Method and system for extracting traveling wave mode of gear

Abstract

The invention relates to a mechanical vibration simulation / test analysis technology, and discloses a method and system for extracting a gear traveling wave modal, and the method comprises the steps: obtaining a gear time domain vibration response signal of any point on a gear through simulation or measurement; performing Fourier transform on the gear time domain vibration response signal to obtain a gear frequency domain response signal; extracting a side frequency amplitude and a phase under the resonance rotating speed; enabling the amplitude and the phase of each side frequency to correspond to the amplitude and the phase of the pitch diameter component of the gear; and determining the traveling wave resonance modal response through the amplitude and phase of the pitch diameter component of the gear and the inherent frequency. According to the invention, only one sensor rotating along with the gear is needed in an experimental test, so that a vibration signal on the whole circumference of the gear can be obtained; in dynamics simulation, vibration signals on the whole circumference of the gear can be obtained only by storing vibration data of one point on the gear, and the storage space is greatly reduced.

Description

Technical Field

[0001] This invention relates to mechanical vibration simulation / testing analysis technology, and in particular to a method and system for extracting gear traveling wave modes. Background Technology

[0002] Gears, as commonly used transmission components, are widely used in various fields, such as aerospace, automobiles, wind power, and robotics.

[0003] Lightweight gear design leads to noticeable elastic vibrations. The increasing speed of transmission systems (such as aerospace gears and gears in new energy vehicles) results in more resonance occurring within the operating speed range. When resonance occurs, the vibration amplitude of the gear increases dramatically. Excessive gear vibration can cause excessive loads on the gear itself and the supporting bearings, leading to pitting on the tooth surface, tooth root fracture, and bearing damage. Excessive gear vibration also results in higher noise levels, negatively impacting the user experience.

[0004] Natural frequencies and modes are fundamental to the study and solution of resonance problems. Resonance occurs when the excitation frequency (an overtone of the meshing frequency) is close to the natural frequency; the vibration mode of the gear at resonance is called a mode. For rotating gears, the resonant modes are traveling wave modes, not standing wave modes. Commonly used impact mode tests and commercial finite element eigenvalue solutions are performed when the gear is in a non-rotating state. The natural frequencies and standing wave modes obtained from impact tests or finite element solutions differ from the resonant frequencies and traveling wave modes of rotating gears. While some models considering high-speed rotation effects can solve for traveling wave modes and natural frequencies, the reliability of the results depends on the accuracy of the model.

[0005] As described in prior art 1: CN202010050870.5, the traveling wave mode of the gear can be obtained by calculating its eigenvalues. The mode obtained through eigenvalue calculation and simulation model correction is a standing wave mode, which is not a true traveling wave resonance mode for the gear.

[0006] Existing technology 2: Abnormal peak signal used for gear fault identification in CN202110707786.0.

[0007] Existing technology 3: CN202110714899.3: The vibration simulation signal of the planetary gear train generated considering meshing impact and path modulation does not consider the influence of rotational speed, so it is impossible to identify the resonance frequency and extract the traveling wave resonance mode by analyzing the signal. Summary of the Invention

[0008] This invention addresses the problem that existing technologies can only obtain standing wave modes and their natural frequencies, and cannot be performed simultaneously with frequency sweep testing, requiring separate testing; and that standing wave modes are obtained by tapping multiple points along the circumference of the gear. It provides a method and system for extracting traveling wave modes from gears.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A method for extracting gear traveling wave modes, the method comprising: The time-domain vibration response signal of the gear is obtained by simulation or measurement to obtain the time-domain vibration response signal of any point on the gear. The gear frequency domain response signal is obtained by Fourier transforming the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The sideband amplitude spectrum and sideband phase spectrum are obtained by extracting the sideband response at the gear resonant frequency Ω, thus obtaining the sideband amplitude spectrum and sideband phase spectrum under the resonant state. The amplitude and phase of the gear pitch diameter component are determined by establishing a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination is made by the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

[0010] Preferably, before acquiring the time-domain vibration response signal of the gear, the acquisition of the vibration signal is also included, by installing a sensor on the gear to collect the sensor vibration signal.

[0011] Preferably, before acquiring the time-domain vibration response signal of the gear, the acquisition of the vibration signal also includes obtaining the vibration signal through simulation calculation using a finite element model.

[0012] Preferably, the sensor is mounted on the rim of the gear or on the spokes of the gear.

[0013] As a preferred option, gear resonant frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. The natural frequency ω of the gear is calculated based on the number of gear teeth Z. ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear.

[0014] Preferably, the amplitude of the gear pitch diameter component and phase And the natural frequency ω determines the traveling wave resonant mode response. , ; in, Let be the spatial angular position of the gear, and ; Let ω be the pitch diameter of the gear, and ω be the natural frequency of the gear. The phase of the gear pitch diameter component; This represents the amplitude of the gear pitch diameter component.

[0015] To address the aforementioned technical problems, the present invention also provides a system for extracting gear traveling wave modes, which implements the aforementioned method for extracting gear traveling wave modes, comprising: The gear time-domain vibration response signal acquisition module obtains the gear time-domain vibration response signal at any point on the gear through simulation or measurement; The gear frequency domain response signal acquisition module obtains the gear frequency domain response signal by performing a Fourier transform on the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And a gear natural frequency ω calculation module to identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The module for acquiring the sideband amplitude spectrum and the sideband phase spectrum obtains the sideband amplitude spectrum and the sideband phase spectrum in the resonant state by extracting the sideband response at the gear resonant frequency Ω. The module for determining the amplitude and phase of the gear pitch diameter component establishes a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination module uses the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

[0016] This invention, by adopting the above technical solutions, has significant technical effects: This invention only requires one sensor to be placed in the circumferential direction of the gear; the signal is collected during the gear frequency sweep test, without the need for additional impact test; the traveling wave mode and its natural frequency can be obtained through frequency domain analysis of the sweep signal.

[0017] This invention directly analyzes the frequency domain signal of the sweep frequency response at a point on the circumferential direction of the gear to obtain the traveling wave mode of the gear resonance response and its natural frequency.

[0018] This invention is not only applicable to the extraction of traveling wave modes at resonance, but also to the extraction of gear circumferential vibration at any rotational speed. In experimental testing, only one sensor that rotates with the gear is needed to obtain the vibration signal on the entire circumference of the gear. In dynamic simulation, only the vibration data of one point on the gear needs to be saved to obtain the vibration signal on the entire circumference of the gear, which greatly reduces storage space.

[0019] This invention is applicable to spur gears, helical gears, planetary gears, bevel gears, and spiral bevel gears. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0021] Figure 2 It is the frequency domain response of a point on the gear of the present invention.

[0022] Figure 3 This is the spectrum at the gear resonance frequency of 23.42Hz in this invention.

[0023] Figure 4 This is the spectrum at the gear resonance frequency of 34.38Hz in this invention.

[0024] Figure 5-1 This is the modal response diagram of the present invention when ωt is 0.

[0025] Figure 5-2 This is the modal response diagram of the present invention when ωt is π / 3.

[0026] Figure 5-3 This is the modal response diagram of the present invention with ωt = 2π / 3.

[0027] Figure 5-4 This is the modal response diagram of the present invention with ωt as π.

[0028] Figure 5-5 This is the modal response diagram of the present invention with ωt = 4π / 3.

[0029] Figure 5-6 This is the modal response diagram of the present invention with ωt = 2π. Detailed Implementation

[0030] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0031] Example 1 A method for extracting gear traveling wave modes, the method comprising: The time-domain vibration response signal of the gear is obtained by simulation or measurement to obtain the time-domain vibration response signal of any point on the gear. The gear frequency domain response signal is obtained by Fourier transforming the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The sideband amplitude spectrum and sideband phase spectrum are obtained by extracting the sideband response at the gear resonant frequency Ω, thus obtaining the sideband amplitude spectrum and sideband phase spectrum under the resonant state. The amplitude and phase of the gear pitch diameter component are determined by establishing a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination is made by the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. , ; in, Let be the spatial angular position of the gear, and k is the pitch diameter of the gear, and ω is the natural frequency of the gear. The phase of the gear pitch diameter component; This represents the amplitude of the gear pitch diameter component.

[0032] Example 2 A method for extracting gear traveling wave modes, the method comprising: The time-domain vibration response signal of the gear is obtained by simulation or measurement to obtain the time-domain vibration response signal of any point on the gear. The gear frequency domain response signal is obtained by Fourier transforming the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The sideband amplitude spectrum and sideband phase spectrum are obtained by extracting the sideband response at the gear resonant frequency Ω, thus obtaining the sideband amplitude spectrum and sideband phase spectrum under the resonant state. The amplitude and phase of the gear pitch diameter component are determined by establishing a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination is made by the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

[0033] Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signal is also included. This is done by installing a sensor on the gear to collect the sensor vibration signal.

[0034] Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signals also includes obtaining the vibration signal through simulation calculation using a finite element model.

[0035] Amplitude of the gear pitch diameter component and phase And the natural frequency ω determines the traveling wave resonant mode response. , ; in, Let be the spatial angular position of the gear, and ; ω is the natural frequency of the gear; The phase of the gear pitch diameter component; This represents the amplitude of the gear pitch diameter component.

[0036] Example 3 A method for extracting gear traveling wave modes, the method comprising: The time-domain vibration response signal of the gear is obtained by simulation or measurement to obtain the time-domain vibration response signal of any point on the gear. The gear frequency domain response signal is obtained by Fourier transforming the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The sideband amplitude spectrum and sideband phase spectrum are obtained by extracting the sideband response at the gear resonant frequency Ω, thus obtaining the sideband amplitude spectrum and sideband phase spectrum under the resonant state. The amplitude and phase of the gear pitch diameter component are determined by establishing a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination is made by the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

[0037] Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signal is also included. This is done by installing a sensor on the gear to collect the sensor vibration signal.

[0038] Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signals also includes obtaining the vibration signal through simulation calculation using a finite element model.

[0039] The sensor is mounted on the spokes of the gear.

[0040] Amplitude of the gear pitch diameter component and phase And the natural frequency ω determines the traveling wave resonant mode response. , ; in, Let be the spatial angular position of the gear, and ; , where k is an integer and ω is the natural frequency of the gear; The phase of the gear pitch diameter component; This represents the amplitude of the gear pitch diameter component.

[0041] Example 4 This embodiment is a system for extracting gear traveling wave modes, which is used to implement the aforementioned method for extracting gear traveling wave modes, and includes: The gear time-domain vibration response signal acquisition module obtains the gear time-domain vibration response signal at any point on the gear through simulation or measurement; The gear frequency domain response signal acquisition module obtains the gear frequency domain response signal by performing a Fourier transform on the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And a gear natural frequency ω calculation module to identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ; Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The module for acquiring the sideband amplitude spectrum and the sideband phase spectrum obtains the sideband amplitude spectrum and the sideband phase spectrum in the resonant state by extracting the sideband response at the gear resonant frequency Ω. The module for determining the amplitude and phase of the gear pitch diameter component establishes a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination module uses the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

[0042] Example 5 Based on the above embodiments, this embodiment Figure 2The gear frequency corresponding to each peak is the gear resonant frequency Ω, and the corresponding natural frequency is the resonant frequency |Ω| * number of teeth Z (Z=97). For example, the natural frequencies corresponding to the peaks at gear frequencies of 23.42 Hz and 34.38 Hz are 2272 Hz and 3335 Hz, respectively.

[0043] By extracting the frequency domain responses at the gear resonant frequencies of 23.42 Hz and 34.38 Hz, the following results can be obtained: Figure 2 The sideband amplitude and phase spectrum of 3. Figure 1 In the process, the amplitude response at gear rotation frequencies of 23.42Hz and 34.38Hz can be extracted to obtain... Figure 3 and Figure 4 The amplitude spectrum; a similar method can be used to obtain Figure 3 and 4 The phase spectrum. Fourier transforms of the time-domain responses at gear frequencies of 23.42 Hz and 34.38 Hz can also yield the results. Figure 3 and Figure 4 The amplitude and phase spectrum.

[0044] The response of a point on the gear at resonance can be expressed as: ; Where, u( ,t) represents the angular position of the gear in space. The response at the location; Because the gear rotates, the angular position of a point on the gear... in For gear rotation frequency (when rotating clockwise), (negative; positive) The initial phase angle (without loss of generality, ); Let be the component of the traveling wave mode at the k-th node, which is a complex number; For k-node radius basis functions (circumferential Fourier functions); This represents the natural frequency of gear resonance. It is the natural frequency The time-domain Fourier function; is the imaginary unit; cc represents the complex conjugate of the preceding term; and These are the nodal diameter amplitude and phase, respectively. In this embodiment, If the value is negative, the gear rotates clockwise, therefore .

[0045] Depend on Figure 3 and Figure 4 The sideband spectrum can be obtained and The traveling wave resonant modal response can be obtained by superimposing the components of each nodal diameter.

[0046] ; Among them, the spatial angular position of the gear .

[0047] Figure 3 The amplitude spectrum shows that the gear has amplitudes at the 90th, 93rd, 96th, 99th, and 102nd revolutions per minute, which correspond to pitch diameters of 7, 4, 1, -2, and -5, respectively. The amplitudes at the 93rd and 99th orders are relatively high, indicating that the traveling wave mode is dominated by pitch diameters of 4 and -2. Figure 3 The corresponding traveling wave modal response. Unlike standing wave modes (where vibrations are synchronized at each location), traveling wave modes exhibit asynchronous vibrations at each location. Here, Figures 5-1 to 5-6 Only the traveling wave mode is shown. , and The modal response is shown; a more comprehensive modal response requires an animated demonstration.

Claims

1. A method for extracting gear traveling wave modes, characterized in that the method... include: The time-domain vibration response signal of the gear is obtained by simulation or measurement to obtain the time-domain vibration response signal of any point on the gear. The gear frequency domain response signal is obtained by Fourier transforming the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ； Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The sideband amplitude spectrum and sideband phase spectrum are obtained by extracting the sideband response at the gear resonant frequency Ω, thus obtaining the sideband amplitude spectrum and sideband phase spectrum under the resonant state. The amplitude and phase of the gear pitch diameter component are determined by establishing a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination is made by the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

2. The method for extracting gear traveling wave modes according to claim 1, characterized in that, Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signal is also included. This is done by installing a sensor on the gear to collect the sensor vibration signal.

3. The method for extracting gear traveling wave modes according to claim 1, characterized in that, Before acquiring the time-domain vibration response signal of the gear, the acquisition of vibration signals also includes obtaining the vibration signal through simulation calculation using a finite element model.

4. The method for acquiring time-domain vibration signals of gears according to claim 2, characterized in that, The sensor is mounted on the rim of the gear or on the spokes of the gear.

5. The method for extracting gear traveling wave modes according to claim 1, characterized in that, Gear Resonance Frequency And calculate the natural frequency ω of the gear, and identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. The natural frequency ω of the gear is calculated based on the number of gear teeth Z. ; Where ω is the natural frequency of the gear. Z represents the rotational frequency of the gear, and Z represents the number of teeth on the gear.

6. The method for extracting gear traveling wave modes according to claim 1, characterized in that, Amplitude of the gear pitch diameter component and phase And the natural frequency ω determines the traveling wave resonant mode response. , ； in, Let be the spatial angular position of the gear, and K is the pitch diameter of the gear, and ω is the natural frequency of the gear. The phase of the gear pitch diameter component; This represents the amplitude of the gear pitch diameter component.

7. A system for extracting the traveling wave mode of a gear, characterized in that, A method for extracting gear traveling wave modes according to any one of claims 1-6, comprising: The gear time-domain vibration response signal acquisition module obtains the gear time-domain vibration response signal at any point on the gear through simulation or measurement; The gear frequency domain response signal acquisition module obtains the gear frequency domain response signal by performing a Fourier transform on the gear time domain vibration response signal. The gear frequency domain response signal includes the gear amplitude spectrum signal and the gear phase spectrum signal. Gear Resonance Frequency And a gear natural frequency ω calculation module to identify the gear rotation frequency corresponding to the resonance peak from the gear amplitude spectrum signal. And the corresponding natural frequency ω of the gear is calculated based on the number of gear teeth Z; ； Where ω is the natural frequency of the gear. Z is the resonant rotational frequency of the gear, and Z is the number of teeth on the gear. The module for acquiring the sideband amplitude spectrum and the sideband phase spectrum obtains the sideband amplitude spectrum and the sideband phase spectrum in the resonant state by extracting the sideband response at the gear resonant frequency Ω. The module for determining the amplitude and phase of the gear pitch diameter component establishes a correspondence between each sideband component in the sideband amplitude spectrum and the sideband phase spectrum and the gear pitch diameter component of the gear resonance mode, thereby determining the amplitude of the gear pitch diameter component. and phase ; Traveling wave resonant modal response The determination module uses the amplitude of the gear pitch diameter component. and phase And the natural frequency ω determines the traveling wave resonant mode response. .

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