CN106802997B - Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring - Google Patents

Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring Download PDF

Info

Publication number
CN106802997B
CN106802997B CN201710022997.4A CN201710022997A CN106802997B CN 106802997 B CN106802997 B CN 106802997B CN 201710022997 A CN201710022997 A CN 201710022997A CN 106802997 B CN106802997 B CN 106802997B
Authority
CN
China
Prior art keywords
spring
stage
main spring
stage main
stiffness
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN201710022997.4A
Other languages
Chinese (zh)
Other versions
CN106802997A (en
Inventor
周长城
杨腾飞
袁光明
赵雷雷
汪晓
王凤娟
邵明磊
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong University of Technology
Original Assignee
Shandong University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shandong University of Technology filed Critical Shandong University of Technology
Priority to CN201710022997.4A priority Critical patent/CN106802997B/en
Publication of CN106802997A publication Critical patent/CN106802997A/en
Application granted granted Critical
Publication of CN106802997B publication Critical patent/CN106802997B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Computer Hardware Design (AREA)
  • Mechanical Engineering (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Springs (AREA)
  • Vehicle Body Suspensions (AREA)

Abstract

The invention relates to a method for calculating the deflection characteristic of a two-stage main spring type unequal-frequency-bias gradually-changed-stiffness plate spring, and belongs to the technical field of suspension leaf springs. The invention can calculate the deflection characteristic of the two-stage main spring type unequal-frequency gradient-stiffness plate spring on the basis of calculation of each stage of clamping stiffness and two-stage gradient-stiffness according to the structural parameters, the elastic modulus, the clamping distance of the saddle bolt and the contact load of each main spring and each auxiliary spring. According to ANSYS simulation and loading deflection tests of a prototype, the method for calculating the deflection characteristic of the two-stage main spring type unequal frequency gradient stiffness plate spring is correct, and a reliable technical basis is laid for initial tangent arc height, two-stage gradient clearance design and CAD software development of the two-stage main spring type unequal frequency gradient stiffness plate spring. The method can obtain deflection calculation values which can lean against different loads, and improve the design level, quality and performance of products and the running smoothness of vehicles; meanwhile, the design and test cost is reduced, and the product development speed is accelerated.

Description

Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring
Technical Field
The invention relates to a vehicle suspension steel plate spring, in particular to a method for calculating the deflection characteristic of a two-stage main spring type unequal-frequency gradient-stiffness plate spring.
Background
In order to further improve the driving smoothness of the vehicle under the condition of half load, the main spring of the original one-stage gradual-change stiffness plate spring can be split into two stages of main springs, namely a two-stage main spring type gradual-change stiffness plate spring; meanwhile, in order to ensure the stress strength of the main spring, the second-stage main spring and the auxiliary spring are enabled to bear load in advance by the initial tangent arc height of the first-stage main spring, the second-stage main spring and the auxiliary spring and two-stage gradual change gaps, so that the stress of the first-stage main spring is reduced, namely the stress of the two-stage main spring type non-equal-bias-frequency gradual change stiffness plate spring, wherein the deflection characteristics of the two-stage main spring type non-equal-bias-frequency gradual change stiffness plate spring under different loads influence the suspension frequency bias and the vehicle driving smoothness and safety; meanwhile, deflection calculation under different loads is also an important technical basis for designing the tangential arc height, the gradual change gap and the maximum limiting deflection of the plate spring. However, due to the restriction of two-stage gradient stiffness calculation, the deflection calculation of the two-stage main spring type non-equal bias frequency gradient stiffness plate spring is very complex, and according to the found data, a method for calculating the deflection characteristic of the two-stage main spring type non-equal bias frequency gradient stiffness plate spring has not been provided previously, and most of the deflection characteristic is determined through test tests, so that the method cannot meet the requirements of rapid development of the vehicle industry and the modern CAD design of a suspension spring. Along with the continuous improvement of the vehicle running speed and the requirement on the smoothness, higher requirements are provided for the suspension of the plate spring with the gradual change stiffness, therefore, an accurate and reliable calculation method for the deflection characteristic of the two-stage main spring type non-equal bias frequency type gradual change stiffness plate spring is required to be established, a reliable technical basis is laid for the design and CAD software development of the two-stage main spring type non-equal bias frequency type gradual change stiffness plate spring, the rapid development of the vehicle industry, the vehicle running smoothness and the design requirement on the gradual change stiffness plate spring are met, and the design level, the product quality and the performance of the two-stage main spring type non-equal bias frequency type gradual change stiffness plate spring, and the vehicle running smoothness and the safety are improved; meanwhile, the design and test cost is reduced, and the product development speed is accelerated.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a simple and reliable method for calculating the deflection characteristic of a two-stage main spring type unequal-frequency gradient-stiffness plate spring, and the calculation flow is shown in fig. 1. The half symmetrical structure of the two-stage main spring type unequal frequency bias gradient stiffness plate spring is shown in fig. 2 and consists of a first-stage main spring 1, a second-stage main spring 2 and an auxiliary spring 3. Adopts two stages of main springs and has initial tangent arc height H passing through the first stage main spring 1, the second stage main spring 2 and the auxiliary springgM10、HgM20And HgA0Two-stage gradual change gaps are arranged between the first-stage main spring 1 and the second-stage main spring 2 and between the second-stage main spring 2 and the auxiliary spring 3M12AndMAto improve the running smoothness of the vehicle under the half-load condition. In order to ensure that the stress strength design requirement of the first-stage main spring 1 is met, the second-stage main spring 2 and the auxiliary spring 3 bear loads properly in advance, and the gradient load and the offset frequency of the suspension are unequal, namely the two-stage main spring type unequal offset frequency type gradient stiffness plate spring. Half total span of the gradual stiffness plate spring is equal to half action length L of the first main spring11THalf of the clamping distance of the riding bolt is L0Width b, and elastic modulus E. The number of the first-stage main spring 1 is n1The thickness of each leaf of the first-stage main spring is h1iHalf action length is L1iTHalf the clamping length L1i＝Li＝LiT-L0/2，i＝1,2,…,n1. The number of the second stage main spring 2 is n2The thickness of each leaf of the second-stage main spring is h2jHalf action length is L2jTHalf the clamping length L2j＝Ln1+j＝LiT-L0/2，j＝1,2,…,n2. The sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n2. The number of the auxiliary spring 3 is m, and the thickness of each auxiliary spring is hAkHalf action length is LAkTHalf the clamping length LAk＝Ln+k＝LAkT-L0And/2, k is 1,2, …, m. The total number N of the main and auxiliary springs is N1+n2+ m. According to the structural parameters, the elastic modulus, the clamping distance of the horseback bolts and each secondary contact load of the first-stage main spring, the second-stage main spring and the auxiliary spring, on the basis of calculation of each-stage clamping rigidity and two-stage gradual-change clamping rigidity, the deflection characteristics of the two-stage main spring type unequal-frequency gradual-change rigidity plate spring under different loads are calculated.
In order to solve the technical problem, the invention provides a method for calculating the deflection characteristic of a two-stage main spring type unequal frequency gradient stiffness plate spring, which is characterized by comprising the following calculation steps of:
(1) equivalent thickness h of each different number of overlapping sections of two-stage main spring type unequal frequency bias gradient stiffness plate springleThe calculation of (2):
according to the number n of the main spring of the first stage1Thickness of each leaf of the first-stage main springDegree h1i，i＝1,2,…,n1(ii) a Number n of second stage main spring2Thickness h of each leaf of the second-stage main spring2j，j＝1,2,…,n2(ii) a Number m of auxiliary spring pieces, thickness h of each auxiliary spring pieceAkK is 1,2, …, m; the sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n2The total number of the main and auxiliary springs is N + m, and the equivalent thickness h of the overlapped section for different number of the main and auxiliary springs isle1,2, …, N, i.e.:
Figure GDA0002188281190000021
(2) calculating the clamping rigidity of each level of the two-level main spring type unequal frequency bias gradually-changed rigidity plate spring:
i, step: clamping stiffness K of first stage main springM1The calculation is carried out according to the width b and the elastic modulus E of the two-stage main spring type unequal frequency bias gradient stiffness plate spring; number n of primary main reed1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1And h calculated in step (1)le，l＝i＝1,2，…,n1Clamping stiffness K to the first stage main springM1Perform calculations, i.e.
Figure GDA0002188281190000022
II, step (2): composite clamping rigidity K of first-stage main spring and second-stage main springM2Calculating the width b and the elastic modulus E of the two-stage main spring type unequal frequency bias gradient stiffness plate spring; number n of primary main reed1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1(ii) a Number n of main reed of second stage2Half of the clamping length L of each leaf of the second-stage main spring2j＝Ln1+j，j＝1,2,…,n2(ii) a The sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n2And h calculated in step (1)le1,2, n, a composite clamping stiffness K for the first and second main springsM2Perform calculations, i.e.
Figure GDA0002188281190000023
Step III: total composite clamping stiffness K of main and auxiliary springsMACalculating the width b and the elastic modulus E of the steel plate spring according to the gradient stiffness; number n of first-stage main spring1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1(ii) a Number n of second stage main spring2Half of the clamping length L of each leaf of the second-stage main spring2j＝Ln1+j，j＝1,2,…,n2(ii) a The number of the auxiliary spring pieces is m, and half of the clamping length of each auxiliary spring piece is LAk＝Ln+kK is 1,2, …, m; n + m total number of main and auxiliary springs, and h calculated in step (1)le1,2, N, total clamping compound stiffness K for the main and auxiliary springsMAPerform a calculation, i.e.
Figure GDA0002188281190000024
(3) Two-stage gradual change clamping rigidity K of two-stage main spring type unequal frequency bias type gradual change rigidity plate springkwP1And KkwP2And (3) calculating:
step A: first-stage gradient composite clamping stiffness KkwP1Is calculated according to the 1 st initial contact load P k12 nd initial contact load Pk2K calculated in step (2)M1And KM2For load P in [ P ]k1,Pk2]First-order gradual-change composite clamping stiffness K in rangekwP1Perform calculations, i.e.
Figure GDA0002188281190000025
And B, step: second-stage gradient composite clamping stiffness KkwP2Is calculated according to the 2 nd initial contact load P k22 nd full contact load Pw2K calculated in step (2)M2And KMAFor load P in [ P ]k2,Pw2]Second-stage progressive composite clamping stiffness K over rangekwP2Perform calculations, i.e.
Figure GDA0002188281190000031
(4) Calculating the deflection characteristics of the two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring under different loads:
according to the 1 st initial contact load P k12 nd initial contact load P k22 nd full contact load Pw2K calculated in step (2)M1And KMAAnd K calculated in step (3)kwP1And KkwP2Calculating the deflection characteristics of the two-stage main spring type unequal frequency gradient stiffness plate spring under different loads P, namely
Figure GDA0002188281190000032
The invention has the advantages over the prior art
Due to the restriction of two-stage gradient stiffness calculation, the deflection calculation of the two-stage main spring type non-equal bias frequency gradient stiffness plate spring is very complex, a calculation method for the deflection characteristic of the two-stage main spring type non-equal bias frequency gradient stiffness plate spring cannot be provided in the prior art, and most of the deflection characteristic is determined through test tests, so that the rapid development of the vehicle industry and the modern CAD design requirement of a suspension spring cannot be met. The invention can calculate the clamping rigidity characteristic of the two-stage main spring type unequal-frequency gradient rigidity plate spring under different loads according to the structural parameters, the elastic modulus and the clamping distance of the riding bolt of each primary main spring, each secondary main spring and each auxiliary spring. According to ANSYS simulation and loading deflection tests of a prototype, the method for calculating the deflection characteristic of the two-stage main spring type unequal frequency gradient stiffness plate spring is correct, and a reliable technical basis is laid for design and CAD software development of the two-stage main spring type unequal frequency gradient stiffness plate spring. By using the method, the calculated value of the clamping rigidity which can lean against different loads can be obtained, and the design level, the quality and the performance of the product and the running smoothness of the vehicle can be obtained; meanwhile, the design and test cost can be reduced, and the product development speed is accelerated.
Drawings
For a better understanding of the present invention, reference is made to the following further description taken in conjunction with the accompanying drawings.
FIG. 1 is a flow chart of the calculation of the deflection characteristic of a two-stage main spring type unequal frequency bias gradient-type gradual-change stiffness plate spring;
FIG. 2 is a schematic diagram of a semi-symmetrical structure of a two-stage main spring type unequal frequency bias gradient stiffness plate spring;
FIG. 3 shows the clamping rigidity K of the two-stage main spring type unequal deviation frequency gradual change rigidity plate spring of the embodimentPA curve of variation with load P;
fig. 4 is a deflection characteristic curve of the two-stage main spring type unequal bias frequency type gradual stiffness plate spring of the embodiment under different loads.
Detailed Description
The present invention will be described in further detail by way of examples.
Example (b): the width b of a certain two-stage main spring type unequal frequency gradient stiffness plate spring is 63mm, and the clamping distance of a saddle bolt is half L050mm, and 200 GPa. Number n of primary main reed 12, thickness h of each leaf of the first-stage main spring11＝h12Half of the action length L of each leaf of the first-stage main spring is 8mm11T＝525mm，L12T450 mm; half of the clamping length is L11＝L1＝L11T-L0/2＝500mm，L12＝L2＝L12T-L0425 mm/2. Number n of main reed of second stage2Thickness h 1218 mm; half action length L21T350mm, half the clamping length L21＝L3＝L21T-L0325 mm. And the sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is 3. The number m of auxiliary springs is 2, and the thickness h of each auxiliary spring isA1＝hA213 mm; half of the action length of each leaf of the auxiliary spring is LA1T＝250mm，LA2T150 mm; half of the clamping length of each leaf of the auxiliary spring is LA1＝L4＝LA1T-L0/2＝225mm，LA2＝L5＝LA2T-L0125 mm/2. The total number N of the main and auxiliary springs is 5. 1 st initial contact load P k11851N, 2 nd initial contact load Pk22602N, full contact load P for 2 nd timew23658N. According to the structural parameters, the elastic modulus, the clamping distance of the saddle bolts and each secondary contact load of each primary main spring, each secondary main spring and each auxiliary spring, on the basis of calculation of each level of clamping rigidity and two levels of gradient rigidity, the deflection characteristics of the two-level main spring type non-equal-frequency-bias gradient-rigidity plate spring under different loads are calculated.
The calculation method for the deflection characteristic of the two-stage main spring type unequal frequency gradient stiffness plate spring provided by the embodiment of the invention has the calculation flow as shown in figure 1, and comprises the following specific calculation steps:
(1) equivalent thickness h of each different number of overlapping sections of two-stage main spring type unequal frequency bias gradient stiffness plate springleThe calculation of (2):
according to the number n of the main spring of the first stage 12, thickness h of each leaf of the first-stage main spring11＝h128 mm; number n of second stage main spring2Thickness h 1218 mm; the number m of auxiliary springs is 2, and the thickness h of each auxiliary spring isA1＝hA213 mm; the total number N of the main and auxiliary springs is 5, wherein the equivalent thickness h of the overlapped section of each different number l of the main and auxiliary springs isle1,2, …, N, i.e.:
h1e＝h11＝8.0mm；
Figure GDA0002188281190000041
Figure GDA0002188281190000042
Figure GDA0002188281190000043
Figure GDA0002188281190000044
(2) calculating the clamping rigidity of each level of the two-level main spring type unequal frequency bias gradually-changed rigidity plate spring:
i, step: clamping stiffness K of first stage main springM1Is calculated by
According to the width b of the two-stage main spring type unequal frequency bias gradient stiffness plate spring, which is 63mm, and the elastic modulus E, which is 200 GPa; number n of primary main reed 12, half of the clamping length L of each leaf of the first-stage main spring11＝L1＝500mm，L12＝L2425mm and h calculated in step (1)1e＝8.0mm，h2e10.1mm, i 1,2, clamping stiffness K for the first main spring stageM1Perform calculations, i.e.
Figure GDA0002188281190000045
II, step (2): composite clamping rigidity K of first-stage main spring and second-stage main springM2Computing
According to the width b of the two-stage main spring type unequal frequency bias gradient stiffness plate spring, which is 63mm, and the elastic modulus E, which is 200 GPa; number n of primary main reed 12, half of the clamping length L of each leaf of the first-stage main spring11＝L1＝500mm，L12＝L2425 mm; number n of main reed of second stage2Half the clamping length L of the second stage main spring as 121＝L3325mm, the sum of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n 23 and h calculated in step (1)1e＝8.0mm，h2e＝10.1mm，h3e11.5mm, 1,2, n, a composite clamping stiffness K for the first and second stage main springsM2Perform calculations, i.e.
Figure GDA0002188281190000046
Step III: total composite clamping stiffness K of main and auxiliary springsMAComputing
According to the width b of the two-stage main spring type unequal frequency bias gradient stiffness plate spring, which is 63mm, and the elastic modulus E, which is 200 GPa; number n of first-stage main spring 12, half of the clamping length L of each leaf of the first-stage main spring11＝L1＝500mm，L12＝L2425 mm; number n of second stage main spring2Half the clamping length L of the second stage main spring as 121＝L3325 mm; the number m of the auxiliary springs is 2, and half of the clamping length of each auxiliary spring is LA1＝L4＝225mm，LA2＝L5125 mm; the total number N of the main and auxiliary springs is 5, and h is calculated in the step (1)1e＝8.0mm，h2e＝10.1mm，h3e＝11.5mm，h4e＝15.5mm，h5e18.1mm, 1,2, N, total clamp compound stiffness K for the main and auxiliary springsMAPerform a calculation, i.e.
Figure GDA0002188281190000051
(3) Two-stage gradual change clamping rigidity K of two-stage main spring type unequal frequency bias type gradual change rigidity plate springkwP1And KkwP2And (3) calculating:
step A: first-stage gradient composite clamping stiffness KkwP1Is calculated by
According to the 1 st initial contact load P k11851N, 2 nd initial contact load Pk22602N, K calculated in step (2)M151.4N/mm and KM275.4N/mm, P is [ P ] for loadk1,Pk2]First-order gradual-change composite clamping stiffness K in rangekwP1Perform calculations, i.e.
Figure GDA0002188281190000052
And B, step: second-stage gradient composite clamping stiffness KkwP2Is calculated by
According to the 2 nd contact load Pk22602N, full contact load P for 2 nd timew23658N, calculated in step (2)K ofM275.4N/mm and KMA172.9N/mm, P is [ P ] for loadk2,Pw2]Second-stage progressive composite clamping stiffness K over rangekwP2Perform calculations, i.e.
Figure GDA0002188281190000053
Utilizing a Matlab calculation program to calculate the clamping rigidity K of the two-stage main spring type unequal bias frequency gradient rigidity plate springPThe curve with load P is shown in fig. 3.
(4) Calculating the deflection characteristics of the two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring under different loads:
according to the 1 st initial contact load P k11851N, 2 nd initial contact load Pk22602N, full contact load P for 2 nd timew23658N, K calculated in step (2)M151.43N/mm and KMA172.9N/mm, and K calculated in step (3)kwP1And KkwP2Calculating the deflection characteristics of the two-stage main spring type unequal frequency gradient stiffness plate spring under different loads P, namely
Figure GDA0002188281190000054
The deflection characteristic curves of the two-stage main spring type unequal frequency gradient stiffness plate spring under different loads are calculated by utilizing a Matlab calculation program, as shown in figure 4, wherein, P isk1、Pk2、Pw2And PNThe lower deflection is fMk1＝36mm，fMk2＝47.9mm，fMw257.1mm and fMN＝77.6mm。
According to ANSYS simulation and loading deflection tests of a prototype, the method for calculating the deflection characteristic of the two-stage main spring type unequal frequency gradient stiffness plate spring is correct, and a reliable technical basis is laid for designing the initial tangent arc height, the two-stage gradient clearance and the maximum limiting deflection of the two-stage main spring type unequal frequency gradient stiffness plate spring and developing CAD software. The method can obtain deflection calculation values which can lean against different loads, and improve the design level, quality and performance of products and the running smoothness of vehicles; meanwhile, the design and test cost is reduced, and the product development speed is accelerated.

Claims (1)

1. The method for calculating the deflection characteristic of the two-stage main spring type non-equal frequency bias type gradual-change rigidity plate spring comprises the steps that each plate spring is of a structure symmetrical about a center through hole, and half of the installation clamping distance is half of the clamping distance of a saddle bolt; the main spring of the original one-stage gradient stiffness plate spring is split and designed into two-stage main springs, and the vehicle running smoothness under the half-load condition is improved through the initial tangent arc height and the two-stage gradient clearance of the two-stage main springs and the auxiliary spring; meanwhile, in order to ensure that the stress strength design requirement of the first-stage main spring is met, the second-stage main spring and the auxiliary spring bear loads in advance, and the offset frequencies of the suspension under the gradual load are unequal, namely the two-stage main spring type unequal offset frequency type gradual-change stiffness plate spring; according to the structural parameters, the elastic modulus, the clamping distance of a saddle bolt and the contact load of each plate spring, on the basis of calculation of two-stage gradual change clamping rigidity, the deflection characteristics of the two-stage main spring type unequal frequency gradual change rigidity plate spring under different loads are calculated, and the specific calculation steps are as follows:
(1) equivalent thickness h of each different number of overlapping sections of two-stage main spring type unequal frequency bias gradient stiffness plate springleThe calculation of (2):
according to the number n of the main spring of the first stage1Thickness h of each leaf of the first-stage main spring1i，i＝1,2,…,n1(ii) a Number n of second stage main spring2Thickness h of each leaf of the second-stage main spring2j，j＝1,2,…,n2(ii) a Number m of auxiliary spring pieces, thickness h of each auxiliary spring pieceAkK is 1,2, …, m; the sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n2The total number of the main and auxiliary springs is N + m, and the equivalent thickness h of the overlapped section for different number of the main and auxiliary springs isle1,2, …, N, i.e.:
Figure FDA0002188281180000011
(2) calculating the clamping rigidity of each level of the two-level main spring type unequal frequency bias gradually-changed rigidity plate spring:
i, step: clamping stiffness K of first stage main springM1Is calculated by
According to the width b and the elastic modulus E of the two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring; number n of primary main reed1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1And h calculated in step (1)le，l＝i＝1,2，…,n1Clamping stiffness K to the first stage main springM1Perform calculations, i.e.
Figure FDA0002188281180000012
II, step (2): composite clamping rigidity K of first-stage main spring and second-stage main springM2Computing
According to the width b and the elastic modulus E of the two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring; number n of primary main reed1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1(ii) a Number n of main reed of second stage2Half of the clamping length L of each leaf of the second-stage main spring2j＝Ln1+j，j＝1,2,…,n2(ii) a The sum n of the leaf numbers of the first-stage main spring and the second-stage main spring is n1+n2And h calculated in step (1)le1,2, n, a composite clamping stiffness K for the first and second main springsM2Perform calculations, i.e.
Figure FDA0002188281180000013
Step III: total composite clamping stiffness K of main and auxiliary springsMAComputing
According to the width b and the elastic modulus E of the steel plate spring with the gradually changed stiffness; number n of first-stage main spring1Half of the clamping length L of each leaf of the first-stage main spring1i＝Li，i＝1,2,…,n1(ii) a Number n of second stage main spring2Half of the clamping length L of each leaf of the second-stage main spring2j＝Ln1+j，j＝1,2,…,n2(ii) a The number of the auxiliary spring pieces is m, and half of the clamping length of each auxiliary spring piece is LAk＝Ln+kK is 1,2, …, m; n + m total number of main and auxiliary springs, and h calculated in step (1)le1,2, N, total clamping compound stiffness K for the main and auxiliary springsMAPerform a calculation, i.e.
Figure FDA0002188281180000021
(3) Two-stage gradual change clamping rigidity K of two-stage main spring type unequal frequency bias type gradual change rigidity plate springkwP1And KkwP2And (3) calculating:
step A: first-stage gradient composite clamping stiffness KkwP1Is calculated by
According to the 1 st initial contact load Pk12 nd initial contact load Pk2K calculated in step (2)M1And KM2For load P in [ P ]k1,Pk2]First-order gradual-change composite clamping stiffness K in rangekwP1Perform calculations, i.e.
Figure FDA0002188281180000022
And B, step: second-stage gradient composite clamping stiffness KkwP2Is calculated by
According to the 2 nd contact load Pk22 nd full contact load Pw2K calculated in step (2)M2And KMAFor load P in [ P ]k2,Pw2]Second-stage progressive composite clamping stiffness K over rangekwP2Perform calculations, i.e.
Figure FDA0002188281180000023
(4) Calculating the deflection characteristics of the two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring under different loads:
according to the 1 st initial contact load Pk12 nd initial contact load Pk22 nd full contact load Pw2K calculated in step (2)M1And KMAAnd K calculated in step (3)kwP1And KkwP2Calculating the deflection characteristics of the two-stage main spring type unequal frequency gradient stiffness plate spring under different loads P, namely
Figure FDA0002188281180000024
CN201710022997.4A 2017-01-12 2017-01-12 Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring Expired - Fee Related CN106802997B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710022997.4A CN106802997B (en) 2017-01-12 2017-01-12 Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710022997.4A CN106802997B (en) 2017-01-12 2017-01-12 Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring

Publications (2)

Publication Number Publication Date
CN106802997A CN106802997A (en) 2017-06-06
CN106802997B true CN106802997B (en) 2020-08-11

Family

ID=58984322

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710022997.4A Expired - Fee Related CN106802997B (en) 2017-01-12 2017-01-12 Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring

Country Status (1)

Country Link
CN (1) CN106802997B (en)

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106295086A (en) * 2016-10-18 2017-01-04 山东理工大学 The method for designing of the few sheet parabolic type spacing amount of deflection of major-minor spring of ends contact formula
CN106326605A (en) * 2016-10-18 2017-01-11 山东理工大学 Computing method of deflection of non-end-contact type few-leaf parabolic main and auxiliary spring structure

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
车辆钢板弹簧悬架***减振器最佳阻尼匹配;周长城，潘礼军，于曰伟，赵雷雷;《农业工程学报》;20160731(第7期);第106-113页 *

Also Published As

Publication number Publication date
CN106802997A (en) 2017-06-06

Similar Documents

Publication Publication Date Title
CN105653883B (en) The auxiliary spring of non-ends contact formula bias type major-minor spring works the Method for Checking of load
CN105740591A (en) Method for verifying strength of each leaf of end contact type few-leaf oblique main and auxiliary springs
CN106802997B (en) Method for calculating deflection characteristic of two-stage main spring type unequal frequency bias gradually-changed stiffness plate spring
CN106802996B (en) Checking calculation method for contact load of two-stage auxiliary spring type unequal frequency bias gradient-type plate spring
CN106909712B (en) Design method for tangential arc height of two-stage main spring type unequal frequency bias gradient stiffness plate spring
CN106844925B (en) Adjusting design method for contact load of two-stage auxiliary spring type gradient stiffness plate spring based on offset frequency simulation
CN106777790B (en) Simulation calculation method for stiffness characteristic of two-stage main spring type non-offset frequency type gradient stiffness plate spring
CN106777805B (en) Method for designing blanking length of main spring of two-stage main spring type unequal-frequency-bias gradually-changed-stiffness plate spring
CN106855905B (en) Simulation calculation method for deflection characteristic of two-stage auxiliary spring type unequal-frequency-type gradient-stiffness plate spring
CN106709204B (en) Simulation calculation method for deflection characteristic of high-strength two-stage gradient stiffness plate spring
CN106812849B (en) The Method for Checking of the contact load of the offset frequencys type three-level progressive rate leaf spring such as non-
CN106682358B (en) Matching design method for contact load of two-stage main spring type unequal-frequency-bias gradually-changed-stiffness plate spring
CN106802995B (en) Checking calculation method for contact load of equal-gradient offset frequency high-strength two-stage gradient stiffness plate spring
CN106803000B (en) Design method for maximum limiting deflection of high-strength three-level gradient stiffness plate spring
CN106802999B (en) Design method for initial tangent arc height of main spring of high-strength three-stage gradient stiffness plate spring
CN106682357B (en) The emulated computation method of high-intensitive three-level progressive rate plate spring suspension system offset frequency characteristic
CN106650167B (en) Simulation verification algorithm for maximum limiting deflection of high-strength first-level gradient stiffness plate spring
CN106777804B (en) The adjusted design method of three-level progressive rate leaf spring contact load based on offset frequency emulation
CN106777810B (en) The calculation method for the offset frequencys type progressive rate rigidity of plate spring characteristics such as the main spring formula of two-stage is non-
CN106599524B (en) The design method of the initial tangential camber of the offset frequencys type three-level progressive rate leaf spring such as non-
CN106548002B (en) The design method in the gradual change gap of the offset frequencys type three-level progressive rate leaf spring such as non-
CN106802998B (en) The offset frequencys type three-level progressive rate leaf spring such as non-clamps the simulation calculation method of stiffness characteristics
CN106599525A (en) Simulating calculation method for offset frequency characteristics of non-equal offset frequency type three-stage gradient rigidity leaf spring suspension
CN106763384A (en) The method for designing of the offset frequency type progressive rate leaf spring tangent line camber such as two-stage auxiliary spring formula is non-
CN106844902B (en) Deflection calculation method of non-equal-frequency-bias one-level gradient stiffness plate spring suspension

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20200811

Termination date: 20220112