CN106089993B - A kind of method and device for obtaining ball cone mixing double-row hub bearing load distribution - Google Patents
A kind of method and device for obtaining ball cone mixing double-row hub bearing load distribution Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- 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
- F16C19/49—Bearings with both balls and rollers
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Abstract
The present invention relates to a kind of method and device for obtaining ball cone mixing double-row hub bearing load distribution, the present invention derives steel ball any position angle ψ firstiThe normal direction contact load Q at place1iWith taper roller any position angle φiThe normal direction contact load Q at place and outer ring2i, then draw total radial load Q that steel ball generates inner ring1r, axial force Q1aWith moment of resistance M1The total radial load Q generated with taper roller to inner ring2r, axial force Q2aWith moment of resistance M2；It resettles with δr、δa, θ be unknown quantity ball bore mixing double-row hub bearing inner ring mechanical balance equation, can obtain bearing inner race radial displacement δ with Newton iterative method equilibrium equationsr, axial displacement δaWith angular displacement θ, and then obtain bearing each column loading conditions.The present invention can be quickly obtained the accurate bearer properties parameter of ball cone mixing double-row hub bearing, can intuitively judge whether the design of ball cone mixing double-row hub bearing structure is reasonable, improve the reasonability and accuracy of ball cone mixing double-row hub bearing design.
Description
Technical field
The present invention relates to a kind of method and devices for obtaining ball cone mixing double-row hub bearing load distribution, belong to bearing and set
Count technical field.
Background technology
Instantly mainstream vehicle wheel hub bearing is divided into two kinds：Double-row angular contact bal bearing and double-row conical bearing；Biserial
Angular contact ball bearing is small with moment of friction compared with double-row conical bearing, and limit speed height, light weight, compact are strong and make
This low advantage is caused, is chiefly used in household small-size car；And double-row conical bearing has that load-carrying properties are strong, bearing rigidity is big
The advantages that, it is chiefly used in truck.Nowadays family car manufacture is more intended to improve comfort and multifunctionality, strives expanding automobile
So family car weight increases therewith, higher is required for hub bearing bearing capacity for inner space.Due to biserial hub spindle
It holds only close steering axles side row bearing in most cases and bears Main Load, another row bearing stand under load time is shorter,
It is primarily subjected to minor loading.Based on the bearing behavior of two row stand under load unevenness of biserial hub bearing, occurs a kind of new wheel now
Hub axle bearing structure：Ball bores mixing double-row hub bearing, i.e. a row steel ball, a row tapered roller, taper roller row are installed on close
Steering spindle side, bears Main Load.The existing good load-carrying properties of ball cone mixing double-row bearing and rigidity, structure is compared with biserial circular cone
It is again compacter, and manufacture at low cost, it is likely that the Main Trends of The Development of following hub bearing can be become, and for ball cone mixing
Double-row bearing although proposing the design structure of this novel hub bearing, is a lack of dividing this kind of turntable bearing load
The accurate description of cloth situation.
The content of the invention
The object of the present invention is to provide it is a kind of obtain ball, cone mixing double-row hub bearing load distribution method and device,
To solve the problems, such as to be difficult at present to obtain ball, cone mixing double-row hub bearing load accurate distribution.
The present invention provides a kind of ball that obtains and bores the distribution of mixing double-row hub bearing load to solve above-mentioned technical problem
Method, this method comprise the following steps：
1) combined bearing structure is bored according to ball and stressing conditions derives steel ball any position angle ψiThe normal direction contact at place is negative
Carry Q1iWith bearing inner race final deformation amount δr、δaWith the relation of θ and taper roller any position angle φiThe normal direction of the outer ring at place
Contact load Q2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions；
2) total radial load Q that steel ball generates inner ring is derived according to normal direction contact load and stressing conditions1r, axial force
Q1aWith moment of resistance M1And total radial load Q that taper roller generates inner ring2r, axial force Q2aWith moment of resistance M2；
3) it is lower in equilibrium-like under the force action of external load and all rolling element reaction forces according to bearing inner race
State is established with bearing inner race final deformation amount δr、δa, ball that θ is unknown quantity bore mixing double-row hub bearing inner ring mechanical balance side
Journey group, and the equilibrium equation group is solved, obtain bearing inner race final deformation amount δr、δaAnd θ；
4) the bearing inner race final deformation amount δ that will be obtainedr、δaThe normal direction contact load determined in step 1) is brought into θ to close
It is formula, obtains bearing each column loading conditions Q1iAnd Q2i。
The mechanic nonlinearity equilibrium equation group established in step 3) is：
Wherein FrFor the outer radial load that inner ring is subject to, FaFor the external axial load that inner ring is subject to, M is subject to for inner ring
Disturbing moment, Q1rFor total radial load that steel ball generates inner ring, Q1aFor total axial force that steel ball generates inner ring, M1For steel ball
Total resistance square, Q2rFor total radial load that taper roller generates inner ring, Q2aFor taper roller to the line shaft that inner ring generates to
Power, M2For taper roller total resistance square.
Steel ball any position angle ψ in step 1)iThe normal direction contact load Q at place1iFor：
Q1i=Kn1[max(δ1i,0)]3/2
δ1i=S1ψi-A
A=(fi+fe-1)Dw1
Wherein δ1iFor the deflection of any position steel ball, A is the outer ring primitive groove center of curvature away from S1ψiFor by load displacement
The Internal and external cycle ditch center of curvature of any position is away from R afterwardsiFor radius of circle, α where the raceway ditch center of curvature in steel ball0For steel ball with
Original contact angle between raceway, ψiFor the position angle of steel ball, Kn1Total load-deformation between rolling element and Internal and external cycle is normal
Number, Dw1For steel ball size, fiFor septal fossula coefficient of curvature, feFor outer fissure coefficient of curvature, δrFor bearing inner race radial displacement, δaFor
Bearing inner race axial displacement, θ are angular displacement.
Taper roller any position angle φ in step 1)iThe normal direction contact load Q at place and outer ring2iFor：
Q2i=Kn2[max(δ2i,0)]10/9
δ2i=(δr-R22θ)cosφicosαe+(δ0-0.5dm2θcosφi-δa)sinαe
Kn2=2.89 × 104×l0.82×Dw2 0.11
R22For bearing inner race center O and roller centre of pitch circle O2The distance between ', dm2For roller pitch diameter, φiFor rolling
Sub- any position angle, αeFor roller and outer ring contact angle, αiFor roller and inner ring contact angle, δ0For end-play, Kn2For roller with
The global stiffness coefficient of outer raceway contact point, l be the effective contact length of roller, Dw2For roller average diameter, δrFor bearing inner race footpath
To displacement, δaFor bearing inner race axial displacement, θ is angular displacement.
Total radial load Q that steel ball generates inner ring1r, axial force Q1aWith moment of resistance M1Respectively：
Wherein α1ψiThe contact angle of any position steel ball, Z after expression stand under load1For steel ball quantity, de1For bearing inner race center O with
Steel ball centre of pitch circle O1' between twice of distance, M1irFor the contact load radial component moment of resistance of all steel balls, M1iaTo connect
Touch load axial component moment of resistance.
Total radial load Q that taper roller generates inner ring2r, axial force Q2aWith moment of resistance M2Respectively：
Wherein Z2For roller number, de2For bearing inner race center O and roller centre of pitch circle O2' between 2 times of distance.
Equilibrium equation group is solved using Newton-Raphson iterative methods.
The present invention also provides a kind of device for obtaining ball cone mixing double-row hub bearing load distribution, which includes method
Formwork erection block is set up to contact load determining module, total radial load, axial force and moment of resistance determining module, nonlinear balance equation
With contact load computing module,
The normal direction contact load determining module is used to bore combined bearing structure according to ball and stressing conditions derive steel ball
Any position angle ψiThe normal direction contact load Q at place1iWith bearing inner race final deformation amount δr、δaWith the relation and taper roller of θ
Any position angle φiThe normal direction contact load Q of the outer ring at place2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions；
Total radial load, axial force and moment of resistance determining module are used to be pushed away according to normal direction contact load and stressing conditions
Total radial load Q that export steel ball generates inner ring1r, axial force Q1aWith moment of resistance M1And taper roller generates inner ring
Total radial load Q2r, axial force Q2aWith moment of resistance M2；
The nonlinear balance equation sets up formwork erection block for anti-in external load and all rolling elements according to bearing inner race
The force action of active force is lower in equilibrium state, establishes with bearing inner race final deformation amount δr、δa, θ be unknown quantity ball bore
Mixing double-row hub bearing inner ring mechanical balance equation, and equilibrium equation is solved, obtain bearing inner race final deformation amount
δr、δaAnd θ；
The contact load computing module is used for the bearing inner race final deformation amount δ that will be obtainedr、δaIt is brought into θ identified
Normal direction contact load relational expression obtains bearing each column loading conditions Q1iAnd Q2i。
The beneficial effects of the invention are as follows：The present invention bores combined bearing structure according to ball first and stressing conditions derive steel ball
Any position angle ψiThe normal direction contact load Q at place1iWith taper roller any position angle φiThe normal direction contact load at place and outer ring
Q2i；Then total radial load Q that steel ball generates inner ring is obtained1r, axial force Q1aWith moment of resistance M1It is internal with right row tapered roller
Enclose the total radial load Q generated2r, axial force Q2aWith moment of resistance M2；Further according to bearing inner race in external load and all rolling elements
The force action of reaction force is lower in equilibrium state, establishes with bearing inner race final deformation amount δr、δa, θ be unknown quantity ball
Mixing double-row hub bearing inner ring mechanical balance equation is bored, and equilibrium equation is solved, bearing inner race is obtained and finally deforms
Measure δr、δaAnd θ, and then obtain bearing each column loading conditions.By the above process, it is mixed that the present invention can be quickly obtained ball cone
The accurate bearer properties parameter of biserial hub bearing is closed, more deeply can intuitively judge that ball bores mixing double-row hub bearing
Whether the design of structure is reasonable, improves the reasonability and accuracy of ball cone mixing double-row hub bearing design.
Description of the drawings
Fig. 1 is ball cone combined bearing inner ring stress diagram；
Fig. 2 is ball cone mixing double-row hub bearing geometric representation；
Fig. 3 is the displacement component schematic diagram that rotational angle theta generates right row bearing；
Fig. 4 is radial displacement and the outer raceway perspective view of axial displacement；
Fig. 5 is flat road surface straight trip bearing load curve synoptic diagram in present example；
Fig. 6 is present example moderately gusty air road surface straight trip bearing load curve synoptic diagram；
Fig. 7 is normal turn bearing load curve synoptic diagram in present example；
Fig. 8 is zig zag bearing load curve synoptic diagram in present example.
Specific embodiment
The specific embodiment of the present invention is described further below in conjunction with the accompanying drawings.
The present invention obtains the embodiment of the method for ball cone mixing double-row hub bearing load distribution
The present invention derives steel ball any position angle ψ firstiThe normal direction contact load Q at place1iWith taper roller any position
Angle φiThe normal direction contact load Q at place and outer ring2i, then draw total radial load Q that left column steel ball generates inner ring1r, axial force
Q1aWith moment of resistance M1The total radial load Q generated with right row tapered roller to inner ring2r, axial force Q2aWith moment of resistance M2；According to
Bearing inner race is lower in equilibrium state under the force action of external load and all rolling element reaction forces, establishes in bearing
Enclose final deformation amount δr、δa, ball that θ is unknown quantity bore mixing double-row hub bearing inner ring mechanical balance equation, and to equilibrium equation
It is solved, obtains bearing inner race final deformation amount δr、δaAnd θ；And then obtain bearing each column loading conditions.This method
Specific implementation process is as follows：
1. combined bearing structure is bored according to ball and stressing conditions derive steel ball any position angle ψiThe normal direction contact at place is negative
Carry Q1iWith bearing inner race final deformation amount δr、δaWith the relation of θ.
Assuming that its outer ring of ball cone combined bearing is fixed, when inner ring bears radial load Fr, axial force FaCombine with disturbing moment M
During effect, radial displacement δr, axial displacement δa, angular displacement θ, make the increased position of rolling element load for each column bearing
It moves as positive displacement, it is on the contrary then be negative displacement.Ball bores combined bearing structure and stress diagram is as shown in Figure 1.Below with left column steel
1 is designated as under ball associated expression is used, 2 are designated as under right row tapered roller associated expression is used, and represents that rolling element is (left with i
Row steel ball, right row tapered roller) position.It is point contact between left column steel ball and raceway, α0For original contact angle, after stand under load
Different variations, ψ can occur for the contact angle of different position steel balliIt represents the position angle of steel ball, uses α1ψiArbitrary position after expression stand under load
The contact angle of steel ball is put, then：
A=(fi+fe-1)Dw1(4)
The deflection δ of any position steel ball1iEqual to the Internal and external cycle ditch center of curvature after being loaded away from in primitive groove curvature
The heart is away from its difference：
δ1i=S1ψi-A (6)
Steel ball is point contact, so raceway is to the relation of the juxtaposition metamorphose of the normal load and steel ball of steel ball：
Q1i=Kn1[max(δ1i,0)]3/2 (7)
Wherein δ1iFor the deflection of any position steel ball, A is the outer ring primitive groove center of curvature away from S1ψiFor by load displacement
The Internal and external cycle ditch center of curvature of any position is away from R afterwardsiFor radius of circle, α where the raceway ditch center of curvature in steel ball0For steel ball with
Original contact angle between raceway, ψiFor the position angle of steel ball, Kn1Total load-deformation between rolling element and Internal and external cycle is normal
Number, Dw1For steel ball size, fiFor septal fossula coefficient of curvature, feFor outer fissure coefficient of curvature, δrFor bearing inner race radial displacement, δaFor
Bearing inner race axial displacement, θ are angular displacement.
2. determine total radial load Q that steel ball generates inner ring1r, axial force Q1aWith moment of resistance M1。
Left column steel ball quantity is Z1, then angular contact steel ball contact load radial component summation be：
Angular contact steel ball contact load axial component summation is：
Since ball-cone combined bearing is double-row bearing, bearing inner race center is with the decentraction of steel ball centre of pitch circle (such as Fig. 2 institutes
It is R to show two centre distances12), therefore its contact load radial component can also generate moment of resistance M1ir, the contact load of all steel balls
Radial component moment of resistance M1irWith contact load axial component moment of resistance M1iaIt is added and forms left column steel ball total resistance square M1,
As shown in Figure 2.
M1ir=R12Q1icosα1ψicosψi=0.5de1Q1icosα1ψicosψi (10)
M1ia=0.5dm1Q1isinα1ψicosψi (11)
Wherein dm1For left column steel ball pitch diameter (dm1=2R11), to state convenient introducing de1(de1=2R12), R12For axis
Hold interior circle center O and steel ball centre of pitch circle O1The distance between '.
3. combined bearing structure is bored according to ball and stressing conditions derive taper roller any position angle φiThe outer ring at place
Normal direction contact load Q2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions.
As shown in Figure 1, being contacted between right row tapered roller and raceway for line, for right row roller load is made to generate displacement
Direction is otherwise varied with left column.At i-th of roller, rotational angle thetaiComponent be：
θi=θ cos φi (13)
Wherein, φiFor the position angle of i-th of taper roller.
Make the radial and axial displacement component that right row tapered roller generates as shown in Figure 3 due to moment loading.At i-th
The radial displacement component δ generated at rollerrθiWith axial displacement component δaθiFor：
δrθi=R22θcosφi (14)
δaθi=0.5dm2θcosφi (15)
R in above formula22For bearing inner race center O and taper roller centre of pitch circle O2The distance between ', dm2For taper roller section
Circular diameter, then the radial direction total displacement δ at i-th of roller2riFor：
δ2ri=δrcosφi-δrθi=(δr-R22θ)cosφi (16)
Axial total displacement δ at i-th of roller2aiFor：
δ2ai=δ0-δaθi-δa=δ0-0.5dm2θcosφi-δa (17)
δ0For end-play；Its outer raceway normal direction contact total displacement δ at i-th of roller2iFor radial direction total displacement δ2riAnd axis
To total displacement δ2aiIn the sum of outer raceway projection, wherein αeFor taper roller and outer ring contact angle, αiIt is connect for taper roller and inner ring
Feeler, as shown in Figure 4.
δ2i=δ2ricosαe+δ2aisinαe (18)
I.e.：δ2i=(δr-R22θ)cosφicosαe+(δ0-0.5dm2θcosφi-δa)sinαe (19)
Then i-th of roller is with outer ring contact load：
Q2i=Kn2[max(δ2i,0)]10/9 (20)
For taper roller, the difference of inside and outside contact angle is equal to cone angle, if its semi-cone angle is smaller, inside and outside contact angle
Difference it is also smaller therewith, then the global stiffness COEFFICIENT K of roller and outer raceway contact pointn2It can be according to cylindrical roller contact stiffness formula meter
It calculates：
Wherein l be the effective contact length of roller, Dw2For taper roller average diameter.
4. determine total radial load Q that taper roller generates inner ring2r, axial force Q2aWith moment of resistance M2。
Taper roller contact load radial component summation is：
Taper roller contact load axial component summation is：
Since ball-cone combined bearing is double-row bearing, bearing inner race center is with the decentraction of roller centre of pitch circle (such as Fig. 2 institutes
It is R to show two centre distances22), therefore its contact load radial component can also generate moment of resistance M2ir, the contact load of right row roller
Radial component total resistance square M2irWith contact load axial component total resistance square M2iaIt is added and forms taper roller total resistance
Square M2, it is shown below：
Wherein dm2For right row roller pitch diameter (dm2=2R21), to state convenient introducing de2(de2=2R22), R22For axis
Hold interior circle center O and roller centre of pitch circle O2The distance between '.
5. with lower in equilibrium-like under the force action of external load and all rolling element reaction forces according to bearing inner race
State is established with bearing inner race final deformation amount δr、δa, ball that θ is unknown quantity bore mixing double-row hub bearing inner ring mechanical balance side
Journey group, and the equilibrium equation group is solved, obtain bearing inner race final deformation amount δr、δaAnd θ.The equilibrium equation established
Group is：
6. the bearing inner race final deformation amount δ that will be obtainedr、δaIdentified normal direction contact load relational expression is brought into θ,
Obtain bearing each column loading conditions Q1iAnd Q2i。
It is illustrated below by taking a certain specific ball cone mixing double-row hub bearing as an example, the related ginseng of the bearing in the example
Number is as follows：
Left column steel ball size, steel ball quantity and steel ball pitch diameter are respectively：DW1=12.6mm, Z1=16, dm1=65mm, steel
The original contact angle α of ball0=45 °, inside and outside ditch coefficient of curvature is f respectivelyi=0.513, fe=0.523, bearing inner race center O and steel
Ball centre of pitch circle O1' the distance between R12=10.5mm；Right row tapered roller average diameter, roller number, roller busbar contact length
Degree and roller pitch diameter are respectively：DW2=9.46mm, Z2=21, L=12.3mm, dm2=63mm, taper roller and outer ring connect
Feeler αe=25.46 °, taper roller and inner ring contact angle αi=22.16 °, bearing inner race center O and roller centre of pitch circle O2' it
Between distance R22=10.5mm.
Using weight as under several basic operations and road conditions in the automobile normal running of 1.5t, mixing hub spindle is bored to ball
The load for holding generation is analyzed as external loading.
1) flat road surface is kept straight on,：Fr=5000N, Fa=-500N, M=0Nm；By inner ring stress balance equation calculation
It draws:Radial displacement δr=0.018967mm, axial displacement δa=-0.006mm, angular displacement=0.000347rad；Roller loads
Figure is as shown in Figure 5.
2) bumpy road is kept straight on,：Fr=10000N, Fa=-800N, M=200Nm；By inner ring stress balance equation meter
It draws:Radial displacement δr=0.044524mm, axial displacement δa=-0.016209mm, angular displacement=0.000879rad；Rolling
Sub- load diagram is as shown in Figure 6.
3) normal turn,：Fr=5000N, Fa=-1200N, M=400Nm；It is obtained by inner ring stress balance equation calculation
Go out:Radial displacement δr=0.048474mm, axial displacement δa=-0.018872mm, angular displacement=0.001039rad；Roller is born
It is as shown in Figure 7 to carry figure.
4) take a sudden turn,：Fr=5000N, Fa=-2000N, M=1000Nm；It is obtained by inner ring stress balance equation calculation
Go out:Radial displacement δr=0.087038mm, axial displacement δa=-0.037425mm, angular displacement=0.001923rad；Roller is born
It is as shown in Figure 8 to carry figure.
The present invention obtains the embodiment of the device of ball cone mixing double-row hub bearing load distribution
The device that ball cone mixing double-row hub bearing load distribution is obtained in the present embodiment connects including the device including normal direction
Touch load determining module, total radial load, axial force and moment of resistance determining module, nonlinear balance equation sets up formwork erection block and connects
LOAD FOR module normal direction contact loads determining module is touched to be used to bore combined bearing structure and stressing conditions derivation tapping according to ball
Ball any position angle ψiThe normal direction contact load Q at place1iWith bearing inner race final deformation amount δr、δaIt is rolled with the relation and circular cone of θ
Sub- any position angle φiThe normal direction contact load Q of the outer ring at place2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions；Total footpath
Xiang Li, axial force and moment of resistance determining module are used to derive that steel ball produces inner ring according to normal direction contact load and stressing conditions
Raw total radial load Q1r, axial force Q1aWith moment of resistance M1And total radial load Q that taper roller generates inner ring2r, it is axial
Power Q2aWith moment of resistance M2；Nonlinear balance equation is set up formwork erection block and is used for according to bearing inner race in external load and all rollings
The force action of body reaction force is lower in equilibrium state, establishes with bearing inner race final deformation amount δr、δa, θ be unknown quantity
Ball bores mixing double-row hub bearing inner ring mechanical balance equation, and equilibrium equation is solved, and obtains bearing inner race and finally becomes
Shape amount δr、δaAnd θ；Contact load computing module is used for the bearing inner race final deformation amount δ that will be obtainedr、δaIt brings into and determines with θ
Normal direction contact load relational expression, obtain bearing each column loading conditions Q1iAnd Q2i.The specific implementation means of each module exist
It is illustrated in the embodiment of method, which is not described herein again.
The present invention by the above process can quick obtaining ball bore mixing double-row hub bearing loading conditions, so as to
It is enough more to go deep into intuitively judging whether the design of ball cone mixing double-row hub bearing structure is reasonable, and mixing double-row wheel is bored for ball
The rational design that hub axle holds each parameter provides foundation, improves the reasonability of ball cone mixing double-row hub bearing design and accurate
Property.
Claims (8)
1. obtain the method for ball cone mixing double-row hub bearing load distribution, which is characterized in that this method comprises the following steps：
1) combined bearing structure is bored according to ball and stressing conditions derives steel ball any position angle ψiThe normal direction contact load Q at place1i
With bearing inner race final deformation amount δr、δaWith the relation of θ and taper roller any position angle φiThe normal direction contact of the outer ring at place
Load Q2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions；
2) total radial load Q that steel ball generates inner ring is derived according to normal direction contact load and stressing conditions1r, axial force Q1aWith to
Resisting moment M1And total radial load Q that taper roller generates inner ring2r, axial force Q2aWith moment of resistance M2；
3) equilibrium state is under the force action of external load and all rolling element reaction forces according to bearing inner race, established
With bearing inner race final deformation amount δr、δa, θ be unknown quantity ball bore mixing double-row hub bearing inner ring mechanical balance equation group, and
The equilibrium equation group is solved, obtains bearing inner race final deformation amount δr、δaAnd θ；
4) the bearing inner race final deformation amount δ that will be obtainedr、δaThe normal direction contact load relation determined in step 1) is brought into θ
Formula obtains bearing each column loading conditions Q1iAnd Q2i。
2. the method according to claim 1 for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that step
It is rapid 3) in the mechanic nonlinearity equilibrium equation group established be：
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Wherein FrFor the outer radial load that inner ring is subject to, FaFor the external axial load that inner ring is subject to, M is the top that inner ring is subject to
Cover torque, Q1rFor total radial load that steel ball generates inner ring, Q1aFor total axial force that steel ball generates inner ring, M1It is always supported for steel ball
Resisting moment, Q2rFor total radial load that taper roller generates inner ring, Q2aFor total axial force that taper roller generates inner ring, M2For
Taper roller total resistance square.
3. the method according to claim 1 for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that step
It is rapid 1) in steel ball any position angle ψiThe normal direction contact load Q at place1iFor：
Q1i=Kn1[max(δ1i,0)]3/2
δ1i=S1ψi-A
A=(fi+fe-1)Dw1
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<mn>0</mn>
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<mi>a</mi>
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<mn>1</mn>
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<mrow>
<mi>m</mi>
<mn>1</mn>
</mrow>
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Wherein δ1iFor the deflection of any position steel ball, A is the outer ring primitive groove center of curvature away from S1ψiFor after by load displacement
The Internal and external cycle ditch center of curvature of any position is away from RiFor radius of circle, α where the raceway ditch center of curvature in steel ball0For steel ball and raceway
Between original contact angle, ψiFor the position angle of steel ball, Kn1Total load-deformation constant between rolling element and Internal and external cycle, Dw1
For steel ball size, fiFor septal fossula coefficient of curvature, feFor outer fissure coefficient of curvature, δrFor bearing inner race radial displacement, δaFor in bearing
Axial displacement is enclosed, θ is angular displacement, dm1For left column steel ball pitch diameter.
4. the method according to claim 1 for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that step
It is rapid 1) in taper roller any position angle φiThe normal direction contact load Q at place and outer ring2iFor：
Q2i=Kn2[max(δ2i,0)]10/9
δ2i=(δr-R22θ)cosφicosαe+(δ0-0.5dm2θcosφi-δa)sinαe
Kn2=2.89 × 104×l0.82×Dw2 0.11
R22For bearing inner race center O and roller centre of pitch circle O2The distance between ', dm2For roller pitch diameter, φiAppoint for roller
Meaning position angle, αeFor roller and outer ring contact angle, δ0For end-play, Kn2For roller and the global stiffness system of outer raceway contact point
Number, l be the effective contact length of roller, Dw2For roller average diameter, δrFor bearing inner race radial displacement, δaFor bearing inner race axis
To displacement, θ is angular displacement.
5. the method according to claim 3 for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that steel
Total radial load Q that ball generates inner ring1r, axial force Q1aWith moment of resistance M1Respectively：
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<mn>1</mn>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>cos&psi;</mi>
<mi>i</mi>
</msub>
</mrow>
Wherein α1ψiThe contact angle of any position steel ball, Z after expression stand under load1For steel ball quantity, de1For bearing inner race center O and steel ball
Centre of pitch circle O1' between twice of distance, M1irFor the contact load radial component moment of resistance of all steel balls, M1iaIt is carried for contact
Lotus axial component moment of resistance.
6. the method according to claim 4 for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that circle
Total radial load Q that cone roller generates inner ring2r, axial force Q2aWith moment of resistance M2Respectively：
<mrow>
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<mn>2</mn>
</msub>
</munderover>
<msub>
<mi>Q</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>cos&alpha;</mi>
<mi>e</mi>
</msub>
<msub>
<mi>cos&phi;</mi>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
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<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>Z</mi>
<mn>2</mn>
</msub>
</munderover>
<msub>
<mi>Q</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>sin&alpha;</mi>
<mi>e</mi>
</msub>
</mrow>
Wherein Z2For roller number, M2irFor the contact load radial component total resistance square of right row roller, M2iaFor connecing for right row roller
Touch load axial component total resistance square, de2For bearing inner race center O and roller centre of pitch circle O2' between 2 times of distance.
7. the method for obtaining ball cone mixing double-row hub bearing load distribution according to any one of claim 1-6,
It is characterized in that, equilibrium equation is solved using Newton-Raphson iterative methods.
8. a kind of device for obtaining ball cone mixing double-row hub bearing load distribution, which is characterized in that the device connects including normal direction
Touch load determining module, total radial load, axial force and moment of resistance determining module, nonlinear balance equation sets up formwork erection block and connects
LOAD FOR module is touched,
The normal direction contact load determining module is used to bore combined bearing structure according to ball and stressing conditions derive that steel ball is arbitrary
Position angle ψiThe normal direction contact load Q at place1iWith bearing inner race final deformation amount δr、δaIt is arbitrary with the relation and taper roller of θ
Position angle φiThe normal direction contact load Q of the outer ring at place2iWith bearing inner race final deformation amount δr、δaWith θ relational expressions；
Total radial load, axial force and moment of resistance determining module are used to be derived according to normal direction contact load and stressing conditions
Total radial load Q that steel ball generates inner ring1r, axial force Q1aWith moment of resistance M1And total footpath that taper roller generates inner ring
To power Q2r, axial force Q2aWith moment of resistance M2；
The nonlinear balance equation is set up formwork erection block and is used for according to bearing inner race in external load and all rolling element reactions
The force action of power is lower in equilibrium state, establishes with bearing inner race final deformation amount δr、δa, θ be unknown quantity ball cone mixing
Biserial hub bearing inner ring mechanical balance equation, and equilibrium equation is solved, obtain bearing inner race final deformation amount δr、δa
And θ；
The contact load computing module is used for the bearing inner race final deformation amount δ that will be obtainedr、δaIdentified normal direction is brought into θ
Contact load relational expression obtains bearing each column loading conditions Q1iAnd Q2i。
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| CN106326570B (en) * | 2016-08-27 | 2019-09-13 | 河南科技大学 | Ball, cone mixing double-row hub bearing most preferably pre-tighten method for determination of amount and device |
| CN106499725A (en) * | 2016-12-28 | 2017-03-15 | 贵州虹轴轴承有限公司 | A kind of machine bearing |
| CN107066699B (en) * | 2017-03-20 | 2020-02-21 | 河南科技大学 | Method for acquiring load distribution of crossed tapered roller bearing |
| CN106934165B (en) * | 2017-03-20 | 2020-02-14 | 河南科技大学 | Method for rapidly extracting static stiffness of crossed tapered roller bearing |
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| CN108009342B (en) * | 2017-11-29 | 2019-08-16 | 河南科技大学 | A kind of W2R type shaft connecting bearing and its load distributional analysis method |
| CN108228991B (en) * | 2017-12-26 | 2021-04-23 | 三门峡职业技术学院 | Method for solving numerical value of high-speed angular contact ball bearing |
| CN108090312B (en) * | 2018-01-30 | 2021-03-30 | 中国航空发动机研究院 | Method for acquiring load distribution of cylindrical roller bearing |
| CN109580223B (en) * | 2018-12-14 | 2020-07-28 | 河南科技大学 | Combined type shaft connecting bearing load analysis method considering deformation influence of mandrel |
| CN112594289B (en) * | 2020-12-14 | 2022-07-01 | 上海航天控制技术研究所 | Bearing device under high overload resistance configuration of bearing and characteristic evaluation method |
| CN114462162B (en) * | 2022-01-25 | 2024-04-12 | 中国铁建重工集团股份有限公司 | Load distribution calculation method for multi-row roller turntable bearing with axial play |
| CN117057170B (en) * | 2023-10-12 | 2024-01-26 | 齐鲁工业大学(山东省科学院) | Double-row self-aligning roller bearing contact mechanical model based on flexible contact and play |
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Application publication date: 20161109 Assignee: Zhejiang Zhaofeng Mechanical and Electronic Co., Ltd. Assignor: Henan University of Science and Technology Contract record no.: X2019980000489 Denomination of invention: Method and device for obtaining load distribution of ball-cone mixed double-row hub bearing Granted publication date: 20180601 License type: Exclusive License Record date: 20191104 |