CN107013616B - High-intensitive first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics - Google Patents
High-intensitive first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics Download PDFInfo
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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
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F3/00—Spring units consisting of several springs, e.g. for obtaining a desired spring characteristic
- F16F3/02—Spring units consisting of several springs, e.g. for obtaining a desired spring characteristic with springs made of steel or of other material having low internal friction
- F16F3/023—Spring units consisting of several springs, e.g. for obtaining a desired spring characteristic with springs made of steel or of other material having low internal friction composed only of leaf springs
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F1/00—Springs
- F16F1/02—Springs made of steel or other material having low internal friction; Wound, torsion, leaf, cup, ring or the like springs, the material of the spring not being relevant
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Abstract
The present invention relates to the emulated computation methods that high-intensitive first-order gradient rigidity leaf spring steps up stiffness characteristics, belong to suspension leaf spring technical field.The present invention can carry out simulation calculation to step up stiffness characteristics of the high-intensitive first-order gradient rigidity leaf spring under different loads according to the parameter of structure design and main spring and auxiliary spring initial tangential camber design value of main spring and auxiliary spring, on the basis of contact load simulation calculation.By the prototype test results compare, it is correct that high intensity first-order gradient rigidity leaf spring provided by the present invention, which steps up the emulated computation method of stiffness characteristics, it can be obtained and accurately and reliably step up rigidity simulation calculation value under different loads, established reliable technical foundation for high-intensitive first-order gradient rigidity leaf spring characteristic Simulation；Ensure that designed leaf spring meets gradual change and steps up stiffness characteristics requirement using this method, improves horizontal product design, quality and performance and vehicle driving ride comfort；Meanwhile design and experimental test expense can be also reduced, accelerate product development speed.
Description
Technical field
The present invention relates to vehicle suspension leaf spring, especially high-intensitive first-order gradient rigidity leaf spring clamps the emulation of stiffness characteristics
Calculation method.
Background technique
With the appearance of high strength steel plate material, high-intensitive first-order gradient rigidity leaf spring can be used, to meet in different loads
The design requirement that vehicle driving ride comfort and suspension gradual change offset frequency under lotus remain unchanged, wherein the clamping of progressive rate leaf spring
Stiffness effect suspension system offset frequency and vehicle driving ride comfort, and its gradual change clamp stiffness characteristics, not only with progressive rate plate
Each main spring of spring is related with the structural parameters of auxiliary spring, but also starts contact load with major-minor spring and completely attach to load to have
It closes.Therefore, for the high-intensitive first-order gradient rigidity leaf spring of given design structural parameters, if the design for meeting stiffness characteristics is wanted
It asks, the clamping rigidity of designed leaf spring should be provided by simulation calculation with load change characteristic curve.However, due in gradual change
Leaf spring amount of deflection calculating in journey is extremely complex, and by the calculating of lap equivalent thickness and the system of contact load reverse critical issue
About, according to consulting reference materials it is found that not providing high-intensitive first-order gradient rigidity leaf spring inside and outside predecessor State always clamps the imitative of stiffness characteristics
True calculation method.With Vehicle Speed and its continuous improvement required ride comfort, high-intensitive first-order gradient rigidity is set
Meter leaf spring proposes requirements at the higher level, therefore, it is necessary to establish, one kind is accurate, reliably high-intensitive first-order gradient rigidity leaf spring clamps just
Spend the emulated computation method of characteristic, calculated for high-intensitive first-order gradient rigidity leaf spring characteristic Simulation and Development of Simulation Software establish can
The technical foundation leaned on meets Vehicle Industry fast development, vehicle driving ride comfort sets high-intensitive first-order gradient rigidity leaf spring
Meter requires, and can find problem present in product design in time by stiffness characteristics simulation calculation, it is ensured that meets stiffness characteristics design
It wants, to improve horizontal product design, quality and performance；Meanwhile design and testing expenses can be also reduced, accelerate product development speed
Degree.
Summary of the invention
For above-mentioned defect existing in the prior art, technical problem to be solved by the invention is to provide it is a kind of it is easy,
Reliable high intensity first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics, simulation calculation flow process figure, such as Fig. 1 institute
Show.Leaf spring uses high-strength steel sheet, width b, elasticity modulus E, each leaf spring be with center mounting hole symmetrical structure,
Installation clamp away from half L0For U-bolts clamp away from half L0；The half symmetrical junction of high-intensitive first-order gradient rigidity leaf spring
Structure main spring 1 and auxiliary spring 2 as shown in Fig. 2, be made of, wherein the piece number of main spring 1 is n, each main spring with a thickness of hi, half work
It is L with lengthit, half clamping length is Li=Lit-L0/ 2, i=1,2 ..., n；The piece number of auxiliary spring 2 is m, the thickness of each auxiliary spring
Degree is hAj, half action length is LAjt, half clamping length is LAj=Ln+j=LAjt-L0/ 2, j=1,2 ..., m.The main spring of tailpiece
Lower surface and first auxiliary spring upper surface between major-minor spring gradual change gap deltaMA, size be by main spring initial tangential camber with
Auxiliary spring initial tangential camber is determined.Load p is started working when load reacheskWhen, it clamps in U-bolts away from outside, end
The main spring lower surface of piece starts to contact with first auxiliary spring upper surface；When load reaches full contact load pwWhen, the main spring following table of tailpiece
Face is completely attached to first auxiliary spring upper surface.When load is in [Pk,Pw] in range when variation, main spring tailpiece lower surface and auxiliary spring are first
The contact position of piece upper surface and the compound clamping stiffness K of major-minor spring gradual changekwPChange with load, to meet suspension offset frequency guarantor
Hold constant design requirement.In the case where the parameter of structure design of high-intensitive first-order gradient rigidity leaf spring gives situation, to it in difference
Clamping stiffness characteristics under load carry out simulation calculation.
In order to solve the above technical problems, high intensity first-order gradient rigidity leaf spring provided by the present invention clamps stiffness characteristics
Emulated computation method, it is characterised in that use following simulation calculation step：
(1) equivalent thickness of the variant the piece number overlay segment of high-intensitive first-order gradient rigidity leaf spring calculates：
According to main reed number n, the thickness h of each main springi, i=1,2 ..., n；Auxiliary spring the piece number m, the thickness of each auxiliary spring
hAj, j=1,2 ..., m；The total the piece number N=n+m of major-minor spring is overlapped the variant the piece number k of high-intensitive first-order gradient rigidity leaf spring
The equivalent thickness h of sectionkeIt is calculated, k=1,2 ..., N, i.e.,
Wherein, the equivalent thickness of main spring root lap
(2) the main spring of high-intensitive first-order gradient rigidity leaf spring clamps rigidity and the compound emulation meter for clamping rigidity of major-minor spring
It calculates：
I step：Main spring clamps stiffness KMSimulation calculation
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；Main reed number n, the half of each main spring
Clamping length LiAnd the h being calculated in step (1)ke, k=i=1,2 ..., n clamp stiffness K to main springMCarry out emulation meter
It calculates, i.e.,
II step：The compound clamping stiffness K of major-minor springMASimulation calculation
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；Main reed number n, the half of each main spring
Clamping length Li, i=1,2 ..., n；Auxiliary spring the piece number m, the half clamping length L of each auxiliary springAj=Ln+j, j=1,2 ..., m,
The h being calculated in the total the piece number N of major-minor spring and step (1)ke, k=1,2 ..., N；To the compound clamping stiffness K of major-minor springMAInto
Row simulation calculation, i.e.,
(3) the beginning contact load P of high-intensitive first-order gradient rigidity leaf springkSimulation calculation：
Step A：The main spring lower surface initial curvature radius R of tailpieceM0bSimulation calculation
According to main reed number n, the thickness h of each main springi, i=1,2 ..., n, the half clamping length L of first main spring1,
Main spring initial tangential camber HgM0, to the initial curvature radius R of the main spring lower surface of tailpieceM0bMinute calculating is carried out, i.e.,
Step B：First auxiliary spring upper surface initial curvature radius RA0aSimulation calculation
According to the half clamping length L of first auxiliary springA1, auxiliary spring initial tangential camber HgA0, to first auxiliary spring upper surface just
Beginning radius of curvature RA0a, i.e.,
Step C：High-intensitive first-order gradient rigidity leaf spring starts contact load PkSimulation calculation：
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；The half of first main spring clamps span length's degree
L1, the h that is calculated in step (1)Me；The R being calculated in step AM0b, the R that is calculated in step BA0a, to high intensity one
The beginning contact load P of grade progressive rate leaf springkSimulation calculation is carried out, i.e.,
(4) the full contact load p of high-intensitive first-order gradient rigidity leaf springwSimulation calculation：
According to the K that simulation calculation obtains in step (2)MAnd KMA, simulation calculation obtains in step (3) Pk, to high intensity
The full contact load p of first-order gradient rigidity leaf springwSimulation calculation is carried out, i.e.,
(5) simulation calculation of clamping stiffness characteristics of the high-intensitive first-order gradient rigidity leaf spring under different loads：
According to rated load PN, the K that is calculated in step (2)MAnd KMA；The P that simulation calculation obtains in step (3)k, step
Suddenly the P that simulation calculation obtains in (4)w, to clamping stiffness K of the high-intensitive first-order gradient rigidity leaf spring at different loads PPCharacteristic into
Row simulation calculation, i.e.,
The present invention has the advantage that than the prior art
Since the amount of deflection calculating in major-minor spring gradual change contact process is extremely complex, while by leaf spring lap equivalent thickness
It calculates and restriction key issues of contact load reverse, according to consulting reference materials it is found that not providing high intensity inside and outside predecessor State always
The emulated computation method of first-order gradient rigidity leaf spring clamping stiffness characteristics.The present invention can be designed according to the structure of main spring and auxiliary spring to join
Several and main spring and auxiliary spring initial tangential camber design value, on the basis of contact load simulation calculation, to high-intensitive first-order gradient
Clamping stiffness characteristics of the rigidity leaf spring under different loads carry out simulation calculation, provide the variation characteristic song for clamping rigidity with load
Line.By the prototype test results comparison it is found that high intensity first-order gradient rigidity leaf spring provided by the present invention clamps stiffness characteristics
Emulated computation method be that correctly, the clamping rigidity simulation calculation value accurately and reliably under different loads can be obtained, to be high-strength
Degree first-order gradient rigidity leaf spring characteristic Simulation has established reliable technical foundation；Ensure that designed leaf spring meets gradually using this method
Become the design requirement for clamping stiffness characteristics, improves horizontal product design, quality and performance and vehicle driving ride comfort；Meanwhile also
Design and experimental test expense can be reduced, product development speed is accelerated.
Detailed description of the invention
For a better understanding of the present invention, it is described further with reference to the accompanying drawing.
Fig. 1 is the simulation calculation flow process figure that high-intensitive first-order gradient rigidity leaf spring clamps stiffness characteristics；
Fig. 2 is the half symmetrical structure schematic diagram of high-intensitive first-order gradient rigidity leaf spring；
Fig. 3 is the clamping stiffness K of the obtained high-intensitive first-order gradient rigidity leaf spring of the simulation calculation of embodimentPWith load
The variation characteristic curve of P.
Specific embodiment
Below by embodiment, invention is further described in detail.
Embodiment：The width b=63mm of certain high-intensitive first-order gradient rigidity leaf spring, U-bolts clamp away from half L0=
50mm, elastic modulus E=200Gpa.Main reed number n=3 piece, the thickness h of each main spring1=h2=h3=7mm, each main spring
Half action length is respectively L1t=525mm, L2t=461mm, L3t=399mm；The half clamping length of each main spring is respectively
L1=L1t-L0/ 2=500mm, L2=L2t-L0/ 2=436mm, L3=L3t-L0/ 2=374mm.Auxiliary spring the piece number m=2 piece, each pair
The thickness h of springA1=hA2The half action length of=12mm, each auxiliary spring are respectively LA1t=350mmLA2t=250mm, each pair
The half clamping length of spring is respectively LA1=L4=LA1t-L0/ 2=325mm, LA2=L5=LA2t-L0/ 2=200mm.Main spring is initial
Tangent line camber design value HgM0=112.5mm, the initial tangential camber design value H of first auxiliary springgA0=21.5mm.Rated load PN
=7227N.According to the structural parameters of each main spring and auxiliary spring, main spring initial tangential camber HgM0With auxiliary spring initial tangential camber
HgA0, stiffness characteristics are clamped to the high intensity first-order gradient rigidity leaf spring and carry out simulation calculation.
High intensity first-order gradient rigidity leaf spring provided by present example clamps the emulated computation method of stiffness characteristics,
Simulation calculation flow process is as shown in Figure 1, specifically steps are as follows for simulation calculation：
(1) equivalent thickness of the variant the piece number overlay segment of high-intensitive first-order gradient rigidity leaf spring calculates：
According to main reed number n=3, the thickness h of each main spring1=h2=h3=7mm；Auxiliary spring the piece number m=2, each auxiliary spring
Thickness hA1=hA2=12mm, the total the piece number N=n+m=5 of major-minor spring, to variant of the high intensity first-order gradient rigidity leaf spring
The equivalent thickness h of number k overlay segmentkeIt is calculated, k=1,2 ..., N, i.e.,
h1e=h1=7.0mm,
Wherein, the equivalent thickness h of main spring root lapMe=h3e=10.1mm.
(2) the main spring of high-intensitive first-order gradient rigidity leaf spring clamps rigidity and the compound emulation meter for clamping rigidity of major-minor spring
It calculates：
I step：Main spring clamps stiffness KMSimulation calculation
According to the width b=63mm of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E=200GPa；Main reed number n=
3, the half clamping length L of each main spring1=500mm, L2=436mm, L3H is calculated in=374mm and step (1)1e=
7.0mm, h2e=8.8mm, h3e=10.1mm, k=i=1,2 ..., n clamps stiffness K to main springMSimulation calculation is carried out, i.e.,
II step：The compound clamping stiffness K of major-minor springMASimulation calculation
According to the width b=63mm of progressive rate leaf spring, elastic modulus E=200GPa；Main reed number n=3, each main spring
Half clamping length L1=500mm, L2=436mm, L3=374mm；The half of auxiliary spring the piece number m=2, each auxiliary spring clamp length
Spend LA1=L4=325mm, LA2=L5=200mm；The total the piece number N=5 of major-minor spring；And the h being calculated in step (1)1e=
7.0mm, h2e=8.8mm, h3e=10.1mm, h4e=14mm, h5e=16.5mm；K=1,2 ..., N, to the compound clamping of major-minor spring
Stiffness KMASimulation calculation is carried out, i.e.,
(3) the beginning contact load P of high-intensitive first-order gradient rigidity leaf springkSimulation calculation：
Step A：The main spring lower surface initial curvature radius R of tailpieceM0bSimulation calculation
According to main reed number n=3, the thickness h of each main springi=7mm, i=1,2,3, the half of first main spring clamps length
Spend L1=500mm, main spring initial tangential camber HgM0=112.5mm, spring lower surface initial curvature radius R main to tailpieceM0bIt carries out
Minute calculates, i.e.,
Step B：First auxiliary spring upper surface initial curvature radius RA0aSimulation calculation
According to the half clamping length L of first auxiliary springA1=325mm, auxiliary spring initial tangential camber HgA0=21.5mm, to head
Piece auxiliary spring upper surface initial curvature radius RA0a, i.e.,
Step C：The beginning contact load P of high-intensitive first-order gradient rigidity leaf springkSimulation calculation
According to the width b=63mm of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E=200GPa；First main spring
Half clamps span length's degree L1=500mm, the h being calculated in step (1)Me=10.1mm；The R being calculated in step AM0b=
1188.4mm, the R being calculated in step BA0a=2467.1mm starts to contact to the high intensity first-order gradient rigidity leaf spring
Load pkSimulation calculation is carried out, i.e.,
(4) the full contact load p of high-intensitive first-order gradient rigidity leaf springwSimulation calculation：
According to the K that simulation calculation obtains in step (2)M=51.3N/mm and KMAIt is imitated in=173.7N/mm and step (3)
The P being really calculatedk=1885N, to the full contact load p of the high intensity first-order gradient rigidity leaf springwSimulation calculation is carried out,
I.e.
(5) simulation calculation of clamping stiffness characteristics of the high-intensitive first-order gradient rigidity leaf spring under different loads：
According to rated load PN=7227N, the K that simulation calculation obtains in step (2)M=51.3N/mm and KMA=
173.7N/mm；The P that simulation calculation obtains in step (3)k=1885N, the P that simulation calculation obtains in step (4)w=6383N is right
The clamping stiffness K of the high intensity first-order gradient rigidity leaf spring at different loads PPCharacteristic carries out simulation calculation, i.e.,
Using Matlab calculation procedure, the clamping rigidity of the obtained high intensity first-order gradient rigidity leaf spring of simulation calculation
KPWith the variation characteristic curve of load p, as shown in Figure 3, wherein as load p=PkWhen=1885N, KP=KM=51.3N/mm,
As load p=PwWhen=6383N, KP=KMA=173.7N/mm；When load p is in [Pk,Pw] in range when variation, gradual change clamps rigid
Spend KPIncrease with the increase of load p, i.e.,Gradual change clamps stiffness KPFrom KM=51.3N/mm is gradually increased
To KMA=173.7N/mm.
It is tested by model machine load deflection it is found that the main spring of the high intensity first-order gradient rigidity leaf spring clamps rigidity, major-minor
Spring is compound to clamp rigidity and the compound simulation calculation value for clamping rigidity of gradual change, approaches, shows provided by the present invention with test result
High-intensitive first-order gradient rigidity leaf spring clamp stiffness characteristics emulated computation method be correctly, it is rigid for high-intensitive first-order gradient
The clamping rigidity simulating, verifying and characteristic Simulation software development for spending leaf spring have established reliable technical foundation.It can be obtained using this method
To accurately and reliably clamping rigidity simulation calculation value of the high-intensitive first-order gradient rigidity leaf spring in different loads, it is ensured that folder
Tight stiffness characteristics meet leaf spring design requirement, improve design level, quality and the performance and vehicle driving ride comfort of product；Together
When, design and testing expenses are reduced, product development speed is accelerated.
Claims (1)
1. the emulated computation method that high-intensitive first-order gradient rigidity leaf spring clamps stiffness characteristics, wherein leaf spring uses high strength steel
Plate, each leaf spring be with center mounting hole symmetrical structure, installation clamp away from half be U-bolts clamp away from half；It is logical
Cross initial tangential camber and the gradual change gap of main spring and auxiliary spring, it is ensured that meet leaf spring contact load, progressive rate and carry in gradual change
The design requirement that suspension offset frequency under lotus remains unchanged, i.e., the offset frequencys type first-order gradient rigidity leaf spring such as；Joined according to the structure of leaf spring
Several, main spring initial tangential camber and auxiliary spring initial tangential camber, on the basis of contact load simulation calculation, to high-intensitive level-one
Clamping stiffness characteristics of the progressive rate leaf spring under different loads carry out simulation calculation, it is characterised in that use and emulate in detail below
Calculate step：
(1) equivalent thickness of the variant the piece number overlay segment of high-intensitive first-order gradient rigidity leaf spring calculates：
According to main reed number n, the thickness h of each main springi, i=1,2 ..., n；Auxiliary spring the piece number m, the thickness h of each auxiliary springAj, j
=1,2 ..., m；The total the piece number N=n+m of major-minor spring, to the variant the piece number k overlay segment of high-intensitive first-order gradient rigidity leaf spring
Equivalent thickness hkeIt is calculated, k=1,2 ..., N, i.e.,
Wherein, the equivalent thickness of main spring root lap
(2) the main spring of high-intensitive first-order gradient rigidity leaf spring clamps rigidity and the compound simulation calculation for clamping rigidity of major-minor spring：
I step：Main spring clamps stiffness KMSimulation calculation
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；The half of main reed number n, each main spring clamp
Length LiAnd the h being calculated in step (1)ke, k=i=1,2 ..., n clamp stiffness K to main springMSimulation calculation is carried out,
I.e.
II step：The compound clamping stiffness K of major-minor springMASimulation calculation
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；The half of main reed number n, each main spring clamp
Length Li, i=1,2 ..., n；Auxiliary spring the piece number m, the half clamping length L of each auxiliary springAj=Ln+j, j=1,2 ..., m, major-minor
The h being calculated in the total the piece number N of spring and step (1)ke, k=1,2 ..., N；To the compound clamping stiffness K of major-minor springMAIt is imitated
It is true to calculate, i.e.,
(3) the beginning contact load P of high-intensitive first-order gradient rigidity leaf springkSimulation calculation：
Step A：The main spring lower surface initial curvature radius R of tailpieceM0bSimulation calculation
According to main reed number n, the thickness h of each main springi, i=1,2 ..., n, the half clamping length L of first main spring1, main spring
Initial tangential camber HgM0, to the initial curvature radius R of the main spring lower surface of tailpieceM0bMinute calculating is carried out, i.e.,
Step B：First auxiliary spring upper surface initial curvature radius RA0aSimulation calculation
According to the half clamping length L of first auxiliary springA1, auxiliary spring initial tangential camber HgA0, to the initial song of first auxiliary spring upper surface
Rate radius RA0a, i.e.,
Step C：High-intensitive first-order gradient rigidity leaf spring starts contact load PkSimulation calculation：
According to the width b of high-intensitive first-order gradient rigidity leaf spring, elastic modulus E；The half of first main spring clamps span length's degree L1, step
Suddenly the h being calculated in (1)Me；The R being calculated in step AM0b, the R that is calculated in step BA0a, gradually to high-intensitive level-one
The beginning contact load P of variation rigidity leaf springkSimulation calculation is carried out, i.e.,
(4) the full contact load p of high-intensitive first-order gradient rigidity leaf springwSimulation calculation：
According to the K that simulation calculation obtains in step (2)MAnd KMA, simulation calculation obtains in step (3) Pk, gradually to high-intensitive level-one
The full contact load p of variation rigidity leaf springwSimulation calculation is carried out, i.e.,
(5) simulation calculation of clamping stiffness characteristics of the high-intensitive first-order gradient rigidity leaf spring under different loads：
According to rated load PN, the K that is calculated in step (2)MAnd KMA；The P that simulation calculation obtains in step (3)k, step (4)
The P that middle simulation calculation obtainsw, to clamping stiffness K of the high-intensitive first-order gradient rigidity leaf spring at different loads PPCharacteristic is emulated
It calculates, i.e.,
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| RU2482345C1 (en) * | 2011-09-13 | 2013-05-20 | Открытое акционерное общество "Чусовской металлургический завод" | Formation method of progressive spring stiffness, elastic suspension member, and suspension (versions) of transport vehicle |
| CN105740591A (en) * | 2016-04-28 | 2016-07-06 | 王炳超 | Method for verifying strength of each leaf of end contact type few-leaf oblique main and auxiliary springs |
| CN105912743A (en) * | 2016-03-12 | 2016-08-31 | 周长城 | Method of designing gap between end of root-reinforced few-leaf variable-section main spring at end and auxiliary spring |
| CN105956270A (en) * | 2016-05-04 | 2016-09-21 | 山东理工大学 | Computing method of stress of each of end contact type less-leaf end part enhanced main spring and secondary spring |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| RU2482345C1 (en) * | 2011-09-13 | 2013-05-20 | Открытое акционерное общество "Чусовской металлургический завод" | Formation method of progressive spring stiffness, elastic suspension member, and suspension (versions) of transport vehicle |
| CN105912743A (en) * | 2016-03-12 | 2016-08-31 | 周长城 | Method of designing gap between end of root-reinforced few-leaf variable-section main spring at end and auxiliary spring |
| CN105740591A (en) * | 2016-04-28 | 2016-07-06 | 王炳超 | Method for verifying strength of each leaf of end contact type few-leaf oblique main and auxiliary springs |
| CN105956270A (en) * | 2016-05-04 | 2016-09-21 | 山东理工大学 | Computing method of stress of each of end contact type less-leaf end part enhanced main spring and secondary spring |
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