Rolling bearing rotation precision uncertainty analysis method considering roundness error of raceway

Abstract

The invention discloses a rolling bearing rotation precision uncertainty analysis method considering roundness errors of a raceway. The method comprises the following steps: firstly, providing a rotation precision calculation method with radial runout of a bearing outer ring as a representation; secondly, on the basis of roundness error test data of the raceway of the bearing outer ring, a Newton iteration method is adopted to correct roundness errors, and the errors can be controlled within 1% after correction; establishing a regression function of harmonic distribution parameters and radial run-out of the bearing outer ring raceway through a regression analysis method; and finally, based on the regression function, performing uncertainty analysis by adopting a multi-peak random uncertainty analysis method, and accurately obtaining a cumulative distribution function value and a probability density function value of the radial run-out of the outer ring. According to the high-efficiency ternary dimension reduction (ETDRM) method, high-dimensional integrals meeting conditions are disassembled to improve the calculation efficiency, compared with a Monte Carlo method, the simulation result greatly improves the calculation efficiency and precision, the accuracy and high efficiency of the ETDRM method are verified, and the result shows that the rotation precision of the rolling bearing can be effectively predicted.

Description

Technical Field

[0001] The invention relates to a rolling bearing rotation accuracy uncertainty analysis method, in particular to a rolling bearing rotation accuracy uncertainty analysis method based on multi-peak theory, and belongs to the technical field of bearing rotation accuracy. Background Art

[0002] Rolling bearings are important components in mechanical systems and are widely used in various important precision equipment. The service performance of bearings plays a key role in the safe operation of equipment. As an important indicator to measure bearing performance, rotation accuracy is affected by many factors, such as the roundness error of the inner and outer ring raceways, the number of rollers, radial clearance, and working conditions. Radial runout is an important indicator to measure the rotation accuracy of bearings. After long-term and high-intensity work, the raceways of bearings will inevitably wear or slightly deform, causing the roundness error to change, which will significantly affect the radial runout value of the bearings and reduce the rotation accuracy of the bearings. Therefore, based on the analysis of the harmonic distribution characteristics of the raceway roundness error, further analysis of its influence on the rotation accuracy of the bearings can provide a theoretical reference for the development of high-precision bearings and the improvement of the service performance of bearings, which is of great significance.

[0003] Rolling bearings are mostly used in equipment with low speed and large load, but with the development of precision manufacturing technology, rolling bearings are also used in high-speed mechanical equipment. The relationship between their rotation accuracy and part geometric error deserves attention. Wei Jianbo et al. used copula function to study the influence of roller diameter error on bearing radial runout; BHATEJA et al. analyzed the influence of changes in the diameter of the inner and outer rings of hollow cylindrical roller bearings, the geometric dimensions of rollers and their relative positions on the bearing rotation accuracy through numerical simulation calculation; Yu Yongjian et al. proposed a numerical model of rotation accuracy under the condition of considering the geometric errors of the inner and outer ring raceways and roller surfaces of cylindrical roller bearings, and obtained the influence of the number of rollers, arrangement mode and roundness error order on the bearing rotation accuracy; Shi Wenxiang et al. predicted the outer ring radial runout simulation algorithm of cylindrical roller bearings through C++ programming, and obtained the special relationship between the outer ring radial runout and the harmonic order and the number of rollers. This type of research mainly focuses on the quantitative analysis of the influence of component errors such as the roundness error of the inner and outer ring raceways of the bearings, the number of rollers and the geometric error on the rotation accuracy, and there are few studies on the uncertainty analysis of bearing rotation accuracy. Therefore, the study of bearing rotation accuracy uncertainty is of great significance.

[0004] Uncertainty analysis is to obtain the probability distribution of the response function based on the distribution type of independent random variables. The research on uncertainty analysis methods is relatively mature and can be generally divided into four categories: the most likely failure point method, sampling method, surrogate model method and numerical integration method. The most likely failure point method includes the first-order and second-order reliability methods. Sampling methods include Monte Carlo method and important sampling method. Surrogate model methods include chaotic polynomial expansion method and Kriging model method. The numerical integration method uses methods such as dimensionality reduction integral and sparse grid to calculate the statistical moment of the response function, and uses the response statistical moment to calculate the probability distribution of the response function.

[0005] The above four uncertainty analysis methods can achieve good analysis results for random variables that obey unimodal distribution. However, random variables in many engineering problems obey multimodal distribution. For example, the damping characteristics of train shock absorbers obey bimodal distribution during long-term service; the fatigue stress of steel bridge structures in road traffic obeys multimodal distribution. In order to more accurately understand the impact of multimodal random variables, domestic and foreign scholars have studied uncertainty propagation analysis methods in multimodal random distribution and achieved certain results. Hu and Du proposed a mean saddle point approximation method for bimodal distribution functions, which can more accurately estimate the failure probability of the system; Guo Tong et al. used the extreme value distribution function and the weighted value of the normal distribution function to fit the characteristics of multimodal distribution of various vehicle loads; Zhang et al. proposed a univariate dimensionality reduction method for multimodal distribution functions, and used the maximum entropy method to calculate the probability distribution of the response. At the same time, a method for uncertainty analysis of multimodal random parameters was also proposed, which used sparse grid numerical integration method and maximum entropy method to improve the accuracy of uncertainty propagation.

[0006] The rotation accuracy of bearings is affected by many uncertain factors, and the uncertainty analysis of rotation accuracy has also received attention in recent years. Viitala analyzed the uncertainty of the four-point roundness measurement of the inner ring of the bearing; Fu conducted a comprehensive evaluation of the key performance of the fluid dynamic sliding bearing affected by uncertainty; Sun studied the influence of bearing misalignment and inherent uncertainty on the stability of the bearing rotor system; Stocki combined multi-dimensional random models to analyze uncertainty variables and estimate the vibration response of the bearing rotor shaft. Existing research has little research on the uncertainty law of rolling bearing rotation accuracy. The introduction of multi-peak uncertainty analysis method to study the rotation accuracy of rolling bearings has certain theoretical reference significance and positive engineering value. Summary of the invention

[0007] The purpose of the present invention is to provide a rolling bearing rotation accuracy uncertainty analysis method taking into account the raceway roundness error, so as to solve the problem that there is little research on the uncertainty law of rolling bearing rotation accuracy and provide a new idea for improving the bearing rotation accuracy.

[0008] The innovation of this technology is mainly reflected in: based on the analysis of the geometric relationship and motion characteristics of each bearing unit such as the bearing outer ring raceway curve equation and the coordinates of the outer ring raceway center, a rotation accuracy calculation method characterized by the radial runout of the bearing outer ring raceway is established; based on the outer ring raceway roundness error test data, the least squares circle method is used to evaluate the roundness error, the error is corrected by the Newton iteration method, and the harmonic distribution parameters of the outer ring raceway are obtained by analysis using MATLAB; based on the relationship between the outer ring raceway curve and the roundness error, the outer ring raceway radial runout value is calculated by simulation, and the regression function of the outer ring raceway harmonic distribution parameters and the outer ring raceway radial runout is established by regression analysis, and the mapping relationship between the two is explored; a multi-peak uncertainty analysis method is introduced, and a rotation accuracy uncertainty analysis is carried out based on the regression function to obtain the cumulative distribution function value (CDF) and probability density function value (PDF) of the outer ring raceway radial runout, and the accuracy is verified by comparing with the classical Monte Carlo (MCS) method. The method verifies the accuracy of the outer ring radial runout model of the bearing through program simulation. The model can effectively predict the outer ring radial runout of the bearing and can be used to characterize the rotation accuracy of the bearing. After the Newton iteration method is used to correct the roundness error data measured by the roundness meter, the error can be controlled within 1%, which improves the measurement accuracy of the roundness meter. After the harmonic analysis of the roundness error data, it is found that the amplitude of the outer ring raceway roundness error is approximately exponentially related to the harmonic order. The method uses the regression analysis method to establish a regression function between the harmonic distribution parameters of the outer ring raceway and the radial runout of the outer ring raceway. The regression function can be used to predict the outer ring radial runout value of the bearing. The multi-peak uncertainty analysis method used in this method has extremely high efficiency and high accuracy. Based on the regression function, the cumulative distribution function value and probability density function value of the outer ring radial runout of the bearing can be accurately obtained. The research provides a new perspective for predicting the rotation accuracy of bearings. Existing research focuses on analyzing the correlation between the number and arrangement of rollers, the geometric errors of the inner and outer ring raceways and roller surfaces and the rotation accuracy, and lacks research on the distribution characteristics and probability density of the rotation accuracy. Compared with the existing technology, the advantages of this method are: the established regression function can truly reflect the mapping relationship between the harmonic distribution parameters of the outer ring raceway and the radial runout of the outer ring raceway; the multi-peak uncertainty analysis method adopted performs well in terms of computational efficiency and analysis accuracy, and can accurately obtain the cumulative distribution function value and probability density function value of the radial runout of the bearing outer ring; the research work is the first to introduce multi-peak theory from the perspective of the harmonic distribution parameters of the outer ring raceway to study the uncertainty law of the rotation accuracy of rolling bearings, which has strong theoretical value and positive engineering significance.

[0009] To achieve the above-mentioned purpose, the present invention adopts a rolling bearing rotation accuracy uncertainty analysis method taking into account the raceway roundness error, the method comprising establishing a rotation accuracy calculation method characterized by the radial runout of the bearing outer ring; analyzing the harmonic distribution characteristics based on the outer ring raceway roundness error test data; according to the relationship between the outer ring raceway curve and the roundness error, using the regression analysis method to establish the regression function of the outer ring raceway harmonic distribution parameters and the outer ring raceway radial runout, and exploring the mapping relationship therebetween; using a multi-peak uncertainty analysis method, based on the regression function, a rotation accuracy uncertainty analysis is carried out to obtain the cumulative distribution function value (CDF) and probability density function value (PDF) of the outer ring radial runout.

[0010] The S1 rotation accuracy numerical characterization method takes the outer ring raceway of the cylindrical roller bearing as the research object. According to the periodic and radial characteristics of the bearing raceway roundness error, the Fourier series can be used to represent the bearing raceway roundness error curve, and then the bearing outer ring raceway curve equation is established:

[0011]

[0012] Where ρ(θ) is the vector radius at any angle θ, R0 is the ideal circle radius of the outer ring raceway of the bearing, N is the maximum harmonic order of the harmonic component of the outer ring raceway roundness error, and c n ,d n They are the sine and cosine coefficients of the nth-order harmonic component of the outer ring raceway respectively.

[0013] When the outer ring of the bearing rotates a certain angle, determine whether the bearing is in a stable state. When the rolling elements are in contact with the inner ring raceway in pairs, the coordinates of the center of the outer ring raceway and the center of the rolling element can be calculated. At the same time, by calculating the distance from other rolling elements to the origin of the plane rectangular coordinate system, determine whether there is interference between the rolling element and the inner ring raceway. Repeat the above operation and record the coordinates of the center of the outer ring raceway when all are in a stable state.

[0014] Given the basic assumptions, the radial runout value of the outer ring raceway of the bearing is used as the main basis for determining the rotation accuracy of the cylindrical roller bearing. The bearing geometric radial runout model is established by recording the coordinates of the center of the outer ring raceway when it is in a stable state:

[0015] K ea =|y 0max |-|y 0min |

[0016] In the formula, K ea is the radial runout value of the outer ring, |y 0max | is the maximum value of the outer ring's vibration along the Y axis; |y 0min | is the minimum value of the outer ring's runout along the Y axis.

[0017] The model is verified based on the principle of outer ring radial runout.

[0018] S2 harmonic distribution characteristics analysis, using a roundness meter to measure the roundness error of the outer ring raceway of the bearing. The roundness meter is mainly composed of a measuring device, a computer system and a printer. The roundness error of the outer ring raceway of 10 sets of bearings of the same model is measured. During the measurement, the bearing is fixed on the test bench and the bearing is adjusted using a fine-tuning mechanism to make the bearing concentric with the measuring spindle. A contact sensor is installed on the spindle. During the measurement, the probe on the sensor will rotate at a constant speed with the spindle and contact the outer ring raceway; when the sensor rotates one circle, 1024 data can be obtained, and the actual curve of the outer ring raceway of the measured bearing is converted into an electrical signal, which is transmitted to the computer system through an amplifier, a filter, etc.

[0019] The least squares circle method is used to calculate the measurement point data set (m i ,n i ),i=1,2,...,Z, get the least squares circle radius and circle center coordinates. Since the outer circle curve data measured by the roundness instrument is the square of the difference between the distance from the measuring point to the circle center coordinates (u,v) and the square of the radius, the radius solved in this way is too small, and the circle center coordinates will also be offset, resulting in errors in the calculation results. Therefore, the Newton iteration method is used to correct the above problems and improve the measurement accuracy of the data.

[0020] Based on the corrected bearing outer ring raceway roundness error data, the outer ring raceway harmonic distribution characteristics are analyzed, and the optimal solution of the outer ring raceway harmonic distribution parameters is obtained.

[0021] S3 rotation accuracy regression analysis, based on the relationship between the outer ring raceway curve and the roundness error, calculates the outer ring raceway radial runout value through program simulation. The regression analysis method is used to establish the regression function between the outer ring raceway harmonic distribution parameters and the outer ring raceway radial runout:

[0022]

[0023] Where K ea is the radial runout value of the outer ring raceway, g h is the regression coefficient, h=0,1,2,3,4,5.

[0024] A significance test was performed on the regression function, and an ideal regression function was obtained which can be used to predict the influence of the harmonic distribution parameters of the bearing outer ring raceway on the radial runout of the outer ring raceway.

[0025] S4 rotation accuracy uncertainty analysis;

[0026] The Gaussian mixture model (GMM) is used to model uncertainty for multi-peak random variables. The probability density function of the response function can be expressed as follows:

[0027]

[0028]

[0029] Where α n represents the coefficient of the nth Gaussian component, satisfying α n ≥ 0. φ(T|θ n ) represents the Gaussian probability density function of the nth component, where k represents the number of sub-models, μ n , represent the mean and variance respectively.

[0030] Calculate the statistical moment of the response function. According to the probability density function of each input random variable T, the statistical moment of the response function F = p(T) is calculated as follows:

[0031]

[0032] T=(T1,T2,T3,...T n )

[0033]

[0034] Where m l represents the lth-order statistical moment of F, T represents n multimodal random variables, f T (T) represents the multi-peak joint probability density function of T, R n represents the domain of multidimensional integral, is the expectation operator.

[0035] The efficient ternary dimensionality reduction method can be used to meet the calculation accuracy of high-order statistical moments in multi-peak uncertainty analysis problems. By reducing the dimensionality and decomposing high-dimensional integrals, the calculation efficiency and accuracy can be improved.

[0036] After obtaining the first l-order statistical moments based on the above method, the probability distribution of the response function F can be estimated by the maximum entropy cycle (MEM) to obtain the uncertainty analysis results of the rotation accuracy.

[0037] Compared with the prior art, the present invention has the following research value.

[0038] The present invention proposes a rolling bearing rotation accuracy uncertainty analysis method considering the raceway roundness error. First, a rotation accuracy calculation method characterized by the radial runout of the outer ring of the rolling bearing is established; secondly, based on the test data of the outer ring raceway roundness geometric error, the harmonic distribution characteristics are analyzed; then, based on the relationship between the outer ring raceway curve and the roundness error, the regression analysis method is used to establish the regression function of the outer ring raceway harmonic distribution parameters and the outer ring raceway radial runout, and the mapping relationship between them is explored; a multi-peak uncertainty analysis method is used to carry out rotation accuracy uncertainty analysis based on the regression function, and the cumulative distribution function value (CDF) and probability density function value (PDF) of the outer ring radial runout are obtained. This invention applies the above method to the field of rolling bearing rotation accuracy for the first time, forming a complete set of rolling bearing rotation accuracy uncertainty analysis methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the rolling bearing rotation accuracy uncertainty analysis method considering the raceway roundness error in the present invention.

[0040] Figure 2 It is a flow chart of the method for numerical characterization of the rotation accuracy of rolling bearings in the present invention.

[0041] Figure 3 It is a flow chart of the rolling bearing harmonic distribution characteristic analysis and regression analysis in the present invention.

[0042] Figure 4 It is a graph showing the analysis results of the harmonic distribution characteristics of the rolling bearing in the present invention.

[0043] Figure 5 It is a flow chart of the uncertainty analysis of the rolling bearing rotation accuracy in the present invention.

[0044] Figure 6 It is a CDF simulation result diagram of the rolling bearing rotation accuracy uncertainty analysis in the present invention.

[0045] Figure 7 It is a PDF simulation result diagram of the rolling bearing rotation accuracy uncertainty analysis in the present invention.

[0046] Figure 8 It is a response convergence simulation diagram of the rolling bearing rotation accuracy uncertainty analysis in the present invention. DETAILED DESCRIPTION

[0047] The following is combined with Figure 1-8 The present invention is further described with specific implementation modes.

[0048] Figure 1The flowchart of the uncertainty analysis method of the rolling bearing rotation accuracy considering the raceway roundness error in the present invention is as follows. The principle of the uncertainty analysis of the rolling bearing rotation accuracy using the multi-peak theory is introduced in detail in conjunction with the flowchart. (1) Based on the analysis of the geometric relationship and motion characteristics of each bearing unit such as the bearing outer ring raceway curve equation and the outer ring raceway center coordinates, a rotation accuracy calculation method characterized by the radial runout of the bearing outer ring raceway is established.

[0049] (2) Based on the outer ring raceway roundness error test data, the least squares circle method is used to evaluate the roundness error, the error is corrected by the Newton iteration method, and MATLAB is used to analyze and obtain the harmonic distribution parameters of the outer ring raceway.

[0050] (3) Based on the relationship between the outer ring raceway curve and the roundness error, the radial runout value of the outer ring raceway is calculated by simulation. The regression analysis method is used to establish the regression function of the outer ring raceway harmonic distribution parameters and the radial runout of the outer ring raceway, and the mapping relationship between them is explored.

[0051] (4) A multi-peak uncertainty analysis method is introduced, and the rotation accuracy uncertainty analysis is carried out based on the regression function. The cumulative distribution function (CDF) and probability density function (PDF) of the outer ring radial runout are obtained, and the accuracy is verified by comparing with the classical Monte Carlo (MCS) method.

[0052] Figure 2 This is a flow chart of the numerical characterization method for the rotation accuracy of rolling bearings in the present invention. The specific process is as follows:

[0053] (1) Representation method of rolling bearing outer ring raceway roundness error curve:

[0054]

[0055] Where ρ(θ) is the vector radius at any angle θ, R0 is the ideal circle radius of the outer ring raceway of the bearing, N is the maximum harmonic order of the harmonic component of the outer ring raceway roundness error, and c n ,d n They are the sine and cosine coefficients of the nth-order harmonic component of the outer ring raceway respectively.

[0056] (2) Given the basic assumptions, the bearing geometric radial runout model is established:

[0057] K ea =|y 0max |-|y 0min |

[0058] In the formula, K ea is the radial runout value of the outer ring, |y 0max | is the maximum value of the outer ring's vibration along the Y axis; |y 0min | is the minimum value of the outer ring's runout along the Y axis.

[0059] (3) Model verification is carried out based on the principle of outer ring radial runout.

[0060] Figure 3 This is a flow chart of the analysis and regression analysis of the harmonic distribution characteristics of the outer ring raceway of the rolling bearing in the present invention. The specific process is as follows:

[0061] (1) Measurement of the roundness error of the outer ring raceway of rolling bearings.

[0062] (2) Roundness error evaluation and correction: The least squares circle method is used to evaluate the roundness error of the bearing outer ring raceway, and the least squares circle error is corrected by the Newton iteration method to improve the measurement accuracy of the data.

[0063] (3) Analysis of the harmonic distribution characteristics of the outer ring raceway. Based on the relationship between roundness error and harmonics, the harmonic distribution model of the outer ring raceway is established:

[0064]

[0065] Where F s is the outer ring raceway roundness error amplitude, a s 、b s is the harmonic distribution parameter of the outer ring raceway, q (q = 2, 3..., r) is the harmonic order, and r is the highest harmonic order.

[0066] (4) Based on the regression analysis theory, the outer ring raceway harmonic distribution parameters are regressed and the regression function is obtained:

[0067]

[0068] Where K ea is the radial runout value of the outer ring raceway, g h is the regression coefficient, h=0,1,2,3,4,5.

[0069] Figure 4 This is a graph showing the analysis results of the harmonic distribution characteristics of the rolling bearing in the present invention. It can be seen from the graph that the outer ring raceway roundness error amplitude is approximately exponentially related to the harmonic order.

[0070] Figure 5 This is a flow chart of uncertainty analysis of rolling bearing rotation accuracy in the present invention. The specific process is as follows:

[0071] (1) The Gaussian mixture model (GMM) is used to model the uncertainty of multi-peak random variables. The probability density function of the response function is expressed as follows:

[0072]

[0073]

[0074] Where α n represents the coefficient of the nth Gaussian component, satisfying α n ≥ 0. φ(T|θ n ) represents the Gaussian probability density function of the nth component, where k represents the number of sub-models, μ n , represent the mean and variance respectively.

[0075] (2) Calculate the statistical moment of the response function. Based on the obtained probability density function of each input random variable T, the statistical moment of the response function F = p(T) is calculated as follows:

[0076]

[0077] T=(T1,T2,T3,...T n )

[0078]

[0079] Where m l represents the lth-order statistical moment of F, T represents the vector of n multimodal independent random variables, f T (T) represents the multi-peak joint probability density function of T, R n represents the domain of multidimensional integral, is the expectation operator.

[0080] The efficient ternary dimensionality reduction method can be used to meet the computational accuracy of high-order statistical moments in multi-peak uncertainty analysis problems. Using it to reduce the dimension and decompose high-dimensional integrals can improve computational efficiency and accuracy.

[0081] (3) Calculate the probability density function of the response function. After obtaining the first l-order statistical moments based on the above method, the maximum entropy cycle (MEM) is used to estimate the probability density function of the response function F, and the uncertainty analysis results of the rotation accuracy are obtained.

[0082] (4) Convergence mechanism. The order of the statistical moment is determined by using a suitable convergence mechanism, and the accuracy of the response probability density function is gradually improved to eventually achieve the required uncertainty propagation accuracy.

[0083] Figure 6 This is a CDF simulation result diagram of the uncertainty analysis of the rolling bearing rotation accuracy in the present invention. It can be seen from the figure that the CDF values ​​calculated by the method proposed by the present invention and the traditional method are almost the same.

[0084] Figure 7This is the PDF simulation result diagram of the uncertainty analysis of the rolling bearing rotation accuracy in the present invention. It can be seen from the figure that under the action of the convergence mechanism, the response gradually approaches the true value. The PDF values ​​calculated by the method proposed by the present invention are almost the same as those calculated by the traditional method, but the amount of calculation is much less than that of the traditional method.

[0085] Figure 8 This is a simulation diagram of the convergence of the statistical moment order for the rolling bearing rotation accuracy uncertainty analysis in the present invention. Under the convergence mechanism proposed by the method of the present invention, the response function gradually improves its accuracy as the statistical moment order increases until the order that best suits the required uncertainty propagation accuracy is determined.

Claims

1. A rolling bearing rotation accuracy uncertainty analysis method considering raceway roundness error, characterized by: Firstly, a rotation accuracy calculation method characterized by the radial runout of the bearing outer ring is established. Secondly, based on the test data of the outer ring raceway roundness error, the harmonic distribution characteristics of the outer ring raceway are analyzed. Then, according to the relationship between the outer ring raceway curve and the roundness error, the regression function between the harmonic distribution parameters of the outer ring raceway and the rotation accuracy is established by the regression analysis method, and the mapping relationship between them is discussed. Finally, the multi-peak random uncertainty analysis method is used to carry out the rotation accuracy uncertainty analysis based on the regression function, and the cumulative distribution function value (CDF) and probability density function value (PDF) of the outer ring radial runout are obtained.

2. The rolling bearing rotation accuracy uncertainty analysis method considering raceway roundness error according to claim 1 is characterized in that: The implementation steps of the bearing rotation accuracy numerical characterization method are as follows: Step 1: Take the outer ring raceway of the cylindrical roller bearing as the research object. Since the roundness error of the bearing raceway has the characteristics of periodicity and radiality, the Fourier series can be used to represent the roundness error curve of the bearing raceway, and then the equation of the outer ring raceway curve of the bearing is established: Where ρ(θ) is the vector radius at any angle θ, R0 is the ideal circle radius of the outer ring raceway curve of the bearing, N is the maximum harmonic order of the harmonic component of the outer ring raceway roundness error, and c n ,d n are the sine and cosine coefficients of the nth order harmonic component of the outer ring raceway respectively; Step 2: When the outer ring of the bearing rotates a certain angle, it is necessary to determine whether the bearing is in a stable state. When the rolling elements are in contact with the inner ring raceway in pairs, the coordinates of the center of the outer ring raceway and the center of the rolling element can be calculated. By calculating the distance from other rolling elements to the origin of the plane rectangular coordinate system, it is determined whether there is interference between the rolling element and the inner ring raceway. Repeat the above operation and record the coordinates of the center of the outer ring raceway when all are in a stable state. Step 3: Given the basic assumptions, the radial runout value of the outer ring raceway of the bearing is used as the main basis for determining the rotation accuracy of the cylindrical roller bearing. The coordinates of the center of the outer ring raceway in a stable state are recorded, and then the bearing geometric radial runout model is established: K ea =|and 0max |-|and 0min | In the formula, K ea is the radial runout value of the outer ring, |y 0max | is the maximum value of the outer ring's vibration along the Y axis; |y 0min | is the minimum value of the outer ring's runout along the Y axis; Step 4: Verify the model based on the principle of radial runout of the bearing outer ring.

3. The rolling bearing rotation accuracy uncertainty analysis method considering raceway roundness error according to claim 2 is characterized in that: The implementation steps of the outer ring raceway harmonic distribution characteristic analysis are as follows: Step 1: The roundness instrument is mainly composed of a measuring device, a computer system and a printer. The roundness instrument is used to measure the roundness errors of the outer ring raceways of 10 sets of bearings of the same model. During the measurement, the bearing is fixed on the test bench and the bearing is adjusted using a fine-tuning mechanism to make the bearing concentric with the measuring spindle. A contact sensor is installed on the spindle. During the measurement, the probe on the sensor will rotate at a constant speed with the spindle and contact the outer ring raceway. When the sensor rotates one circle, 1024 data will be obtained, and the actual curve of the outer ring raceway of the measured bearing will be converted into an electrical signal, which will be transmitted to the computer system through an amplifier, a filter, etc.; Step 2: Use the least squares circle method to calculate the measurement point data set (m i ,n i ), i=1,2,...,Z, get the least square circle radius and circle center coordinates. Since the outer ring raceway curve data measured by the roundness instrument is the square of the difference between the distance from the measuring point to the circle center coordinates (u,v) and the square of the radius, the radius is too small and the circle center coordinates will also shift. The calculated result has errors. Therefore, the Newton iteration method is used to correct the above problems and improve the measurement accuracy of the data. Step 3: Based on the corrected bearing outer ring raceway roundness error data, the harmonic distribution characteristics of the outer ring raceway are analyzed to obtain the optimal solution of the outer ring raceway harmonic distribution parameters.

4. The rolling bearing rotation accuracy uncertainty analysis method considering raceway roundness error according to claim 3 is characterized in that: The implementation steps of rotation accuracy regression analysis are as follows: Step 1: Based on the relationship between the outer ring raceway curve and the roundness error, the radial runout value of the outer ring raceway is calculated through program simulation; Step 2: Use regression analysis to establish the regression function between the outer ring raceway harmonic distribution parameters and the outer ring raceway radial runout: Where K ea is the radial runout value of the outer ring raceway, g h is the regression coefficient, h=0,1,2,3,4,5; Step 3: Perform a significance test on the regression function to obtain an ideal regression function that can be used to predict the influence of the harmonic distribution parameters of the bearing outer ring raceway on the radial runout of the outer ring raceway.

5. The rolling bearing rotation accuracy uncertainty analysis method considering raceway roundness error according to claim 4 is characterized in that: The implementation steps of rotation accuracy uncertainty analysis are as follows: Step 1: Use Gaussian mixture model (GMM) to model uncertainty of multi-peak random variables. The probability density function of the response function is expressed as follows: Where α n represents the coefficient of the nth Gaussian component, satisfying α n ≥0,φ(T|θ n ) represents the Gaussian probability density function of the nth component, where k represents the number of sub-models, μ n , denote the mean and variance respectively; Step 2: Calculate the statistical moment of the response function. According to the probability density function of each input random variable T, the statistical moment of the response function F = p(T) is calculated as follows: T=(T1,T2,T3,...T n ) Where m l represents the lth-order statistical moment of F, T represents the vector of n multimodal independent random variables, f T (T) represents the multi-peak joint probability density function of T, R n represents the domain of multidimensional integral, is the expectation operator; Step 3: The efficient ternary dimensionality reduction method can meet the calculation accuracy of high-order statistical moments in multi-peak random uncertainty analysis problems. By reducing the dimension and decomposing high-dimensional integrals, the calculation efficiency and accuracy can be improved. Step 4: After obtaining the first l-order statistical moments based on the above method, the maximum entropy loop (MEM) is used to estimate the probability distribution of the response function F and obtain the rotation accuracy uncertainty analysis results.

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