Evaluation method for quantifying discrete degree of uncertain interference fit parameters on fatigue life of bearing

Abstract

The invention discloses a method for evaluating the dispersion degree of a bearing fatigue life by quantizing an uncertain interference fit parameter, and the method comprises the following steps: 1, analyzing the uncertain interference magnitude in a shaft-hole interference fit model based on a Chebyshev interval method, and obtaining an interpolation point; step 2, combining a quasi-statics model of the angular contact ball bearing based on the no-raceway control hypothesis with a shaft-hole interference fit model, and determining ball-raceway contact forces under different interference magnitudes corresponding to the interpolation points; and Step 3, analyzing the values of the ball-raceway contact forces under different interference magnitudes corresponding to the interpolation points in a ball-raceway rolling contact fatigue life model to obtain the maximum Von-Mises stress and the corresponding position depth, and quantifying the influence of uncertain parameters on the dispersion degree of the bearing life. According to the method, the specific influence of the uncertainty interference fit parameters on the bearing fatigue life dispersion degree under different working condition parameters can be considered.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical engineering, and particularly relates to a method for evaluating the influence of uncertain interference fit parameters on the dispersion degree of bearing fatigue life. BACKGROUND

[0002] As the core component of rotating equipment, the accurate prediction of the fatigue life of rolling bearings is crucial to the reliability of mechanical systems. Currently, the fatigue life of rolling bearings is mainly estimated based on the Lundberg-Palmgren theory through the rated dynamic load and the correction coefficient; the material failure under cyclic loading is analyzed by applying the stress-life (S-N curve), strain-life or fracture mechanics method; the dispersion of bearing life is evaluated by statistical methods (such as Weibull distribution) to quantify the relationship between reliability and service life. Although existing research has made progress in predicting the fatigue life of rolling bearings, it mainly relies on probability distribution to evaluate the fatigue life, and it is difficult to determine the specific influence of non-probabilistic uncertain parameters on the fatigue life under complex working conditions. SUMMARY

[0003] Based on the bearing quasi-static model, the shaft-hole interference fit model, and the ball-race contact fatigue life model, and combined with Chebyshev interpolation fitting technology, the application provides a method for evaluating the influence of uncertain interference fit parameters on the dispersion degree of bearing fatigue life, which can consider the specific influence of uncertain interference fit parameters on the dispersion degree of bearing fatigue life under different working condition parameters.

[0004] To achieve the above-mentioned purposes, the technical solutions adopted by the application are as follows:

[0005] A method for evaluating the influence of uncertain interference fit parameters on the dispersion degree of bearing fatigue life, the evaluation method is as follows:

[0006] Step 1: Based on the Chebyshev interval method, the uncertain interference amount in the shaft-hole interference fit model is analyzed to obtain the interpolation points;

[0007] Step 2: Based on the quasi-static model of angular contact ball bearings without raceway control assumption and the shaft-hole interference fit model, the ball-race contact force Q is determined ij , Q oj ;

[0008] Step 3: Based on the ball-race rolling contact fatigue life model, the influence of uncertain parameters on the dispersion degree of bearing life is quantified.

[0009] Further, the analysis method of Step 1 is as follows:

[0010] Chebyshev interval analysis method is proposed based on Chebyshev polynomials, assuming that the interval variable is △ I , the upper and lower limits of which are represented by △ U and △ L respectively, then the average interference amount can be represented as △ 0

[0011]

[0012] To describe the degree of uncertainty, the coefficient of variation ε is introduced, and the uncertain interference amount in interference fit can be represented as

[0013] △ I = △ 0 (1+3ε[-1,1]) (2)

[0014] According to Chebyshev interpolation theory, the output response F of the rotor system under the influence of the uncertainty of the interference amount can be approximated as

[0015]

[0016] where T is the Chebyshev polynomial, i represents the order of the polynomial, and ξ is the normalized form of the interval variable, which can be represented as

[0017]

[0018] is the Chebyshev orthogonal polynomial, and its recursive form can be represented as

[0019]

[0020] f i is the coefficient of the Chebyshev series, which can be calculated by

[0021]

[0022] where the variable ξ can be represented as

[0023]

[0024] t is the number of interpolation points, and by calculating the zero points of the Chebyshev polynomial, the corresponding interpolation points can be obtained as

[0025]

[0026] Further, the method of Step 2 is as follows:

[0027] ​In the quasi-static model of angular contact ball bearing without raceway control, the shaft-hole interference fit model is coupled to predict the mechanical behavior of bearing more accurately, r1, r2, r3 represent the inner radius, outer radius and inner raceway radius of bearing groove, respectively. The equilibrium equation can be obtained by the axisymmetric plane stress theory as

[0028]

[0029] where σ r ,σ θ ,ω,ρ are the radial stress, tangential stress, rotating speed and density, respectively;

[0030] The elastic constitutive equation is

[0031]

[0032] where ε r ,ε θ ,ν, E are the radial strain, tangential strain, Poisson's ratio and elastic modulus, respectively. Therefore, the geometric deformation equation can be expressed as

[0033]

[0034] where s is the assembly deformation. Substituting equation (10) and equation (11) into equation (9), the differential equation is obtained as

[0035]

[0036] The radial displacement and stress can be obtained by solving equation (12) as

[0037]

[0038] Assuming that the stress at r1 is P1, according to the axisymmetric plane stress theory, the stresses at r2 and r3 are -P1 and 0, respectively. Therefore, the radial deformation of inner ring at r2 and r3 can be expressed as

[0039]

[0040] where the elastic deformation coefficients C1, C2 can be expressed as

[0041]

[0042] Similarly, the stress and deformation of shaft are solved according to the axisymmetric plane stress theory. At this time, the elastic modulus and Poisson's ratio should be replaced by E / (1-ν 2 ) and ν / (1-ν), respectively. The elastic deformation of shaft at r2 is

[0043]

[0044] Where the elastic deformation coefficients C3, C4 can be expressed as

[0045]

[0046] Let the initial interference be Δ0, then the actual interference Δ is

[0047]

[0048] Where Δc is the loss interference caused by centrifugal force, which can be expressed as

[0049]

[0050] The assembly pressure can be expressed as

[0051]

[0052] The radial displacement of the inner ring at position is

[0053]

[0054] Therefore, in the shaft-hole interference fit model, the uncertainty of the interference fit between the bearing and the shaft changes the size of the bearing component, i.e. the change of r2, r3, which leads to the change of the initial radial clearance, thereby affecting the change of the initial contact angle in the quasi-static model of angular contact ball bearings. Assuming that the bearing outer ring is fixed and the inner ring rotates with the shaft, the contact between the ball and the raceway is purely elastic deformation, the geometric constraint equation and the load balance equation of the jth ball are obtained:

[0055]

[0056] Where A 1j ,A 2j can be expressed as

[0057]

[0058] δ ij ,δ oj are the elastic deformations of the ball when it contacts the inner and outer rings, respectively, and α ij ,α oj are the contact angles of the ball with the inner and outer rings, respectively, which can be expressed as

[0059]

[0060] Assuming that the gyroscopic moment of the ball is affected by the friction when it contacts the inner and outer raceways, and the friction coefficients of the ball with the inner and outer raceways are the same, we can get

[0061]

[0062] The gyroscopic moment and the centrifugal force can be expressed as

[0063]

[0064] Assuming no macroscopic slip between the ball and the raceway, the ball rotational speed ω cj and the rotational speed ω bj can be expressed as

[0065]

[0066] where φj is the pitch angle of the jth ball, which can be expressed as

[0067]

[0068] When the axial load is insufficient, not all balls participate in load transmission, so an inequality is introduced to represent the difference between the initial and final ball-inner ring center distances If the inequality holds, the ball has left the inner raceway, and in this case it is assumed that the ball-outer ring contact angle is exactly zero, and Q oj -F cj = 0, according to the Hertz contact theory, the ball-raceway contact force can be expressed as

[0069]

[0070] where K is the stiffness coefficient between the ball and the raceway. According to the load analysis of the inner ring, the force balance equation can be expressed as

[0071]

[0072] where the position angle of the ball

[0073] Integrating equations (22)-(30), there are δ x , δ y , δ z , θ x , θ y , δ ij , δ oj , X 1j , X 2j 9 variables, where the main variables are (δ x , δ y , δ z , θ x , θ y ), and the auxiliary variables are (δ ij , δ oj , X 1j , X 2j); first, assume the value of the given primary variable into the above formula, and then update the auxiliary variable by Newton iteration method, finally, put the obtained auxiliary variable result into the above formula, and update the primary variable by iteration to get the solution of all unknown variables, and put all the solutions into formula (29) to get the ball-raceway contact force Q ij , oj .

[0074] Further, the method of Step 3 is as follows:

[0075] Based on the Ioannides fatigue life model and the stress volume integral simplification method, there are

[0076]

[0077] where N is the stress cycle number of reliability S, σ eq is the maximum equivalent stress, e and c are the Weibull slope and stress index, V is the integral volume, is the volume damage constant, a and b are the major and minor axes of the contact ellipse, z is the position depth corresponding to the maximum subsurface stress, and h is the position depth index;

[0078] Taking the inner raceway as an example, the relationship between the contact fatigue life of the jth ball and a, b, z, σ eq is obtained from formula (31) as

[0079]

[0080] To get the contact fatigue life of the jth ball and the inner raceway, the maximum value of the equivalent stress needs to be calculated, and the position depth and the major and minor axes of the contact ellipse corresponding to the maximum value need to be determined. Since the shaft-hole interference fit is uncertain, a, b, z, σ eq and L ij are uncertain; in the RCF life model of ball-raceway contact, the major and minor axes of the contact ellipse are taken as the x and y axes, and the radial direction of the raceway is taken as the z axis. For any point on the contact surface, the normal, tangential and axial loads can be represented as

[0081] P N = Pdxdy, P T = Pf T dxdy, P A = Pf A dxdy (33)

[0082] where f A , f T are the axial and tangential friction coefficients. In the case of y1 = 0, the general method for determining the stress tensor components of any point can be represented as

[0083]

[0084] where For the convenience of integral calculation, each parameter should be dimensionless, using ξ = x / z, η = y / z, k = b / a, instead of x, y, z, then the normal, tangential and axial loads can be expressed as

[0085]

[0086]

[0087] The maximum Von-Mises stress is

[0088]

[0089] where ν is Poisson's ratio, k is the elliptic parameter, Take the inner raceway as an example, the contact ellipse long and short semi-axes are

[0090]

[0091] where κ is the elliptic eccentricity parameter, E is the first kind of complete elliptic integral, D is the ball diameter, d m is the pitch diameter, α 0 is the initial contact angle, f i is the inner raceway groove curvature; record the position coordinates corresponding to the maximum stress (σ vmi,x , σ vmi,y ), then z ij = b ij × |Z(σ vmi,x , σ vmi,y )|, put all the parameters obtained into equation (32) to determine L ij , it should be noted that, since the shaft-hole interference fit is uncertain, a, b, z, σ eq and L ij are uncertain, the outer raceway is the same, and because the contact fatigue life formula of the rolling bearing is

[0092]

[0093] Put all the uncertain interference fit parameters calculated at the Chebyshev interpolation points into equation (43) to get the overall life L b of the rolling bearing, it is obvious that, since the shaft-hole interference fit is uncertain, the overall life of the rolling bearing is also uncertain, denoted as where L b lowL b up respectively represent the upper limit and lower limit of the overall life of the rolling bearing, in order to evaluate the dispersion degree of the life of the rolling bearing, an uncertainty formula of the uncertain but bounded interval [L b low L b up The uncertainty formula of the uncertain but bounded interval [L

[0094]

[0095] The relationship between the input and output uncertainties can be obtained from formula (2) and formula (44) as β = 3ε;

[0096] Based on the Chebyshev interpolation fitting technology, the overall life L b of the rolling bearing corresponding to the shaft-hole uncertain interference fit parameter at the Chebyshev interpolation point is taken as the interpolation object to obtain an approximate expression of the overall life of the rolling bearing, and then the upper and lower limits L b up L b low Finally, by changing the parameters in the quasi-static model, the influence of each parameter on the dispersion degree of the life of the rolling bearing is discussed by using formula (44).

[0097] The above technical solutions can achieve the following beneficial effects:

[0098] The present application combines the Chebyshev interpolation fitting technology, considers the influence of various parameters such as axial load, radial load and rotating speed on the dispersion of bearing fatigue life under uncertain interference fit parameters, realizes the direct quantification of the influence of uncertain parameters on the dispersion degree of bearing fatigue life through the derived uncertainty formula, solves the problem that the traditional method relies on statistical distribution (such as Weibull distribution) to evaluate the life dispersion, and it is difficult to consider the uncertainty of bearing life under uncertain parameters, and improves the fatigue life evaluation and reliability of the rolling bearing. BRIEF DESCRIPTION OF DRAWINGS

[0099] Figure 1 is a schematic diagram of the shaft-hole fit with uncertain interference amount;

[0100] Figure 2 is a schematic diagram of the ball-race contact geometry and force diagram;

[0101] Figure 3 is a schematic diagram of the ball-race Hertz point contact;

[0102] Figure 4 is a diagram of the relationship between the axial load and the dispersion degree of the life of the bearing. DETAILED DESCRIPTION

[0103] The application is further described below in conjunction with the accompanying drawings:

[0104] As Figures 1-4 shown, a method for quantitatively evaluating the influence of uncertain interference fit parameters on the dispersion of bearing fatigue life, the method is as follows:

[0105] Step 1: Based on Chebyshev interval method, the uncertain interference amount in shaft-hole interference fit model is analyzed to obtain the interpolation point, the specific implementation is as follows:

[0106] In the shaft-hole interference fit model, due to the existence of tolerance before shaft-hole fit, the interference amount during interference fit is uncertain. Based on Chebyshev polynomial, Chebyshev interval analysis method is proposed. Assuming that the interval variable is △ I , the upper and lower limits are represented by △ U and △ L respectively, then the average interference amount can be represented as △ 0

[0107]

[0108] To describe the uncertainty, the coefficient of variation ε is introduced. In the interference fit, the uncertain interference amount can be represented as

[0109] △ I = △ 0 (1+3ε[-1,1]) (2)

[0110] According to the Chebyshev interpolation theory, the output response F of the rotor system under the influence of uncertain interference amount can be approximated as

[0111]

[0112] Where T is the Chebyshev polynomial, i represents the order of the polynomial, and ξ is the normalized form of the interval variable, which can be represented as

[0113]

[0114] is the Chebyshev orthogonal polynomial, and its recursive form can be represented as

[0115]

[0116] f i is the coefficient of Chebyshev series, which can be calculated by the following formula

[0117]

[0118] Where variable ξ can be represented as

[0119] ​

[0120] Let t be the number of interpolation points. By calculating the zeros of the Chebyshev polynomial, the corresponding interpolation points can be obtained.

[0121]

[0122] Step 2: In the conventional quasi-static model, a shaft-bore interference fit model needs to be coupled. Because the uncertainty of the shaft-bore interference fit will cause a change in the inner raceway groove bottom radius r3, indirectly affecting the change in the initial contact angle in the quasi-static model of the angular contact ball bearing, and thus affecting the value of the ball-raceway contact force. Therefore, this step, based on the quasi-static model of the angular contact ball bearing without raceway control assumptions, combines the shaft-bore interference fit model to determine the ball-raceway contact force Q under the corresponding interference at each interpolation point. ij Q oj The specific implementation method is as follows:

[0123] In the quasi-static model of an angular contact ball bearing with the raceway-free control assumption (i.e., the gyroscopic torque of the ball is provided by the contact between the ball and the inner and outer raceways), a shaft-bore interference fit model needs to be coupled. Figure 1 To more accurately predict bearing mechanical behavior, in Figure 1 In the equation, r1, r2, and r3 represent the inner radius, outer radius, and inner raceway radius of the bearing groove, respectively. The equilibrium equation can be obtained from the axisymmetric plane stress theory as follows:

[0124]

[0125] Where σ r ,σ θ ω and ρ represent radial stress, tangential stress, rotational speed, and density, respectively.

[0126] And because the elastic constitutive equation is

[0127]

[0128] Where ε r ,ε θ Let ν and E represent the radial strain, tangential strain, Poisson's ratio, and elastic modulus, respectively. Therefore, the geometric deformation equation can be expressed as:

[0129]

[0130] Where s is the assembly deformation. Substituting equations (10) and (11) into equation (9) yields the differential equation.

[0131]

[0132] By solving equation (12), the radial displacement and stress can be obtained as follows:

[0133]

[0134] Assume the stress at r1 is P1, according to the axisymmetric plane stress theory, the stresses at r2 and r3 are -P1 and 0 respectively. Therefore, the radial deformation of the inner ring at r2 and r3 can be expressed as

[0135]

[0136] Where the elastic deformation coefficients C1, C2 can be expressed as

[0137]

[0138] Similarly, according to the axisymmetric plane stress theory to solve the stress and deformation of the shaft, the elastic modulus and Poisson's ratio should be replaced with E / (1-ν 2 ) and ν / (1-ν), then the elastic deformation of the shaft at r2 is

[0139]

[0140] Where the elastic deformation coefficients C3, C4 can be expressed as

[0141]

[0142] Let the initial interference be △0, then the actual interference △ is

[0143]

[0144] Where is the loss of interference caused by centrifugal force, which can be expressed as

[0145]

[0146] The assembly pressure can be expressed as

[0147]

[0148] The radial displacement of the inner ring at position is

[0149]

[0150] Therefore, in the shaft-hole interference fit model, the uncertainty of the interference fit between the bearing and the shaft changes the size of the bearing components (the change of r2, r3), which leads to the change of the initial radial clearance, thereby affecting the change of the initial contact angle in the quasi-static model of the angular contact ball bearing Figure 2 ) Assuming that the outer ring of the bearing is fixed and the inner ring rotates with the shaft, the contact between the ball and the raceway is purely elastic deformation, according to Figure 2 the geometric constraint equation and the load balance equation of the jth ball are obtained:

[0151]

[0152] where A 1j , A 2j may be expressed as

[0153]

[0154] δ ij , δ oj are the elastic deformations of the ball and inner and outer raceways, respectively, and a ij , a oj are the contact angles of the ball with the inner and outer raceways, respectively, and may be expressed as

[0155]

[0156] Assuming that the gyroscopic moment of the ball is influenced by the friction forces when the ball is in contact with the inner and outer raceways, and that the friction coefficients of the ball with the inner and outer raceways are the same, it follows that

[0157]

[0158] The gyroscopic moment and the centrifugal force can be expressed as

[0159]

[0160] Assuming that there is no macroscopic slip between the ball and the raceways, the rotational speed ω cj and the spin speed ω bj may be expressed as

[0161]

[0162] where φj is the pitch angle of the jth ball, and may be expressed as

[0163]

[0164] In the above equation

[0165] When the axial load is insufficient, not all balls participate in load transmission, and therefore an inequality is introduced that represents the difference between the initial and final ball-inner raceway center distances (see Figure 2 ). If the inequality is valid, the ball has left the inner raceway, and in this case it is assumed that the contact angle of the ball with the outer raceway is exactly zero, and it follows that Q oj - F cj = 0. According to the Hertz contact theory, the ball-raceway contact force can be expressed as

[0166] Q ij = K ij δij 1.5 Q oj = K oj δ oj 1.5 (29)

[0167] where K is the stiffness coefficient between the ball and the raceway. According to the load analysis of the inner ring, the force balance equation can be expressed as

[0168]

[0169] where the position angle of the ball is

[0170] Integrating equations (22)-(30), there are δ x , δ y , δ z , θ x , θ y , δ ij , δ oj , X 1j , X 2j 9 variables, in which the main variables are (δ x , δ y , δ z , θ x , θ y ), and the auxiliary variables are (δ ij , δ oj , X 1j , X 2j ). First, assume that the values of the given main variables are substituted into the above equations, and the auxiliary variables are updated by the Newton iteration method. Finally, the auxiliary variable results obtained are substituted into the above equations, and the main variables are updated by iteration to obtain the solutions of all unknown variables. Substituting all the solutions obtained into equation (29), the ball-raceway contact force Q ij , Q oj .

[0171] Step 3: Based on the rolling contact fatigue (RCF) model of the ball-raceway, the influence of the uncertain parameters on the bearing life dispersion is quantified, and the specific implementation is as follows:

[0172] Based on the Ioannides fatigue life model and the stress volume integral simplification method, there are

[0173]

[0174] where N is the stress cycle number of reliability S, σ eq is the maximum equivalent stress, e and c are the Weibull slope and stress index, and V is the integral volume, is the volumetric damage constant, a and b are the major and minor semi-axes of the contact ellipse, z is the depth of the location corresponding to the maximum subsurface stress, and h is the depth index.

[0175] Taking the inner raceway as an example, from equation (31), the contact fatigue life of the j-th ball can be obtained as a, b, z, σ eq The relationship is

[0176]

[0177] To obtain the contact fatigue life of the j-th ball and the inner raceway, the maximum value of the equivalent stress needs to be calculated, and the corresponding depth and the major and minor semi-axes of the contact ellipse need to be determined. It should be noted that since the shaft-hole interference fit is uncertain, a, b, z, and σ... eq and L ij It is uncertain. In the RCF life model of ball-raceway contact, Figure 3 This is a schematic diagram of a Hertzian point contact between a ball and a raceway. With the minor and major semi-axes of the contact ellipse as the x and y axes, and the radial direction of the raceway as the z-axis, the normal, tangential, and axial loads at any point on the contact surface can be expressed as follows:

[0178] P N =Pdxdy,P T =Pf T dxdy,P A =Pf A dxdy (33)

[0179] Where f A ,f T Let be the axial and tangential friction coefficients. The general method for determining the stress tensor components at any point when y1 = 0 can be expressed as:

[0180]

[0181] in To facilitate integration calculations, all parameters should be dimensionless. ξ = x / z, η = y / z, k = b / a, Replacing x, y, and z, the normal, tangential, and axial loads can be expressed as:

[0182]

[0183]

[0184] The maximum Von-Mises stress is

[0185]

[0186] in ν is Poisson's ratio. k is an elliptic parameter,

[0187] Take the inner raceway as an example, the contact ellipse major and minor axes are

[0188]

[0189] wherein κ is the elliptic eccentricity parameter, E is the first kind complete elliptic integral, D is the ball diameter, d m is the pitch diameter, α 0 is the initial contact angle, f i is the inner raceway groove curvature. Record the position coordinates corresponding to the maximum stress (σ vmi,x ,σ vmi,y ), then z ij =b ij ×|Z(σ vmi,x ,σ vmi,y )|, put all the parameters obtained into equation (32) to determine L ij , it should be noted that since the shaft-hole interference fit is uncertain, a, b, z, σ eq and L ij are uncertain, the outer raceway is the same. Because the contact fatigue life formula of the rolling bearing is

[0190]

[0191] Put all the uncertain interference fit parameters calculated at the Chebyshev interpolation points into equation (43) to get the overall life L b of the rolling bearing, it is obvious that since the shaft-hole interference fit is uncertain, the overall life of the rolling bearing is also uncertain, denoted as [L b low , L b up ], wherein L b low , L b up represent the upper and lower limits of the overall life of the rolling bearing respectively. In order to evaluate the dispersion degree of the life of the rolling bearing, the uncertainty formula of measuring the uncertain but bounded interval [L b low , L b up ] is introduced here

[0192]

[0193] The relationship between input and output uncertainty can be obtained from equation (2) and equation (44) as β = 3ε.

[0194] Based on Chebyshev interpolation fitting technology, the overall life L of the rolling bearing corresponding to the shaft-hole uncertain interference fit parameter at the Chebyshev interpolation point is obtained b As an interpolation object, an approximate expression of the overall life of the rolling bearing is obtained, and then, the upper and lower limits L of the overall life of the rolling bearing are further obtained by a scanning method b up ,L b low Finally, by changing the parameters (axial load, radial load, rotating speed, interference fit parameter, etc.) in the quasi-static model, the influence of each parameter on the life dispersion degree of the rolling bearing is discussed by using formula (44).

[0195] In this embodiment, the RCF life dispersion degree quantization model of the ball-raceway contact is taken as the research object, other initial conditions are fixed, and the influence of the axial load on the bearing life dispersion is discussed by changing the axial load. The specific implementation is as follows:

[0196] The bearing of type NSK7212C is selected, and the related parameters and calculation formula are as follows: e=10 / 9, c=31 / 3, h=7 / 3, the elastic modulus of the ring and the ball E1, E2=2.06×10 11 N / m 2 , Poisson's ratio v1, v2=0.3, the density of the ball p=7.85×10 3 kg / m 3 , the comprehensive elastic modulus E=2 / ((1-v1 2 ) / E1+(1-v2 2 ) / E2), the number of balls Z=14, the diameter of the ball D=15.875, r i =8.176, r o =8.334, d i =69.109, d o =100.902 (all units are mm), the curvature of the raceway groove f i =r i / D, f o =r o / D, the total curvature of the bearing B=f i +f o -1, the effective clearance of the bearing P d0 =d o -d i -2D, the initial contact angle a 0 =cos -1 (1-P d0 / 2BD), the mass and moment of inertia of the ball m=pD 3 / 6, J=pD 5 / 60.

[0197] Only the influence of axial load on the dispersion of the total life of rolling bearing is considered, and the mean value and the coefficient of variation of interference are set as μ=10μm, ε=0.1, the rotating speed ω=10000r / min, F x =0, F y =0, M x =0, M y =0, the axial load F z In the interval (200N, 3000N), 9 values are randomly taken, and the bearing life uncertainty under different axial loads is calculated by the steps described in 4.2 All the obtained data are plotted into a curve graph (the horizontal coordinate is the axial load F z , and the vertical coordinate is the bearing life uncertainty , see Figure 4 ), and it can be obtained through Figure 4 that with the increase of the axial load, the dispersion of the contact fatigue life of the rolling bearing gradually decreases, the value of the uncertainty changes between 6% and 13%, which conforms to the actual situation, and further proves the applicability and effectiveness of the method.

[0198] The above described are preferred embodiments of the present application, and for the ordinary skilled in the art, the modifications of various equivalent forms of the present application without departing from the principles of the present application all belong to the protection scope of the appended claims of the present application.

Claims

1. A method for evaluating the dispersion of bearing fatigue life by quantifying uncertain interference fit parameters, characterized in that: The evaluation method is as follows: Step 1: Based on the Chebyshev interval method, analyze the uncertain interference in the shaft-hole interference fit model to obtain the interpolation point; Step 2: Based on the raceway-free control assumption, the quasi-static model of the angular contact ball bearing is combined with the shaft-bore interference fit model to determine the ball-raceway contact force Q under different interference amounts corresponding to the above interpolation points. ij Q oj ; Step 3: Analyze the ball-raceway contact force values ​​corresponding to different interference amounts at the above interpolation points in the ball-raceway rolling contact fatigue life model to obtain the maximum Von-Mises stress and the corresponding location depth, and quantify the influence of uncertain parameters on the bearing life dispersion.

2. The method for evaluating the dispersion of bearing fatigue life based on quantified uncertain interference fit parameters according to claim 1, characterized in that: The analysis method in Step 1 is as follows: Based on Chebyshev polynomials, a Chebyshev interval analysis method is proposed, assuming the interval variable is Δ. I Its upper and lower limits are represented by △ U and △ L The average interference can be expressed as △ 0 Shown as To describe the degree of uncertainty, a coefficient of variation ε is introduced. In an interference fit, the uncertain interference amount can be expressed as Δ. I =△ 0 (1+3ε[-1,1]) (2) According to Chebyshev interpolation theory, the output response F of the rotor system under the influence of interference uncertainty can be approximated as: Where T is the Chebyshev polynomial, i represents the order of the polynomial, and ξ is the normalized form of the interval variable, which can be expressed as: Let Chebyshev be an orthogonal polynomial, and its recurrence relation can be expressed as: f i The coefficients of the Chebyshev series can be calculated using the following formula. Where the variable ξ can be represented as Let t be the number of interpolation points. By calculating the zeros of the Chebyshev polynomial, the corresponding interpolation points can be obtained.

3. The method for evaluating the dispersion of bearing fatigue life based on quantified uncertain interference fit parameters according to claim 1, characterized in that: The method in Step 2 is as follows: In the quasi-static model of an angular contact ball bearing without the raceway control assumption, a coupled shaft-bore interference fit model is needed to more accurately predict the bearing's mechanical behavior. r1, r2, and r3 represent the inner and outer radii of the shaft and the inner raceway radius at the bottom of the bearing groove, respectively. The equilibrium equations can be obtained from axisymmetric plane stress theory as follows: Where σ r ,σ θ ω and ρ represent radial stress, tangential stress, rotational speed, and density, respectively. And because the elastic constitutive equation is Where ε r ,ε θ ν and E represent radial strain, tangential strain, Poisson's ratio, and elastic modulus, respectively. Therefore, the geometric deformation equation can be expressed as: Where s is the assembly deformation, substituting equations (10) and (11) into equation (9) yields the differential equation. By solving equation (12), the radial displacement and stress can be obtained as follows: Assuming the stress at position r1 is P1, according to the axisymmetric plane stress theory, the stresses at positions r2 and r3 are -P1 and 0, respectively. Therefore, the radial deformation of the bearing inner ring at r2 and r3 can be expressed as... The elastic deformation coefficients C1 and C2 can be expressed as: Similarly, the stress and deformation of the shaft are solved using the axisymmetric plane stress theory. In this case, the elastic modulus and Poisson's ratio should be replaced by E / (1-ν). 2 Given ν / (1-ν), the elastic deformation of the shaft at r2 is: The elastic deformation coefficients C3 and C4 can be expressed as follows: Let the initial interference quantity be Δ0, then the actual interference quantity Δ is... Where is the loss interference caused by centrifugal force, which can be expressed as: Assembly pressure can be expressed as The radial displacement of the inner ring at position is Therefore, in the shaft-bore interference fit model, the uncertainty of the interference fit between the bearing and the shaft will change the dimensions of the bearing components, i.e., the changes in r2 and r3, leading to a change in the initial radial clearance. This, in turn, affects the change in the initial contact angle in the quasi-static model of the angular contact ball bearing. Assuming that the outer ring of the bearing is fixed, the inner ring rotates with the shaft, and the contact between the ball and the raceway is a purely elastic deformation, the geometric constraint equation and load balance equation of the j-th ball are obtained: Where A 1j A 2j It can be represented as δ ij ,δ oj These represent the elastic deformation of the ball when it contacts the inner and outer rings, α. ij ,α oj Let be the contact angles between the ball and the inner and outer rings, respectively, which can be expressed as: Assuming that the ball's gyroscopic torque is affected by friction when it contacts the inner and outer raceways, and that the coefficients of friction between the ball and the inner and outer raceways are the same, then we can obtain... The gyroscopic torque and centrifugal force can be expressed as: Assuming there is no macroscopic slippage between the balls and the raceways, then the ball rotational speed ω cj and rotational speed ω bj It can be represented as Where is the pitch angle of the j-th ball, which can be expressed as: In the above formula When the axial load is insufficient, not all balls participate in load transfer. Therefore, an inequality is introduced to represent the difference between the initial and final ball-inner ring center distances. If the inequality holds, then the ball has disengaged from the inner raceway. In this case, assuming the contact angle between the ball and the outer ring is exactly zero, we can obtain Q. oj -F cj =0, according to Hertz's contact theory, the ball-roller contact force can be expressed as Q ij =K ij δ ij 1.5 ,Q oj =K oj δ oj 1.5 (29) Where K is the stiffness coefficient between the balls and the raceway. Based on the load analysis of the inner ring, the force balance equation can be expressed as: The position angle of the ball Combined formulas (22) to (30), we have δ x ,δ y ,δ z ,θ x ,θ y ,δ ij ,δ oj ,X 1j ,X 2j There are 9 variables, of which the main variable is (δ x ,δ y ,δ z ,θ x ,θ y ), with auxiliary variables being (δ) ij ,δ oj ,X 1j ,X 2j First, assume the value of the given main variable and substitute it into the above formula. Then, continuously update the auxiliary variable using Newton's iteration method. Finally, substitute the obtained auxiliary variable result into the above formula and iteratively update the main variable to obtain the solution of all unknown variables. Substitute all the obtained solutions into formula (29) to obtain the ball-roller contact force Q. ij Q oj .

4. The method for evaluating the dispersion of bearing fatigue life based on quantified uncertain interference fit parameters according to claim 1, characterized in that: The method in Step 3 is as follows: Based on the Ioannides fatigue life model and the stress volume integral simplification method, there are Where N is the stress cycle number of the reliability S, σ eq It is the maximum equivalent stress, e and c are the Weibull slope and stress exponent, and V is the integral volume. is the volumetric damage constant, a and b are the major and minor semi-axes of the contact ellipse, z is the depth of the location corresponding to the maximum subsurface stress, and h is the depth index. Taking the inner raceway as an example, the contact fatigue life of the j-th ball can be obtained from equation (31) as a function of a, b, z, σ. eq The relationship is To obtain the contact fatigue life of the j-th ball and the inner raceway, it is necessary to calculate the maximum value of the equivalent stress, determine its corresponding depth, and the major and minor semi-axes of the contact ellipse. Since the shaft-hole interference fit is uncertain, a, b, z, and σ... eq and L ij It is uncertain; in the RCF life model of ball-raceway contact, with the minor and major semi-axes of the contact ellipse as the x and y axes, and the radial direction of the raceway as the z-axis, the normal, tangential, and axial loads at any point on the contact surface can be expressed as: P N =Pdxdy,P T =Pf T dxdy,P A =Pf A dxdy (33) Where f A ,f T Let be the axial and tangential friction coefficients. The general method for determining the stress tensor components at any point when y1 = 0 can be expressed as: in To facilitate integration calculations, all parameters should be dimensionless. ξ = x / z, η = y / z, k = b / a, Replacing x, y, and z, the normal, tangential, and axial loads can be expressed as: The maximum Von-Mises stress is in ν is Poisson's ratio. k is the ellipse parameter. Taking the inner raceway as an example, the major and minor semi-axes of the contact ellipse are... in κ is the elliptic eccentricity parameter, Ε is the first-order elliptic integral, D is the ball diameter, and d m Let α be the pitch circle diameter. 0 Let f be the initial contact angle. i The inner raceway groove curvature is recorded; the coordinates of the position corresponding to the maximum stress (σ) are also recorded. vmi,x ,σ vmi,y ), then z ij =b ij ×Z(σ vmi,x ,σ vmi,y Substituting the obtained parameters into equation (32) will determine L. ij It should be noted that because the shaft-hole interference fit is uncertain, therefore a, b, z, σ eq and L ij It is uncertain, and the same applies to the outer raceway. Furthermore, the formula for the contact fatigue life of a rolling bearing is... Substituting the calculated contact fatigue lives corresponding to all uncertain interference fit parameters at the Chebyshev interpolation points into equation (43), the overall life L of the rolling bearing is obtained. b Obviously, since the shaft-bore interference fit is uncertain, the overall life of the rolling bearing is also uncertain, denoted as [L]. b low ,L b up ], where L b low ,L b up These represent the upper and lower limits of the overall lifespan of the rolling bearing, respectively. To assess the dispersion of the rolling bearing lifespan, a bounded interval [L] is introduced to measure the uncertainty. b low ,L b up Uncertainty formula From equations (2) and (44), the relationship between input and output uncertainty can be obtained as β = 3ε; Based on Chebyshev interpolation fitting technology, the overall life L of the rolling bearing at the Chebyshev interpolation point corresponding to the uncertain shaft-bore interference fit parameters is calculated. b Using the interpolation object, an approximate expression for the overall life of the rolling bearing is obtained. Then, the upper and lower limits L of the overall life of the rolling bearing are further obtained through the scanning method. b up ,L b low Finally, by changing the parameters in the quasi-static model, the influence of each parameter on the dispersion of rolling bearing life is explored using equation (44).

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