CN112507486A - Method for checking key parameters of unequal-length few-leaf oblique-line-type variable-section plate spring - Google Patents

Method for checking key parameters of unequal-length few-leaf oblique-line-type variable-section plate spring Download PDF

Info

Publication number
CN112507486A
CN112507486A CN202011365409.5A CN202011365409A CN112507486A CN 112507486 A CN112507486 A CN 112507486A CN 202011365409 A CN202011365409 A CN 202011365409A CN 112507486 A CN112507486 A CN 112507486A
Authority
CN
China
Prior art keywords
leaf spring
calculated
section
leaf
length
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.)
Granted
Application number
CN202011365409.5A
Other languages
Chinese (zh)
Other versions
CN112507486B (en
Inventor
周长城
杨林
郑伟
耿向阳
许金兵
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 Automobile Spring Factory Zibo Co ltd
Shandong University of Technology
Original Assignee
Shandong Automobile Spring Factory Zibo Co ltd
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 Automobile Spring Factory Zibo Co ltd, Shandong University of Technology filed Critical Shandong Automobile Spring Factory Zibo Co ltd
Priority to CN202011365409.5A priority Critical patent/CN112507486B/en
Publication of CN112507486A publication Critical patent/CN112507486A/en
Application granted granted Critical
Publication of CN112507486B publication Critical patent/CN112507486B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00Springs
    • F16F1/02Springs 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
    • F16F1/18Leaf springs
    • F16F1/185Leaf springs characterised by shape or design of individual leaves
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00Springs
    • F16F1/02Springs 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
    • F16F1/18Leaf springs
    • F16F1/20Leaf springs with layers, e.g. anti-friction layers, or with rollers between the leaves
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00Springs
    • F16F1/02Springs 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
    • F16F1/18Leaf springs
    • F16F1/26Attachments or mountings
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/15Vehicle, aircraft or watercraft design
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mechanical Engineering (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Automation & Control Theory (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Springs (AREA)

Abstract

本发明涉及非等长少片斜线型变截面板簧的校核方法,属于车辆悬架少片变截面板簧技术领域。本发明可根据所给定板簧的设计结构参数、弹性模量、额定载荷及在额定载荷下的许用应力和在冲击载荷下的最大许用应力,对非等长少片斜线型变截面板簧的夹紧刚度、悬架偏频、应力强度、初始切线弧高和最大限位挠度进行校核。通过样机试验可知,本发明所提供的非等长少片斜线型变截面板簧的校核方法是正确的,确保所设计板簧的夹紧刚度、悬架偏频、初始弧高和最大限位挠度满足板簧的设计要求,提高非等长少片斜线型变截面板簧的设计水平和性能及车辆行驶平顺性和安全性;同时,降低产品的试验费用,加快产品开发速度。The invention relates to a checking method for a non-equal-length and few-piece oblique variable-section leaf spring, belonging to the technical field of a vehicle suspension with fewer-piece variable-section leaf springs. According to the design structure parameters, elastic modulus, rated load, allowable stress under rated load, and maximum allowable stress under impact load of the given leaf spring, the present invention can be used for non-equal length and few-piece oblique deformation. The clamping stiffness, suspension bias frequency, stress intensity, initial tangent arc height and maximum limit deflection of the section leaf spring are checked. Through the prototype test, it can be seen that the calibration method of the non-equal length and few-piece oblique variable section leaf spring provided by the present invention is correct, ensuring the clamping stiffness, suspension bias frequency, initial arc height and maximum value of the designed leaf spring. The limit deflection meets the design requirements of the leaf spring, improving the design level and performance of the non-equal-length, less-slanted, variable-section leaf spring, as well as the ride comfort and safety of the vehicle; at the same time, it reduces the test cost of the product and accelerates the product development speed.

Description

Method for checking key parameters of unequal-length few-leaf oblique-line-type variable-section plate spring
Technical Field
The invention relates to a few-leaf variable-section plate spring of a vehicle suspension, in particular to a method for checking key parameters of a non-isometric few-leaf diagonal variable-section plate spring.
Background
The half-symmetrical structure of the few-leaf oblique line type variable cross-section plate spring is composed of a root straight section, an oblique line section and an end straight section, and the two ends of the cross section of the half-symmetrical structure are in a shape of an arc, a chamfer or a right angle. In order to further reduce the weight of the plate spring with less variable cross section and meet the design requirements of suspension offset frequency and plate spring rigidity, a few-piece oblique line type variable cross section plate spring with unequal length is usually adopted, wherein the lengths of oblique line segments and end straight segments of all the plate springs are unequal, and the thickness of the end straight segment of the first plate spring is larger than that of the end straight segments of other plate springs. However, the stiffness of each leaf spring of the unequal-length few-leaf oblique line type variable-section leaf spring is not equal, and the calculation of the clamping stiffness is very complicated in consideration of the shapes of two ends of the cross section and the influence on the stiffness. According to the checked data, for the unequal-length few-leaf oblique-line type variable-section plate spring with given design structure parameters, due to the restriction of clamping rigidity calculation and load distribution of each leaf spring, a checking method for key parameters of the unequal-length few-leaf oblique-line type variable-section plate spring is not provided at home and abroad at present, so that the design requirements of suspension offset frequency, initial arc height and maximum limit deflection of the designed plate spring are difficult to ensure. Therefore, an accurate and reliable checking method for key parameters of the unequal-length few-leaf diagonal variable-section plate spring is required to be established, so that the key parameters of the plate spring are ensured to meet the design requirements of the plate spring, and the product quality and performance of the product and the driving smoothness and safety of a vehicle are improved; meanwhile, the test cost of the product is reduced, and the product development speed is accelerated.
Disclosure of Invention
In view of the above-mentioned drawbacks in the prior art, the technical problem to be solved by the present invention is to provide an accurate and reliable method for checking key parameters of a leaf spring with variable cross-section and less inclined pieces of unequal lengths, wherein a design flow chart is shown in fig. 1. Each plate spring is composed of a root straight section, an oblique line section and an end straight section, the root straight section of each plate spring is equal in length, the oblique line section is unequal in length to the end straight section, namely, a half-symmetrical structural schematic diagram of a small number of oblique line type variable cross-section plate springs with unequal length is shown in figure 2, wherein each oblique line type variable cross-section plate spring 1, a root gasket 2, an end gasket 3 and a half length L of each plate spring areTThe U clamping distance of the U is equal to half of the L clamping length of the plate springTU/4, half the clamping length L of the root flat section2The number of the plate springs is n, n is more than or equal to 2 and less than or equal to 5, and the length L of the oblique line of each plate springxiThe length of the straight section at the end of each leaf spring is L1iClamping length L of each leaf springci=L2+Lxi+L1iThe difference of half length of each plate spring is DeltaLi=Lci-Lci+1. The length from the root of the oblique line segment of each plate spring to the end point of the plate spring is L2x=L-L2The length L from the end of the diagonal line segment of each leaf spring to the end point of the leaf spring1xi=L2x-Lxi. The length from the root of the oblique line section of the end plate spring to the end point is Lxn+L1nGreater than or equal to the length L of the diagonal segment of the first leaf springx1I.e. Lxn+L1n>Lx1To increase the strength of the leaf spring ends. Thickness h of root straight section of each leaf spring2iThickness h of the end straight section1iThickness ratio of diagonal line segment betai=h1i/h2iThe thickness h of the diagonal line segment at the x position is determined by taking the end point of the plate spring as the origin of coordinatesxi=khix+Chi,khiThe slope of the expression for the thickness of the inclined line segment of each leaf spring, ChiIs a constant of the oblique line segment thickness expression, i is 1,2, …, n. Leaf spring width B, modulus of elasticity E. DeltacThickness of root washer 2, deltaeIs a terminalThe thickness of the partial washer 3. The two ends of the cross section of each leaf spring are in the shapes of arc, chamfer and right angle, wherein the different types of cross sections can be uniformly used for chamfering the radius-thickness ratio krDenotes that 0. ltoreq. kr1/2 is not more than r, k is 0r0, the cross section is right-angled; when r is h/2, kr1/2, the cross section is circular arc; when 0 is present<r<h/2,kr1/2, the cross section is of a chamfer type, wherein each leaf spring is a schematic diagram of the shape of both ends of the cross section, as shown in fig. 3. Checking key parameters of clamping rigidity, suspension offset frequency, stress intensity, initial arc height and maximum limit of the plate spring according to design structure parameters, vehicle suspension parameters, allowable stress and maximum allowable stress under impact load of the given unequal-length few-piece oblique line type variable-section plate spring.
In order to solve the technical problem, the invention provides a method for checking key parameters of a non-isometric few-leaf diagonal variable-section leaf spring, which is characterized by adopting the following checking steps:
(1) equivalent width b of root straight section and end straight section of each leaf spring2iAnd b1iThe calculation of (2):
according to the width B of the plate spring, the types of two ends of the cross section and the thickness ratio k of the chamfer radiusr,0≤krNot more than 1/2, the number of the leaf springs is n, and the thickness h of the root straight section of each leaf spring2iAnd the thickness h of the end straight section1iFor the equivalent width b of the root straight section of each leaf spring2iAnd equivalent width b of the end straight section1iMake a calculation where i is 1,2, …, n, i.e.
b2i=B+Dbrh2i;b1i=B+Dbrh1i
In the formula (I), the compound is shown in the specification,
Figure BDA0002805272740000021
is an equivalent width reduction coefficient, wherein k is more than or equal to 0r≤1/2,-0.411≤Dbr≤0。
(2) Clamping rigidity K of unequal-length few-leaf oblique-line-type variable-cross-section plate springCChecking:
step A:root straight section flexibility R of each plate springdriIs calculated by
According to half length L of the plate springTThe U clamping distance of the U is equal to half of the L clamping length of the plate springTU/4, the number n of leaf springs, the length L from the root of the diagonal segment of each leaf spring to the leaf spring end point2xThickness h of straight section of root2iElastic modulus E, b calculated in step (1)2iFor the root straight section flexibility R of each plate springdriMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000022
And B, step: bias line segment flexibility R of each plate springdxiIs calculated by
According to the width B, the elastic modulus E, the number n of the leaf springs and the h of each leaf spring2i,h1i,LXiThe thickness ratio beta of the oblique line segments of each leaf springi=h1i/h2iLength L from end of oblique line segment of each leaf spring to end point of leaf spring1xiConstant of expression of thickness of oblique line segment
Figure BDA0002805272740000023
D obtained by calculation in step (1)br,b2i,b1iAnd the equivalent width ratio lambda of the oblique line segment of each leaf springbi=b1i/b2iFlexibility R of each leaf spring in oblique line sectiondxiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000024
When the two ends of the cross section are right-angled, the radius-thickness ratio k of the chamfer isr0, equivalent width reduction factor Dbr=0,b2i=b1i=B,λi=b1i/b2i1, the oblique line segment flexibility R of each plate springdxiIs composed of
Figure BDA0002805272740000025
C, step C: r from root of end straight section of each leaf spring to end point section of end leaf springd1ciIs calculated by
H of each plate spring according to the number n of the plate springs1i,L1xiDifference DeltaL of half length of each plate springiElastic modulus E, b calculated in step (1)1iFor R of the root of the end straight section of each leaf spring to the end point section of the last leaf springd1ciMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000026
D, step: compliance R of the overlapping section of the last leaf spring of a leaf springdrxcIs calculated by
According to the number n of the plate springs, R calculated in the step AdriR calculated in step BdxiR calculated in step Cd1ciCompliance R of the overlapping section of the last leaf spring of the leaf springdrxcPerform calculations, i.e.
Figure BDA0002805272740000027
E, step E: compliance R of the overlapping section of the end of the leaf spring outside the last leaf springdeIs calculated by
According to the number n of the leaf springs, the number n of the overlapped sections of the leaf spring end parts outside the last leaf springcThickness h of end straight section of front n-1 plate spring1iDifference DeltaL of half length of each plate springiElastic modulus E, b calculated in step (1)1iCompliance R of the overlapping section of the end of the leaf spring outside the last leaf springdePerform calculations, i.e.
Figure BDA0002805272740000031
And F, step: few-leaf oblique-line type plate spring clamping rigidity KCChecking calculation of
According to the R calculated in the step DdrxcR calculated in step EdeClamping stiffness K to leaf springCPerforming check calculations, i.e.
Figure BDA0002805272740000032
(3) Checking the stress intensity of the unequal-length few-leaf oblique line type variable-section plate spring:
i, step: bending moment load sharing M of each plate springiIs calculated by
According to half length L of the plate springTU clamping distance of riding bolt and P rated loadNN number of leaf springs, R calculated in step (2) AdriR calculated in step BdxiR calculated in step Cd1ciFor each plate spring, sharing bending moment load MiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000033
II, step (2): root maximum stress sigma of each leaf springmaxiCalculation and intensity checking
According to the number n of the leaf springs, the root h of each leaf spring2iAllowable stress [ sigma ] under rated loadN]B calculated in step (1)2iM calculated in step IiFor root maximum stress σ of each leaf springmaxiPerform calculations, i.e.
Figure BDA0002805272740000034
Will sigmamaxiAnd [ sigma ]N]Making a comparison if σmaxi<[σN]The plate spring satisfies the stress strengthRequiring; otherwise, the leaf spring does not meet the stress strength requirements.
(4) Suspension offset frequency f of unequal-length few-leaf oblique line type variable-section plate spring0Checking:
according to the rated load PNChecking the calculated K in step (2)CFor unequal length few-leaf oblique line type variable cross-section plate spring suspension offset frequency f0Is checked, i.e.
Figure BDA0002805272740000035
F calculated from the check0Design requirement value f of suspension offset frequency0RMaking a comparison if f0=f0RIf not, the suspension offset frequency does not meet the design requirement value.
(5) Initial arc height H of unequal-length few-leaf oblique line type variable-section plate springgCChecking:
according to the rated load PNInitial arc height design value HgCdesK obtained by checking in step (2)CFor the initial arc height H of the unequal length few-leaf oblique line type variable cross-section plate springgCdesAnd residual arc height H under rated loadgsyIs checked, i.e.
Figure BDA0002805272740000036
H calculated by checkinggsyDesign requirement value H of residual arc heightgsyRMaking a comparison if Hgsy=HgsyRInitial arc height design value HgCdesIs reasonable, otherwise, the initial arc height design value HgCdesIs not reasonable.
(6) Maximum limit deflection f of non-isometric few-leaf oblique line type variable cross-section plate springmaxXChecking:
i, step: maximum allowable load P under impact loadXIs calculated by
According to the maximum limit deflection design value fmaxXdesChecking the calculated K in step (2)CMaximum allowable load P under impact loadXPerform calculations, i.e.
PX=KCfmaxXdes
ii, step: maximum impact bending moment M shared by each leaf spring under maximum limit deflectionXi
According to half length L of the plate springTU clamping distance of the horseback bolt, n number of leaf spring pieces, and R calculated in the step (2) AdriR calculated in step BdxiR calculated in step Cd1ciP calculated in step iXFor each plate spring, sharing bending moment load MXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000041
And iii, step (ii): maximum limit deflection fmaxXRoot maximum impact stress sigma of lower leaf springsXiAnd checking
H of each plate spring according to the number n of the plate springs2iMaximum allowable stress [ sigma ] under impact loadX]B calculated in step (1)2iIi M calculated in stepXiFor the maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000042
Will calculate the obtained sigmaXiAnd [ sigma ]X]Making a comparison if σXi<[σX]Design value f of maximum limit deflection of plate springmaxXdesThe design requirement of the impact stress strength is met; otherwise, the design value f of the maximum limit deflection of the plate springmaxXdesThe design requirement of impact stress strength is not satisfied.
The invention has the advantages over the prior art
Because the lengths of the inclined line sections and the end parts of the unequal-length few-leaf oblique-line-type variable-section plate springs are unequal, and under the condition of considering the shapes of the two ends of the cross section and the influence on the rigidity, the rigidity calculation of the unequal-length few-leaf oblique-line-type variable-section plate springs and the calculation of the shared load of each leaf spring are very complicated, so that an accurate and reliable checking method for key parameters of the unequal-length few-leaf oblique-line-type variable-section plate springs has not been provided at home and abroad in the prior art. The method can check the clamping rigidity, the suspension offset frequency, the stress intensity, the initial tangent arc height and the maximum limit deflection of the unequal-length few-leaf oblique line type variable-section plate spring according to the design structure parameters, the elastic modulus, the rated load, the allowable stress under the rated load and the maximum allowable stress under the impact load of the given plate spring. As can be seen from the test of examples and prototype machines, the method for checking the key parameters of the variable-section plate spring with the non-equal length and few-leaf oblique lines is correct. The method is utilized to obtain accurate and reliable checking calculation values of key parameters of the unequal length diagonal variable cross-section plate spring, ensure that the key parameters of the clamping rigidity, the suspension offset frequency, the stress intensity, the initial arc height and the maximum limit deflection of the plate spring meet the design requirements of the plate spring and the suspension, and improve the design level of the plate spring and the driving smoothness and safety of a vehicle; meanwhile, the test cost of the product 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 for checking key parameters of a variable cross-section leaf spring with a plurality of unequal length pieces and a plurality of oblique lines;
FIG. 2 is a schematic view of a semi-symmetrical structure of a variable cross-section leaf spring with a plurality of oblique sheets of unequal length;
fig. 3 is a schematic diagram of the shapes of both ends of the cross section of a variable section plate spring of a non-equal length few-leaf oblique line type.
Detailed Description
The present invention will be described in further detail by way of examples.
The first embodiment is as follows: the width B of some unequal-length few-leaf oblique line type variable-section plate spring is known to be 70mm, and the elastic dieThe quantity E is 206GPa, the number n of plate springs is 3, and the half length L of the plate springT650mm, U100 mm, half L of the first leaf springT-U/4-625 mm, wherein the effective length L of the root flat section2The length L from the root of each inclined line segment of each leaf spring to the end point of the leaf spring is 25mm2x=L-L2600 mm. Root straight section thickness h of each plate spring2iI.e. h21=16mm,h22=h2315mm, the thickness h of the end straight section of each leaf spring1iI.e. h11=10mm,h12=h139mm, the oblique line section thickness ratio beta of each plate spring1=0.625,β2=β30.6. Length L of straight end portion of each leaf spring1iI.e. L11=220mm,L12=L13110 mm. Length L of oblique line of each leaf springX1=380mm,LX2=352.5mm,LX3325mm, the length L from the end of each oblique line segment of the leaf spring to the end point of the leaf spring1xi=L2x-LXiI.e. L1x1=220mm,L1x2=247.5mm,L1x3275.0 mm. Clamping length L of each leaf springci=L2+LXi+L1iI.e. Lc1=625mm,Lc2=487.5mm,Lc3460mm, half the length difference DeltaL of each leaf springi=Lci-Lci+1I.e. Δ L1=137.5mm,ΔL227.5 mm. The two ends of the cross section of the plate spring are arc-shaped, namely the radius-thickness ratio k of the chamferr1/2. Rated load P of plate springN10651N, the design value requirement f of the suspension offset frequency0R1.9Hz, initial arc height design value HgCdes98.8mm, a design requirement value H of high residual arc of plate spring under rated loadgsyR30mm, allowable stress [ sigma ] of plate spring under rated loadN]Maximum allowable stress [ sigma ] under impact load at 500MPaX]700MPa, design value f of maximum limit deflectionmaxXdes99.7 mm. According to the design structure parameters, the elastic modulus, the rated load, the allowable stress under the rated load and the impact load of the given plate springAnd checking and calculating the clamping rigidity, the suspension offset frequency, the stress intensity, the initial tangent arc height and the maximum limiting deflection of the unequal-length few-leaf oblique-line-type variable-section plate spring to obtain the maximum allowable stress.
The checking method for the key parameters of the unequal-length few-leaf oblique line type variable-section leaf spring provided by the embodiment of the invention has the checking flow as shown in figure 1, and specifically comprises the following checking steps:
(1) equivalent width b of root straight section and end straight section2iAnd b1iThe calculation of (2):
according to the width B of the plate spring being 70mm, the number n of the plate springs being 3, the thickness h of the root straight section of each plate spring21=16mm,h22=h2315mm, the thickness h of the end straight section of each leaf spring11=10mm,h12=h139mm, and the radius-thickness ratio k of the chamfer is arc-shaped at two ends of the cross sectionr1/2, the equivalent width b of each flat section of the root of each leaf spring of the unequal few-leaf oblique line type variable cross-section leaf spring2iEquivalent width b of straight end section1iPerform calculations, i.e.
b2i=B+Dbrh2i;b1i=B+Dbrh1i
In the formula (I), the compound is shown in the specification,
Figure BDA0002805272740000051
wherein, b21=63.4mm,b22=b23=63.8mm;b11=65.9mm,b12=b13=66.3mm;
(2) Unequal-length few-leaf oblique-line-type variable-cross-section plate spring clamping rigidity KCChecking:
step A: root straight section flexibility R of each plate springdriIs calculated by
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, U100 mm, half L of the first leaf springT-625 mm, length L from root of oblique line segment to end point of leaf spring2xH of each leaf spring being 600mm21=16mm,h22=h23=15mm,Elastic modulus E206 GPa, calculated in step (1)21=63.4mm,b22=b23Flexibility R of root straight section of each plate spring is 63.8mmdriMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000052
Wherein R isdr1=1.052×10-3mm/N,Rdr2=Rdr3=1.268×10-3mm/N,
And B, step: bias line segment flexibility R of each plate springdxiIs calculated by
According to the width B of the plate spring being 70mm, the elastic modulus E being 206GPa, the number n of the plate springs being 3, h of each plate spring21=16mm,h22=h23=15mm;h11=10mm,h12=h13=9mm;L2x600mmm, length L from end of oblique line segment of each leaf spring to end point of leaf spring1x1=220mm,L1x2=247.5mm,L1x3275.0mm, length L of oblique line of each leaf springX1=380mm,LX2=352.5mm,LX3325 mm; constant of thickness expression of inclined line segment of each leaf spring
Figure BDA0002805272740000053
I.e. Ch1=6.5mm,Ch2=4.8mm,Ch33.9mm, the thickness ratio beta of the oblique line segments of each leaf spring1=0.625,β2=β3D calculated in step (1) when equal to 0.6br=-0.411,b21=63.4mm,b22=b23=63.8mm;b11=65.9mm,b12=b1366.3 mm; equivalent width ratio lambda of inclined line segment of each leaf springbi=b1i/b2iI.e. λb1=λb2=λb3When the total number of leaf springs is 1.0386, i is 1,2, …, n, the flexibility of the oblique line section of each leaf spring is calculated, namely
Figure BDA0002805272740000061
Namely Rdx1=1.264×10-2mm/N,Rdx2=1.597×10-2mm/N,Rdx3=1.586×10-2mm/N;
C, step C: flexibility R of root of end straight section of each leaf spring to end point section of last leaf springd1ciIs calculated by
The spring modulus E is 206GPa, and h of each plate spring is calculated according to the number n of the plate springs to be 3 and the elastic modulus E to be 206GPa11=10mm,h12=h139mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL2L of each leaf spring of 27.5mm1x1=220mm,L1x2=247.5mm,L1x3275mm, b calculated in step (1)11=65.9mm,b12=b1366.3 mm; r for the root of the end straight section of each leaf spring to the end point section of the last leaf springd1ciMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000062
Wherein R isd1c1=0.907×10-3mm/N,Rd1c2=2.142×10-3mm/N,Rd1c3=3.274×10-3mm/N,
D, step: compliance R of the overlapping section of the last leaf spring of a leaf springdrxcIs calculated by
According to the number n of the plate springs being 3, R calculated in the step Adr1=1.052×10-3mm/N,Rdr2=Rdr3=1.268×10-3mm/N, R calculated in step Bdx1=1.264×10-2mm/N,Rdx2=1.597×10-2mm/N,Rdx3=1.586×10-2R calculated in mm/N, C stepd1c1=0.907×10-3mm/N,Rd1c2=2.142×10-3mm/N,Rd1c3=3.274×10-3mm/N, for overlapping sections of the last leaf springs of the leaf springsCompliance RdrxcPerform calculations, i.e.
Figure BDA0002805272740000063
E, step E: compliance R of the overlapping section of the end of the leaf spring outside the last leaf springdeIs calculated by
According to the number n of the leaf springs being 3, the number n of the leaf springs at the overlapping section of the leaf spring end outside the last leaf springcThe thickness h of the end straight section of the front 2 plate springs is equal to n-1 and 211=10mm,h129mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL227.5mm, modulus of elasticity E206 GPa, calculated in step (1)11=65.9mm,b12Compliance R of the overlapping section of the end of the leaf spring outside the last leaf spring of 66.3mmdePerform calculations, i.e.
Figure BDA0002805272740000064
And F, step: leaf spring clamping stiffness KCChecking calculation of
According to the R calculated in the step Ddrxc=5.9142×10-3mm/N, R calculated in step Ede=5.4372×10-4mm/N, clamping stiffness K for leaf springCPerforming check calculations, i.e.
Figure BDA0002805272740000065
(3) Checking the stress intensity of the unequal-length few-leaf oblique line type variable-section plate spring:
i, step: bending moment load sharing M of each plate springiIs calculated by
According to half length L of the plate springT650mm, 100mm clamping distance U of riding bolt, and rated load PN10651N, the number of leaf spring pieces N being 3, R calculated in step (2) adr1=1.052×10-3mm/N,Rdr2=Rdr3=1.268×10-3mm/N, R calculated in step Bdx1=1.264×10-2mm/N,Rdx2=1.597×10-2mm/N,Rdx3=1.586×10-2R calculated in mm/N, C stepd1c1=0.907×10-3mm/N,Rd1c2=2.142×10-3mm/N,Rd1c3=3.274×10-3mm/N, bending moment load M shared by each plate springiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000071
Wherein M is1=2.588×103N.m,M2=1.9499×103N.m,M3=1.8525×103N.m。
II, step (2): root maximum stress sigma of each leaf springmaxiCalculation and intensity checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h23Allowable stress [ sigma ] at rated load of 15mmN]B calculated in step (1) at 500MPa21=63.4mm,b22=b23M calculated in step I, 63.8mm1=2.588×103N.m,M2=1.9499×103N.m,M3=1.8525×103N.m. root maximum stress σ to each leaf springmaxiPerform calculations, i.e.
Figure BDA0002805272740000072
Wherein σmax1=478.18MPa,σmax2=407.28MPa,σmax3=386.92MPa,
As can be seen, σmaxi<[σN]And the plate spring meets the design requirement of stress strength.
(4) Unequal length few-leaf oblique line type variable cross-section plate spring suspension offset frequency f0Checking:
according to the rated load PNChecking the calculated K in step (2) 10651NCChecking the bias frequency of the variable cross-section plate spring suspension with unequal length and few inclined pieces when the suspension is 154.89N/mm, namely
Figure BDA0002805272740000073
Checking the value f of the suspension offset frequency0And the design requirement value f0RBy contrast, it can be seen that f0=f0RThe bias frequency of the variable cross-section plate spring suspension with the unequal length and few pieces of oblique lines meets the design requirement value because the bias frequency of the variable cross-section plate spring suspension with the unequal length and few pieces of oblique lines is 1.9 Hz.
(5) Initial arc height H of unequal-length few-leaf oblique line type variable-section plate springgCChecking:
according to the rated load PN10651N, initial arc height set value HgCdesChecking the obtained K in step (2) at 98.8mmCThe initial arc height design value H of the unequal length few-leaf oblique line type variable cross-section plate spring is 154.89N/mmgCdesAnd residual arc height H under rated loadgsyIs checked, i.e.
Figure BDA0002805272740000074
H calculated by checkinggsy30mm and the design requirement value HgsyRWhen the thickness of the film was compared with 30mm, H was foundgsy=HgsyRTherefore, the design value of the initial arc height of the plate spring is reasonable, and the design requirement value of the residual arc height under the rated load is met.
(6) Maximum limit deflection f of non-isometric few-leaf oblique line type variable cross-section plate springmaxXChecking:
i, step: maximum allowable load P under impact loadXIs calculated by
According to the maximum limit deflection design value fmaxXdesChecking the calculated K in step (2) at 99.7mmC154.89N/mm, maximum allowable load P under impact loadXIs checked, i.e.
PX=KCfmaxXdes=15436N。
ii, step: maximum impact bending moment M shared by each leaf spring under maximum limit deflectionXi
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, and 100mm as the U clamping distance of the saddle bolt, and R calculated in step (2) adr1=1.052×10-3mm/N,Rdr2=Rdr3=1.268×10-3mm/N, R calculated in step Bdx1=1.264×10-2mm/N,Rdx2=1.597×10-2mm/N,Rdx3=1.586×10-2R calculated in mm/N, C stepd1c1=0.907×10-3mm/N,Rd1c2=2.142×10-3mm/N,Rd1c3=3.274×10-3P calculated in mm/N, i stepX15436N, the moment load M is shared by the leaf springsXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000081
Wherein M isX1=3.7509×103N.m,MX2=2.8261×103N.m,MX3=2.6848×103N.m。
And iii, step (ii): maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXiAnd checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h23Maximum allowable stress [ sigma ] under impact load of 15mmX]700MPa, b calculated in step (1)21=63.4mm,b22=b23M calculated in step ii of 63.8mmX1=3.7509×103N.m,MX2=2.8261×103N.m,MX3=2.6848×103N.m. design value f for maximum limit deflectionmaxXdesRoot maximum impact stress sigma of lower leaf springsXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000082
Wherein σX1=693.05MPa,σX2=590.28MPa,σX3=560.78MPa,
It can be seen that the maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXi<[σX]Therefore, the design value of the maximum limit deflection of the plate spring is reasonable, and the maximum allowable stress [ sigma ] under the impact load is satisfiedX]The design requirements of (2).
Example two: the known variable-section plate spring with a few inclined pieces of unequal length has the same structural parameters as those of the first embodiment except for the shapes of two ends of the cross section, the rated load, the initial arc height and the maximum limit deflection. Wherein, both ends of the cross section of the plate spring are chamfer-shaped, and the radius-thickness ratio k of the chamfer isr1/4. Rated load P of plate springN11217N, design value f of maximum limit deflectionmaxXdes101.0 mm. And checking and calculating the clamping rigidity, the suspension offset frequency, the stress intensity, the initial tangent arc height and the maximum limit deflection of the unequal-length few-leaf oblique line type variable-section plate spring according to the design structure parameters, the elastic modulus, the rated load, the allowable stress under the rated load and the maximum allowable stress under the impact load of the given plate spring.
The embodiment of the invention adopts the checking step of the first embodiment to check the unequal length few-leaf diagonal variable section plate spring, and the specific checking step is as follows:
(1) equivalent width b of root straight section and end straight section2iAnd b1iThe calculation of (2):
according to the width B of the plate spring being 70mm, the chamfer radius thickness ratio k at the two ends of the cross sectionr1/4, the number n of the leaf springs is 3, and the thickness h of the root straight section of each leaf spring21=16mm,h22=h2315mm, the ends of each leaf spring are straightSection thickness h11=10mm,h12=h13Equal to 9mm, equal width b of each flat section of root of each leaf spring of unequal few-leaf oblique line type variable cross-section leaf spring2iEquivalent width b of straight end section1iPerform calculations, i.e.
b2i=B+Dbrh2i;b1i=B+Dbrh1i
In the formula (I), the compound is shown in the specification,
Figure BDA0002805272740000083
wherein, b21=67.9mm,b22=b23=68.1mm;b11=68.7mm,b12=b13=68.8mm;
(2) Unequal-length few-leaf oblique-line-type variable-cross-section plate spring clamping rigidity KCChecking:
step A: root straight section flexibility R of each plate springdriIs calculated by
According to half length L of the plate springT650mm, U100 mm, and L, half of the leaf springT-U/4-625 mm, E-206 GPa, n-3 leaf springs, h of each leaf spring21=16mm,h22=h2315mm, length L from the root of the oblique line section to the end point of the plate spring2xB calculated in step (1) at 600mm21=67.9mm,b22=b23Flexibility R of root straight section of each plate spring is 68.1mmdriMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000084
Wherein R isdr1=0.982×10-3mm/N,Rdr2=Rdr3=1.189×10-3mm/N,
And B, step: bias line segment flexibility R of each plate springdxiIs calculated by
According to the width B of the plate spring being 70mm, the elastic modulus E being 206GPa, the number n of the plate springs being 3, h of each plate spring21=16mm,h22=h23=15mm;h11=10mm,h12=h139 mm; the length L from the root of the oblique line section of each plate spring to the plate spring2x600mmm, L from the end of each leaf spring oblique line segment to the leaf spring end point1x1=220mm,L1x2=247.5mm,L1x3275.0 mm; length L of oblique line of each leaf springX1=380mm,LX2=352.5mm,LX3325 mm. Constant of thickness expression of inclined line segment of each leaf spring
Figure BDA0002805272740000091
I.e. Ch1=6.5mm,Ch2=4.8mm,Ch33.9mm, the thickness ratio beta of the oblique line segments of each leaf spring1=0.625,β2=β3D calculated in step (1) when equal to 0.6br=-0.1284,b21=67.9mm,b22=b23=68.1mm;b11=68.7mm,b12=b1368.8mm, the equivalent width ratio lambda of each leaf spring oblique line segmentb1=λb2=λb3When the total number of leaf springs is 1.0113, i is 1,2, …, n, the flexibility of the oblique line section of each leaf spring is calculated, namely
Figure BDA0002805272740000092
Namely Rdx1=1.195×10-2mm/N,Rdx2=1.517×10-2mm/N,Rdx3=1.507×10-2mm/N;
C, step C: r from root of end straight section of each leaf spring to end point section of last leaf springd1ciIs calculated by
The spring modulus E is 206GPa, and h of each plate spring is calculated according to the number n of the plate springs to be 3 and the elastic modulus E to be 206GPa11=10mm,h12=h139mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL2L of each leaf spring of 27.5mm1x1=220mm,L1x2=247.5mm,L1x3275mm, b calculated in step (1)11=68.7mm,b12=b1368.8 mm; r for the root of the end straight section of each leaf spring to the end point section of the last leaf springd1ciMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000093
Wherein R isd1c1=0.869×10-3mm/N,Rd1c2=2.063×10-3mm/N,Rd1c3=3.153×10-3mm/N,
D, step: compliance R of the overlapping section of the last leaf spring of a leaf springdrxcIs calculated by
According to the number n of the plate springs being 3, R calculated in the step Adr1=0.982×10-3mm/N,Rdr2=Rdr3=1.189×10-3mm/N, R calculated in step Bdx1=1.195×10-2mm/N,Rdx2=1.517×10-2mm/N,Rdx3=1.507×10-2R calculated in mm/N, C stepd1c1=0.869×10-3mm/N,Rd1c2=2.063×10-3mm/N,Rd1c3=3.153×10-3mm/N, flexibility R of overlapping section of last leaf spring of leaf springdrxcPerform calculations, i.e.
Figure BDA0002805272740000094
E, step E: compliance R of the overlapping section of the end of the leaf spring outside the last leaf springdeIs calculated by
According to the number n of the plate springs being 3, the elastic modulus E being 206GPa, the number n of the overlapped sections of the end parts of the plate spring outside the last plate springcThe thickness h of the end straight section of the front 2 plate springs is equal to n-1 and 211=10mm,h129mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL2B calculated in step (1) 27.5mm11=68.7mm,b1268.8mm, and the end part of the plate spring outside the last plate spring is weightedCompliance R of the stackdePerform calculations, i.e.
Figure BDA0002805272740000095
And F, step: leaf spring clamping stiffness KCChecking calculation of
According to the R calculated in the step Edrxc=5.6106×10-3R calculated in mm/N, F stepde=5.2165×10-4mm/N, clamping stiffness K for leaf springCPerforming check calculations, i.e.
Figure BDA0002805272740000096
(3) Checking the stress intensity of the unequal-length few-leaf oblique line type variable-section plate spring:
i, step: bending moment load sharing M of each plate springiIs calculated by
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, 100mm clamping distance U of the saddle bolt, and rated load P of the plate springN11217N, R calculated in step (2) adr1=0.982×10-3mm/N,Rdr2=Rdr3=1.189×10-3mm/N, R calculated in step Bdx1=1.195×10-2mm/N,Rdx2=1.517×10-2mm/N,Rdx3=1.507×10-2R calculated in mm/N, C stepd1c1=0.869×10-3mm/N,Rd1c2=2.063×10-3mm/N,Rd1c3=3.153×10-3mm/N, bending moment load M shared by each plate springiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000101
Wherein M is1=2.7358×103N.m,M2=2.0493×103N.m,M3=1.9448×103N.m。
II, step (2): root maximum stress sigma of each leaf springmaxiCalculation and intensity checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h2315mm, allowable stress [ sigma ]N]B calculated in step (1) at 500MPa21=67.9mm,b22=b23M calculated in step I, 68.1mm1=2.7358×103N.m,M2=2.0493×103N.m,M3=1.9448×103N.m. root maximum stress σ to each leaf springmaxiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000102
Wherein σmax1=471.86MPa,σmax2=401.39MPa,σmax3=380.92MPa,
As can be seen, σmaxi<[σN]The leaf spring meets the stress strength requirements under rated load.
(4) Unequal length few-leaf oblique line type variable cross-section plate spring suspension offset frequency f0Checking:
according to the rated load PN11217N, checking the calculated K in step (2)C163.12N/mm, offset frequency f for unequal length small piece oblique line type variable cross section plate spring suspension0Is checked, i.e.
Figure BDA0002805272740000103
Checking the value f of the suspension offset frequency0Design requirement value f of suspension offset frequency0RBy comparison, it is found that f0=f0RThe bias frequency of the variable cross-section plate spring suspension with unequal length and few inclined sheets meets the design requirement value because the bias frequency of the variable cross-section plate spring suspension with unequal length and few inclined sheets is 1.9 Hz.
(5) Initial arc height H of unequal-length few-leaf oblique line type variable-section plate springgCChecking:
according to the rated load PN11217N, initial arc height design value HgCdesChecking the obtained K in step (2) at 98.8mmC163.12N/mm, initial arc height H for unequal length small piece oblique line type variable section plate springgCdesAnd residual arc height H under rated loadgsyIs checked, i.e.
Figure BDA0002805272740000104
Checking the calculated value H of the residual arc heightgsyAnd the design requirement value HgsyRBy comparison, H is knowngsy=HgsyRThe initial arc height design value of the unequal length few-leaf oblique line type variable cross-section plate spring is reasonable and meets the design requirement of the residual arc height under the rated load.
(6) Maximum limit deflection f of non-isometric few-leaf oblique line type variable cross-section plate springmaxXChecking:
i, step: maximum allowable load P under impact loadXIs calculated by
According to the maximum limit deflection design value fmaxXdesChecking the calculated K in step (2) at 101.0mmC163.12N/mm, maximum allowable load P under impact loadXIs checked, i.e.
PX=KCfmaxXdes=16477N。
ii, step: maximum impact bending moment M shared by each leaf spring under maximum limit deflectionXi
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, and 100mm as the U clamping distance of the saddle bolt, and R calculated in step (2) adr1=0.982×10-3mm/N,Rdr2=Rdr3=1.189×10-3mm/N, R calculated in step Bdx1=1.195×10-2mm/N,Rdx2=1.517×10-2mm/N,Rdx3=1.507×10-2R calculated in mm/N, C stepd1c1=0.869×10-3mm/N,Rd1c2=2.063×10-3mm/N,Rd1c3=3.153×10-3P calculated in mm/N, i stepX16477N, the bending moment load M is shared by each plate springXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000111
Wherein M isX1=4.0188×103N.m,MX2=3.0103×103N.m,MX3=2.8586×103N.m。
And iii, step (ii): maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXiAnd checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h2315mm, maximum allowable stress [ sigma ] under impact loadX]700MPa, b calculated in step (1)21=67.9mm,b22=b2368.1mm, M calculated in step iiX1=4.0188×103N.m,MX2=3.0103×103N.m,MX3=2.8586×103N.m, design value f for maximum limiting deflectionmaxXdesRoot maximum impact stress sigma of lower leaf springsXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000112
Wherein σX1=693.14MPa,σX2=589.62MPa,σX3=559.55MPa,
It can be seen that the maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXi<[σX]Therefore, the design value of the maximum limit deflection of the plate spring is reasonable, and the maximum allowable stress [ sigma ] under the impact load is metX]The design requirements of (2).
Example three: the known variable-section plate spring with a few inclined pieces of unequal length has the same structural parameters as those of the first embodiment except for the shapes of two ends of the cross section, the rated load, the initial arc height and the maximum limit deflection. Wherein, the two ends of the cross section of the plate spring are right-angled, and the radius-thickness ratio k of the chamfer angler0; rated load P of plate springN11473N, design initial arc height H of plate springgCdes98.8mm, design value f of maximum limit deflectionmaxXdes101.6 mm. And checking and calculating the clamping rigidity, the suspension offset frequency, the stress intensity, the initial tangent arc height and the maximum limit deflection of the unequal-length few-leaf oblique line type variable-section plate spring according to the design structure parameters, the elastic modulus, the rated load, the allowable stress under the rated load and the maximum allowable stress under the impact load of the given plate spring.
The embodiment of the invention adopts the checking step of the first embodiment to check the unequal-length few-leaf diagonal variable-section plate spring, and the specific checking step comprises the following steps:
(1) equivalent width b of root straight section and end straight section2iAnd b1iIs calculated by
According to the width B of the plate spring being 70mm, the number n of the plate spring being 3, and the two ends of the cross section being right-angled, namely the chamfer radius thickness ratio kr0, so that the root of each leaf spring has the equivalent width b of the straight section2iEquivalent width b of straight end section1iAre all equal to the leaf spring width B, i.e.
b2i=B;b1i=B,
Wherein, b21=b22=b23=70mm;b11=b12=b13=70mm;
(2) Unequal-length few-leaf oblique-line-type variable-cross-section plate spring clamping rigidity KCChecking:
step A: root straight section flexibility R of each plate springdriIs calculated by
According to half length L of the plate springT650mm, U100 mm, and L, half of the leaf springT-U/4-625 mm, modulus of elasticity E-206 GPa, number of leaf springs n-3, eachLength L from oblique line section root of leaf spring to leaf spring end point2x600mm, root straight section thickness h of each leaf spring21=16mm,h22=h23B calculated in step (1) 15mm21=b22=b2370mm, and the compliance R of the root straight section of each plate springdriMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000121
Wherein R isdr1=0.953×10-3mm/N,Rdr2=Rdr3=1.156×10-3mm/N,
And B, step: bias line segment flexibility R of each plate springdxiIs calculated by
According to the width B of the plate spring being 70mm, the cross section is right-angled, i.e. the chamfer radius thickness ratio kr0, 206GPa, 3 and h for each plate spring21=16mm,h22=h23=15mm;h11=10mm,h12=h139 mm; length L of oblique line of each leaf springX1=380mm,LX2=352.5mm,LX3325 mm; the length L from the root of the oblique line section of each plate spring to the plate spring2x600mmm, length L from end of oblique line segment of each leaf spring to end point of leaf spring1x1=220mm,L1x2=247.5mm,L1x3275.0mm, constant C of thickness expression of oblique line segment of each leaf springh1=6.5mm,Ch2=4.8mm,Ch33.9mm, the thickness ratio beta of the oblique line segments of each leaf spring1=0.625,β2=β3The oblique line segment flexibility of each leaf spring is calculated as 0.6, i is 1,2, …, n, that is
Figure BDA0002805272740000122
Namely Rdx1=1.166×10-2mm/N,Rdx2=1.484×10-2mm/N,Rdx3=1.474×10-2mm/N,
C, step C: r from root of end straight section of each leaf spring to end point section of last leaf springd1ciIs calculated by
The spring modulus E is 206GPa, and h of each plate spring is calculated according to the number n of the plate springs to be 3 and the elastic modulus E to be 206GPa11=10mm,h12=h139mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL2L of each leaf spring of 27.5mm1x1=220mm,L1x2=247.5mm,L1x3275mm, b calculated in step (1)11=b12=b1370 mm; b, calculating R of the root part of the end straight section of each plate spring to the end point partial section of the last plate spring obtained in the step Bd1ciMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000123
Wherein R isd1c1=0.854×10-3mm/N,Rd1c2=2.029×10-3mm/N,Rd1c3=3.101×10-3mm/N,
D, step: compliance R of the overlapping section of the last leaf spring of a leaf springdrxcIs calculated by
According to the number n of the plate springs being 3, R calculated in the step Adr1=0.953×10-3mm/N,Rdr2=Rdr3=1.156×10-3mm/N, R calculated in step Bdx1=1.166×10-2mm/N,Rdx2=1.484×10-2mm/N,Rdx3=1.474×10-2R calculated in mm/N, C stepd1c1=0.854×10-3mm/N,Rd1c2=2.029×10-3mm/N,Rd1c3=3.101×10-3mm/N, flexibility R of overlapping section of last leaf spring of leaf springdrxcPerform calculations, i.e.
Figure BDA0002805272740000124
E, step E: compliance R of the overlapping section of the end of the leaf spring outside the last leaf springdeIs calculated by
According to the number n of the leaf springs being 3, the number n of the leaf springs at the overlapping section of the leaf spring end outside the last leaf springcThe thickness h of the end straight section of the front 2 plate springs is equal to n-1 and 211=10mm,h129mm, the difference DeltaL of half the length of each leaf spring1=137.5mm,ΔL227.5mm, modulus of elasticity E206 GPa, calculated in step (1)11=b12Compliance R of 70mm to the overlapping section of the end of the leaf spring outside the last leaf springdePerform calculations, i.e.
Figure BDA0002805272740000125
And F, step: leaf spring clamping stiffness KCChecking calculation of
According to the R calculated in the step Ddrxc=5.4828×10-3mm/N, R calculated in step Ede=5.1219×10-4mm/N, clamping stiffness K for leaf springCPerforming check calculations, i.e.
Figure BDA0002805272740000131
(3) Checking the stress intensity of the unequal-length few-leaf oblique line type variable-section plate spring:
i, step: bending moment load sharing M of each plate springiIs calculated by
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, 100mm clamping distance U of riding bolt, and rated load PNR calculated in step (2) a when 11473N is satisfieddr1=0.953×10-3mm/N,Rdr2=Rdr3=1.156×10-3mm/N, R calculated in step Bdx1=1.166×10-2mm/N,Rdx2=1.484×10-2mm/N,Rdx3=1.474×10-2mm/N, C in stepCalculated Rd1c1=0.854×10-3mm/N,Rd1c2=2.029×10-3mm/N,Rd1c3=3.101×10-3mm/N, bending moment load M shared by each plate springiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000132
Wherein M is1=2.8029×103N.m,M2=2.0944×103N.m,M3=1.9867×103N.m。
II, step (2): root maximum stress sigma of each leaf springmaxiCalculation and intensity checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h2315mm, allowable stress [ sigma ]N]B calculated in step (1) at 500MPa21=b22=b2370mm, M calculated in step I1=2.8029×103N.m,M2=2.0944×103N.m,M3=1.9867×103N.m. root maximum stress σ to each leaf springmaxiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000133
Wherein σmax1=469.23MPa,σmax2=398.93MPa,σmax3=378.42MPa,
As can be seen, σmaxi<[σN]The leaf spring meets the design requirements for stress strength under rated load.
(4) Unequal length few-leaf oblique line type variable cross-section plate spring suspension offset frequency f0Checking:
according to the rated load PNChecking the calculated K in step (2) 11473NC166.85N/mm, offset frequency f for unequal length small piece oblique line type variable cross section plate spring suspension0Check is carried outIs calculated, i.e.
Figure BDA0002805272740000134
Is known as f0=f0RThe suspension offset frequency of the unequal length few-leaf oblique line type variable cross-section plate spring meets the design requirement value when the suspension offset frequency is 1.9 Hz.
(5) Initial arc height H of unequal-length few-leaf oblique line type variable-section plate springgCChecking:
according to the rated load PN11473N, residual arc height design requirement H under rated loadgsyR30mm, design value H of initial arc heightgCdesChecking the obtained K in step (2) at 98.8mmC166.85N/mm, initial arc height H for unequal length small piece oblique line type variable section plate springgCAnd residual arc height H under rated loadgsyIs checked, i.e.
Figure BDA0002805272740000135
Can know Hgsy=HgsyR30mm, therefore, the design value of the initial arc height of the plate spring is reasonable, and the design requirement of the residual arc height under the rated load is met.
(6) Maximum limit deflection f of non-isometric few-leaf oblique line type variable cross-section plate springmaxXChecking:
i, step: maximum allowable load P under impact loadXIs calculated by
According to the maximum limit deflection design value fmaxXdesChecking the calculated K in step (2) at 101.6mmC166.85N/mm, maximum allowable load P under impact loadXIs checked, i.e.
PX=KCfmaxXdes=16949N。
ii, step: maximum impact bending moment M shared by each leaf spring under maximum limit deflectionXi
Half the length L of the plate spring according to the number n of the plate springs being 3T650mm, and 100mm as the U clamping distance of the saddle bolt, and R calculated in step (2) adr1=0.953×10-3mm/N,Rdr2=Rdr3=1.156×10-3mm/N, R calculated in step Bdx1=1.166×10-2mm/N,Rdx2=1.484×10-2mm/N,Rdx3=1.474×10-2R calculated in mm/N, C stepd1c1=0.854×10-3mm/N,Rd1c2=2.029×10-3mm/N,Rd1c3=3.101×10-3P calculated in mm/N, i stepX16949N, bending moment load M is shared by each plate springXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000141
Wherein M isX1=4.1406×103N.m,MX2=3.0939×103N.m,MX3=2.9348×103N.m。
And iii, step (ii): maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of lower leaf springsXiAnd checking
H of each plate spring is 3 according to the number n of the plate springs21=16mm,h22=h2315mm, maximum allowable stress [ sigma ] under impact loadX]700MPa, b calculated in step (1)21=b22=b2370mm, M calculated in step iiX1=4.1406×103N.m,MX2=3.0939×103N.m,MX3=2.9348×103N.m, design value f for maximum limiting deflectionmaxXdesRoot maximum impact stress sigma of lower leaf springsXiMake a calculation where i is 1,2, …, n, i.e.
Figure BDA0002805272740000142
Wherein σX1=693.18MPa,σX2=589.31MPa,σX3=559.01MPa。
It can be seen that the maximum limit deflection design value fmaxXdesRoot maximum impact stress sigma of each leaf spring belowXi<[σX]Therefore, the design value f of the maximum limit deflection of the plate springmaxXdesIs reasonable and meets the maximum allowable stress [ sigma ] under the impact loadX]The design requirements of (2).
According to the plate spring prototype test, the method for checking the key parameters of the unequal length few-leaf oblique line type variable cross-section plate spring is correct, and a reliable technical method is provided for checking the clamping rigidity, the suspension offset frequency, the initial arc height, the stress intensity and the maximum limit deflection of the unequal length oblique line type variable cross-section plate spring. By utilizing the method, the key parameters and strength of the unequal length diagonal variable cross-section plate spring with given design structure parameters can be checked, the clamping rigidity, suspension offset frequency, stress strength and initial arc height of the plate spring and the maximum limit deflection of the plate spring are ensured to meet the design requirements of the plate spring and the suspension, and the design level and performance of the plate spring and the driving smoothness and safety of a vehicle are improved; meanwhile, the test cost of the product is reduced, and the product development speed is accelerated.

Claims (4)

1.一种非等长少片斜线型变截面板簧关键参数的校核方法,其中,各片板簧是由根部平直段、斜线段和端部平直段构成,各片板簧的端部平直段的长度不相等,即非等长少片斜线型变截面板簧;根据所给定板簧的设计结构参数、弹性模量、额定载荷及在额定载荷下的许用应力和在冲击载荷下的最大许用应力,对非等长少片斜线型变截面板簧的夹紧刚度、悬架偏频、应力强度、初始切线弧高和最大限位挠度进行校核;其特征在于包含以下校核步骤:1. A method for checking the key parameters of non-equal-length, slash-type, variable-section leaf springs, wherein each leaf spring is composed of a straight section at the root, an oblique line, and a straight section at the end, and each leaf spring is composed of The lengths of the straight sections at the ends are not equal, that is, the non-equal length and few-piece oblique variable section leaf springs; Stress and the maximum allowable stress under impact load, check the clamping stiffness, suspension bias frequency, stress intensity, initial tangent arc height and maximum limit deflection of non-equal length and few-piece oblique variable section leaf springs ; It is characterized in that comprising the following checking steps: (1)各片板簧的根部平直段和端部平直段的等效宽度b2i和b1i的计算:(1) Calculation of the equivalent widths b 2i and b 1i of the root straight section and the end straight section of each leaf spring: (2)非等长少片斜线型变截面板簧的夹紧刚度KC的校核:(2) Checking the clamping stiffness K C of the non-equal length and few-piece oblique variable section leaf spring: (3)非等长少片斜线型变截面板簧应力强度的校核;(3) Checking the stress strength of non-equal-length and few-piece oblique variable-section leaf springs; (4)非等长少片斜线型变截面板簧悬架偏频的校核;(4) Check the offset frequency of the non-equal-length and few-piece slash-type variable-section leaf spring suspension; (5)非等长少片斜线型变截面板簧的初始弧高HgC的校核:(5) Checking the initial arc height H gC of the non-equal length and few-piece oblique variable section leaf spring: (6)非等长少片斜线型变截面板簧的最大限位挠度fmaxX的校核。(6) Check the maximum limit deflection f maxX of the non-equal-length and few-piece oblique variable-section leaf springs. 2.根据权利要求1的步骤(2)所述的非等长少片斜线型变截面板簧的夹紧刚度KC的校核,其特征在于采用以下校核步骤:2. The checking of the clamping rigidity K C of the described non-equal length few-piece oblique variable section leaf spring according to the step (2) of claim 1, it is characterized in that adopting the following checking steps: A步骤:各片板簧的根部平直段柔度Rdri的计算Step A: Calculation of the flexibility R dri of the root straight section of each leaf spring 根据板簧的一半长度LT,骑马螺栓夹紧距U,板簧的一半夹紧长度L=LT-U/4,板簧片数n,各片板簧的斜线段的根部到板簧端点的长度L2x,根部平直段厚度h2i,弹性模量E,步骤(1)中计算得到的b2i,对各片板簧的根部平直段柔度Rdri进行计算,i=1,2,…,n,即According to the half length L T of the leaf spring, the clamping distance U of the riding bolt, the half clamping length of the leaf spring L=L T -U/4, the number of leaf springs n, the root of the oblique line segment of each leaf spring to the leaf spring The length L 2x of the end point, the thickness h 2i of the straight section at the root, the elastic modulus E, and the b 2i calculated in step (1), calculate the flexibility R dri of the straight section at the root of each leaf spring, i=1 ,2,…,n, i.e.
Figure FDA0002805272730000011
Figure FDA0002805272730000011
B步骤:各片板簧的斜线段柔度Rdxi的计算Step B: Calculation of the oblique line segment compliance R dxi of each leaf spring 根据板簧宽度B,弹性模量E,板簧片数n,各片板簧的h2i,h1i,LXi,各片板簧斜线段的厚度比βi=h1i/h2i,各片板簧斜线段的端部到板簧端点的长度L1xi,斜线段厚度表达式的常数
Figure FDA0002805272730000012
权利要求1的步骤(1)中计算得到的Dbr,b2i,b1i,及各片板簧斜线段的等效宽度比λbi=b1i/b2i,对各片板簧的斜线段柔度Rdxi进行计算,i=1,2,…,n,即
According to the width B of the leaf spring, the elastic modulus E, the number of leaf springs n, the h 2i , h 1i , L Xi of each leaf spring, the thickness ratio β i =h 1i /h 2i of each leaf spring slanted line segment, each The length L 1xi from the end of the oblique segment of the leaf spring to the end point of the leaf spring, the constant of the expression for the thickness of the oblique segment
Figure FDA0002805272730000012
D br , b 2i , b 1i calculated in step (1) of claim 1, and the equivalent width ratio λ bi =b 1i /b 2i of the oblique line segment of each leaf spring, for the oblique line segment of each leaf spring The flexibility R dxi is calculated, i=1,2,...,n, that is
Figure FDA0002805272730000013
Figure FDA0002805272730000013
当横截面两端形状为直角时,倒角半径厚度比kr=0,等效宽度缩减系数Dbr=0,b2i=b1i=B,λi=b1i/b2i=1,则各片板簧的斜线段柔度RdxiWhen the shape of both ends of the cross section is a right angle, the chamfer radius thickness ratio k r =0, the equivalent width reduction factor D br =0, b 2i =b 1i =B, λ i =b 1i /b 2i =1, then The oblique line segment compliance R dxi of each leaf spring is
Figure FDA0002805272730000014
Figure FDA0002805272730000014
C步骤:各片板簧的端部平直段根部至末片板簧端点部分段的Rd1ci的计算Step C: Calculation of R d1ci from the root of the flat end section of each leaf spring to the end section of the last leaf spring 根据板簧片数n,各片板簧的一半长度之差ΔLi,h1i,L1xi,弹性模量E,权利要求1的步骤(1)中计算得到的b1i,对各片板簧的端部平直段的根部至末片板簧端点部分段的Rd1ci进行计算,i=1,2,…,n,即According to the number n of leaf springs, the difference ΔL i , h 1i , L 1xi between the half lengths of the leaf springs, the elastic modulus E, and the b 1i calculated in step (1) of claim 1, for each leaf spring Calculate the R d1ci from the root of the end straight section to the end section of the last leaf spring, i=1,2,...,n, that is
Figure FDA0002805272730000015
Figure FDA0002805272730000015
D步骤:板簧的末片板簧重叠段的柔度Rdrxc的计算Step D: Calculation of the compliance R drxc of the overlapping section of the last leaf spring of the leaf spring 根据板簧片数n,A步骤中计算得到的Rdri,B步骤中计算得到的Rdxi,C步骤中计算得到的Rd1ci,对板簧的末片板簧重叠段的柔度Rdrxc进行计算,即According to the number of leaf springs n, the R dri calculated in step A, the R dxi calculated in step B, and the R d1ci calculated in step C, the flexibility R drxc of the overlapping section of the last leaf spring of the leaf spring is calculated. calculate, i.e.
Figure FDA0002805272730000021
Figure FDA0002805272730000021
E步骤:末片板簧外侧的板簧端部重叠段的柔度Rde的计算Step E: Calculation of the flexibility R de of the overlapping section of the end of the leaf spring outside the last leaf spring 根据板簧片数n,末片板簧外侧的板簧端部重叠段的片数nc=n-1,前n-1片板簧的端部平直段厚度h1i,各片板簧的一半长度之差ΔLi,弹性模量E,权利要求1的(1)步骤中计算得到的b1i,对末片板簧外侧的板簧端部重叠段的柔度Rde进行计算,即According to the number of leaf springs n, the number of overlapping sections of the end of the leaf spring outside the last leaf spring n c =n-1, the thickness h 1i of the flat end section of the first n-1 leaf spring, each leaf spring ΔL i , the elastic modulus E, b 1i calculated in step (1) of claim 1, calculate the flexibility R de of the overlapping section of the end of the leaf spring outside the last leaf spring, that is,
Figure FDA0002805272730000022
Figure FDA0002805272730000022
F步骤:少片斜线型板簧夹紧刚度KC的校核计算Step F: Checking and Calculation of Clamping Stiffness K C 根据D步骤中计算得到的Rdrxc,E步骤中计算得到的Rde,对板簧夹紧刚度KC进行校核计算,即According to the R drxc calculated in the D step and the R de calculated in the E step, the clamping stiffness K C of the leaf spring is checked and calculated, that is,
Figure FDA0002805272730000023
Figure FDA0002805272730000023
3.根据权利要求1的步骤(3)所述的非等长少片斜线型变截面板簧的应力强度的校核,其特征在于:3. The checking of the stress intensity of the non-equal length few-piece oblique variable section leaf spring described in the step (3) of claim 1, it is characterized in that: I步骤:各片板簧的分担弯矩载荷Mi的计算Step I: Calculation of the shared bending moment load Mi of each leaf spring 根据板簧的一半长度LT,骑马螺栓夹紧距U,额定载荷PN,板簧片数n,权利要求2的A步骤中计算得到的Rdri,B步骤中计算得到的Rdxi,C步骤中计算得到的Rd1ci,对各片板簧的分担弯矩载荷Mi进行计算,i=1,2,…,n,即According to the half length L T of the leaf spring, the clamping distance U of the saddle bolt, the rated load P N , the number of leaf springs n, the R dri calculated in the step A of claim 2, the R dxi calculated in the step B, C For the R d1ci calculated in the step, calculate the shared bending moment load Mi of each leaf spring, i =1, 2,...,n, that is
Figure FDA0002805272730000024
Figure FDA0002805272730000024
II步骤:各片板簧的根部最大应力σmaxi计算和强度校核Step II: Calculation and strength check of the maximum stress σ maxi at the root of each leaf spring 根据板簧片数n,各片板簧的h2i,额定载荷下的许用应力[σN],权利要求1的步骤(1)中计算得到的b2i,I步骤中计算得到的Mi,对各片板簧的根部最大应力σmaxi进行计算,即According to the number n of leaf springs, h 2i of each leaf spring, allowable stress under rated load [σ N ], b 2i calculated in step (1) of claim 1, Mi calculated in step I , calculate the maximum stress σ maxi at the root of each leaf spring, that is
Figure FDA0002805272730000025
Figure FDA0002805272730000025
将σmaxi与[σN]进行比较,如果σmaxi<[σN],板簧满足应力强度要求;否则,板簧不满足应力强度要求。Comparing σ maxi with [σ N ], if σ maxi <[σ N ], the leaf spring meets the stress strength requirement; otherwise, the leaf spring does not meet the stress strength requirement.
4.根据权利要求1的步骤(6)所述的非等长少片斜线型变截面板簧的最大限位挠度的校核,其特征在于:4. The checking of the maximum limit deflection of the non-equal-length few-piece oblique variable section leaf spring according to the step (6) of claim 1, characterized in that: i步骤:冲击载荷下的最大许用载荷PX的计算Step i: Calculation of maximum allowable load P X under shock load 根据最大限位挠度设计值fmaxXdes,权利要求2中校核计算得到的KC,对冲击载荷下的最大许用载荷PX进行计算,即According to the maximum limit deflection design value f maxXdes , and the K C obtained by checking and calculating in claim 2, the maximum allowable load P X under the impact load is calculated, that is, PX=KCfmaxXdesP X =K C f maxXdes ; ii步骤:最大限位挠度下的各片板簧分担的最大冲击弯矩MXi Step ii: The maximum impact bending moment shared by each leaf spring under the maximum deflection limit M Xi 根据板簧的一半长度LT,骑马螺栓夹紧距U,板簧片数n,权利要求2的A步骤中计算得到的Rdri,B步骤中计算得到的Rdxi,C步骤中计算得到的Rd1ci,i步骤中计算得到的PX,对各片板簧的分担弯矩载荷MXi进行计算,i=1,2,…,n,即According to the half length L T of the leaf spring, the clamping distance U of the saddle bolt, the number of leaf springs n, the R dri calculated in the A step of claim 2, the R dxi calculated in the B step, and the C calculated in the step C. R d1ci , P X calculated in step i, calculate the shared bending moment load M Xi of each leaf spring, i=1,2,...,n, namely
Figure FDA0002805272730000031
Figure FDA0002805272730000031
iii步骤:最大限位挠度fmaxX下的各片板簧的根部最大冲击应力σXi及校核Step iii: The maximum impact stress σ Xi at the root of each leaf spring under the maximum limit deflection f maxX and check 根据板簧片数n,各片板簧的h2i,冲击载荷下的最大许用应力[σX],权利要求1的步骤(1)中计算得到的b2i,ii步骤中计算得到的MXi,对最大限位挠度设计值fmaxXdes下的各片板簧的根部最大冲击应力σXi进行计算,i=1,2,…,n,即According to the number of leaf springs n, the h 2i of each leaf spring, the maximum allowable stress under impact load [σ X ], b 2i calculated in step (1) of claim 1, and M calculated in step ii Xi , calculate the maximum impact stress σ Xi at the root of each leaf spring under the maximum limit deflection design value f maxXdes , i=1,2,...,n, that is,
Figure FDA0002805272730000032
Figure FDA0002805272730000032
将计算得到的σXi与[σX]进行比较,如果σXi<[σX],则板簧最大限位挠度设计值fmaxXdes,满足冲击应力强度设计要求;否则,板簧最大限位挠度设计值fmaxXdes不满足冲击应力强度设计要求。Comparing the calculated σ Xi with [σ X ], if σ Xi <[σ X ], then the maximum limit deflection design value f maxXdes of the leaf spring meets the design requirements of impact stress strength; otherwise, the maximum limit deflection of the leaf spring The design value f maxXdes does not meet the impact stress strength design requirements.
CN202011365409.5A 2020-11-28 2020-11-28 A Checking Method for Key Parameters of Leaf Springs with Unequal Length and Few Oblique Lines Active CN112507486B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011365409.5A CN112507486B (en) 2020-11-28 2020-11-28 A Checking Method for Key Parameters of Leaf Springs with Unequal Length and Few Oblique Lines

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011365409.5A CN112507486B (en) 2020-11-28 2020-11-28 A Checking Method for Key Parameters of Leaf Springs with Unequal Length and Few Oblique Lines

Publications (2)

Publication Number Publication Date
CN112507486A true CN112507486A (en) 2021-03-16
CN112507486B CN112507486B (en) 2022-11-29

Family

ID=74967365

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011365409.5A Active CN112507486B (en) 2020-11-28 2020-11-28 A Checking Method for Key Parameters of Leaf Springs with Unequal Length and Few Oblique Lines

Country Status (1)

Country Link
CN (1) CN112507486B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105740591A (en) * 2016-04-28 2016-07-06 王炳超 Method for verifying strength of each leaf of end contact type few-leaf oblique main and auxiliary springs
CN105912757A (en) * 2016-04-07 2016-08-31 周长城 Method for checking strength of end contact type few-leaf parabola-shaped section-variable master and slave springs
CN106802996A (en) * 2017-01-12 2017-06-06 山东理工大学 The Method for Checking of the offset frequency type progressive rate leaf spring contact load such as two-stage auxiliary spring formula is non-
CN108006134A (en) * 2018-01-19 2018-05-08 山东理工大学 The non-matched design method for waiting the pre- clamping stress of structure bias type changeable section plate spring in end

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105912757A (en) * 2016-04-07 2016-08-31 周长城 Method for checking strength of end contact type few-leaf parabola-shaped section-variable master and slave springs
CN105740591A (en) * 2016-04-28 2016-07-06 王炳超 Method for verifying strength of each leaf of end contact type few-leaf oblique main and auxiliary springs
CN106802996A (en) * 2017-01-12 2017-06-06 山东理工大学 The Method for Checking of the offset frequency type progressive rate leaf spring contact load such as two-stage auxiliary spring formula is non-
CN108006134A (en) * 2018-01-19 2018-05-08 山东理工大学 The non-matched design method for waiting the pre- clamping stress of structure bias type changeable section plate spring in end

Also Published As

Publication number Publication date
CN112507486B (en) 2022-11-29

Similar Documents

Publication Publication Date Title
CN106246778B (en) The non-design method for waiting the spacing amount of deflection of the few piece both ends reinforced type leaf spring of structure in end
CN112507482B (en) A Checking Method for Key Parameters of Unequal-Length Few Parabolic Variable Section Leaf Springs
CN112507486A (en) Method for checking key parameters of unequal-length few-leaf oblique-line-type variable-section plate spring
JP3618767B2 (en) Pneumatic tire
JP3838455B2 (en) Pneumatic radial tire
CN100587294C (en) Automobile wheel balance weight with concave or convexly curved contact surface and method of manufacture
CN115935554A (en) Design method and design terminal of multi-stage rigidity rear leaf spring for light truck truck
CN112507450B (en) Design method of non-isometric few-piece standard parabolic variable-section plate spring
WO2022264496A1 (en) Composite sheet and steel wire
CN113459748B (en) Two-piece guide arm
CN112507483B (en) A design method of non-standard parabolic leaf spring with unequal length and few pieces with variable cross-section
CN107013616B (en) High-intensitive first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics
CN217539834U (en) A bush subassembly for metallurgical machinery
CN220594575U (en) Novel leaf spring guide arm assembly
US20070063473A1 (en) Vehicle stabilizer for high stress
CN204470293U (en) A kind of high-speed wire rolling finishing mill guide apparatus structure
CN111046495A (en) Method for calculating transverse rigidity of oblique-line type hanging plate spring of high-speed rail driving motor
WO2022245033A1 (en) Steel cord for reinforcing tire belt plies
CN216478416U (en) Corrosion-resistant industrial rubber roller with long service life
EP4046823B1 (en) Airless tire
CN112507484B (en) Design method of unequal-length few-leaf oblique line type variable-section plate spring
CN114297781B (en) Checking method of parabolic guide arm type air suspension system
US20240208268A1 (en) Non-pneumatic tire
CN106777790B (en) Simulation calculation method for stiffness characteristic of two-stage main spring type non-offset frequency type gradient stiffness plate spring
CN114297780B (en) Checking method of diagonal guide arm type trailer air suspension system

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