CN105956270B - End contact lacks the computational methods of piece reinforcement end each stress of major-minor spring - Google Patents
End contact lacks the computational methods of piece reinforcement end each stress of major-minor spring Download PDFInfo
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- CN105956270B CN105956270B CN201610285905.7A CN201610285905A CN105956270B CN 105956270 B CN105956270 B CN 105956270B CN 201610285905 A CN201610285905 A CN 201610285905A CN 105956270 B CN105956270 B CN 105956270B
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Abstract
End contact of the present invention lacks the computational methods of piece reinforcement end each stress of major-minor spring, belongs to suspension leaf spring technical field.The present invention can work load and major-minor spring borne load according to structural parameters, elasticity modulus, the auxiliary spring of each main spring and auxiliary spring, lack each main spring of piece reinforcement end major-minor spring to end contact and the stress of auxiliary spring at different locations calculates.By example calculation and ANSYS simulating, verifyings it is found that the available accurately and reliably Stress calculation value of each main spring and auxiliary spring at different locations of this method；Design level, product quality, the Performance And Reliability that end contact lacks piece reinforcement end major-minor spring are improved using this method, improves ride comfort and the safety of vehicle traveling；Bearing spring quality and cost are reduced, meanwhile, product design and testing expenses are reduced, product development and design speed is accelerated.
Description
Technical field
Lack each of piece reinforcement end major-minor spring the present invention relates to vehicle suspension leaf spring, especially end contact and answer
The computational methods of power.
Background technology
Small, noise is small because having many advantages, such as to rub between light-weight, piece for few piece variable-section steel sheet spring, is widely used in vehicle
In Leaf Spring Suspension System.In order to meet the design requirement of processing technology, stress intensity, rigidity and lifting lug thickness, in reality
During the engineer application of border, few piece variable-section steel sheet spring is usually designed as end contact and lacks piece reinforcement end major-minor spring
Form.Main spring rigidity and major-minor spring complex stiffness should meet suspension performance requirement, and each main spring and auxiliary spring are at different locations
Stress, service life and the reliability requirement of leaf spring should be met.However, due to the non-equal structures of the end flat segments of each main spring,
Auxiliary spring length is less than main spring length, and after load works the contact of load major-minor spring more than auxiliary spring, the change of each major-minor spring
Shape and endpoint power have coupling, therefore, extremely difficult to each main spring and the Stress calculation of auxiliary spring at different locations.According to being looked into
Data is read it is found that current state, inside and outside each for not provided reliable end contact always and having lacked piece reinforcement end major-minor spring
The calculation method for stress of main spring and auxiliary spring at different locations.Lack piece reinforcement end for end contact both at home and abroad at present to become
Section major-minor spring is mostly using finite element emulation softwares such as ANSYS, by solid modelling to the variable cross-section steel plates of given structure
Spring carries out stress numerical emulation, although reliable stress simulation value can be obtained in this method, however, finite element modeling emulates
Analysis method can only carry out numerical simulation verification to the leaf spring stress for giving structure and load, cannot provide accurate stress
Analytical formula, so cannot meet end contact lacks piece reinforcement end variable cross-section major-minor spring modernization design CAD design
And the requirement of software development.Therefore, it is necessary to which establishing a kind of accurate, reliable end contact lacks piece reinforcement end major-minor spring
The computational methods of each main spring and auxiliary spring stress at different locations, meet end contact and lack piece reinforcement end variable cross-section master
The requirement of Stress calculation and strength check at each main spring and auxiliary spring different location of auxiliary spring improves few piece variable cross-section steel plates bullet
Design level, quality, performance, reliability and the vehicle ride performance of spring and safety；Meanwhile reducing product design and experiment
Expense accelerates product development and design speed.
Invention content
Defect present in for the above-mentioned prior art, technical problem to be solved by the invention is to provide it is a kind of it is easy,
Reliable end contact lacks the computational methods of piece reinforcement end each stress of major-minor spring, calculation flow chart, as shown in Figure 1.
It is symmetrical structure that end contact, which lacks piece reinforcement end variable cross-section major-minor spring, and the half symmetrical structure of major-minor spring can be seen as outstanding
Arm beam, i.e. symmetrical center line be root fixing end, the end stress point of main spring and the contact of auxiliary spring respectively as main spring endpoint and
Auxiliary spring endpoint, the schematic diagram of half symmetrical structure major-minor spring, as shown in Figure 2, wherein including：Main spring 1, root shim 2, auxiliary spring
3, end pad 4；The half symmetrical structure of main spring 1 and auxiliary spring 3 is by root flat segments, parabolic segment, oblique line section, end flat segments
Four sections of compositions, oblique line section play booster action to variable cross-section end；Each root flat segments and main spring 1 of main spring 1 and auxiliary spring 3 and pair
Root shim 2 is equipped between spring 3, the end flat segments of main spring 1 each are equipped with end pad 4, and the material of end pad 4 is carbon
Fibrous composite, produced frictional noise when for reducing spring works.The width of main spring 1 and auxiliary spring 3 is b, oblique line section
Length be Δ l, clipping room away from half length be l3, elasticity modulus E.Main reed number is m, the thickness of the root flat segments of main spring
Degree is h2M, the distance of root to the main spring endpoint of main spring parabolic segment is l2M=LM-l3, the end thickness of each main spring parabolic segment
Degree is h1Mpi, the thickness ratio β of parabolic segmenti=h1Mpi/h2M, i=1,2 ..., m, the end of parabolic segment to main spring endpoint away from
From l1Mpi=l2Mβi 2；The non-equal structures of end flat segments of each main spring, i.e., the thickness and length of the end flat segments of the 1st main spring,
More than the thickness and length of the end flat segments of other each main spring, wherein the thickness and length of the end flat segments of each main spring
Degree is respectively h1MiAnd l1Mi=l1Mpi-Δl；The thickness ratio γ of each main spring oblique line sectionMi=h1Mi/h1Mpi.Auxiliary spring the piece number is n, secondary
The half length of spring is LA, the thickness of each auxiliary spring root flat segments is h2A, the root of auxiliary spring parabolic segment to auxiliary spring endpoint
Distance is l2A=LA-l3, the end thickness of each auxiliary spring parabolic segment is h1Apj, the thickness ratio β of auxiliary spring parabolic segmentAj=h1Apj/
h2A, the distance l of the end of auxiliary spring parabolic segment to auxiliary spring endpoint1Apj=l2AβAj 2；The thickness of the end flat segments of each auxiliary spring and
Length is respectively h1AjAnd l1Aj=l1ApjΔ l, the thickness ratio γ of auxiliary spring oblique line sectionAj=h1Aj/h1Apj.Auxiliary spring ends points and master
The horizontal distance of spring endpoint is l0, the major-minor spring gap delta between auxiliary spring ends points and the main spring end flat segments of m pieces；Work as load
Lotus more than auxiliary spring work load when, certain point is in contact in auxiliary spring and main spring end flat segments；After major-minor spring end contacts,
The main spring that each end stress of major-minor spring is differed, and be in contact with auxiliary spring at contact point in addition to other than by endpoint power, also holding
By the support force of auxiliary spring.It works load and major-minor spring institute in structural parameters, elasticity modulus, the auxiliary spring of each main spring and auxiliary spring
Bear load it is given in the case of, to end contact lack piece reinforcement end major-minor spring each main spring and auxiliary spring in different location
The stress at place is calculated.
It is answered in order to solve the above technical problems, end contact provided by the present invention lacks each of piece reinforcement end major-minor spring
The computational methods of power, it is characterised in that use following calculating step：
(1) end contact lacks the half rigidimeter of each main spring and auxiliary spring of piece reinforcement end variable cross-section major-minor spring
It calculates：
I steps：The half stiffness K of each main spring before the contact of major-minor springMiIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact, elasticity
Modulus E；The half length L of main springM, the distance l of the root of main spring parabolic segment to spring endpoint2M, the root of each main spring is put down
The thickness h of straight section2M, main reed number m, wherein the thickness ratio β of the parabolic segment of i-th main springi, the thickness ratio γ of oblique line sectionMi,
Distance l of the root of oblique line section to main spring endpoint1Mpi, the distance l of the end of oblique line section to main spring endpoint1Mi, i=1,2 ..., m；
The half stiffness K of each main spring before being contacted to major-minor springMiIt is calculated, i.e.,
In formula, GX-EiFor in the endpoint deformation coefficient of i-th main spring of endpoint force effect, i.e.,
II steps：The half stiffness K of each main spring after the contact of major-minor springMAiIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact, elasticity
Modulus E；The half length L of main springM, the thickness h of the root flat segments of each main spring2M, the root of main spring parabolic segment to spring
The distance l of endpoint2M, main reed number m, wherein the thickness ratio β of the parabolic segment of i-th main springi, the thickness ratio γ of oblique line sectionMi,
Distance l of the root of oblique line section to main spring endpoint1Mpi, the distance l of the end of main spring oblique line section to main spring endpoint1Mi, i=1,
2,…,m；The half length L of auxiliary springA, the thickness h of the root flat segments of each auxiliary spring2A, the root of auxiliary spring parabolic segment to auxiliary spring
The distance l of endpoint2A, auxiliary spring the piece number n, wherein the thickness ratio β of the parabolic segment of jth piece auxiliary springAj, the thickness ratio γ of oblique line sectionAj,
Distance l of the root of oblique line section to secondary endpoint1Apj, the distance l of the end of oblique line section to auxiliary spring endpoint1Aj, j=1,2 ..., n；It is secondary
The horizontal distance l of spring contact and main spring endpoint0, the half stiffness K of each main spring after being contacted to major-minor springMAiIt is calculated,
I.e.
In formula, GX-EiFor in the endpoint deformation coefficient of i-th main spring of endpoint force effect；GX-EATFor in endpoint
Total endpoint deformation coefficient of n pieces superposition auxiliary spring in the case of force effect, GX-EAjFor in the jth piece pair of endpoint force effect
The endpoint deformation coefficient of spring；Gx-DEIt is the main spring of m pieces under endpoint stressing conditions at end flat segments and auxiliary spring contact point
Deformation coefficient；Gx-EzmFor the endpoint deformation coefficient of the main spring of m pieces under the stressing conditions at major-minor spring contact point；Gx-DEzFor
Deformation coefficient of the main spring of m pieces at end flat segments and auxiliary spring contact point under stressing conditions at major-minor spring contact point, i.e.,
III steps：The half stiffness K of each auxiliary springAjIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact, elasticity
Modulus E；The half length L of auxiliary springA, the thickness h of the root flat segments of each auxiliary spring2A, the root of auxiliary spring parabolic segment to auxiliary spring
The distance l of endpoint2A, auxiliary spring the piece number n, wherein the thickness ratio β of the parabolic segment of jth piece auxiliary springAj, the thickness ratio γ of oblique line sectionAj,
Distance l of the root of oblique line section to auxiliary spring endpoint1Apj, the distance l of the end of oblique line section to auxiliary spring endpoint1Aj, to each auxiliary spring
Half stiffness KAjIt is calculated, i.e.,
In formula,
(2) the endpoint power for each main spring and auxiliary spring that end contact lacks piece reinforcement end variable cross-section major-minor spring calculates：
I steps：The endpoint power P of each main springiIt calculates：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P loaded according to end contact,
Auxiliary spring works load pK, the K that is calculated in I stepsMiAnd obtained K is calculated in II stepsMAi, to the end of each main spring
Point power PiIt is calculated, i.e.,
Ii steps：The endpoint power P of each auxiliary springAjIt calculates：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P loaded according to end contact,
Auxiliary spring works load pK, main reed number m, the thickness h of the root flat segments of each main spring2M, auxiliary spring the piece number n, each auxiliary spring
The thickness h of root flat segments2A, the K that is calculated in II stepsMAi、Gx-DE、Gx-DEzAnd Gx-EATAnd it is calculated in III steps
KAj, to the endpoint power P of each auxiliary springAjIt is calculated, i.e.,
(3) end contact lacks the calculating of each main spring different location stress of piece reinforcement end variable cross-section major-minor spring：
Step A：The calculating of stress at the preceding main spring different location x of m-1 pieces：
Lack the half length L of the main spring of piece reinforcement end variable cross-section according to end contactM, the length Δ l of oblique line section, respectively
The thickness h of the root flat segments of the main spring of piece2M, the distance l of the root of main spring parabolic segment to main spring endpoint2M, main reed number m,
In, the end thickness h of the parabolic segment of i-th main spring1Mpi, the thickness h of the end flat segments of i-th main spring1Mi, i-th main spring
Parabolic segment end to main spring endpoint distance l1Mpi, the length l of the end flat segments of i-th main spring1Mi；And in i steps
The P being calculatedi, using main spring free end as coordinate origin, using main spring endpoint as coordinate origin, few piece reinforcement end is become and is cut
Stress of the preceding main spring of m-1 pieces of face leaf spring at different location x is calculated, i.e.,
In formula, h2Mi(x) it is thickness of i-th main spring oblique line section at x position, h2Mpi(x) it is i-th main spring parabola
Thickness of the section at x position, i.e.,
Step B：The calculating of stress at the main spring different location x of m pieces：
Lack the half length L of the main spring of piece reinforcement end variable cross-section according to end contactM, the length Δ l of oblique line section, respectively
The thickness h of the root flat segments of the main spring of piece2M, the distance l of the root of parabolic segment to spring endpoint2M, auxiliary spring contact and main spring end
The horizontal distance l of point0；Main reed number m, wherein the end thickness h of the parabolic segment of the main spring of m pieces1Mpm, the throwing of the main spring of m pieces
Distance l of the end of object line segment to main spring endpoint1Mpm, the length l of the end flat segments of the main spring of m pieces1MmAnd thickness h1Mm；And step
Suddenly the P being calculated in the i steps of (2)m, the P that is calculated in ii stepsAj, using main spring endpoint as coordinate origin, to few bit end
Stress σ of the main spring of m pieces of the reinforced variable-section steel sheet spring in portion at different location xMmIt is calculated, i.e.,
In formula, h2Mm(x) it is thickness of the main spring oblique line section of m pieces at x position, h2Mpm(x) it is the main spring parabola of m pieces
Thickness of the section at x position, i.e.,
(4) end contact lacks meter of each auxiliary spring in different location stress of piece reinforcement end variable cross-section major-minor spring
It calculates：
According to the half length L of few piece reinforcement end variable cross-section auxiliary springA, width b, the thickness of auxiliary spring root flat segments
h2A, the length Δ l of oblique line section, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A, auxiliary spring the piece number n, wherein jth piece
Distance l of the end of the parabolic segment of auxiliary spring to auxiliary spring endpoint1Apj, the end thickness of auxiliary spring parabolic segment is h1Apj, end is straight
The thickness h of section1AjWith length l1Aj；And the P being calculated in ii stepsAj, j=1,2 ..., n, using auxiliary spring free end as coordinate original
Point calculates the stress of each auxiliary spring of few piece reinforcement end variable-section steel sheet spring at different location x, i.e.,
In formula, h2Aj(x) it is thickness of the jth piece auxiliary spring oblique line section at x position, h2Apj(x) it is jth piece auxiliary spring parabola
Thickness of the section at x position, i.e.,
The present invention has the advantage that than the prior art
Due to the non-equal structures of the end flat segments of each main spring, auxiliary spring length is less than main spring length, and when load is more than auxiliary spring
After the contact of the load that works major-minor spring, the deformation of each major-minor spring and endpoint power have coupling, therefore, to each main spring and pair
The Stress calculation of spring at different locations is extremely difficult, had not provided reliable end contact inside and outside predecessor State always and has lacked bit end
The calculation method for stress of each main spring and auxiliary spring of the reinforced major-minor spring in portion at different locations.End is connect both at home and abroad at present
Piece reinforcement end variable cross-section major-minor spring is lacked in touch, is mostly to pass through solid modelling pair using finite element emulation softwares such as ANSYS
The variable-section steel sheet spring of given structure carries out stress numerical emulation, although reliable stress simulation can be obtained in this method
Value, however, since finite element modeling simulating analysis can only carry out numerical value to the leaf spring stress for giving structure and load
Simulating, verifying cannot provide accurate stress analysis calculating formula, so cannot meet end contact lacks the change of piece reinforcement end
The requirement of section major-minor spring modernization design CAD design and software development.The present invention can lack bit end according to each end contact
Each main spring of the reinforced variable cross-section major-minor spring in portion and structural parameters, elasticity modulus, the auxiliary spring of auxiliary spring work load and major-minor
Spring borne load lacks end contact each main spring and auxiliary spring the answering at different locations of piece reinforcement end major-minor spring
Power carries out accurate Analysis calculating.
By example and ANSYS simulating, verifyings it is found that accurate, reliable end contact, which can be obtained, in this method lacks piece end
The Stress calculation value of each main spring and auxiliary spring of reinforced major-minor spring at different locations lacks the reinforcement of piece end for end contact
The calculating of type each stress of major-minor spring provides reliable computational methods, and strong for few piece variable cross-section reinforcement end major-minor spring
Degree is checked and reliable technical foundation has been established in CAD software exploitation.Vehicle suspension variable cross-section major-minor spring can be improved using this method
Design level, product quality, performance and reliability, improve ride performance and the safety of vehicle；Meanwhile also reducing product
Product development speed is accelerated in design and testing expenses.
Description of the drawings
For a better understanding of the present invention, it is described further below in conjunction with the accompanying drawings.
Fig. 1 is the calculation flow chart that end contact lacks piece reinforcement end each stress of major-minor spring；
Fig. 2 is the half symmetrical structure schematic diagram that end contact lacks piece reinforcement end major-minor spring；
Fig. 3 is that the end contact of embodiment lacks the 1st stress variation of main spring at different locations of piece reinforcement end
Curve；
Fig. 4 is that the end contact of embodiment lacks the 2nd stress variation of main spring at different locations of piece reinforcement end
Curve；
Fig. 5 is that the end contact of embodiment lacks the stress variation song of 1 auxiliary spring of piece reinforcement end at different locations
Line；
Fig. 6 is that the end contact of embodiment lacks the ANSYS stress simulation cloud atlas of the 1st main spring of piece reinforcement end；
Fig. 7 is that the end contact of embodiment lacks the ANSYS stress simulation cloud atlas of the 2nd main spring of piece reinforcement end；
Fig. 8 is that the end contact of embodiment lacks the ANSYS stress simulation cloud atlas of 1 auxiliary spring of piece reinforcement end.
Specific embodiment
Below by embodiment, invention is further described in detail.
Embodiment：Certain end contact lacks the width b=60mm of piece reinforcement end variable cross-section major-minor spring, clipping room away from
Half l3=55mm, the length Δ l=30mm of oblique line section, elastic modulus E=200GPa.Main reed number m=2, the half of main spring
Length LM=575mm, the thickness h of the root flat segments of each main spring2M=11mm, the root of main spring parabolic segment to main spring endpoint
Distance l2M=LM-l3=520mm；The end thickness h of the parabolic segment of 1st main spring1Mp1=6mm, the thickness ratio of parabolic segment
β1=h1Mp1/h2M=0.55, the distance l of the end of parabolic segment to main spring endpoint1Mp1=l2Mβ1 2=157.30mm, end are straight
The thickness h of section1M1=7mm, the thickness ratio γ of oblique line sectionM1=h1M1/h1Mp1=1.17, the length l of end flat segments1M1=l1Mp1-
Δ l=127.30mm；The end thickness h of the parabolic segment of 2nd main spring1Mp2=5mm, the thickness ratio β of parabolic segment2=h1Mp2/
h2M=0.45, the distance l of the end of parabolic segment to main spring endpoint1Mp2=l2Mβ2 2=105.30mm, the thickness of end flat segments
h1M2=6mm, the thickness ratio γ of oblique line sectionM2=h1M2/h1Mp2=1.20, the length l of end flat segments1M2=l1Mp2Δ l=
75.30mm.The half length L of auxiliary springA=525mm, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A=LA-l3=
470mm, auxiliary spring the piece number n=1, the thickness h of the root flat segments of the piece auxiliary spring2AThe end of=14mm, the parabolic segment of auxiliary spring are thick
Spend h1Ap1=7mm, the thickness ratio β of parabolic segmentA1=h1Ap1/h2A=0.50, the distance of the end of parabolic segment to auxiliary spring endpoint
l1Ap1=l2AβA1 2=117.50mm, the thickness h of end flat segments1A1=8mm, the thickness ratio γ of oblique line sectionA1=h1A1/h1Ap1=
1.14, the length l of end flat segments1A1=l1Ap1Δ l=87.50mm.The horizontal distance l of auxiliary spring contact and main spring endpoint0=
LM-LA=50mm, major-minor spring work load pK=2404.2N.In major-minor spring half loaded, that is, single-ended point load P=
In the case of 3040N, the stress at each main spring and auxiliary spring different location of piece reinforcement end variable-section steel sheet spring is lacked to this
It is calculated.
The end contact that present example is provided lacks the computational methods of piece reinforcement end each stress of major-minor spring,
Calculation process is as shown in Figure 1, specifically steps are as follows for calculating：
(1) end contact lacks the half rigidimeter of each main spring and auxiliary spring of piece reinforcement end variable cross-section major-minor spring
It calculates：
I steps：The half stiffness K of each main spring before the contact of major-minor springMiIt calculates：
Lack the width b=60mm of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact
=30mm, elastic modulus E=200GPa；The half length L of main springM=575mm, the thickness h of main spring root flat segments2M=
11mm, the distance l of the root of main spring parabolic segment to main spring endpoint2M=520mm；Main reed number m=2, wherein the 1st main spring
Parabolic segment thickness ratio β1=0.55, the distance l of the root of oblique line section to main spring endpoint1Mp1=157.30mm, oblique line section
Thickness ratio γM1=1.17, the distance l of the end of oblique line section to main spring endpoint1M1=127.30mm；The parabolic segment of 2nd main spring
Thickness ratio β2=0.45, the thickness ratio γ of oblique line sectionM2=1.20, the distance l of the root of oblique line section to main spring endpoint1Mp2=
105.30mm, the distance l of the end of oblique line section to spring endpoint1M2=75.30mm；To auxiliary spring contact before the 1st main spring and
The half stiffness K of 2nd main springM1And KM2It is respectively calculated, i.e.,
In formula, GX-E1And GX-E2The endpoint of the 1st main spring and the 2nd main spring deformation system respectively under endpoint stressing conditions
Number, i.e.,
II steps：The half stiffness K of each main spring after the contact of major-minor springMAiCalculating：
Lack the width b=60mm of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact
=30mm, elastic modulus E=200GPa.The half length L of main springM=575mm, the thickness h of the root flat segments of each main spring2M
=11mm, the distance l of the root of the parabolic segment of main spring to spring endpoint2M=520mm, main reed number m=2, wherein the 1st
The thickness ratio β of the parabolic segment of main spring1=0.55, the thickness ratio γ of oblique line sectionM1=1.17, the root of oblique line section to main spring endpoint
Distance l1Mp1=157.30mm, the distance l of the end of oblique line section to main spring endpoint1M1=127.30mm；The throwing of 2nd main spring
The thickness ratio β of object line segment2=0.45, the thickness ratio γ of oblique line sectionM2=1.20, the distance of the root of oblique line section to spring endpoint
l1Mp2=105.30mm, the distance l of the end of oblique line section to spring endpoint1M2=75.30mm.The half length L of auxiliary springA=
525mm, the thickness h of auxiliary spring root flat segments2A=14mm, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A=
470mm, auxiliary spring the piece number n=1, the thickness ratio β of the parabolic segment of the piece auxiliary springA1=0.50, the thickness ratio γ of oblique line sectionA1=
1.14, the distance l of the root of oblique line section to auxiliary spring endpoint1Ap1=117.50mm, the distance of the end of oblique line section to auxiliary spring endpoint
l1A1=87.50mm；The horizontal distance l of auxiliary spring contact and main spring endpoint0=50mm.The 1st main spring after being contacted to major-minor spring
With the half stiffness K of the 2nd main springMA1And KMA2It is respectively calculated, i.e.,
In formula,
III steps：The half stiffness K of each auxiliary springAjIt calculates：
Lack the width b=60mm of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section according to end contact
=30mm, elastic modulus E=200GPa.The half length L of auxiliary springA=525mm, auxiliary spring the piece number n=1, the root of the piece auxiliary spring
The thickness h of flat segments2A=14mm, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A=470mm, auxiliary spring oblique line section
End to auxiliary spring endpoint distance l1A1=87.50mm, the distance l of the root of auxiliary spring oblique line section to spring endpoint1Ap1=
117.50mm；The thickness ratio β of the parabolic segment of the piece auxiliary springA1=0.50, the thickness ratio γ of oblique line sectionA1=1.14；To the piece pair
The half stiffness K of springA1It is calculated, i.e.,
In formula,
(2) the endpoint power for each main spring and auxiliary spring that end contact lacks piece reinforcement end variable cross-section major-minor spring calculates：
I steps：The endpoint power P of each main springiIt calculates：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P=loaded according to end contact
3040N, auxiliary spring work load pK=2404.2N, main reed number m=2；The K being calculated in I stepsM1=13.29N/mm and
KM2Obtained K is calculated in=12.71N/mm and II stepsMA1=13.29N/mm and KMA2=35.94N/mm, to the 1st master
The endpoint power P of spring and the 2nd main spring1And P2It is respectively calculated, i.e.,
Ii steps：Each auxiliary spring endpoint power PAjCalculating：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P=loaded according to end contact
3040N, auxiliary spring work load pK=2404.2N, main reed number m=2, the thickness h of the root flat segments of each main spring2M=
11mm；Auxiliary spring the piece number n=1, the thickness h of the root flat segments of the piece auxiliary spring2AThe K being calculated in=14mm, II stepMA1=
13.29N/mm、KMA2=35.94N/mm, Gx-DE=86.43mm4/N、Gx-DEz=72.75mm4/N、Gx-EAT=77.53mm4/ N, and
The K being calculated in III stepsA1=35.39N/mm, to the endpoint power P of the piece auxiliary springA1It is calculated, i.e.,
(3) end contact lacks stress of each main spring of piece reinforcement end variable cross-section major-minor spring at different location x
It calculates：
Step A：1st Stress calculation of the main spring at different location x：
Lack the width b=60mm of the main spring of piece reinforcement end variable cross-section, the half length L of main spring according to end contactM
=575mm, the distance l of the root of main spring parabolic segment to main spring endpoint2M=520mm, the thickness of the root flat segments of each main spring
Spend h2M=11mm, main reed number m=2, the thickness ratio β of the parabolic segment of the 1st main spring1The oblique line section of=0.55, the 1st main spring
Root to spring endpoint distance l1Mp1=157.30mm, the end thickness h of parabolic segment1Mp1=6mm, the end of the 1st main spring
The thickness h of portion's flat segments1M1=7mm and length l1M1=127.30mm；And the P being calculated in i steps1=1110.6N, with master
Spring endpoint is coordinate origin, lacks the 1st main spring of piece reinforcement end variable cross-section major-minor spring in different positions to the end contact
It sets the stress at x to be calculated, i.e.,
In formula, h2M1(x)=- 33.33x+11.24,Wherein, obtained 1st main spring is calculated
Stress changing curve at different locations, as shown in Figure 3；
Step B：2nd Stress calculation of the main spring at different location x：
Lack the width b=60mm of the main spring of piece reinforcement end variable cross-section, the half length L of main spring according to end contactM
=575mm, the thickness h of the root flat segments of each main spring2M=11mm, the distance l of the root of parabolic segment to main spring endpoint2M
=520mm, main reed number m=2, wherein the thickness ratio β of the parabolic segment of the 2nd main spring2=0.45, the root of oblique line section is arrived
The distance l of spring endpoint1Mp2=105.30mm, the end thickness h of parabolic segment1Mp2=5mm, the end flat segments of the 2nd main spring
Thickness h1M2=6mm and length l1M2=75.30mm；The horizontal distance l of auxiliary spring contact and main spring endpoint0In=50mm, i step
The P being calculated2The P being calculated in=1929.4N, ii stepA1=1050.8N, using main spring endpoint as coordinate origin, to this
The 2nd stress of the main spring at different location x that end contact lacks piece reinforcement end variable cross-section major-minor spring is calculated, i.e.,
In formula, h2M2(x)=- 33.33x+8.51,Wherein, obtained 2nd main spring is calculated
Stress changing curve at different location x, as shown in Figure 4；
(4) end contact lacks each auxiliary spring Stress calculation of piece reinforcement end variable cross-section major-minor spring：
Lack the width b=60mm of piece reinforcement end variable cross-section auxiliary spring, the half length L of auxiliary spring according to end contactA
=525mm, the thickness h of the root flat segments of auxiliary spring2A=14mm, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A
=470mm, auxiliary spring the piece number n=1, the thickness ratio β of the parabolic segment of the piece auxiliary springA1=0.50, the end of parabolic segment to auxiliary spring
The distance l of endpoint1Ap1The end thickness of=117.50mm, parabolic segment are h1Ap1=7mm, the end flat segments of the piece auxiliary spring
Thickness h1A1=8mm and length l1A1=87.50mm；And the P being calculated in ii stepsA1=1053.1N is to sit with auxiliary spring endpoint
Mark origin, to the end contact lack stress of 1 auxiliary spring of piece reinforcement end variable cross-section major-minor spring at different location x into
Row calculates, i.e.,
In formula, h2A1(x)=- 33.33x+10.92,Wherein, obtained 1 auxiliary spring is calculated to exist
Stress changing curve at different location x, as shown in Figure 5.
Using ANSYS finite element emulation softwares, piece reinforcement end variable cross-section major-minor spring is lacked according to the end contact
The structural parameters and elasticity modulus of each main spring and auxiliary spring establish the ANSYS simulation models of half symmetrical structure major-minor spring, divide
Grid, setting auxiliary spring endpoint are contacted with main spring, and apply fixed constraint in the root of simulation model, are applied in major-minor spring endpoint and are collected
Middle load F=P-PK/ 2=1837.9N lacks the end contact major-minor spring of piece reinforcement end variable-section steel sheet spring
Stress progress ANSYS emulation, the ANSYS stress simulation cloud atlas of obtained 1st main spring, as shown in Figure 6；2nd main spring
ANSYS stress simulation cloud atlas, as shown in Figure 7；The ANSYS stress simulation cloud atlas of 1 auxiliary spring, as shown in Figure 8, wherein the 1st master
Stress σ of the spring at parabolic segment and root contact positionMA1=213.86MPa, the 2nd main spring are in parabolic segment and oblique line section
Stress σ at contact positionMA2The stress σ of=337.61MPa, 1 auxiliary spring at parabolic segment and oblique line section contact positionA1=
253.79MPa。
It is found that in same load, the ANSYS of the leaf spring the 1st and the 2nd main spring and 1 auxiliary spring stress
Simulating, verifying value σMA1=213.86MPa, σMA2=337.61MPa, σA1=253.79MPa, respectively with analytical Calculation value σMA1=
213.22MPa、σMA2=339.45MPa, σA1=251.99MPa matches, relative deviation is respectively 0.30%, 0.55%,
0.71%；The result shows that the end contact that the invention is provided lacks the computational methods of piece reinforcement end each stress of major-minor spring
It is correct, the Stress calculation value of each main spring and auxiliary spring at different locations is accurate, reliable.
Claims (1)
1. end contact lacks the computational methods of piece reinforcement end each stress of major-minor spring, wherein end contact lacks bit end
The half symmetrical structure of the reinforced major-minor spring in portion is made of 4 sections of root flat segments, parabolic segment, oblique line section and end flat segments,
Oblique line section plays booster action to the end of variable cross-section major-minor spring；The non-equal structures of the end flat segments of each main spring, i.e. the 1st main spring
The thickness and length of end flat segments are more than the thickness and length of the end flat segments of other each main spring, meet the 1st main spring
The requirement of complicated applied force；It is equipped with major-minor spring gap between auxiliary spring contact and main spring end flat segments, is worked load with meeting auxiliary spring
The design requirement of lotus；When load works load more than auxiliary spring, and the contact of major-minor spring works together, each main spring and auxiliary spring by
Power and stress at different locations are unequal；It works load in structural parameters, elasticity modulus, the auxiliary spring of each main spring and auxiliary spring
Lotus, major-minor spring bear load it is given in the case of, each main spring of piece reinforcement end variable cross-section major-minor spring is lacked to end contact
It is calculated with the stress of auxiliary spring at different locations, steps are as follows for specific calculating：
(1) end contact lacks the half Rigidity Calculation of each main spring and auxiliary spring of piece reinforcement end variable cross-section major-minor spring：
I steps：The half stiffness K of each main spring before the contact of major-minor springMiIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section, elasticity modulus according to end contact
E；The half length L of main springM, the distance l of the root of main spring parabolic segment to spring endpoint2M, the root flat segments of each main spring
Thickness h2M, main reed number m, wherein the thickness ratio β of the parabolic segment of i-th main springi, the thickness ratio γ of oblique line sectionMi, oblique line
Distance l of the root of section to main spring endpoint1Mpi, the distance l of the end of oblique line section to main spring endpoint1Mi, i=1,2 ..., m；To master
The half stiffness K of each main spring before auxiliary spring contactMiIt is calculated, i.e.,
In formula, GX-EiFor in the endpoint deformation coefficient of i-th main spring of endpoint force effect, i.e.,
II steps：The half stiffness K of each main spring after the contact of major-minor springMAiIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section, elasticity modulus according to end contact
E；The half length L of main springM, the thickness h of the root flat segments of each main spring2M, the root of main spring parabolic segment to spring endpoint
Distance l2M, main reed number m, wherein the thickness ratio β of the parabolic segment of i-th main springi, the thickness ratio γ of oblique line sectionMi, oblique line
Distance l of the root of section to main spring endpoint1Mpi, the distance l of the end of main spring oblique line section to main spring endpoint1Mi, i=1,2 ..., m；
The half length L of auxiliary springA, the thickness h of the root flat segments of each auxiliary spring2A, the root of auxiliary spring parabolic segment to auxiliary spring endpoint
Distance l2A, auxiliary spring the piece number n, wherein the thickness ratio β of the parabolic segment of jth piece auxiliary springAj, the thickness ratio γ of oblique line sectionAj, oblique line section
Root to secondary endpoint distance l1Apj, the distance l of the end of oblique line section to auxiliary spring endpoint1Aj, j=1,2 ..., n；Auxiliary spring contact
With the horizontal distance l of main spring endpoint0, the half stiffness K of each main spring after being contacted to major-minor springMAiIt is calculated, i.e.,
In formula, GX-EiFor in the endpoint deformation coefficient of i-th main spring of endpoint force effect；GX-EATFor in endpoint force effect
In the case of n pieces superposition auxiliary spring total endpoint deformation coefficient, GX-EAjFor at the end of the jth piece auxiliary spring of endpoint force effect
Point deformation coefficient；Gx-DEFor deformation of the main spring of m pieces under endpoint stressing conditions at end flat segments and auxiliary spring contact point
Coefficient；Gx-EzmFor the endpoint deformation coefficient of the main spring of m pieces under the stressing conditions at major-minor spring contact point；Gx-DEzFor in major-minor
Deformation coefficient of the main spring of m pieces at end flat segments and auxiliary spring contact point at spring contact point under stressing conditions, i.e.,
III steps：The half stiffness K of each auxiliary springAjIt calculates：
Lack the width b of piece reinforcement end variable cross-section major-minor spring, the length Δ l of oblique line section, elasticity modulus according to end contact
E；The half length L of auxiliary springA, the thickness h of the root flat segments of each auxiliary spring2A, the root of auxiliary spring parabolic segment to auxiliary spring endpoint
Distance l2A, auxiliary spring the piece number n, wherein the thickness ratio β of the parabolic segment of jth piece auxiliary springAj, the thickness ratio γ of oblique line sectionAj, oblique line
Distance l of the root of section to auxiliary spring endpoint1Apj, the distance l of the end of oblique line section to auxiliary spring endpoint1Aj, to the half of each auxiliary spring
Stiffness KAjIt is calculated, i.e.,
In formula,
(2) the endpoint power for each main spring and auxiliary spring that end contact lacks piece reinforcement end variable cross-section major-minor spring calculates：
I steps：The endpoint power P of each main springiIt calculates：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P loaded, auxiliary spring according to end contact
Work load pK, the K that is calculated in I stepsMiAnd obtained K is calculated in II stepsMAi, to the endpoint power of each main spring
PiIt is calculated, i.e.,
Ii steps：The endpoint power P of each auxiliary springAjIt calculates：
Lack piece reinforcement end variable cross-section major-minor spring half, that is, single-ended point load P loaded, auxiliary spring according to end contact
Work load pK, main reed number m, the thickness h of the root flat segments of each main spring2M, auxiliary spring the piece number n, the root of each auxiliary spring
The thickness h of flat segments2A, the K that is calculated in II stepsMAi、Gx-DE、Gx-DEzAnd Gx-EATAnd be calculated in III steps
KAj, to the endpoint power P of each auxiliary springAjIt is calculated, i.e.,
(3) end contact lacks the calculating of each main spring different location stress of piece reinforcement end variable cross-section major-minor spring：
Step A：The calculating of stress at the preceding main spring different location x of m-1 pieces：
Lack the half length L of the main spring of piece reinforcement end variable cross-section according to end contactM, the length Δ l of oblique line section, each master
The thickness h of the root flat segments of spring2M, the distance l of the root of main spring parabolic segment to main spring endpoint2M, main reed number m, wherein
The end thickness h of the parabolic segment of i-th main spring1Mpi, the thickness h of the end flat segments of i-th main spring1Mi, i-th main spring
Distance l of the end of parabolic segment to main spring endpoint1Mpi, the length l of the end flat segments of i-th main spring1Mi；And i steps are fallen into a trap
Obtained Pi, using main spring free end as coordinate origin, using main spring endpoint as coordinate origin, to few piece reinforcement end variable cross-section
Stress of the preceding main spring of m-1 pieces of leaf spring at different location x is calculated, i.e.,
In formula, h2Mi(x) it is thickness of i-th main spring oblique line section at x position, h2Mpi(x) be i-th main spring parabolic segment in x
Thickness at position, i.e.,
Step B：The calculating of stress at the main spring different location x of m pieces：
Lack the half length L of the main spring of piece reinforcement end variable cross-section according to end contactM, the length Δ l of oblique line section, each master
The thickness h of the root flat segments of spring2M, the distance l of the root of parabolic segment to spring endpoint2M, auxiliary spring contact and main spring endpoint
Horizontal distance l0；Main reed number m, wherein the end thickness h of the parabolic segment of the main spring of m pieces1Mpm, the parabola of the main spring of m pieces
Distance l of the end of section to main spring endpoint1Mpm, the length l of the end flat segments of the main spring of m pieces1MmAnd thickness h1Mm；And step
(2) P being calculated in i stepsm, the P that is calculated in ii stepsAj, using main spring endpoint as coordinate origin, to few piece end
Stress σ of the main spring of m pieces of reinforced variable-section steel sheet spring at different location xMmIt is calculated, i.e.,
In formula, h2Mm(x) it is thickness of the main spring oblique line section of m pieces at x position, h2Mpm(x) be the main spring parabolic segment of m pieces in x
Thickness at position, i.e.,
(4) end contact lacks calculating of each auxiliary spring in different location stress of piece reinforcement end variable cross-section major-minor spring：
According to the half length L of few piece reinforcement end variable cross-section auxiliary springA, width b, the thickness h of auxiliary spring root flat segments2A, tiltedly
The length Δ l of line segment, the distance l of the root of auxiliary spring parabolic segment to auxiliary spring endpoint2A, auxiliary spring the piece number n, wherein jth piece auxiliary spring
Distance l of the end of parabolic segment to auxiliary spring endpoint1Apj, the end thickness of auxiliary spring parabolic segment is h1Apj, the thickness of end flat segments
Spend h1AjWith length l1Aj；And the P being calculated in ii stepsAj, j=1,2 ..., n, using auxiliary spring free end as coordinate origin, to few
Stress of each auxiliary spring of piece reinforcement end variable-section steel sheet spring at different location x is calculated, i.e.,
In formula, h2Aj(x) it is thickness of the jth piece auxiliary spring oblique line section at x position, h2Apj(x) be jth piece auxiliary spring parabolic segment in x
Thickness at position, i.e.,
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| CN106855906B (en) * | 2017-01-12 | 2019-11-05 | 山东理工大学 | The calculation method of the stiffness characteristics of high-intensitive three-level progressive rate leaf spring |
| CN106548003B (en) * | 2017-01-12 | 2019-03-29 | 山东理工大学 | The simulation calculation method of the offset frequencys type three-level progressive rate leaf spring such as non-root maximum stress |
| CN106682360B (en) * | 2017-01-12 | 2019-07-30 | 山东理工大学 | The simulation calculation method of the maximum stress characteristic of high-intensitive two-stage progressive rate major-minor spring |
| CN106529107A (en) * | 2017-01-12 | 2017-03-22 | 山东理工大学 | Simulation calculation method for maximum stress characteristic of root of high-strength leaf spring with three-level gradient stiffness |
| CN106855907B (en) * | 2017-01-12 | 2019-10-08 | 山东理工大学 | The emulated computation method for the offset frequencys type progressive rate plate spring suspension brackets offset frequency characteristics such as two-stage auxiliary spring formula is non- |
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