CN113487180A - Gear tooth surface evaluation method based on cloud platform - Google Patents

Gear tooth surface evaluation method based on cloud platform Download PDF

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CN113487180A
CN113487180A CN202110758977.XA CN202110758977A CN113487180A CN 113487180 A CN113487180 A CN 113487180A CN 202110758977 A CN202110758977 A CN 202110758977A CN 113487180 A CN113487180 A CN 113487180A
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张登攀
李键
岳佳佳
闫勇刚
郑义博
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Henan University of Technology
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Abstract

The invention discloses a gear tooth surface evaluation method based on a cloud platform, which comprises the following specific steps of: a: a user provides gear tooth surface coordinate point cloud data of the gear to be detected to a gear measurement cloud platform through a gear measurement cloud terminal; b: the gear measurement cloud platform calculates tooth surface deviation values corresponding to all tooth surface points to obtain tooth surface deviation point cloud data; c: the gear measurement cloud platform processes the coordinate value data and the tooth surface deviation value of the tooth surface point to obtain tooth surface deviation point cloud data under a tooth surface coordinate system after normalization processing; d: the gear measurement cloud platform uses the first 6 terms of the two-dimensional Legendre polynomial and/or the two-dimensional Chebyshev polynomial as basis functions to fit to obtain a deviation surface equation of the gear to be detected; e: the gear measurement cloud platform detects and evaluates a gear to be detected; f: and the gear measurement cloud platform feeds back a result through the gear measurement cloud terminal. The invention can realize more comprehensive and faster measurement and evaluation of the gear surface.

Description

Gear tooth surface evaluation method based on cloud platform
Technical Field
The invention relates to the field of gear tooth surface measurement, in particular to a gear tooth surface evaluation method based on a cloud platform.
Background
The gear is a standardized typical transmission part and is widely applied to motion transmission, load transmission and precise indexing of machine equipment and instruments. The precision and dynamic characteristics of the gear directly determine the working performance of machine equipment and instruments and meters, and the quality of the gear directly determines the running performance, service life, safety and reliability of equipment.
At present, a plurality of instruments are needed to measure one gear, and the problems of low measurement efficiency, inconsistent measurement precision and the like exist. For example, the existing gear tooth profile deviation measurement is to measure and evaluate an involute tooth profile trace in the whole tooth surface as the tooth profile deviation of the whole tooth surface; the gear pitch deviation measurement is to select a point on each tooth surface of the gear to replace the whole tooth surface and evaluate the uniform distribution condition of the gear teeth. The gear precision evaluation is based on the geometric error of local points on the gear tooth surface, and because the geometric error reflects part of the information of the complex profile of the tooth surface, the gear quality control is not strict, the error characteristics for recognizing the gear are incomplete, and the error sources for analyzing are inaccurate. In order to comprehensively reflect the gear machining quality, a new method is needed for measuring the gear tooth surface precision, and reliable data are provided for gear precision evaluation and gear machining process parameters.
With the development of internet technology in China, cloud platforms which are based on hardware resources and software resource services and provide computing, networking and storage capabilities are increasingly widely applied. The gear tooth surface evaluation based on the cloud platform is used as a product combining a new generation of information technology and a gear measurement technology, and has important significance for improving the gear measurement level of digital, informationized and network big data. If a data interconnection unified technology based on a cloud platform is introduced into the measurement and evaluation system, data in each link of gear measurement and evaluation are collected, processed, analyzed and visually displayed at the cloud end, so that the gear measurement and evaluation technical means can be qualitatively run away.
Disclosure of Invention
The invention aims to provide a gear tooth surface evaluation method based on a cloud platform, which can realize more comprehensive and faster measurement and evaluation of the gear tooth surface and overcome the defects of low measurement efficiency, inconsistent measurement precision and the like of the conventional gear.
The invention adopts the following technical scheme:
a gear tooth surface evaluation method based on a cloud platform sequentially comprises the following specific steps:
a: a user provides tooth surface coordinate point cloud data of a gear to be detected to a gear measurement cloud platform through a gear measurement cloud terminal, wherein the tooth surface coordinate point cloud data comprises coordinate data of a plurality of tooth surface points on the gear to be detected, and the coordinate data of each tooth surface point comprises a three-dimensional coordinate value of the tooth surface point;
the gear measurement cloud terminal is a local client used by a user, is used for realizing data interaction with the gear measurement cloud platform, and provides gear tooth surface evaluation service and gear tooth surface evaluation result display service for the user; the gear measurement cloud platform is a cloud server side and is used for calculating and evaluating a gear to be detected provided by a user through a gear measurement cloud terminal and feeding an evaluation result back to the gear measurement cloud terminal;
b: for the coordinate value data of each tooth surface point in the tooth surface coordinate point cloud data, the gear measurement cloud platform respectively calculates the tooth surface deviation value corresponding to each tooth surface point through the following formula, and then combines the tooth surface deviation values corresponding to all the tooth surface points in the tooth surface coordinate point cloud data to form tooth surface deviation point cloud data;
Figure BDA0003148498570000021
wherein d islotRepresenting the corresponding tooth surface deviation value of the tooth surface point, the lower corner mark lot represents the direction according to the plumb line, K represents a constant coefficient, rho represents the polar diameter, etabRepresenting the half angle of the basic space width, beta representing the pitch angle, rbDenotes the base radius, X denotes the displacement coefficient, alphanIndicating the normal pressure angle of the gear, Z indicating the number of teeth, the internal gear of the number of teeth being negative, the external gear being positive, inv indicating involuteLine function, αtRepresenting the pressure angle of the end face of the gear, and x, y and z respectively representing coordinates of a tooth face point on an x axis, a y axis and a z axis under a three-dimensional Cartesian coordinate system;
c: the gear measurement cloud platform carries out coordinate conversion processing on coordinate value data and a tooth surface deviation value of each tooth surface point in the tooth surface coordinate point cloud data, and carries out normalization processing after the coordinate value data and the tooth surface deviation value are converted from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, so that tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing are finally obtained;
d: the gear measurement cloud platform uses the first 6 terms of the two-dimensional Legendre polynomial and/or the two-dimensional Chebyshev polynomial as basis functions, and obtains a deviation surface equation of the gear to be detected by fitting the tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing through a least square method;
the deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Chebyshev polynomial as the basis function, is as follows:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
coefficient of equation AC0、AC1、AC2、AC3、AC4And AC5Respectively used for evaluating tooth pitch deviation, tooth profile slope, helix slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortioncThe deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected is obtained;
the deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Legendre polynomial as the basis function, is as follows:
Figure BDA0003148498570000031
coefficient AL0、AL1、AL2、AL3、AL4And AL5For evaluating pitch deviation,Tooth profile slope, helix slope, tooth profile convexity, tooth crown and tooth surface twist; calculated dLThe deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected is obtained;
e: the gear measurement cloud terminal transmits the coordinates of any one tooth surface point (u, v) or the coordinates of any one tooth surface line u ═ a on the gear to be evaluated, which are input by a user, to a gear measurement cloud platform, and the gear measurement cloud platform firstly carries out coordinate conversion processing and normalization processing on the coordinates of the tooth surface point or the tooth surface line, which are input by the user, into corresponding (u ', v ') or u ' according to the method in the step C; secondly, calculating a deviation value D of the position corresponding to the tooth surface point or the tooth surface line by using the coordinate data after the coordinate conversion and the deviation surface equation of the gear to be detected obtained in the step D; the gear measurement cloud platform also obtains the pitch deviation, the tooth profile slope, the spiral line slope, the tooth profile convexity, the gear tooth bulging degree and the tooth surface distortion of the gear to be evaluated according to the coefficient in the deviation surface equation of the gear to be evaluated, and then the gear measurement cloud platform carries out qualified or unqualified evaluation on the gear to be evaluated by combining the gear precision parameters selected by a user and the gear measurement evaluation standard;
f: and the gear measurement cloud platform transmits the calculated pitch deviation, tooth profile slope, spiral slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortion of the gear to be evaluated, and the deviation value d and the evaluation result of the position corresponding to the tooth surface point or the tooth surface line input by the user to the gear measurement cloud terminal and feeds back the result to the user.
In the step C:
when the coordinate conversion processing is carried out, the gear measurement cloud platform firstly converts coordinate value data and a tooth surface deviation value of each tooth surface point in tooth surface coordinate point cloud data from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, and then carries out normalization processing on coordinate values (u, v, d) of the tooth surface point in the u-v-d tooth surface coordinate system to obtain coordinate values (u ', v', d), wherein the value range of a plane u 'v' is in [ -1,1 ];
the coordinate transformation formula is as follows:
Figure BDA0003148498570000041
Figure BDA0003148498570000042
d＝dlot；
wherein u represents a coordinate value in the tooth profile direction, phimRepresenting polar angle, ΛnomIndicating the starting angle of the involute, rbRepresenting base radius, xinomRepresenting tooth profile roll angle, thetakRepresenting the spread angle, v representing a coordinate value in the tooth width direction, Z representing the number of teeth, beta representing the pitch angle, d representing a coordinate value in a direction perpendicular to the uv plane, dlotRepresenting the corresponding tooth surface deviation value of the tooth surface point; involute initial angle LambdanomAnd tooth profile roll angle xinomAre all basic parameters of the gear to be detected.
In the step C:
when normalization processing is performed, any point (u, v, d) in the tooth surface coordinate system is converted into (u ', v', d) in the following way, and finally converted into coordinate values (u ', v', d) of the tooth surface point on the [ -1,1] < 1,1] rectangular area;
Figure BDA0003148498570000043
Figure BDA0003148498570000044
d＝dlot；
wherein L isαDenotes the value range of u, LβAnd represents the value range of v.
In the step D:
when a two-dimensional Chebyshev polynomial is independently adopted as a basis function to calculate a deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data;
establishing an equation set by using a least square method, and solving a deviation surface equation d from the equation setC：
Figure BDA0003148498570000051
And solving a deviation surface equation defined under a u '-v' -d tooth surface coordinate system by a two-dimensional Chebyshev polynomial, wherein the deviation surface equation comprises the following components:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
pitch deviation equal to AC0The slope of the tooth profile is equal to 2AC1The slope of the helix being equal to-2AC2Convexity of tooth profile equal to 2AC3The gear tooth drum degree is equal to-4AC4Tooth flank twist equal to-2AC5Calculated deviation value dcNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
In the step D:
when a two-dimensional Legendre polynomial is independently adopted as a basis function to calculate a deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data;
establishing an equation set by using a least square method, and solving a deviation surface equation d from the equation setL：
Figure BDA0003148498570000052
D is solved by a two-dimensional Legendre polynomialLThe surface equation of the deviation defined under the u '-v' -d tooth surface coordinate system is as follows:
Figure BDA0003148498570000053
pitch deviation equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Convexity of tooth profile equal to 1.5AL3Gear tooth drum degree equal to 2AL4Tooth flank twist equal to 1.5AL5(ii) a Calculated deviation value dLNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
In the step D:
respectively adopting a two-dimensional Legendre polynomial and a two-dimensional Chebyshev polynomial as basis functions to obtain corresponding deviation surface equations, and then selecting coefficients of the corresponding deviation surface equations according to evaluation requirements on different types of tooth surface deviations to obtain more accurate different types of tooth surface deviation evaluation results;
setting s tooth surface deviation point data in the tooth surface deviation point cloud data;
the deviation surface equations obtained by using the two-dimensional Chebyshev polynomial as the basis function are respectively as follows:
dC＝AC0*1+AC1*u'+AC2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
the deviation surface equation obtained by using the two-dimensional Chellenged polynomial as the basis function is as follows:
Figure BDA0003148498570000061
when the convexity and the distortion of the tooth surface of the tooth profile need to be accurately evaluated, a deviation surface equation d is fitted by utilizing a two-dimensional Chebyshev polynomialcThe coefficients of the fourth term and the sixth term are solved, and the convexity of the tooth profile is equal to 2AC3Tooth flank twist equal to-2AC5(ii) a When tooth pitch deviation, tooth profile slope, spiral line slope and gear tooth drum degree need to be accurately evaluated, a deviation curved surface equation d is fitted by utilizing a two-dimensional Legendre polynomialLThe coefficients of the first term, the second term, the third term and the fifth term are solved, and the tooth pitch deviation is equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Gear tooth drum degree equal to 2AL4；
Selecting a deviation surface equation d fitting by a two-dimensional Chebyshev polynomial when more accurate fitting surface peak value and detail are requiredcThe curve is used as a final deviation curve equation of the gear to be detected; selecting a deviation surface equation d fitting by a two-dimensional Legendre polynomial when the overall trend and the outline of the fitting surface need to be more accurateLAnd the curve equation is used as the final deviation curve equation of the gear to be detected.
The gear precision parameters adopt 6-level precision gear parameters.
The invention adopts the following technical scheme: firstly, gear surface coordinate point cloud data of a gear to be detected are provided for a gear measurement cloud platform through a gear measurement cloud terminal, and a deviation curved surface equation is respectively fitted to tooth surface deviation point clouds obtained through calculation of the tooth surface coordinate point cloud data by using a two-dimensional Legendre polynomial and a two-dimensional Chebyshev polynomial. Then, each item coefficient of the fitted deviation surface equation can evaluate the tooth pitch, the tooth profile slope, the spiral line slope, the tooth profile convexity, the gear tooth bulging degree, the tooth surface distortion and the like. And combining the fitted deviation surface equation under the u '-v' -d tooth surface coordinate system to obtain the deviation of any point line of the tooth surface. And finally, performing visual expression on the evaluation indexes and the data generated by the algorithm on the cloud platform through a front-end interface.
Compared with the traditional two-dimensional detection which is calculated by a few points, the method can evaluate the whole tooth surface deviation more comprehensively and more accurately by using the tooth surface coordinate point cloud data which comprises a plurality of points. In addition, the two fitting methods are used for complementation to realize tooth surface deviation evaluation, and compared with a single fitting method, the tooth surface deviation evaluation is more accurate and objective. And the method can more quickly realize the resource sharing of the measurement and evaluation result based on the cloud platform, thereby providing data support for the follow-up guidance production.
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FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
The invention is described in detail below with reference to the following figures and examples:
as shown in fig. 1, the gear tooth surface evaluation method based on the cloud platform sequentially comprises the following specific steps:
a: a user provides tooth surface coordinate point cloud data of a gear to be detected to a gear measurement cloud platform through a gear measurement cloud terminal, wherein the tooth surface coordinate point cloud data comprises coordinate data of a plurality of tooth surface points on the gear to be detected, and the coordinate data of each tooth surface point comprises a three-dimensional coordinate value of the tooth surface point;
the gear measurement cloud terminal is a local client used by a user, is used for realizing data interaction with the gear measurement cloud platform, and provides gear tooth surface evaluation service and gear tooth surface evaluation result display service for the user;
the gear measurement cloud platform is a cloud server side, and is used for calculating and evaluating a gear to be detected provided by a user through the gear measurement cloud terminal, and feeding back an evaluation result to the gear measurement cloud terminal.
In the invention, the gear measurement cloud terminal and the gear measurement cloud platform are similar to the construction principle and the information interaction principle of a local client and a server on the cloud in the existing numerous software programs, only the functions are different, and the details are not repeated.
In the invention, a tooth surface point of a gear to be detected is a point on the tooth surface of the gear to be detected, the coordinate of the tooth surface point under a three-dimensional Cartesian coordinate system is (x, y, z), and tooth surface coordinate point cloud data is a data group consisting of coordinate value data of a plurality of tooth surface points on the tooth surface of the gear to be detected;
b: for the coordinate value data of each tooth surface point in the tooth surface coordinate point cloud data, the gear measurement cloud platform respectively calculates the tooth surface deviation value corresponding to each tooth surface point through the following formula, and then combines the tooth surface deviation values corresponding to all the tooth surface points in the tooth surface coordinate point cloud data to form tooth surface deviation point cloud data;
Figure BDA0003148498570000081
wherein d islotIndicating the corresponding tooth flank deviation value of the tooth flank point, the lower corner mark lot indicates the direction according to the plumb line, K indicatesConstant coefficient, p represents the pole diameter, ηbRepresenting the half angle of the basic space width, beta representing the pitch angle, rbDenotes the base radius, X denotes the displacement coefficient, alphanIndicating the normal pressure angle of the gear, Z indicating the number of teeth, the internal gear in the number of teeth being negative, the external gear being positive, inv indicating the involute function, alphatRepresenting the pressure angle of the end face of the gear, and x, y and z respectively representing coordinates of a tooth face point on an x axis, a y axis and a z axis under a three-dimensional Cartesian coordinate system;
in the present invention, the number of teeth Z, the displacement coefficient X, the helix angle beta, and the normal pressure angle alpha are setnEnd face pressure angle αtAnd base radius rbThe gear parameter values are all basic parameters of the gear to be detected and can be obtained by inquiring the factory specifications of the gear to be detected.
C: the gear measurement cloud platform carries out coordinate conversion processing on coordinate value data and a tooth surface deviation value of each tooth surface point in the tooth surface coordinate point cloud data, and carries out normalization processing after the coordinate value data and the tooth surface deviation value are converted from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, so that tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing are finally obtained;
when the coordinate conversion processing is carried out, the gear measurement cloud platform firstly converts coordinate value data and a tooth surface deviation value of each tooth surface point in tooth surface coordinate point cloud data from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, and then carries out normalization processing on coordinate values (u, v, d) of the tooth surface point in the u-v-d tooth surface coordinate system to obtain coordinate values (u ', v', d), wherein the value range of a plane u 'v' is in [ -1,1 ];
the coordinate transformation formula is as follows:
Figure BDA0003148498570000082
Figure BDA0003148498570000083
d＝dlot；
wherein u represents an edgeCoordinate value of tooth profile direction, phimRepresenting polar angle, ΛnomIndicating the starting angle of the involute, rbRepresenting base radius, xinomRepresenting tooth profile roll angle, thetakRepresenting the spread angle, v representing a coordinate value in the tooth width direction, Z representing the number of teeth, beta representing the pitch angle, d representing a coordinate value in a direction perpendicular to the uv plane, dlotRepresenting the corresponding tooth surface deviation value of the tooth surface point; involute initial angle LambdanomAnd tooth profile roll angle xinomThe gear parameter values are all basic parameters of the gear to be detected and can be obtained by inquiring the factory specifications of the gear to be detected.
The three-dimensional coordinates (x, y, z) of the tooth surface point and the tooth surface deviation value d can not be simultaneously expressed under the three-dimensional Cartesian coordinate systemlotThe four parameters need to be converted into a u-v-d tooth surface coordinate system to achieve the using condition of polynomial fitting, and then the four parameters are used for performing least square surface fitting on the tooth surface deviation point cloud data by taking the first 6 terms of the two-dimensional legendre polynomial and/or the two-dimensional chebyshev polynomial as basis functions.
After the conversion of the coordinate value data and the tooth flank deviation value of the tooth flank point from the three-dimensional Cartesian coordinate system to the u-v-d tooth flank coordinate system is completed, the coordinate value (u, v) is at [0, L ]α]*[0,Lβ]And the two-dimensional legendre polynomial and/or the two-dimensional chebyshev polynomial are defined as [ -1,1]*[-1,1]The polynomial in the rectangular region is required to normalize the coordinate values (u, v) of the tooth surface point in the tooth surface coordinate system to obtain coordinate values (u ', v'), where the value range of (u ', v') is [ -1,1 [ ]]*[-1,1]Internal;
in the normalization process, any point (u, v, d) in the tooth surface coordinate system is converted into (u ', v', d) as follows, and finally into coordinate values (u ', v', d) of the tooth surface point on the [ -1,1] rectangular region.
Figure BDA0003148498570000091
Figure BDA0003148498570000092
d＝dlot；
Wherein L isαDenotes the value range of u, LβRepresenting the value range of v;
d: the gear measurement cloud platform uses the first 6 terms of the two-dimensional Legendre polynomial and/or the two-dimensional Chebyshev polynomial as basis functions, and obtains a deviation surface equation of the gear to be detected by fitting the tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing through a least square method;
the deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Chebyshev polynomial as the basis function, is as follows:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
the first term of the two-dimensional Chebyshev polynomial is C0(u ', v') -1, with equation coefficients aC0Can represent the pitch deviation, the second term being C1(u ', v ') -u ', coefficient of equation aC1Can represent the slope of the tooth profile, and the third term is C2(u ', v ') -v ', its equation coefficient aC2Can be expressed in terms of the slope of the helix, with the fourth term being C3(u′，v′)＝2u′2-1, the coefficients of equation AC3Can express the convexity of the tooth profile, and the fifth term is C4(u ', v') -u 'v', coefficient of equation aC4Can express the gear tooth drum degree, and the sixth term is C5(u′，v′)＝2v′2-1, the coefficients of equation AC5The tooth surface can be twisted; i.e. coefficient aC0、AC1、AC2、AC3、AC4And AC5Can be respectively used for evaluating tooth pitch deviation, tooth profile slope, helix slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortioncNamely the deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected.
C above0(u′And v') is 1, which is a standard expression of a polynomial in the field of mathematics, meaning that the value of the first term of the polynomial is 1, and subsequent expressions all have the same meaning as the expression, and are not repeated herein.
The deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Legendre polynomial as the basis function, is as follows:
Figure BDA0003148498570000101
the first term of the two-dimensional Legendre polynomial is L0(u ', v') -1, with equation coefficients aL0Can represent the pitch deviation, the second term being L1(u ', v ') -u ', coefficient of equation aL1Can represent the slope of the tooth profile, and the third term is L2(u ', v ') -v ', its equation coefficient aL2Can be expressed in terms of the slope of the helix, the fourth term being
Figure BDA0003148498570000102
Coefficient of equation AL3Can express the convexity of the tooth profile, and the fifth term is L4(u ', v') -u 'v', coefficient of equation aL4Can represent the gear tooth drum degree, and the sixth term is
Figure BDA0003148498570000103
Coefficient of equation AL5Can represent tooth surface distortion; i.e. coefficient aL0、AL1、AL2、AL3、AL4And AL5Can be used for evaluating tooth pitch deviation, tooth profile slope, helix slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortion respectively; calculated dLNamely the deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected.
L above0(u ', v') -1 is a standard expression of a polynomial in the field of mathematics, meaning that the value of the first term of the polynomial is 1, and the subsequent expressions all have the same meaning as the expression, and are not repeated herein.
In the present invention, it is considered that the tooth surface can be equivalent to the tooth surface coordinateThe underlying rectangular surface, the two-dimensional Legendre polynomial and the two-dimensional Chebyshev polynomial are themselves defined as [ -1,1]*[-1,1]The polynomial over the rectangular area approaches the tooth surface deviation equation in a two-dimensional legendre polynomial or a two-dimensional chebyshev polynomial. Since the tooth surface deviation point cloud data is calculated in the approaching process, compared with the evaluation of a single tooth surface point or tooth surface line, the involved tooth surface data is more comprehensive, and the tooth surface deviation can be more accurately characterized. Meanwhile, the first six terms of the two-dimensional Legendre polynomial and the two-dimensional Chebyshev polynomial have similar characteristics with the tooth surface deviation, and the orthogonal characteristic among the terms of the polynomial enables the coefficients to be independent from each other without crosstalk, so that the interference caused by accidental factors can be eliminated. Therefore, in the invention, the first 6 terms of the two-dimensional Legendre polynomial and/or the two-dimensional Chebyshev polynomial are/is selected as a basis function, the least square surface fitting is carried out on the tooth surface deviation point cloud data, and the tooth pitch deviation, the tooth profile slope, the spiral line slope, the tooth profile convexity, the gear tooth bulging degree and the tooth surface distortion are evaluated through the coefficients of the first six terms of the fitting surface; simultaneously obtaining the equation d of the deviation curved surfacecAnd dLAnd then the deviation value d of any tooth surface point or tooth surface line on the tooth surface of the gear to be detected can be obtained.
In the invention:
1. the two-dimensional Chebyshev polynomial can be directly and independently adopted to fit a deviation curved surface equation dcAnd using the equation d of the deviation surfacecCoefficient A of each item inC0、AC1、AC2、AC3、AC4And AC5To evaluate tooth pitch deviation, tooth profile slope, helix slope, tooth profile crown, tooth flank crowning and tooth flank twist.
2. The two-dimensional Legendre polynomial can be directly and independently adopted to fit a deviation curved surface equation dLAnd using the equation d of the deviation surfaceLCoefficient A of each item inL0、AL1、AL2、AL3、AL4And AL5To evaluate tooth pitch deviation, tooth profile slope, helix slope, tooth profile crown, tooth flank crowning and tooth flank twist.
3. Because the two-dimensional Chebyshev polynomial is expressing the deviation surfaceMore excellent in peak value and detail, i.e. coefficient AC3And AC5Coefficient of ratio AL3And AL5The convexity and the distortion of the tooth surface of the tooth profile can be more accurately evaluated; while the two-dimensional Legendre polynomial is superior in expressing the overall trend and contour of the curved surface, namely AL0、AL1、AL2And AL4Ratio AC0、AC1、AC2And AC4The pitch deviation, the tooth profile slope, the helix slope and the gear tooth bulging can be more accurately evaluated. Therefore, when the tooth profile convexity and the tooth surface distortion need to be accurately evaluated, a deviation surface equation d is fitted by utilizing a two-dimensional Chebyshev polynomialcThe accuracy is higher; and when the tooth pitch deviation, the tooth profile slope, the spiral line slope and the gear tooth bulging degree need to be accurately evaluated, fitting a deviation curved surface equation d by using a two-dimensional Legendre polynomiallIs more accurate.
Therefore, according to the evaluation requirements of different types of tooth surface deviations (tooth pitch deviation, tooth profile slope, spiral slope, tooth profile convexity, gear tooth bulging and tooth surface distortion), a two-dimensional Legendre polynomial and/or a two-dimensional Chebyshev polynomial are used for fitting a deviation surface equation, and a deviation surface equation d fitted by the two-dimensional Chebyshev polynomial is selected when more accurate fitting surface peak value and detail are requiredcThe curve is used as a deviation curve equation of the gear to be detected; selecting a deviation surface equation d fitting by a two-dimensional Legendre polynomial when the overall trend and the outline of the fitting surface need to be more accurateLThe curve is used as a deviation curve equation of the gear to be detected; and corresponding coefficients are selected for obtaining more accurate tooth surface deviation evaluation results of different types.
Example 1
When the two-dimensional Chebyshev polynomial is independently adopted as the basis function to calculate the deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data, and when the deviation curved surface equation is solved by the least square method, the deviation curved surface equation is corrected for s times, namely the optimal approximate curved surface after s times of correction is obtained.
The following equation is a set of equations created using the least squares method, from whichSolving the equation d of the deviation curved surfaceC：
Figure BDA0003148498570000121
And solving a deviation surface equation defined under a u '-v' -d tooth surface coordinate system by a two-dimensional Chebyshev polynomial, wherein the deviation surface equation comprises the following components:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
the specific proportional relation between the deviation term and the coefficient is as follows: pitch deviation equal to AC0The slope of the tooth profile is equal to 2AC1The slope of the helix being equal to-2AC2Convexity of tooth profile equal to 2AC3The gear tooth drum degree is equal to-4AC4Tooth flank twist equal to-2AC5Calculated deviation value dcNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
Example 2
When the two-dimensional Legendre polynomial is independently used as a basis function to calculate the deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data, and when the deviation curved surface equation is solved by the least square method, the deviation curved surface equation is corrected for s times, namely the optimal approximate curved surface after s times of correction is obtained.
The following equation is a set of equations established by the least square method, and the equation d of the deviation surface is solved from the set of equationsL：
Figure BDA0003148498570000131
D is solved by a two-dimensional Legendre polynomialLThe surface equation of the deviation defined under the u '-v' -d tooth surface coordinate system is as follows:
Figure BDA0003148498570000132
the specific proportional relationship between the deviation term and the coefficient is as follows: pitch deviation equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Convexity of tooth profile equal to 1.5AL3Gear tooth drum degree equal to 2AL4Tooth flank twist equal to 1.5AL5(ii) a Calculated deviation value dLNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
Example 3
And then selecting coefficients of the corresponding deviation surface equations according to the evaluation requirements for different types of tooth surface deviations to obtain more accurate different types of tooth surface deviation evaluation results.
And setting s tooth surface deviation point data in the tooth surface deviation point cloud data, and when solving the deviation surface equation by using the least square method, the deviation surface equation is corrected for s times, namely the optimal approximate surface after s times of correction is obtained.
The deviation surface equations obtained by using the two-dimensional Chebyshev polynomial as the basis function are respectively as follows:
dC＝AC0*1+AC1*u'+AC2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
the deviation surface equation obtained by using the two-dimensional Chellenged polynomial as the basis function is as follows:
Figure BDA0003148498570000133
when the convexity and the distortion of the tooth surface of the tooth profile need to be accurately evaluated, a deviation surface equation d is fitted by utilizing a two-dimensional Chebyshev polynomialcThe coefficients of the fourth term and the sixth term are solved, and the convexity of the tooth profile is equal to 2AC3Tooth flank twist equal to-2AC5(ii) a Accurately evaluating tooth pitch deviation, tooth profile slope and spiral lineAnd (3) during the slope and the gear tooth bulging degree, fitting a deviation curved surface equation d by using a two-dimensional Legendre polynomialLThe coefficients of the first term, the second term, the third term and the fifth term are solved, and the tooth pitch deviation is equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Gear tooth drum degree equal to 2AL4。
Selecting a deviation surface equation d fitting by a two-dimensional Chebyshev polynomial when more accurate fitting surface peak value and detail are requiredcThe curve is used as a final deviation curve equation of the gear to be detected; selecting a deviation surface equation d fitting by a two-dimensional Legendre polynomial when the overall trend and the outline of the fitting surface need to be more accurateLAnd the curve equation is used as the final deviation curve equation of the gear to be detected.
E: the gear measurement cloud terminal transmits the coordinates of any one tooth surface point (u, v) or the coordinates of any one tooth surface line u ═ a on the gear to be evaluated, which are input by a user, to a gear measurement cloud platform, and the gear measurement cloud platform firstly carries out coordinate conversion processing and normalization processing on the coordinates of the tooth surface point or the tooth surface line, which are input by the user, into corresponding (u ', v ') or u ' according to the method in the step C; secondly, calculating a deviation value D of the position corresponding to the tooth surface point or the tooth surface line by using the coordinate data after the coordinate conversion and the deviation surface equation of the gear to be detected obtained in the step D; the gear measurement cloud platform also obtains the pitch deviation, the tooth profile slope, the spiral line slope, the tooth profile convexity, the gear tooth bulging degree and the tooth surface distortion of the gear to be evaluated according to the coefficient in the deviation surface equation of the gear to be evaluated, and then the gear measurement cloud platform carries out qualified or unqualified evaluation on the gear to be evaluated by combining the gear precision parameters selected by a user and the gear measurement evaluation standard;
the gear precision parameters are the existing gear evaluation precision standards selected by users, in the existing gear evaluation, the gear precision grades are divided into 13 precision grades from 0 grade to 12 grade, the higher the gear precision grade is, the larger the allowable deviation value is, and the specific deviation values allowed by different precision grades can be known by consulting a mechanical design manual. The gear used in the invention is a 6-grade precision gear, and the calculated deviation value only needs to be compared with the allowable tolerance band of the 6-grade precision gear given in the mechanical design manual, and the deviation value is qualified within the allowable tolerance band.
F: and the gear measurement cloud platform transmits the calculated pitch deviation, tooth profile slope, spiral slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortion of the gear to be evaluated, and the deviation value d and the evaluation result of the position corresponding to the tooth surface point or the tooth surface line input by the user to the gear measurement cloud terminal and feeds back the result to the user.

Claims (7)

1. A gear tooth surface evaluation method based on a cloud platform is characterized by sequentially comprising the following specific steps:
a: a user provides tooth surface coordinate point cloud data of a gear to be detected to a gear measurement cloud platform through a gear measurement cloud terminal, wherein the tooth surface coordinate point cloud data comprises coordinate data of a plurality of tooth surface points on the gear to be detected, and the coordinate data of each tooth surface point comprises a three-dimensional coordinate value of the tooth surface point;
the gear measurement cloud terminal is a local client used by a user, is used for realizing data interaction with the gear measurement cloud platform, and provides gear tooth surface evaluation service and gear tooth surface evaluation result display service for the user; the gear measurement cloud platform is a cloud server side and is used for calculating and evaluating a gear to be detected provided by a user through a gear measurement cloud terminal and feeding an evaluation result back to the gear measurement cloud terminal;
b: for the coordinate value data of each tooth surface point in the tooth surface coordinate point cloud data, the gear measurement cloud platform respectively calculates the tooth surface deviation value corresponding to each tooth surface point through the following formula, and then combines the tooth surface deviation values corresponding to all the tooth surface points in the tooth surface coordinate point cloud data to form tooth surface deviation point cloud data;
Figure FDA0003148498560000011
wherein d islotIndicating the corresponding tooth flank deviation value of the tooth flank point, and the lower corner mark lotFrom the direction of the plumb line, K represents a constant coefficient, ρ represents the pole diameter, ηbRepresenting the half angle of the basic space width, beta representing the pitch angle, rbDenotes the base radius, X denotes the displacement coefficient, alphanIndicating the normal pressure angle of the gear, Z indicating the number of teeth, the internal gear in the number of teeth being negative, the external gear being positive, inv indicating the involute function, alphatRepresenting the pressure angle of the end face of the gear, and x, y and z respectively representing coordinates of a tooth face point on an x axis, a y axis and a z axis under a three-dimensional Cartesian coordinate system;
c: the gear measurement cloud platform carries out coordinate conversion processing on coordinate value data and a tooth surface deviation value of each tooth surface point in the tooth surface coordinate point cloud data, and carries out normalization processing after the coordinate value data and the tooth surface deviation value are converted from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, so that tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing are finally obtained;
d: the gear measurement cloud platform uses the first 6 terms of the two-dimensional Legendre polynomial and/or the two-dimensional Chebyshev polynomial as basis functions, and obtains a deviation surface equation of the gear to be detected by fitting the tooth surface deviation point cloud data under a u '-v' -d tooth surface coordinate system after normalization processing through a least square method;
the deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Chebyshev polynomial as the basis function, is as follows:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
coefficient of equation AC0、AC1、AC2、AC3、AC4And AC5Respectively used for evaluating tooth pitch deviation, tooth profile slope, helix slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortioncThe deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected is obtained;
the deviation surface equation of the gear to be detected, which is obtained by using the first 6 terms of the two-dimensional Legendre polynomial as the basis function, is as follows:
Figure FDA0003148498560000021
coefficient AL0、AL1、AL2、AL3、AL4And AL5Respectively evaluating tooth pitch deviation, tooth profile slope, helix slope, tooth profile convexity, gear tooth bulging and tooth surface distortion; calculated dLThe deviation value d of the corresponding tooth surface point or tooth surface line on the tooth surface of the gear to be detected is obtained;
e: the gear measurement cloud terminal transmits the coordinates of any one tooth surface point (u, v) or the coordinates of any one tooth surface line u ═ a on the gear to be evaluated, which are input by a user, to a gear measurement cloud platform, and the gear measurement cloud platform firstly carries out coordinate conversion processing and normalization processing on the coordinates of the tooth surface point or the tooth surface line, which are input by the user, into corresponding (u ', v ') or u ' according to the method in the step C; secondly, calculating a deviation value D of the position corresponding to the tooth surface point or the tooth surface line by using the coordinate data after the coordinate conversion and the deviation surface equation of the gear to be detected obtained in the step D; the gear measurement cloud platform also obtains the pitch deviation, the tooth profile slope, the spiral line slope, the tooth profile convexity, the gear tooth bulging degree and the tooth surface distortion of the gear to be evaluated according to the coefficient in the deviation surface equation of the gear to be evaluated, and then the gear measurement cloud platform carries out qualified or unqualified evaluation on the gear to be evaluated by combining the gear precision parameters selected by a user and the gear measurement evaluation standard;
f: and the gear measurement cloud platform transmits the calculated pitch deviation, tooth profile slope, spiral slope, tooth profile convexity, gear tooth bulging degree and tooth surface distortion of the gear to be evaluated, and the deviation value d and the evaluation result of the position corresponding to the tooth surface point or the tooth surface line input by the user to the gear measurement cloud terminal and feeds back the result to the user.
2. The cloud platform-based gear tooth surface evaluation method according to claim 1, wherein in the step C:
when the coordinate conversion processing is carried out, the gear measurement cloud platform firstly converts coordinate value data and a tooth surface deviation value of each tooth surface point in tooth surface coordinate point cloud data from a three-dimensional Cartesian coordinate system to a u-v-d tooth surface coordinate system, and then carries out normalization processing on coordinate values (u, v, d) of the tooth surface point in the u-v-d tooth surface coordinate system to obtain coordinate values (u ', v', d), wherein the value range of a plane u 'v' is in [ -1,1 ];
the coordinate transformation formula is as follows:
Figure FDA0003148498560000031
Figure FDA0003148498560000032
d＝dlot；
wherein u represents a coordinate value in the tooth profile direction, phimRepresenting polar angle, ΛnomIndicating the starting angle of the involute, rbRepresenting base radius, xinomRepresenting tooth profile roll angle, thetakRepresenting the spread angle, v representing a coordinate value in the tooth width direction, Z representing the number of teeth, beta representing the pitch angle, d representing a coordinate value in a direction perpendicular to the uv plane, dlotRepresenting the corresponding tooth surface deviation value of the tooth surface point; involute initial angle LambdanomAnd tooth profile roll angle xinomAre all basic parameters of the gear to be detected.
3. The cloud platform-based gear tooth surface evaluation method according to claim 2, wherein in the step C:
when normalization processing is performed, any point (u, v, d) in the tooth surface coordinate system is converted into (u ', v', d) in the following way, and finally converted into coordinate values (u ', v', d) of the tooth surface point on the [ -1,1] < 1,1] rectangular area;
Figure FDA0003148498560000033
Figure FDA0003148498560000034
d＝dlot；
wherein L isαDenotes the value range of u, LβAnd represents the value range of v.
4. The cloud platform-based gear tooth surface evaluation method according to claim 1, wherein in the step D:
when a two-dimensional Chebyshev polynomial is independently adopted as a basis function to calculate a deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data;
establishing an equation set by using a least square method, and solving a deviation surface equation d from the equation setC：
Figure FDA0003148498560000041
And solving a deviation surface equation defined under a u '-v' -d tooth surface coordinate system by a two-dimensional Chebyshev polynomial, wherein the deviation surface equation comprises the following components:
dC＝AC0*1+AC1*u'+Ac2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
pitch deviation equal to AC0The slope of the tooth profile is equal to 2AC1The slope of the helix being equal to-2AC2Convexity of tooth profile equal to 2AC3The gear tooth drum degree is equal to-4AC4Tooth flank twist equal to-2AC5Calculated deviation value dcNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
5. The cloud platform-based gear tooth surface evaluation method according to claim 1, wherein in the step D:
when a two-dimensional Legendre polynomial is independently adopted as a basis function to calculate a deviation curved surface equation of the gear to be detected, s tooth surface deviation point data are set in the tooth surface deviation point cloud data;
establishing an equation set by using a least square method, and solving a deviation surface equation d from the equation setL：
Figure FDA0003148498560000042
D is solved by a two-dimensional Legendre polynomialLThe surface equation of the deviation defined under the u '-v' -d tooth surface coordinate system is as follows:
Figure FDA0003148498560000043
pitch deviation equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Convexity of tooth profile equal to 1.5AL3Gear tooth drum degree equal to 2AL4Tooth flank twist equal to 1.5AL5(ii) a Calculated deviation value dLNamely a deviation value d corresponding to the point (u, v) on the tooth surface of the gear to be detected normalized to (u ', v').
6. The cloud platform-based gear tooth surface evaluation method according to claim 1, wherein in the step D:
respectively adopting a two-dimensional Legendre polynomial and a two-dimensional Chebyshev polynomial as basis functions to obtain corresponding deviation surface equations, and then selecting coefficients of the corresponding deviation surface equations according to evaluation requirements on different types of tooth surface deviations to obtain more accurate different types of tooth surface deviation evaluation results;
setting s tooth surface deviation point data in the tooth surface deviation point cloud data;
the deviation surface equations obtained by using the two-dimensional Chebyshev polynomial as the basis function are respectively as follows:
dC＝AC0*1+AC1*u'+AC2*v'+AC3*(2u'2-1)+AC4*u'v'+AC5*(2v'2-1)；
the deviation surface equation obtained by using the two-dimensional Chellenged polynomial as the basis function is as follows:
Figure FDA0003148498560000051
when the convexity and the distortion of the tooth surface of the tooth profile need to be accurately evaluated, a deviation surface equation d is fitted by utilizing a two-dimensional Chebyshev polynomialcThe coefficients of the fourth term and the sixth term are solved, and the convexity of the tooth profile is equal to 2AC3Tooth flank twist equal to-2AC5(ii) a When tooth pitch deviation, tooth profile slope, spiral line slope and gear tooth drum degree need to be accurately evaluated, a deviation curved surface equation d is fitted by utilizing a two-dimensional Legendre polynomialLThe coefficients of the first term, the second term, the third term and the fifth term are solved, and the tooth pitch deviation is equal to AL0The slope of the tooth profile is equal to AL1The slope of the helix being equal to AL2Gear tooth drum degree equal to 2AL4；
Selecting a deviation surface equation d fitting by a two-dimensional Chebyshev polynomial when more accurate fitting surface peak value and detail are requiredcThe curve is used as a final deviation curve equation of the gear to be detected; selecting a deviation surface equation d fitting by a two-dimensional Legendre polynomial when the overall trend and the outline of the fitting surface need to be more accurateLAnd the curve equation is used as the final deviation curve equation of the gear to be detected.
7. The cloud platform-based gear tooth surface evaluation method according to claim 1, wherein: the gear precision parameters adopt 6-level precision gear parameters.
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