CN104239654A - Bearing simplifying method in finite element simulation analysis - Google Patents

Abstract

The invention discloses a bearing simplifying method in finite element simulation analysis. According to the method, a three-dimensional gap unit is used for simplifying finite element analysis of an angular contact bearing, and a three-dimensional model of the bearing is drawn in three-dimensional mapping software solidworks. The bearing model is imported into finite element pre-processing software Hypermesh. An outer ring and an inner ring of the bearing are divided into hexahedral meshes. The outer ring and the inner ring of the bearing are connected through the three-dimensional gap unit. The spring stiffness K in the gap unit is worked out through a bearing radial stiffness calculation program. The finite element model is exported from the Hypermesh, then the finite element model is imported into engineering simulation software ANSYS, and mechanical calculation is conducted. According to the method, the calculation amount of finite element analysis can be simplified, the efficiency can be increased, and the calculation accuracy cannot be damaged.

Description

Bearing short-cut method in a kind of Finite Element Simulation Analysis

Technical field

The present invention is applicable to carry out statics and dynamic (dynamical) Finite Element Simulation Analysis to the mechanical system containing bearing, belongs to machine emulated CAE field, is specifically related to the bearing short-cut method in a kind of Finite Element Simulation Analysis.

Background technology

Rolling bearing is important mechanical basic part, is widely used in the fields such as lathe, precision movement platform, boats and ships, space flight.In present big machinery system as in the design system of aircraft, automobile, computer-aided design (CAD) due to its can be cost-saving greatly, shorten the cycle, apply more and more general.Finite element analysis, as mechanical analysis means most important in mechanical system, has been integrated into widespread use in many large softwares.As the Hypermesh that this patent adopts, the softwares such as ANASYS.

Traditional bearing finite element analysis adopts solid modelling, and this method has the shortcomings such as calculated amount is large, efficiency is low, and especially in big machinery system, owing to there being a large amount of bearings, this shortcoming is especially outstanding.So seem particularly important to adopting which kind of method to simplify bearing and do not affect computational accuracy in finite element analysis software.This patent adopts three-dimensional gap element to replace the Internal and external cycle of the rolling body connection bearing of bearing in finite-element preprocessing software Hypermesh, simulation ball contacts with bearing, is imported to by the finite element model obtained in finite element analysis software ANSYS and just can carry out mechanical analysis to the mechanical system containing bearing.

Summary of the invention

The present invention, in order to overcome the above-mentioned defect of prior art, proposes the bearing short-cut method in a kind of Finite Element Simulation Analysis, and the method both can simplify the calculated amount of finite element analysis, increases efficiency not costing bio disturbance precision again.

The technical solution used in the present invention is: the bearing short-cut method in a kind of Finite Element Simulation Analysis, is characterized in that, the method performing step is as follows:

Step 1): the geometry stereoscopic model drawing angular contact bearing in Solidworks software, and save as zhoucheng.stp form;

Step 2): open Hypermesh software, import zhoucheng.stp geometry stereoscopic model, inner ring and outer ring are divided into hexahedral mesh;

Step 3): calculation bearing ball radial rigidity K;

Step 4): add three-dimensional gap element and replace ball, the spring constant wherein in three-dimensional gap element is K;

Step 5): finite element model is imported in engineering analysis software ANSYS, carry out the analysis of statics and dynamics aspect.

Further, the geometry stereoscopic model of bearing is drawn in described Solidworks, select the design library " Toolbox " of Solidworks, select GB " GB " menu again, select again " bearing "---" rolling bearing ", kind required for selection, right-click, adds required sizing sequence code name and size in the dialog box ejected.

Further, described calculation bearing ball radial rigidity K, concrete steps are as follows:

Step 1): the contact angle of each ball is the numbering j of α, ball, and Angle Position is ψ, and the deflection of a jth ball and outer ring is δ _ej, the contact force of a jth ball and outer ring is Q _ej, the deflection of a jth ball and inner ring is δ _ij, the contact force of a jth ball and outer ring is Q _ij, obtain according to Hertzian contact theory:

$Q_{\mathrm{ij}}=\frac{4}{3}\mathrm{sqrt}(\frac{R_i{R}_j}{R_i-R_j}*\frac{E^2}{2E(1-{\mathrm{\μ}}^2)}{\mathrm{\δ}}_{\mathrm{ij}}^3)$

$Q_{\mathrm{ej}}=\frac{4}{3}\mathrm{sqrt}(\frac{R_e{R}_j}{R_e-R_j}*\frac{E^2}{2E(1-{\mathrm{\μ}}^2)}{\mathrm{\δ}}_{\mathrm{ej}}^3)$

Wherein E is the elastic modulus of material, and μ is Poisson ratio, R _jthe radius of a jth ball, R _ethe radius-of-curvature of contact position outer ring raceway, R _iit is the radius-of-curvature of contact position inner ring raceway;

Step 2): the centrifugal force F being calculated a jth ball by kinetic theory _cj, gyroscopic couple M _gjand friction force F _ej:

M _gj＝Jω _bjω _mj

$F_{\mathrm{ej}}=\frac{{2M}_{\mathrm{gj}}}{D_b}$

$F_{\mathrm{cj}}=\frac{\mathrm{\π}}{12}\mathrm{\ρ}{D}_b{D}_m{\mathrm{\ω}}_{\mathrm{mj}}^2$

Wherein J is the moment of inertia of rolling body, ω _bjrolling body spin velocity, ω _mjrolling body revolution angular velocity, D _bbe rolling body diameter, ρ is rolling body density, D _mit is place, ball center diameter of a circle;

Step 3): through the force analysis of rolling body list each ball in the horizontal direction with the stress balance equation of vertical direction,

Q _ijsinα _ij-Q _ejsinα _ej+F _ejcosα _ej＝0 (1)

Q _ijcosα _ij-Q _ejcosα _ej-F _ejsinα _ej+F _cj＝0 (2)

And the stress balance equation of bearing inner race,

$F_a-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\sin {\mathrm{\α}}_{\mathrm{ij}}=0---\left(3\right)$

$F_r-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\cos {\mathrm{\α}}_{\mathrm{ij}}\cos {\mathrm{\ψ}}_j=0---\left(4\right)$

Wherein, ψ _j=(2 π/N) * (j-1), N is the number of ball in bearing, F _aand F _rthe axis suffered by bearing and radial external applied load, α _ij, α _ejit is the contact angle after distortion;

Step 4): outer ring raceway centre of radius A remains unchanged, and rolling body centre of radius O moves to O ', and inner ring raceway centre of radius moves to B ' by B, and the compatibility of deformation relation obtaining rolling body and bearing enclose is as follows:

(A _aj-x _aj) ²+(A _rj-x _rj) ²-(R _i-R _j+δ _ij) ²＝0 (5)

$x_{\mathrm{aj}}^2+x_{\mathrm{rj}}^2-{(R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}})}^2=0---\left(6\right)$

$\left\{\begin{array}{c}D=R_e+R_i-2R_j\\ A_{\mathrm{aj}}=D\sin \mathrm{\α}+{\mathrm{\δ}}_a\\ A_{\mathrm{rj}}=D\cos \mathrm{\α}+{\mathrm{\δ}}_r\cos {\mathrm{\ψ}}_j\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}\sin {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{rj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \cos {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{aj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \cos {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{rj}}-x_{\mathrm{rj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \sin {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{aj}}-x_{\mathrm{aj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ij}}}\end{array}\right.---\left(8\right)$

Wherein δ _athe axial displacement of inner ring relative to outer ring, δ _rthe radial displacement of inner ring relative to outer ring, R _jthe radius of a jth ball, R _ethe radius-of-curvature of contact position outer ring raceway, R _ibe the radius-of-curvature of contact position inner ring raceway, outer ring raceway centre of radius A remains unchanged, and rolling body centre of radius O moves to O ', and inner ring raceway centre of radius moves to B ' by B, A _ajthe axial component of AB ', A _rjthe radial component of AB ', x _ajthe axial component of AO ', x _rjbe the radial component of AO ', the Angle Position of ball is ψ _j, α _ij, α _ejthe contact angle after distortion, δ _ijthe juxtaposition metamorphose amount of a jth ball and interior raceway, δ _ejit is the juxtaposition metamorphose amount of a jth ball and outer raceway;

Step 5): there are equation (1), (2), (5), (6) to each rolling body, above four equations are listed for each rolling body, form 4Z equation, combine equation (3), (4) again, 4Z+2 equation altogether, separate this system of equations, remove unknown quantity δ _ij, δ _ej, x _rj, x _aj, δ _a, δ _r;

Step 6): solving bearing radial rigidity K is:

$K=\frac{F_r}{{\mathrm{\δ}}_r}.$

Further, described interpolation gap element replaces ball, is specially:

(1) gap element is made up of A, B 2, A, B are the corresponding node pair that Internal and external cycle contacts with rolling body, primary clearance between A, B 2 is set to the diameter of rolling body, when the relative displacement of A, B is less than primary clearance, show that surface in contact is in contact condition, normal force will be there is in the normal direction of gap element, and normal force is negative value, now gap element is just as a Hookean spring, its normal contact stiffness is Ks, and Internal and external cycle will pass through gap element transmitted load between two points; Otherwise when relative displacement is greater than primary clearance, surface in contact is non-contact condition, and normal force value is zero, gap element does not stress not transmitted load yet, thus does not have an impact to the motion state of analytic target;

(2) the A point of gap element is added on the surface of contact center of ball and inner ring, and B point is added on the surface of contact center of ball and outer ring, and stiffness K s is defined as bearing radial rigidity K, does such unit replace each ball.

Principle of the present invention is:

Required angular contact bearing is drawn by the Toolbox of Solidworks, geometric model is imported in finite-element preprocessing software Hypermesh, the Internal and external cycle of angular contact bearings divides hexahedral mesh, adopts three-dimensional gap element to simulate ball and contacts with the Internal and external cycle of bearing.When three-dimensional gap element interval is less than or equal to initial gap, calculate the radial rigidity K of angular contact bearing, give three-dimensional gap element radial rigidity K, simulate contacting of ball and Internal and external cycle; When three-dimensional gap element interval is greater than initial gap, three-dimensional gap element is equivalent to disconnect, and simulates ball and does not now contact with Internal and external cycle.This patent proposes the new algorithm calculating angular contact bearing radial rigidity, the relation of ball contact power and juxtaposition metamorphose is obtained by Hertzian contact theory, stress balance equation is listed to each ball, list stress balance equation and the juxtaposition metamorphose equation of comptability to whole bearing, these equations of simultaneous obtain radial rigidity K.

The present invention's characteristic and advantage is compared to the prior art:

(1) the present invention is directed to each ball and carry out the radial rigidity that force analysis carrys out calculation bearing, obtain result closer to truly.

(2) the present invention adopts many software to combine simulation analysis.

(3) the present invention adopts three-dimensional gap element to simulate ball, can simulate contacting and disengaging of ball and Internal and external cycle.

(4) the present invention both can simplify the calculated amount of finite element analysis, increased efficiency not costing bio disturbance precision again.

Accompanying drawing explanation

Fig. 1 is the bearing short-cut method process flow diagram in a kind of Finite Element Simulation Analysis of the present invention;

Fig. 2 is the contact angle schematic diagram of angular contact bearing;

Fig. 3 is bearing ball numbering and Angle Position schematic diagram;

Fig. 4 is single ball force analysis figure;

Fig. 5 is the compatibility of deformation graph of a relation of bearing;

Fig. 6 is the geometric model that Solidworks draws bearing;

Fig. 7 carries out stress and strain model to bearing inner race and outer ring in Hypermesh;

Fig. 8 is the bearing finite element model after applying three-dimensional gap element.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.

Illustrate for angular contact bearing S7000.The geometric model of bearing is drawn as shown in Figure 1 in Solidworks.Import in Hypermesh, inner ring and outer ring are carried out stress and strain model, as shown in Figure 2.Next according to the radial rigidity of step calculation bearing.Calculating parameter is as shown in table 1 below.

Table 1

Parameter	Numerical value
		Ball quantity	13
Contact angle α (°)	15
		Ball bearing radius R j(mm)	2
The radius R of outer ring raceway e(mm)	1.99
		The radius R of inner ring raceway i(mm)	1.99
Bearing material	Bearing steel
		Axial external applied load F a(N)	100
Radial external applied load F r(N)	50
		Ball rotating speed r (r/min)	1e5

Step 1): calculate contact force and juxtaposition metamorphose equation.

$Q_{\mathrm{ij}}=2.8299e5*\sqrt{{\mathrm{\δ}}_{\mathrm{ij}}^3}$

$Q_{\mathrm{ej}}=2.8299e5*\sqrt{{\mathrm{\δ}}_{\mathrm{ej}}^3}$

Step 2): calculate gyroscopic couple, friction force, centrifugal force.

The moment of inertia of ball is $J=\frac{8\mathrm{\π}{R}_j^5\mathrm{\ρ}}{15}=4.185\×{10}^{-10}{\mathrm{kgm}}^2,$

Ρ is the density of bearing steel, gets 7850kg/m ³, easily known by kinematics knowledge,

The spin velocity of ball is ${\mathrm{\ω}}_{\mathrm{bj}}=\frac{2\mathrm{r\π}}{60}=1.047\×{10}^4,$

Ball around the angular velocity of bearing center is ${\mathrm{\ω}}_{\mathrm{mj}}=\frac{2\mathrm{\πr}*R_i}{60*R_j}=2.97\×{10}^3\mathrm{rad}/s,$

R ₁the distance of contact point to bearing center, according to computing formula:

M _gj＝Jsinbω _bjω _mj

$F_{\mathrm{ej}}=\frac{{2M}_{\mathrm{gj}}}{D_b}$

$F_{\mathrm{cj}}=\frac{\mathrm{\π}}{12}\mathrm{\ρ}{D}_b{D}_m{\mathrm{\ω}}_{\mathrm{mj}}^2$

Calculate gyroscopic couple M _gj=6.5438N*m;

Friction force F _ej=3.2719N;

Centrifugal force F _cj=167.0681N;

Step 3): the force analysis balance equation calculating single ball, and the force analysis balance equation listing all balls.The stress balance equation of ball both direction can be obtained, α by force analysis Fig. 3 _ij, α _ejbeing the contact angle after distortion, is unknown quantity,

Q _ijsinα _ij-Q _ejsinα _ej+F _ejcosα _ej＝0

Q _ijcosα _ij-Q _ejcosα _ej-F _ejsinα _ej+F _cj＝0

And the stress balance equation of bearing enclose,

$100-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\sin {\mathrm{\α}}_{\mathrm{ij}}=0$

$50-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\cos {\mathrm{\α}}_{\mathrm{ij}}\cos {\mathrm{\ψ}}_j=0$

Wherein, Ψ j=(2 π/13) * (j-1);

Step 4): there is a Coordinate deformation equation for each ball, obtain deflection and contact angle relation by Coordinate deformation equation, and the bulk deformation amount of Internal and external cycle and the deformation relationship of single ball.The compatibility of deformation relation of rolling body and bearing enclose as shown in Figure 4, δ _athe axial displacement of inner ring relative to outer ring, δ _rthe radial displacement of inner ring relative to outer ring;

(A _aj-x _aj) ²+(A _rj-x _rj) ²-(R _i-R _j+δ _ij) ²＝0

$x_{\mathrm{aj}}^2+x_{\mathrm{rj}}^2-{(R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}})}^2=0$

D＝R _e+R _i-2R _j

A _aj＝Dsinα+δ _a

A _rj＝Dcosα+δ _rcosψ _j

$\cos {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{rj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}$

$\cos {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{aj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}$

$\cos {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{rj}}-x_{\mathrm{rj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}$

$\sin {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{aj}}-x_{\mathrm{aj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ij}}}$

Step 5): simultaneous equations calculate, and solve radial rigidity

Being loaded into by three-dimensional gap element and bearing being used for replace ball, on the Internal and external cycle that two nodes of three-dimensional gap element are connected in bearing respectively and ball contact point, is the bearing radial rigidity K that previous step is tried to achieve by optimum configurations.Effect as shown in Figure 5.The finite element model of such bearing just completes, and then model derivation is saved as zhoucheng.cdb file and just can import to finite element analysis software as carried out statics and dynamic (dynamical) simulation analysis in ANSYS.

Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.

The above; be only the embodiment in the present invention, but protection scope of the present invention is not limited thereto, any people being familiar with this technology is in the technical scope disclosed by the present invention; the conversion or replacement expected can be understood, all should be encompassed in of the present invention comprising within scope.

Claims (4)

1. the bearing short-cut method in Finite Element Simulation Analysis, is characterized in that, the method performing step is as follows:

Step 1): the geometry stereoscopic model drawing angular contact bearing in Solidworks software, and save as zhoucheng.stp form;

Step 2): open Hypermesh software, import zhoucheng.stp geometry stereoscopic model, inner ring and outer ring are divided into hexahedral mesh;

Step 3): calculation bearing ball radial rigidity K;

Step 4): add three-dimensional gap element and replace ball, the spring constant wherein in three-dimensional gap element is K;

Step 5): finite element model is imported in engineering analysis software ANSYS, carry out the analysis of statics and dynamics aspect.

2. the bearing short-cut method in a kind of Finite Element Simulation Analysis according to claim 1, it is characterized in that: the geometry stereoscopic model drawing bearing in described Solidworks, select the design library " Toolbox " of Solidworks, select GB " GB " menu again, select again " bearing "---" rolling bearing ", kind required for selection, right-click, adds required sizing sequence code name and size in the dialog box ejected.

3. the bearing short-cut method in a kind of Finite Element Simulation Analysis according to claim 1, is characterized in that: described calculation bearing ball radial rigidity K, and concrete steps are as follows:

Step 1): the contact angle of each ball is the numbering j of α, ball, and Angle Position is ψ, and the deflection of a jth ball and outer ring is δ _ej, the contact force of a jth ball and outer ring is Q _ej, the deflection of a jth ball and inner ring is δ _ij, the contact force of a jth ball and outer ring is Q _ij, obtain according to Hertzian contact theory:

$Q_{\mathrm{ij}}=\frac{4}{3}\mathrm{sqrt}(\frac{R_i{R}_j}{R_i-R_j}*\frac{E^2}{2E(1-{\mathrm{\μ}}^2)}{{\mathrm{\δ}}_{\mathrm{ij}}}^3)$

$Q_{\mathrm{ej}}=\frac{4}{3}\mathrm{sqrt}(\frac{R_e{R}_j}{R_e-R_j}*\frac{E^2}{2E(1-{\mathrm{\μ}}^2)}{{\mathrm{\δ}}_{\mathrm{ej}}}^3)$

Wherein E is the elastic modulus of material, and μ is Poisson ratio, R _jthe radius of a jth ball, R _ethe radius-of-curvature of contact position outer ring raceway, R _iit is the radius-of-curvature of contact position inner ring raceway;

Step 2): the centrifugal force F being calculated a jth ball by kinetic theory _cj, gyroscopic couple M _gjand friction force F _ej:

M _gj＝Jω _bjω _mj

$F_{\mathrm{ej}}=\frac{{2M}_{\mathrm{gj}}}{D_b}$

$F_{\mathrm{cj}}=\frac{\mathrm{\π}}{12}\mathrm{\ρ}{D}_b{D}_m{\mathrm{\ω}}_{\mathrm{mj}}^2$

Wherein J is the moment of inertia of rolling body, ω _bjrolling body spin velocity, ω _mjrolling body revolution angular velocity, D _bbe rolling body diameter, ρ is rolling body density, D _mit is place, ball center diameter of a circle;

Step 3): through the force analysis of rolling body list each ball in the horizontal direction with the stress balance equation of vertical direction,

Q _ijsinα _ij-Q _ejsinα _ej+F _ejcosα _ej＝0 (1)

Q _ijcosα _ij-Q _ejcosα _ej-F _ejsinα _ej+F _cj＝0 (2)

And the stress balance equation of bearing inner race,

$F_a-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\sin {\mathrm{\α}}_{\mathrm{ij}}=0---\left(3\right)$

$F_r-\underset{j=1}{\overset{Z}{\mathrm{\Σ}}}{Q}_{\mathrm{ij}}\cos {\mathrm{\α}}_{\mathrm{ij}}\cos {\mathrm{\ψ}}_j=0---\left(4\right)$

Wherein, ψ _j=(2 π/N) * (j-1), N is the number of ball in bearing, F _aand F _rthe axis suffered by bearing and radial external applied load, α _ij, α _ejit is the contact angle after distortion;

Step 4): outer ring raceway centre of radius A remains unchanged, and rolling body centre of radius O moves to O ', and inner ring raceway centre of radius moves to B ' by B, and the compatibility of deformation relation obtaining rolling body and bearing enclose is as follows:

(A _aj-x _aj) ²+(A _rj-x _rj) ²-(R _i-R _j+δ _ij) ²＝0 (5)

$x_{\mathrm{aj}}^2+x_{\mathrm{rj}}^2-{(R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}})}^2=0---\left(6\right)$

$\left\{\begin{array}{c}D=R_e+R_i-{2R}_j\\ A_{\mathrm{aj}}=D\sin \mathrm{\α}+{\mathrm{\δ}}_a\\ A_{\mathrm{rj}}=D\cos \mathrm{\α}+{\mathrm{\δ}}_r\cos {\mathrm{\ψ}}_j\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}\sin {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{rj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \cos {\mathrm{\α}}_{\mathrm{ej}}=\frac{x_{\mathrm{aj}}}{R_e-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \cos {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{rj}}-x_{\mathrm{rj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ej}}}\\ \sin {\mathrm{\α}}_{\mathrm{ij}}=\frac{A_{\mathrm{aj}}-x_{\mathrm{aj}}}{R_i-R_j+{\mathrm{\δ}}_{\mathrm{ij}}}\end{array}\right.---\left(8\right)$

Wherein, δ _athe axial displacement of inner ring relative to outer ring, δ _rthe radial displacement of inner ring relative to outer ring, R _jthe radius of a jth ball, R _ethe radius-of-curvature of contact position outer ring raceway, R _ibe the radius-of-curvature of contact position inner ring raceway, outer ring raceway centre of radius A remains unchanged, and rolling body centre of radius O moves to O ', and inner ring raceway centre of radius moves to B ' by B, A _ajthe axial component of AB ', A _rjthe radial component of AB ', x _ajthe axial component of AO ', x _rjbe the radial component of AO ', the Angle Position of ball is ψ _j, α _ij, α _ejthe contact angle after distortion, δ _ijthe juxtaposition metamorphose amount of a jth ball and interior raceway, δ _ejit is the juxtaposition metamorphose amount of a jth ball and outer raceway;

Step 5): there are equation (1), (2), (5), (6) to each rolling body, above four equations are listed for each rolling body, form 4Z equation, combine equation (3), (4) again, 4Z+2 equation altogether, separate this system of equations, remove unknown quantity δ _ij, δ _ej, x _rj, x _aj, δ _a, δ _r;

Step 6): solving bearing radial rigidity K is:

$K=\frac{F_r}{{\mathrm{\δ}}_r}.$

4. the bearing short-cut method in a kind of Finite Element Simulation Analysis according to claim 1, is characterized in that: described interpolation gap element replaces ball, is specially:

(1), gap element is made up of A, B 2, A, B are the corresponding node pair that Internal and external cycle contacts with rolling body, primary clearance between A, B 2 is set to the diameter of rolling body, when the relative displacement of A, B is less than primary clearance, show that surface in contact is in contact condition, normal force will be there is in the normal direction of gap element, and normal force is negative value, now gap element is just as a Hookean spring, its normal contact stiffness is Ks, and Internal and external cycle will pass through gap element transmitted load between two points; Otherwise when relative displacement is greater than primary clearance, surface in contact is non-contact condition, and normal force value is zero, gap element does not stress not transmitted load yet, thus does not have an impact to the motion state of analytic target;

(2), the A point of gap element is added on the surface of contact center of ball and inner ring, and B point is added on the surface of contact center of ball and outer ring, and stiffness K s is defined as bearing radial rigidity K, does such unit replace each ball.