CN105736614B - The design method of the reinforced few piece variable-section steel sheet spring in root - Google Patents
The design method of the reinforced few piece variable-section steel sheet spring in root Download PDFInfo
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- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 103
- 239000010959 steel Substances 0.000 title claims abstract description 103
- 238000013461 design Methods 0.000 title claims abstract description 84
- 238000000034 method Methods 0.000 title claims abstract description 23
- 238000004364 calculation method Methods 0.000 claims description 9
- 238000009434 installation Methods 0.000 claims description 8
- 230000003014 reinforcing effect Effects 0.000 claims description 2
- 239000000725 suspension Substances 0.000 abstract description 6
- 239000000463 material Substances 0.000 abstract description 4
- 238000012356 Product development Methods 0.000 abstract description 3
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- 239000000295 fuel oil Substances 0.000 description 1
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- 239000004334 sorbic acid Substances 0.000 description 1
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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
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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Abstract
The present invention relates to the design methods of the reinforced few piece variable-section steel sheet spring in root, belong to suspension leaf spring technical field.The present invention can be according to root reinforced the rigidity Design required value of piece variable-section steel sheet spring, structure and material parameter less, it is first determined goes out the root thickness h of equivalent one-chipe, and according to allowable stress, determine root maximum allowable thickness [h2]；Then, according to he[h2], the piece number N, the root thickness h of few piece variable-section steel sheet spring reinforced to root2, each end flat segments thickness h1iWith length l1iAnd the thickness h of variable cross-section section at different locationsi(x) it is designed.By ANSYS simulating, verifyings it is found that can obtain accurate, reliable leaf spring parameter design value using this method, the design level and performance of spring can be improved, reduces spring-mass and cost, improves vehicle ride performance；Meanwhile design and testing expenses are also reduced, accelerate product development speed.
Description
Technical Field
The invention relates to a vehicle suspension steel plate spring, in particular to a design method of a root reinforced few-leaf variable cross-section steel plate spring.
Background
Compared with a plurality of superposed leaf springs, the variable cross-section leaf spring has reasonable stress, tends to balance stress load, saves materials and cost, realizes light weight of the vehicle, reduces dynamic load of wheels, improves the running safety of the vehicle, saves fuel oil and improves the transportation efficiency of the vehicle, thereby having good economic and social benefits and arousing high attention of vehicle experts. For the few-leaf variable-section steel plate spring, an oblique line section is usually additionally arranged between a root straight section and a parabolic section, namely, a root reinforced few-leaf variable-section steel plate spring is adopted, so that the stress of the spring can be reduced, the stress intensity of the spring is improved, meanwhile, the accurate design value of the rigidity can be met, the processing of the parabolic section can be facilitated, and the processing manufacturability of the parabolic section is improved. Although a design method of a few parabolic variable cross-section leaf spring has been proposed previously, for example, penmo and high force have been proposed in "automotive engineering" 14, 3 rd, a design calculation method of a variable cross-section leaf spring is proposed, the method can only design a few parabolic variable cross-section leaf spring with unreinforced root and equistructured end parts, and the defect is that the design requirement of the root reinforced type few variable cross-section leaf spring cannot be met.
For the root-reinforced few-leaf variable-section steel plate spring, because of the restriction of the computational theories of deformation, rigidity and the like and the equivalent thickness and splitting design theory, a simple, accurate and reliable design method has not been provided so far, the influence of a root-reinforced oblique line segment is mostly ignored at present, the oblique line segment is directly and approximately regarded as a parabolic line segment, and the root-reinforced few-leaf variable-section steel plate spring is approximately designed, so that the accurate and reliable parameter design value is difficult to obtain. With the simulation of computer and finite element simulation software, although some people adopt an ANSYS modeling simulation method for root-reinforced few-leaf variable-section steel plate springs at present, the method can only perform simulation verification on the deformation or rigidity of the reinforced few-leaf variable-section steel plate springs with a given design structure, cannot provide an accurate analytic design formula, and cannot meet the requirements of rapid development of vehicles and development of modern CAD (computer-aided design) software for the steel plate springs.
Therefore, an accurate and reliable design method of the root-reinforced few-leaf variable-section steel plate spring is required to be established, the requirements of rapid development of the vehicle industry and accurate design of the suspension steel plate spring are met, the design level, quality and performance of the few-leaf variable-section steel plate spring are improved, and the driving smoothness and safety of a vehicle are improved; meanwhile, the spring quality and cost are reduced, 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 design method of a root-reinforced few-leaf variable-section steel plate spring. The variable cross-section steel plate spring comprises at least two steel plate springs, each steel plate spring is of a symmetrical structure taking a central bolt penetrating hole as an axis, a half symmetrical structure on one side of a central hole of each steel plate spring is composed of a root straight section, an oblique line section, a parabolic line section and 4 steel plate sections of an end straight section, and the oblique line section is arranged between the root straight section and the parabolic line section and plays a role in reinforcing the root of each steel plate spring; the end straight sections of the 1 st leaf spring are in non-equal structures, and the thickness and the length of the end straight section of the 1 st leaf spring from top to bottom are larger than those of other pieces, so that the requirement that the stress on the end part of the 1 st leaf spring is complex is met; wherein L is half of the length of the leaf spring, L3Is half of the mounting pitch, b is the width, h2Is the thickness of the root straight section of each leaf spring, h2pRoot thickness of a parabolic segment; the length of the diagonal line segment is Deltal, and the thickness ratio gamma of the diagonal line segment is h2p/h2；h1i、l1ithe thickness and length of the end straight section of the ith flat spring and the thickness ratio β of the parabolic section of each variable cross-section springi＝h1i/h2p. And under the given conditions of the length, the width, the mounting distance, the rigidity design required value, the maximum load and the allowable stress of the variable cross-section leaf spring, designing the root reinforced few-leaf variable cross-section leaf spring.
In order to solve the technical problems, the invention provides a design method of a root-reinforced few-leaf variable cross-section steel plate spring, which is characterized by comprising the following design steps:
(1) equivalent single-piece root thickness h of root-reinforced few-piece variable-section steel plate springeThe calculation of (2):
firstly, selecting β thickness ratio beta of a parabolic segment of an equivalent single-piece variable cross-section steel plate spring, wherein β selection range of beta is 0.5-0.6, and then, selecting a few variable cross-section steel platesHalf length L and half rigidity design required value K of springMWidth b, elastic modulus E; the thickness ratio γ of the diagonal segments; length of diagonal line segment, Δ l, half of installation pitch, l3Distance l from the root of the diagonal to the end of the spring2＝L-l3The distance l from the root of the parabolic segment to the end point of the spring2p＝L-l3- Δ l, equivalent single leaf root thickness h for root reinforced few leaf variable section leaf springs meeting stiffness requirementsePerform calculations, i.e.
Wherein,
(2) the number N of the root-enhanced few-leaf variable-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
step A: determining the maximum allowable thickness [ h ] of the root thickness of the leaf spring2]：
According to half length L and width b of the root reinforced few-leaf variable cross-section steel plate spring, half of the maximum load, namely single end point load P, allowable stress [ sigma ]]And the equivalent single-chip root thickness h calculated in the step (1)eDetermining the maximum allowable thickness [ h ] of the root thickness of the few-leaf variable-section steel plate spring2]I.e. by
And B, step: the number N of the few variable cross-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
selecting an initial value N of the number of the root-reinforced few-leaf variable-section steel plate springs, wherein N can be an integer between 2 and 5; designed byThe thicknesses of the root straight sections of the leaf springs of the few leaf variable cross-section leaf springs are equal and are all equal to h2(ii) a According to [ h ] determined in step A2]And h calculated in step (1)eFor the root part thickness h of each leaf spring of the root part enhanced few leaf variable cross-section leaf spring2Is designed, i.e.
If h2≤[h2]Then h is2The initial value N is 2, namely the number of the designed pieces of the root-reinforced few-piece variable cross-section steel plate spring;
if h2＞[h2]If the number of the leaf springs N is equal to N +1, the step B is returned to and continuously executed, and the root thickness h under the condition of increasing 1 leaf is increased2Designing until h is reached2≤[h2]The number N of the root-reinforced few-leaf variable-section steel plate springs and the root thickness h of each leaf spring2Finishing the design;
(3) the design of the thickness and the length of the end part straight section of each leaf spring of the root reinforced type few-leaf variable cross-section leaf spring is as follows:
i, step: h is obtained according to the design in the step (2)2determining the thickness ratio beta of the parabolic segment of the 1 st leaf spring1I.e. by
Distance l from the root of the parabolic segment to the end point of the spring2pThe thickness ratio gamma of the diagonal line segment, h designed in the step (2)2and the determined thickness ratio β of the parabolic segment of the 1 st leaf spring1Determining the thickness h of the end straight section of the 1 st variable cross-section spring11And length l11Are respectively as
h11＝β1γh2，
l11＝β1 2l2p；
II, determining the thickness ratio beta of the parabolic segment of the 1 st leaf spring according to the thickness ratio beta of the parabolic segment of the 1 st leaf spring determined in the step I1Root thickness h of the equivalent single-piece variable cross-section spring determined in the step (1)ethe thickness ratio β of the parabolic line segment, and N and h obtained by the design of the step B in the step (2)2Determining the thickness ratio of the parabolic segment of the No. 2, …, N-th leaf spring, i.e. the thickness ratio
according to the determined thickness ratio β of the parabolic segment of the No. 2, …, N sheet steel spring2＝β3＝…＝βNThe distance l from the root of the parabolic segment to the end point of the spring2pThe thickness ratio gamma of the diagonal line segment, and h designed in the step (2)2Determining the thickness and the length of the end straight section of the No. 2, … and N leaf spring respectively
(4) Thickness h of each leaf spring of root-reinforced few-leaf variable-section leaf spring at different positionsi(x) The design of (2):
according to the half length L of the root reinforced few-leaf variable cross-section steel plate spring and the distance L from the root of the parabolic segment to the spring end point2pDistance l from the root of the diagonal to the end of the spring2Oblique lineThe thickness ratio gamma of the sections, the thickness and the length of the end straight sections of each variable cross-section spring determined in the step (3), and the root thickness h of each variable cross-section spring designed in the step (2)2Taking the end point of the spring as the origin of coordinates, and setting the thickness h of each leaf spring of the root reinforced few-leaf variable cross-section leaf spring at different positions xi(x) Is designed, i.e.
Wherein i is 1,2, …, N.
The invention has the advantages over the prior art
Because the root-reinforced few-leaf variable-section steel plate spring is formed by additionally arranging an oblique line segment between a root straight segment and a root parabolic segment, the analysis and calculation are very complicated, and therefore, a reliable analytical design method cannot be provided at home and abroad. At present, the influence of an oblique line segment is mostly ignored, the oblique line segment is directly and approximately regarded as a parabolic segment, and the root-reinforced few-leaf variable-section steel plate spring is approximately designed, so that an accurate and reliable parameter design value is difficult to obtain, and the root of the few-leaf variable-section spring cannot be designed in an enhanced mode. With the development of computer and finite element simulation software, although some people adopt an ANSYS modeling simulation method for the root-reinforced few-leaf variable-section steel plate spring, the method can only perform simulation verification on the deformation or rigidity of the few-leaf variable-section steel plate spring with an actual design structure, cannot provide an accurate analytic design formula related to the root-reinforced few-leaf variable-section steel plate spring, and cannot meet the requirements of rapid development of vehicles and development of modern CAD (computer aided design) software for suspension steel plate springs.
according to the design rigidity and installation structure size of the leaf spring, the thickness ratio β of a parabolic segment, the thickness ratio gamma of a root reinforced oblique segment, the length delta l of the oblique segment and the end deformation coefficient of the parabolic variable cross-section leaf spring of an equivalent single-leaf root reinforced variable cross-section leaf spring are selected, and firstly, the design rigidity and the installation structure size of the leaf spring are adjustedEquivalent single-piece root thickness h of root-reinforced few-piece variable-section steel plate springeDesigning; then, according to the single end point load P which is half of the maximum load of the steel plate spring and the allowable stress [ sigma ]]For the root maximum allowable thickness [ h ] of the root reinforced few-leaf variable cross-section steel plate spring2]Designing; then, according to the root thickness h of the equivalent single piece of the root reinforced few-piece variable cross-section steel plate springeFor the root-reinforced few-leaf variable-section steel plate spring, the number N of leaves and the root thickness h2finally, according to the design value beta h of the thickness of the end straight section of the equivalent single chipeFor the thickness h of the flat section at the end of each sheet1iAnd length l1iAnd thickness h at different positionsi(x) The design is carried out.
Through design examples and ANSYS simulation verification, the method can obtain accurate and reliable parameter design values of the root-reinforced few-leaf variable-section steel plate spring, provides a reliable design method for the root-reinforced few-leaf variable-section steel plate spring, and lays a reliable technical foundation for CAD software development. By using the method, the design level and the performance of the few-leaf variable-section steel plate spring of the vehicle suspension can be improved, the quality and the cost of the suspension spring are reduced, and the transportation efficiency and the driving safety of a vehicle are improved; meanwhile, the design and test cost is 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 a design of a root-reinforced few leaf variable cross-section leaf spring;
FIG. 2 is a schematic view of a one-piece, semi-symmetrical structure of a root-reinforced few-leaf variable cross-section leaf spring;
FIG. 3 is a parameter diagram of a half symmetrical structure of a 1 st root reinforced variable cross-section leaf spring according to an embodiment;
FIG. 4 is a parameter diagram of a semi-symmetrical structure of a 2 nd root reinforced variable cross-section leaf spring according to an embodiment;
FIG. 5 is a simulated cloud of the deformation of the root-reinforced few-leaf variable cross-section leaf spring according to the first embodiment;
FIG. 6 is a parameter diagram of a half symmetrical structure of a first root reinforced variable cross-section leaf spring according to the second embodiment;
FIG. 7 is a parameter diagram of a half symmetrical structure of the second 2 nd leaf spring with a root reinforced variable cross-section according to the second embodiment;
fig. 8 is a simulated cloud of the deformation of the root-reinforced few-leaf variable cross-section leaf spring designed in the second embodiment.
Detailed description of the preferred embodiments
The present invention will be described in further detail by way of examples.
FIG. 1 is a flow chart of the design of the present invention, and the following steps are described in detail with reference to the embodiment:
the first embodiment is as follows: a schematic diagram of a symmetrical structure of a single leaf spring of a root-reinforced few leaf variable cross-section leaf spring is shown in fig. 2, wherein a half length L of each few leaf variable cross-section leaf spring is 575mm, a width b thereof is 60mm, an elastic modulus E thereof is 200GPa, and a half of a mounting distance L thereof3The thickness ratio gamma of the diagonal line segment is 0.90, the length delta l of the diagonal line segment is 30mm, the single end point load P which is half of the maximum load borne by the steel plate is 1200N, and the allowable stress [ sigma ] is]500 MPa. Half-rigidity design requirement value K of root-reinforced few-leaf variable-section steel plate springMThe root-reinforced few-leaf variable-section leaf spring is designed as 24N/mm.
The design process of the root-reinforced few-leaf variable-section steel plate spring provided by the embodiment of the invention is shown in figure 1, and the specific steps are as follows:
(1) equivalent single-piece root thickness h of root-reinforced few-piece variable-section steel plate springeThe calculation of (2):
firstly, selecting the thickness ratio β of the parabola section of the equivalent single-piece root reinforced variable-section leaf spring as 0.55, and then, according to the design requirement value K of half rigidityM24N/mm, half length L575 mm, width b 60mm, elastic modulus E200 GPa, thickness ratio gamma 0.90, length delta L30 mm, half of installation space L355mm, the distance l from the root of the diagonal to the end point of the spring2＝L-l3520mm, the distance l from the base of the parabolic segment to the end point of the spring2p＝L-l3-490 mm, equivalent single leaf root thickness h for root reinforced few leaf variable section leaf springs meeting stiffness requirementsePerform calculations, i.e.
Wherein,
(2) the number N of the root-enhanced few-leaf variable-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
step A: determining the maximum allowable thickness [ h ] of the root thickness of each leaf spring2]：
According to the root reinforced type few-leaf variable cross-section steel plate spring, the half length L is 575mm, the width b is 60mm, the half of the maximum load, namely the single end point load P is 1200N, and allowable stress [ sigma ]]500MPa, and h calculated in step (1)eDetermining the maximum allowable thickness [ h ] of the root thickness of each variable cross-section spring as 14.39mm2]I.e. by
And B, step: the number N of the few variable-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
selecting an initial value N of the number of the root-reinforced few-leaf variable-section steel plate springs to be 2, wherein N can be an integer between 2 and 5; the root thicknesses of the designed few-leaf variable-section steel plate springs are the same, namely the root thicknesses are all equal to h2(ii) a According to [ h ] determined in step A2]21.59mm, and h calculated in step (1)eThe root thickness h of each leaf spring of the root reinforced few-leaf variable cross-section leaf spring is 14.39mm2Is designed, i.e.
Because of h2≤[h2]The design value h of the root thickness of each leaf spring of the root-enhanced few-leaf variable cross-section leaf spring211.42mm, and the number N of the steel plate spring pieces is 2;
(3) the design of the thickness and the length of the end part straight section of each leaf spring of the root reinforced type few-leaf variable cross-section leaf spring is as follows:
i, step: designing the obtained h according to the step (2)2determining the thickness ratio β of the parabolic segment of the 1 st leaf spring as 11.42mm1I.e. by
β1＝0.60；
Distance l from the root of the parabolic segment to the end point of the spring2p490mm, the thickness ratio γ of the diagonal line segment is 0.90, and h obtained by the design in step (2)211.42mm and β10.60, the thickness h of the end straight section of the 1 st leaf spring is determined11And length l11Are respectively as
h11＝β1γh2＝6.17mm，
l11＝β1 2l2＝176.40mm；
step II β ═ 0.55 and h β ═ determined in step (1)e14.39mm, β determined in step I10.60, and N obtained by designing in step (2) is 2 and h2The thickness ratio of the parabolic segment of the 2 nd leaf spring is determined as 11.42mm, namely
according to the determined thickness ratio beta of the parabolic segment of the 2 nd leaf spring20.49, distance l from the base of the parabolic segment to the spring end point2p490mm, thickness ratio γ of diagonal line segment 0.90, and h designed in step (2)2The thickness h of the end straight section of the 2 nd leaf spring is determined as 11.42mm12And length l12Are respectively as
(4) Thickness h of each leaf spring of root-reinforced few-leaf variable-section leaf spring at different positionsi(x) The design of (2):
according to half length L of the root reinforced few-leaf variable-section steel plate spring, which is 575mm, the distance L from the root of the oblique line segment to the end point of the spring2520mm, the distance l from the base of the parabolic segment to the end point of the spring2p490mm, the thickness ratio γ of the diagonal line segment is 0.90, and h is determined in step (3)11＝6.17mm、l11＝176.40mm、h125.04mm and l12117.65mm, and stepsH obtained by designing in step (2)2The thickness h of the two leaf spring root reinforced few-leaf variable cross-section leaf springs at different positions x is obtained by taking the spring end point as the origin of coordinates (11.42 mm)1(x)、h2(x) Respectively is
The thicknesses of the 1 st leaf spring at different positions x of the parabolic segment and the oblique line segment are shown in the table I; the thickness of the 2 nd leaf spring at different positions x of the parabolic segment and the oblique line segment is shown in the table II;
TABLE 1 thickness h of the first variable-section leaf spring at different positions x of the parabolic segment and the oblique line segment1(x)
| Position x/(mm) | 520 | 491.40 | 456.40 | 421.40 | 386.40 | 351.40 | 316.40 | 281.40 | 246.40 | 211.40 | 176.40 |
| Thickness h1(x)/(mm) | 11.42 | 10.33 | 9.92 | 9.53 | 9.13 | 8.70 | 8.26 | 7.79 | 7.29 | 6.75 | 6.17 |
Table 2 thickness h of variable cross-section leaf spring at different position x of parabolic segment and oblique line segment2(x)
| Position x/(mm) | 520 | 495.65 | 453.65 | 411.65 | 369.65 | 327.65 | 285.65 | 243.65 | 201.65 | 159.65 | 117.65 |
| Thickness h2(x)/(mm) | 11.42 | 10.49 | 9.89 | 9.42 | 8.93 | 8.40 | 7.85 | 7.25 | 6.59 | 5.87 | 5.04 |
Designing a half symmetrical structure parameter of the obtained 1 st root reinforced variable cross-section leaf spring, as shown in fig. 3; and the 2 nd root reinforced variable-section leaf spring has a half symmetrical structural parameter, as shown in figure 4.
Using ANSYS finite element simulation software, according to the structural parameters and material characteristic parameters of the root-reinforced few-leaf variable cross-section steel plate spring obtained by design, establishing an ANSYS simulation model of the root-reinforced few-leaf variable cross-section steel plate spring with a half-symmetrical structure, dividing grids, applying fixed constraint at the root of the simulation model, applying a concentrated load P to an end point to be 1200N, performing ANSYS simulation on the deformation of the root-reinforced few-leaf variable cross-section steel plate spring, and obtaining a deformation simulation cloud picture, wherein the maximum deformation amount f of the steel plate spring at the end position is 49.58mm, so that half of the rigidity of the steel plate spring is KM＝P/f＝24.20N/mm。
It can be known that the ANSYS simulation verification value K of half rigidity of the steel plate springM24.20N/mm, and the design requirement value KMThe relative deviation is only 0.83 percent when the relative deviation is equal to 24N/mm; the result shows that the design method of the root reinforced type few-leaf variable cross-section steel plate spring provided by the invention is correct, and the parameter design value is accurate and reliable.
Example two: a schematic diagram of a symmetrical structure of a single leaf spring of a root-reinforced few-leaf variable cross-section leaf spring is shown in fig. 2, wherein a half length L of each leaf spring is 600mm, a width b is 60mm, an elastic modulus E is 200GPa, and a half of an installation space L360mm, 30mm in the length Δ l of the diagonal line segment, 0.90 in the thickness ratio γ of the diagonal line segment, 3000N in the single end point load P, which is half of the maximum load, and allowable stress [ σ [ ]]500 MPa. Half-rigidity design requirement value K of root-reinforced few-leaf variable-section steel plate springMThe root-reinforced few-leaf variable-section leaf spring is designed at 46N/mm.
The root-reinforced few-leaf variable-section steel plate spring is designed by adopting the same design method and steps as the first embodiment, and the specific design steps are as follows:
(1) equivalent single-piece root thickness h of root-reinforced few-piece variable-section steel plate springeThe calculation of (2):
firstly, selecting the thickness ratio β of a parabolic segment of an equivalent single root reinforced variable-section leaf spring to be 0.55, and then designing a required value K of half rigidity according to the half length L of the root reinforced few-leaf variable-section leaf spring to be 600mmM46N/mm, 60mm width b, 200GPa elastic modulus E, 30mm diagonal length Delta l, 0.90 diagonal thickness ratio gamma, and half of installation interval l360mm, the distance l from the base of the diagonal to the end of the spring2＝L-l3540mm, the distance l from the base of the parabolic segment to the end point of the spring2p＝L-l3- Δ l 510mm, equivalent single leaf root thickness h for root reinforced few leaf variable section leaf springePerform calculations, i.e.
Wherein,
(2) the number N of the root-enhanced few-leaf variable-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
step A: determining the maximum allowable thickness [ h ] of the root thickness of each leaf spring2]：
According to the root reinforced type few-leaf variable-section leaf spring, the half length L is 600mm, the width b is 60mm, the half of the maximum load, namely the single end point load P is 3000N, and allowable stress [ sigma ] is]500MPa, and h calculated in step (1)eThe maximum allowable thickness [ h ] of the root thickness of each leaf spring is determined at 18.62mm2]I.e. by
And B, step: variable cross-section steel plate spring leafNumber N and thickness h of root of each leaf spring2The design of (2):
selecting an initial value N of the number of the root-reinforced few-leaf variable-section steel plate springs to be 2, wherein N is an integer between 2 and 5; according to [ h ] determined in step A2]17.93mm, and h calculated in step (1)e18.62mm, and the root thickness h of each piece of the root reinforced few-piece variable cross-section steel plate spring2Is designed, i.e.
Because of h2≤[h2]Therefore, the number of the root-reinforced type few-leaf variable cross-section leaf springs N is 2, and the designed value of the root thickness h of each leaf2＝14.78mm；
(3) The design of the thickness and the length of the end part straight section of each leaf spring of the root reinforced type few-leaf variable cross-section leaf spring is as follows:
i, step: h is obtained according to the design in the step (2)2determining the thickness ratio β of the parabolic segment of the 1 st variable cross-section spring as 14.78mm1I.e. by
β1＝0.60；
Distance l from the root of the parabolic segment to the end point of the spring2p510mm, the thickness ratio γ of the diagonal line segment is 0.90, and h is designed in step (2)214.78mm and β10.60, the thickness h of the end straight section of the 1 st leaf spring is determined11And length l11Are respectively as
h11＝β1γh2＝7.98mm，
l11＝β1 2l2＝183.60mm；
II, determining the thickness ratio beta of the parabolic segment of the 1 st variable cross-section spring determined in the step I1Step 0.60 ═ stepthe thickness ratio β of the parabolic segment determined in step (1) is 0.55 and he18.62mm, and N2 and h as designed in step (2)2determining the thickness ratio β of the parabolic segment of the 2 nd leaf spring as 14.78mm2I.e. by
according to the determined thickness ratio beta of the parabolic segment of the 2 nd leaf spring20.49, distance l from the base of the parabolic segment to the spring end point2p510mm, the thickness ratio γ of the diagonal line segment is 0.90, and h designed in step (2)2The thickness and length of the end straight section of the 2 nd leaf spring are determined as 14.78mm, respectively
(4) Thickness h of each leaf spring of root-reinforced few-leaf variable-section leaf spring at different positionsi(x) The design of (2):
according to the half length L of the root reinforced few-leaf variable-section leaf spring being 600mm, the distance L from the root of the oblique line segment to the end point of the spring2540mm, the distance l from the base of the parabolic segment to the end point of the spring2p510mm, the thickness ratio γ of the diagonal line segment is 0.90, and h is determined in step (3)117.98mm and l11＝183.60mm、h126.52mm and l12122.45mm, and h designed in step (2)2The thickness h of each piece of the root reinforced few-piece variable cross-section steel plate spring at different positions x is obtained by taking the spring end point as the origin of coordinates (14.78 mm)1(x)、h2(x) Respectively is
The thickness of the 1 st leaf spring at different positions x of the parabolic segment and the oblique line segment is shown in table three; the thickness of the 2 nd leaf spring at different positions x of the parabolic segment and the oblique line segment is shown in the fourth table;
thickness h of the third 1 st variable cross-section leaf spring at different positions x of the parabolic segment and the oblique line segment1(x)
| Position x/(mm) | 540 | 525.60 | 487.60 | 449.60 | 411.60 | 373.60 | 335.60 | 297.60 | 259.60 | 221.60 | 183.60 |
| Thickness h1(x)/(mm) | 14.78 | 14.07 | 13.01 | 12.49 | 11.95 | 11.39 | 10.79 | 10.16 | 9.49 | 8.77 | 7.98 |
TABLE 2 thickness h of variable-section leaf spring at different positions x of parabolic segment and oblique line segment2(x)
| Position x/(mm) | 540 | 500.45 | 458.45 | 416.45 | 374.45 | 332.45 | 290.45 | 248.45 | 206.45 | 164.45 | 122.45 |
| Thickness h2(x)/(mm) | 14.78 | 13.18 | 12.61 | 12.02 | 11.40 | 10.74 | 10.04 | 9.28 | 8.46 | 7.55 | 6.52 |
Designing a half symmetrical structure parameter of the obtained 1 st root reinforced variable cross-section leaf spring, as shown in fig. 6; and the 2 nd root reinforced variable-section leaf spring has a half symmetrical structural parameter, as shown in figure 7.
Establishing an ANSYS simulation model of the root-enhanced few-leaf variable-section steel plate spring with a semi-symmetrical structure according to structural parameters and material characteristic parameters of the root-enhanced few-leaf variable-section steel plate spring obtained by design by using ANSYS finite element simulation software, dividing grids, and applying force to the root of the simulation modelAdding fixed constraint, applying a concentrated load P at an end point to be 3000N, performing ANSYS simulation on the deformation of the root reinforced type few-piece variable cross-section leaf spring, and obtaining a deformation simulation cloud chart as shown in FIG. 8, wherein the maximum deformation f of the leaf spring at the end position is 64.84mm, so that the half stiffness of the leaf spring is KM＝P/f＝46.27N/mm。
It can be known that the ANSYS simulation verification value K of half rigidity of the steel plate springM46.27N/mm, and K is the value required by designM46N/mm, the relative deviation is only 0.59%; the result shows that the design method of the root reinforced type few-leaf variable cross-section steel plate spring provided by the invention is correct, and the parameter design value is accurate and reliable.
Claims (1)
1. The design method of the root-reinforced few-leaf variable-section steel plate spring comprises at least two steel plate springs, each steel plate spring is of a symmetrical structure taking a central bolt through hole as an axis, a half symmetrical structure on one side of the central bolt through hole of each steel plate spring is composed of a root straight section, an oblique line section, a parabolic line section and 4 steel plate sections of an end straight section, and the oblique line section is arranged between the root straight section and the parabolic line section and plays a role in reinforcing the root of each steel plate spring; the end straight sections of the 1 st leaf spring are in non-equal structures, and the thickness and the length of the end straight section of the 1 st leaf spring from top to bottom are larger than those of other pieces, so that the requirement that the stress on the end part of the 1 st leaf spring is complex is met; under the given conditions of length, width, installation distance, rigidity design requirement value, maximum load and allowable stress of the variable cross-section leaf spring, designing the root reinforced few-leaf variable cross-section leaf spring, wherein the specific design steps are as follows:
(1) calculating the equivalent single-sheet root thickness he of the root-reinforced few-leaf variable-section steel plate spring:
firstly, selecting β thickness ratio beta of a parabolic segment of an equivalent single-piece variable cross-section leaf spring, wherein β selection range of beta is 0.5-0.6, and then, according to β half length L of β variable cross-section leaf spring and β half L of β installation space3Half K of the design requirement value of rigidityMWidth b, elastic modulus E; the length delta l of a preset oblique line segment, the thickness ratio gamma of the oblique line segment, and the distance l from the root of the oblique line segment to the end point of the spring2＝L-l3(ii) a Distance l from root of parabolic segment to spring end point2p＝L-l3Δ l, equivalent single leaf root thickness h for an equivalent single leaf variable-section leaf spring meeting the stiffness requirementePerform calculations, i.e.
Wherein,
(2) the number N of the root-enhanced few-leaf variable-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
step A: determining the maximum allowable thickness [ h ] of the root thickness of the leaf spring2]：
According to half length L and width b of the root reinforced few-leaf variable cross-section steel plate spring, half of the maximum load, namely single end point load P, allowable stress [ sigma ]]And the equivalent single-chip root thickness h calculated in the step (1)eDetermining the maximum allowable thickness of the root of the few-leaf variable-section steel plate springThickness [ h ]2]I.e. by
And B, step: the number N of the few variable cross-section steel plate springs and the root thickness h of each steel plate spring2The design of (2):
selecting an initial value N of the number of the root-reinforced few-leaf variable-section steel plate springs, wherein N can be an integer between 2 and 5; the thicknesses of root straight sections of all the designed few leaf springs of the variable cross-section leaf spring are equal and are all equal to h2(ii) a According to [ h ] determined in step A2]And h calculated in the step (1)eFor the root thickness h of each leaf spring of the root-enhanced few-leaf variable cross-section leaf spring2Is designed, i.e.
If h2≤[h2]Then h is2The initial value N is 2, namely the number of the designed pieces of the root-reinforced few-piece variable cross-section steel plate spring;
if h2＞[h2]If the number of the leaf springs N is equal to N +1, the step B is returned to and continuously executed, and the root thickness h under the condition of increasing 1 leaf is increased2Designing until h is reached2≤[h2]The number N of the root-reinforced few-leaf variable-section steel plate springs and the root thickness h of each leaf spring2Finishing the design;
(3) the design of the thickness and the length of the end part straight section of each leaf spring of the root reinforced type few-leaf variable cross-section leaf spring is as follows:
i, step: h is obtained according to the design in the step (2)2determining the thickness ratio beta of the parabolic segment of the 1 st leaf spring1I.e. by
Distance l from the root of the parabolic segment to the end point of the spring2pThe thickness ratio gamma of the diagonal line segment, h designed in the step (2)2and the determined thickness ratio β of the parabolic segment of the 1 st leaf spring1Determining the thickness h of the end straight section of the 1 st variable cross-section spring11And length l11Are respectively as
h11＝β1γh2，
II, determining the thickness ratio beta of the parabolic segment of the 1 st leaf spring according to the thickness ratio beta of the parabolic segment of the 1 st leaf spring determined in the step I1Root thickness h of the equivalent single-piece variable cross-section spring determined in the step (1)ethe thickness ratio β of the parabolic line segment, and N and h obtained by the design of the step B in the step (2)2Determining the thickness ratio of the parabolic segment of the No. 2, …, N piece variable cross-section spring, i.e. determining the thickness ratio
according to the determined thickness ratio β of the parabolic segment of the No. 2, …, N piece variable cross-section spring2，β3…… ， βNThe distance l from the root of the parabolic segment to the end point of the spring2pThe thickness ratio gamma of the diagonal line segment, and h designed in the step (2)2Determining the thickness and the length of the end straight section of the No. 2, No. 3, … and No. N leaf springs respectively
(4) Each leaf spring of root reinforced few leaf variable cross-section leaf springThickness h at the same positioni(x) The design of (2):
according to the half length L of the root reinforced few-leaf variable cross-section steel plate spring and the distance L from the root of the parabolic segment to the spring end point2pDistance l from the root of the diagonal to the end of the spring2The thickness ratio gamma of the diagonal line segment, the thickness and the length of the end straight section of each variable cross-section spring determined in the step (3), and the root thickness h of each variable cross-section spring designed in the step (2)2Taking the end point of the spring as the origin of coordinates, and setting the thickness h of each leaf spring of the root reinforced few-leaf variable cross-section leaf spring at different positions xi(x) Is designed, i.e.
Wherein i is 1,2, …, N.
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