A method for designing an excitation signal for parameter identification of a machine tool feed system

Abstract

The application belongs to the technical field of excitation signal design, and discloses a design method of an excitation signal for parameter identification of a machine tool feeding system, which comprises the following steps: establishing a feeding model of the machine tool feeding system, determining the type and value range of the parameter to be identified, selecting a standard parameter in the value range, and designing candidate excitation signals of different types; inputting the standard parameter into the feeding model to obtain a standard simulation result; selecting a parameter initial value in the value range, and performing parameter expansion to generate a value set; inputting each value in the value set into the feeding model to obtain a corresponding simulation result, and calculating the simulation error of the simulation result and the standard simulation result; obtaining the sensitivity of the parameter; selecting different excitation signals to sequentially execute the above steps, obtaining the sensitivity of different parameters under the corresponding type of excitation signal, and taking the excitation signal with the highest sensitivity as the excitation signal required for identifying the parameter. The application can significantly improve the design precision of the parameter excitation signal.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field related to excitation signal design, and more particularly, to a design method of an excitation signal for parameter identification of a machine tool feeding system. BACKGROUND

[0002] As a high-efficiency, high-precision, and high-automation machining equipment, a numerical control machine tool has a very important position in the manufacturing industry and is widely used in the fields of aerospace, automobile, nuclear power, medical machinery, engineering machinery, etc. The numerical control machine tool has a complex structure, and the establishment of a mathematical model of the machine tool is helpful for analyzing the dynamic characteristics of the machine tool, and plays an important role in improving the machining precision of the machine tool and improving the dynamic characteristics of the machine tool.

[0003] The mathematical model of the machine tool feeding system mainly involves a servo control system and a mechanical transmission system. The purpose of parameter identification of the feeding system is to make the simulation model of the feeding system built have higher simulation precision, so as to more accurately reflect the dynamic characteristics of the real machine tool feeding system, so that the simulation model can provide better help for improving the dynamic characteristics of the machine tool feeding system, improving the tracking precision, machining efficiency, and machining quality.

[0004] The machine tool feeding system is a complex electromechanical coupling system, and the mathematical model of the feeding system often contains a large number of parameters, some of which are difficult to obtain directly through measurement and table lookup, such as the mass of the worktable, the friction coefficient of the worktable, the stiffness of the feeding system, the damping, etc. The main object of parameter identification of the feeding system is these parameters which are difficult to determine and have a significant influence on the dynamic characteristics of the feeding system.

[0005] When identifying the parameters of the mathematical model of the feeding system, a specific signal needs to be used as an excitation to obtain the response data of the feeding system and the mathematical model, and then the least square method, genetic algorithm, artificial intelligence, etc. are used to identify the model parameters. According to the difference between the identification methods and the identification objects, different excitation signals are used in the existing parameter identification. Kaan Erkorkmaz et al. used a series of step input signals with different speeds to identify the dynamic parameters and friction characteristics of the machine tool feeding system. Guo Yongcai designed an inverse repetitive m-sequence signal as an identification signal in the parameter identification of the machine tool feeding system. Zhao Fei et al. designed a G code with a frequency of 100 Hz to excite the machine tool, and obtained the response characteristics of the machine tool through the internal sensors of the machine tool to identify the natural frequency of the feeding system.

[0006] When identifying the parameters of a machine tool feed system, the selection of the excitation signal is important because different types of parameters often have different sensitivities to the excitation signal. For example, when the system is in uniform motion, the inertia parameter has little effect on the system, and when the system is running at high speed, the Stribeck speed parameter in the Stribeck friction model has little effect on the system. In the existing parameter identification method for the feed system, the sensitivity of the identification parameter to the excitation signal is not analyzed when designing the excitation signal, and some parameters may have low sensitivity, which affects the accuracy of parameter identification. Therefore, there is an urgent need to design a method for improving the accuracy of parameter identification. SUMMARY

[0007] In view of the above defects or improvement needs of the prior art, the present application provides a design method of an excitation signal for parameter identification of a machine tool feed system, which can significantly improve the design accuracy of the excitation signal.

[0008] To achieve the above-mentioned purpose, according to one aspect of the present application, a design method of an excitation signal for parameter identification of a machine tool feed system is provided, the method comprising: S1: establishing a feed model of the machine tool feed system, determining the type and value range of the to-be-identified parameter, selecting a parameter in the value range as a standard parameter for each type, and designing different types of candidate excitation signals; S2: selecting an excitation signal, and inputting the standard parameter into the feed model to obtain a standard simulation result under the excitation signal; S3: selecting a parameter initial value in the value range, and generating a value set by parameter expansion with the parameter initial value as a starting point; S4: inputting each value in the value set into the feed model to obtain a corresponding simulation result under the excitation signal, and calculating the error between the simulation result and the standard simulation result to obtain the simulation error of each value in the value set; S5: obtaining the average value of the change rate of the simulation error of each value in the value set to obtain the sensitivity of the parameter; S6: selecting different excitation signals to sequentially execute steps S3-S5, obtaining the sensitivity of different parameters under the corresponding type of excitation signal, and selecting the excitation signal with the highest sensitivity as the excitation signal for identifying the corresponding parameter.

[0009] Preferably, the specific formula for calculating the error between the simulation result and the standard simulation result to obtain the simulation error of each value in the value set in step S4 is:

[0010]

[0011] wherein, is the simulation error of each value in the value set, K is the number of simulation result types, rms is a function for calculating the root mean square, i is the number of the to-be-identified excitation signal, j is the parameter number in the value set, is the kth type in the standard simulation result.

[0012] Preferably, the formula for calculating the sensitivity in step S5 is:

[0013]

[0014] Where, η i Let be the sensitivity of the parameter to be identified, with number i, and j be the parameter number in the set of values. M represents the simulation error for each value in the set of values, and M represents the total number of elements in the set of values.

[0015] Preferably, in step S3, the parameters are expanded forward and backward from the initial value, and the expanded value range is within a preset value range. The specific formula is as follows:

[0016]

[0017] in, Initialize parameter p i The lower bound of the range of values. Initialize parameter p i The upper bound of the value range, l is the step size, n is the nth value of forward or backward expansion, and i is the number of the excitation signal to be identified.

[0018] Preferably, in step S3, expanding the parameters to generate a set of values ​​starting from the initial parameter value specifically involves expanding the parameters to generate a set of values ​​with a specific step size starting from the initial parameter value.

[0019] Preferably, the specific step size is selected as a preset proportion of the length of the value range.

[0020] Preferably, the excitation signal in step S1 includes a sine wave signal, a triangular wave signal, a trapezoidal wave signal, and a white noise signal.

[0021] Preferably, in step S1, parameters are randomly selected as standard parameters, and in step S3, the initial values ​​of the parameters selected are not repeated with the standard parameters.

[0022] Preferably, in step S4, calculating the error between the simulation result and the standard simulation result specifically involves calculating the root mean square error between the simulation result and the standard simulation result.

[0023] In summary, compared with the prior art, the design method for excitation signals for parameter identification in a machine tool feed system provided by the present invention has the following advantages:

[0024] 1. The application takes the sensitivity of model parameters to the excitation signal as the evaluation standard of whether the excitation signal is suitable for parameter identification, and selects the excitation signal with the highest sensitivity for parameter identification, which can improve the accuracy of parameter identification.

[0025] 2. The application expands the number system according to a certain rule with the initial value as the starting point, which ensures the uniformity of the value set and makes it easier to find reasonable parameters.

[0026] 3. Compared with the existing mathematical model parameter identification signal of the numerical control machine tool feeding system, the application can select the identification signal with the highest sensitivity according to the different identification objects, so that the best identification effect can be achieved for different identification objects. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a step schematic diagram of the machine tool feeding system mechanism signal design method based on parameter sensitivity of the embodiment of the application;

[0028] Figure 2 is a flow chart of the machine tool feeding system mechanism signal design method based on parameter sensitivity of the embodiment of the application;

[0029] Figure 3 is a numerical control machine tool feeding system mathematical model built by the embodiment of the application using simulink;

[0030] Figure 4 (a) in is the displacement curve diagram of the sinusoidal speed signal of the embodiment of the application, and (b) is the speed curve diagram of the sinusoidal speed signal of the embodiment of the application;

[0031] Figure 5 (a) in is the displacement curve diagram of the triangular wave speed signal of the embodiment of the application, and (b) is the speed curve diagram of the triangular wave speed signal of the embodiment of the application;

[0032] Figure 6 is the sensitivity heat map of the model parameters under different excitation signals in the embodiment of the application. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0034] The application provides a design method of an excitation signal for parameter identification of a machine tool feeding system, such as Figure 1 and Figure 2As shown, the method comprises the following steps S1-S6.

[0035] S1: establishing a feed model of the machine tool feed system, determining the type and value range of the to-be-identified parameters, selecting parameters as standard parameters in the value range for each type, and designing candidate excitation signals of different types.

[0036] The feed model is a mathematical model constructed by prior art, such as a lumped mass model, a distributed mass model, etc. The feed model has no strict requirements, but should be able to reflect the composition and characteristics of the machine tool feed system, and be able to obtain simulation results such as the rotation angle, rotation speed, angular acceleration of the motor, displacement, speed, acceleration of the workbench, and motor current, etc.

[0037] The types of excitation signals include sine signals, triangular wave signals, trapezoidal wave signals, white noise signals, etc.

[0038] In a further preferred scheme, the parameters are randomly selected as standard parameters P std .

[0039] As shown in Figure 2 , when analyzing the sensitivity of the model parameters to the excitation signals, a mathematical model of the numerical control machine tool feed system needs to be established first, and the embodiment of the present application uses simulink to establish a mathematical model of the feed system, as shown in Figure 3 , the mathematical modeling of the machine tool feed system can be summarized as the following general process:

[0040] (1) Establish a schematic diagram of the known or initially proposed system, and determine the basic parameters.

[0041] (2) Simplify the actual structure, or divide it into several sub-structures, and apply the dynamics theorem to establish the mathematical model of the system. For cases that cannot be directly modeled by the dynamics theorem, test data can be used to establish an empirical mathematical model of input-output.

[0042] (3) Prove the accuracy of the mathematical model through tests.

[0043] According to the actual structure of the machine tool, different dynamics models can be established through different ways and degrees of simplification, the most common ones being: lumped mass model, distributed mass model, finite element model, and hybrid model. The mathematical model of the mechanical part of the machine tool feed system established in this embodiment is a lumped mass model, the moment of inertia of the motor, coupling, and lead screw is equivalent to one moment of inertia, and the model also contains the equivalent axial stiffness and damping of the feed system. In addition to the above moment of inertia and stiffness and damping parameters, the mathematical model of the machine tool feed system of this embodiment also contains the following parameters: related parameters of the stribeck friction model of the workbench, related parameters of the servo control model, and 11 excitation signals to be identified.

[0044] After the mathematical model of the machine tool feed system is established, some different types and different amplitude frequency signals are selected as candidate excitation signals for parameter identification. In this embodiment, sinusoidal velocity signals and triangular wave velocity signals of different amplitudes and frequencies are selected. Because the sinusoidal signal is a periodic signal with a single frequency component, it can be combined into any periodic signal through different amplitudes and frequencies and phases. The sinusoidal signal is also one of the widely used input signals in feed system parameter identification. The triangular wave velocity signal is a uniform acceleration motion, and the acceleration remains unchanged during acceleration and deceleration, which is convenient for analyzing the sensitivity change of parameters under different accelerations. The triangular wave can be regarded as a waveform composed of multiple sinusoidal waves, containing multiple harmonic components, and is often used as a test signal for system identification. The amplitudes and frequencies of the candidate signals are shown in Table 1. The sinusoidal velocity signal with a frequency of 1 Hz is shown in Figure 4 , the triangular wave velocity signal is shown in Figure 5 , and the signals run for 3 cycles.

[0045]

[0046]

[0047] Table 1

[0048] S2: input the standard parameters into the feed model to obtain standard simulation results.

[0049] The standard parameters and parameters that can be obtained by measurement and table lookup are input into the feed model to obtain simulation results Y std , the simulation results Y std include K different types, and the simulation results can be represented as:

[0050]

[0051] The mathematical model has a plurality of different types of simulation results. In this embodiment, the simulation result types and their symbol correspondence are shown in Table 2.

[0052]

[0053] Table 2

[0054] Wherein the worktable displacement error and the velocity error are the differences between the worktable displacement and velocity and the screw nut displacement and velocity. The displacement and velocity of the screw nut can be converted according to the motor rotation angle and speed through the ball screw transmission pair, i.e.

[0055]

[0056]

[0057] wherein h is the lead of the ball screw, in the embodiment, h = 16 mm.

[0058] S3: selecting a parameter initial value in the value range, and generating a value set by parameter expansion with the parameter initial value as a starting point.

[0059] selecting a parameter initial value P in the value range init , wherein the parameter initial value is different from the standard parameter P std .

[0060] In a further preferred scheme, the parameter initial value is expanded forward and backward, and the expanded value range is within the preset value range, and the specific formula is:

[0061]

[0062] wherein, is the lower limit of the value range of the parameter initial value p i , and is the upper limit of the value range of the parameter initial value p i , l is a step length, n is the nth value of the forward or backward expansion, i is the number of the to-be-recognized excitation signal, and M is the number of elements in the value set P i . Since the value ranges of different parameters are different, the parameter step length is set to a certain percentage of the length of the parameter value range when calculating the sensitivity of the parameter, and the step lengths of different parameters are different. In the embodiment, the parameter variation step length l is 5% of the length of the parameter value range, i.e. l = (X h -X l ) x 5%, and the variation step lengths of different parameters are different. The value set of the to-be-recognized excitation signal is determined according to the parameter variation step length l and P init . In the embodiment, the value range and the initial value P init of each parameter of the mathematical model are set as shown in Table 3.

[0063]

[0064]

[0065] Table 3

[0066] S4: inputting each value in the value set into the model to obtain a corresponding simulation result, and calculating the error between the simulation result and the standard simulation result to obtain the simulation error of each value in the value set.

[0067] Further preferably, the error between the simulation result and the standard simulation result is specifically the root mean square error between the simulation result and the standard simulation result.

[0068] The simulation error of each value in the value set is calculated according to the following formula:

[0069]

[0070] wherein, is the simulation error of each value in the value set, K is the number of simulation result types, and rms is a function of calculating the root mean square, i is the number of the to-be-identified excitation signal, and j is the parameter number in the value set, is the kth type in the standard simulation result.

[0071] S5: The average value of the change rate of the simulation error of each value in the value set is calculated to obtain the sensitivity of the parameter.

[0072] The calculation formula of the sensitivity is:

[0073]

[0074] wherein, η i is the sensitivity of the to-be-identified parameter numbered i, and j is the parameter number in the value set, is the simulation error of each value in the value set, and M is the total number of elements in the value set.

[0075] S6: Different parameter initial values are selected to sequentially execute steps S3-S5, the sensitivities of different parameters under the corresponding type of excitation signal are obtained, and the excitation signal with the highest sensitivity is selected as the excitation signal for identifying the corresponding parameter.

[0076] For each type of excitation signal in Table 1, the corresponding sensitivity calculation result is obtained. In order to reflect the signal type with the highest sensitivity of different parameters, the sensitivity values of each parameter are adjusted to the interval (0, 1), the horizontal axis is the model parameter, the vertical axis is the excitation signal, the sensitivity of the parameter is the value, and the heat map of the parameter sensitivity is drawn, as shown in Figure 6 The vertical axis coordinate value of the heat map shown in the figure is the input signal type, such as sine_A1000F0.2 representing a sine speed signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz, and tri_A1000F0.2 representing a triangular wave speed signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz. From the heat map, it can be seen that the excitation signal with the highest sensitivity of each parameter is, for example, H The sensitivity of the parameter is the highest under the sine wave speed signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz, so the axial damping parameter B HWhen the parameter is sensitive, a sine velocity signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz or a triangular wave velocity signal should be used. The signals with sensitive parameters are marked in the figure, and the excitation signal can be selected according to the identification object.

[0077] The embodiment simultaneously identifies multiple parameters using a single excitation signal, selects a signal with high sensitivity of all parameters as the identification signal from the candidate excitation signals, selects a sine velocity signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz as the excitation signal for simultaneous identification of multiple parameters, sets the nominal value of the model parameter in the simulation environment, identifies the model parameter using the gradient descent algorithm, calculates the relative error of each parameter identification, simultaneously identifies using a triangular wave velocity signal with an amplitude of 8000 mm / min and a frequency of 1 Hz with low sensitivity, and compares the identification errors under the two excitation signals, as shown in Tables 4 and 5.

[0078]

[0079] Table 4

[0080]

[0081] Table 5

[0082] It can be seen from the table that when the sine velocity signal with an amplitude of 1000 mm / min and a frequency of 0.2 Hz with high sensitivity is used as the excitation signal, the maximum identification error is 24.31%, and when the triangular wave velocity signal with an amplitude of 8000 mm / min and a frequency of 1 Hz with low sensitivity is used, the maximum identification error is 55.52%, so it can be seen that the identification signal with higher parameter sensitivity has higher identification accuracy.

[0083] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for designing excitation signals for parameter identification in a machine tool feed system, characterized in that, The method includes: S1: Establish the feed model of the machine tool feed system, determine the type and value range of the parameters to be identified, select parameters as standard parameters within the value range for each type, and design candidate excitation signals for different types; S2: Select an excitation signal and input the standard parameters into the feed model to obtain the standard simulation results under the excitation signal; S3: Select an initial value for the parameter within the range of values, and use the initial value as the starting point to expand the parameter and generate a set of values; S4: Input each value in the set of values ​​into the feed model to obtain the simulation result corresponding to the excitation signal, and calculate the error between the simulation result and the standard simulation result to obtain the simulation error of each value in the set of values; S5: Calculate the average of the simulation error change rate for each value in the set of values ​​to obtain the sensitivity of the parameter; S6: Select different excitation signals and execute steps S3~S5 in sequence to obtain the sensitivity of different parameters under the corresponding type of excitation signal, and take the excitation signal with the highest sensitivity as the excitation signal for identifying the corresponding parameter. In step S1, parameters are randomly selected as standard parameters, and in step S3, the initial values ​​of the selected parameters are not repeated with the standard parameters.

2. The method according to claim 1, characterized in that, In step S4, the specific formula for calculating the simulation error of each value in the set of values ​​by comparing the simulation result with the standard simulation result is as follows: in, Let K be the simulation error for each value in the set of values, K be the number of simulation result types, and rms be the function for calculating the root mean square. , i The number of the excitation signal to be identified. j The parameter number in the value set, This is the kth type in the standard simulation results.

3. The method according to claim 1 or 2, characterized in that, The formula for calculating the sensitivity in step S5 is as follows: in, For the number i The sensitivity of the parameter to be identified, j The parameter number in the value set, M represents the simulation error for each value in the set of values, and M represents the total number of elements in the set of values.

4. The method according to claim 1, characterized in that, In step S3, the parameters are expanded forward and backward from the initial value, and the expanded value range is within the preset value range. The specific formula is as follows: in, Initialize the parameters The lower bound of the range of values. Initialize the parameters The upper bound of the range of values. l Let n be the step size, and n be the nth value of the forward or backward expansion. i The parameter number is to be identified.

5. The method according to claim 1, characterized in that, In step S3, the parameter expansion to generate a set of values ​​starting from the initial parameter value specifically involves expanding the parameter to generate a set of values ​​with a specific step size, starting from the initial parameter value.

6. The method according to claim 5, characterized in that, The specific step size is selected as a preset proportion of the length of the value range.

7. The method according to claim 1, characterized in that, The types of excitation signals in step S1 include sine wave signals, triangular wave signals, trapezoidal wave signals, and white noise signals.

8. The method according to claim 1, characterized in that, In step S4, calculating the error between the simulation result and the standard simulation result specifically involves calculating the root mean square error between the simulation result and the standard simulation result.

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