Mechanical structure frequency response function identification method based on variable main shaft rotating speed excitation

Abstract

The invention belongs to the field of numerical control machining and manufacturing, and discloses a mechanical structure frequency response function identification method based on variable spindle rotating speed excitation. Taking cutting force borne by a tail end cutter as a quasi input signal, taking a machine tool driving shaft tracking error as an output signal, and determining a signal sampling period according to an identification precision requirement; according to the virtual work principle, the cutting force borne by the tail end cutter is converted into equivalent loads of all driving shafts of the machine tool in combination with a machine tool Jacobian matrix; then, calculating a cross-power spectrum of the input signal and the output signal and an auto-power spectrum of the input signal by using fast Fourier transform; and finally, the frequency response function of the mechanical structure can be obtained by calculating the ratio of the cross-power spectrum to the self-power spectrum. The method effectively avoids physical damage to the mechanical structure of the numerical control machine tool caused by an existing excitation identification method, has the advantages of being simple and easy to operate, and has great significance in perfecting the efficient and high-precision machining technology of mechanical parts.

Description

Technical Field

[0001] This invention belongs to the field of CNC machining and manufacturing, and relates to a method for identifying the frequency response function of a mechanical structure based on variable spindle speed excitation. Background Technology

[0002] Complex curved surface parts, such as integral bladed disks for aero-engines, turbine blades, and marine propellers, are widely used in the manufacturing of major high-end equipment in China. Especially with the rapid development of my country's aviation, aerospace, shipbuilding, and defense industries, higher demands are being placed on the machining accuracy and efficiency of these parts. Currently, CNC machining is the main means of achieving efficient and precise machining of complex curved surface parts. However, due to the nonlinear frequency response characteristics of the machine tool's mechanical structure, the end-effector often struggles to accurately and promptly track the input command under cutting load disturbances, resulting in a large contour error between the actual trajectory and the desired trajectory. This severely affects the profile accuracy and service performance of the curved surface parts. Accurately identifying the frequency response function of the mechanical structure is crucial for predicting contour errors, optimizing CNC machining process parameters, and ultimately ensuring the quality of part machining.

[0003] A review of existing literature revealed that patent CN 110032142 B discloses a contour error pre-compensation method based on minimizing the CNC machining path. This method establishes a time-domain analytical relationship between the machine tool feed system's follow-up error and the tool position command sequence based on the servo system's error response to typical input signals, and presents a progressive follow-up error prediction model, but it does not consider the influence of cutting load. Patent CN 112731865 B discloses a multi-axis machining contour error pre-compensation method based on interpolation data. This method calculates the contour error of each tool position command point based on the actual interpolation data fed back by the CNC system, avoiding the establishment of a prediction model, but it suffers from a contour error compensation lag problem, making it difficult to effectively guarantee contour accuracy. The literature “Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools”, Yusuf Altintas et al., CIRP Annals - Manufacturing Technology, (2019) 68(1): 377-380, proposes a contour error prediction method that considers cutting load disturbances. This method requires excitation of the CNC machine tool through hammering experiments to obtain the frequency response characteristics of the mechanical structure, and then quantify the mathematical relationship between cutting load and contour error. However, hammering operations usually cause damage to the machine tool hardware system, especially for precision machine tools, such operations are often prohibited.

[0004] To date, no research report has provided a method for non-destructive identification of the frequency response characteristics of CNC machine tool mechanical structures. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a technique for identifying the frequency response function of mechanical structures based on variable spindle speed excitation. This technique is the first to apply self-power spectrum and cross-power spectrum analysis methods to the identification of the frequency response function of mechanical structures. Compared with existing technologies, this technique has the advantages of being non-destructive and simple to operate. In principle, this invention can be applied to any m, where m≤5-axis CNC machine tools. For a given machine tool, based on the feedback control method of its servo system, the response bandwidth of the servo system can be improved through parameter tuning to minimize the impact of response delay.

[0006] The technical solution of this invention:

[0007] A method for identifying the frequency response function of a mechanical structure based on variable spindle speed excitation, comprising the following steps:

[0008] Step 1: Using the cutting force borne by the end tool as the input signal and the tracking error signal of the machine tool servo drive axis as the output signal, determine the signal sampling period according to the identification accuracy requirements, and ensure that the signal sampling satisfies the Nyquist theorem;

[0009] Step 2: Assume the acquired cutting force signal is... f t i = [ f x t i , f y t i , f z t i ] T The machine tool servo drive axis tracking error signal is ,in, Indicates the sampling time. Denotes the sequence index of the sampling points, and satisfies 1 ≤ ≤ , This indicates the total number of sampling points. This represents the component of the cutting force along the x-axis of the workpiece coordinate system. This represents the component of the cutting force along the y-axis of the workpiece coordinate system. Let represent the component of the cutting force along the z-axis of the workpiece coordinate system, and k represent the index of the machine tool servo drive axis, satisfying 1 ≤ ≤ , This represents the total number of servo drive axes of the machine tool; based on the principle of virtual work, the cutting force borne by the end tool is converted into the equivalent load of each servo drive axis of the machine tool using the following formula:

[0010]

[0011] in, T t i = [ T 1 t i ,⋯, T k t i ,⋯, T m t i ] T Indicates at the sampling time Below, the equivalent load of each drive axis of the machine tool servo, Indicates at the sampling time The inverse of the Jacobian matrix of the lower machine tool;

[0012] Step 3: Connect the machine tool servo... The equivalent load on each drive bearing As an input signal, the machine tool servo... The tracking error signal for each drive shaft is As the output signal, a Fast Fourier Transform is used to obtain the cross-power spectrum of the equivalent load and tracking error of each drive axis of the computer tool servo, as well as the self-power spectrum of the equivalent load of each drive axis of the machine tool servo:

[0013]

[0014] in, This represents the generalized operation of the Fast Fourier Transform. This represents the frequency domain representation of the input signal. This represents the frequency domain representation of the output signal. Represents the complex conjugate of the input signal. Indicates the frequency difference between the input signal and the output signal. Cross-power spectral density at [location] Indicates the frequency of the input signal. The self-power spectrum value at that location;

[0015] Step 4: Finally, by calculating the ratio of the cross-power spectrum to the self-power spectrum, the frequency response function curve of the mechanical structure is obtained.

[0016]

[0017] in, The mathematical expression representing the frequency response function.

[0018] The beneficial effects of this invention are as follows: This invention proposes a technique for identifying the frequency response function of mechanical structures based on variable spindle speed excitation, and provides specific embodiments. This technique not only enables non-destructive identification of the frequency response characteristics of mechanical structures, but also has the advantages of being simple and easy to operate. Attached Figure Description

[0019] Figure 1 A flowchart of a method for identifying the frequency response function of a mechanical structure based on variable spindle speed excitation;

[0020] Figure 2A comparison is made between the nominal amplitude-frequency response curve of the mechanical structure and the identification results of the proposed method;

[0021] Figure 3 The nominal phase frequency characteristic curve of the mechanical structure is compared with the identification results of the proposed method. Detailed Implementation

[0022] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0023] Example

[0024] Without loss of generality, this invention uses the machine tool mechanical structure frequency response function disclosed in the literature "Novel servo-feed-drive model considering cutting force and structural effects in milling to predict servo dynamicbehaviors", Chen-Jung Li et al., The International Journal of Advanced Manufacturing Technology, (2020) 106(3), 1441-1451 as an example to illustrate the implementation method and identification effect. The mathematical expression and detailed parameters of the disclosed machine tool mechanical structure frequency response function are as follows:

[0025]

[0026]

[0027] The implementation process of this invention is as follows: Figure 1 As shown in the flowchart, the specific steps include:

[0028] Step 1: Using the cutting force borne by the end tool as the input signal and the tracking error of the machine tool servo drive axis as the output signal, determine the signal sampling period according to the identification accuracy requirements, and ensure that the signal sampling satisfies the Nyquist theorem;

[0029] Step 2: Assume the acquired cutting force signal is... f t i = [ f x t i , f y t i , f z t i ] T The machine tool drive axis tracking error signal is ,in, Indicates the sampling time. Denotes the sequence index of the sampling points, and satisfies 1 ≤ ≤ , This indicates the total number of sampling points. This represents the component of the cutting force along the x-axis of the workpiece coordinate system. This represents the component of the cutting force along the y-axis of the workpiece coordinate system. Let represent the component of the cutting force along the z-axis of the workpiece coordinate system, and k represent the index of the machine tool drive axis, satisfying 1 ≤ ≤ , This represents the total number of machine tool drive axes. Based on the principle of virtual work, the cutting force borne by the end tool can be converted into the equivalent load of each drive axis of the machine tool using the following formula:

[0030]

[0031] in, T t i = [ T 1 t i ,⋯, T k t i ,⋯, T m t i ] T Indicates at the sampling time Below, the equivalent load of each drive axis of the machine tool, Indicates at the sampling time The inverse of the Jacobian matrix of the lower machine tool;

[0032] Step 3, Place the machine tool in the first position. The equivalent load on each drive bearing As an input signal, the machine tool's first The tracking error signal for each drive shaft is As the output signal, a fast Fourier transform is used to calculate the cross-power spectrum of the equivalent load of the drive shaft and the tracking error, as well as the self-power spectrum of the equivalent load of the drive shaft:

[0033]

[0034] in, This represents the generalized operation of the Fast Fourier Transform. This represents the frequency domain representation of the input signal. This represents the frequency domain representation of the output signal. Represents the complex conjugate of the input signal. Indicates the frequency difference between the input signal and the output signal. Cross-power spectral density at [location] Indicates the frequency of the input signal. The self-power spectrum value at that location;

[0035] Step 4: Finally, by calculating the ratio of the cross-power spectrum to the self-power spectrum, the frequency response function curve of the mechanical structure can be obtained.

[0036]

[0037] in, The mathematical expression representing the frequency response function.

[0038] In this embodiment, the nominal amplitude-frequency characteristic curve of the machine tool mechanical structure disclosed in the literature "Novel servo-feed-drive model considering cutting force and structural effects in milling to predict servo dynamic behaviors", Chen-Jung Li et al., The International Journal of Advanced Manufacturing Technology, (2020) 106(3), 1441-1451 is as follows: Figure 2 The nominal phase frequency response curve of the publicly disclosed machine tool mechanical structure, as shown by the dashed line with the marking symbol, is as follows: Figure 3 As shown by the dashed line with markings, the amplitude-frequency response curve of the mechanical structure identified according to the above steps is as follows. Figure 2 As shown by the solid line in the figure, the phase frequency characteristic curve of the mechanical structure identified according to the above steps is as follows: Figure 3 As shown by the solid line in the figure, it can be seen that the identification results obtained using this invention are highly consistent with the nominal frequency response characteristic curves (including amplitude frequency characteristic curves and phase frequency characteristic curves) of the machine tool mechanical structure, proving the effectiveness of this invention.

[0039] The above embodiments are only for better explaining the present invention. The method of the present invention is not limited to CNC machine tools, but is also applicable to industrial robots, 3D additive manufacturing equipment, etc.

[0040] Those skilled in the art will readily understand 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 within the scope of protection of the present invention.

Claims

1. A method for identifying the frequency response function of a mechanical structure based on variable spindle speed excitation, characterized in that, The steps are as follows: Step 1: Using the cutting force borne by the end tool as the input signal and the tracking error signal of the machine tool servo drive axis as the output signal, determine the signal sampling period according to the identification accuracy requirements, and ensure that the signal sampling satisfies the Nyquist theorem; Step 2: Assume the acquired cutting force signal is... f t i = [ f x t i , f y t i , f z t i ] T The machine tool servo drive axis tracking error signal is ,in, Indicates the sampling time. Denotes the sequence index of the sampling points, and satisfies 1 ≤ ≤ , This indicates the total number of sampling points. This represents the component of the cutting force along the x-axis of the workpiece coordinate system. This represents the component of the cutting force along the y-axis of the workpiece coordinate system. Let represent the component of the cutting force along the z-axis of the workpiece coordinate system, and k represent the index of the machine tool servo drive axis, satisfying 1 ≤ ≤ , This represents the total number of servo drive axes of the machine tool; based on the principle of virtual work, the cutting force borne by the end tool is converted into the equivalent load of each servo drive axis of the machine tool using the following formula: ； in, T t i = [ T 1 t i ,⋯, T k t i ,⋯, T m t i ] T Indicates at the sampling time Below, the equivalent load of each drive axis of the machine tool servo, Indicates at the sampling time The inverse of the Jacobian matrix of the lower machine tool; Step 3: Connect the machine tool servo... The equivalent load on each drive bearing As an input signal, the machine tool servo... The tracking error signal for each drive shaft is As the output signal, a Fast Fourier Transform is used to obtain the cross-power spectrum of the equivalent load and tracking error of each drive axis of the computer tool servo, as well as the self-power spectrum of the equivalent load of each drive axis of the machine tool servo: ； in, This represents the generalized operation of the Fast Fourier Transform. This represents the frequency domain representation of the input signal. This represents the frequency domain representation of the output signal. Represents the complex conjugate of the input signal. Indicates the frequency difference between the input signal and the output signal. Cross-power spectral density at [location] Indicates the frequency of the input signal. The self-power spectrum value at that location; Step 4: Finally, by calculating the ratio of the cross-power spectrum to the self-power spectrum, the frequency response function curve of the mechanical structure is obtained. ； in, The mathematical expression representing the frequency response function.

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