CN105822661B - A kind of design method and device of elliptic roller track ball bearing length semi-axis structure parameter - Google Patents
A kind of design method and device of elliptic roller track ball bearing length semi-axis structure parameter Download PDFInfo
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- CN105822661B CN105822661B CN201610381486.7A CN201610381486A CN105822661B CN 105822661 B CN105822661 B CN 105822661B CN 201610381486 A CN201610381486 A CN 201610381486A CN 105822661 B CN105822661 B CN 105822661B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C19/00—Bearings with rolling contact, for exclusively rotary movement
- F16C19/02—Bearings with rolling contact, for exclusively rotary movement with bearing balls essentially of the same size in one or more circular rows
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C33/00—Parts of bearings; Special methods for making bearings or parts thereof
- F16C33/30—Parts of ball or roller bearings
- F16C33/58—Raceways; Race rings
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2240/00—Specified values or numerical ranges of parameters; Relations between them
- F16C2240/30—Angles, e.g. inclinations
- F16C2240/34—Contact angles
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Abstract
The present invention relates to a kind of design method and device of elliptic roller track ball bearing length semi-axis structure parameter, the present invention calculation bearing inner ring radial displacement, axial displacement and corner displacement amount first；Then according to normal direction contact load at the obtained each contact position of above-mentioned displacement calculation, to determine Max.contact stress that maximum stand under load rolling element contact load and bearing are born；And the quiet endurance curves of bearing are drawn for index according to this Max.contact stress, radius of circle coefficient t, design contact angle are determined by bearing limit load parameter；Design contact angle, radius of circle coefficient and steel ball radius calculation ellipse major semiaxis and the semi-minor axis that last basis obtains.By the said process present invention can fast, accurately design the long semi-minor axis of elliptic roller track and, the long semi-minor axis selection of bearing elliptic roller track is solved without according to problem, and method for drafting is designed according to quiet endurance curves of the present invention, foundation can be provided for the judgement of external applied load applying working condition.
Description
Technical field
The present invention relates to a kind of design method and device of elliptic roller track ball bearing length semi-axis structure parameter, belong to rotating disk
Bearing design technology field.
Background technology
Turntable bearing as engineering machinery and the important foundation element of building machinery, be both needed to make relative gyration and
Need to bear necessary important force transfer element between two mechanical parts of axial force, radial load and tilting moment simultaneously again.
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 contact balls formula, goalpost
Association type etc..Its ball type turntable bearing market occupation proportion is maximum, reaches more than 90%, is widely used in host computer system etc.
Field.As all kinds of host computer system densifications develop, the requirement to ball turntable bearing radially installed space and bearing capacity is got over
Come higher, in order to improve the bearing capacity of turntable bearing, meet the market requirement, a kind of new raceway is proposed to ball turntable bearing
Structure, traditional peach-shaped groove-section pattern is changed to oval raceway (as shown in Fig. 1-a and Fig. 1-b), remaining parameter and peach-shaped
Rolling way turntable bearing is identical.Research shows, makes peach-shaped raceway into ellipse, and its raceway form accuracy is more easy to control, and due to
Elliptic roller track is variable curvature raceway, and when contact angle changes, the raceway curvature of contact point also changes, therefore it can improve steel
The contact stress state of ball and raceway, so as to improve the bearing capacity in the life-span of bearing and raceway.
Bearing capacity is the highly important performance indications of turntable bearing, commonly uses the carrying of quiet endurance curves expression bearing at present
Performance.Quiet endurance curves are using contact stress as set-point, and setting radial load is constant, calculate the maximum rolling of stand under load in bearing
Body and raceway contact center reach the axial load and tilting moment born during this given contact stress, by axial load-incline
Cover the endurance curves that torque corresponding relation is drawn out.The drafting of quiet endurance curves is by such as contact angle, raceway radius of curvature and steel
The influence of the bearing structure parameters such as bulb diameter.Most structural parameters of turntable bearing have clear and definite value foundation, such as bearing
The parameters such as internal diameter, external diameter, steel ball size and pitch diameter of ball set have all standardized, and are available for new elliptic roller track turntable bearing bearing
With reference to selection.But for new elliptic roller track bearing, have differences, cause in terms of its elliptic roller track and traditional peach-shaped raceway parameter
The long a and b of major and minor axis half, original contact angle α of elliptic roller track etc. have its selection of the parameter of considerable influence to bearing capacity and life-span
It can not be provided with reference to existing design, and full value by rule of thumb is very unreliable, and the pole of turntable bearing can not be given full play to
Bearing capacity is limited, therefore one kind, which rationally may be used, be proposed to structural parameters such as the oval long a and b of raceway major and minor axis half, original contact angle α
The value reference scheme leaned on is significant.
The content of the invention
It is an object of the invention to provide a kind of design method and device of elliptic roller track ball bearing length semi-axis structure parameter,
To solve the problems, such as the long semi-minor axis selection of elliptic roller track ball bearing without foundation.
The present invention provides a kind of setting for elliptic roller track ball bearing length semi-axis structure parameter to solve above-mentioned technical problem
Meter method, this method comprise the following steps：
1) using bearing working limit load as equilibrium equation external loading, obtained by the mechanic nonlinearity equilibrium equation of inner ring
To bearing inner race radial displacement δr, axial displacement δaWith corner displacement amount θ；
2) according to obtained bearing inner race radial displacement δr, axial displacement δaEach contact is calculated with corner displacement amount θ
Opening position normal direction contact load, to determine maximum stand under load rolling element contact load QmaxThe Max.contact stress born with bearing
σmax；
3) Max.contact stress σ is judgedmaxWhether the ultimate bearing stress of bearing is reached, as Max.contact stress σmaxReach
During the ultimate bearing stress of bearing, according to this Max.contact stress σmaxThe quiet endurance curves of bearing are drawn for index, by the bearing limit
Load parameter determines radius of circle coefficient t, design contact angle α；
4) according to obtained design contact angle α, radius of circle coefficient t and steel ball radius calculation ellipse major semiaxis and semi-minor axis.
The radius of circle coefficient t, design contact angle α determination process are as follows：
A. with Max.contact stress σmaxThe quiet endurance curves under different designs contact angle are drawn for index, find abscissa
For bearing axial direction limit load value, ordinate is the point P of bearing tilting moment limiting value, outer lateral curvature nearest chosen distance point P
Design contact angle is as design load α corresponding to line；
B. the quiet endurance curves corresponded under the contact angle that design load is α under different radius of circle coefficient values are drawn, find horizontal seat
It is designated as bearing axial direction limit load value, ordinate is the point of bearing tilting moment limiting value, the nearest outside of the chosen distance point
Radius factor corresponding to curve is as design load t.
The mechanic nonlinearity equilibrium equation of inner ring employed in the step 1)：
Wherein FrIt is inner ring by outer radial load, FaFor axial load, M is tilting moment,For position angle, dmFor axle
Hold pitch radius,WithFor steel ball position angle2 of place contact the contact angle to formation,For in position angleContact
Contact load to steel ball at one to inner ring elliptic roller track,For in position angleContact is to steel ball at two to inner ring elliptic roller track
Contact load.
Max.contact stress σmaxCalculation formula be：
Wherein σmaxFor bearing Max.contact stress；na、nbFor the coefficient relevant with contact point principal curvatures difference function F (ρ), ∑
ρ be contact point principal curvatures and, η be two articles synthesis elastic constant.
When identified point P is fallen on outside contact angle α spans in step A, parameter need to be redesigned；As step B
In identified point P when falling on outside radius of circle coefficient t spans, also need to redesign parameter；Radius of circle coefficient t value
Scope is 1.02~1.10, and contact angle α spans are 35 °~50 °.
The major semiaxis of the bearing elliptic roller track and the calculation formula of semi-minor axis are：
Wherein a, b are respectively the major semiaxis and semi-minor axis of bearing elliptic roller track, and r is steel ball radius, and α is to design contact angle, t
For radius of circle coefficient.
Described Max.contact stress σmaxThe criterion for reaching the ultimate bearing stress of bearing is：
By σmaxWith [σmax]/fs 0.5It is compared, judges both ratio whether in error range, if is illustrating
Max.contact stress σmaxThe ultimate bearing stress of bearing, [σ are reachedmax] be bearing allowable contact stress, fsPacify for bearing
Full coefficient.
Present invention also offers a kind of design device of elliptic roller track ball bearing length semi-axis structure parameter, the design device
Module and ellipse is chosen including displacement calculation module, Max.contact stress computing module, radius of circle coefficient and design contact angle
Circle major semiaxis and semi-minor axis computing module
The displacement calculation module is used for using bearing working limit load as equilibrium equation external loading, by inner ring
Mechanic nonlinearity equilibrium equation obtains bearing inner race radial displacement δr, axial displacement δaWith corner displacement amount θ；
The Max.contact stress computing module is used for according to obtained bearing inner race radial displacement δr, axial displacement
δaNormal direction contact load at each contact position is calculated with corner displacement amount θ, to determine maximum stand under load rolling element contact load Qmax
The Max.contact stress born with bearing；
The radius of circle coefficient and design contact angle choose module and are used to judge whether Max.contact stress reaches bearing
Ultimate bearing stress, it is index according to this Max.contact stress when Max.contact stress reaches the ultimate bearing stress of bearing
The quiet endurance curves of bearing are drawn, radius of circle coefficient t, design contact angle α are determined by bearing limit load parameter；
The oval major semiaxis and semi-minor axis computing module be used for according to obtained design contact angle α, radius of circle coefficient t and
Steel ball radius calculation ellipse major semiaxis and semi-minor axis.
The selection process that the radius of circle coefficient and design contact angle choose module is as follows：
A. with Max.contact stress σmaxThe quiet endurance curves under different designs contact angle are drawn for index, find abscissa
For bearing axial direction limit load value, ordinate is the point P of bearing tilting moment limiting value, outer lateral curvature nearest chosen distance point P
Design contact angle is as design load α corresponding to line；
B. the quiet endurance curves corresponded under the contact angle that design load is α under different radius of circle coefficient values are drawn, find horizontal seat
It is designated as bearing axial direction limit load value, ordinate is the point of bearing tilting moment limiting value, the nearest outside of the chosen distance point
Radius factor corresponding to curve is as design load t.
The mechanic nonlinearity equilibrium equation of the inner ring used in the displacement calculation module：
Wherein FrIt is inner ring by outer radial load, FaFor axial load, M is tilting moment,For position angle, dmFor axle
Hold pitch radius,WithFor steel ball position angle2 of place contact the contact angle to formation,For in position angleContact
Contact load to steel ball at one to inner ring elliptic roller track,For in position angleContact is to steel ball at two to inner ring elliptic roller track
Contact load.
The beneficial effects of the invention are as follows:The present invention calculation bearing inner ring radial displacement, axial displacement and corner first
Displacement；Then each contact position is calculated according to obtained bearing inner race radial displacement, axial displacement and corner displacement amount
Place's normal direction contact load is put, to determine Max.contact stress that maximum stand under load rolling element contact load and bearing are born；And according to
Max.contact stress σ accordinglymaxThe quiet endurance curves of bearing are drawn for index, radius of circle coefficient is determined by bearing limit load parameter
T, contact angle α is designed；It is last according to obtained design contact angle α, radius of circle coefficient t and steel ball radius calculation ellipse major semiaxis and
Semi-minor axis.The long semi-minor axis a and b of elliptic roller track can fast, accurately be designed by the said process present invention, it is new to solve this
The long semi-minor axis selection of ball bearing elliptic roller track is painted without foundation problem, and according to quiet endurance curves design of the present invention
Method processed, foundation can be provided for the judgement of external applied load applying working condition.
Brief description of the drawings
Fig. 1-a are traditional peach-shaped steel ball rolling channel schematic diagram；
Fig. 1-b are oval steel ball rolling channel schematic diagram；
Fig. 2 is that the coordinate position of oval inside and outside 4 centers of curvature of raceway and 2 are contacted to schematic diagram；
Fig. 3 is quiet endurance curves figure of the elliptic roller track ball turntable bearing under different designs contact angle α；
Fig. 4 is quiet carrying of the elliptic roller track ball turntable bearing in the design lower different radii coefficient t values in contact angle α=35 °
Curve；
Fig. 5 is quiet carrying of the elliptic roller track ball turntable bearing in the design lower different radii coefficient t values in contact angle α=40 °
Curve；
Fig. 6 is quiet carrying of the elliptic roller track ball turntable bearing in the design lower different radii coefficient t values in contact angle α=45 °
Curve；
Fig. 7 is quiet carrying of the elliptic roller track ball turntable bearing in the design lower different radii coefficient t values in contact angle α=50 °
Curve；
Fig. 8 is to obtain design contact angle α schematic diagrames using Fig. 3 by point P；
Radius factor t schematic diagrames are obtained when Fig. 9 is by point P using Fig. 6 contact angle α=45 °.
Embodiment
The embodiment of the present invention is described further below in conjunction with the accompanying drawings.
A kind of embodiment of the design method of elliptic roller track ball bearing length semi-axis structure parameter of the present invention
The present invention loads Q by establishing statical model and calculating bearing maximum rolling bodymaxConnect with the maximum carrying of bearing
Touch stress index σmax, draw FaThe quiet endurance curves of-M, radius of circle coefficient t, design contact angle are determined by bearing limit load parameter
α；Elliptic roller track major semiaxis a and semi-minor axis b value are calculated according to radius of circle coefficient t, design contact angle α and steel ball radiuscope.It is logical
The long semi-minor axis a and b of elliptic roller track can fast, accurately be designed by crossing the said process present invention, solve this novel ball type bearing
The long semi-minor axis selection of elliptic roller track designs method for drafting without foundation problem, and according to quiet endurance curves of the present invention,
Foundation can be provided for the judgement of external applied load applying working condition.The specific implementation process of this method is as follows：
First, establish that stand under load is forward and backward, the coordinate position of oval inside and outside 4 centers of curvature of raceway.
1. inside and outside circle center of curvature point coordinates determines before stand under load.
What the present invention was directed to oval inside and outside is rolled into the center of curvature and contact to as shown in Fig. 2 diFor inner ring elliptic roller track top
Hold diameter；deFor outer ring elliptic roller track top end diameter；DwFor steel ball size；ai, biRespectively inner ring ellipse major semiaxis and short by half
Axle；ae, beRespectively outer ring ellipse major semiaxis and semi-minor axis；WithFor steel ball position angle2 contacts at place are to formation
Contact angle；For the distributing position angle of steel ball.
Contact represents an inner ring center point of curvature position coordinates, formula (2) contact pair before stand under load before above formula (1) represents stand under load
Contact is to an outer ring center point of curvature position coordinates, formula (4) before two inner ring center point of curvature position coordinateses, formula (3) represent stand under load
Contacted before representing stand under load to two outer ring center point of curvature position coordinateses, wherein：
2. inside and outside circle center of curvature point coordinates determines after stand under load.
Assuming that turntable bearing outer ring is fixed, inner ring is in outside radial load Fr, axial load FaCombine with tilting moment M and make
Under, it is respectively radially, axially δ with corner displacement amountr、δa, θ, then the final position of the inner ring center of curvature is after stand under load：
Contact represents an inner ring center point of curvature position coordinates, formula (6) contact pair after stand under load after above formula (5) represents stand under load
Two inner ring center point of curvature position coordinateses.
2nd, the contact angle that each position angle goes out is determinedThe contact angle at placeWith
After Internal and external cycle center of curvature final position is obtained, contact angle nonlinear equation can be established according to position relationship
Group, it is as follows：
Contact angle nonlinear equation at each position angle：
In known δr、δa, above-mentioned contact angle Nonlinear System of Equations is carried out using Newton-Raphson method in the case of θ
Solve, you can determine the contact angle of each opening positionWith
3rd, each position angle is determinedLocate contact load.
In each opening position contact angleWithAfter it is determined that, you can determine that each steel ball contacts with Internal and external cycle elliptic roller track
Rigidity, the center of curvature are away from then according to the progress contact load calculating of Hertz contact theories.At each position angle the center of curvature away from：
Wherein：
According to Hertz contact theories, the contact stiffness of 2 contacts pair at each position angle can be obtained, contact stiffness is
Contact angle α, radius of curvature r, steel ball size DwWith bearing pitch radius dmFunction.
Contact stiffness and the center of curvature by obtaining, then according to Hertz point contact theories, can derive away from position relationship
The normal direction contact load gone out at each contact position.
For in position angleThe contact load to inner ring elliptic roller track to steel ball at one is contacted,For in position angle
Contact the contact load to inner ring elliptic roller track to steel ball at two.
4th, inner ring mechanical balance equation is established.
Inner ring is by outer radial load Fr, axial load FaWith tilting moment M synergy, and in Angle PositionPlace
Contact load of the steel ball to inner ring elliptic roller trackWithEffect.Inner ring is in external load and all rolling elements and inner ring raceway
Contact load effect it is lower be in poised state, the mechanic nonlinearity equilibrium equation of inner ring is：
5th, according to the maximum carrying contact stress index σ of ball bearingmax, establish FaThe quiet endurance curves of-M
In rolling bearing technology, the quiet bearing capacity of bearing refers to act on non-rotating bearing, and makes maximum stand under load
Rolling element contacts weakness with inner ring or outer ring raceway and produces 0.0001 load for being permanently deformed to rolling element diameter, for point
The allowable stress of contact ball bearing is 4200MPa.Bearing point contacts Max.contact stress and the relation of Maximum Contact load is:
Parameters symbol represents that implication is as follows in formula:σmaxFor bearing Max.contact stress；na、nbFor with contact point master
Coefficient relevant curvature difference function F (ρ), ∑ ρ be contact point principal curvatures and, η be two articles synthesis elastic constant.
The safe handling Max.contact stress of ball turntable bearing is
Wherein：[σmax] be bearing allowable contact stress, fsFor the coefficient of bearing safety.
Point in the quiet endurance curves of bearing is the static borderline failure point of bearing, and the present invention makes σmax=[σmax]/fs 0.5's
Point is as a point on bearing dead load curve, to draw dead load curve.
Specific method is as follows:
1. make FrEqual to radial load suffered under bearing limiting condition, to FaContinuous value is carried out with M, it is corresponding each group
Value, bearing inner race radial displacement δ is obtained according to the mechanic nonlinearity equilibrium equation (formula 13) of inner ringr, axial displacement δaWith
Corner displacement amount θ, back substitution enter normal direction contact load calculation formula (formula 12) at each contact position, obtain each contact position two
Normal direction contact load of the individual contact to placeWithAfterwards, the size of more each position contact load absolute value, absolute value is most
Big load is maximum stand under load rolling element contact load Qmax, the maximum that bearing born then is obtained according to formula (15) and connect
Touch stress σmax；
2. compare σmaxWith [σmax]/fs 0.5Value, if in the error range of setting, now σmaxReach the pole of bearing
Bearing stress is limited, extracts now corresponding FaWith M as the point formed in quiet endurance curves；
3. connecting a little of obtaining just is obtained to the quiet endurance curves of bearing.
6th, the long semi-minor axis of bearing elliptic roller track and original contact angle are designed using quiet endurance curves
By theory deduction, the major semiaxis a and semi-minor axis b of bearing elliptic roller track can be accurately determined by formula 17, formula 18.
The long semi-minor axis of formula middle (center) bearing elliptic roller track is 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, so as to the long semi-minor axis a and b according to formula (17) and (18) calculation bearing elliptic roller track.
Comprise the following steps that:
1) limiting condition (F according to suffered by bearingrmax、FamaxAnd Mmax), make FrEqual to Frmax, axle is drawn according to the above method
Hold quiet endurance curves；
2) change radius of circle coefficient t and design the value of original contact angle, required according to working condition, general parameters t's takes
It is 1.02~1.10 to be worth scope, and contact angle α spans are 35 °~50 °, according to drawing quiet holding under different designs contact angle α
Curve (as shown in Figure 3) is carried, and draws quiet endurance curves (such as Fig. 4 under respective design contact angle α under different radii coefficient t values
Shown in Fig. 7).
3) axial force F in limiting condition conditionamaxWith torque MmaxValue, carried in different designs contact angle bent
Coordinate points P (F are found in line chartamax、Mmax), this time point P has three kinds of situations：
The first situation is that point P is fallen in α=35 °, illustrates that this structure design is excessively safe, can cause waste of material, carry
High manufacturing cost, it should redesign parameter；
Second situation is that point P falls on α=50 ° outside, illustrates that this structure design can not meet bearing requirements, parameter is unreasonable
It should redesign；
The third situation is that point P is fallen between α=35 ° and α=50 °, then answers the nearest outside curve pair of chosen distance P points
The design contact angle answered is as design load.
4) after choosing design contact angle α by step 3), find under this contact angle α under corresponding different radii coefficient t values
Quiet endurance curves (one of Fig. 4-7), according to the axial force F in limiting condition conditionamaxWith torque MmaxValue, look in figure
To coordinate points P (Famax、Mmax), this time point P has also three kinds of situations：
The first situation is that point P is fallen in t=1.02, illustrates that this structure design is excessively safe, can cause waste of material, carry
High manufacturing cost, it should redesign parameter；
Second of situation is that point P is fallen on outside t=1.10, illustrates that this structure design can not meet bearing requirements, parameter does not conform to
It ought to redesign；
The third situation is that point P is fallen between t=1.02 and t=1.10, then answers the nearest outside curve of chosen distance P points
Corresponding radius factor is as design load.
, just can be by formula (17) and formula after selecting design contact angle α and radius of circle coefficient t according to above-mentioned 4 steps
(18) the major semiaxis a and semi-minor axis b of bearing elliptic roller track are accurately determined.
Illustrated below by taking a certain specific elliptic roller track four point touching ball slewing bearing as an example, 4 points of the elliptic roller track
Contact the structural parameters and material parameter of ball slewing bearing：dm=1543mm, Dw=24.64mm, Z=158, v=0.3, E=
207GPa, the load of its working limit are：Fr=100kN, Fa=400kN, M=1000kNm.
1. using bearing working limit load as equilibrium equation external loading, by the mechanic nonlinearity equilibrium equation of inner ring
(formula 13) obtains bearing inner race radial displacement δr, axial displacement δaWith corner displacement amount θ, back substitution enters at each contact position
Normal direction contact load calculation formula (formula 12), obtain normal direction contact load at each contact position and rolled so as to obtain maximum stand under load
Body contact load Qmax, the Max.contact stress σ that bearing born then is obtained according to formula (15)max。
2. compare σmaxWith [σmax]/fs 0.5Value, if in the error range of setting, now σmaxReach the pole of bearing
Bearing stress is limited, according to this maximum carrying contact stress σmaxAs index, the quiet carrying drawn under different designs contact angle α is bent
Line simultaneously finds point P (shown in Fig. 8) in figure, and its abscissa is bearing axial direction limit load value, and ordinate is bearing tilting moment
Limiting value, to this bearing point P (400,1000), corresponding to the nearest outside curve of chosen distance P points, design contact angle, which is used as, sets
Evaluation, i.e.,：α=45 °.
3. after choosing design contact angle α=45 °, quiet under different radii coefficient t values corresponding to contact angle α=45 ° is held
Carry in curve and find point P (400,1000), as shown in Figure 9：Radius factor corresponding to the nearest outside curve of chosen distance P points is made
For design load, i.e.,：T=1.06.
4. by the parameter of selection：Contact angle α=45 °, radius factor t=1.06, steel ball radius r=Dw/ 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 elliptic roller track ball bearing length semi-axis structure parameter of the present invention
Design device in the present embodiment includes displacement calculation module, Max.contact stress computing module, radius of circle system
Number and design contact angle choose module and oval major semiaxis and semi-minor axis computing module, and displacement calculation module is used for bearing
Working limit load is used as equilibrium equation external loading, and bearing inner race radial direction position is obtained by the mechanic nonlinearity equilibrium equation of inner ring
Shifting amount δr, axial displacement δaWith corner displacement amount θ；Max.contact stress computing module is used for according to obtained bearing inner race footpath
To displacement δr, axial displacement δaNormal direction contact load at each contact position is calculated with corner displacement amount θ, to determine maximum
Stand under load rolling element contact load QmaxThe Max.contact stress born with bearing；Radius of circle coefficient and design contact angle choose mould
Block is used to judge whether Max.contact stress reaches the ultimate bearing stress of bearing, when Max.contact stress reaches the limit of bearing
During bearing stress, it is that index draws the quiet endurance curves of bearing according to this Max.contact stress, is determined by bearing limit load parameter
Radius of circle coefficient t, design contact angle α；Oval major semiaxis and semi-minor axis computing module be used for according to obtain design contact angle α,
Radius of circle coefficient t and steel ball radius calculation ellipse major semiaxis and semi-minor axis.The specific implementation of each module is in the reality of method
Apply in example and be described in detail, repeat no more here.
Claims (10)
1. a kind of design method of elliptic roller track ball bearing length semi-axis structure parameter, it is characterised in that this method includes following
Step：
1) using bearing working limit load as equilibrium equation external loading, axle is obtained by the mechanic nonlinearity equilibrium equation of inner ring
Hold inner ring radial displacement δr, axial displacement δaWith corner displacement amount θ；
2) according to obtained bearing inner race radial displacement δr, axial displacement δaEach contact position is calculated with corner displacement amount θ
Locate normal direction contact load, to determine maximum stand under load rolling element contact load QmaxThe Max.contact stress σ born with bearingmax；
3) Max.contact stress σ is judgedmaxWhether the ultimate bearing stress of bearing is reached, as Max.contact stress σmaxReach bearing
Ultimate bearing stress when, according to this Max.contact stress σmaxThe quiet endurance curves of bearing are drawn for index, by bearing limit load
Parameter determines radius of circle coefficient t, design contact angle α；
4) according to obtained design contact angle α, radius of circle coefficient t and steel ball radius calculation ellipse major semiaxis and semi-minor axis.
2. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 1, it is characterised in that
The radius of circle coefficient t, design contact angle α determination process are as follows：
A. with Max.contact stress σmaxThe quiet endurance curves under different designs contact angle are drawn for index, it is axle to find abscissa
Hold axial limit load value, ordinate is the point P of bearing tilting moment limiting value, outside curve pair nearest chosen distance point P
The design contact angle answered is as design load α；
B. the quiet endurance curves corresponded under the contact angle that design load is α under different radius of circle coefficient values are drawn, finding abscissa is
Bearing axial direction limit load value, ordinate be bearing tilting moment limiting value point, the nearest outside curve of the chosen distance point
Corresponding radius factor is as design load t.
3. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 1, it is characterised in that
The mechanic nonlinearity equilibrium equation of inner ring employed in the step 1)：
Wherein FrIt is inner ring by outer radial load, FaFor axial load, M is tilting moment,For position angle, dmFor bearing section
Radius of circle,WithFor steel ball position angleContact angle of 2 contacts at place to formation；For in position angleContact is to one
Locate contact load of the steel ball to inner ring elliptic roller track,For in position angleContact connects to steel ball at two to inner ring elliptic roller track
Touch load.
4. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 1, it is characterised in that
Max.contact stress σmaxCalculation formula be：
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>max</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>&pi;n</mi>
<mi>a</mi>
</msub>
<msub>
<mi>n</mi>
<mi>b</mi>
</msub>
</mrow>
</mfrac>
<msup>
<mrow>
<mo>&lsqb;</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>&Sigma;</mi>
<mi>&rho;</mi>
</mrow>
<mi>&eta;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<msub>
<mi>Q</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
Wherein σmaxFor bearing Max.contact stress；na、nbFor the coefficient relevant with contact point principal curvatures difference function F (ρ), ∑ ρ is
Contact point principal curvatures and, η be two articles synthesis elastic constant.
5. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 2, it is characterised in that
When identified point P is fallen on outside contact angle α spans in step A, parameter need to be redesigned；Determined when in step B
Point P when falling on outside radius of circle coefficient t spans, also need to redesign parameter；Radius of circle coefficient t span is
1.02~1.10, contact angle α span are 35 °~50 °.
6. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 1, it is characterised in that
The major semiaxis of the bearing elliptic roller track and the calculation formula of semi-minor axis are：
<mrow>
<mi>a</mi>
<mo>=</mo>
<mi>r</mi>
<mi> </mi>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mi>&alpha;</mi>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>t</mi>
<mi> </mi>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mi>r</mi>
<mi> </mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&alpha;</mi>
<mo>/</mo>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>t</mi>
<mi> </mi>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mi>&alpha;</mi>
</mrow>
</msqrt>
</mrow>
Wherein a, b are respectively the major semiaxis and semi-minor axis of bearing elliptic roller track, and r is steel ball radius, and α is design contact angle, and t is circle
Radius factor.
7. the design method of elliptic roller track ball bearing length semi-axis structure parameter according to claim 1, it is characterised in that
Described Max.contact stress σmaxThe criterion for reaching the ultimate bearing stress of bearing is：
By σmaxWith [σmax]/fs 0.5It is compared, judges both ratio whether in error range, if is illustrating that maximum connects
Touch stress σmaxThe ultimate bearing stress of bearing, [σ are reachedmax] be bearing allowable contact stress, fsFor bearing safety be
Number.
8. a kind of design device of elliptic roller track ball bearing length semi-axis structure parameter, it is characterised in that the design device includes
Displacement calculation module, Max.contact stress computing module, radius of circle coefficient and design contact angle choose module and oval length
Semiaxis and semi-minor axis computing module,
The displacement calculation module is used for using bearing working limit load as equilibrium equation external loading, by the mechanics of inner ring
Nonlinear balance equation obtains bearing inner race radial displacement δr, axial displacement δaWith corner displacement amount θ；
The Max.contact stress computing module is used for according to obtained bearing inner race radial displacement δr, axial displacement δaWith
Corner displacement amount θ calculates normal direction contact load at each contact position, to determine maximum stand under load rolling element contact load QmaxAnd axle
Hold born Max.contact stress；
The radius of circle coefficient and design contact angle choose module and are used to judge whether Max.contact stress reaches the limit of bearing
Bearing stress, when Max.contact stress reaches the ultimate bearing stress of bearing, drawn according to this Max.contact stress for index
The quiet endurance curves of bearing, radius of circle coefficient t, design contact angle α are determined by bearing limit load parameter；
The oval major semiaxis and semi-minor axis computing module are used for according to obtained design contact angle α, radius of circle coefficient t and steel ball
Radius calculation ellipse major semiaxis and semi-minor axis.
9. the design device of elliptic roller track ball bearing length semi-axis structure parameter according to claim 8, it is characterised in that
The selection process that the radius of circle coefficient and design contact angle choose module is as follows：
A. with Max.contact stress σmaxThe quiet endurance curves under different designs contact angle are drawn for index, it is axle to find abscissa
Hold axial limit load value, ordinate is the point P of bearing tilting moment limiting value, outside curve pair nearest chosen distance point P
The design contact angle answered is as design load α；
B. the quiet endurance curves corresponded under the contact angle that design load is α under different radius of circle coefficient values are drawn, finding abscissa is
Bearing axial direction limit load value, ordinate be bearing tilting moment limiting value point, the nearest outside curve of the chosen distance point
Corresponding radius factor is as design load t.
10. the design device of elliptic roller track ball bearing length semi-axis structure parameter according to claim 8 or claim 9, its feature
It is, the mechanic nonlinearity equilibrium equation of the inner ring used in the displacement calculation module：
Wherein FrIt is inner ring by outer radial load, FaFor axial load, M is tilting moment,For position angle, dmFor bearing section
Radius of circle,WithFor steel ball position angle2 of place contact the contact angle to formation,For in position angleContact is to one
Locate contact load of the steel ball to inner ring elliptic roller track,For in position angleContact connects to steel ball at two to inner ring elliptic roller track
Touch load.
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| CN112855755B (en) * | 2021-02-23 | 2023-01-24 | 青岛理工大学 | Method for selecting use condition of high-speed four-point contact ball bearing |
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Application publication date: 20160803 Assignee: Luoyang Hongyuan Bearing Technology Co., Ltd. Assignor: Henan University of Science and Technology Contract record no.: X2019980000608 Denomination of invention: Design method and device of structural parameters of major and minor semi axes of elliptical race ball bearing Granted publication date: 20180119 License type: Exclusive License Record date: 20191115 |