A method and device for determining the matching relationship between the micro-roughness of a tooth surface and macro-vibration of a gear

Abstract

The present application relates to a kind of method and device for determining the matching relationship of gear macroscopic vibration and tooth surface micro-roughness.The method is as follows:(1) using three-dimensional profilometer, the profile height data of gear tooth surface is measured, with space frequency and power spectral density as horizontal and vertical coordinates, height data is plotted in double logarithmic graph, linear regression method is used for fitting, and the fractal parameter of tooth surface is calculated according to the slope and intercept of fitting function;(2) the vibration acceleration signal of gear transmission system and the signal of given speed and load are collected;Then, the collected signal is filtered and analyzed in time-frequency domain, and the acceleration amplitude corresponding to meshing frequency is extracted;(3) replace the gear with different micro-morphology, change the speed and load conditions, repeat the above operation, and obtain the quantitative matching relationship of tooth surface micro-morphology and macroscopic vibration response under different conditions.The present application realizes the quantitative matching of tooth surface micro-morphology characteristics and gear macroscopic vibration response.

Description

Technical Field

[0001] This invention relates to the field of gear transmission technology, specifically to a method and apparatus for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear. Background Technology

[0002] Gear transmission, as a crucial component of mechanical transmission systems, is widely used in industrial production. Vibration during gear transmission affects its accuracy and stability, making research on the dynamic response of gear transmissions particularly important. The microscopic geometry of the gear tooth surface undergoes elastic and plastic deformation under the influence of external loads during meshing, storing and dissipating external excitation energy in the form of strain energy, exhibiting significant damping characteristics that affect the vibration characteristics of gear transmissions. Therefore, exploring the influence of tooth surface morphology on the dynamic response of gears is of great significance.

[0003] Current research on gear technology devices and methods mainly focuses on two aspects. One approach utilizes various types of gear transmission test benches to collect vibration signals under different operating conditions using sensors. This involves extracting and processing various signal characteristics for analysis, analyzing dynamic response patterns, and then monitoring gear operation through the vibration signals of the gear transmission. However, this type of research concentrates on fault factors such as pitting and tooth breakage, neglecting the influence of gear roughness as a microscopic factor. On the other hand, research on gear micro-roughness currently focuses on measurement methods and devices for acquiring tooth surface morphology data, such as the reconstruction of three-dimensional tooth surface morphology, simulation models of tooth surface morphology, and clamping devices for tooth surface roughness measuring instruments. However, this type of research overlooks the influence of gear micro-roughness on the macroscopic vibration of gears.

[0004] Therefore, it is necessary to propose a method and design a corresponding device to quantitatively match the micro-fractal parameters of the tooth surface with the macro-vibration response of the gear, and to determine the matching relationship between the micro-roughness morphology of the tooth surface and the macro-vibration response of the gear, which will help improve the accuracy of the gear transmission system and improve the dynamic characteristics of the system. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention aims to provide a method and apparatus for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear, so as to determine the matching relationship between the micro-roughness morphology characteristics of the tooth surface and the macro-vibration response of the gear under a given working condition.

[0006] The technical solution provided by this invention is as follows:

[0007] In a first aspect, the present invention provides an apparatus for determining the matching relationship between the micro-roughness of the gear tooth surface and the macro-vibration of the gear, comprising a three-phase asynchronous motor (1), an input speed and torque sensor (2), an input shaft (3), a drive wheel (4), and an input shaft bearing housing (6) connected in sequence, a frequency converter (13), and...

[0008] The magnetic powder brake (9), the output speed and torque sensor (7), the driven wheel (10) and the output shaft bearing seat (12) are connected in sequence, along with the brake tension controller (8) and the magnetic acceleration sensor (11).

[0009] The driving wheel (4) and the driven wheel (10) mesh;

[0010] The frequency converter (13) is connected to the three-phase asynchronous motor (1) to control the speed;

[0011] The brake tension controller (8) is connected to the magnetic powder brake (9);

[0012] The magnetic accelerometer (11) is attached to the output shaft bearing housing (12).

[0013] Secondly, the present invention provides a method for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear, comprising the following steps:

[0014] S1. Using a 3D profilometer, measure the profile height data of the gear tooth surface. Plot the height data on a logarithmic graph with spatial frequency and power spectral density as the horizontal and vertical axes, respectively. Fit the graph using the least squares linear regression method, and calculate the fractal parameters of the tooth surface based on the slope and intercept of the fitted function. D , G ;

[0015] S2. Install the driving wheel (4) and driven wheel (10), and attach the magnetic accelerometer (11) to the output shaft bearing seat (12); start the device, save the speed and load signals obtained by the input speed and torque sensor (2) and the output speed and torque sensor (7), and record the vibration acceleration signal collected by the magnetic accelerometer (11). A ( t The frequency domain signal is obtained by performing a Fourier transform on the filtered vibration acceleration signal. A ( f );

[0016] S3. Replace with gears of different microstructures, repeat step S1, and obtain the fractal parameters of gears with different microstructures. D , GRepeat step S2 to extract the acceleration amplitude corresponding to the meshing frequency in the gear vibration acceleration signal under different micromorphologies, while keeping the rotational speed and load conditions constant.

[0017] S4. Draw a quantitative matching diagram of the micro fractal parameters of the tooth surface and the acceleration amplitude corresponding to the macro gear meshing frequency to obtain the matching relationship between the micro roughness morphology of the tooth surface and the macro vibration response of the gear.

[0018] Furthermore, step S1 includes the following sub-steps:

[0019] S1.1, according to the following Fourier transform formula:

[0020]

[0021] Discrete tooth surface profile data obtained by measurement h ( x Perform a Fourier transform to obtain the power spectral density function of the tooth profile height. P ( ω ); e It is a natural constant. j The imaginary unit, ω Spatial frequency ，x This is the sampling length.

[0022] S1.2, with the spatial frequency logarithm lg ω The x-axis represents the logarithm of the power spectral density (lg). P ( ω Establish a rectangular coordinate system with y as the vertical axis and plot the logarithmic power spectral density plot;

[0023] S1.3, the logarithmic graph is fitted using the least squares linear regression method, and the slope of the fitted function is... k With intercept b The formula is as follows:

[0024]

[0025] In the formula N Indicates the number of samples for the tooth profile height data; The expected value of the logarithm of spatial frequency. This is the mathematical expectation of the logarithm of the power spectral density;

[0026] S1.4, calculate the fractal parameters of the tooth surface using the slope and intercept of the fitted function. D , G The formula is as follows:

[0027]

[0028] In the formula, γThis is the scale parameter, typically taken as 1.5; where, D It is the fractal dimension, which reflects the effectiveness of a complex shape in occupying space and is a measure of the irregularity of a complex shape; G It is fractal roughness, which reflects the magnitude of the rough surface profile at the microscopic scale.

[0029] Furthermore, the input and output speed and torque sensors acquire the system's speed. n ,load T The signal is the acceleration signal of the gear vibration response, which is collected by a magnetic accelerometer.

[0030] Furthermore, in step S2, the gear vibration acceleration signal collected by the magnetic accelerometer is... A ( t Perform a Fourier transform to obtain the frequency domain signal. A ( f The formula is as follows:

[0031]

[0032] In the formula, e It is a natural constant. j The imaginary unit, ω For frequency ，t Sampling time;

[0033] meshing frequency f m The calculation formula is as follows:

[0034]

[0035] In the formula n For gear speed, z The gear has the number of teeth; the acceleration amplitude corresponding to the gear meshing frequency is extracted as the dynamic response of gear vibration.

[0036] Furthermore, in step S3, the fractal dimension is used. D The horizontal axis represents the fractal roughness. G The vertical axis represents the acceleration amplitude corresponding to the meshing frequency. A GMF A spatial coordinate system is established for the vertical axis, and the coordinate points that quantitatively match the micro fractal parameters of the tooth surface with the acceleration amplitude corresponding to the macro gear meshing frequency under given speed and load conditions are marked. Then, a matching diagram of the micro morphology parameters of the tooth surface and the macro vibration response of the gear can be approximately fitted under given speed and load conditions.

[0037] The beneficial effects of this invention are as follows:

[0038] 1. This invention considers the self-similar fractal characteristics of tooth surface roughness at different scales, overcoming the limitations of statistical parameters of roughness caused by instrument resolution and sampling length. The least squares linear regression method is used to fit the logarithmic plot of the power density function to obtain fractal parameters characterizing the micro-roughness of the tooth surface.

[0039] 2. This invention considers the influence of the micro-roughness of the tooth surface on the dynamic response of the gear. By plotting the matching relationship between the micro-fractal parameters of the tooth surface and the acceleration amplitude corresponding to the gear meshing frequency, a quantitative matching between the micro-morphological features of the tooth surface and the macro-vibration response of the gear is achieved.

[0040] 3. In this invention, the gear and shaft are fastened together with screws, which avoids the defect of keyway weakening the shaft strength and reduces the impact of shaft runout on gear vibration.

[0041] 4. The present invention also provides a device for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear. The device has a simple structure, is easy to install and operate, can realize a complete set of tests, and is conducive to promotion and application. Attached Figure Description

[0042] Figure 1 This is a flowchart of a method for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear according to the present invention;

[0043] Figure 2 A two-dimensional contour image of the microstructure of the gear tooth surface obtained by wire EDM;

[0044] Figure 3 The plot shows the fitted logarithm of the power spectral density function.

[0045] Figure 4 (a) is a schematic diagram of a device for determining the matching relationship between the micro-roughness morphology of the tooth surface and the macro-vibration response of the gear transmission system according to the present invention; in the figure: 1-three-phase asynchronous motor, 2-input end speed and torque sensor, 3-input shaft, 4-driving wheel, 5-acrylic baffle, 6-input shaft bearing seat, 7-output end speed and torque sensor, 8-brake tension controller, 9-magnetic powder brake, 10-driven wheel, 11-magnetic acceleration sensor, 12-output shaft bearing seat, 13-frequency converter;

[0046] Figure 4 (b) is a physical diagram of the device for determining the matching relationship between the micro-roughness morphology of the tooth surface and the macro-vibration response of the gear transmission system according to the present invention;

[0047] Figure 5 This is a schematic diagram of the gear and shaft connection method of the present invention; in the figure: 14 - fastening screw;

[0048] Figure 6(a) is a time-domain plot of the gear vibration acceleration signal acquired by a magnetic accelerometer;

[0049] Figure 6 (b) is the frequency domain diagram of the gear vibration acceleration signal after Fourier transform;

[0050] Figure 7 This is a quantitative matching diagram of the micro-roughness of the tooth surface and the acceleration amplitude corresponding to the macro-meshing frequency. Detailed Implementation

[0051] To make the technical problem, technical solution and advantages of the present invention clearer, the following detailed description will be made with reference to the accompanying drawings and specific embodiments, taking a pair of spur gears with a module of 3mm, 30 and 36 teeth respectively, and 20Cr material as an example. The gears are processed by laser wire cutting.

[0052] Figure 4 The diagram illustrates an apparatus for determining the matching relationship between the micro-roughness morphology of gear teeth and the macro-vibration response of a gear transmission system. The apparatus includes a three-phase asynchronous motor 1, an input speed and torque sensor 2, an input shaft 3, a drive wheel 4, and an input shaft bearing housing 6, all connected in sequence by shafts. A frequency converter 13 is also shown.

[0053] The magnetic powder brake 9, the output speed and torque sensor 7, the driven wheel 10 and the output shaft bearing seat 12 are connected in sequence; the brake tension controller 8 and the magnetic acceleration sensor 11 are connected in sequence.

[0054] The driving wheel 4 and the driven wheel 10 are engaged; an acrylic baffle 5 is provided as a protective cover;

[0055] The frequency converter 13 is connected to the three-phase asynchronous motor 1 to control the speed;

[0056] The brake tension controller 8 is connected to the magnetic powder brake 9;

[0057] The magnetic accelerometer 11 is attached to the output shaft bearing housing 12.

[0058] The input speed and torque sensor can acquire the speed and torque signal of the driving wheel in real time; the output speed and torque sensor can acquire the speed and torque signal of the driven wheel in real time; the magnetic powder brake is the load end, providing the system with a load, namely a torque opposite to the current rotation direction; the frequency converter controls the speed of the three-phase asynchronous motor; the brake tension controller changes the torque of the magnetic powder brake by controlling the current of the magnetic powder brake; the magnetic acceleration sensor acquires the vibration acceleration signal at the output end.

[0059] Figure 1 The flowchart illustrates a method for determining the matching relationship between the micro-roughness morphology of the gear tooth surface and the macro-vibration response of the gear transmission system, including the following steps:

[0060] S1. Using a 3D profilometer, measure the profile height data of the gear tooth surface. Plot the height data on a logarithmic graph with spatial frequency and power spectral density as the horizontal and vertical axes, respectively. Fit the graph using the least squares linear regression method, and calculate the fractal parameters of the tooth surface based on the slope and intercept of the fitted function. D , G ;

[0061] The sub-steps are as follows:

[0062] S1.1, the microstructure of the gear tooth surface was measured using a Nano-μScan 3D profilometer. A region with a sampling length of 2.6 mm was selected on the tooth surface for measurement to obtain the gear profile height data, such as... Figure 2 As shown.

[0063] S1.2, according to equation (1), the measured tooth surface profile height data is... h ( x Perform a Fourier transform to obtain the power spectral density function of the tooth profile height. P ( ω ):

[0064] (1)

[0065] In the formula, e It is a natural constant. j The imaginary unit, ω Spatial frequency ，x This is the sampling length.

[0066] S1.3, spatial frequency ω and its corresponding power spectral density P ( ω Take the logarithm, and use the logarithm of spatial frequency (lg) ω The x-axis represents the logarithm of the power spectral density (lg). P ( ω Plot the logarithmic power spectral density using y as the ordinate, as shown below. Figure 3 As shown.

[0067] S1.4, the logarithmic graph is fitted using the least squares linear regression method, and the slope of the fitted function is... k With intercept b The formula is as follows:

[0068] (2)

[0069] In the formula N Indicates the number of samples for the tooth profile height data; The expected value of the logarithm of spatial frequency. This is the mathematical expectation of the logarithm of the power spectral density;

[0070] The slope of the fitted function was calculated. k =-1.831, intercept b =-15.1532.

[0071] S1.5, calculate the fractal parameters of the tooth surface using the slope and intercept of the fitted function. D , G The formula is as follows:

[0072] (3)

[0073] In the formula, γ This is the scale parameter, typically taken as 1.5. Wherein, D It is the fractal dimension, which reflects the effectiveness of a complex shape in occupying space and is a measure of the irregularity of a complex shape; G It is fractal roughness, which reflects the magnitude of the rough surface profile at the microscopic scale. k =-1.831, b Substituting -15.1532 into (3), the fractal dimension of the wire-cut gear is calculated: D= 1.585, fractal roughness G =1.75×10 -9 m.

[0074] S2. Record the vibration acceleration signal collected by the magnetic accelerometer (11). A ( t The frequency domain signal is obtained by performing a Fourier transform on the filtered vibration acceleration signal. A ( f The details are as follows:

[0075] like Figure 4 As shown in (a) schematic diagram and (b) actual picture, remove the input shaft bearing housing (6), remove the acrylic baffle (5), and then refer to... Figure 5 In the connection between the gear and the fastening screw, the four fastening screws (14) on the input shaft (3) can be loosened to install the driving wheel (4). A similar method can be used to install the driven wheel (10) on the output shaft, and the magnetic accelerometer (11) can be attached to the output shaft bearing seat (12). Turn on the switch of the brake tension controller (8). After setting the parameters, the magnetic powder brake (9) provides a stable load T. Turn on the switch of the frequency converter (13). After setting the parameters, the three-phase asynchronous motor (1) outputs a constant speed n. Monitor the signals collected by the input speed torque sensor (2) and the output speed torque sensor (7). After the speed and load of the device stabilize, record the speed as 380 rpm and the load as 1.29 N∙m. Figure 6(a) shows the vibration signal collected by the magnetic accelerometer (11). A ( t The gear vibration response acceleration signal A(t) acquired by the magnetic accelerometer is subjected to Fourier transform to obtain the frequency domain signal. A ( f The formula is as follows:

[0076] (4)

[0077] In the formula, e It is a natural constant. j The imaginary unit, ω For frequency ，t Sampling time.

[0078] meshing frequency f m The calculation formula is as follows:

[0079] (5)

[0080] In formula (5) n For gear speed, z This represents the number of teeth on the gear. The calculated meshing frequency is 190Hz. For example... Figure 6 As shown in (b), considering sensor error and modulation phenomena, the figure... f =186Hz is the first-order meshing frequency. Extract the acceleration amplitude corresponding to the gear meshing frequency. A GMF×1 =0.043m / s 2 It is analyzed as a dynamic response quantity of gear vibration.

[0081] S3. Extract the acceleration amplitude corresponding to the meshing frequency from the gear vibration acceleration signal under different microstructures, as detailed below:

[0082] Gears with different tooth surface roughness are formed through milling and grinding. The operation in step 1 is repeated, and the roughness of the milled and ground gears are calculated respectively. D , G The values ​​are shown in Table 1. Among them, milling machining: D =1.72、 G =2.7×10 -11 m, grinding process: D =1.85、 G =3.42×10 -13 m; Repeat step 2, changing the gear while keeping the rotational speed and load constant, to obtain vibration signals with different tooth surface micromorphologies. Record the acceleration amplitude corresponding to the first meshing frequency, and then perform milling. AGMF×1 =0.039m / s 2 Grinding process: A GMF×1 =0.029m / s 2 .

[0083] S4. Using fractal dimension D The horizontal axis represents the fractal roughness. G The logarithmic value is on the vertical axis, representing the acceleration amplitude corresponding to the first-order meshing frequency. A GMF×1 Establish a three-dimensional coordinate system for the vertical axis, and mark the coordinate points corresponding to the three machining methods in the coordinate system. For example... Figure 7 As shown, based on the axiom that a plane can be determined by three points, the relationship between the micro-fractal parameters of the tooth surface and the acceleration amplitude corresponding to the gear meshing frequency can be approximately fitted using the three marked coordinate points mentioned above. This achieves quantitative matching between the micro-roughness morphology of the tooth surface and the macro-vibration response of the gear.

[0084] Table 1 shows the micro-fractal parameters and statistical parameters of the tooth surface under the three processing methods:

[0085] Table 1

[0086]

[0087] The above embodiments are not limiting embodiments of the present invention. Any modifications or equivalent variations made by those skilled in the art based on the essential content of the present invention are within the technical scope of the present invention.

[0088] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the invention.

Claims

1. A method for determining the matching relationship between the micro-roughness of the gear tooth surface and the macro-vibration of the gear, characterized in that, The method is based on a device for determining the matching relationship between the micro-roughness of the tooth surface and the macro-vibration of the gear. This device includes a three-phase asynchronous motor (1), an input speed and torque sensor (2), an input shaft (3), a drive wheel (4), and an input shaft bearing housing (6), connected in sequence by shafts, along with a frequency converter (13). The magnetic powder brake (9), the output speed and torque sensor (7), the driven wheel (10) and the output shaft bearing seat (12) are connected in sequence, along with the brake tension controller (8) and the magnetic acceleration sensor (11). The driving wheel (4) and the driven wheel (10) mesh; The frequency converter (13) is connected to the three-phase asynchronous motor (1) to control the speed; The brake tension controller (8) is connected to the magnetic powder brake (9). The magnetic accelerometer (11) is attached to the output shaft bearing housing (12); The method includes the following steps: S1. Using a 3D profilometer, measure the profile height data of the gear tooth surface. Plot the height data on a logarithmic graph with spatial frequency and power spectral density as the horizontal and vertical axes, respectively. Fit the graph using the least squares linear regression method, and calculate the fractal parameters of the tooth surface based on the slope and intercept of the fitted function. D , G ; S2. Install the driving wheel (4) and driven wheel (10), and attach the magnetic accelerometer (11) to the output shaft bearing seat (12); start the device, save the speed and load signals obtained by the input speed and torque sensor (2) and the output speed and torque sensor (7), and record the vibration acceleration signal collected by the magnetic accelerometer (11). A ( t The frequency domain signal is obtained by performing a Fourier transform on the filtered vibration acceleration signal. A ( f ); S3. Replace with gears of different microstructures, repeat step S1, and obtain the fractal parameters of gears with different microstructures. D , G Repeat step S2 to extract the acceleration amplitude corresponding to the meshing frequency in the gear vibration acceleration signal under different micromorphologies, while keeping the rotational speed and load conditions constant. S4. Draw a quantitative matching diagram of the micro fractal parameters of the tooth surface and the acceleration amplitude corresponding to the macro gear meshing frequency to obtain the matching relationship between the micro roughness morphology of the tooth surface and the macro vibration response of the gear.

2. The method according to claim 1, characterized in that, Step S1 includes the following sub-steps: S1.1, Use a three-dimensional profilometer to measure the profile height data of the gear tooth surface; S1.2, according to the following Fourier transform formula: Discrete tooth surface profile data obtained by measurement h ( x Perform a Fourier transform to obtain the power spectral density function of the tooth profile height. P ( ω ); e It is a natural constant. j The imaginary unit, ω Spatial frequency ，x The sampling length; S1.3, with the spatial frequency logarithm lg ω The x-axis represents the logarithm of the power spectral density (lg). P ( ω Establish a rectangular coordinate system with y as the vertical axis and plot the logarithmic power spectral density plot; S1.4, the logarithmic graph is fitted using the least squares linear regression method, and the slope of the fitted function is... k With intercept b The formula is as follows: In the formula N Indicates the number of samples for the tooth profile height data; Let be the mathematical expectation of the logarithm of spatial frequency. This is the mathematical expectation of the logarithm of the power spectral density; S1.5, calculate the fractal parameters of the tooth surface using the slope and intercept of the fitted function. D , G The formula is as follows: In the formula, γ This is the scale parameter, typically taken as 1.5; where, D It is the fractal dimension, which reflects the effectiveness of a complex shape in occupying space and is a measure of the irregularity of a complex shape; G It is fractal roughness, which reflects the magnitude of the rough surface profile at the microscopic scale.

3. The method according to claim 1, characterized in that: Input speed and torque sensor, output speed and torque sensor acquire system speed n ,load T The signal is the acceleration signal of the gear vibration response, which is collected by a magnetic accelerometer.

4. The method according to claim 1, characterized in that, In step S2, the gear vibration acceleration signal collected by the magnetic accelerometer is... A ( t Perform a Fourier transform to obtain the frequency domain signal. A ( f The formula is as follows: In the formula, e It is a natural constant. j The imaginary unit, ω For frequency ，t Sampling time; meshing frequency f m The calculation formula is as follows: In the formula n For gear speed, z The gear has the number of teeth; the acceleration amplitude corresponding to the gear meshing frequency is extracted as the dynamic response of gear vibration.

5. The method according to claim 1, characterized in that, In step S3, the fractal dimension is used. D The horizontal axis represents the fractal roughness. G The vertical axis represents the acceleration amplitude corresponding to the meshing frequency. A GMF A spatial coordinate system is established for the vertical axis, and the coordinate points that quantitatively match the micro fractal parameters of the tooth surface with the acceleration amplitude corresponding to the macro gear meshing frequency under given speed and load conditions are marked. Then, a matching diagram of the micro morphology parameters of the tooth surface and the macro vibration response of the gear can be approximately fitted under given speed and load conditions.

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