CN106545609B - The simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula is non- - Google Patents
The simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula is non- Download PDFInfo
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- CN106545609B CN106545609B CN201710023252.XA CN201710023252A CN106545609B CN 106545609 B CN106545609 B CN 106545609B CN 201710023252 A CN201710023252 A CN 201710023252A CN 106545609 B CN106545609 B CN 106545609B
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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
- 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
- F16F1/18—Leaf springs
- F16F1/185—Leaf springs characterised by shape or design of individual leaves
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract
The present invention relates to the simulation calculation methods for the offset frequencys progressive rate rigidity of plate spring characteristic such as two-stage auxiliary spring formula is non-, belong to suspension leaf spring technical field.The present invention can be according to each main spring and the structural parameters of auxiliary spring, U-bolts clamp away from, elasticity modulus, the initial tangential camber design load of main spring and auxiliary spring at different levels, on the basis of contact load simulation calculation, clamping stiffness characteristics of the offset frequencys type progressive rate leaf spring such as non-to two-stage auxiliary spring formula under different loads carry out simulation calculation.Pass through prototype test, the simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula provided by the present invention is non-is correct, and reliable technical method is provided for the clamping stiffness characteristics simulation calculation for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-.Using this method can obtain it is reliable clamp stiffness characteristics simulation calculation value, improve the design level of product and performance and vehicle ride performance；Meanwhile design and testing expenses are reduced, accelerate product development speed.
Description
Technical field
The present invention relates to vehicle suspension leaf spring, the offset frequencys progressive rate rigidity of plate spring such as particularly two-stage auxiliary spring formula is non-are special
The simulation calculation method of property.
Background technology
It, can be firm by former first-order gradient in order to further improve the design requirement of ride performance of the vehicle under rated load
The auxiliary spring fractionation of degree leaf spring is designed as two-stage auxiliary spring, i.e., using two-stage auxiliary spring formula progressive rate leaf spring；Simultaneously as acceptor's spring is strong
The restriction of degree, usually by main spring initial tangential camber, first order auxiliary spring and second level auxiliary spring initial tangential camber and two-stage gradually
Varied clearance makes auxiliary spring suitably undertake load in advance, and so as to reduce main spring stress, the suspension offset frequency under contact load is unequal,
The offset frequencys type progressive rate leaf springs such as i.e. two-stage auxiliary spring formula is non-, wherein, two-stage auxiliary spring formula progressive rate leaf spring is under different loads
Stiffness characteristics are clamped, influence suspension offset frequency and vehicle ride performance and security, and the clamping rigidity of progressive rate leaf spring,
It is not only related but also related with contact load with the structural parameters of each main spring and auxiliary spring.However, due to by two-stage auxiliary spring formula
The root lap equivalent thickness and progressive rate of the offset frequencys type progressive rate leaf spring such as non-calculate and contact load emulation is crucial
The restriction of problem previously fails to provide the simulation calculation for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula is non-always
Method, it is thus impossible to meet the fast-developing requirement that CAD design and software development are modernized with bearing spring suspension of Vehicle Industry.
Continuous improvement with Vehicle Speed and to vehicle ride performance and security requirement carries progressive rate plate spring suspension brackets
Requirements at the higher level are gone out, therefore, it is necessary to which it is special to establish the offset frequencys progressive rate rigidity of plate spring such as one kind is accurate, reliable two-stage auxiliary spring formula is non-
The simulation calculation method of property, for the clamping stiffness characteristics simulation calculation of the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, provide can
The technical method leaned on meets fast-developing Vehicle Industry, vehicle ride performance and the design requirement to progressive rate leaf spring, carries
Design level, product quality and the vehicle ride performance for the offset frequencys type progressive rate leaf springs such as high two-stage auxiliary spring formula is non-；Meanwhile it drops
Low design and experimental test expense, accelerate product development speed.
The content of the invention
Defect present in for the above-mentioned prior art, the technical problems to be solved by the invention be to provide it is a kind of it is easy,
The simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as reliable two-stage auxiliary spring formula is non-, simulation calculation flow process such as Fig. 1 institutes
Show.The half symmetrical structure for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-is as shown in Fig. 2, be by main spring 1, first order pair
Spring 2 and second level auxiliary spring 3 form.Using two-stage auxiliary spring, between main spring and first order auxiliary spring and first order auxiliary spring and second level pair
Two-stage gradual change gap delta is equipped between springMA1And δA12, to improve the vehicle ride performance under rated load；In order to ensure meeting
Main spring stress intensity design requirement, first order auxiliary spring and second level auxiliary spring suitably undertake load, suspension gradual change load offset frequency in advance
It is unequal, i.e., leaf spring is designed as the offset frequencys type progressive rate leaf spring such as non-.The half total span of leaf spring is equal to the one of first main spring
Half action length L1T, U-bolts clamp away from half be L0, width b, elasticity modulus E.The piece number of main spring 1 be n, main spring
The thickness of each is hi, half action length is LiT, half clamping length Li=LiT-L0/ 2, i=1,2 ..., n.First order pair
Reed number is m1, the thickness that first order auxiliary spring is each is hA1j, half action length is LA1jT, half clamping length LA1j=Ln+j=
LA1jT-L0/ 2, j=1,2 ..., m1, the sum of the piece number of main spring and the first auxiliary spring N1=n+m1.Second level auxiliary spring the piece number is m2, second
The thickness of each of auxiliary spring of grade is hA2k, half action length is LA2kT, half clamping length LA2k=LN1+k=LA2kT-L0/ 2, k=
1,2,…,m2.Total the piece number N=n+m of major-minor spring1+m2.According to the structural parameters of each main spring and auxiliary spring, main spring and auxiliary spring at different levels
It is initial cut camber design load, U-bolts is clamped away from non-to two-stage auxiliary spring formula etc. on the basis of contact load simulation calculation
Clamping stiffness characteristics of the offset frequency type progressive rate leaf spring under different loads carry out simulation calculation.
In order to solve the above technical problems, the offset frequencys progressive rate rigidity of plate spring such as two-stage auxiliary spring formula provided by the present invention is non-are special
Property simulation calculation method, it is characterised in that use following simulation calculation step：
(1) the main springs of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-and its meter that rigidity is clamped with auxiliary springs at different levels
It calculates：
I steps：The equivalent thickness h of different the piece number overlay segmentsleIt calculates
According to main reed number n, the thickness h of main each of springi, i=1,2 ..., n；First order auxiliary spring the piece number m1, first order auxiliary spring
The thickness h of eachA1j, j=1,2 ..., m1；Second level auxiliary spring the piece number m2, thickness h that second level auxiliary spring is eachA2k, k=1,2 ...,
m2；The sum of the piece number of main spring and first order auxiliary spring N1=n+m1, total the piece number N=n+m of major-minor spring1+m2；It is non-to two-stage auxiliary spring formula etc.
The equivalent thickness h of the different the piece number l overlay segments of offset frequency type progressive rate leaf springleIt is calculated, l=1,2 ..., N, i.e.,：
Wherein, the equivalent thickness h of main spring root lapMe, main spring and the root lap of first order auxiliary spring etc.
Imitate thickness hMA1eAnd the root lap equivalent thickness h that major-minor spring is totalMA2e, it is respectively
Ii steps：Main spring clamps stiffness KMIt calculates
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, main spring
The half clamping length L of eachi, i=1,2 ..., n；And the h being calculated in i stepsle, l=i=1,2 ..., n, to main spring
It clamps rigidity to be calculated, i.e.,
Iii steps：The clamping complex stiffness K of main spring and first order auxiliary springMA1It calculates
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, main spring
The half clamping length L of eachi, i=1,2 ..., n；First order auxiliary spring the piece number m1, the half clamping length of each of first order auxiliary spring
For LA1j=Ln+j, j=1,2 ..., m1；The sum of the piece number of main spring and first order auxiliary spring N1=n+m1And be calculated in i steps
hle, l=1,2 ..., N1, to the clamping complex stiffness K of main spring and first order auxiliary springMA1It is calculated, i.e.,
Iv steps：Total compound clamping stiffness K of major-minor springMA2It calculates：
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each
The half clamping length L of main springi, i=1,2 ..., n；First order auxiliary spring the piece number m1, the half clamping length of each of first order auxiliary spring
For LA1j=Ln+j, j=1,2 ..., m1；Second level auxiliary spring the piece number m2, the half clamping length L of each of second level auxiliary springA2k=
LN1+k, k=1,2 ..., m2；Total the piece number N=n+m of major-minor spring1+m2And the h being calculated in i stepsle, l=1,2 ..., N,
To total compound clamping stiffness K of major-minor springMA2It is calculated, i.e.,
(2) calculating of the main spring for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-and the radius of curvature of auxiliary spring at different levels：
I steps：Main spring tailpiece lower surface initial curvature radius RM0bCalculating
According to main spring initial tangential camber HgM0, the half clamping length L of main first of spring1, main reed number n, main each of spring
Thickness hi, i=1,2 ..., n；To main spring tailpiece lower surface initial curvature radius RM0bIt is calculated, i.e.,
II steps：First upper surface initial curvature radius R of first order auxiliary springA10aCalculating
According to the first order auxiliary spring half clamping length L of firstA11, the initial tangential camber design load of first order auxiliary spring
HgA10, to first upper surface initial curvature radius R of first order auxiliary springA10aIt is calculated, i.e.,
III steps：First order auxiliary spring tailpiece lower surface initial curvature radius RA10bCalculating
According to first order auxiliary spring the piece number m1, thickness h that first order auxiliary spring is eachA1j, j=1,2 ..., m1；And II steps are fallen into a trap
Obtained RA10a, to first order auxiliary spring tailpiece lower surface initial curvature radius RA10bIt is calculated, i.e.,
IV steps：First upper surface initial curvature radius R of second level auxiliary springA20aCalculating
According to the second level auxiliary spring half clamping length L of firstA21, the initial tangential camber design load of second level auxiliary spring
HgA20, to first upper surface initial curvature radius R of second level auxiliary springA20aIt is calculated, i.e.,
(3) simulation calculation for each secondary contact loads of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-：
Step A：1st beginning contact load Pk1Simulation calculation
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；The half of main first of spring
Clamping length L1, the h that is calculated in step (1)Me, the R that is calculated in step (2)M0bAnd RA10a, the 1st time is started to contact
Load pk1Simulation calculation is carried out, i.e.,
Step B：2nd beginning contact load Pk2Simulation calculation
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Step calculates in (1)
The h arrivedMA1e, the R that is calculated in step (2)A10bAnd RA20aAnd the P that simulation calculation obtains in step Ak1, the 2nd time is started to connect
Touch load pk2Simulation calculation is carried out, i.e.,
Step C：2nd full contact load pw2Simulation calculation
The P obtained according to simulation calculation in step Ak1, simulation calculation obtains in step B Pk2, the 2nd time is completely attached to
Load pw2Simulation calculation is carried out, i.e.,
(4) simulation calculation of the clamping stiffness characteristics for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-：
According to the K being calculated in step (1)M、KMA1And KMA2, the obtained P of simulation calculation in step (3)k1、Pk2With
Pw2, clamping stiffness characteristics of the offset frequencys type progressive rate leaf spring such as non-to two-stage auxiliary spring formula under different loads P carry out simulation calculation,
I.e.
The present invention has the advantage that than the prior art
Since the root lap equivalent thickness by the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-and gradual change are firm
Degree calculates and the restriction of contact load emulation key issue, previously fails to provide the offset frequencys progressive rates such as two-stage auxiliary spring formula is non-always
The simulation calculation method of rigidity of plate spring characteristic, it is thus impossible to meet, Vehicle Industry is fast-developing and bearing spring suspension modernizes CAD
Design and the requirement of software development.The present invention can be according to each main spring and the structural parameters of auxiliary spring, elasticity modulus, main spring and at different levels
The initial tangential camber design load of auxiliary spring, on the basis of contact load simulation calculation, the offset frequencys type such as non-to two-stage auxiliary spring formula is gradually
Clamping stiffness characteristics of the variation rigidity leaf spring under different loads carry out simulation calculation.Loading stiffness characteristics experiment by model machine can
Know, the simulation calculation method of the offset frequencys progressive rate rigidity of plate spring characteristic such as two-stage auxiliary spring formula provided by the present invention is non-be it is correct,
Reliable technical method is provided for the clamping stiffness characteristics simulation calculation for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-.
Using this method can obtain it is reliable clamp stiffness characteristics simulation calculation value, improve the design level of product and performance and vehicle row
Sail ride comfort；Meanwhile design and testing expenses are reduced, accelerate product development speed.
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 simulation calculation flow process figure for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula is non-；
Fig. 2 is the half symmetrical structure schematic diagram for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-；
Fig. 3 is the clamping stiffness K for the offset frequencys type progressive rate leaf springs such as the two-stage auxiliary spring formula of embodiment is non-with the variation of load p
Characteristic curve.
Specific embodiment
The present invention is described in further detail below by embodiment.
Embodiment：The width b=63mm for the offset frequencys type progressive rate leaf springs such as certain two-stage auxiliary spring formula is non-, U-bolts clamp away from
Half L0=50mm, elastic modulus E=200GPa.Main reed number n=3 pieces, the thickness h of main each of spring1=h2=h3=8mm,
Half action length is respectively L1T=525mm, L2T=450mm, L3T=350mm；The half clamping length of main each of spring is respectively
L1=L1T-L0/ 2=500mm, L2=L2T-L0/ 2=425mm, L3=L3T-L0/ 2=325mm.The piece number m of first order auxiliary spring1=1
Piece, thickness hA11=13mm, half action length are LA11T=250mm, half clamping length are LA11=L4=LA11T-L0/ 2=
225mm.The sum of the piece number of main spring and first order auxiliary spring N1=n+m1=4.The piece number m of second level auxiliary spring2=1, thickness hA21=
13mm, half action length are LA21T=150mm, half clamping length are LA21=L5=LA21T-L0/ 2=125mm.Zero load carries
Lotus P0=1715N, rated load PN=7227N.Total the piece number N=5 of major-minor spring.The initial tangential camber H of main springgM0=
85.3mm, the initial tangential camber H of first order auxiliary springgA10=9.1mm, the initial tangential camber H of second level auxiliary springgA20=
2.4mm.According to each main spring of the leaf spring with gradually changing stiffness and the first order and the structural parameters of second level auxiliary spring, springform
The initial tangential camber design load of amount, unloaded load and rated load, main spring and auxiliary spring at different levels, it is inclined to the non-grade of two-stage auxiliary spring formula
Clamping stiffness characteristics of the frequency type progressive rate leaf spring under different loads carry out simulation calculation.
The simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula that present example is provided is non-,
Its simulation calculation flow process, as shown in Figure 1, specific simulation calculation step is as follows：
(1) the main springs of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-and its meter that rigidity is clamped with auxiliary springs at different levels
It calculates：
I steps：The equivalent thickness h of different the piece number overlay segmentsleCalculating
According to main reed number n=3, the thickness h of main each of spring1=h2=h3=8mm；First order auxiliary spring the piece number m1=1, it is thick
Spend hA11=13mm；Second level auxiliary spring the piece number m2=1, thickness hA21=13mm；Total the piece number N=5 of major-minor spring, to two-stage auxiliary spring formula
The equivalent thickness h of the different the piece number l overlay segments of the offset frequencys type progressive rate leaf spring such as non-leIt is calculated, l=1,2 ..., N, i.e.,：
h1e=h1=8.0mm；
Wherein, the equivalent thickness h of main spring root lapMe, main spring and the root lap of first order auxiliary spring etc.
Imitate thickness hMA1eAnd the root lap equivalent thickness h that major-minor spring is totalMA2e, it is respectively
Ii steps：Main spring clamps stiffness KMCalculating
According to the width b=63mm for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa；
Main reed number n=3, wherein, the half clamping length L of each main spring1=500mm, L2=425mm, L3=325mm and i steps
In the h that is calculated1e=8.0mm, h2e=10.1mm, h3e=11.5mm, l=i=1,2 ..., n, to main spring clamp rigidity into
Row calculates, i.e.,
Iii steps：The compound clamping stiffness K of main spring and first order auxiliary springMA1It calculates
According to the width b=63mm for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa；
Main reed number n=3, the half clamping length L of main each of spring1=500mm, L2=425mm, L3=325mm；First order auxiliary spring piece
Number m1=1, the half clamping length of first order auxiliary spring is LA11=L4=225mm；Total the piece number N of main spring and first order auxiliary spring1=n
+m1The h being calculated in=4 and i steps1e=8.0mm, h2e=10.1mm, h3e=11.5mm, h4e=15.5mm, l=1,
2,...,N1, to the compound clamping stiffness K of main spring and first order auxiliary springMA1It is calculated, i.e.,
Iv steps：Total compound clamping stiffness K of major-minor springMA2It calculates：
According to the width b=63mm for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200Gpa；
Main reed number n=3, the half clamping length L of main each of spring1=500mm, L2=425mm, L3=325mm；First order auxiliary spring piece
Number m1=1, the half clamping length of first order auxiliary spring is LA11=L4=225mm；Second level auxiliary spring the piece number m2=1, second level pair
The half clamping length L of springA21=L5=125mm；The h being calculated in the total the piece number N=5 and i steps of major-minor spring1e=
8.0mm, h2e=10.1mm, h3e=11.5mm, h4e=15.5mm, h5e=18.1mm, l=1,2 ..., N, to the total of major-minor spring
Compound clamping stiffness KMA2It is calculated, i.e.,
(2) calculating of the main spring for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-and the radius of curvature of auxiliary spring at different levels：
I steps：Main spring tailpiece lower surface initial curvature radius RM0bCalculating
According to the initial tangential camber H of main springgM0=85.3mm, the half clamping length L of main first of spring1=500mm, it is main
Reed number n=3, the thickness h of main each of springi=8mm, i=1,2 ..., n；To main spring tailpiece lower surface initial curvature radius RM0b
It is calculated, i.e.,
II steps：First upper surface initial curvature radius R of first order auxiliary springA10aCalculating
According to the first order auxiliary spring half clamping length L of firstA11=225mm, the initial tangential camber of first order auxiliary spring
HgA10=9.1mm, to first upper surface initial curvature radius R of first order auxiliary springA10aIt is calculated, i.e.,
III steps：First order auxiliary spring tailpiece lower surface initial curvature radius RA10bCalculating
According to first order auxiliary spring the piece number m1=1, thickness hA11The R being calculated in=13mm and II stepsA10a=
2786.1mm, to first order auxiliary spring tailpiece lower surface initial curvature radius RA10bIt is calculated, i.e.,
IV steps：First upper surface initial curvature radius R of second level auxiliary springA20aCalculating
According to the second level auxiliary spring half clamping length L of firstA21=125mm, the initial tangential camber of second level auxiliary spring
HgA20=2.4mm, to second level auxiliary spring tailpiece upper surface initial curvature radius RA20aIt is calculated, i.e.,
(3) simulation calculation for each secondary contact loads of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-：
Step A：1st beginning contact load Pk1Simulation calculation
According to the width b=63mm for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa；
The half clamping length L of main first of spring1=500mm, the h being calculated in step (1)Me=11.5mm, step calculate in (2)
The R arrivedM0b=1532.1mm and RA10a=2786.1mm starts contact load P to the 1st timek1Simulation calculation is carried out, i.e.,
Step B：2nd beginning contact load Pk2Simulation calculation
According to the width b=63mm for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa；
The half clamping length L of main first of spring1=500mm, the h being calculated in step (1)MA1e=15.5mm, step (2) is middle to be calculated
Obtained RA10b=2799.1mm and RA20aThe P that simulation calculation obtains in=3256.4mm and step Ak1=1895N, to the 2nd time
Start contact load Pk2Simulation calculation is carried out, i.e.,
Step C：2nd full contact load pw2Simulation calculation
The P obtained according to simulation calculation in step Ak1=1895N, the P that simulation calculation obtains in step Bk2=2677N is right
2nd full contact load pw2Simulation calculation is carried out, i.e.,
(4) simulation calculation of the clamping stiffness characteristics for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-：
According to unloaded load p0=1715N, rated load PN=7227N, the K being calculated in step (1)M=75.4N/
mm、KMA1=144.5N/mm and KMA2=172.9N/mm, the obtained P of simulation calculation in step (3)k1=1895N, Pk2=
2677N and Pw2=3781N, clamping rigidity of the offset frequencys type progressive rate leaf spring such as non-to two-stage auxiliary spring formula under different loads P are special
Property carry out simulation calculation, i.e.,
Using Matlab calculation procedures, the offset frequencys type progressive rate leaf springs such as the obtained two-stage auxiliary spring formula of simulation calculation is non-
Clamping stiffness K with load p variation characteristic curve, as shown in figure 3, wherein, start contact load P at the 1st timek1, start the 2nd time
Contact load Pk2, completely attach to load p the 2nd timew2With rated load PNIn the case of clamping rigidity be respectively Kk1=KM=
75.4N/mm Kk2=KMA1=144.5N/mm, Kw2=KN=KMA2=172.9N/mm.
By prototype test, the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula provided by the present invention is non-
Simulation calculation method be correct, provided for the stiffness characteristics simulation calculation for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-
Reliable technical method.The reliable design for clamping stiffness characteristics simulation calculation value, improving product is can obtain using this method
Horizontal and performance and vehicle ride performance；Meanwhile design and testing expenses are reduced, accelerate product development speed.
Claims (1)
1. the simulation calculation method for the offset frequencys progressive rate rigidity of plate spring characteristics such as two-stage auxiliary spring formula is non-, wherein, each leaf spring is in
Heart mounting hole symmetrical structure, installation clamp away from half for U-bolts clamp away from half；Auxiliary spring is designed as two-stage pair
Spring by main spring and the initial tangential camber of two-stage auxiliary spring and two-stage gradual change gap, improves traveling of the vehicle under rated load
Ride comfort；In order to ensure meeting main spring stress intensity design requirement, first order auxiliary spring and second level auxiliary spring is made suitably to undertake in advance
The offset frequencys type progressive rate leaf springs such as load, the offset frequency being suspended under gradual change load is unequal, i.e., two-stage auxiliary spring formula is non-；According to each
The structural parameters of leaf spring, U-bolts clamp the initial tangential camber design load away from, elasticity modulus, main spring and two-stage auxiliary spring,
On the basis of contact load simulation calculation, clamping of the offset frequencys type progressive rate leaf spring such as non-to two-stage auxiliary spring formula under different loads
Stiffness characteristics carry out simulation calculation, and specific simulation calculation step is as follows：
(1) the main springs of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-and its calculating that rigidity is clamped with auxiliary springs at different levels：
I steps：The equivalent thickness h of different the piece number overlay segmentsleIt calculates
According to main reed number n, the thickness h of main each of springi, i=1,2 ..., n；First order auxiliary spring the piece number m1, each of first order auxiliary spring
Thickness hA1j, j=1,2 ..., m1；Second level auxiliary spring the piece number m2, thickness h that second level auxiliary spring is eachA2k, k=1,2 ..., m2；
The sum of the piece number of main spring and first order auxiliary spring N1=n+m1, total the piece number N=n+m of major-minor spring1+m2；It is inclined to the non-grade of two-stage auxiliary spring formula
The equivalent thickness h of the different the piece number l overlay segments of frequency type progressive rate leaf springleIt is calculated, l=1,2 ..., N, i.e.,：
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<mi>i</mi>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>1</mn>
<mo>&le;</mo>
<mi>l</mi>
<mo>&le;</mo>
<mi>n</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mroot>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>h</mi>
<mi>i</mi>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>l</mi>
<mo>-</mo>
<mi>n</mi>
</mrow>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>1</mn>
<mi>j</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
<mo>&le;</mo>
<mi>l</mi>
<mo>&le;</mo>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mroot>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>h</mi>
<mi>i</mi>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>1</mn>
<mi>j</mi>
</mrow>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>l</mi>
<mo>-</mo>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</mrow>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>2</mn>
<mi>k</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mn>1</mn>
<mo>&le;</mo>
<mi>l</mi>
<mo>&le;</mo>
<mi>N</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, the equivalent thickness h of main spring root lapMe, main spring and the root lap of first order auxiliary spring equivalent thickness
Spend hMA1eAnd the root lap equivalent thickness h that major-minor spring is totalMA2e, it is respectively
<mrow>
<msub>
<mi>h</mi>
<mrow>
<mi>M</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>h</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<mroot>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>h</mi>
<mi>i</mi>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>;</mo>
<msub>
<mi>h</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
<mn>1</mn>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>h</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<mroot>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>h</mi>
<mi>i</mi>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>1</mn>
<mi>j</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>;</mo>
<msub>
<mi>h</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
<mn>2</mn>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>h</mi>
<mrow>
<mi>N</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<mroot>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>h</mi>
<mi>i</mi>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>1</mn>
<mi>j</mi>
</mrow>
<mn>3</mn>
</msubsup>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</munderover>
<msubsup>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>2</mn>
<mi>k</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mrow>
<mn>3</mn>
</mroot>
<mo>;</mo>
</mrow>
Ii steps：Main spring clamps stiffness KMIt calculates
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, main each of spring
Half clamping length Li, i=1,2 ..., n；And the h being calculated in i stepsle, l=i=1,2 ..., n clamp main spring
Rigidity is calculated, i.e.,
<mrow>
<msub>
<mi>K</mi>
<mi>M</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>b</mi>
<mi>E</mi>
</mrow>
<mrow>
<mn>2</mn>
<mo>&lsqb;</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<msubsup>
<mi>h</mi>
<mrow>
<mn>1</mn>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>l</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msubsup>
<mi>L</mi>
<mn>1</mn>
<mn>3</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Iii steps：The clamping complex stiffness K of main spring and first order auxiliary springMA1It calculates
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, main each of spring
Half clamping length Li, i=1,2 ..., n；First order auxiliary spring the piece number m1, the half clamping length of each of first order auxiliary spring is
LA1j=Ln+j, j=1,2 ..., m1；The sum of the piece number of main spring and first order auxiliary spring N1=n+m1And be calculated in i steps
hle, l=1,2 ..., N1, to the clamping complex stiffness K of main spring and first order auxiliary springMA1It is calculated, i.e.,
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>b</mi>
<mi>E</mi>
</mrow>
<mrow>
<mn>2</mn>
<mo>&lsqb;</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<msubsup>
<mi>h</mi>
<mrow>
<mn>1</mn>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<mrow>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>l</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msubsup>
<mi>L</mi>
<mn>1</mn>
<mn>3</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Iv steps：Total compound clamping stiffness K of major-minor springMA2It calculates：
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each main spring
Half clamping length Li, i=1,2 ..., n；First order auxiliary spring the piece number m1, the half clamping length of each of first order auxiliary spring is
LA1j=Ln+j, j=1,2 ..., m1；Second level auxiliary spring the piece number m2, the half clamping length L of each of second level auxiliary springA2k=LN1+k, k
=1,2 ..., m2；Total the piece number N=n+m of major-minor spring1+m2And the h being calculated in i stepsle, l=1,2 ..., N, to major-minor
Total compound clamping stiffness K of springMA2It is calculated, i.e.,
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>b</mi>
<mi>E</mi>
</mrow>
<mrow>
<mn>2</mn>
<mo>&lsqb;</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<msubsup>
<mi>h</mi>
<mrow>
<mn>1</mn>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>l</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msubsup>
<mi>L</mi>
<mn>1</mn>
<mn>3</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>N</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<msubsup>
<mi>h</mi>
<mrow>
<mi>N</mi>
<mi>e</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
(2) calculating of the main spring for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-and the radius of curvature of auxiliary spring at different levels：
I steps：Main spring tailpiece lower surface initial curvature radius RM0bCalculating
According to main spring initial tangential camber HgM0, the half clamping length L of main first of spring1, main reed number n, the thickness of main each of spring
hi, i=1,2 ..., n；To main spring tailpiece lower surface initial curvature radius RM0bIt is calculated, i.e.,
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>M</mi>
<mn>0</mn>
<mi>b</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>H</mi>
<mrow>
<mi>g</mi>
<mi>M</mi>
<mn>0</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>H</mi>
<mrow>
<mi>g</mi>
<mi>M</mi>
<mn>0</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mo>;</mo>
</mrow>
II steps：First upper surface initial curvature radius R of first order auxiliary springA10aCalculating
According to the first order auxiliary spring half clamping length L of firstA11, the initial tangential camber design load H of first order auxiliary springgA10, it is right
First upper surface initial curvature radius R of first order auxiliary springA10aIt is calculated, i.e.,
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>10</mn>
<mi>a</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mi>L</mi>
<mrow>
<mi>A</mi>
<mn>11</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>H</mi>
<mrow>
<mi>g</mi>
<mi>A</mi>
<mn>10</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>H</mi>
<mrow>
<mi>g</mi>
<mi>A</mi>
<mn>10</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
III steps：First order auxiliary spring tailpiece lower surface initial curvature radius RA10bCalculating
According to first order auxiliary spring the piece number m1, thickness h that first order auxiliary spring is eachA1j, j=1,2 ..., m1；And it is calculated in II steps
The R arrivedA10a, to first order auxiliary spring tailpiece lower surface initial curvature radius RA10bIt is calculated, i.e.,
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>10</mn>
<mi>b</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>10</mn>
<mi>a</mi>
</mrow>
</msub>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</munderover>
<msub>
<mi>h</mi>
<mrow>
<mi>A</mi>
<mn>1</mn>
<mi>j</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
IV steps：First upper surface initial curvature radius R of second level auxiliary springA20aCalculating
According to the second level auxiliary spring half clamping length L of firstA21, the initial tangential camber design load H of second level auxiliary springgA20, it is right
First upper surface initial curvature radius R of second level auxiliary springA20aIt is calculated, i.e.,
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>20</mn>
<mi>a</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mi>L</mi>
<mrow>
<mi>A</mi>
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(3) simulation calculation for each secondary contact loads of offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-：
Step A：1st beginning contact load Pk1Simulation calculation
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；The half of main first of spring clamps
Length L1, the h that is calculated in step (1)Me, the R that is calculated in step (2)M0bAnd RA10a, to the 1st beginning contact load
Pk1Simulation calculation is carried out, i.e.,
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<mn>0</mn>
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</mrow>
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</mrow>
</mrow>
<mrow>
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<msub>
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<mn>1</mn>
</msub>
<msub>
<mi>R</mi>
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<mi>M</mi>
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<mi>b</mi>
</mrow>
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<msub>
<mi>R</mi>
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<mi>A</mi>
<mn>10</mn>
<mi>a</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Step B：2nd beginning contact load Pk2Simulation calculation
According to the width b for the offset frequencys type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；It is calculated in step (1)
hMA1e, the R that is calculated in step (2)A10bAnd RA20aAnd the P that simulation calculation obtains in step Ak1, start contact to the 2nd time and carry
Lotus Pk2Simulation calculation is carried out, i.e.,
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<mn>1</mn>
</msub>
<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>10</mn>
<mi>b</mi>
</mrow>
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<msub>
<mi>R</mi>
<mrow>
<mi>A</mi>
<mn>20</mn>
<mi>a</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
Step C：2nd full contact load pw2Simulation calculation
The P obtained according to simulation calculation in step Ak1, simulation calculation obtains in step B Pk2, to the 2nd full contact load
Pw2Simulation calculation is carried out, i.e.,
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<mi>P</mi>
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<mi>w</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
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<mi>P</mi>
<mrow>
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<mi>P</mi>
<mrow>
<mi>k</mi>
<mn>1</mn>
</mrow>
</msub>
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<mo>;</mo>
</mrow>
(4) simulation calculation of the clamping stiffness characteristics for the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-：
According to the K being calculated in step (1)M、KMA1And KMA2, the obtained P of simulation calculation in step (3)k1、Pk2And Pw2, it is right
Clamping stiffness characteristics of the offset frequencys type progressive rate leaf springs such as two-stage auxiliary spring formula is non-under different loads P carry out simulation calculation, i.e.,
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</mtable>
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</mrow>
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| JP3511873B2 (en) * | 1997-12-26 | 2004-03-29 | 三菱ふそうトラック・バス株式会社 | Leaf spring clip fastening structure |
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| CN2573300Y (en) * | 2002-09-18 | 2003-09-17 | 中国重型汽车集团有限公司 | Dislocation preventing rear steel plate spring for double axle automobile |
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