectral radius through the Gaussian process regression model; The flutter probability model construction module constructs a flutter probability model based on Floquet theory and builds a Bernoulli likelihood function based on flutter label data; The Bayesian inference module is used to introduce physical constraints, perform Bayesian inference based on the MAP optimization algorithm, and obtain the posterior mean estimate of the model coefficients. The probability distribution calculation module is used to determine the specific functional expressions of the milling dynamics system parameters and obtain the probability distribution of the chatter stability domain.
9. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and when the processor executes part or all of the computer-executable program, it can implement the mechanism-data fusion driven milling chatter stability prediction method according to any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of a mechanism-data fusion-driven milling chatter stability prediction method as described in any one of claims 1-7.