CN-122019940-A - Self-reference measurement positioning method for standard involute gear tooth profile parameters

Abstract

A self-reference measurement positioning method for standard involute gear tooth profile parameters belongs to the field of gear parameter measurement. The realization method comprises the steps of measuring involute gear tooth profiles by using a three-coordinate measuring machine to obtain involute coordinate measuring sequence points, utilizing the measuring curve involute of the gear tooth profile to approximate the shape of a sinusoidal curve in a section applied by the tooth profile, optimizing and determining an optimal demarcation point in a residual error effective value balancing mode during tooth profile characterization, using left and right curve waveforms to respectively perform local sinusoidal curve approximation to characterize the involute, performing regression residual error estimation in a local sinusoidal curve fitting mode, performing approximate parameterization characterization on the involute by using double sinusoidal model parameters, searching a starting point parameter and a termination point parameter of a fitted sinusoidal curve section, obtaining the boundary of the involute section corresponding to the gear tooth profile according to the obtained starting point parameter measuring and the termination point parameter, obtaining a complete tooth profile parameter measuring and characterization result with self-reference characteristics, and realizing self-reference measurement positioning.

Inventors

• LIANG ZHIGUO
• HE XUAN
• WU TENGFEI
• Geng Shuya

Assignees

• 中国航空工业集团公司北京长城计量测试技术研究所

Dates

Publication Date

20260512

Application Date

20251203

Claims (5)

1. 1. A self-reference measurement positioning method for standard involute gear tooth profile parameters is characterized by comprising the following steps: Measuring the tooth profile of the involute gear by using a three-coordinate measuring machine to obtain an involute coordinate measuring sequence point { [ x i ,y i ] } (i=0, 1.,. The n-1), wherein x 0 ,x 1 ,...,x n-1 is the abscissa of a sampling measuring point of the tooth profile of the gear at equal intervals, and y 0 ,y 1 ,...,y n-1 is the ordinate of a sampling measuring coordinate point sequence of the tooth profile of the gear; The method comprises the steps of obtaining a reference point of an involute measuring curve, namely, obtaining a geometric position of the actual measuring curve section in the involute by taking the reference point of the measuring characterization as a reference, and uniquely determining the geometric position of the actual measuring curve section in the involute through the length and the slope of the straight line section between the actual measuring point of the involute and the reference point, namely, realizing sinusoidal model fitting, and obtaining the geometric position of the actual measuring curve section in the involute; And step three, because of the appearance difference between the involute waveform and the sinusoidal waveform, when the involute is fitted by the sinusoidal waveform, the effective value of the fitting residual error can change in an increasing trend along with the increase of the fitted sinusoidal curve sections, dividing the fitted involute waveform sections into a section and a section, searching a boundary point which enables the effective values of the fitting residual errors of the section a section and the section b to be closest to each other, respectively executing the sinusoidal model fitting process of the step two on the waveform sections on the two sides of the boundary point to obtain corresponding fitting parameters, further realizing double sinusoidal involute fitting, and according to the double sinusoidal involute fitting result, combining the step one to determine the geometric relative position of the actually measured involute PQ in the standard involute, thereby realizing the self-reference measurement positioning of the tooth profile parameters of the standard involute.
2. 2. The method of claim 1 wherein the initial phase of the sinusoidal fitted curve of the a-segment curve divided using the optimal demarcation point characterizes the initial point location of the involute.
3. 3. The method of claim 2, wherein the end phase of the sinusoidal fitted curve of the b-piece curve divided using the optimal demarcation point characterizes the end point position of the involute on the basis of claim 1.
4. 4. The method of claim 3, wherein the second implementation method comprises the following steps: the radius of the base circle of the involute is r b , the unfolding angle of the involute generating line BK is theta, and then the parameter equation of the involute is as follows: wherein r b is a base circle radius, θ is an expansion angle of the generating line BK, the point corresponding to θ D = 0;D at the involute starting point D is an involute starting point located on the base circle radius, (x D ,y D ) is a coordinate of the point D, and is characterized as a coordinate point D (x D ,y D ), wherein in the formula (1), x D ＝r b ,y D =0; With the point D (x D ,y D ) as a reference point, the straight line segment length r KD and the slope K KD of any point K (x, y) on the involute and the reference point D (x D ,y D ) are respectively The combination of each point K (x, y) on the involute with the straight line segment length r KD and slope K KD of reference point D (x D ,y D ) is unique and is used to determine the location of point K (x, y) in the involute when reference point D (x D ,y D ) is known; The involute of the circle is an open curve with a starting point and no end point, and the tooth profile contour line used on the gear is only a part of the starting phase in which the abscissa x and the ordinate y change monotonically; When the radius of the base circle is r b and theta is 0 and pi/2, the value range of the abscissa x and the ordinate y is x is r b ,r b ·π/2],y∈[0,r b ; The measurement and characterization of the tooth profile of involute gear is limited to the interval theta epsilon 0 pi/2, and the range of the values of the abscissa x and the ordinate y is x epsilon r b ,r b ·π/2],y∈[0,r b , and the value is obtained by differentiating the formula (1) When theta is E [0, pi/2 ], x is E [ r b ,r b ·π/2],y∈[0,r b ], X (r b , θ) and y (r b , θ) both belong to a monotonically increasing function curve within the interval; Involute shape in the limited interval theta E [0, pi/2 ] approximates to sine curve shape in interval [ pi/2, 0] to contain measuring point geometric position abscissa information The phase value of a measuring point of a fitting sinusoidal curve approximated by an involute is represented, and the rectangular coordinate representation mode of a point on the involute is [ x (r b ,θ),y(r b , theta) ]; Let x 0 ,x 1 ,...,x n-1 be the abscissa of the equally spaced sampling measurement points of the gear profile segment PQ, y 0 ,y 1 ,...,y n-1 be the ordinate of the sampling measurement points of the gear profile, the corresponding involute generating line expansion angle be θ 0 ,θ 1 ,...,θ n-1 , the corresponding fitting sinusoidal phase angle be Then due to the selection and characterization of the measurement reference points, constant coordinate offsets x d and y d exist between the sampled measurement coordinate point [ x i ,y i ] and the involute model theoretical value point [ x (r b ,θ i ),y(r b ,θ i ) ], namely Obtaining amplitude A, digital angular frequency omega, frequency f and initial phase by changing search Several fitting parameters of the direct current component d are used for enabling the effective value rho of the fitting residual error to be minimum Containing information about the abscissa of the geometrical position of the measuring point Is that Δx i ＝x i -x i-1 (i=0,1,...,n-1) (9) Obtaining a fitting sinusoidal curve of the sequence of sampled measurement coordinate points [ x i ,y i ] as On each measurement coordinate point, the ordinate fitting value is Amplitude A, digital angular frequency omega, frequency f, initial phase The direct current component d is used as an approximate fitting parameter of the involute; the method comprises the steps of representing phase values corresponding to measuring points of a fitting sinusoidal curve of an involute waveform for measuring point geometric position abscissa information; Involute measurement starting endpoint P ordinate fitting regression value Involute measuring terminal endpoint Q ordinate fitting regression value Regression residual Fitting residual effective values Fitting phase values corresponding to sinusoidal troughs The angle of the involute corresponding to θ=0, i.e. the coordinates of the intersection point D of the involute with the base circle Has the following components Then, any point K (x, y) on the involute is compared with the reference point Length of straight line segment of (2) And slope of Respectively is Each point K (x, y) on the involute is equal to the reference point Length of straight line segment of (2) And slope of Is unique in combination with at the reference point When known, the standard involute of formula (1) is found to have the same slope value Determining the geometric position of the point K (x, y) in the involute; When the involute is actually measured, the initial point P and the reference point are measured Length of straight line segment of (2) And slope of Involute measuring end point Q and reference point Length of straight line segment of (2) And slope of After all calculation, the standard involute of the formula (1) is searched for a value theoretically having the same slope The position of the point can determine the geometric relative position of the measured involute PQ in the standard involute.
5. 5. The method of claim 4, wherein the third implementation method is as follows: Step 3.1, optimizing a demarcation point q; For equidistant sampling measurement coordinate points (x 0 ,y 0 ),...,(x n-1 ,y n-1 ) of a gear tooth profile line segment PQ, selecting a positive integer sequence number q epsilon [10, n-10], dividing the sampling measurement coordinate point sequence into a part (x 0 ,y 0 ),...,(x q-1 ,y q-1 ) and a part b (x q ,y q ),...,(x n-1 ,y n-1 ), and fitting the waveform of the involute of the part a according to the second step to obtain a fitting parameter A aq 、f aq , D aq 、ρ aq , fitting the involute waveform of the part b according to the second step to obtain fitting parameters A bq 、f bq , d bq 、ρ bq ; Starting to perform piecewise fitting from q=10 to obtain fitting parameters, sequentially increasing q values, performing fitting again, obtaining fitting parameters until q=n-10 is increased, and completing the whole fitting process; The envelope of ρ aq is changed in a monotonic way along with the increase of q value, the envelope of ρ bq is changed in a monotonic way along with the increase of q value, and when the magnitude of ρ aq and ρ bq is closest, the q=q 0 value is taken as the optimal demarcation point of the involute line segment; step 3.2, double sine fitting, and realizing self-reference measurement positioning of standard involute gear tooth profile parameters; Taking the optimal demarcation point q 0 as a boundary, dividing a sampling measurement point into an a part and a b part, respectively performing sine fitting on involute segments on two sides of the demarcation point to obtain an optimal fitting result, and marking as Reference point Fitting the parameter characterization result of the involute as a double sine method, and obtaining a fitting sine curve according to the fitting parameter, wherein Then, the initial point P (x 0 ,y 0 ) and the reference point are measured on the involute Length of straight line segment And slope of Respectively is Measuring end point Q (x n-1 ,y n-1 ) and reference point on involute Length of straight line segment And slope of Respectively is At the position of After the calculation, the standard involute of the formula (1) is searched for the value with the same slope The position of the point is used for determining the geometric relative position of the actually measured involute PQ in the standard involute, thereby realizing the self-reference measurement and positioning of the standard involute gear tooth profile parameters, wherein the reference point is

Description

Self-reference measurement positioning method for standard involute gear tooth profile parameters Technical Field The invention relates to a self-reference measurement positioning method for standard involute gear tooth profile parameters, in particular to a gear tooth profile parameter and a position positioning and quantitative characterization method thereof on a standard involute, belonging to the technical field of gear parameter measurement. Background The standard involute gear is the most widely applied gear in the practical engineering technology, the measurement and characterization of the gear profile parameters are the most important means for evaluating the gear quality, including the tooth profile deviation, the effective involute length, the available involute length and the like, and the gear profile parameters are generally measured by using a special gear measuring center, a universal gear measuring machine, a three-coordinate measuring machine and the like, and the gear profile parameters are characterized by the deviation and distribution between the actual measurement result and the standard involute. Under the condition of polar coordinate measurement and characterization, the current national standard GB/T13924 'involute cylindrical gear precision inspection rule' prescribes that the measurement result takes each tooth form period of a gear as a reference period, the gear axis as a reference shaft, and the rotation angle and the corresponding radius are used for representing tooth profile measurement data points, and each tooth form period corresponds to 0-360 degrees. Under the measurement characterization condition of the three-coordinate measuring machine, the measurement result is completely characterized by a coordinate point mode of each measurement point in a rectangular coordinate system. And then, curve fitting is carried out on the tooth profile measuring points of the gear so as to calculate and acquire regression deviation. The problems still existing at present are: 1) The standard involute equation is an overdetermined equation with complex functional relation, the radius of a base circle and the starting point of an involute are required to be known firstly, and then the corresponding coordinate relation of other contour points on the involute can be determined according to the expansion angle theta of the involute generating line. However, the base circle radius and the involute starting point may not be in the tooth profile measuring points of the gear, and the expansion angle theta of the involute generating line is also unknown, in the involute measuring sequence represented by the normal rectangular coordinates, reference values such as the base circle radius, the involute starting point and the like are lacking, so that the determination of the involute representing reference point of the gear measuring result is problematic, and it is difficult for people to directly find and determine the involute reference point from the tooth profile measuring points and to measure the base circle radius; 2) In actual work, the radius of the base circle is unknown or not known precisely, the actual tooth profile parameter is only a part of the involute, and the initial point of the involute is probably not included due to the reasons of processing technology and the like, so that the difference between the initial point and the standard involute is difficult to determine, therefore, other curves such as arc curves and the like are often used for replacing the involute to perform local tooth profile fitting, and the fitting regression residual error is evaluated, so that the processing quality of the gear is evaluated. 3) The tooth profile curve fitted by using the arc curve faces the problems of complex selection of arc parameters, possibly non-unique result, difficult optimization and the like. Disclosure of Invention The invention provides a self-reference measurement positioning method for involute gear tooth profile parameters, aiming at the problems in measurement and characterization of an involute gear tooth profile, which utilizes involute of a gear tooth profile to approximate to a sinusoidal curve shape in a section applied by the tooth profile, so that when the tooth profile is characterized, a measurement curve section is divided into two sections to be respectively subjected to sinusoidal fitting, an optimal demarcation point is optimized and determined in a balanced mode of residual effective values of the two sections, on the basis, partial sinusoidal curve approximation characterization involute is respectively performed by using left and right sections of curve waveforms, regression residual error estimation is performed in a partial sinusoidal curve fitting mode, parameterization characterization is performed on the involute is performed by using double sinusoidal model parameters, starting point parameters and end point parameters of a fitted sinusoidal sect