CN105822661A - Design method and device of structural parameters of major and minor semi axes of elliptical race ball bearing - Google Patents

Abstract

The invention relates to a design method and a device of structural parameters of major and minor semi axes of an elliptical race ball bearing. The design method comprises the steps of firstly, calculating radial displacement, axial displacement and corner displacement of an inner ring of the bearing; calculating normal contact loads of all contact positions according to the obtained displacements to determine the contact load of a rolling body with the maximum load and the maximum contact stress received by the bearing; drawing a bearing static load curve through adopting the maximum contact stress as the index, and determining a circle radius coefficient t and a design contact angle according to limit load parameters of the bearing; and finally, calculating a major semi-axis and a minor semi-axis of an ellipse according to the obtained design contact angle, the circle radius coefficient and the radius of a steel ball. According to the design method, the major semi-axis and the minor semi-axis of an elliptical race can be quickly and accurately designed through the process, the problem that the selection of the major semi-axis and the minor semi-axis of the bearing elliptical race has no reference is solved, and reference can be provided for judgment of utilization conditions of external loads according to the adopted static load curve design drawing method.

Description

The method for designing of a kind of elliptic roller track ball bearing length semi-axis structure parameter and device

Technical field

The present invention relates to method for designing and the device of a kind of elliptic roller track ball bearing length semi-axis structure parameter, belong to turntable bearing design field.

Background technology

Turntable bearing, as the important foundation element of engineering machinery and building machinery, is not only to have needed make relative gyration and but also simultaneously need to bear necessary important force transfer element between two mechanical parts of axial force, radial force and tilting moment.Turntable bearing can be divided into by its structural shape: single-row ball type, three organ timbering formulas, crossed pin roller type, double eight point cantact ball, bowling pin combination type etc..Its ball type turntable bearing market occupation proportion is maximum, reaches more than 90%, is widely used in the fields such as host computer system.Along with all kinds of host computer system densifications develop, requirement to ball turntable bearing radially installing space and bearing capacity is more and more higher, in order to improve the bearing capacity of turntable bearing, meeting the market requirement, ball turntable bearing is proposed a kind of novel roller path structure, tradition peach-shaped groove-section pattern changes into oval raceway (as shown in Fig. 1-a and Fig. 1-b), and remaining parameter is identical with peach-shaped rolling way turntable bearing.Research shows, make peach-shaped raceway into ellipse, its raceway form accuracy is more easy to control, and owing to elliptic roller track is variable curvature raceway, when contact angle changes, the raceway curvature of contact point also changes, therefore it can improve the contact stress state of steel ball and raceway, thus improves the life-span of bearing and the bearing capacity of raceway.

Bearing capacity is the highly important performance indications of turntable bearing, and the most conventional quiet endurance curves expresses the load-carrying properties of bearing.Quiet endurance curves is with contact stress as set-point, setting radial load is constant, calculate stand under load maximum rolling body and raceway contact center in bearing and reach axial load and the tilting moment born during this given contact stress, axial load-tilting moment corresponding relation endurance curves drawn out.The drafting of quiet endurance curves is affected by bearing structure parameters such as such as contact angle, raceway radius of curvature and steel ball sizes.Most structural parameters of turntable bearing have clear and definite value foundation, such as the parameter standardization the most such as internal diameter, external diameter, steel ball size and pitch diameter of ball set of bearing, are available for novel elliptic roller track turntable bearing bearing with reference to selecting.But for novel elliptic roller track bearing, its elliptic roller track there are differences with tradition peach-shaped raceway parameter aspect, cause long a and b of major and minor axis half of elliptic roller track, original contact angle α etc. bearing capacity and life-span are had considerable influence parameter its choose can not be with reference to existing design code, and value is the most unreliable the most by rule of thumb, and the ultimate bearing capacity of turntable bearing can not be given full play to, therefore the structural parameters such as oval long a and b of raceway major and minor axis half, original contact angle α are proposed a kind of value reference scheme the most reliably significant.

Summary of the invention

It is an object of the invention to provide method for designing and the device of a kind of elliptic roller track ball bearing length semi-axis structure parameter, to solve the elliptic roller track ball bearing long semi-minor axis selection problem without foundation.

The present invention solves that above-mentioned technical problem provides the method for designing of a kind of elliptic roller track ball bearing length semi-axis structure parameter, the method comprises the following steps:

1) using bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation of inner ring bearing inner race radial displacement δ is obtained_r, axial displacement δ_aWith corner displacement amount θ；

2) according to the bearing inner race radial displacement δ obtained_r, axial displacement δ_aNormal direction contact load at each contact position is calculated, to determine maximum stand under load rolling element contact load Q with corner displacement amount θ_maxThe Max.contact stress σ born with bearing_max；

3) Max.contact stress σ is judged_maxWhether reach the ultimate bearing stress of bearing, as Max.contact stress σ_maxWhen reaching the ultimate bearing stress of bearing, according to this Max.contact stress σ_maxThe quiet endurance curves of bearing is drawn, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α for index；

4) according to design contact angle α, the radius of circle coefficient t obtained and steel ball radius calculation ellipse major semiaxis and semi-minor axis.

Described radius of circle coefficient t, design contact angle α determination process as follows:

A. with Max.contact stress σ_maxDraw the quiet endurance curves under different designs contact angle for index, finding abscissa is bearing axial limit load value, and vertical coordinate is the some P of bearing tilting moment ultimate value, and design contact angle corresponding to outside curve nearest for chosen distance point P is as design load α；

B. the quiet endurance curves under corresponding different radius of circle coefficient values under the contact angle that design load is α is drawn, finding abscissa is bearing axial limit load value, vertical coordinate is the point of bearing tilting moment ultimate value, and radius factor corresponding to the nearest outside curve of this point of chosen distance is as design load t.

Described step 1) employed in the mechanic nonlinearity equilibrium equation of inner ring:

Wherein F_rFor inner ring by outer radial load, F_aFor axial load, M is tilting moment,For position angle, d_mFor bearing pitch radius,WithFor steel ball position angle2 contacts at the place contact angle to being formed,For in position angleContact the steel ball contact load to inner ring elliptic roller track at,For in position angleContact the steel ball contact load to inner ring elliptic roller track at two.

Max.contact stress σ_maxComputing formula be:

${\mathrm{\σ}}_{\max }=\frac{1}{{\mathrm{\πn}}_a{b}_b}{\[\frac{3}{2}{\left(\frac{\mathrm{\Σ}\mathrm{\ρ}}{\mathrm{\η}}\right)}^2{Q}_{max}\]}^{1/3}$

Wherein σ_maxFor bearing Max.contact stress；n_a、n_bFor the coefficient relevant with contact point principal curvatures difference function F (ρ), ∑ ρ be contact point principal curvatures and, η is the comprehensive elastic constant of two articles.

Put P determined by step A when falling outside contact angle α span, parameter need to be redesigned；Put P determined by step B when falling outside radius of circle coefficient t span, also need to redesign parameter；The span of radius of circle coefficient t is 1.02～1.10, and contact angle α span is 35 °～50 °.

The major semiaxis of described bearing elliptic roller track and the computing formula of semi-minor axis be:

$a=r{\sin }^2\mathrm{\α}\sqrt{t}/(1-t{\cos }^2\mathrm{\α})$

$b=rsin\mathrm{\α}/\sqrt{1-t{\cos }^2\mathrm{\α}}$

Wherein a, b are respectively major semiaxis and the semi-minor axis of bearing elliptic roller track, and r is steel ball radius, and α is design contact angle, and t is radius of circle coefficient.

Described Max.contact stress σ_maxThe criterion of the ultimate bearing stress reaching bearing is:

By σ_maxWith [σ_max]/f_s ^0.5Compare, it is judged that both ratio whether in range of error, if, then explanation Max.contact stress σ_maxThe ultimate bearing stress of bearing, [σ are reached_max] it is the allowable contact stress of bearing, f_sCoefficient for bearing safety.

Present invention also offers the design device of a kind of elliptic roller track ball bearing length semi-axis structure parameter, this design device includes that displacement calculation module, Max.contact stress computing module, radius of circle coefficient and design contact angle choose module and oval major semiaxis and semi-minor axis computing module

Described displacement calculation module is used for bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation of inner ring obtain bearing inner race radial displacement δ_r, axial displacement δ_aWith corner displacement amount θ；

Described Max.contact stress computing module is for according to the bearing inner race radial displacement δ obtained_r, axial displacement δ_aNormal direction contact load at each contact position is calculated, to determine maximum stand under load rolling element contact load Q with corner displacement amount θ_maxThe Max.contact stress born with bearing；

Described radius of circle coefficient and design contact angle choose module for judging whether Max.contact stress reaches the ultimate bearing stress of bearing, when Max.contact stress reaches the ultimate bearing stress of bearing, it is that index draws the quiet endurance curves of bearing according to this Max.contact stress, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α；

Described oval major semiaxis and semi-minor axis computing module are for according to design contact angle α, the radius of circle coefficient t obtained and steel ball radius calculation ellipse major semiaxis and semi-minor axis.

Described radius of circle coefficient and design contact angle choose module to choose process as follows:

A. with Max.contact stress σ_maxDraw the quiet endurance curves under different designs contact angle for index, finding abscissa is bearing axial limit load value, and vertical coordinate is the some P of bearing tilting moment ultimate value, and design contact angle corresponding to outside curve nearest for chosen distance point P is as design load α；

B. the quiet endurance curves under corresponding different radius of circle coefficient values under the contact angle that design load is α is drawn, finding abscissa is bearing axial limit load value, vertical coordinate is the point of bearing tilting moment ultimate value, and radius factor corresponding to the nearest outside curve of this point of chosen distance is as design load t.

The mechanic nonlinearity equilibrium equation of the inner ring used in described displacement calculation module:

Wherein F_rFor inner ring by outer radial load, F_aFor axial load, M is tilting moment,For position angle, d_mFor bearing pitch radius,WithFor steel ball position angle2 contacts at the place contact angle to being formed,For in position angleContact the steel ball contact load to inner ring elliptic roller track at,For in position angleContact the steel ball contact load to inner ring elliptic roller track at two.

The invention has the beneficial effects as follows: the present invention first calculation bearing inner ring radial displacement, axial displacement and corner displacement amount；Then normal direction contact load at each contact position is calculated according to bearing inner race radial displacement, axial displacement and the corner displacement amount obtained, to determine the Max.contact stress that maximum stand under load rolling element contact load and bearing are born；And according to this Max.contact stress σ_maxThe quiet endurance curves of bearing is drawn, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α for index；Finally according to the design contact angle α obtained, radius of circle coefficient t and steel ball radius calculation ellipse major semiaxis and semi-minor axis.Elliptic roller track long semi-minor axis a and b can be designed fast, accurately by the said process present invention, solve this Novel ball type long semi-minor axis of bearing elliptic roller track and select without according to problem, and design method for drafting according to quiet endurance curves of the present invention, can be that the judgement of external applied load applying working condition provides foundation.

Accompanying drawing explanation

Fig. 1-a is tradition peach-shaped steel ball rolling channel schematic diagram；

Fig. 1-b is oval steel ball receway schematic diagram；

Fig. 2 is that the coordinate position of oval 4 centers of curvature of inside and outside raceway and 2 contacts are to schematic diagram；

Fig. 3 is the elliptic roller track ball turntable bearing quiet endurance curves figure under different designs contact angle α；

Fig. 4 is the elliptic roller track ball turntable bearing quiet endurance curves in design contact angle α=35 ° lower different radii coefficient t value；

Fig. 5 is the elliptic roller track ball turntable bearing quiet endurance curves in design contact angle α=40 ° lower different radii coefficient t value；

Fig. 6 is the elliptic roller track ball turntable bearing quiet endurance curves in design contact angle α=45 ° lower different radii coefficient t value；

Fig. 7 is the elliptic roller track ball turntable bearing quiet endurance curves in design contact angle α=50 ° lower different radii coefficient t value；

Fig. 8 is for being utilized Fig. 3 to obtain design contact angle α schematic diagram by a P；

Radius factor t schematic diagram is obtained when Fig. 9 is for being utilized Fig. 6 contact angle α=45 ° by a P.

Detailed description of the invention

Below in conjunction with the accompanying drawings the detailed description of the invention of the present invention is described further.

A kind of embodiment of the method for designing of the elliptic roller track ball bearing length semi-axis structure parameter of the present invention

The present invention is by setting up statical model and calculating bearing maximum rolling body load Q_maxContact stress index σ is carried with bearing maximum_max, draw F_aThe quiet endurance curves of-M, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α；Elliptic roller track major semiaxis a and the value of semi-minor axis b is calculated according to radius of circle coefficient t, design contact angle α and steel ball radiuscope.Elliptic roller track long semi-minor axis a and b can be designed fast, accurately by the said process present invention, solve this Novel ball type long semi-minor axis of bearing elliptic roller track and select without according to problem, and design method for drafting according to quiet endurance curves of the present invention, can be that the judgement of external applied load applying working condition provides foundation.The specific implementation process of the method is as follows:

One, stand under load is set up forward and backward, the coordinate position of oval inside and outside 4 centers of curvature of raceway.

1. before stand under load, inside and outside circle center of curvature point coordinates determines.

The ellipse that the present invention is directed to is inside and outside to be rolled into the center of curvature and contacts as in figure 2 it is shown, d_iFor inner ring elliptic roller track top end diameter；d_eFor outer ring elliptic roller track top end diameter；D_wFor steel ball size；a_i, b_iIt is respectively inner ring ellipse major semiaxis and semi-minor axis；a_e, b_eIt is respectively outer ring ellipse major semiaxis and semi-minor axis；WithFor steel ball position angle2 contacts at the place contact angle to being formed；Distributing position angle for steel ball.

Above formula (1) contacts before representing stand under load and contacts contacting contacting two outer ring center point of curvature position coordinateses, wherein before an outer ring center point of curvature position coordinates, formula (4) expression stand under load before two inner ring center point of curvature position coordinateses, formula (3) expression stand under load before an inner ring center point of curvature position coordinates, formula (2) are represented stand under load:

$h\left(\mathrm{\α},a,b\right)=a-{\left(\frac{a^4}{b^2{\tan }^2\mathrm{\α}+a^2}\right)}^{\frac{1}{2}};r\left(\mathrm{\α},a,b\right)=a^2{b}^2{\left(\frac{{\tan }^2\mathrm{\α}+1}{b^2{\tan }^2\mathrm{\α}+a^2}\right)}^{\frac{3}{2}}$

2. after stand under load, inside and outside circle center of curvature point coordinates determines.

Assuming that turntable bearing outer ring is fixed, inner ring is at outside radial load F_r, axial load F_aWith under the synergy of tilting moment M, it is radially, axially respectively δ with corner displacement amount_r、δ_a, θ, then after stand under load, the final position of the inner ring center of curvature is:

$\begin{array}{c}{\mathrm{XC}}_{ii}^{\′}={\mathrm{XC}}_{ii}-{\mathrm{ZC}}_{ii}\mathrm{\θ}+{\mathrm{\δ}}_r\\ {\mathrm{YC}}_{ii}^{\′}={\mathrm{YC}}_{ii}\\ {\mathrm{ZC}}_{ii}^{\′}={\mathrm{ZC}}_{ii}+{\mathrm{XC}}_{ii}\mathrm{\θ}+{\mathrm{\δ}}_a\end{array}---\left(5\right)$

$\begin{array}{c}{\mathrm{XC}}_{is}^{\′}={\mathrm{XC}}_{is}-{\mathrm{ZC}}_{is}\mathrm{\θ}+{\mathrm{\δ}}_r\\ {\mathrm{YC}}_{is}^{\′}={\mathrm{YC}}_{is}\\ {\mathrm{ZC}}_{is}^{\′}={\mathrm{ZC}}_{is}+{\mathrm{XC}}_{is}\mathrm{\θ}+{\mathrm{\δ}}_a\end{array}---\left(6\right)$

Above formula (5) contacts after representing stand under load after an inner ring center point of curvature position coordinates, formula (6) are represented stand under load and contacts two inner ring center point of curvature position coordinateses.

Two, the contact angle that each position angle goes out is determinedThe contact angle at placeWith

After obtaining Internal and external cycle center of curvature final position, contact angle Nonlinear System of Equations can be set up according to position relationship, as follows:

$\begin{array}{c}{r}_{ii}={\left({{\mathrm{XC}}_{ii}^{\′}}^2+{{\mathrm{YC}}_{ii}^{\′}}^2\right)}^{\frac{1}{2}}\\ r_{is}={\left({{\mathrm{XC}}_{is}^{\′}}^2+{{\mathrm{YC}}_{is}^{\′}}^2\right)}^{\frac{1}{2}}\\ r_{ei}={\left({{\mathrm{XC}}_{ei}^{\′}}^2+{{\mathrm{YC}}_{ei}^{\′}}^2\right)}^{\frac{1}{2}}\\ r_{es}={\left({{\mathrm{XC}}_{es}^{\′}}^2+{{\mathrm{YC}}_{es}^{\′}}^2\right)}^{\frac{1}{2}}\end{array}---\left(7\right)$

Contact angle nonlinear equation at each position angle:

At known δ_r、δ_a, use in the case of θ Newton-Raphson method that above-mentioned contact angle Nonlinear System of Equations is solved, i.e. can determine that the contact angle of each positionWith

Three, each position angle is determinedPlace's contact load.

At each position contact angleWithAfter determining, i.e. can determine that each steel ball and Internal and external cycle elliptic roller track contact stiffness, the center of curvature away from, then carry out contact load calculating according to Hertz contact theory.At each position angle the center of curvature away from:

Wherein:

According to Hertz contact theory, can obtain at each position angle 2 contacts to contact stiffness, contact stiffness is contact angle α, radius of curvature r, steel ball size D_wWith bearing pitch radius d_mFunction.

Contact stiffness and the center of curvature by obtaining are away from position relationship, then theoretical according to Hertz point cantact, can derive the normal direction contact load at each contact position.

For in position angleContact the steel ball contact load to inner ring elliptic roller track at,For in position angleContact the steel ball contact load to inner ring elliptic roller track at two.

Four, inner ring mechanical balance equation is set up.

Inner ring is by outer radial load F_r, axial load F_aWith the synergy of tilting moment M, and at Angle PositionPlace's steel ball contact load to inner ring elliptic roller trackWithEffect.Inner ring is in poised state at external load and all rolling elements under the contact load effect with inner ring raceway, and the mechanic nonlinearity equilibrium equation of inner ring is:

Five, contact stress index σ is carried according to ball bearing maximum_max, set up F_aThe quiet endurance curves of-M

In rolling bearing technology, the quiet bearing capacity of bearing refers to act on non-rotating bearing, and making maximum stand under load rolling element contact the load that weakness generation is permanently deformed to the 0.0001 of rolling element diameter with inner ring or outer ring raceway, the allowable stress for point contact ball bearing is 4200MPa.Bearing point cantact Max.contact stress with the relation of maximum contact load is:

${\mathrm{\σ}}_{\max }=\frac{1}{{\mathrm{\πn}}_a{n}_b}{\[\frac{3}{2}{\left(\frac{\mathrm{\Σ}\mathrm{\ρ}}{\mathrm{\η}}\right)}^2{Q}_{max}\]}^{1/3}---\left(15\right)$

In formula, parameters symbol represents that implication is as follows: σ_maxFor bearing Max.contact stress；n_a、n_bFor the coefficient relevant with contact point principal curvatures difference function F (ρ), ∑ ρ be contact point principal curvatures and, η is the comprehensive elastic constant of two articles.

The safe handling Max.contact stress of ball turntable bearing is

${\mathrm{\&sigma;}}_{max}<\frac{\&lsqb;{\mathrm{\&sigma;}}_{max}\&rsqb;}{f_s^{0.5}}---\left(16\right)$

Wherein: [σ_max] it is the allowable contact stress of bearing, f_sCoefficient for bearing safety.

Point in the quiet endurance curves of bearing is the static borderline failure point of bearing, and the present invention makes σ_max=[σ_max]/f_s ^0.5Point as a point on bearing dead load curve, draw dead load curve.

Concrete grammar is as follows:

1. F is made_rEqual to radial load suffered under bearing limiting condition, to F_aCarry out continuous value, corresponding each group of value with M, obtain bearing inner race radial displacement δ according to the mechanic nonlinearity equilibrium equation (formula 13) of inner ring_r, axial displacement δ_aWith corner displacement amount θ, back substitution enters normal direction contact load computing formula (formula 12) at each contact position, obtains each contact position two contact normal direction contact load to placeWithAfter, comparing the size of each position contact load absolute value, the load of maximum absolute value is maximum stand under load rolling element contact load Q_max, then obtain, according to formula (15), the Max.contact stress σ that bearing is born_max；

2. σ is compared_maxWith [σ_max]/f_s ^0.5Value, if arrange range of error in, the most now σ_maxReach the ultimate bearing stress of bearing, extract now corresponding F_aWith M as the point constituted in quiet endurance curves；

3. coupling together a little of obtaining just is obtained the quiet endurance curves of bearing.

Six, the quiet endurance curves design long semi-minor axis of bearing elliptic roller track and original contact angle are utilized

Through theoretical derivation, can accurately be determined the major semiaxis a and semi-minor axis b of bearing elliptic roller track by formula 17, formula 18.

$a=r{\sin }^2\mathrm{\&alpha;}\sqrt{t}/(1-t{\cos }^2\mathrm{\&alpha;})---\left(17\right)$

$b=rsin\mathrm{\&alpha;}/\sqrt{1-t{\cos }^2\mathrm{\&alpha;}}---\left(18\right)$

The long semi-minor axis of formula middle (center) bearing elliptic roller track is to be determined by radius of circle coefficient t, design contact angle α and steel ball radius r, in order to ensure the bearing capacity of bearing, radius of circle coefficient t and design contact angle α can be selected by the quiet endurance curves of bearing, steel ball radius r is generally known quantity, thus can be according to formula (17) and long semi-minor axis a and b of (18) calculation bearing elliptic roller track.Specifically comprise the following steps that

1) according to limiting condition (F suffered by bearing_rmax、F_amaxAnd M_max), make F_rEqual to F_rmax, draw the quiet endurance curves of bearing according to said method；

2) change radius of circle coefficient t and design the value of original contact angle, according to working condition requirement, the span of general parameters t is 1.02～1.10, contact angle α span is 35 °～50 °, according to the quiet endurance curves (as shown in Figure 3) drawn under different designs contact angle α, and the quiet endurance curves (as shown in Figures 4 to 7) drawn under respective design contact angle α under different radii coefficient t value.

3) according to the axial force F in limiting condition condition_amaxWith moment M_maxValue, in different designs contact angle endurance curves figure, find coordinate points P (F_amax、M_max), this time point P has three kinds of situations:

The first situation is fallen in α=35 ° for some P, illustrates that the design of this structure is the safest, can cause waste of material, improve manufacturing cost, it should redesign parameter；

The second situation is fallen outside α=50 ° for some P, illustrates that the design of this structure can not meet bearing requirements, and parameter is unreasonable should be redesigned；

The third situation is fallen between α=35 ° and α=50 ° for a some P, then design contact angle corresponding to the outside curve of answering chosen distance P point nearest is as design load.

4) by step 3) choose design contact angle α after, find under this contact angle α quiet endurance curves under corresponding different radii coefficient t value (Fig. 4-7 one of them), according to the axial force F in limiting condition condition_amaxWith moment M_maxValue, figure finds coordinate points P (F_amax、M_max), this time point P has also three kinds of situations:

The first situation is fallen in t=1.02 for some P, illustrates that the design of this structure is the safest, can cause waste of material, improve manufacturing cost, it should redesign parameter；

The second situation is fallen outside t=1.10 for some P, illustrates that the design of this structure can not meet bearing requirements, and parameter is unreasonable should be redesigned；

The third situation is fallen between t=1.02 and t=1.10 for a some P, then radius factor corresponding to the outside curve of answering chosen distance P point nearest is as design load.

After selecting design contact angle α and radius of circle coefficient t according to above-mentioned 4 steps, just can accurately be determined the major semiaxis a and semi-minor axis b of bearing elliptic roller track by formula (17) and formula (18).

Illustrate as a example by a certain concrete elliptic roller track four point touching ball slewing bearing below, the structural parameters of this elliptic roller track four point touching ball slewing bearing and material parameter: d_m=1543mm, D_w=24.64mm, Z=158, v=0.3, E=207GPa, the load of its working limit is: F_r=100kN, F_a=400kN, M=1000kN m.

1. using bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation (formula 13) of inner ring obtain bearing inner race radial displacement δ_r, axial displacement δ_aWith corner displacement amount θ, back substitution enters normal direction contact load computing formula (formula 12) at each contact position, obtains normal direction contact load at each contact position thus obtains maximum stand under load rolling element contact load Q_max, then obtain, according to formula (15), the Max.contact stress σ that bearing is born_max。

2. compare σ_maxWith [σ_max]/f_s ^0.5Value, if arrange range of error in, the most now σ_maxReach the ultimate bearing stress of bearing, according to this maximum carrying contact stress σ_maxAs index, draw the quiet endurance curves under different designs contact angle α and find a P (shown in Fig. 8) in the drawings, its abscissa is bearing axial limit load value, vertical coordinate is bearing tilting moment ultimate value, to this bearing point P (400,1000) design contact angle corresponding to outside curve that, chosen distance P point is nearest is as design load, it may be assumed that α=45 °.

3. after choosing design contact angle α=45 °, a P (400 is found in the quiet endurance curves under the different radii coefficient t value that contact angle α=45 ° are corresponding, 1000), as shown in Figure 9: radius factor corresponding to the nearest outside curve of chosen distance P point is as design load, it may be assumed that t=1.06.

4. the parameter will chosen: contact angle α=45 °, radius factor t=1.06, steel ball radius r=D_w/ 2 substitute into formula (17) and formula (18), obtain: oval major semiaxis a=13.4938mm, oval semi-minor axis b=12.7071mm.

A kind of embodiment of the design device of the elliptic roller track ball bearing length semi-axis structure parameter of the present invention

Design device in the present embodiment includes that displacement calculation module, Max.contact stress computing module, radius of circle coefficient and design contact angle choose module and oval major semiaxis and semi-minor axis computing module, displacement calculation module is used for bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation of inner ring obtain bearing inner race radial displacement δ_r, axial displacement δ_aWith corner displacement amount θ；Max.contact stress computing module is for according to the bearing inner race radial displacement δ obtained_r, axial displacement δ_aNormal direction contact load at each contact position is calculated, to determine maximum stand under load rolling element contact load Q with corner displacement amount θ_maxThe Max.contact stress born with bearing；Radius of circle coefficient and design contact angle choose module for judging whether Max.contact stress reaches the ultimate bearing stress of bearing, when Max.contact stress reaches the ultimate bearing stress of bearing, it is that index draws the quiet endurance curves of bearing according to this Max.contact stress, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α；Oval major semiaxis and semi-minor axis computing module are for according to design contact angle α, the radius of circle coefficient t obtained and steel ball radius calculation ellipse major semiaxis and semi-minor axis.The specific implementation of each module has been described in detail in the embodiment of method, repeats no more here.

Claims (10)

1. the method for designing of an elliptic roller track ball bearing length semi-axis structure parameter, it is characterised in that the method comprises the following steps:

1) using bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation of inner ring bearing inner race radial displacement δ is obtained_r, axial displacement δ_aWith corner displacement amount θ；

2) according to the bearing inner race radial displacement δ obtained_r, axial displacement δ_aNormal direction contact load at each contact position is calculated, to determine maximum stand under load rolling element contact load Q with corner displacement amount θ_maxThe Max.contact stress σ born with bearing_max；

3) Max.contact stress σ is judged_maxWhether reach the ultimate bearing stress of bearing, as Max.contact stress σ_maxWhen reaching the ultimate bearing stress of bearing, according to this Max.contact stress σ_maxThe quiet endurance curves of bearing is drawn, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α for index；

4) according to design contact angle α, the radius of circle coefficient t obtained and steel ball radius calculation ellipse major semiaxis and semi-minor axis.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 1, it is characterised in that described radius of circle coefficient t, design contact angle α determination process as follows:

A. with Max.contact stress σ_maxDraw the quiet endurance curves under different designs contact angle for index, finding abscissa is bearing axial limit load value, and vertical coordinate is the some P of bearing tilting moment ultimate value, and design contact angle corresponding to outside curve nearest for chosen distance point P is as design load α；

B. the quiet endurance curves under corresponding different radius of circle coefficient values under the contact angle that design load is α is drawn, finding abscissa is bearing axial limit load value, vertical coordinate is the point of bearing tilting moment ultimate value, and radius factor corresponding to the nearest outside curve of this point of chosen distance is as design load t.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 1, it is characterised in that described step 1) employed in the mechanic nonlinearity equilibrium equation of inner ring:

Wherein F_rFor inner ring by outer radial load, F_aFor axial load, M is tilting moment,For position angle, d_mFor bearing pitch radius,WithFor steel ball position angle2 contacts at the place contact angle to being formed；For in position angleContact the steel ball contact load to inner ring elliptic roller track at,For in position angleContact the steel ball contact load to inner ring elliptic roller track at two.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 1, it is characterised in that Max.contact stress σ_maxComputing formula be:

${\mathrm{\&sigma;}}_{\max }=\frac{1}{{\mathrm{\&pi;n}}_a{n}_b}{\&lsqb;\frac{3}{2}{\left(\frac{\mathrm{\&Sigma;}\mathrm{\&rho;}}{\mathrm{\&eta;}}\right)}^2{Q}_{max}\&rsqb;}^{1/3}$

Wherein σ_maxFor bearing Max.contact stress；n_a、n_bFor the coefficient relevant with contact point principal curvatures difference function F (ρ), ∑ ρ be contact point principal curvatures and, η is the comprehensive elastic constant of two articles.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 2, it is characterised in that put P determined by step A when falling outside contact angle α span, parameter need to be redesigned；Put P determined by step B when falling outside radius of circle coefficient t span, also need to redesign parameter；The span of radius of circle coefficient t is 1.02～1.10, and contact angle α span is 35 °～50 °.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 1, it is characterised in that the major semiaxis of described bearing elliptic roller track and the computing formula of semi-minor axis be:

$a=r{\sin }^2\mathrm{\&alpha;}\sqrt{t}/(1-t{\cos }^2\mathrm{\&alpha;})$

$b=rsin\mathrm{\&alpha;}/\sqrt{1-t{\cos }^2\mathrm{\&alpha;}}$

Wherein a, b are respectively major semiaxis and the semi-minor axis of bearing elliptic roller track, and r is steel ball radius, and α is design contact angle, and t is radius of circle coefficient.

The method for designing of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 1, it is characterised in that described Max.contact stress σ_maxThe criterion of the ultimate bearing stress reaching bearing is:

By σ_maxWith [σ_max]/f_s ^0.5Compare, it is judged that both ratio whether in range of error, if, then explanation Max.contact stress σ_maxThe ultimate bearing stress of bearing, [σ are reached_max] it is the allowable contact stress of bearing, f_sCoefficient for bearing safety.

8. the design device of an elliptic roller track ball bearing length semi-axis structure parameter, it is characterized in that, this design device includes that displacement calculation module, Max.contact stress computing module, radius of circle coefficient and design contact angle choose module and oval major semiaxis and semi-minor axis computing module

Described displacement calculation module is used for bearing working limit load as equilibrium equation external loading, the mechanic nonlinearity equilibrium equation of inner ring obtain bearing inner race radial displacement δ_r, axial displacement δ_aWith corner displacement amount θ；

Described Max.contact stress computing module is for according to the bearing inner race radial displacement δ obtained_r, axial displacement δ_aNormal direction contact load at each contact position is calculated, to determine maximum stand under load rolling element contact load Q with corner displacement amount θ_maxThe Max.contact stress born with bearing；

Described radius of circle coefficient and design contact angle choose module for judging whether Max.contact stress reaches the ultimate bearing stress of bearing, when Max.contact stress reaches the ultimate bearing stress of bearing, it is that index draws the quiet endurance curves of bearing according to this Max.contact stress, by bearing limit load parameter determination radius of circle coefficient t, design contact angle α；

Described oval major semiaxis and semi-minor axis computing module are for according to design contact angle α, the radius of circle coefficient t obtained and steel ball radius calculation ellipse major semiaxis and semi-minor axis.

The design device of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 8, it is characterised in that described radius of circle coefficient and design contact angle choose module to choose process as follows:

A. with Max.contact stress σ_maxDraw the quiet endurance curves under different designs contact angle for index, finding abscissa is bearing axial limit load value, and vertical coordinate is the some P of bearing tilting moment ultimate value, and design contact angle corresponding to outside curve nearest for chosen distance point P is as design load α；

B. the quiet endurance curves under corresponding different radius of circle coefficient values under the contact angle that design load is α is drawn, finding abscissa is bearing axial limit load value, vertical coordinate is the point of bearing tilting moment ultimate value, and radius factor corresponding to the nearest outside curve of this point of chosen distance is as design load t.

The design device of elliptic roller track ball bearing length semi-axis structure parameter the most according to claim 8 or claim 9, it is characterised in that the mechanic nonlinearity equilibrium equation of the inner ring used in described displacement calculation module:

Wherein F_rFor inner ring by outer radial load, F_aFor axial load, M is tilting moment,For position angle, d_mFor bearing pitch radius,WithFor steel ball position angle2 contacts at the place contact angle to being formed,For in position angleContact the steel ball contact load to inner ring elliptic roller track at,For in position angleContact the steel ball contact load to inner ring elliptic roller track at two.