Reliability and sensitivity analysis method for interference fit between bearing and shaft

Abstract

The invention provides a reliability and sensitivity analysis method for interference fit of a bearing and a shaft, and the method comprises the steps: building a bearing-shaft interference fit model, and taking actual fit pressure as an index as a criterion for judging whether the interference fit of the bearing and the shaft is reliable or not based on plane stress and plane strain theories. And then a limit state function of bearing-shaft interference fit failure is established, and bearing-shaft interference fit reliability analysis is carried out through a four-moment reliability method (FMRM). When the bearing-shaft interference fit model is established, the influence of centrifugal force generated by rotation on the actual interference fit amount is considered, the method adopts the combination of a four-moment reliability method (FMRM), and when the probability distribution of a state function cannot be determined, the method greatly improves the calculation efficiency of a complex engineering problem, and the calculation efficiency of the bearing-shaft interference fit model is greatly improved. And guidance is provided for reliability analysis of complex problems when probability distribution is unknown.

Description

Technical Field

[0001] The invention belongs to the technical field of sensitivity analysis, and in particular relates to a reliability sensitivity analysis method for interference fit between a bearing and a shaft. Background Art

[0002] With the rapid development of modern industry, rotating machinery is shifting towards high speed and high precision. As the core component of rotating machinery, the bearing-rotor system also has very high requirements for reliability. The interference fit connection between the bearing and the shaft is a common connection method between the bearing and the shaft in the bearing-rotor system. Reasonable interference fit can ensure the stability of the bearing operation, increase the service life of the bearing, and reduce the occurrence of failures in rotating machinery. For the interference fit of the bearing and the shaft, the reliability can be described as the probability that the pressure between the shaft and the bearing is greater than 0 during operation, or the probability that the shaft and the bearing do not loosen during operation. In order to ensure the stable operation of the bearing, the reliability analysis of the interference fit of the bearing and the shaft must be carried out. Summary of the invention

[0003] The purpose of the present invention is to design a reliability sensitivity analysis method involving a bearing and shaft interference fit, improve the calculation efficiency of the bearing-shaft interference fit reliability analysis, develop the application of reliability theory in practical engineering, and provide certain theoretical guidance for designers during design.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A reliability sensitivity analysis method for interference fit between a bearing and a shaft, characterized in that: the method is as follows:

[0006] S1: Based on the influence of centrifugal force on the interference fit between bearings and shafts, the deformation of the shaft outer diameter and the bearing inner ring is obtained according to the plane stress and plane strain theory in elastic mechanics, and finally the actual interference fit amount between the bearing and shaft is obtained, and the bearing-shaft interference fit model is established;

[0007] S2: Obtain the actual assembly pressure P of the bearing inner ring and the shaft according to the bearing-shaft interference fit model;

[0008] S3: According to the actual assembly pressure P in S2, the limit state function g(X) of the bearing-shaft interference fit failure is established, the size parameters and material parameters of the shaft and bearing are substituted into the limit state function g(X), and the first four moments of the limit state function g(X) are solved by the fourth-order moment method. Based on the first four moments combined with the reliability theory, the reliability of the bearing-shaft interference fit model is solved;

[0009] S4: Reliability sensitivity analysis in S3: By analyzing the sensitivity of each random variable to the reliability of the bearing-shaft interference fit, the importance of each random variable to the reliability of the bearing-shaft interference fit can be obtained;

[0010] S5: The reliability sensitivity of each random variable is dimensionless, and the reliability sensitivity between each random variable is compared, which can more intuitively show the influence of each random variable on the reliability of the bearing-shaft interference fit.

[0011] Furthermore, the method for establishing the bearing-shaft interference fit model in S1 is as follows:

[0012] Step 1: Determine r1 and r2 as the inner radius and outer radius of the shaft respectively, r3 as the inner raceway radius, and di as the inner raceway diameter;

[0013] Step 2: Based on the elastic wall thickness ring theory, the axisymmetric plane stress theory is used to solve the stress deformation of the bearing inner ring;

[0014]

[0015] In the formula, σ r and σ θ denote radial stress and tangential stress respectively, ω represents rotation speed, ρ represents density, d is the derivative sign, and r refers to the general radius;

[0016] The elastic constitutive equation can be written as:

[0017]

[0018] In the formula, ε r and ε θ represent radial strain and tangential strain respectively, E and ν represent the elastic modulus and Poisson's ratio of the material respectively;

[0019] The geometric equation can be written as:

[0020]

[0021] Where s represents radial displacement;

[0022] Substituting equation (2) and equation (3) into equation (1), we can get the following equation:

[0023]

[0024] By solving the above equations, the radial displacement and radial stress of the bearing inner ring can be obtained:

[0025]

[0026] Where: C1 and C2 are the coefficients for solving the differential equation of equation (4), equation (5) refers to the radial displacement, and equation (6) refers to the radial stress;

[0027] Step 3: Assuming that the assembly pressure between the bearing inner ring and the shaft is P, the boundary condition formula of the bearing inner ring is written as:

[0028]

[0029] Substituting the boundary conditions into equation (6) yields:

[0030]

[0031] Compared with the inner ring of the bearing, the axial dimension of the shaft is much larger than its cross-sectional dimension and can be regarded as a long cylinder. According to the elasticity theory, the axisymmetric plane strain theory is applied to solve the stress and deformation of the shaft. By replacing the constants E and V in equations (5) and (6) with E / (1-v2) and v / (1-v), the radial displacement and stress of the shaft can be obtained:

[0032]

[0033] Similar to the inner ring of the bearing, the boundary condition formula of the shaft is written as:

[0034]

[0035] Substituting the boundary condition formula (11) into formula (10), we can obtain:

[0036]

[0037] Step 4: Assuming that the initial interference fit between the inner ring of the bearing and the shaft is Δ0, the actual interference fit Δ between the inner ring of the bearing and the shaft can be expressed as:

[0038]

[0039] Where: Refers to s in the above formula (5), which represents the radial displacement of the inner ring of the bearing. refers to the s in the above formula (9), which represents the radial displacement of the shaft; Δ ω The interference loss caused by centrifugal force can be expressed by the following formula:

[0040]

[0041] The actual assembly pressure P of the bearing inner ring and the shaft can be expressed as:

[0042]

[0043] Furthermore, the specific method process in S3 is as follows:

[0044] According to the strength-stress interference theory, since the limit pressure of the bearing-shaft interference fit is zero, the limit state equation g(X) of the assembly pressure P and reliability R can be expressed as:

[0045] g(X)=P-0=P (16)

[0046]

[0047] Where X=[X1,X2,…,X n ] T It is a parameter vector containing structural parameters and material parameters. When g(X) is greater than 0, it represents safety, and the rest represents failure.

[0048] If the random parameters in the design parameter vector X are independent of each other, assuming σ 2 =Var(g(X)), denote the mean, variance, third-order moment and fourth-order moment respectively; the first-order mean, first-order variance, first-order third-order moment and first-order fourth-order moment of g(X) can be expressed as

[0049]

[0050] Where: It refers to the partial derivative of g(X) with respect to the i-th variable in X.

[0051] When the first four moments are known, the fourth-order moment method can be used to estimate the reliability, and the reliability index is defined as

[0052]

[0053] Where: is the skewness coefficient of the state function g(X), is the kurtosis coefficient of the state function g(X), β SM is a reliability index based on the second-order moment, which can be expressed as

[0054]

[0055] In formula (23): E(·) refers to the mean, Var(·) refers to the variance;

[0056] The reliability index β is calculated using the fourth-order moment reliability method. FM Then, the reliability can be calculated as

[0057] R FM =Φ(β FM ) (twenty four)

[0058] in: is the standard normal distribution function.

[0059] Furthermore, the sensitivity of the reliability of the mechanical structure in S4 to the mean and variance of the design variable X vector can be expressed as:

[0060]

[0061] in for Sensitivity to the mean of vector X, for Variance sensitivity of vector X; the expressions on the right side of equations (25) and (26) can be expressed as

[0062]

[0063]

[0064] Refers to the probability density function of the normal distribution.

[0065] Furthermore, the reliability sensitivity of the mean and variance of each design variable X = [X1, X2, ..., Xn]T in S5 can be expressed after dimensionless sensitivity as:

[0066]

[0067] In equations (34) and (35), Var(X) represents the mean and variance of the design parameter vector X, R * , and Var(X) * Respectively represent the corresponding values

[0068] The following beneficial effects can be obtained through the above technical solution:

[0069] The invention provides a reliability sensitivity analysis method for a bearing-shaft interference fit, which establishes a bearing-shaft interference fit model, and based on the plane stress and plane strain theory, takes the actual fit pressure as an indicator as a criterion for whether the bearing-shaft interference fit is reliable, and then establishes a limit state function of the bearing-shaft interference fit failure, and then uses the fourth-order moment reliability method (FMRM) to perform a reliability analysis of the bearing-shaft interference fit. When establishing the bearing-shaft interference fit model, the influence of the centrifugal force generated by the rotation on the actual interference fit amount is considered, and the method is combined with the fourth-order moment reliability method (FMRM). When the probability distribution of the state function cannot be determined, this method greatly improves the calculation efficiency of complex engineering problems, and provides guidance for the reliability analysis of complex problems when the probability distribution is unknown. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1It is a flow chart;

[0071] Figure 2 It is a schematic diagram of the bearing-shaft interference fit;

[0072] Figure 3 It is the actual fit pressure of the bearing-shaft interference fit as the speed changes and the loosening speed diagram at each initial interference amount;

[0073] Figure 4 is the reliability diagram of the bearing-shaft interference fit;

[0074] Figure 5 It is the dimensionless mean sensitivity curve of each random variable and the mean sensitivity histogram of each variable under a single speed;

[0075] Figure 6 It is the dimensionless variance sensitivity curve of each random variable and the variance sensitivity histogram of each variable under a single speed. DETAILED DESCRIPTION

[0076] The present invention will be further described below in conjunction with the accompanying drawings:

[0077] like Figure 1-6 As shown, the present invention provides a reliability sensitivity analysis method for a bearing-shaft interference fit, which establishes a bearing-shaft interference fit model, and based on the plane stress and plane strain theory, takes the actual fitting pressure as an indicator as a criterion for whether the bearing-shaft interference fit is reliable, and then establishes a limit state function of the bearing-shaft interference fit failure, and then uses the fourth-order moment reliability method (FMRM) to perform reliability analysis of the bearing-shaft interference fit.

[0078] The specific analysis method is as follows:

[0079] Step 1: Consider the influence of centrifugal force on the interference fit between the bearing and the shaft during operation, solve the deformation of the shaft outer diameter and the bearing inner ring according to the plane stress and plane strain theory in elastic mechanics, obtain the actual interference fit amount, and establish the bearing-shaft interference fit model. The details are as follows:

[0080] In order to prevent micro-wear caused by the relative movement between the inner ring of the bearing and the shaft, the shaft and the bearing are generally connected by an interference fit. In addition, at high speeds, the interference between the bearing and the shaft will change due to centrifugal force. Considering this factor, a bearing-shaft interference fit model is established, such as Figure 2 As shown, r1 and r2 are the inner radius and outer radius of the shaft respectively, r3 is the inner raceway radius, and di is the inner raceway diameter.

[0081] Since the thickness of the inner ring of the bearing is smaller than the radius, according to the elastic wall thickness ring theory, the axisymmetric plane stress theory can be used to solve the stress deformation of the inner ring of the bearing:

[0082]

[0083] In the formula, σ r and σ θ They represent radial stress and tangential stress respectively, ω represents the rotational speed, and ρ represents the density.

[0084] The elastic constitutive equation can be written as:

[0085]

[0086] In the formula, ε r and ε θ They represent radial strain and tangential strain respectively, E and v represent the elastic modulus and Poisson's ratio of the material respectively.

[0087] The geometric equation can be written as:

[0088]

[0089] Where s represents the radial displacement.

[0090] Substituting equation (2) and equation (3) into equation (1), we can get the following equation:

[0091]

[0092] By solving the above equations, the radial displacement and radial stress of the bearing inner ring can be obtained:

[0093]

[0094] Where: C1 and C2 are the coefficients for solving the differential equation of equation (4), equation (5) refers to the radial displacement, and equation (6) refers to the radial stress;

[0095] Assuming that the assembly pressure between the bearing inner ring and the shaft is P, the boundary condition formula of the bearing inner ring is written as:

[0096]

[0097] Substituting the boundary conditions into equation (6) yields:

[0098]

[0099] Compared with the inner ring of the bearing, the axial dimension of the shaft is much larger than its cross-sectional dimension and can be regarded as a long cylinder. According to the elasticity theory, the axisymmetric plane strain theory is applied to solve the stress and deformation of the shaft. By replacing the constants E and V in equations (5) and (6) with E / (1-v2) and v / (1-v), the radial displacement and stress of the shaft can be obtained:

[0100]

[0101] Similar to the inner ring of the bearing, the boundary condition formula of the shaft is written as:

[0102]

[0103] Substituting the boundary condition formula (11) into formula (10), we can obtain:

[0104]

[0105] Assuming that the initial interference between the inner ring of the bearing and the shaft is Δ0, the actual interference between the inner ring of the bearing and the shaft can be expressed as:

[0106]

[0107] Where: Refers to s in the above formula (5), which represents the radial displacement of the inner ring of the bearing. refers to the s in the above formula (9), which represents the radial displacement of the shaft; Δ ω The interference loss caused by centrifugal force can be expressed by the following formula:

[0108]

[0109] The actual assembly pressure P of the bearing inner ring and the shaft can be expressed as:

[0110]

[0111] Step 2: According to the above-mentioned fitting pressure, establish the limit state function g(X) of the bearing-shaft interference fit failure, substitute the size parameters and material parameters of the shaft and bearing into the above limit state function, and solve the first four moments of the above limit state function g(X) by the fourth-order moment method. Based on the first four moments combined with reliability theory, solve the reliability of the bearing-shaft interference fit model.

[0112] The bearing-shaft interference fit pressure is an important indicator for measuring the reliability of the bearing-rotor system. According to the strength-stress interference model, since the limit pressure of the bearing-shaft interference fit is zero, the limit state equation g(X) of the assembly pressure P and reliability R can be expressed as:

[0113] g(X)=P-0=P (16)

[0114] R=P[g(X)>0] (17)

[0115] Where X=[X1,X2,…,X n ] T is a parameter vector containing structural parameters and material parameters. When g(X) is greater than 0, the system is safe, and the rest are faults.

[0116] If the random parameters in the design parameter vector X are independent of each other, assuming σ 2 =Var(g(X)), denote the mean, variance, third-order moment and fourth-order moment respectively; the first-order mean, first-order variance, first-order third-order moment and first-order fourth-order moment of g(X) can be expressed as

[0117]

[0118] When the first four moments are known, the fourth-order moment method can be used to estimate the reliability, and the reliability index is defined as

[0119]

[0120] In the formula is the skewness coefficient of the state function g(X), is the kurtosis coefficient of the state function g(X), β SM is a reliability index based on the second-order moment, which can be expressed as

[0121]

[0122] The reliability index β is calculated using the fourth-order moment reliability method. FM Then, the reliability can be calculated as

[0123] R FM =Φ(β FM ) (twenty four)

[0124] in is the standard normal distribution function.

[0125] Step 3: Conduct reliability sensitivity analysis. By analyzing the sensitivity of each random parameter to the reliability of the bearing-shaft interference fit, the importance of each parameter to the reliability of the bearing-shaft interference fit can be obtained.

[0126] The sensitivity of mechanical structure reliability to the mean and variance of design variable X vector can be expressed as:

[0127]

[0128] in for Sensitivity to the mean of vector X, for Variance sensitivity of vector X. The expressions on the right side of equations (25) and (26) can be expressed as

[0129]

[0130] Step 4: In order to compare the reliability sensitivity between the design variables, the reliability sensitivity of each random variable is dimensionless.

[0131] In the design stage of mechanical structures, multiple design parameters are often selected, and the impact of various factors on the failure of mechanical structures is different. Therefore, in the reliability sensitivity study, it is of certain practical significance to sort the importance of various parameters. In fact, due to the non-uniformity of parameter units, the numerical results of the reliability sensitivity of various parameters cannot be directly compared, which brings certain difficulties to the reliability sensitivity analysis of mechanical structures. Therefore, it is necessary to perform dimensionless processing on the reliability sensitivity of various parameters.

[0132] The reliability sensitivity of the system to the mean and variance of each design variable X = [X1, X2, ..., Xn]T can be expressed after dimensionless sensitivity as

[0133]

[0134] In equations (34) and (35), X, Var(X) represents the mean and variance of the design parameter vector X, R * , and Var(X) * Represent the corresponding values ​​respectively.

[0135] Example:

[0136] This example takes deep groove ball bearing 209 as the research object, and its parameters are shown in the following table:

[0137] Table 1 Specific parameters of deep groove ball bearing 209

[0138]

[0139] In order to improve the stability of the connection between the inner ring of the bearing and the shaft, an interference fit is used. Figure 3 As shown in (a), as the speed increases, the deformation of the inner ring is greater than the deformation of the shaft, and the actual fit pressure between the inner ring and the shaft gradually decreases as the speed increases. When the interference fit is equal to zero, the corresponding speed is the loosening speed. Loosening has an impact on the stability of the bearing-rotor system. Figure 3 (b) The corresponding loosening speeds for different initial interference fits are given, providing theoretical guidance for the design of the initial interference fit between the bearing inner ring and the shaft.

[0140] In the bearing-rotor system, as the rotor rotates, the bearing-shaft interference fit decreases with the increase of speed, resulting in a decrease in the interference fit pressure between the inner ring of the bearing and the shaft, which eventually leads to loosening and system failure. In some cases, loosening occurs when the interference fit is equal to zero, but under actual working conditions, the system parameters are uncertain, which leads to the uncertainty of the actual interference fit pressure. This paper selects the parameter X=[d i Δ0E Vρr1 r2] is used as the design variable. The reliability of the system under various working conditions is studied based on the fourth-order moment reliability method (FMRM) theory, and the influence of each parameter on the system reliability is analyzed. The probability properties of each random variable are shown in Table 2:

[0141] Table 2 Probability properties of each random variable

[0142]

[0143] In this example, in order to study the influence of interference mean and variance on the reliability of bearing-shaft interference fit, it is assumed that the initial interference coefficient is 0.8% and the initial interference amount mean is 10μm. The variation law of bearing-shaft interference fit reliability with rotor speed is studied through numerical examples. The results are shown in Figure 4 As shown in the figure, when the speed is low, the bearing-shaft interference fit is always reliable, and the reliability is 1. As the speed increases, the reliability begins to decrease and eventually becomes 0, at which point the system is in a failure state.

[0144] In order to describe the influence of each random variable on reliability, the reliability sensitivity of each random variable will be further calculated. At the same time, in order to facilitate the comparison of the sensitivity of each parameter, the reliability sensitivity is dimensionless and calculated using the FMRM method to obtain the mean reliability sensitivity and variance reliability sensitivity of each random variable at different speeds, as shown in Figure 5 and Figure 6 As shown in the figure, it can be seen that when a certain speed is reached, the reliability sensitivity curve begins to change, which is consistent with Figure 4 The reliability curves shown have similar trends. When the reliability sensitivity value is positive, it indicates that the random variable is positively correlated with the reliability of the rotor system, and the reliability of the system increases with the increase of the mean value of the random variable. When the reliability sensitivity is negative, it indicates that the random variable is negatively correlated with the reliability of the rotor system, and the reliability of the system decreases with the increase of the mean value of the random variable.

[0145] from Figure 5It can be seen from (a) that when the mean sensitivity curve begins to change, the mean sensitivity of r1, Δ0, and E is positive, that is, as the mean of these variables increases, the system reliability increases; d i The mean sensitivity of , V, and ρ is negative, that is, as the mean of these variables increases, the system reliability decreases. Due to the nonlinearity of the system, the reliability sensitivity curve of the r2 mean is not always positive or negative, but in actual working conditions, the change of the reliability sensitivity before the bearing-shaft interference fit loosens should be considered. At this time, the reliability sensitivity of the r2 mean is negative, that is, as the r2 mean increases, the system reliability decreases. In order to better compare the influence of each random variable on the bearing-shaft interference fit reliability, Figure 5 (b) shows the histogram of the influence of various random variables on the reliability of bearing-shaft interference fit when the rotor speed is 35200r / min. It can be seen from the figure that d i , Δ0, r1, and r2 have a greater impact on the reliability of the bearing-shaft interference fit, while the parameters E, V, and ρ have a smaller impact on the reliability of the bearing-shaft interference fit. Based on this finding, each parameter should be reasonably controlled during processing and assembly.

[0146] Figure 6 (a) is the variance sensitivity of each random variable to the reliability of the bearing-shaft interference fit. From the figure we can see that d i The variance of has the greatest impact on reliability, followed by r1, Δ0, r2, ρ, E and v. When the rotor speed changes near the loosening speed, the variance sensitivity of each random variable is negative, which shows that no matter how large the speed is at this time, the variance sensitivity of each random variable is negatively correlated with the system reliability. At this time, as the variance of each random variable decreases, the system reliability will increase. It can be seen that in order to ensure the reliability of the system under actual working conditions, the variance of each variable needs to be reduced within a reasonable range. In order to intuitively compare the degree of influence of each random variable on reliability, Figure 6 (b) shows the histogram of the influence of various random variables on the reliability of bearing-shaft interference fit when the rotor speed is 35600r / min, d i The variance of , Δ0, r1 and r2 has a greater impact on the reliability of the system, while the variance of E, v and ρ has a smaller impact on the reliability of the system. From the above analysis, it can be seen that the changes of sensitive parameters should be strictly controlled during the design, manufacture, assembly and use of the rotor system.

[0147] The above are all preferred embodiments of the present invention. For ordinary technicians in this technical field, without departing from the principle of the present invention, various equivalent modifications to the present invention belong to the protection scope of the claims attached to this application.

Claims

1. A reliability sensitivity analysis method for interference fit between a bearing and a shaft, characterized by: The method is as follows: S1: Based on the influence of centrifugal force on the interference fit between bearings and shafts, the deformation of the shaft outer diameter and the bearing inner ring is obtained according to the plane stress and plane strain theory in elastic mechanics, and finally the actual interference fit amount between the bearing and shaft is obtained, and the bearing-shaft interference fit model is established; S2: Obtain the actual assembly pressure P of the bearing inner ring and the shaft according to the bearing-shaft interference fit model; S3: According to the actual assembly pressure P in S2, the limit state function g(X) of the bearing-shaft interference fit failure is established, the size parameters and material parameters of the shaft and bearing are substituted into the limit state function g(X), and the first four moments of the limit state function g(X) are solved by the fourth-order moment method. Based on the first four moments combined with the reliability theory, the reliability of the bearing-shaft interference fit model is solved; S4: Reliability sensitivity analysis in S3: By analyzing the sensitivity of each random variable to the reliability of the bearing-shaft interference fit, the importance of each random variable to the reliability of the bearing-shaft interference fit can be obtained; S5: The reliability sensitivity of each random variable is dimensionless, and the reliability sensitivity between each random variable is compared, which can more intuitively show the influence of each random variable on the reliability of the bearing-shaft interference fit.

2. The reliability sensitivity analysis method of the interference fit between a bearing and a shaft according to claim 1 is characterized in that: The method for establishing the bearing-shaft interference fit model in S1 is as follows: Step 1: Determine r1 and r2 as the inner radius and outer radius of the shaft respectively, r3 as the inner raceway radius, and di as the inner raceway diameter; Step 2: Based on the elastic wall thickness ring theory, the axisymmetric plane stress theory is used to solve the stress deformation of the inner ring of the bearing; In the formula, σ r and σ θ denote radial stress and tangential stress respectively, ω represents rotation speed, ρ represents density, d is the derivative sign, and r refers to the general radius; The elastic constitutive equation can be written as: In the formula, ε r and ε θ represent radial strain and tangential strain respectively, E and V represent the elastic modulus and Poisson's ratio of the material respectively; The geometric equation can be written as: Where s represents radial displacement; Substituting equation (2) and equation (3) into equation (1), we can get the following equation: By solving the above equations, the radial displacement and radial stress of the bearing inner ring can be obtained: Where: C1 and C2 are the coefficients for solving the differential equation of equation (4), equation (5) refers to the radial displacement, and equation (6) refers to the radial stress; Step 3: Assuming that the assembly pressure between the bearing inner ring and the shaft is P, the boundary condition formula of the bearing inner ring is written as: Substituting the boundary conditions into equation (6) yields: Compared with the inner ring of the bearing, the axial dimension of the shaft is much larger than its cross-sectional dimension and can be regarded as a long cylinder. According to the elasticity theory, the axisymmetric plane strain theory is applied to solve the stress and deformation of the shaft. By replacing the constants E and V in equations (5) and (6) with E / (1-v2) and v / (1-v), the radial displacement and stress of the shaft can be obtained: Similar to the inner ring of the bearing, the boundary condition formula of the shaft is written as: Substituting the boundary condition formula (11) into formula (10), we can obtain: Step 4: Assuming that the initial interference fit between the inner ring of the bearing and the shaft is Δ0, the actual interference fit Δ between the inner ring of the bearing and the shaft can be expressed as: Where: Refers to s in the above formula (5), which represents the radial displacement of the inner ring of the bearing. refers to the s in the above formula (9), which represents the radial displacement of the shaft; Δ ω The interference loss caused by centrifugal force can be expressed by the following formula: The actual assembly pressure P of the bearing inner ring and the shaft can be expressed as:

3. A reliability sensitivity analysis method for interference fit between a bearing and a shaft according to claim 1 or 2, characterized in that: The specific method process in S3 is as follows: According to the strength-stress interference theory, since the limit pressure of the bearing-shaft interference fit is zero, the limit state equation g(X) of the assembly pressure P and reliability R can be expressed as: g(X)=P-0=P (16) Where X=[X1,X2,…,Xn] T It is a parameter vector containing structural parameters and material parameters. When g(X) is greater than 0, it represents safety, and the rest represents failure. If the random parameters in the design parameter vector X are independent of each other, assuming σ 2 =Var(g(X)), denote the mean, variance, third-order moment and fourth-order moment respectively; the first-order mean, first-order variance, first-order third-order moment and first-order fourth-order moment of g(X) can be expressed as Where: It refers to the partial derivative of g(X) with respect to the i-th variable in X. When the first four moments are known, the fourth-order moment method can be used to estimate the reliability, and the reliability index is defined as Where: is the skewness coefficient of the state function g(X), is the kurtosis coefficient of the state function g(X), β SM is a reliability index based on the second-order moment, which can be expressed as In formula (23): E(·) refers to the mean, Var(·) refers to the variance; The reliability index β is calculated using the fourth-order moment reliability method. FM Then, the reliability can be calculated as R FM =Φ(β FM ) (24) in: is the standard normal distribution function.

4. The reliability sensitivity analysis method of the interference fit between a bearing and a shaft according to claim 3 is characterized in that: The sensitivity of the reliability of the mechanical structure in S4 to the mean and variance of the design variable X vector can be expressed as: in for Sensitivity to the mean of vector X, for Variance sensitivity of vector X; the expressions on the right side of equations (25) and (26) can be expressed as Refers to the probability density function of the normal distribution.

5. The reliability sensitivity analysis method of the interference fit between a bearing and a shaft according to claim 4 is characterized in that: The reliability sensitivity of the mean and variance of each design variable X = [X1, X2, ..., Xn]T in S5 can be expressed after dimensionless sensitivity as: In equations (34) and (35), X, Var(X) represents the mean and variance of the design parameter vector X, R * ,σ * X and Var(X) * Represent the corresponding values ​​respectively.

Images