Structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables

Abstract

The present invention belongs to the technical field related to modeling of whole machine structural dynamics, and discloses a structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables, comprising the following steps: (1) correlating multi-dimensional variables in the equipment processing process, and using a clustering algorithm to reduce the dimension of the dynamic characteristic data obtained by correlation; (2) using the frequency response function corresponding to the main vibration mode at the weak link to uniformly characterize the dynamic characteristic data of the whole machine structure of the equipment during the processing; (3) using the whole machine mechanism model of the equipment to pre-process the data; (4) using the data model of the mixed Gaussian process to analyze the data to track the multi-time scale evolution of the system performance parameters in the whole machine mechanism model; (5) performing multi-time scale dynamic modeling of the whole machine structural dynamic characteristics, and using the obtained multi-time scale dynamic model to predict the structural performance of the equipment. The present invention improves the accuracy and prediction speed.

Description

Technical Field

[0001] The present invention belongs to the technical field related to modeling of whole machine structural dynamics, and more specifically, relates to a structural performance prediction method of whole machine structural dynamics based on multi-dimensional variables. Background Art

[0002] The overall structural dynamics of a CNC machine tool directly impacts machining performance and determines the product's machining accuracy and efficiency. Different machining positions occur during different machining steps. As the functional positions of machine tool components (such as the worktable, sleeve, crossbeam, and column) change, the structural stiffness matrix, damping matrix, and mass matrix change during system motion. Simultaneously, as cutting excitation variables (such as cutting force, feed rate, and spindle speed) change during machining, the structural dynamics of the corresponding system also undergo associated changes. These associated changes represent short-timescale characteristics of the structural dynamics during machining. On the other hand, factors such as wear at the joints of machine tool components will lead to long-term performance evolution trends in the machine tool structure itself. Therefore, in addition to its inherent short-timescale variations that vary with machining state variables, the structural dynamics of the machine tool during machining also evolve over a long timescale.

[0003] Existing dynamic models in this field, due to the partially unknown physical properties of the research object, are mostly based on a deterministic model of a specific sub-problem, thus providing single-input, single-output process control. As a result, these models struggle to capture the changing characteristics of structural dynamics during actual machining. For example, they are unable to determine the dynamic characteristics associated with factors such as operating position, speed, and joint characteristics, making the current model simulation applications difficult to promote in practice. Therefore, it is necessary to develop a multi-time-scale dynamic modeling method for the dynamics of the entire machine structure under multi-dimensional variables. Summary of the Invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a structural performance prediction method based on the structural dynamics of the whole machine under multi-dimensional variables. It takes the unified follow-up representation of the structural dynamics of the whole machine under multi-dimensional variables as the basic data, and adopts a multi-time-scale dynamic model that integrates the mechanism model and the data model to accurately identify the short-time-scale characteristics associated with the operating state variables of the structural stiffness, mass and damping matrix and the long-time-scale characteristics associated with factors such as joint wear, so as to be used for accurate prediction and health management of machine tool structural performance.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for predicting structural performance of an entire machine based on structural dynamics under multi-dimensional variables is provided, the method comprising the following steps:

[0006] (1) Based on the weak links of the equipment, the position variables and cutting excitation variables of the processing equipment are associated during the processing. At the same time, a clustering algorithm is used to reduce the dimension of the dynamic characteristic data obtained by the association, thereby realizing the division of the equipment workspace;

[0007] (2) Using the frequency response function corresponding to the main vibration mode at the weak link, the dynamic characteristic data of the entire equipment structure during the processing is uniformly characterized;

[0008] (3) Using the whole machine mechanism model of the equipment to pre-process the data of the unified follow-up characterization;

[0009] (4) Analyze the preprocessed data using a mixed Gaussian process data model to track the multi-time-scale evolution of system performance parameters in the overall machine mechanism model;

[0010] (5) The obtained multi-time scale evolution results are integrated with the whole machine mechanism model to carry out multi-time scale dynamic modeling of the whole machine structural dynamic characteristics, and the obtained multi-time scale dynamic model is used to predict the structural performance of the equipment; the mathematical expression of the multi-time scale dynamic model is:

[0011]

[0012] Where f0(t) is the excitation force of the system; m0 is the mass of the system; y0(t) is the dynamic response of the system; c0 is the dynamic response of the system; t is the natural time of the system; k0 is the stiffness of the system; Δk(t s ) is the stiffness evolution on a long time scale; t s is the time for the long-term evolution of the structure.

[0013] Further, among them,

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Where ω0 and σ0 are t s =0 when the natural frequency and damping ratio of the equipment; ω s (t s ),σ s (ts ) and ω ds (t s ) represent the natural frequency, damping ratio and damped natural frequency at t s The evolution of the situation.

[0021] Furthermore, the corresponding formula for evolution is:

[0022] x q |t~gp(μ q (t; h),κ q (t1, t2; l)), q=1, 2, ... Q

[0023] μ q (t) = h T φ(t)

[0024] Where μ q (t) represents the mean value of the Gaussian process; h represents the unknown coefficient; φ(t) represents the basis function vector; κ q represents the correlation function with the length scale parameter l; h and l are called hyperparameters of the Gaussian process.

[0025] Furthermore, the mathematical expression of the whole machine mechanism model considering multiple time scales is:

[0026]

[0027] Where, t s is the time of long-term structural evolution, a system parameter; among them,

[0028] K(t s )=K0(1+ΔK(t s ))

[0029] and M(t s )=M0(1+ΔM(t s ));

[0030] Where, K(t s ) is expected to be a long-term decay function; M(t s ) is an increasing or decreasing function.

[0031] Furthermore, the damped natural frequency of the system is:

[0032]

[0033] Where ω0 and σ0 are t s =0 when the natural frequency and damping ratio of the equipment; ω s (t s ),σ s (t s )and They represent the natural frequency, damping ratio and damped natural frequency at t respectively. s The evolution of the situation.

[0034] Furthermore, the dynamic characteristics of the whole machine structure are uniformly characterized as follows:

[0035]

[0036] Where H(ω) is the frequency response function of the weak link corresponding to the t-th order mode; ω t is the natural frequency of the t-th mode; ξ t is the normalized mode shape of the t-th mode; σ t is the damping ratio of the t-th mode.

[0037] Furthermore, the position variables are correlated with the changes in the weak links of the equipment, and the chip excitation variables are correlated with the dynamic response of the weak links.

[0038] Furthermore, the weak link is a part of the entire machine where the amplitude of the modal mass distribution is greater than a preset threshold.

[0039] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0040] 1. The present invention performs process association on multi-dimensional variables in complex machining processes, and uses clustering algorithms to perform dimensionality reduction and compression on massive data related to position variables, thereby reducing the amount of data processing and improving efficiency.

[0041] 2. The frequency response function corresponding to the main vibration mode at the weak link is used to uniformly characterize the structural dynamic characteristics data of the entire machine under multi-dimensional variables during the processing process. According to the variables that appear during the processing, the corresponding system model can be transformed to capture the actual changes in the structural dynamic characteristics, which is highly flexible.

[0042] 3. Effectively integrate the multi-time scale evolution results of the data model with the mechanism model (system dynamics equation) to realize the multi-time scale dynamic modeling of the whole machine structure dynamic characteristics, and be able to track the multi-time scale evolution of the system performance parameters in the mechanism model.

[0043] 4. Based on the multi-time-scale dynamic model, the short-time-scale characteristics associated with the operating state variables of the structural stiffness, mass and damping matrix and the long-time-scale characteristics associated with factors such as joint wear are accurately identified to achieve accurate prediction of machine tool structural performance and health management, thereby improving machining accuracy and reducing maintenance costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a method for predicting structural performance of a whole machine based on structural dynamics under multi-dimensional variables provided by the present invention;

[0045] Figure 2 It is a schematic diagram of the multi-dimensional process variable association and unified follow-up representation based on weak links;

[0046] Figure 3 This is a schematic diagram of the unified follow-up representation of the dynamic characteristics based on the frequency response function;

[0047] Figure 4 Schematic diagram of the evolution of dynamic stiffness under multi-time scale modeling during the machining process. DETAILED DESCRIPTION

[0048] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0049] The present invention provides a structural performance prediction method based on the structural dynamics of the whole machine under multi-dimensional variables, and the prediction method mainly includes the following steps:

[0050] In the first step, based on the weak links of the equipment, the position variables and cutting excitation variables of the processing equipment during the processing are associated. At the same time, a clustering algorithm is used to reduce the dimension of the dynamic characteristic data obtained by the association, thereby realizing the division of the equipment workspace.

[0051] See also Figure 1 and Figure 2 In this implementation, a machine tool is used as an example. The machine tool structure is the fundamental component of the machining process. The weak links in the machine tool structure are used as a benchmark to correlate multidimensional variables (position variables and cutting excitation variables) during the machining process. The dynamic characteristic data associated with position variables is multidimensional, massive, and non-uniform, making it difficult to effectively classify. Therefore, a clustering algorithm is used to reduce the dimensionality of this massive amount of dynamic characteristic data, using changes in the weak links of the machine tool structure as a criterion.

[0052] The position variables are correlated with changes in the machine tool's weak links, and the chip excitation variables are correlated with the dynamic response of the weak links. A weak link is a location in the machine where the modal mass distribution amplitude is greater than a preset threshold.

[0053] Step 2: Use the frequency response function corresponding to the main vibration mode of the weak link to uniformly characterize the dynamic characteristic data of the entire equipment structure during the processing.

[0054] See also Figure 3 In this embodiment, under the multi-dimensional variable correlation interaction during the machine tool processing process, the main vibration mode for unified representation of the dynamic characteristics of the entire machine structure is the t-th order mode, and the modal mass distribution of the t-th order mode is expressed as:

[0055]

[0056]

[0057] Where m t represents the distribution of the modal mass of the t-th mode of the entire machine structure across each degree of freedom. The degree of freedom with the largest modal mass distribution amplitude is the weakest link in the structure. r represents the r-th degree of freedom among the n degrees of freedom of the machine tool structure, M is the mass matrix of the structure, and ξ is the modal vibration shape.

[0058] Then, the final unified follow-up representation of the dynamic characteristics of the whole machine structure is:

[0059]

[0060] Where H(ω) is the frequency response function of the weak link corresponding to the t-th order mode; ω t is the natural frequency of the t-th mode; ξ t is the normalized mode shape of the t-th mode; σ t is the damping ratio of the t-th mode.

[0061] Step three: Use the whole machine mechanism model of the equipment to preprocess the data of the unified follow-up characterization.

[0062] Among them, the expression of the mechanism model of the whole machine structural dynamics at a single time scale is:

[0063]

[0064] Where M0, C0 and K0 are the mass, damping and stiffness of the system respectively, t is the natural time of the system, F0(t) and y0(t) are the excitation force and dynamic response of the system respectively. Then, the mathematical expression of the whole machine mechanism model considering multiple time scales is:

[0065]

[0066] Where, t s is the time of long-term evolution of the structure. System parameters, such as mass, damping and stiffness, will change with the use time t sAnd the changes, it should be noted that t s Much slower than t.

[0067] Without loss of generality, consider the following functional forms for mass and stiffness:

[0068] K(t s )=K0(1+ΔK(t s ))

[0069] and M(t s )=M0(1+ΔM(t s ))

[0070] Generally speaking, K(t s ) is expected to be a long-term decay function to represent the loss of system stiffness. On the other hand, M(t s ) can be an increasing or decreasing function. Here, a single degree of freedom system is used. Assuming that the mass and damping of the model remain unchanged and only the stiffness changes, the corresponding dynamic equation is:

[0071]

[0072] Solving the characteristic equation, the damped natural frequency of the system can be expressed as:

[0073]

[0074] Here, ω0 and σ0 are t s =0 when the system's natural frequency and damping ratio; ω s (t s ),σ s (t s ) and ω ds (t s ) represent the natural frequency, damping ratio and damped natural frequency at t s The evolution of the situation is as follows:

[0075]

[0076]

[0077]

[0078] Then, we can get Δk(t s ) is used for dynamic modeling under multi-time scale evolution and is expressed as:

[0079]

[0080] Step 4: Use the data model of mixed Gaussian processes to analyze the preprocessed data to track the multi-time scale evolution of system performance parameters in the whole machine mechanism model.

[0081] See also Figure 4 , the evolution of system parameters has multi-time scale characteristics and is difficult to learn, so the data model of mixed Gaussian process is used to learn the evolution of system parameters. Assume that the parameter evolution is in discrete time t s There is an observation sequence Assume that the observation sequence x is generated from Q hidden states t (q) , q = 1, 2, ..., Q is also called an expert. Such hidden states are usually considered independent and can evolve independently of each other. Here, it is assumed that the independent hidden states evolve according to a Gaussian process, then:

[0082] x q |t~gp(μ q (t; h),κ q (t1, t2; l)), q=1, 2, ... Q

[0083] μ q (t) = h T φ(t)

[0084] Where μ q (t) represents the mean value of the Gaussian process; h represents the unknown coefficient; φ(t) represents the basis function vector, κ q Denotes the function related to the length scale parameter l, h and l are called the hyperparameters of the Gaussian process. These hidden states can be coupled in a generative manner to obtain the underlying data, expressed as:

[0085]

[0086] x q is the qth Gaussian process expert, z q (t) is the qth gating function, expressed as:

[0087]

[0088] in, is the hyperparameter of the gating function; is a hyperparameter associated with the expert function. All hyperparameters need to be estimated based on the training data. One way to achieve this is to perform maximum likelihood estimation on the data model, which can be expressed as:

[0089]

[0090] In order to reduce computation time, some of the hyperparameters are treated in a Bayesian manner:

[0091]

[0092] Step 5: The obtained multi-time scale evolution results are integrated with the whole machine mechanism model, and then the multi-time scale dynamic modeling of the whole machine structural dynamic characteristics is carried out. The mathematical expression of the obtained multi-time scale dynamic model is:

[0093]

[0094] Where f0(t) is the excitation force of the system; m0 is the mass of the system; y0(t) is the dynamic response of the system; c0 is the damping of the system; t is the natural time of the system; k0 is the stiffness of the system; Δk(t s ) is the stiffness evolution on a long time scale; t s is the time for the long-term evolution of the structure.

[0095] Step six: Use the multi-time-scale dynamic model to predict the structural performance of the equipment.

[0096] Among them, the structural performance includes stiffness and damping. After obtaining the prediction results, the health management of the equipment is also carried out; the machine tool is preferably a CNC machine tool, and it is also aimed at the whole machine structural dynamics at multiple time scales under multi-dimensional variables during the processing process.

[0097] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A structural performance prediction method based on the structural dynamics of a whole machine under multi-dimensional variables, characterized in that: The method comprises the following steps: (1) Based on the weak links of the equipment, the position variables and cutting excitation variables of the processing equipment are associated during the processing. At the same time, a clustering algorithm is used to reduce the dimension of the dynamic characteristic data obtained by the association, thereby realizing the division of the equipment workspace; (2) Using the frequency response function corresponding to the main vibration mode at the weak link, the dynamic characteristic data of the entire equipment structure during the processing is uniformly characterized; (3) Using the whole machine mechanism model of the equipment to pre-process the data of the unified follow-up characterization; (4) Analyze the preprocessed data using a mixed Gaussian process data model to track the multi-time-scale evolution of system performance parameters in the overall machine mechanism model; (5) The obtained multi-time scale evolution results are integrated with the whole machine mechanism model to conduct multi-time scale dynamic modeling of the whole machine structural dynamic characteristics, and the obtained multi-time scale dynamic model is used to predict the structural performance of the equipment; the mathematical expression of the multi-time scale dynamic model is: Where f0(t) is the excitation force of the system; m0 is the mass of the system; y0(t) is the dynamic response of the system; c0 is the damping of the system; t is the natural time of the system; k0 is the stiffness of the system; Δk(t s ) is the stiffness evolution on a long time scale; t s is the time for the long-term evolution of the structure.

2. The structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables according to claim 1, characterized in that: in, Where ω0 and σ0 are t s =0 when the natural frequency and damping ratio of the equipment; ω s (t s ),σ s (t s )and They represent the natural frequency, damping ratio and damped natural frequency at t respectively. s The evolution of the situation.

3. The structural performance prediction method based on the whole machine structural dynamics under multi-dimensional variables according to claim 2, characterized in that: The corresponding formula for evolution is: x q |t~gp(μ q (t;h),κ q (t1,t2;l)),q=1,2,…Q m q (t)=h T φ(t) Where μ q (t) represents the mean value of the Gaussian process; h represents the unknown coefficient; φ(t) represents the basis function vector; κ q represents the correlation function with the length scale parameter l; Among them, the hidden state is coupled in a generative manner to obtain the basic data, which is expressed as: x q is the qth Gaussian process expert, z q (t) is the qth gating function, expressed as: in, is the hyperparameter of the gating function; is a hyperparameter related to the expert function; all hyperparameters need to be estimated based on the training data, which is achieved by performing maximum likelihood estimation on the data model, expressed as: In order to reduce the computation time, some of the hyperparameters are processed in a Bayesian way, specifically:

4. The structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables according to claim 1, characterized in that: The mathematical expression of the whole machine mechanism model considering multiple time scales is: Where, t s is the time of long-term structural evolution, a system parameter; among them, K(t s )=K0(1+ΔK(t s )) and M(t s )=M0(1+ΔM(t s )); Where, K(t s ) is expected to be a long-term decay function; M(t s ) is an increasing or decreasing function.

5. The structural performance prediction method based on the whole machine structural dynamics under multi-dimensional variables according to claim 4, characterized in that: The damped natural frequency of the system is: Where ω0 and σ0 are t s =0 when the natural frequency and damping ratio of the equipment; ω s (t s ),σ s (t s )and They represent the natural frequency, damping ratio and damped natural frequency at t respectively. s The evolution of the situation.

6. The structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables according to any one of claims 1 to 5, characterized in that: The unified characterization of the dynamic characteristics of the whole machine structure is: Where H(ω) is the frequency response function of the weak link corresponding to the t-th order mode; ω t is the natural frequency of the t-th mode; ξ t is the normalized mode shape of the t-th mode; σ t is the damping ratio of the t-th mode.

7. The structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables according to any one of claims 1 to 5, characterized in that: The position variables are correlated with the changes in the weak links of the equipment, and the chip excitation variables are correlated with the dynamic response of the weak links.

8. The structural performance prediction method based on whole machine structural dynamics under multi-dimensional variables according to claim 7, characterized in that: The weak link is the part of the whole machine where the amplitude of the modal mass distribution is greater than the preset threshold.

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