CN106560815A - Ball bearing reliability design method - Google Patents

Abstract

A ball bearing reliability design method is based on the following prerequisites: 1, the contact between an antifriction bearing rolling body and internal/external raceway satisfies the Hertz contact theory, and the contact type between the rolling body and the bearing internal/external raceway is point contact or/and line contact; 2, the ball bearing reliability design method satisfies the following requirements: firstly building a deep groove ball bearing flexible multi-body contact dynamics model, simulating and parsing a deep groove ball bearing rotation process so as to obtain each part angular velocity and dynamic contact impact stress changing rules, and using obtained data to finish the ball bearing reliability design. The invention provides the reference method for ball bearing reliability design and fatigue life research; related principles can be promoted to all transplantable related technical fields; the ball bearing reliability design method has large latent economy value and social value.

Description

Ball bearing reliability design approach

Technical field

The present invention relates to the reliability design of ball bearing and related application technical field, specifically provide a kind of ball bearing Reliability design approach.

Background technology

When rolling bearing rotates, its rolling element comes in contact with raceway, produces various rotary motions with friction, axle The rigidity held, bearing capacity depend primarily on connecing between the working condition and rolling element and raceway of bearing even with the life-span Tactile property, thus the research of rolling bearing Contact Dynamics problem is had become the important research direction of scientific research personnel (referring to Document：Xiong little Jin, a dawn Kun, etc. the non linear finite element analysis [J] of rolling bearing contact. measuring technology journal, 2009,23 (1)：23-27.).Additionally, the reliability design of ball bearing has always some technical problems urgently to be resolved hurrily, lack more real With and effective principle scheme, people are highly desirable to obtain a kind of excellent ball bearing reliability design approach of technique effect.

The content of the invention

It is an object of the invention to provide a kind of excellent ball bearing reliability design approach of technique effect.

The invention provides a kind of ball bearing reliability design approach, it is characterised in that：

(1) the ball bearing reliability design approach is based on following premises：Think that rolling bearing rolling element is rolled with Internal and external cycle The contact in road meets hertz (Hertz) contact theory, rolling element contact for point with the contact type of bearing internal external circle raceway or/and Linear contact lay, wherein belongs to a contact between ball bearing roller kinetoplast and Internal and external cycle, cylinder and taper roll bearing contact belong to line and connect Touch；The correlation of hertz (Hertz) contact theory specifically requires as follows：

1. in ball bearing, contact between rolling element and Internal and external cycle raceway belongs to a contact, in the presence of load Q, contact Point gradually expands to elliptical-shaped contact face, and in oval central spot, stress is σ to the maximum_max, a length of 2a of major axis of ellipse, short axle A length of 2b, as shown in figure 1, the stress distribution in contact zone, as shown in Figure 2.Known by Hertzian contact theory：

In formula, Q is the contact load of rolling element and Internal and external cycle raceway；A is the axial length of the Contact Ellipse head of district half；B is semi-minor axis It is long；σ_maxTo contact maximum stress；δ is deflection (also known as convergence amount)；Equivalent elastic modulus E ' is expressed as：

In formula, E₁, E₂, μ₁, μ₂The respectively elastic modelling quantity and Poisson's ratio of rolling element and Internal and external cycle raceway；

2. principal curvatures and ∑ ρ are the principal curvatures sum of rolling element and raceway contact point, i.e.,：

∑ ρ=ρ₁₁+ρ₁₂+ρ₂₁+ρ₂₂ (6)

m_aAnd m_bRespectively major axis and short axle coefficient, are expressed as：

In formula, k is ellipticity,E is oval eccentric rate,K (e) and L (e) is respectively and ellipse Eccentricity it is relevant first and two class integration：

Oval eccentric rate e is with the relation of ellipticity：

Principal curvature function F (ρ) is expressed as：

It also is indicated as simultaneously：

If bearing each several part physical dimension by formula (13)-formula (17) and formula (11), it is known that can try to achieve principal curvature function F (ρ)；Again formula (9), (10) are substituted into into (12) and try to achieve k, then e can be tried to achieve by formula (10), bearing rigidity can be weighed whereby；

3. in the presence of rolling element and Internal and external cycle contact load Q, major semiaxis and semi-minor axis can respectively be asked by formula (7), (8) Coefficient；Contact zone Max.contact stress σ can be asked by formula (1) and (4)_maxWith convergence amount δ；

For point contact ball bearing, its principal curvatures is respectively：

Spin：

Inner ring：

Outer ring：

In formula, D_bFor ball diameters；α is contact Angle；D is outer ring internal diameter；D is inner ring external diameter；d_mFor rolling element center circle diameter；r_inFor interior raceway radius；r_ouFor outer raceway half Footpath；By taking deep groove ball bearing as an example, its member and main geometric parameter is as shown in Figure 3.

(2) ball bearing reliability design approach meets following requirements：

The Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing is initially set up, simulation analysis deep groove ball bearing was rotated Journey, obtains the angular speed of each part and the Changing Pattern of dynamic Contact impact stress, and complete ball bearing based on this can By property design；

Bearing internal external circle raceway element stress major frequency components are rolling element by Internal and external cycle frequency and its integral multiple Frequently, illustrating the stress of Internal and external cycle certain point can be affected by neighbouring multiple rolling elements on raceway contact stress simultaneously, analysis knot Fruit is that ball bearing reliability design and Fatigue Life Research provide reference method.

The ball bearing reliability design approach, it is characterised in that：

With transmission input shaft front end deep groove ball bearing as object, the power of each part in rolling bearing operation process is studied Learn characteristic, it is considered to steel ball, the structural flexibility deformation and dynamic Contact relation of lasso raceway, establish in Abaqus/Expicit The Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing, analyzes the dynamics of deep groove ball bearing, obtains the angle of each part The Changing Pattern of speed and dynamic Contact impact stress；

The retainer angular speed of ball bearing, the simulation result of steel ball revolution angular speed and theoretical value are contrasted, Result of calculation is ball bearing dynamic design and fatigue life to provide reference method, realizes ball bearing reliability design.Simulation time For 0.05s, the circle of inner ring rotation 2.5 of bearing, can see rolling element also with the rotation of inner ring by the result animation for emulating Rotate, but rotating speed is slower than inner ring rotating speed.

The ball bearing reliability design approach, it is characterised in that：

In the ball bearing reliability design approach, the Dynamics For Flexible Multibody Contact Dynamics model for setting up ball bearing specifically meets Following requirements：

In the actual course of work, bearing is assemblied on axle, is the dynamics for studying bearing in operation process, On the basis of statical model, the model of retainer and one section of axle is augmented；Whole model has 4 parts, respectively in bearing Circle, bearing outer ring, rolling element and retainer；7 rolling elements are numbered, as shown in Figure 4；To each key node in model Numbering, as shown in Figure 5；Node 1 is outer ring fringe node, and node 2 is inner ring fringe node, and node 3 is rolling element front node, Node 4 is rolling element side node；

The retainer of increase and the material properties of bearing inner race axle are rigid body, its density and Poisson's ratio and bearing material phase Together；Retainer is considered as into rigid body for whole dynamics calculation has no too much influence, bearing deforms mainly in operation process From the mutual extruding of bearing internal external circle and rolling element, and primarily radial deformation；And retainer be mainly used for limit with about Beam bearing roller is moved in the raceway of bearing internal external circle, and certain gap is left between retainer and rolling element, for The deformation effect of bearing is less；The in addition calculating of rigid body can save the substantial amounts of time relative to elastomer, therefore by retainer It is changed to rigid body；

Specific material properties meet following requirements (referring to table 2)：Rolling element, bearing inner race, the material class of bearing outer ring Type is elastomer, elastic modelling quantity 2.07 × 10⁵MPa；The material type of retainer and bearing inner race axle is rigid body；Poisson's ratio 0.3, density is 7.85 × 10^-9；From the linear hexahedral elements of C3D8R to whole model partition grid, FEM model is set up As shown in Figure 4；

All frees degree of constraint bearing outer ring outer surface, describe bearing block to bearing restriction effect, in the rigid body of axle journal Arrange in material model and constrain its axial displacement so as to operate in bearing plane, occur without inclined phenomenon, miscellaneous part Constraint is not applied；According to the working condition of bearing, reference point RP-1 is set up at bearing inner race center, by reference point and rigid body axle Coupling, applies radial load -3000N (Y-axis negative direction) in reference point RP-1, applies axial load -1000N (z-axis losing sides To), acting on for the external applied load that bearing is subject to is described；Its axis is applied through to axle journal and along the angular speed of z positive directions, description Operating condition during bearing working；

Radial load and rotating speed are sequentially applied on bearing, originally radial load are applied to axle journal, radially carried Lotus and axial load increase linearly over time, reach maximum within 0.01 second, keep constant afterwards；Rotating speed is equal from 0 second to 0.05 second Constant rotation is kept with 314.16r/s, while the initial velocity 116.9rad/s of predefined rolling element and retainer, predefines inner ring Initial velocity 314.16rad/s；Rotating speed and radial load are applied on axle journal, meet actual stand under load shape during bearing working Formula, result of calculation is closer to truth.

The ball bearing reliability design approach, it is characterised in that：Under the ball bearing reliability design approach also meets State requirement：

Bearing internal external circle raceway element stress major frequency components are rolling element by Internal and external cycle frequency and its integral multiple Frequently, illustrating the stress of Internal and external cycle certain point can be affected by neighbouring multiple rolling elements on raceway contact stress simultaneously, analysis knot Fruit is that ball bearing reliability design and Fatigue Life Research provide reference method.

The ball bearing reliability design approach, it is characterised in that：The ball bearing reliability design approach specifically meets Following requirements：In the ball bearing reliability design approach, the Dynamics For Flexible Multibody Contact Dynamics model for first setting up ball bearing is concrete Meet following requirements：In the actual course of work, bearing is assemblied on axle, is the dynamics for studying bearing in operation process Characteristic, on the basis of statical model, augments the model of retainer and one section of axle, as shown in Figure 4, Figure 5；Whole model has 4 Individual part, respectively bearing inner race, bearing outer ring, rolling element and retainer；7 rolling elements are numbered, in model Each key node numbering；Node 1 is outer ring fringe node, and node 2 is inner ring fringe node, and node 3 is rolling element front node, Node 4 is rolling element side node；

The vibration acceleration situation of bearing outer ring node 1 is given by Fig. 6, the larger of bearing outer ring presence can be obtained Impact acceleration peak value；Acceleration amplitude substantially increases when every time rolling element passes through, vibration acceleration peak value occur when Between be spaced it is similar to stress mutation (Fig. 8) rule of outer coil unit.By the modal displacement situation that Fig. 7 is each critical component of bearing, Can be derived that and know due to outer ring Complete Bind, therefore outer ring modal displacement is 0；In 0.05s, inner ring corotating about 2.5 In week, node 3 is similar with 4 change in displacement rules on rolling element, and node 3 is affected less by rolling element rotation, and its displacement is mainly received To the impact of rolling element revolution, displacement curve counterpart node 4 is smoother, and rolling element 4 is affected larger by rolling element rotation, its Displacement is subject to the joint effect of rolling element rotation and revolution, displacement curve that fluctuation is presented；

Fig. 8 is bearing outer ring ball track element stress change curve, and Fig. 9 is inner ring raceway element stress change curve.By rolling Kinetoplast and retainer are together 116.67rad/s around the angular speed of axle, by being calculated frequency of the rolling element by outer ring For X₀=129.98Hz, in simulation time, retainer and rolling element have rotated together 0.928 week altogether, a total of 7 rollings The a certain unit that body passes through outer ring raceway.As can be seen from Figure 87 stress mutations are had in 0.05s Internal and external cycle raceway units Peak value.Inner ring rotating speed is 314.16rad/s, retainer and rolling element rotating speed 116.67rad/s, then both speed discrepancy is 197.489rad/s, by calculating, frequency X that rolling element passes through inner ring certain point_i=220Hz is logical in 0.05s rolling elements Inner ring raceway certain point 10 times are crossed, as can be seen from Figure 9 inner ring raceway unit has 10 stress mutation peak values.

Outer ring raceway and inner ring raceway element stress spectrogram are respectively by Figure 10 and Figure 11, it can be seen that outer ring raceway list Frequency and its integer frequency that first stress major frequency components pass through outer ring for rolling element, the main frequency of inner ring raceway element stress Rate composition is frequency and its integer frequency of the rolling element by inner ring, illustrates the stress of Internal and external cycle certain point and can simultaneously be subject to multiple Impact of the rolling element to raceway contact stress；

Figure 12 is certain element stress change curve on rolling element 1, and Figure 13 is certain element stress curve on rolling element 5, can be with Find out that rolling element, due to rotation, is alternately contacted with Internal and external cycle raceway, the certain point stress mutation on rolling element in simulation time Certain point stress mutation number of times is more than Internal and external cycle raceway for number, learns that rolling element stress is more complicated；

The reliability design of ball bearing can be completed according to the analysis of above-mentioned bearing operation dynamic characteristic of the course.

The present invention establishes the Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing, and simulation analysis deep groove ball bearing turns Dynamic process, has obtained the angular speed of each part and the Changing Pattern of dynamic Contact impact stress；Bearing internal external circle raceway unit should Power major frequency components are rolling element by Internal and external cycle frequency and its integer frequency, illustrate the stress meeting of Internal and external cycle certain point Simultaneously raceway contact stress is affected by neighbouring multiple rolling elements, analysis result is ball bearing reliability design and tired longevity Life research provides reference method.The relative theory of the present invention can be generalized to all transplantable correlative technology fields.Its tool There are potential more huge economic worth and social value.

Description of the drawings

Below in conjunction with the accompanying drawings and embodiment the present invention is further detailed explanation：

Fig. 1 be ball bearing in the presence of load Q between rolling element and Internal and external cycle raceway by contact gradually expand to it is ellipse The principle simplified schematic diagram of annular contact；

Fig. 2 is the stress distribution principle sketch in contact zone of correspondence Fig. 1；

Fig. 3 is the relevant geometric parameter figure of ball bearing；

Fig. 4 is the FEM model of the dynamic analysis of the bearing being numbered to rolling element；

The FEM model of the dynamic analysis of the bearing that Fig. 5 positions are numbered to key node in model；

Fig. 6 is the vibration acceleration situation schematic diagram of bearing outer ring node 1；

Fig. 7 is the modal displacement situation schematic diagram of each critical component of bearing；

Fig. 8 is bearing outer ring ball track element stress change curve；

Fig. 9 is bearing inner race raceway element stress curve map；

Figure 10 is outer ring raceway element stress spectrogram；

Figure 11 is inner ring raceway element stress spectrogram；

Figure 12 is certain element stress change curve on rolling element 1；

Figure 13 is certain element stress curve on rolling element 5.

Specific embodiment

Embodiment 1

A kind of ball bearing reliability design approach,

(1) the ball bearing reliability design approach is based on following premises：Think that rolling bearing rolling element is rolled with Internal and external cycle The contact in road meets hertz (Hertz) contact theory, rolling element contact for point with the contact type of bearing internal external circle raceway or/and Linear contact lay, wherein belongs to a contact between ball bearing roller kinetoplast and Internal and external cycle, cylinder and taper roll bearing contact belong to line and connect Touch；The correlation of hertz (Hertz) contact theory specifically requires as follows：

1. in ball bearing, contact between rolling element and Internal and external cycle raceway belongs to a contact, in the presence of load Q, contact Point gradually expands to elliptical-shaped contact face, and in oval central spot, stress is σ to the maximum_max, a length of 2a of major axis of ellipse, short axle A length of 2b, as shown in figure 1, the stress distribution in contact zone, as shown in Figure 2.Known by Hertzian contact theory：

In formula, Q is the contact load of rolling element and Internal and external cycle raceway；A is the axial length of the Contact Ellipse head of district half；B is semi-minor axis It is long；σ_maxTo contact maximum stress；δ is deflection (also known as convergence amount)；Equivalent elastic modulus E ' is expressed as：

In formula, E₁, E₂, μ₂, μ₂The respectively elastic modelling quantity and Poisson's ratio of rolling element and Internal and external cycle raceway；

2. principal curvatures and ∑ ρ are the principal curvatures sum of rolling element and raceway contact point, i.e.,：

∑ ρ=ρ₁₁+ρ₁₂+ρ₂₁+ρ₂₂ (6)

m_aAnd m_bRespectively major axis and short axle coefficient, are expressed as：

In formula, k is ellipticity,E is oval eccentric rate,K (e) and L (e) is respectively and ellipse Eccentricity it is relevant first and two class integration：

Oval eccentric rate e is with the relation of ellipticity：

Principal curvature function F (ρ) is expressed as：

It also is indicated as simultaneously：

If bearing each several part physical dimension by formula (13)-formula (17) and formula (11), it is known that can try to achieve principal curvature function F (ρ)；Again formula (9), (10) are substituted into into (12) and try to achieve k, then e can be tried to achieve by formula (10), bearing rigidity can be weighed whereby；

3. in the presence of rolling element and Internal and external cycle contact load Q, major semiaxis and semi-minor axis can respectively be asked by formula (7), (8) Coefficient；Contact zone Max.contact stress σ can be asked by formula (1) and (4)_maxWith convergence amount δ；

For point contact ball bearing, its principal curvatures is respectively：

Spin：

Inner ring：

Outer ring：

In formula, D_bFor ball diameters；α is contact Angle；D is outer ring internal diameter；D is inner ring external diameter；d_mFor rolling element center circle diameter；r_inFor interior raceway radius；r_ouFor outer raceway half Footpath；By taking deep groove ball bearing as an example, its member and main geometric parameter is as shown in Figure 3.

(2) ball bearing reliability design approach meets following requirements：

The Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing is initially set up, simulation analysis deep groove ball bearing was rotated Journey, obtains the angular speed of each part and the Changing Pattern of dynamic Contact impact stress, and complete ball bearing based on this can By property design.

In the ball bearing reliability design approach, with transmission input shaft front end deep groove ball bearing as object, research rolling The dynamics of each part in dynamic bearing operation process, it is considered to steel ball, the structural flexibility deformation of lasso raceway and dynamic Contact Relation, establishes the Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing in Abaqus/Expicit, analyzes deep-groove ball axle The dynamics for holding, obtains the angular speed of each part and the Changing Pattern of dynamic Contact impact stress；

The retainer angular speed of ball bearing, the simulation result of steel ball revolution angular speed and theoretical value are contrasted, Result of calculation is ball bearing dynamic design and fatigue life to provide reference method, realizes ball bearing reliability design.Simulation time For 0.05s, the circle of inner ring rotation 2.5 of bearing, can see rolling element also with the rotation of inner ring by the result animation for emulating Rotate, but rotating speed is slower than inner ring rotating speed.

In the ball bearing reliability design approach, the Dynamics For Flexible Multibody Contact Dynamics model for setting up ball bearing specifically meets Following requirements：

In the actual course of work, bearing is assemblied on axle, is the dynamics for studying bearing in operation process, On the basis of statical model, the model of retainer and one section of axle is augmented；Whole model has 4 parts, respectively in bearing Circle, bearing outer ring, rolling element and retainer；7 rolling elements are numbered, as shown in Figure 4；To each key node in model Numbering, as shown in Figure 5；Node 1 is outer ring fringe node, and node 2 is inner ring fringe node, and node 3 is rolling element front node, Node 4 is rolling element side node；

The retainer of increase and the material properties of bearing inner race axle are rigid body, its density and Poisson's ratio and bearing material phase Together；Retainer is considered as into rigid body for whole dynamics calculation has no too much influence, bearing deforms mainly in operation process From the mutual extruding of bearing internal external circle and rolling element, and primarily radial deformation；And retainer be mainly used for limit with about Beam bearing roller is moved in the raceway of bearing internal external circle, and certain gap is left between retainer and rolling element, for The deformation effect of bearing is less；The in addition calculating of rigid body can save the substantial amounts of time relative to elastomer, therefore by retainer It is changed to rigid body；

Specific material properties meet following requirements (referring to table 2)：Rolling element, bearing inner race, the material class of bearing outer ring Type is elastomer, elastic modelling quantity 2.07 × 10⁵MPa；The material type of retainer and bearing inner race axle is rigid body；Poisson's ratio 0.3, density is 7.85 × 10^-9；From the linear hexahedral elements of C3D8R to whole model partition grid, FEM model is set up As shown in Figure 4；

All frees degree of constraint bearing outer ring outer surface, describe bearing block to bearing restriction effect, in the rigid body of axle journal Arrange in material model and constrain its axial displacement so as to operate in bearing plane, occur without inclined phenomenon, miscellaneous part Constraint is not applied；According to the working condition of bearing, reference point RP-1 is set up at bearing inner race center, by reference point and rigid body axle Coupling, applies radial load -3000N (Y-axis negative direction) in reference point RP-1, applies axial load -1000N (z-axis losing sides To), acting on for the external applied load that bearing is subject to is described；Its axis is applied through to axle journal and along the angular speed of z positive directions, description Operating condition during bearing working；

Radial load and rotating speed are sequentially applied on bearing, originally radial load are applied to axle journal, radially carried Lotus and axial load increase linearly over time, reach maximum within 0.01 second, keep constant afterwards；Rotating speed is equal from 0 second to 0.05 second Constant rotation is kept with 314.16r/s, while the initial velocity 116.9rad/s of predefined rolling element and retainer, predefines inner ring Initial velocity 314.16rad/s；Rotating speed and radial load are applied on axle journal, meet actual stand under load shape during bearing working Formula, result of calculation is closer to truth.

The ball bearing reliability design approach also meets following requirements：

Bearing internal external circle raceway element stress major frequency components are rolling element by Internal and external cycle frequency and its integral multiple Frequently, illustrating the stress of Internal and external cycle certain point can be affected by neighbouring multiple rolling elements on raceway contact stress simultaneously, analysis knot Fruit is that ball bearing reliability design and Fatigue Life Research provide reference method.

The ball bearing reliability design approach, it is characterised in that：The ball bearing reliability design approach specifically meets Following requirements：In the ball bearing reliability design approach, the Dynamics For Flexible Multibody Contact Dynamics model for first setting up ball bearing is concrete Meet following requirements：In the actual course of work, bearing is assemblied on axle, is the dynamics for studying bearing in operation process Characteristic, on the basis of statical model, augments the model of retainer and one section of axle, as shown in Figure 4, Figure 5；Whole model has 4 Individual part, respectively bearing inner race, bearing outer ring, rolling element and retainer；7 rolling elements are numbered, in model Each key node numbering；Node 1 is outer ring fringe node, and node 2 is inner ring fringe node, and node 3 is rolling element front node, Node 4 is rolling element side node；

The vibration acceleration situation of bearing outer ring node 1 is given by Fig. 6, the larger of bearing outer ring presence can be obtained Impact acceleration peak value；Acceleration amplitude substantially increases when every time rolling element passes through, vibration acceleration peak value occur when Between be spaced it is similar to stress mutation (Fig. 8) rule of outer coil unit.By the modal displacement situation that Fig. 7 is each critical component of bearing, Can be derived that and know due to outer ring Complete Bind, therefore outer ring modal displacement is 0；In 0.05s, inner ring corotating about 2.5 In week, node 3 is similar with 4 change in displacement rules on rolling element, and node 3 is affected less by rolling element rotation, and its displacement is mainly received To the impact of rolling element revolution, displacement curve counterpart node 4 is smoother, and rolling element 4 is affected larger by rolling element rotation, its Displacement is subject to the joint effect of rolling element rotation and revolution, displacement curve that fluctuation is presented；

Fig. 8 is bearing outer ring ball track element stress change curve, and Fig. 9 is inner ring raceway element stress change curve.By rolling Kinetoplast and retainer are together 116.67rad/s around the angular speed of axle, by being calculated frequency of the rolling element by outer ring For X₀=129.98Hz, in simulation time, retainer and rolling element have rotated together 0.928 week altogether, a total of 7 rollings The a certain unit that body passes through outer ring raceway.As can be seen from Figure 87 stress mutations are had in 0.05s Internal and external cycle raceway units Peak value.Inner ring rotating speed is 314.16rad/s, retainer and rolling element rotating speed 116.67rad/s, then both speed discrepancy is 197.489rad/s, by calculating, frequency X that rolling element passes through inner ring certain point_i=220Hz is logical in 0.05s rolling elements Inner ring raceway certain point 10 times are crossed, as can be seen from Figure 9 inner ring raceway unit has 10 stress mutation peak values.

Outer ring raceway and inner ring raceway element stress spectrogram are respectively by Figure 10 and Figure 11, it can be seen that outer ring raceway list Frequency and its integer frequency that first stress major frequency components pass through outer ring for rolling element, the main frequency of inner ring raceway element stress Rate composition is frequency and its integer frequency of the rolling element by inner ring, illustrates the stress of Internal and external cycle certain point and can simultaneously be subject to multiple Impact of the rolling element to raceway contact stress；

Figure 12 is certain element stress change curve on rolling element 1, and Figure 13 is certain element stress curve on rolling element 5, can be with Find out that rolling element, due to rotation, is alternately contacted with Internal and external cycle raceway, the certain point stress mutation on rolling element in simulation time Certain point stress mutation number of times is more than Internal and external cycle raceway for number, learns that rolling element stress is more complicated；

The reliability design of ball bearing can be completed according to the analysis of above-mentioned bearing operation dynamic characteristic of the course.

The present embodiment establishes the Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing, simulation analysis deep groove ball bearing Rotation process, has obtained the angular speed of each part and the Changing Pattern of dynamic Contact impact stress；Bearing internal external circle raceway unit Stress major frequency components are rolling element by Internal and external cycle frequency and its integer frequency, illustrate the stress of Internal and external cycle certain point Simultaneously raceway contact stress can be affected by neighbouring multiple rolling elements, analysis result is ball bearing reliability design and fatigue Life search provides reference method.The relative theory of the present embodiment can be generalized to all transplantable correlative technology fields. It has potential more huge economic worth and social value.

Claims (5)

1. ball bearing reliability design approach, it is characterised in that：

(1) the ball bearing reliability design approach is based on following premises：Think rolling bearing rolling element with Internal and external cycle raceway Contact meets Hertzian contact theory, and rolling element is contacted or/and linear contact lay with the contact type of bearing internal external circle raceway for point；Hertz The correlation of contact theory specifically requires as follows：

1. in ball bearing, contact between rolling element and Internal and external cycle raceway belongs to contact, in the presence of load Q, contact point by Elliptical-shaped contact face is gradually expanded to, in oval central spot, stress is σ to the maximum_max, the oval a length of 2a of major axis, short axle is a length of 2b, is known by Hertzian contact theory：

${\mathrm{\σ}}_{max}=\frac{3Q}{2\mathrm{\π}ab}---\left(1\right)$

$a=m_a\sqrt[3]{\frac{3Q}{E^{\′}\mathrm{\Σ}\mathrm{\ρ}}}---\left(2\right)$

$b=m_b\sqrt[3]{\frac{3Q}{E^{\′}\mathrm{\Σ}\mathrm{\ρ}}}---\left(3\right)$

$\mathrm{\δ}=\frac{2K\left(e\right)}{m_a}\sqrt[3]{\frac{1}{8}{\left(\frac{3}{E^{\′}}\right)}^2{Q}^2\mathrm{\Σ}\mathrm{\ρ}}---\left(4\right)$

In formula, Q is the contact load of rolling element and Internal and external cycle raceway；A is the axial length of the Contact Ellipse head of district half；B is that semi-minor axis is long； σ_maxTo contact maximum stress；δ is deflection；Equivalent elastic modulus E ' is expressed as：

$\frac{1}{E^{\′}}=\frac{1}{2}(\frac{1-{\mathrm{\μ}}_1^2}{E_1}+\frac{1-{\mathrm{\μ}}_2^2}{E_2})---\left(5\right)$

In formula, E₁, E₂, μ₁, μ₂The respectively elastic modelling quantity and Poisson's ratio of rolling element and Internal and external cycle raceway；

2. principal curvatures and ∑ ρ are the principal curvatures sum of rolling element and raceway contact point, i.e.,：

∑ ρ=ρ₁₁+ρ₁₂+ρ₂₁+ρ₂₂ (6)

m_aAnd m_bRespectively major axis and short axle coefficient, are expressed as：

$m_a=\sqrt[3]{\frac{2L\left(e\right)}{{\mathrm{\πk}}^2}}---\left(7\right)$

$m_b=\sqrt[3]{\frac{2L\left(e\right)k}{\mathrm{\π}}}---\left(8\right)$

In formula, k is ellipticity,E is oval eccentric rate,K (e) and L (e) is respectively and oval eccentric rate Relevant first and two class integrations：

Oval eccentric rate e is with the relation of ellipticity：

$e=\sqrt{1-k^2}---\left(10\right)$

Principal curvature function F (ρ) is expressed as：

$F\left(\mathrm{\ρ}\right)=\frac{|({\mathrm{\ρ}}_{11}-{\mathrm{\ρ}}_{12})+({\mathrm{\ρ}}_{21}-{\mathrm{\ρ}}_{22})|}{\mathrm{\Σ}\mathrm{\ρ}}---\left(11\right)$

It also is indicated as simultaneously：

$F\left(\mathrm{\ρ}\right)=\frac{(1+k^2)L\left(e\right)-2k^{2}K\left(e\right)}{(1-k^2)L\left(e\right)}---\left(12\right)$

If bearing each several part physical dimension by formula (13)-formula (17) and formula (11), it is known that can try to achieve principal curvature function F (ρ)；Again Formula (9), (10) are substituted into into (12) and tries to achieve k, then e can be tried to achieve by formula (10), bearing rigidity can be weighed whereby；

3. in the presence of rolling element and Internal and external cycle contact load Q, major semiaxis and semi-minor axis system can respectively be asked by formula (7), (8) Number；Contact zone Max.contact stress σ can be asked by formula (1) and (4)_maxWith convergence amount δ；

For point contact ball bearing, its principal curvatures is respectively：

Spin：

${\mathrm{\ρ}}_{11}={\mathrm{\ρ}}_{12}=\frac{2}{D_b}---\left(13\right)$

Inner ring：

${\mathrm{\ρ}}_{21}=\frac{2}{D_b}\left(\frac{\mathrm{\γ}}{1-\mathrm{\γ}}\right)---\left(14\right)$

${\mathrm{\ρ}}_{22}=-\frac{1}{f_m{D}_b}---\left(15\right)$

Outer ring：

${\mathrm{\ρ}}_{21}=-\frac{1}{D_b}\left(\frac{\mathrm{\γ}}{1-\mathrm{\γ}}\right)---\left(16\right)$

${\mathrm{\ρ}}_{22}=-\frac{1}{f_{ou}{D}_b}---\left(17\right)$

In formula, D_bFor ball diameters； $\mathrm{\γ}=\frac{D_{b}cos\mathrm{\α}}{d_m};d_m=\frac{D+d}{2};f_n=\frac{r_{in}}{D_b};f_{ou}=\frac{r_{ou}}{D_b};$ α is contact angle；D is Outer ring internal diameter；D is inner ring external diameter；d_mFor rolling element center circle diameter；r_mFor interior raceway radius；r_ouFor outer raceway radius；

(2) ball bearing reliability design approach meets following requirements：

The Dynamics For Flexible Multibody Contact Dynamics model of deep groove ball bearing is initially set up, simulation analysis deep groove ball bearing rotation process is obtained To the angular speed and the Changing Pattern of dynamic Contact impact stress of each part, and the reliability of ball bearing is completed based on this set Meter.

2. according to ball bearing reliability design approach described in claim 1, it is characterised in that：

The dynamics of each part in research rolling bearing operation process, it is considered to steel ball, the structural flexibility deformation of lasso raceway With dynamic Contact relation, the Dynamics For Flexible Multibody Contact Dynamics model of ball bearing is set up, analyzes the dynamics of deep groove ball bearing, Obtain the angular speed of each part and the Changing Pattern of dynamic Contact impact stress；

The retainer angular speed of ball bearing, the simulation result of steel ball revolution angular speed and theoretical value are contrasted, is calculated As a result it is ball bearing dynamic design and fatigue life to provide reference method, realizes ball bearing reliability design.

3. according to ball bearing reliability design approach described in claim 2, it is characterised in that：

In the ball bearing reliability design approach, the Dynamics For Flexible Multibody Contact Dynamics model for setting up ball bearing specifically meets following Require：

To study dynamics of the bearing in operation process, on the basis of statical model, retainer and one section of axle are augmented Model, whole model has 4 parts, respectively bearing inner race, bearing outer ring, rolling element and retainer；To rolling element It is numbered, to each key node numbering in model；

Specific material properties meet following requirements：Rolling element, bearing inner race, the material type of bearing outer ring are elastomer, Elastic modelling quantity 2.07 × 10⁵MPa；The material type of retainer and bearing inner race axle is rigid body；Poisson's ratio 0.3, density is 7.85 ×10^-9；From the linear hexahedral elements of C3D8R to whole model partition grid, FEM model is set up；

All frees degree of constraint bearing outer ring outer surface, describe bearing block to bearing restriction effect, in the body material of axle journal Arrange in model and constrain its axial displacement so as to operate in bearing plane, occur without inclined phenomenon, miscellaneous part is not Apply constraint；According to the working condition of bearing, reference point is set up at bearing inner race center, reference point is coupled with rigid body axle, Apply radial load in reference point, apply axial load, describe acting on for the external applied load that bearing is subject to；It is applied through to axle journal Axis and along the angular speed of z positive directions, describes operating condition during bearing working；

Radial load and rotating speed are sequentially applied on bearing, originally apply radial load to axle journal, radial load and Axial load increases linearly over time, reach keep after maximum it is constant；Rotating speed keeps constant rotation, while predefined rolling element With the initial velocity of retainer, inner ring initial velocity is predefined；Rotating speed and radial load are applied on axle journal, meet bearing working When actual loading.

4. according to one of claim 1-3 ball bearing reliability design approach, it is characterised in that：The ball bearing can Also meet following requirements by property method for designing：

Bearing internal external circle raceway element stress major frequency components are rolling element by Internal and external cycle frequency and its integer frequency, are said The stress of bright Internal and external cycle certain point can be affected by neighbouring multiple rolling elements on raceway contact stress simultaneously, and analysis result is ball Bearing reliability design provides reference.

5. according to ball bearing reliability design approach described in claim 3 or 4, it is characterised in that：The ball bearing reliability sets Meter method specifically meets following requirements：

In the ball bearing reliability design approach, under first setting up the concrete satisfaction of Dynamics For Flexible Multibody Contact Dynamics model of ball bearing State requirement：To study dynamics of the bearing in operation process, on the basis of statical model, retainer and one section are augmented The model of axle, whole model has 4 parts, respectively bearing inner race, bearing outer ring, rolling element and retainer；To rolling Body is numbered, to each key node numbering in model；Node 1 is outer ring fringe node, and node 2 is inner ring fringe node, is saved Point 3 is rolling element front node, and node 4 is rolling element side node；

By the vibration acceleration situation of bearing outer ring node 1, the impact acceleration peak value of bearing outer ring can be obtained；Roll every time Acceleration amplitude increases when body passes through, and the time interval that vibration acceleration peak value occurs is advised with the stress mutation of outer coil unit Rule is similar；By the modal displacement situation of each critical component of bearing, can be derived that and know due to outer ring Complete Bind, therefore outer ring node Displacement is 0；In 0.05s, inner ring corotating about 2.5 weeks, node 3 is similar with 4 change in displacement rules on rolling element, node 3 are affected less by rolling element rotation, and its displacement is mainly affected by rolling element revolution, and displacement curve counterpart node 4 compares Smooth, rolling element 4 is affected larger by rolling element rotation, and its displacement is subject to the joint effect of rolling element rotation and revolution, displacement Curve is presented fluctuation；

By rolling element and retainer together around the angular speed of axle, by being calculated frequency of the rolling element by outer ring；

By outer ring raceway and inner ring raceway element stress spectrogram, it can be seen that outer ring raceway element stress major frequency components are Frequency and its integer frequency that rolling element passes through outer ring, the major frequency components of inner ring raceway element stress pass through interior for rolling element The frequency and its integer frequency of circle, illustrating the stress of Internal and external cycle certain point can simultaneously be subject to multiple rolling elements to raceway contact stress Impact；

Rolling element is alternately contacted due to rotation with Internal and external cycle raceway, the certain point stress mutation on rolling element in simulation time Certain point stress mutation number of times is more than Internal and external cycle raceway for number, learns that rolling element stress is more complicated；

The reliability design of ball bearing can be completed according to the analysis of above-mentioned bearing operation dynamic characteristic of the course.