Roundness Uncertainty Evaluation Method

Abstract

The present invention provides a method for evaluating the uncertainty of roundness based on a random process, including: sampling the roundness of a measured object to obtain a coordinate data set of the measured object; fitting a circle according to the coordinate data set, and then obtaining the coordinates of the center of the fitted circle and the first coordinate point farthest from the center and the second coordinate point closest to the center, and then calculating the roundness error of the circle; determining a suggested distribution, constructing a probability density expression based on the suggested distribution and a joint probability density expression based on a random process; constructing an autocorrelation function matrix and a transfer density function based on the probability density expression and the joint probability density expression; constructing a Markov chain using the autocorrelation function matrix and the transfer density function as a transfer kernel, using a sampling method to obtain samples and evaluate the roundness uncertainty of the circle. The present invention can be applied to actual cylindrical parts in engineering such as bearings to ensure measurement accuracy and provide a new method for intelligently evaluating measurement uncertainty.

Description

Technical Field

[0001] The invention relates to precision metrology and computer application, and in particular to a roundness uncertainty evaluation method based on random processes. Background Art

[0002] Mechanical testing theory and technology, especially mechanical metrology standards, theories and methods, play an increasingly important role in the current national economy and scientific and technological development. Among international standards, the Geometric Product Specification is one of the most influential and important basic standard systems, and is the basis for manufacturing informatization, quality management, industrial automation and integration. The new generation of GPS standard system is based on metrological mathematics, introduces the principle of object-image duality in physics, links the specification design process with the measurement certification process, and integrates the product's function, specification, manufacturing, measurement certification, etc. through the transmission relationship of "uncertainty", thereby avoiding the problem of overly abstract technical standards based on geometric theory, and can effectively solve problems such as disputes caused by uncontrolled measurement evaluation due to inconsistent measurement methods. Summary of the invention

[0003] In view of the defects in the prior art, an object of the present invention is to provide a method for evaluating roundness uncertainty.

[0004] The roundness uncertainty evaluation method based on random process provided by the present invention comprises the following steps:

[0005] Step S1: performing roundness sampling on the object to be measured to obtain a coordinate data set of the object to be measured;

[0006] Step S2: fitting a circle according to the coordinate data set, and then obtaining the coordinates of the center of the fitted circle and the first coordinate point farthest from the center of the circle and the second coordinate point closest to the center of the circle, and then calculating the roundness error of the circle;

[0007] Step S3: Determine the proposed distribution, construct a probability density expression based on the proposed distribution and a joint probability density expression based on the random process;

[0008] Step S4: constructing an autocorrelation function matrix and a transfer density function based on the probability density expression and the joint probability density expression;

[0009] Step S5: construct a Markov chain using the autocorrelation function matrix and the transfer density function as the transfer kernel, use the Metropolis-Hastings sampling method to obtain samples and evaluate the circularity uncertainty of the circle.

[0010] Preferably, the sampling method in step S1 is specifically as follows: 64 measuring points evenly distributed around the circumference of the measured object are set to obtain a set of coordinate data P of the measuring points. i (x i ,y i ), i is the serial number of the measuring point.

[0011] Preferably, the step S2 specifically comprises: fitting a circle using the least square method according to the measurement point data to obtain the coordinates of the center of the circle, the first coordinate point farthest from the center of the circle and the second coordinate point closest to the center of the circle, and then calculating the roundness error.

[0012] Preferably, in step S3, the specific construction process of the probability density expression and the joint probability density expression based on the random process is as follows:

[0013] The distribution of the coordinate data is determined to be a normal distribution, and the probability density expression is:

[0014]

[0015] Among them, x is the parameter to be determined; μ(t) is the mean function; σ(t) is the variance function; t is a positive integer;

[0016] The joint probability density function expression is:

[0017]

[0018] Among them, t n is an element in the random variable family, n is a positive integer, X is a random variable, μ is the mean, T is the transposed sign, and C is the determinant.

[0019] Preferably, in step S4, the autocorrelation function matrix is:

[0020] C=[E(x(t 1 )), E(x(t 2 )), ..., E(x(t n ))] T (3)

[0021] Among them, E(x(t 1 )) is expected

[0022] The transition density function of the normal random process is:

[0023]

[0024] where G(·) is the two-dimensional joint probability distribution of random variables at adjacent moments in the random process; F(·) is the marginal distribution of the parameter random variable; x t is a random variable at time t.

[0025] Preferably, in step S5, the Metropolis-Hastings sampling method is used for sampling, and the specific process is as follows:

[0026] From the proposed distribution T(x (t) ,y) to extract samples y,x (t) is the last sampling sample, and y is the potential transfer point;

[0027] Draw a random number u from a uniform distribution in [0, 1] and update it according to the following formula

[0028]

[0029]

[0030] Among them, x (t+1) is the sample for this sampling, r(x (t) ,y) is the probability, ρ(x,y) is the transfer kernel, π(x) is the sample value of the last sampling, π(y) is the sample value of the potential transfer point, T(y,x) is the proposed distribution of y to x, and T(x,y) is the proposed distribution of x to y.

[0031] 7. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that the sample expectation and standard deviation of the random variable are calculated by numerical integration to achieve measurement uncertainty evaluation.

[0032] The roundness uncertainty evaluation method for the circular surface of a part provided by the present invention adopts the roundness uncertainty evaluation method based on random process.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention can be applied to actual cylindrical parts in engineering such as bearings to ensure measurement accuracy and provide a new method for intelligent evaluation of measurement uncertainty, and has important theoretical significance and social and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0036] Figure 1 Flow chart of a roundness uncertainty evaluation method based on random process in an embodiment of the present invention;

[0037] Figure 2 is a flow chart of the Metropolis-Hastings algorithm in an embodiment of the present invention;

[0038] Figure 3 is a sampling result diagram of the Metropolis-Hastings algorithm in an embodiment of the present invention; and

[0039] Figure 4 It is a comparison chart between the roundness error uncertainty evaluation method in the embodiment of the present invention and the national standard method. DETAILED DESCRIPTION

[0040] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0041] In an embodiment of the present invention, a method for evaluating roundness uncertainty based on a random process is provided by the present invention, comprising the following steps:

[0042] Step S1: Perform roundness sampling on the object to be measured by a three-dimensional coordinate measuring machine to obtain coordinate data of a group of measuring points to form a coordinate data set.

[0043] In the embodiment of the present invention, the specific sampling method is: 64 measuring points are set for the circular measured object, and the coordinate data P of a group of measuring points are obtained. i (x i ,y i ). As shown in the following table,

[0044]

[0045] Step S2: fitting a circle using the least square method according to the coordinate data of the measuring points, obtaining a first coordinate point of the measuring point farthest from the center of the fitting circle and a second coordinate point of the measuring point closest to the center of the fitting circle, and then calculating the roundness error of the circle.

[0046] In the embodiment of the present invention, the coordinates of the center of the fitting circle are (2.4961e -4 , 2.8415e -4 ), the first coordinate point of the measuring point farthest from the center of the circle is (35.83915, -0.00062), the second coordinate point of the measuring point closest to the center of the circle is (-19.90971, 29.98736), and the roundness error is 1.6528μm.

[0047] Step S3: Determine that the distribution is normal distribution, and the probability density expression is

[0048]

[0049] Among them, x is the parameter to be determined; μ(t) is the mean function; σ(t) is the variance function; t is a positive integer;

[0050] The joint probability density function expression is:

[0051]

[0052] Among them, t n is an element in the random variable family, n is a positive integer, X is a random variable, μ is the mean, T is the transposed sign, and C is the determinant.

[0053] Step S4: Determine the autocorrelation function matrix C:

[0054] C=[E(x(t 1 )), E(x(t 2 )), ..., E(x(t n ))] T (3)

[0055] Among them, E(x(t 1 )) is the expectation;

[0056] Determine the transition density function of a normal random process:

[0057]

[0058] where G(·) is the two-dimensional joint probability distribution of random variables at adjacent moments in the random process; F(·) is the marginal distribution of the parameter random variable, x t is a random variable at time t.

[0059] Step S5: Set the initial value of x to 1.5

[0060] Set the initial distribution to

[0061]

[0062] Draw sample y from the normal distribution T(1.6528, 0.4219);

[0063] Draw a random number u from a uniform distribution in [0, 1] and update it according to the following principle:

[0064]

[0065]

[0066] Among them, x (t+1) is the sample for this sampling, r(x (t), y) is the probability, ρ(x, y) is the transition kernel, π(x) is the sample value of the last sampling, π(y) is the sample value of the potential transition point, T(y, x) is the proposed distribution of y to x, and T(x, y) is the proposed distribution of x to y.

[0067] The mean and sample variance of the sample data obtained by sampling are calculated to evaluate the uncertainty of roundness.

[0068] In the embodiment of the present invention, the number of measurement point data groups is 10, and the roundness uncertainty is evaluated 10 times in total, as shown in the following table:

[0069]

[0070] In an embodiment of the present invention, the core of the roundness error uncertainty assessment model based on random processes is to regard the process of obtaining assessment parameters as a random process, and to consider the parameters at each moment in the process of calculating the parameters as random variables that obey a certain distribution. In order to obtain sample information of the parameter distribution, the Markov chain Monte Carlo method is introduced for sampling. By calculating the state transfer function of the Markov Monte Carlo model, the autocorrelation characteristics of the parameters under the random process are reflected, and the dynamic assessment of the uncertainty of roundness error measurement is realized, thereby improving the accuracy of the assessment.

[0071] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for evaluating roundness uncertainty based on random processes, characterized in that: The steps include: Step S1: performing roundness sampling on the circular surface of the measured part by a three-dimensional coordinate measuring machine to obtain a coordinate data set of the measured object; Step S2: fitting a circle according to the coordinate data set, and then obtaining the coordinates of the center of the fitted circle and the first coordinate point farthest from the center of the circle and the second coordinate point closest to the center of the circle, and then calculating the roundness error of the circle; Step S3: Determine the proposed distribution, construct a probability density expression based on the proposed distribution and a joint probability density expression based on the random process; Step S4: constructing an autocorrelation function matrix and a transfer density function based on the probability density expression and the joint probability density expression; Step S5: construct a Markov chain using the autocorrelation function matrix and the transfer density function as the transfer kernel, use the Metropolis-Hastings sampling method to obtain samples and evaluate the roundness uncertainty of the circle, and then generate an evaluation result of the part processing quality control.

2. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that: The sampling method in step S1 is specifically as follows: 64 measurement points evenly distributed around the circumference of the measured object are set to obtain a set of coordinate data P of the measurement points. i (x i ,y i ), i is the serial number of the measuring point.

3. The roundness uncertainty evaluation method based on random process according to claim 2 is characterized in that: The step S2 specifically includes: fitting a circle using the least square method according to the measurement point data, obtaining the coordinates of the center of the circle, the first coordinate point farthest from the center of the circle and the second coordinate point closest to the center of the circle, and then calculating the roundness error.

4. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that: In step S3, the specific construction process of the probability density expression and the joint probability density expression based on the random process is as follows: The distribution of the coordinate data is determined to be a normal distribution, and the probability density expression is: Among them, x is the parameter to be determined; μ(t) is the mean function; σ(t) is the variance function; t is a positive integer; The joint probability density function expression is: Among them, t n is an element in the random variable family, n is a positive integer, X is a random variable, μ is the mean, t is the transposed sign, and C is the determinant.

5. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that: In step S4, the autocorrelation function matrix is: C=[E(x(t1)),E(x(t2)),…,E(x(t n ))] T (3) Among them, E(x(t1)) is the expectation; The transition density function of the normal random process is: where G(·) is the two-dimensional joint probability distribution of random variables at adjacent moments in the random process; F(·) is the marginal distribution of the parameter random variable; x t is a random variable at time t.

6. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that: In step S5, the Metropolis-Hastings sampling method is used for sampling, and the specific process is as follows: From the proposed distribution T(x (t) ,y) to extract samples y,x (t) is the last sampling sample, and y is the potential transfer point; Draw a random number u from a uniform distribution in [0,1] and update it according to the following formula Among them, x (t+1) is the sample for this sampling, r(x (t) ,y) is the probability, ρ(x,y) is the transfer kernel, π(x) is the sample value of the last sampling, π(y) is the sample value of the potential transfer point, T(y,x) is the proposed distribution of y to x, and T(x,y) is the proposed distribution of x to y.

7. The roundness uncertainty evaluation method based on random process according to claim 1 is characterized in that: The sample expectation and standard deviation of random variables are calculated by numerical integration to realize the measurement uncertainty evaluation.

8. A method for evaluating the uncertainty of roundness of a circular surface of a part, characterized in that: The roundness uncertainty evaluation method based on random process as described in any one of claims 1 to 7 is adopted.

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