CN115096239B - A Method for Acquisition and Analysis of Tooth Profile Waviness of Involute Spur Gear - Google Patents

Abstract

The invention discloses a method for obtaining and analyzing the tooth profile waviness of an involute spur gear. The method can efficiently and reliably acquire information on the tooth profile waviness of a single tooth surface and Continuous tooth profile waviness information, and its order information. Specifically, the method comprises the following method steps: measuring all tooth surface tooth profile information of the gear, selecting three tooth profile lines at the same position of each tooth surface for measurement, and the measuring device is a gear measurement center. The technical advantage of the present invention is that in addition to obtaining the waviness information of the single-tooth tooth surface, the waviness information of the teeth in the gear can also be continuous, so as to obtain the continuous waviness information of the entire gear.

Description

A Method for Acquisition and Analysis of Tooth Profile Waviness of Involute Spur Gear

technical field

The invention relates to a method for obtaining and analyzing the profile waviness of an involute spur gear, belonging to the technical field of gear transmission.

Background technique

As a key component of transmission, gears are widely used in high-speed rail, automobiles, precision machine tools and other fields because of their stable transmission, high efficiency, and long service life. The improvement of people's requirements for the use of gear transmission systems in equipment has made gears develop in the direction of high precision, low vibration, low noise and high reliability.

The vibration and noise of gear transmission are important indicators to reflect the performance of gear transmission. The vibration and noise levels of gears affect the user's experience, and the surface morphology of gears affects the vibration and noise levels of gear transmission. At present, a large number of studies focus on the influence of gear tooth surface roughness and tooth profile error on gear transmission noise, and improve the transmission noise of gears by improving the surface quality of gears and using tooth surface modification. Focusing on the tooth surface waviness between macroscopic tooth profile deviation and microscopic tooth surface roughness, there are few works on the correlation between it and gear transmission vibration and noise. Therefore, research on gear tooth surface waviness has important theoretical and practical value. One of the key issues involved is the effective extraction and analysis of tooth surface waviness.

Therefore, the present invention is based on the above-mentioned key technical problem: a method for obtaining the tooth profile waviness of involute spur gears is proposed, and the information of the tooth profile waviness is analyzed. This method can be based on the measurement results of the gear measurement center , efficiently and reliably obtain gear tooth profile waviness information, and obtain its order information.

Contents of the invention

The technical solution adopted in the present invention is a method for obtaining and analyzing the profile waviness of involute spur gears. This method can efficiently and reliably obtain the tooth profile of a single gear tooth based on the measurement results of the gear measurement center. Profile waviness information and continuous tooth profile waviness information, and its order information is obtained. Concretely include the following method steps:

To measure the tooth profile information of all gear teeth, select three tooth profiles at the same position on each tooth surface for measurement, and the measuring equipment is the gear measurement center.

(1) Acquisition of tooth profile waviness of a single tooth surface

The information of the three measured tooth profiles is used for analysis. The measurement results include three parts: surface roughness, waviness and shape error. By filtering the tooth profile information, the tooth profile waviness information can be obtained.

The direct measurement result of the gear measurement center takes the rotation angle of the gear as the abscissa during measurement, that is, the value of the spread angle. The coordinate transformation is carried out on the measurement result, and the conversion formula is formula 1.

l: involute length value R _b : base circle radius θ: gear rotation angle

Through the coordinate transformation, the measurement result of the tooth profile is converted into the abscissa by the length of the involute.

Next, extract the waviness of the single-tooth tooth surface, and use the filter method to meet the requirement that the cut-off wavelength is greater than the sampling length. Case 1: When the actually collected tooth profile involute expansion length of the single-tooth tooth surface is greater than the sampling length, directly use the filter method to filter out Shape errors in tooth profile information. Situation 2: When the actually collected tooth profile involute expansion length of a single tooth tooth surface is less than the sampling length, the polynomial fitting method can be used to filter out the shape error.

In this case, directly use the Gaussian filter to filter out the shape error.

In the second case, since the tooth profile shape error is usually a simple curve, the least squares method is used for nonlinear fitting to remove the tooth profile shape error.

Gaussian filtering is currently the most commonly used method for filtering roughness, and its development is relatively mature, so the Gaussian filter is used to filter the surface roughness. The surface roughness is a high-frequency component in the collected signal, and the Gaussian filter is used for low-pass filtering to remove the surface roughness component in the collected signal.

(2) Gear tooth profile waviness is continuous

Gear transmission is a continuous process, and the generated gear transmission noise is a continuous signal, while the single-tooth tooth surface information is independent data, so it is necessary to continue the tooth surface information of each gear tooth next.

According to the generation principle, the tooth profile information of the corresponding position of the single tooth surface of the entire gear is sequentially continuous, and for the part where the abscissa of the tooth surface information overlaps in the continuous process, the value with a high amplitude is selected as the extracted information, that is, Get 360-degree continuous and complete tooth surface information of gears.

The continuous tooth surface information can be directly filtered, and the Gaussian filter can be used to remove the shape error and surface roughness, and the waviness of the continuous tooth profile of the entire gear can be obtained.

(3) Order analysis

Perform order analysis on the filtered data, and the conversion relationship between order and frequency is shown in Equation 2.

Among them, the unit of frequency is Hz, and the unit of speed is r/min.

The order information of the corresponding tooth profile waviness can be obtained by sequentially performing Fourier transform on the obtained single-tooth tooth profile waviness information and continuous tooth surface waviness information, and the first three orders of the order information are high-amplitude. Statistical Analysis.

Compared with the prior art, the technical advantage of the present invention is that in addition to obtaining the profile waviness information of a single tooth surface, the waviness information of the teeth in the gear can also be continuous, so as to obtain the continuous waviness information of the entire gear.

Description of drawings

The invention is described in more detail below based on the accompanying drawings, which show exemplary embodiments. In the example attached image:

Figure 1 shows the measurement position of the tooth surface of a single gear;

Figure 2 shows the principle of continuous tooth profile information; a) before tooth profile information is continuous; b) after tooth profile information is continuous;

Figure 3 shows the extraction process of gear tooth profile waviness; a) shape error filtering, b) waviness and surface roughness, c) surface roughness filtering, d) waviness.

Figure 4 shows the order analysis results of gear tooth profile waviness; a) order information of single tooth profile waviness; b) order information of continuous tooth profile waviness.

Detailed ways

To measure the single-tooth tooth profile information of the gear, select the Klingelnberg P26 gear measurement center, select the appropriate ruby probe, and measure according to the measurement path shown in Figure 1 (3).

After the measurement, three sets of measurement data are obtained, and the coordinate transformation is carried out according to the formula (1), and the abscissa value is transformed from the rotation angle to the involute length value.

In this case, directly use the Gaussian filter to filter out the shape error.

In the second case, the polynomial fitting is carried out by the least square method, and the fitted polynomial is used for filtering to remove the shape error in the collected signal.

Specifically: the original data has n data points, and the corresponding coordinates are P _i ( _xi , y _i ), i=1, 2, . . . , n. Set the objective function type as a low-degree polynomial, such as formula (3):

f(x)=ax ² +bx+c#(3)

Where a, b, and c are constants.

The evaluation function is constructed by the least square method, such as formula (4):

The fitted polynomial can be obtained by obtaining a, b, and c that minimize the value of the evaluation function. The shape error in the acquired signal can be removed by filtering with the fitted polynomial.

Gaussian filtering is performed on the measurement data from which shape errors are removed to remove high-frequency roughness components.

Specifically: the collected tooth surface profile information function is P(x), where the high-frequency signal is h(x), and the low-frequency signal is l(x), then:

P(x)=h(x)+l(x)#(5)

Gaussian filtering is used to remove roughness, and the expression of Gaussian distribution is:

where μ is the mean and σ is the standard deviation.

The weight function of Gaussian filtering is:

Carry out Fourier transform to (5):

Where λ is the wavelength, λ _c is the cut-off wavelength of the Gaussian filter, and α is a constant.

The roughness can be obtained by convolution of the tooth surface profile information function and the Gaussian weight function:

By filtering out the surface roughness information through low-pass filtering, the waviness information of the tooth surface can be obtained.

The information of each tooth surface is measured in turn, and the tooth profile information of the corresponding position of the single tooth tooth surface is sequentially continuous by using the generating principle to obtain continuous and complete tooth surface information. The schematic diagram of the continuous principle is shown in Figure 2. Figure 2b) can be obtained by partially retaining the larger value of the ordinate. The continuous information is directly filtered, and the Gaussian filter is used to remove the shape error and surface roughness, and the waviness of the entire gear tooth profile can be obtained. Extract and analyze the tooth profile waviness based on the information obtained from the actual measurement. The process is shown in Figure 3.

The order information of the waviness can be obtained by performing Fourier transform on the waviness information of the tooth profile of the tooth surface. Taking the information of one position of the tooth surface as an example, the analysis results are shown in Figure 4.

Claims (1)

1. A method for obtaining and analyzing the profile waviness of an involute spur gear, characterized in that: it specifically comprises the following method steps, (1) Obtaining the profile waviness of the tooth surface of a single tooth; The information of the three measured tooth profiles is used for analysis. The measurement results include three parts: surface roughness, waviness and shape error. By filtering the tooth profile information, the information of the tooth profile waviness can be obtained; The direct measurement result of the gear measurement center takes the rotation angle of the gear as the abscissa during measurement, that is, the value of the spread angle, and performs coordinate transformation on the measurement result, and the conversion formula is formula 1; l: involute length value R _b : base circle radius θ: gear rotation angle; Through coordinate transformation, the measurement result of the tooth profile is transformed into the abscissa from the involute length value; To extract the waviness of single-tooth tooth surface, the use of filter method needs to meet the requirement that the cut-off wavelength is greater than the sampling length. Case 1: When the actually collected tooth profile involute expansion length of single-tooth tooth surface is greater than the sampling length, directly use the Gaussian filter method to filter out the tooth surface. The shape error in the profile information; Case 2: When the actually collected tooth profile involute expansion length of the single tooth tooth surface is less than the sampling length, the least square method is used to filter out the shape error by nonlinear fitting; Use a Gaussian filter to filter the surface roughness; the surface roughness is a high-frequency component in the collected signal, and the Gaussian filter is used for low-pass filtering to remove the surface roughness component in the collected signal; (2) The waviness of the gear tooth profile is continuous; According to the generation principle, the tooth profile information of the corresponding position of the single tooth surface of the whole gear is successively continuous, and for the part where the abscissa information of the tooth profile information overlaps in the continuous process, the value with high amplitude is selected as the extracted information, that is, 360-degree continuous and complete tooth surface information of gears; The continuous tooth surface information is directly filtered, and the Gaussian filter is used to remove the shape error and surface roughness, and the waviness of the continuous tooth profile of the entire gear can be obtained; (3) Order analysis; Perform order analysis on the filtered data, and the conversion relationship between order and frequency is shown in Equation 2; Among them, the unit of frequency is Hz, and the unit of speed is r/min; The order information of the corresponding tooth profile waviness can be obtained by sequentially performing Fourier transform on the obtained single-tooth tooth profile waviness information and continuous tooth surface waviness information, and the first three orders of the order information are high-amplitude. Statistical Analysis.