CN115096239B - Involute straight tooth cylindrical gear tooth profile waviness obtaining and analyzing method - Google Patents
Involute straight tooth cylindrical gear tooth profile waviness obtaining and analyzing method Download PDFInfo
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- CN115096239B CN115096239B CN202210660207.6A CN202210660207A CN115096239B CN 115096239 B CN115096239 B CN 115096239B CN 202210660207 A CN202210660207 A CN 202210660207A CN 115096239 B CN115096239 B CN 115096239B
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- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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Abstract
The invention discloses a method for acquiring and analyzing the tooth profile waviness of an involute straight tooth cylindrical gear, which can efficiently and reliably acquire the tooth profile waviness information of a single tooth surface and the tooth profile waviness information of a continuous tooth surface based on the measurement result of a gear measurement center and acquire the order information of the single tooth surface tooth profile waviness information. The method specifically comprises the following steps: and measuring tooth profile information of tooth surfaces of all the gear teeth, wherein three tooth profiles are selected at the same position of the tooth surfaces of all the gear teeth for measurement, and the measuring equipment is a gear measuring center. The method has the technical advantages that besides the single tooth surface tooth profile waviness information, the tooth waviness information in the gear can be continuously obtained, so that continuous waviness information of the whole gear is obtained.
Description
Technical Field
The invention relates to a method for acquiring and analyzing the tooth profile waviness of an involute straight tooth cylindrical gear, and belongs to the technical field of gear transmission.
Background
The gear is used as a key part of transmission, and is widely applied to the fields of high-speed rails, automobiles, precision machine tools and the like due to the characteristics of stable transmission, high efficiency, long service life and the like. The increasing demands on the use of gear drive systems in equipment have led to the development of gears with high accuracy, low vibration, low noise and high reliability.
The vibration and noise of the gear drive are important indicators reflecting the performance of the gear drive, the vibration and noise level of the gear affect the use feeling of the user, and the gear surface morphology affects the vibration and noise level of the gear drive. At present, a great deal of research focuses on the influence of gear tooth surface roughness and tooth form errors on gear transmission noise, and improves the gear transmission noise by improving the gear surface quality and utilizing a tooth surface shaping means. The work of studying its correlation with gear transmission vibrations and noise is less, especially with respect to the tooth surface waviness between macroscopic tooth form deviation and microscopic tooth surface roughness. Therefore, research work is carried out on the tooth surface waviness of the gear, so that the method has important theoretical and practical values, and one of the key problems involved in the research work is effective extraction and analysis of the tooth surface waviness.
The present invention is therefore based on the above-mentioned key technical problems: the method for acquiring the tooth profile waviness of the involute straight tooth cylindrical gear is provided, and the tooth profile waviness information is analyzed.
Disclosure of Invention
The technical scheme adopted by the invention is a method for acquiring and analyzing the tooth profile waviness of the involute straight tooth cylindrical gear, and the method can efficiently and reliably acquire the tooth profile waviness information of the tooth surface of a single gear tooth and the tooth profile waviness information of a continuous gear tooth based on the measurement result of a gear measurement center and acquire the order information of the tooth profile waviness information of the single gear tooth. The method specifically comprises the following steps:
and measuring tooth profile information of tooth surfaces of all the gear teeth, wherein three tooth profiles are selected at the same position of the tooth surfaces of all the gear teeth for measurement, and the measuring equipment is a gear measuring center.
(1) Acquisition of single tooth flank profile waviness
And carrying out analysis by adopting the measured three tooth profile information, wherein the measurement result comprises three parts of surface roughness, waviness and shape error, and the tooth profile waviness information can be obtained by carrying out filtering treatment on the tooth profile information.
The direct measurement result of the gear measurement center is that the rotation angle of the gear during measurement is taken as an abscissa, namely an angular value, the measurement result is subjected to coordinate transformation, and a transformation formula is shown as formula 1.
l: involute length value R b : base circle radius θ: gear wheelCorner angle
The measurement result of the tooth profile is converted into an abscissa from the involute length value through coordinate transformation.
Then, the waviness of the single tooth surface is extracted, and the filter method is used for meeting the condition that the cut-off wavelength is longer than the sampling length, wherein the first condition is: when the unfolding length of the involute of the actually collected tooth profile of the single tooth surface is larger than the sampling length, a filter method is directly used for filtering the shape error in the tooth profile information. And a second case: when the unfolding length of the involute of the actually collected tooth profile of the single tooth surface is smaller than the sampling length, a polynomial fitting method can be adopted to filter out the shape errors.
In this case, the shape error is filtered out directly by using a gaussian filter.
In the second case, since the tooth profile shape error is usually a simple curve, the tooth profile shape error is removed by using a nonlinear fitting of a least square method.
Gaussian filtering is currently the most commonly used method of filtering roughness and has evolved to a relatively sophisticated degree, so that the surface roughness is then filtered using a gaussian filter. The surface roughness is a high-frequency component in the acquired signal, and the surface roughness component in the acquired signal can be removed by adopting a Gaussian filter to carry out low-pass filtering.
(2) Gear tooth profile waviness continuity
Gear transmission is a continuous process, gear transmission noise is generated as a continuous signal, and single tooth flank information is independent data, so that the tooth flank information of each tooth of the gear needs to be continuous.
According to the generating principle, tooth profile information of the corresponding position of the single tooth surface of the whole gear is sequentially continuous, and in the continuous process, a value with high amplitude is selected as extracted information for the part where the abscissa of the tooth surface information is coincident, so that 360-degree continuous complete tooth surface information of the gear can be obtained.
The continuous tooth surface information can be directly filtered, and the shape error and the surface roughness are removed by using a Gaussian filter, so that the waviness of the tooth profile of the continuous tooth surface of the whole gear can be obtained.
(3) Order analysis
And performing order analysis on the filtered data, wherein the relation between the order and the frequency conversion is shown in the formula 2.
Wherein the frequency unit is Hz, and the rotating speed unit is r/min.
Sequentially performing Fourier transformation on the obtained single tooth surface tooth profile waviness and continuous tooth surface tooth profile waviness information to obtain corresponding tooth profile waviness order information, and performing statistical analysis on the first three orders of the order information with high amplitude.
Compared with the prior art, the method has the technical advantages that besides the single tooth surface tooth profile waviness information, the tooth waviness information in the gear can be continuously obtained, so that the continuous waviness information of the whole gear is obtained.
Drawings
The invention is described in more detail below on the basis of the accompanying drawings, which show exemplary embodiments. In the example drawings:
FIG. 1 shows a single-tooth flank profile measurement position;
FIG. 2 shows a tooth flank profile information continuity principle; a) Before the tooth profile information is continuous; b) After the tooth profile information is continuous;
FIG. 3 shows a gear profile waviness extraction process; a) filtering out shape errors, b) waviness and surface roughness, c) filtering out surface roughness, d) waviness.
FIG. 4 shows the results of gear tooth profile waviness order analysis; a) Single tooth profile ripple degree order information; b) Successive profile waviness order information.
Detailed Description
The single tooth surface tooth profile information of the gear is measured, a gram Lin Beige P26 gear measuring center is selected, a proper ruby measuring head is selected, and the measurement is carried out according to a measuring path shown in figure 1 (3 bars).
Three sets of measurement data are obtained after measurement, coordinate transformation is carried out according to the formula (1), and the abscissa value is transformed from a rotation angle to an involute length value.
In this case, the shape error is filtered out directly by using a gaussian filter.
And under the second condition, polynomial fitting is carried out through a least square method, and the fitted polynomial is adopted for filtering, so that the shape error in the acquired signal is removed.
The method comprises the following steps: the original data has n data points corresponding to the coordinates P i (x i ,y i ) I=1, 2, …, n. Setting the objective function type as a low order polynomial as shown in formula (3):
f(x)＝ax 2 +bx+c#(3)
wherein a, b and c are constants.
Constructing an evaluation function by using a least square method, as shown in formula (4):
and obtaining a, b and c which minimize the evaluation function value, and obtaining a fitted polynomial. And filtering by adopting a fitted polynomial, so that the shape error in the acquired signal can be removed.
And carrying out Gaussian filtering on the measurement data from which the shape errors are removed, and removing high-frequency roughness components.
The method comprises the following steps: the acquired tooth surface profile information function is P (x), wherein the high-frequency signal is h (x), and the low-frequency signal is l (x), and then:
P(x)＝h(x)+l(x)#(5)
the roughness is removed by Gaussian filtering, and the Gaussian distribution expression is:
where μ is the mean and σ is the standard deviation.
The weighting function of the gaussian filter is:
fourier transforming (5) to obtain:
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 convolving the tooth surface profile information function with the Gaussian weight function as follows:
and filtering the surface roughness information through low-pass filtering to obtain the waviness information of the tooth surface.
And measuring the tooth surface information of each tooth surface in sequence, and adopting a generating principle to sequentially and continuously obtain continuous complete tooth surface information by adopting the tooth profile information of the corresponding position of the single tooth surface, wherein the continuous principle is shown in figure 2, and the larger value of the ordinate is reserved in the overlapped part of the abscissa of figure 2 a) to obtain figure 2 b). And directly filtering the continuous information, and removing shape errors and surface roughness by using a Gaussian filter to obtain the waviness of the tooth profile of the whole gear tooth surface. The actual measurement information is extracted and analyzed for the waviness of the tooth profile, and the process is shown in fig. 3.
The waviness information of the tooth profile of the tooth surface is subjected to fourier transformation to obtain waviness order information, and the analysis result is shown in fig. 4 by taking the information of one position of the tooth surface as an example.
Claims (1)
1. The method for acquiring and analyzing the tooth profile waviness of the involute straight tooth cylindrical gear is characterized by comprising the following steps of: in particular comprising the steps of the method,
(1) Obtaining the tooth profile waviness of a tooth surface of a single gear tooth;
carrying out analysis by adopting the measured three tooth profile information, wherein the measurement result comprises three parts of surface roughness, waviness and shape error, and the tooth profile waviness information can be obtained by carrying out filtering treatment on the tooth profile information;
the direct measurement result of the gear measurement center is that the rotation angle of the gear during measurement is taken as an abscissa, namely an angular value, the measurement result is subjected to coordinate transformation, and a transformation formula is 1;
l: involute length value R b : base circle radius θ: a gear rotation angle;
converting the measurement result of the tooth profile into an involute length value as an abscissa through coordinate transformation;
extracting the waviness of a single tooth surface, and using a filter method to meet the condition that the cutoff wavelength is longer than the sampling length, wherein the method comprises the following steps: when the unfolding length of the involute of the actually collected tooth profile of the single tooth surface is larger than the sampling length, a Gaussian filter method is directly used for filtering the shape error in the tooth profile information; and a second case: when the unfolding length of the involute of the actually acquired tooth profile of the single tooth surface is smaller than the sampling length, adopting a least square method nonlinear fitting to filter out shape errors;
filtering the surface roughness by using a Gaussian filter; the surface roughness is a high-frequency component in the acquired signal, and a Gaussian filter is adopted to carry out low-pass filtering, so that the surface roughness component in the acquired signal can be removed;
(2) The gear tooth profile waviness is continuous;
according to the generating principle, tooth profile information of a single tooth surface corresponding position of the whole gear is sequentially continuous, and in the continuous process, a value with high amplitude is selected as extracted information for a part where the abscissa of the tooth profile information coincides, so that 360-degree continuous complete tooth surface information of the gear is obtained;
directly filtering the continuous tooth surface information, and removing shape errors and surface roughness by using a Gaussian filter to obtain the waviness of the tooth profile of the continuous tooth surface of the whole gear;
(3) Performing order analysis;
performing order analysis on the filtered data, wherein the relation between the order and the frequency conversion is shown as a formula 2;
wherein the frequency unit is Hz, and the rotating speed unit is r/min;
sequentially performing Fourier transformation on the obtained single tooth surface tooth profile waviness and continuous tooth surface tooth profile waviness information to obtain corresponding tooth profile waviness order information, and performing statistical analysis on the first three orders of the order information with high amplitude.
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Citations (9)
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|---|---|---|---|---|
| JPH0663819A (en) * | 1992-08-20 | 1994-03-08 | Daihatsu Motor Co Ltd | Gear inspection device |
| JPH0911085A (en) * | 1995-06-27 | 1997-01-14 | Kobe Steel Ltd | Gear error measuring method and correction method, and measuring and correcting device |
| JP2004098191A (en) * | 2002-09-06 | 2004-04-02 | Ntn Corp | Ball screw and method for grinding its screw groove |
| CN102706306A (en) * | 2012-03-01 | 2012-10-03 | 北京工业大学 | Involute gear waviness sample plate |
| CN203964850U (en) * | 2014-07-02 | 2014-11-26 | 成都飞机工业（集团）有限责任公司 | The survey instrument of detection plane jump and percent ripple |
| JP2018185166A (en) * | 2017-04-24 | 2018-11-22 | 本田技研工業株式会社 | Tooth surface waviness evaluation method |
| CN110542389A (en) * | 2018-05-29 | 2019-12-06 | 科令志因伯格有限公司 | Method for analyzing waviness of a surface |
| CN113434817A (en) * | 2021-05-06 | 2021-09-24 | 北京工业大学 | Analysis method of gear single topological error map |
| CN114216677A (en) * | 2021-12-15 | 2022-03-22 | 重庆青山工业有限责任公司 | Tooth surface ripple order detection method |
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2022
- 2022-06-13 CN CN202210660207.6A patent/CN115096239B/en active Active
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|---|---|---|---|---|
| JPH0663819A (en) * | 1992-08-20 | 1994-03-08 | Daihatsu Motor Co Ltd | Gear inspection device |
| JPH0911085A (en) * | 1995-06-27 | 1997-01-14 | Kobe Steel Ltd | Gear error measuring method and correction method, and measuring and correcting device |
| JP2004098191A (en) * | 2002-09-06 | 2004-04-02 | Ntn Corp | Ball screw and method for grinding its screw groove |
| CN102706306A (en) * | 2012-03-01 | 2012-10-03 | 北京工业大学 | Involute gear waviness sample plate |
| CN203964850U (en) * | 2014-07-02 | 2014-11-26 | 成都飞机工业（集团）有限责任公司 | The survey instrument of detection plane jump and percent ripple |
| JP2018185166A (en) * | 2017-04-24 | 2018-11-22 | 本田技研工業株式会社 | Tooth surface waviness evaluation method |
| CN110542389A (en) * | 2018-05-29 | 2019-12-06 | 科令志因伯格有限公司 | Method for analyzing waviness of a surface |
| CN113434817A (en) * | 2021-05-06 | 2021-09-24 | 北京工业大学 | Analysis method of gear single topological error map |
| CN114216677A (en) * | 2021-12-15 | 2022-03-22 | 重庆青山工业有限责任公司 | Tooth surface ripple order detection method |
Non-Patent Citations (1)
| Title |
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| 王泽贵.齿轮表面波纹度阶次噪声机理分析及改进.《传动技术》.2020,第第34卷卷(第第34卷期),全文. * |
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