CN112506136B - Positioning point set selection method based on statistical analysis of batch blade curved surface measurement data - Google Patents

Positioning point set selection method based on statistical analysis of batch blade curved surface measurement data Download PDF

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CN112506136B
CN112506136B CN202011454209.7A CN202011454209A CN112506136B CN 112506136 B CN112506136 B CN 112506136B CN 202011454209 A CN202011454209 A CN 202011454209A CN 112506136 B CN112506136 B CN 112506136B
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CN112506136A (en
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张云
许志勇
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North China University of Technology
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a positioning point set selection method based on statistical analysis of batch blade curved surface measurement data, which comprises the following steps: uniformly dispersing the CAD model of the blade curved surface according to the specified precision, and taking the obtained dispersed point set as an initial positioning point set P; extracting sample blades from a batch of blade parts, measuring an initial positioning point set P of the sample blades piece by piece, accumulating measurement point data piece by piece and performing statistical analysis to obtain a minimum sample amount n; in the minimum sample size, the variance of the measured data of each point in P is used as an index, and if the measured data is less than a given variance threshold value e1, the measured data is used as a candidate positioning point set Q; in the minimum sample size, the Spearman rank correlation coefficient of the measured data of each adjacent point in the Q is taken as an index, and if the index is larger than a given threshold value e2, the index is taken as an optimal positioning point set T. The participation of manual experience in the traditional positioning point selection mode is avoided, and the accuracy and the reliability of the subsequent curved surface registration positioning are improved.

Description

Positioning point set selection method based on statistical analysis of batch blade curved surface measurement data
Technical Field
The invention relates to a numerical control machining method for complex curved surface parts, in particular to a positioning point set selection method based on batch blade curved surface measurement data statistical analysis.
Background
The blade is a typical complex curved surface part, and the subsequent numerical control machining reference of the part is changed due to the influence of the early-stage process machining precision and the error caused by secondary clamping in the numerical control machining process. If the original reference is directly adopted, the allowance distribution is uneven or even no processing allowance is generated. Therefore, it is necessary to develop the registration positioning of the curved surfaces of the blades. In a commonly used registration method based on a surface point set, data participating in an iterative registration process is called a localization point set. Whether the curved surface registration positioning process is stable or not and whether the final registration result is reliable or not mainly depend on the selection of the positioning point set.
The first prior art is as follows:
leaf cone beam CT point cloud model registration method based on positioning characteristic points, published in aeronautics manufacturing technology by Kun, Job and Yongyun, 2015,470(1/2) 93-96:
the 6-point positioning principle is adopted: according to a 6-point positioning method, namely a 3-2-l positioning method, 3 points are selected on a blade body of a blade, edge extreme points of the blade are respectively taken on two sections of two given z coordinates of the blade, one point is taken on a flange plate, and a coordinate system is established for positioning the whole blade. 6 point positions P1, P2, P3, P4, P5 and P6 are selected from the CAD model. The 6 points correspond to measurement points Q1, Q2, Q3, Q4, Q5, Q6. Thereby performing subsequent registration positioning.
The first prior art has the following defects:
the method has the advantages of few points and simple operation under the condition that the CAD theoretical model is completely consistent with the measured data. However, the blade curve machining always has errors, namely the CAD theoretical model and the measured data are definitely different, and the errors in Q1, Q2, Q3, Q4, Q5 and Q6 cause the positioning result to deviate from the ideal result.
The second prior art is:
model registration control point set selection in turbine blade shape detection disclosed in mechanical engineering journal, Chengyongg, Zhang Dinghua, Bo Kun, et al, 2009,45(011) 240-doped 246:
adopting area uniform point selection: aiming at the problem of inaccurate positioning caused by blade errors, positioning points are selected in a curved surface area prone to errors by using a uniform point selection method. Dispersing the curved surface of the blade into point cloud data, determining that the upper right corner and the left edge area of the blade are curved surface areas with errors according to engineering experience, and reserving the point cloud data in the areas as a positioning point set.
The second prior art has the following defects:
the judgment of the curved surface area with the error is obtained through manual experience, and the positioning point selection principle under the influence of the error cannot be quantitatively given.
At present, the selection of positioning points in the registration process of the curved surface of the blade is mostly based on a CAD theoretical model, but the machining error is inevitable in the machining process of blade parts. The positioning point determined by the theoretical model is only relied on, and the existence of the actual error is not considered, so that the error is introduced in the registration positioning process, and the accuracy of the registration positioning of the curved surface of the blade is reduced. Even large errors can affect the reliability of the registration fix and even the failure of the fix.
Disclosure of Invention
The invention aims to provide a positioning point set selection method based on batch blade curved surface measurement data statistical analysis.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a positioning point set selection method based on statistical analysis of batch blade curved surface measurement data, which comprises the following steps of:
step 1, uniformly dispersing a blade curved surface CAD model according to specified precision, wherein an obtained dispersion point set is an initial positioning point set P;
step 2, extracting sample blades from the batch of blade parts, measuring an initial positioning point set P of the sample blades piece by piece, accumulating measuring point data piece by piece and performing statistical analysis to obtain a minimum sample amount n;
step 3, in the minimum sample size, taking the variance of the measured data of each point in the P as an index, and if the variance is smaller than a given variance threshold value e1, taking the measured data as a candidate positioning point set Q;
and 4, in the minimum sample size, taking the Spearman rank correlation coefficient of the measured data of each adjacent point in the Q as an index, and if the Spearman rank correlation coefficient is larger than a given threshold value e2, taking the index as an optimal positioning point set T.
According to the technical scheme provided by the invention, the locating point set selecting method based on the batch blade curved surface measurement data statistical analysis provided by the embodiment of the invention utilizes the locating point selecting principle quantitatively given under the influence of the actual error by the statistical analysis method, and calculates the minimum sample size required by the statistical analysis under the influence of the actual error with sufficient confidence and accuracy, thereby avoiding the measurement data redundancy and reducing the measurement cost; by analyzing the point-by-point sample variance and the adjacent point spearman grade correlation coefficient, the subsequent blade curved surface positioning point set under the guidance of the statistical information of the minimum sample size is quantitatively determined, thereby avoiding the participation of manual experience in the traditional positioning point selection mode and improving the accuracy and reliability of subsequent curved surface registration positioning.
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FIG. 1 is a flowchart of a method for selecting a positioning point set based on statistical analysis of batch blade surface measurement data according to an embodiment of the present invention;
FIG. 2 is a schematic view illustrating uniform dispersion of curved surfaces of a blade according to an embodiment of the present invention;
fig. 3 is a schematic diagram of selecting a candidate anchor point Q based on sample variance according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in further detail below. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to the person skilled in the art.
The invention discloses a positioning point set selection method based on batch blade curved surface measurement data statistical analysis, which has the preferred specific implementation mode that:
the method comprises the following steps:
step 1, uniformly dispersing a blade curved surface CAD model according to specified precision, wherein an obtained dispersion point set is an initial positioning point set P;
step 2, extracting sample blades from the batch of blade parts, measuring an initial positioning point set P of the sample blades piece by piece, accumulating measuring point data piece by piece and performing statistical analysis to obtain a minimum sample amount n;
step 3, in the minimum sample size, taking the variance of the measured data of each point in the P as an index, and if the variance is smaller than a given variance threshold value e1, taking the measured data as a candidate positioning point set Q;
and 4, in the minimum sample size, taking the Spearman rank correlation coefficient of the measured data of each adjacent point in the Q as an index, and if the Spearman rank correlation coefficient is larger than a given threshold value e2, taking the index as an optimal positioning point set T.
In the step 1, the method for uniformly dispersing the blade curved surface CAD model comprises the following steps: under the limitation of specified discrete accuracy, uniform discrete points are obtained according to surface fitting parameters or arc length parameters (arc length method) and the like, and are used as an initial positioning point set P { pi, i ═ 1, …, m }.
The step 2 comprises the following steps:
extracting N samples from N pieces of batch blades, measuring an initial positioning point set P { pi, i ═ 1, …, m } of the sample blades one by one, and recording the error between a measuring point and a blade curved surface CAD model as epsilonij(i is 1, …, m; j is 1 …, N), and the total average value of errors of N pieces of batch blades is recorded as muNThe total variance is recorded as
Figure BDA0002827873420000031
The mean of the sampled n sample leaf errors is recorded as
Figure BDA0002827873420000032
The variance of the sample is recorded as
Figure BDA0002827873420000033
To be provided with
Figure BDA0002827873420000034
Estimating muNThe estimation accuracy is usually expressed as an error limit β
Figure BDA0002827873420000035
In equation (1), P represents a probability, γ is a confidence corresponding to β, and is known as an estimated amount of a normal distribution in a limit distribution when the sample volume n is infinitely increased, and can be obtained if the sample mean is an asymptotic normal estimation:
Figure BDA0002827873420000041
in the above formula, the first and second carbon atoms are,
Figure BDA0002827873420000042
is composed of
Figure BDA0002827873420000043
Is known from unbiased estimation
Figure BDA0002827873420000044
Then:
Figure BDA0002827873420000045
wherein muα/2Is a standard normal distribution bilateral quantile, and can be obtained by combining the formula (1) and the formula (3):
Figure BDA0002827873420000046
according to the theory of mathematical statistics, when the sample size is n, the variance of the sample
Figure BDA0002827873420000047
And the total variance
Figure BDA0002827873420000048
As follows:
Figure BDA0002827873420000049
then, when the confidence obtained by combining the equations (4) and (5) is 1- α, the theoretically required detection sample amount is as follows:
Figure BDA00028278734200000410
according to the theory of mathematical statistics, when the sample size is n, a chi-square distribution relationship exists between the sample variance and the overall variance:
Figure BDA00028278734200000411
then the overall variance
Figure BDA00028278734200000412
The confidence interval with a confidence level of 1- α is as follows:
Figure BDA00028278734200000413
to ensure that the number of samples meets the accuracy requirement,
Figure BDA00028278734200000414
taking the boundary between regions in equation (8), equation (6) is expressed as:
Figure BDA00028278734200000415
when n is larger than or equal to nminAnd stopping measuring piece by piece, wherein n is the minimum sample size.
The step 3 comprises the following steps:
with pi (i ═ 1, …, m) as the target, the error of n samples to the CAD model of the blade surface at pi point is epsilonij(j ═ 1 …, n), then at point pi the sample variance
Figure BDA00028278734200000416
Can be calculated as:
Figure BDA00028278734200000417
wherein the content of the first and second substances,
Figure BDA00028278734200000418
is the sample mean of pi points, when a variance threshold e1 is given, if
Figure BDA00028278734200000419
Then pi point is the candidate anchor point qk and the resulting set of points is the candidate anchor point set Q { qk, k ═ 1, …, r }.
The step 4 comprises the following steps:
with qk (k is 1, …, r) as the target, the error of n samples from the CAD model of the blade curved surface at the point qk is epsilonkj(j-1 …, n), i.e. the error vector e at point qkkAnd the error from n samples to the CAD model of the blade curved surface is epsilon at the adjacent point qk +1k+1,j(j-1 …, n), i.e. the error vector e at point qk +1k+1To e ∈kAnd ek+1Sorting (ascending or descending at the same time) to obtain two element sorting sets belonging to the same categoryk、∈k+1Element e ofkj,∈k+1,jAre respectively epsilonkjIn ekRank and epsilon ink+1,jIn ek+1Rank in (c), leave the set ask、∈k+1The elements in the sequence are correspondingly subtracted to obtain a row difference set dk,k+1Wherein d isk,k+1,j＝∈kj-∈k+1,jThen the set is ekAnd ek+1The spearman rank correlation coefficient between can be as follows:
Figure BDA0002827873420000051
given a spearman rank correlation coefficient threshold e2, if ρk,k+1≥e2And the qk point is the optimal positioning point, so that an optimal positioning point set T is formed.
The invention discloses a positioning point set selection method based on batch blade curved surface measurement data statistical analysis, which utilizes a statistical analysis method to quantitatively give a positioning point selection principle under the influence of actual errors.
The specific embodiment is as follows:
the technical process is shown in fig. 1, and is described in detail as follows:
stp1, uniformly dispersing the CAD model of the blade curved surface according to specified precision, and taking an obtained dispersed point set as an initial positioning point set P;
stp2 extracts sample blades from the batch blade parts, measures the initial positioning point set P of the sample blades piece by piece, accumulates the measuring point data piece by piece and carries out statistical analysis to obtain the minimum sample amount n;
stp3 takes the variance of the measured data of each point in P as an index in the minimum sample size, and if the variance is less than a given variance threshold value e1, the index is used as a candidate positioning point set Q;
the Stp4 takes Spearman rank correlation coefficient of measured data of each adjacent point in Q as an index in the minimum sample size, and if the Spearman rank correlation coefficient is greater than a given threshold value e2, the optimal positioning point set T is taken.
The method specifically comprises the following steps:
step one, as shown in fig. 2, uniformly dispersing the blade curved surface CAD model, for example, obtaining uniform discrete points according to a curved surface fitting parameter (parametric method), an arc length parameter (arc length method) and the like under the limitation of specified dispersion accuracy, and taking the uniform discrete points as an initial positioning point set P { pi, i ═ 1, …, m }.
Step two, extracting N samples from N batches of blades, and initially positioning the sample blades one by oneMeasuring a point set P { pi, i ═ 1, …, m }, and recording the error from a measuring point to the CAD model of the blade curved surface as epsilonij(i-1, …, m; j-1 …, n). Let N pieces of bulk blade error overall mean value be recorded as muNThe total variance is recorded as
Figure BDA0002827873420000052
The mean of the sampled n sample leaf errors is recorded as
Figure BDA0002827873420000061
The variance of the sample is recorded as
Figure BDA0002827873420000062
To be provided with
Figure BDA0002827873420000063
Estimating muNThe estimation accuracy is usually expressed as an error limit β
Figure BDA0002827873420000064
In the formula (1), P represents a probability, and γ is a confidence corresponding to β. It is known that when the sample volume n is infinitely increased, the limit distribution is an estimator of a normal distribution, e.g., the sample mean is an asymptotically normal estimate. Then it can be obtained:
Figure BDA0002827873420000065
in the above formula, the first and second carbon atoms are,
Figure BDA0002827873420000066
is composed of
Figure BDA0002827873420000067
Is known from unbiased estimation
Figure BDA0002827873420000068
Then:
Figure BDA0002827873420000069
wherein muα/Is a standard normal distribution bilateral quantile, and can be obtained by combining the formula (1) and the formula (3):
Figure BDA00028278734200000610
according to the theory of mathematical statistics, when the sample size is n, the variance of the sample
Figure BDA00028278734200000611
And the total variance
Figure BDA00028278734200000612
As follows:
Figure BDA00028278734200000613
then, when the confidence obtained by combining the equations (4) and (5) is 1- α, the theoretically required detection sample amount is as follows:
Figure BDA00028278734200000614
according to the theory of mathematical statistics, when the sample size is n, a chi-square distribution relationship exists between the sample variance and the overall variance:
Figure BDA00028278734200000615
then the overall variance
Figure BDA00028278734200000616
The confidence interval with a confidence level of 1- α is as follows:
Figure BDA00028278734200000617
to ensure that the number of samples meets the accuracy requirement,
Figure BDA00028278734200000618
taking the boundary between equations (8), equation (6) can be expressed as:
Figure BDA00028278734200000619
when n is larger than or equal to nminAnd stopping measuring piece by piece, wherein n is the minimum sample size.
And step three, taking pi (i is 1, …, m) as an object, and setting the error of the n samples from the point pi to the CAD model of the blade curved surface as epsilonij(j ═ 1 …, n), then at point pi the sample variance
Figure BDA00028278734200000620
Can be calculated as:
Figure BDA00028278734200000621
wherein the content of the first and second substances,
Figure BDA0002827873420000071
is the sample mean of pi points, when a variance threshold e1 is given, if
Figure BDA0002827873420000072
Then pi point is the candidate anchor point qk and the resulting set of points is the candidate anchor point set Q { qk, k ═ 1, …, r }.
As shown in fig. 3, a schematic diagram is selected for the candidate anchor point Q based on the sample variance.
And step four, taking qk (k is 1, …, r) as an object, and setting the error of the n samples from the point qk to the blade curved surface CAD model as epsilonkj(j-1 …, n), i.e. the error vector e at point qkk. At the adjacent point qk +1, the error from n samples to the CAD model of the blade curved surface is epsilonk+1,j(j-1 …, n), i.e. the error at point qk +1Vector ek+1. For ekAnd ek+1Sorting (ascending or descending at the same time) to obtain two element sorting sets belonging to the same categoryk、∈k+1Element e ofkj,∈k+1,jAre respectively epsilonkjIn ekRank and epsilon ink+1,jIn ek+1Row (2) of (1). Belongs to the set tok、∈k+1The elements in the sequence are correspondingly subtracted to obtain a row difference set dk,k+1Wherein d isk,k+1,j＝∈kj-∈k+1,j. Then the set ekAnd ek+1The spearman rank correlation coefficient between can be as follows:
Figure BDA0002827873420000073
given a spearman rank correlation coefficient threshold e2, if ρk,k+1≥e2And the qk point is the optimal positioning point, so that an optimal positioning point set T is formed.
Because the machining process of the blade curved surface is easy to generate errors, the efficient and high-precision positioning of the blade curved surface is the key for realizing mass production. The invention utilizes the positioning point selection principle under the influence of actual errors quantitatively given by a statistical analysis method, firstly, the minimum sample size required by the statistical analysis under the influence of the actual errors is calculated with enough confidence and accuracy, thereby avoiding the redundancy of the measured data and reducing the measurement cost; and then, a subsequent blade curved surface positioning point set under the guidance of the statistical information of the minimum sample size is quantitatively determined by analyzing the point-by-point sample variance and the adjacent point spearman grade correlation coefficient, so that the participation of manual experience in the traditional positioning point selection mode is avoided, and the accuracy and the reliability of subsequent curved surface registration positioning are improved.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A positioning point set selection method based on batch blade curved surface measurement data statistical analysis is characterized by comprising the following steps:
step 1, uniformly dispersing a blade curved surface CAD model according to specified precision, wherein an obtained dispersion point set is an initial positioning point set P;
step 2, extracting sample blades from the batch of blade parts, measuring an initial positioning point set P of the sample blades piece by piece, accumulating measuring point data piece by piece and performing statistical analysis to obtain a minimum sample amount n;
step 3, in the minimum sample size, taking the variance of the measured data of each point in the P as an index, and if the variance is smaller than a given variance threshold value e1, taking the measured data as a candidate positioning point set Q;
step 4, in the minimum sample size, taking the Spearman rank correlation coefficient of the measured data of each adjacent point in the Q as an index, and if the Spearman rank correlation coefficient is larger than a given threshold value e2, taking the index as an optimal positioning point set T;
in the step 1, the method for uniformly dispersing the blade curved surface CAD model comprises the following steps: under the limitation of appointed discrete precision, obtaining uniform discrete points according to a surface fitting parameter or an arc length parameter, and taking the uniform discrete points as an initial positioning point set P { pi, i is 1, …, m };
the step 2 comprises the following steps:
extracting N samples from N pieces of batch blades, measuring an initial positioning point set P { pi, i ═ 1, …, m } of the sample blades one by one, and recording the error between a measuring point and a blade curved surface CAD model as epsilonij(i is 1, …, m; j is 1 …, N), and the total average value of errors of N pieces of batch blades is recorded as muNThe total variance is recorded as
Figure FDA0003215014680000011
The mean of the sampled n sample leaf errors is recorded as
Figure FDA0003215014680000012
The variance of the sample is recorded as
Figure FDA0003215014680000013
To be provided with
Figure FDA0003215014680000014
Estimating muNThe estimation accuracy is expressed by an error limit β
Figure FDA0003215014680000015
In equation (1), P represents a probability, γ is a confidence corresponding to β, and is known as an estimated amount of a normal distribution in a limit distribution when the sample volume n is infinitely increased, and can be obtained if the sample mean is an asymptotic normal estimation:
Figure FDA0003215014680000016
in the above formula, the first and second carbon atoms are,
Figure FDA0003215014680000017
is composed of
Figure FDA0003215014680000018
Is known from unbiased estimation
Figure FDA0003215014680000019
Then:
Figure FDA00032150146800000110
wherein muα/2Is a standard normal distribution bilateral quantile, and can be obtained by combining the formula (1) and the formula (3):
Figure FDA00032150146800000111
according to the theory of mathematical statistics, when the sample size is n, the variance of the sample
Figure FDA0003215014680000021
And the total variance
Figure FDA0003215014680000022
As follows:
Figure FDA0003215014680000023
then, when the confidence obtained by combining the equations (4) and (5) is 1- α, the theoretically required detection sample amount is as follows:
Figure FDA0003215014680000024
according to the theory of mathematical statistics, when the sample size is n, a chi-square distribution relationship exists between the sample variance and the overall variance:
Figure FDA0003215014680000025
then the overall variance
Figure FDA0003215014680000026
The confidence interval with a confidence level of 1- α is as follows:
Figure FDA0003215014680000027
to ensure that the number of samples meets the accuracy requirement,
Figure FDA0003215014680000028
taking the boundary between regions in equation (8), equation (6) is expressed as:
Figure FDA0003215014680000029
when n is larger than or equal to nminAnd stopping measuring piece by piece, wherein n is the minimum sample size.
2. The method for selecting a positioning point set based on statistical analysis of batch blade curved surface measurement data according to claim 1, wherein the step 3 comprises:
with pi (i ═ 1, …, m) as the target, the error of n samples to the CAD model of the blade surface at pi point is epsilonij(j ═ 1 …, n), then at point pi the sample variance
Figure FDA00032150146800000210
The calculation is as follows:
Figure FDA00032150146800000211
wherein the content of the first and second substances,
Figure FDA00032150146800000213
is the sample mean of pi points, when a variance threshold e1 is given, if
Figure FDA00032150146800000212
Then pi point is the candidate anchor point qk and the resulting set of points is the candidate anchor point set Q { qk, k ═ 1, …, r }.
3. The method for selecting a positioning point set based on statistical analysis of batch blade curved surface measurement data according to claim 2, wherein the step 4 comprises:
with qk (k is 1, …, r) as the target, the error of n samples from the CAD model of the blade curved surface at the point qk is epsilonkj(j-1 …, n), i.e. the error vector e at point qkkAt its adjacent point qk +1, n samples to the bladeError of CAD model of curved surface is epsilonk+1，j(j-1 …, n), i.e. the error vector e at point qk +1k+1To e ∈kAnd ek+1Sorting according to ascending order or descending order at the same time to obtain two element sorting sets belonging to the same categoryk、∈k+1Element e ofkj，∈k+1，jAre respectively epsilonkjIn ekRank and epsilon ink+1，jIn ek+1Rank in (c), leave the set ask、∈k+1The elements in the sequence are correspondingly subtracted to obtain a row difference set dk，k+1Wherein d isk，k+1，j＝∈kj-∈k+1，jThen the set is ekAnd ek+1The spearman rank correlation coefficient between can be as follows:
Figure FDA0003215014680000031
given a spearman rank correlation coefficient threshold e2, if ρk，k+1≥e2And the qk point is the optimal positioning point, so that an optimal positioning point set T is formed.
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