A method and system for obtaining a frequency response function of a machine tool under speed correlation

By combining the force hammer method and servo motor frequency sweep, the frequency response function of the machine tool at different speeds is obtained, which solves the problem that the frequency response function of the machine tool under the operating state is difficult to obtain in the existing technology, and realizes high accuracy and real-time monitoring, thereby improving machining accuracy and stability.

CN119270760BActive Publication Date: 2025-10-17HUAZHONG UNIV OF SCI & TECH
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Patent Information

Application Number
CN202411316600.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-20
Publication Date
2025-10-17
Estimated Expiration
2044-09-20

AI Technical Summary

Technical Problem

Existing technologies make it difficult to accurately obtain the overall frequency response function of a machine tool under operating conditions, especially the dynamic characteristics of large machine tools and servo components, which are difficult to characterize under operating conditions.

Method used

The static frequency response function of the machine tool's follower components is obtained by using the force hammer method, and the frequency response function of the moving components is obtained by combining the servo motor sweep frequency test at different operating speeds. The frequency response function of the entire machine tool at different speeds is obtained by using the encoder feedback angle change.

Benefits of technology

It enables automatic acquisition of frequency response function while the machine tool is running, improves the accuracy of dynamic characteristic monitoring, reduces environmental interference and measurement errors, and can identify potential problems in real time to optimize process parameters to improve machining accuracy and efficiency.

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Abstract

The present invention belongs to the technical field related to mechanical equipment structural dynamics analysis. It discloses a method and system for obtaining the frequency response function of a whole machine tool under speed correlation. The steps are as follows: S1: performing experimental modal analysis on the machine tool follower component based on the force hammer method, using the hammer force as input and the acceleration sensor signal on the machine tool follower component as output, to obtain the frequency response function of the machine tool follower component when it is stationary; S2: using the servo motor and the end encoder of the machine tool moving component, using the motor sweep frequency signal as input and the angular change of the encoder position feedback as output, to perform sweep frequency testing at different machine tool operating speeds to obtain the frequency response function of the machine tool moving component at different operating speeds; S3: combining the frequency response function of the machine tool follower component when it is stationary with the frequency response function of the machine tool moving component at different operating speeds to obtain the frequency response function of the whole machine tool at different speeds. The present invention can automatically obtain the frequency response function of the whole machine tool in operation.
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Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of mechanical equipment structure dynamics analysis, and more particularly relates to a method and system for acquiring a frequency response function of a machine tool whole machine under speed correlation. BACKGROUND

[0002] With the rapid development of manufacturing technology, mechanical equipment is developing towards intelligentization, precision, and integration, and higher requirements are put forward for machine tool high-speed machining, high-precision machining, and machining reliability. Mechanical equipment structure dynamics analysis technology has wide application in mechanical design, performance optimization, health monitoring, and engineering application. Acquiring the frequency response function of the machine tool whole machine and studying the dynamics characteristics of the machine tool whole machine during machining are of great significance for suppressing machine tool position vibration during machining and improving machining accuracy.

[0003] Currently, the methods for acquiring the frequency response function of the machine tool mainly include experimental modal analysis and operational modal analysis. Among them, the force hammer impact test method is a common experimental modal analysis method, but the hammer impact method needs to artificially excite the machine tool. For large machine tools, it is difficult to excite the dynamics characteristics of the whole machine tool structure. In addition, the experimental modal analysis method is only suitable for knocking test of the machine tool in the stopped state. The structural stiffness characteristics of the machine tool in the stopped state and in the running state are quite different, and it is difficult to directly use the frequency response function acquired in the stopped state to represent the structural dynamics characteristics in the running state. The operational modal analysis method usually uses environmental excitation to excite each order mode of the machine tool, but due to the lack of environmental excitation force information, the accuracy of the acquired frequency response function is not high. The follow-up components of the machine tool also vibrate with the movement of the moving components, and the follow-up components also vibrate with the structure. The existing method is difficult to accurately represent the dynamics characteristics of the machine tool whole machine under motion. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a method and system for acquiring a frequency response function of a machine tool whole machine under speed correlation, which aims to solve the problem that the prior art is difficult to acquire the frequency response function of the machine tool whole machine under speed correlation.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a method for acquiring a frequency response function of a machine tool whole machine under speed correlation is provided, which comprises the following steps:

[0006] S1, based on the force hammer method, experimental modal analysis is performed on the follow-up components of the machine tool, the hammering force is taken as the input, and the acceleration sensor signal on the follow-up components of the machine tool is taken as the output, to acquire the frequency response function of the follow-up components of the machine tool under static state;

[0007] S2, based on the servo motor and machine tool moving parts end encoder, motor sweep signal as input, encoder position feedback angle change as output, sweep test at different operating speeds of machine tool to obtain the frequency response function of machine tool moving parts at different operating speeds;

[0008] S3, the frequency response function of the machine tool servo parts at rest is combined with the frequency response function of the machine tool moving parts at different operating speeds to obtain the frequency response function of the machine tool at different speeds.

[0009] Further, the frequency response function of the acceleration sensor arranged at position P of the machine tool servo parts is:

[0010]

[0011] Wherein, X(ω) is the vibration response of the machine tool servo parts at position P, F(ω) is the excitation input of hammering force, FT[·] represents the Fourier transform.

[0012] Further, the maximum frequency of the sweep signal is greater than 2 times the highest frequency of the machine tool moving parts mode.

[0013] Further, the moving part beam and ram are modeled as concentrated masses, and the second-order moving part equation is written as a state space equation:

[0014]

[0015] Wherein, z1=x2,z2=x1, x1、 Is the beam displacement and moving speed, x2、 Is the ram displacement and speed, m1, m2 is the equivalent inertia of the beam and the ram, k, c is the axial stiffness and nut damping of the moving part as a whole, b1, b2 is the beam viscous damping and ram viscous damping, u is the motor torque control signal.

[0016] Further, define u, x as input and output respectively, and perform Laplace transform on the state space equation, and then obtain the transfer function of motor input V and encoder output:

[0017]

[0018] Wherein G r Is the transfer function of motor input V and moving part displacement:

[0019]

[0020] In the formula: ξ is the damping ratio, ω n Is the natural frequency of the moving part, αr is a system inertia related term, a r r nr , b r is a damping related term, b r nr 2 g is a moving part transmission ratio, K T is a motor torque constant, J is the moment of inertia of the moving part rigid body model, and B is the damping coefficient of the moving part rigid body model.

[0021] Further, the transfer function G ux Further transformation, that is, the frequency response function G(ω) of the motor input V and the encoder output:

[0022]

[0023] Further, the frequency response function at the position P of the machine tool whole machine under the speed correlation is:

[0024] H(ω)=Y(ω)·G(ω)

[0025] Wherein, Y(ω) is the frequency response function of the machine tool servo part in the static state; G(ω) represents the frequency response function of the machine tool moving part under the speed correlation.

[0026] Further, the sampling frequency of the force hammer signal is greater than 2 times the highest frequency of the machine tool servo part mode.

[0027] The application also provides a speed correlation machine tool whole machine frequency response function acquisition system, the system includes a memory and a processor, the memory stores a computer program, the processor executes the computer program executes the speed correlation machine tool whole machine frequency response function acquisition method as described above.

[0028] The application also provides a computer readable storage medium, the computer readable storage medium stores machine executable instructions, the machine executable instructions are called and executed by the processor, the machine executable instructions make the processor realize the speed correlation machine tool whole machine frequency response function acquisition method as described above.

[0029] Overall, compared with the prior art, the speed correlation machine tool whole machine frequency response function acquisition method and system provided by the application mainly have the following beneficial effects:

[0030] ​​​​​1. The present invention first uses a hammer to strike a machine tool's follower component while stationary to obtain its frequency response function. The method then controls the machine tool to emit sweep frequency signals at different operating speeds. The angle changes fed back by the encoder provide the frequency response function of the moving component at different speeds. Combining these two factors yields the speed-dependent frequency response function of the entire machine tool. Therefore, the method proposed in the present invention can automatically obtain the frequency response function of the entire machine tool in operation, enabling real-time monitoring of the dynamic characteristics of the entire machine tool with high accuracy.

[0031] 2. This invention monitors the dynamic response characteristics of a machine tool by acquiring its frequency response function in real time while the machine tool is in operation. Compared to existing hammer testing methods that measure machine tool structural characteristics, this method can reflect the dynamic characteristics of the entire machine under actual operating conditions. Through real-time monitoring, dynamic factors that may affect machining accuracy and stability can be promptly identified.

[0032] 3. This invention combines the hammer impact method with a frequency sweep test during machine tool operation. Using the static frequency response function obtained from the hammer impact as a basis, the frequency sweep test provides dynamic corrections, enabling precise measurement of the dynamic characteristics of the entire machine tool at different speeds. These two complementary testing methods improve the accuracy of measuring complex dynamic systems, reduce environmental interference and measurement errors, and save the economic and time costs of acquiring the dynamic characteristics of the entire machine tool.

[0033] 4. By controlling the machine tool to generate sweeping frequency signals at different operating speeds, the frequency response functions of the machine tool's moving components can be obtained at various speeds. The system can comprehensively evaluate the dynamic characteristics of the entire machine tool under various operating conditions, not just static or single speed conditions. Combining the frequency response functions of the entire machine tool at different speeds provides a more complete description of the dynamic characteristics of the entire machine tool during actual machining, helping to improve the system's adaptability and stability.

[0034] 5. By acquiring and analyzing frequency response functions in real time, the present invention can proactively identify and diagnose potential machine tool problems, such as resonance, abnormal vibration, or fatigue damage. Real-time monitoring of equipment can also help optimize process parameters, thereby improving overall performance and machining efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a method for obtaining a frequency response function of a machine tool under speed correlation provided by Example 1 of the present invention;

[0036] Figure 2 This is a schematic diagram of the simplified model disassembly of the machine tool provided in Example 1 of the present invention;

[0037] Figure 3 Schematic diagram of the rigid body dynamics model of the moving parts of a machine tool provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0039] The present application provides a method for obtaining the frequency response function of a machine tool under the condition of speed correlation. The frequency response function of the machine tool is obtained by using a force hammer to hammer the follow-up component of the machine tool in a static state. Further, a sweep frequency signal is sent out by the machine tool under different operating speeds, and the frequency response function of the moving component under different speeds is obtained from the angle change feedback by the encoder. The frequency response function of the machine tool under the condition of speed correlation is obtained by combining the above two. The method proposed in the present application can automatically obtain the frequency response function of the machine tool under the operating state without additional human intervention, and can monitor the dynamic characteristics of the machine tool in real time, with high accuracy.

[0040] The obtaining method mainly includes the following steps:

[0041] S1, based on the force hammer method, the experimental modal analysis is performed on the follow-up component of the machine tool, the hammering force is used as the input, and the acceleration sensor signal on the follow-up component of the machine tool is used as the output, to obtain the frequency response function of the follow-up component of the machine tool in a static state.

[0042] The frequency response function at the position P of the acceleration sensor arranged on the follow-up component of the machine tool is:

[0043]

[0044] Wherein, X(ω) is the vibration response at the position P on the follow-up component of the machine tool, F(ω) is the excitation input of the hammering force, and FT[·] represents the Fourier transform.

[0045] Wherein, the experimental modal analysis test is performed using the force hammer method, the acceleration sensors are uniformly distributed on the surface of the follow-up component of the machine tool, and the number of the acceleration sensors should be as many as possible to represent the complex structural vibration of the follow-up component of the machine tool.

[0046] S2, based on the servo motor and the encoder at the end of the moving component of the machine tool, the motor sweep frequency signal is used as the input, and the angle change feedback by the position of the encoder is used as the output, to perform the sweep frequency test under different operating speeds of the machine tool to obtain the frequency response function of the moving component of the machine tool under different operating speeds.

[0047] The maximum frequency of the sweep frequency signal is greater than 2 times the highest frequency of the mode of the moving component of the machine tool, and the sampling frequency of the force hammer signal is greater than 2 times the highest frequency of the mode of the follow-up component of the machine tool.

[0048] In order to obtain the accurate frequency response function of the moving part of the machine tool in the running process, the servo motor sends the sweep frequency signal, and the encoder obtains the angle change of the end of the moving part, and then the accurate frequency response function of the moving part of the machine tool is obtained.

[0049] Specifically, first, the dynamic characteristics of the moving part are analyzed, the influence of the machine tool servo part on the moving part and the disturbance caused by the environment and other factors are ignored, the moving part beam and ram are modeled as concentrated masses, and the second order moving part equation is written as a state space equation as follows:

[0050]

[0051] Wherein, z1=x2, z2=x1, x1、 are the beam displacement and moving speed respectively, x2、 are the ram displacement and speed respectively, m1 and m2 are the equivalent inertia of the beam and the ram respectively, k and c are the axial stiffness and nut damping of the moving part as a whole respectively, b1 and b2 are the viscous damping of the beam and the ram respectively, and u is the motor torque control signal.

[0052] Define u, x as input and output respectively, and perform Laplace transform on the state space equation, and then the transfer function of the motor input V and the encoder output is:

[0053]

[0054] Wherein G r is the transfer function of the motor input V and the moving part displacement:

[0055]

[0056] In the formula:

[0057] Wherein ξ is the damping ratio, ω n is the natural frequency of the moving part, α r is the inertia related term of the system, α r =2ξ r ω nr , β r is the damping related term, β r =(ω nr ) 2 , r g is the transmission ratio of the moving part, K T is the motor torque constant, J is the rotational inertia of the rigid body model of the moving part, and B is the damping coefficient of the rigid body model of the moving part.

[0058] The transfer function G uxFurther transform (s = jw), namely the frequency response function G(ω) of motor input V and encoder output can be obtained:

[0059]

[0060] S3, the frequency response function of the machine tool servo part at rest is combined with the frequency response function of the machine tool moving part at different operating speeds to obtain the frequency response function of the machine tool at different speeds.

[0061] The frequency response function of the machine tool at position P under the speed correlation is:

[0062] H(ω) = Y(ω) * G(ω)

[0063] Where Y(ω) is the frequency response function of the machine tool servo part at rest; G(ω) represents the frequency response function of the machine tool moving part under the speed correlation.

[0064] The application also provides a system for obtaining the frequency response function of the machine tool under the speed correlation, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method for obtaining the frequency response function of the machine tool under the speed correlation as described above.

[0065] The application also provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions make the processor realize the method for obtaining the frequency response function of the machine tool under the speed correlation when the machine executable instructions are called and executed by the processor.

[0066] The application will be further described in detail below in combination with the drawings.

[0067] Embodiment 1

[0068] The embodiment 1 of the application provides a method for obtaining the frequency response function of the machine tool under the speed correlation, as shown in the formula (1), which comprises the following steps: Figure 1

[0069] S1, the frequency response function of the machine tool servo part is obtained based on the experimental modal analysis hammer method, the hammering force is taken as the input, and the collected acceleration sensor signal is taken as the output to obtain the frequency response function of the machine tool servo part.

[0070] Specifically, as shown in the formula (2), the frequency response function of the machine tool moving part under the speed correlation is obtained based on the experimental modal analysis hammer method, the hammering force is taken as the input, and the collected acceleration sensor signal is taken as the output to obtain the frequency response function of the machine tool moving part under the speed correlation. Figure 2 ​As shown, the machine tool whole machine model can be split into a follow-up component and a moving component according to the main machining direction, the follow-up component includes a tool holder and a spindle, and the moving component includes a cross beam and a ram. Acceleration sensors required for experimental modal analysis testing are uniformly arranged on the follow-up component of the machine tool to be tested, centralized mass modeling is performed on the follow-up component of the machine tool, each sensor position is regarded as a degree of freedom, the follow-up component of the machine tool is divided into a multi-degree-of-freedom system to represent its rich structural modal information. A force hammer is used for excitation, vibration signals at each sensor position on the machine tool are collected through the acceleration sensor, and modal analysis is performed on the vibration signals to obtain the vibration response at each sensor position on the follow-up component of the machine tool. Then, modal parameters of the follow-up component are identified through a modal identification algorithm to obtain the highest frequency of the structural modal of the follow-up component.

[0071] In this embodiment, the sampling frequency of the force hammer signal is greater than 2 times the highest frequency of the modal of the follow-up component of the machine tool; the acceleration sensors are uniformly distributed on the surface of the follow-up component of the machine tool, and the number of acceleration sensors should be as large as possible to represent the complex structural modal information of the follow-up component of the machine tool.

[0072] Specifically, the frequency response function at the position P of the acceleration sensor on the follow-up component of the machine tool is:

[0073]

[0074] wherein X(ω) is the vibration response at the position P on the follow-up component of the machine tool, F(ω) is the excitation input of the hammering force, FT[·] represents Fourier transform, and X(ω) and F(ω) can be obtained through an experimental modal analysis information acquisition system.

[0075] S2, using the servo motor sweep frequency signal as input and the angle change of the position feedback of the encoder at the end of the moving component of the machine tool as output, the frequency response function of the moving component at different speeds is obtained.

[0076] In order to obtain the accurate frequency response function of the moving component of the machine tool in the running process, the sweep frequency signal is sent by the servo motor, the angle change of the end of the moving component is obtained by the encoder, and then the accurate frequency response function of the moving component of the machine tool is obtained.

[0077] Specifically, first, the dynamic characteristics of the moving component are analyzed, the influence of the follow-up component of the machine tool on the moving component and the disturbance caused by environmental factors are ignored, the cross beam and the ram of the moving component are centrally mass modeled, and the second-order moving component equation is written as a state space equation as follows:

[0078]

[0079] wherein z1=x2, z2=x1, x1、 is the cross beam displacement and moving speed, x2, is the ram displacement and speed, m1, m2 are the equivalent inertia of the cross beam and the ram, k, c are the axial stiffness and nut damping of the moving part as a whole, b1, b2 are the tool holder viscous damping and the ram viscous damping, and u is the motor torque control signal.

[0080] Further, as shown in Figure 3 , define u, x as input, output, and perform Laplace transform on the above state space equation, and then the transfer function of the motor input V and the encoder output is:

[0081]

[0082] where G r is the transfer function of the motor input V and the moving part displacement:

[0083]

[0084] In the formula:

[0085] where ξ is the damping ratio, ω n is the natural frequency of the moving part, α r is the system inertia related term, α r = 2ξ r ω nr , β r is the damping related term, β r = (ω nr ) 2 , r g is the transmission ratio of the moving part, K T is the motor torque constant, J is the rotational inertia of the rigid body model of the moving part, and B is the damping coefficient of the rigid body model of the moving part.

[0086] The transfer function G ux of the motor input V and the encoder output can be further transformed (s = jw), that is, the frequency response function G(ω) of the motor input V and the encoder output can be obtained:

[0087]

[0088] Therefore, the frequency response function of the machine tool moving part can be obtained from the angle change of the frequency sweep issued by the servo motor and the position feedback of the encoder at the end of the machine tool moving part.

[0089] S3, combine the frequency response functions of the machine tool servo part and the moving part to obtain the frequency response functions of the machine tool at different speeds.

[0090] Specifically, as shown in Figure 2The machine tool moving part is installed on the machine tool follow-up part, and the frequency response function of the machine tool follow-up part is combined with the frequency response function of the moving part to obtain the frequency response function of the machine tool at different operating speeds.

[0091] Specifically, the frequency response function of the machine tool at the position P under the speed correlation is:

[0092] H(ω) = Y(ω) * G(ω)

[0093] Wherein, Y(ω) is the frequency response function of the machine tool follow-up part in a static state; G(ω) represents the frequency response function of the machine tool moving part under the speed correlation.

[0094] In the present application, when the frequency response function of the machine tool under the speed correlation is needed, the method proposed in the present application is adopted, first, the hammer is used to knock the machine tool follow-up part in a static state to obtain its frequency response function, and then the machine tool is controlled to emit a sweep frequency signal at different operating speeds, and the frequency response function of the moving part at different speeds is obtained from the angle change feedback by the encoder, and the frequency response function of the machine tool follow-up part under the speed correlation is obtained by combining the two. By using the method proposed in the present application, the frequency response function of the machine tool in the running state can be automatically obtained, the dynamic characteristics of the machine tool can be monitored in real time, and the accuracy is high.

[0095] Further, the machine tool speed correlation frequency response function acquisition method provided by the present application can obtain the frequency response function of the machine tool moving part at multiple speeds by controlling the machine tool to emit a sweep frequency signal at different operating speeds. The system can comprehensively evaluate the dynamic characteristics of the machine tool under various working conditions, not limited to static or single speed conditions. The frequency response functions of the machine tool at different speeds are combined, which can provide a more complete description of the dynamic characteristics of the machine tool in the actual machining process, and help to improve the adaptability and stability of the system.

[0096] Further, the machine tool speed correlation frequency response function acquisition method provided by the present application can identify and diagnose potential problems of the machine tool in advance, such as resonance, abnormal vibration or fatigue failure, etc. by real-time acquisition and analysis of the frequency response function. Real-time monitoring of the equipment by the present application can also help to optimize process parameters, thereby improving the overall performance and processing efficiency.

[0097] Embodiment 2

[0098] The embodiment 2 of the present application provides a machine tool speed correlation frequency response function acquisition system, comprising: a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the machine tool speed correlation frequency response function acquisition method as described above.

[0099] Embodiment 3

[0100] The application further provides a computer readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls a device in which the storage medium is located to perform the machine tool overall speed associated frequency response function acquisition method as described above.

[0101] Those skilled in the art can understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for obtaining the frequency response function of a machine tool under speed correlation, characterized by: The method comprises the following steps: S1, based on the force hammer method, experimental modal analysis is performed on the machine tool follower component. The hammer force is used as input, and the acceleration sensor signal on the machine tool follower component is used as output to obtain the frequency response function of the machine tool follower component when it is stationary. S2, based on the servo motor and the end encoder of the machine tool moving part, uses the motor sweep frequency signal as input and the angle change of the encoder position feedback as output. The sweep frequency test is performed at different machine tool operating speeds to obtain the frequency response function of the machine tool moving part at different operating speeds; S3, combining the frequency response function of the machine tool follower component at rest with the frequency response function of the machine tool moving component at different operating speeds to obtain the frequency response function of the entire machine tool at different speeds.

2. The method for obtaining the frequency response function of a machine tool under speed correlation according to claim 1, characterized in that: The frequency response function of the acceleration sensor at position P where the machine tool follower component is located is: Where X(ω) is the vibration response at position P on the machine tool follower, F(ω) is the excitation input of the hammer force, and FT[·] represents the Fourier transform.

3. The method for obtaining the frequency response function of a machine tool under speed correlation according to claim 1, characterized in that: The maximum frequency of the sweep signal is greater than twice the highest modal frequency of the moving parts of the machine tool.

4. The method for obtaining the frequency response function of a machine tool under speed correlation according to claim 1, characterized in that: The moving parts beam and ram are modeled as lumped masses, and their second-order moving part equations are written as state space equations: Among them, z1=x2,z2=x1, x1, They are the beam displacement and moving speed, x2, are the displacement and velocity of the ram, m1 and m2 are the equivalent inertia of the beam and ram, k and c are the overall axial stiffness and nut damping of the moving parts, b1 and b2 are the viscous damping of the beam and ram, and u is the motor torque control signal.

5. The method for obtaining the frequency response function of a machine tool under speed correlation as claimed in claim 4, characterized in that: Define u and x as input and output respectively, perform Laplace transform on the state space equation, and then get the transfer function between the motor input V and the encoder output as: Among them G r is the transfer function between the motor input V and the displacement of the moving part: Where: ξ is the damping ratio, ω n is the natural frequency of the moving part, α r is the system inertia related term, α r =2ξ r ω nr , β r is the damping-related term, β r =(ω nr ) 2 ,r g is the transmission ratio of the moving parts, K T is the motor torque constant, J is the moment of inertia of the rigid body model of the moving part, and B is the damping coefficient of the rigid body model of the moving part.

6. The method for obtaining the frequency response function of a machine tool under speed correlation according to claim 5, characterized in that: The transfer function G between the motor input V and the encoder output ux Further transformation gives the frequency response function G(ω) of the motor input V and the encoder output:

7. The method for obtaining the speed-dependent frequency response function of a machine tool according to any one of claims 1 to 6, characterized in that: The frequency response function at the position P of the machine tool under speed correlation is: H(ω)=Y(ω)·G(ω) Among them, Y(ω) is the frequency response function of the machine tool follower component in a stationary state; G(ω) represents the frequency response function of the machine tool moving component under speed correlation.

8. The method for obtaining the frequency response function of a machine tool under speed correlation according to any one of claims 1 to 6, characterized in that: The sampling frequency of the hammer signal is greater than twice the highest modal frequency of the machine tool follower component.

9. A system for obtaining the frequency response function of a machine tool under speed correlation, characterized by: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the method for obtaining the frequency response function of a machine tool under speed correlation according to any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the method for obtaining the frequency response function of a machine tool under speed correlation according to any one of claims 1 to 8.

Citation Information

Patent Citations

  • Modal parameter acquisition method of numerical control machine tool based on velocity correlation

    CN103336482A

  • Method for identifying frequency response function of mechanical equipment structure in operation state

    CN106502199A