CN106438798B - The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end - Google Patents

The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end Download PDF

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CN106438798B
CN106438798B CN201610907672.XA CN201610907672A CN106438798B CN 106438798 B CN106438798 B CN 106438798B CN 201610907672 A CN201610907672 A CN 201610907672A CN 106438798 B CN106438798 B CN 106438798B
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mrow
msubsup
msub
spring
mfrac
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CN106438798A (en
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周长城
王凤娟
刘灿昌
邵明磊
汪晓
杨腾飞
赵雷雷
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Shandong University of Technology
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Shandong University of Technology
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    • 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
    • GPHYSICS
    • G16INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16ZINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
    • G16Z99/00Subject matter not provided for in other main groups of this subclass

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Springs (AREA)
  • Vehicle Body Suspensions (AREA)

Abstract

The present invention relates to the non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end, belong to suspension leaf spring technical field.The present invention can be designed according to the structural parameters of each flat spring, modulus of elasticity, maximum allowable safe stress and limited block drift, the spacing amount of deflection of few piece end Enhanced type band spring of grade structure non-to end.Tested by model machine deformation under load test, the design method of the spacing amount of deflection of the non-few piece end reinforced type leaf spring of grade structure in end provided by the present invention is correct, accurately and reliably spacing amount of deflection design load is can obtain, reliable technical foundation has been established for the design and CAD software exploitation of few piece end Enhanced type band spring of the non-grade structure in end.Horizontal product design, quality and performance and vehicle ride performance can be improved using this method, meanwhile, product design and experimental test expense are reduced, accelerates product development speed.

Description

The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end
Technical field
The present invention relates to the spacing amount of deflection of the non-few piece end reinforced type leaf spring of grade structure in vehicle suspension leaf spring, particularly end Design method.
Background technology
With vehicle energy saving, comfortableization, lightweight, the fast development of safe, few piece variable-section steel sheet spring is because of tool There is the advantages that in light weight, stock utilization is high, small without rubbing or rubbing between piece, and vibration noise is low, and service life is long, be increasingly subject to The highest attention of vehicle suspension expert, manufacturing enterprise and vehicle manufacture enterprise, and obtained extensively in vehicle suspension system Using., can be by few piece Variable Section Steel generally for the design requirement for meeting processing technology, stress intensity, rigidity and hanger thickness Flat spring is processed as the different structure forms such as reinforced parabolic type, bias type, root, reinforcement end, both ends are reinforced, this Outside, because the stress of the first flat spring of few piece variable-section steel sheet spring is complex, it is subjected to vertical load, while also subject to Torsional load and longitudinal loading, therefore, the thickness and length of the end flat segments of the first flat spring designed by reality, more than other The thickness and length of each flat spring end flat segments, i.e., mostly using the non-few piece variable-section steel sheet spring for waiting structure in end, with full The complicated requirement of the first flat spring stress of foot.However, because reinforcement end lacks the structure type of piece variable-section steel sheet spring more Complexity, it is carried out analysis calculate it is extremely difficult, according to consult reference materials understand, do not provided reliable end always both at home and abroad at present The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure.With Vehicle Speed and its to ride comfort requirement Improve constantly, the few piece end Enhanced type band spring for waiting structure non-to end proposes higher requirement, therefore, it is necessary to establish one The design method of the spacing amount of deflection of the few piece end reinforced type leaf spring of the structures such as kind is accurate, reliable end is non-, lacking for structure is waited for end is non- Reliable technical foundation is established in the spacing amount of deflection design of piece end Enhanced type band spring, meets Vehicle Industry fast development, car The design requirement for few piece end Enhanced type band springs of structure such as ride performance and end are non-, improve product design it is horizontal, Quality and performance, meet the design requirement of vehicle ride performance;Meanwhile design and testing expenses are reduced, accelerate product development Speed.
The content of the invention
For defect present in above-mentioned prior art, the technical problems to be solved by the invention be to provide it is a kind of easy, The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in reliable end, its design flow diagram, as shown in Figure 1. The half symmetrical structure of few piece reinforcement end variable-section steel sheet spring can see Cantilever Beams of Variable Cross Section as, i.e., by symmetrical center line See the root fixing end of half spring as, see spring end stress point as spring end points.The non-few bit end for waiting structure in end The half symmetrical structure schematic diagram of the reinforced variable-section steel sheet spring in portion, as shown in Fig. 2 including, spring 1, root shim 2, end pad 3;The half length of each of spring 1 is LM, it is by root flat segments, parabolic segment, oblique line section, end flat segments Four sections of compositions;Oblique line section plays booster action to variable cross-section end;The thickness of each flat spring root flat segments is h2M, each flat spring peace The half length for filling spacing is l3, the root of each flat spring parabolic segment to the distance of spring end points is l2M=LM-l3, each bullet The end thickness of spring parabolic segment is h1Mpi, i.e., the thickness ratio β of each flat spring parabolic segmenti=h1Mpi/h2M, i=1,2 ..., N, N For number of spring leaf, the distance l of the end of each flat spring parabolic segment to spring end points1Mpi=l2Mβi 2;1 each oblique line section of spring Length is Δ l, and the end of each flat spring is different, i.e., the thickness and length of first flat spring end flat segments, each more than other The thickness and length of piece, the thickness and length of each flat spring end flat segments are respectively h1MiAnd l1Mi=l1Mpi-Δl;Each bullet The thickness ratio γ of spring oblique line sectionMi=h1Mi/h1Mpi.Root shim 2 is provided between the root flat segments of each of spring 1, spring 1 is each End pad 3 is provided between the end flat segments of piece, the material of end pad is carbon fibre composite, to reduce spring works Caused frictional noise.Freely grown in the structural parameters of each flat spring, modulus of elasticity, maximum allowable safe stress and limited block In the case of degree is given, the spacing amount of deflection of few piece end Enhanced type band spring of the structure such as non-to end is designed.
In order to solve the above technical problems, end provided by the present invention is non-to wait the spacing amount of deflection of the few piece end reinforced type leaf spring of structure Design method, it is characterised in that use following design procedure:
(1) the reinforcement end leaf spring head flat spring end points deformation coefficients G under end points stressing conditionsx-E1Calculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM, width b, clipping room away from half l3, tiltedly The length Δ l of line segment, elastic modulus E, the distance l of the root of parabolic segment to spring end points2M, the parabolic segment of first flat spring Thickness ratio β1, the thickness ratio γ of the oblique line section of first flat springM1, the distance of the root of the oblique line section of first flat spring to spring end points l1Mp1, the distance l of the end of the oblique line section of first flat spring to spring end points1M1, the first flat spring under end points stressing conditions is being held Deformation coefficient G at pointx-E1Calculated, i.e.,
(2) the half stiffness K of reinforcement end leaf spring head flat springs in the clamp stateM1Calculating:
According to the root thickness h of few piece reinforcement end variable-section steel sheet spring2M, and be calculated in step (1) Gx-E1, it is determined that the half stiffness K of first flat spring in the clamp stateM1, i.e.,
(3) based on the half maximum load F suffered by the first flat spring of maximum allowable safe stressmaxCalculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM, width b, clipping room away from half l3, root Portion's thickness h2M, and maximum allowable safe stress [σ], it is determined that based on the half suffered by the first flat spring of maximum allowable safe stress most Big load Fmax, i.e.,
(4) the non-spacing amount of deflection h of few piece end Enhanced type band spring for waiting structure in endxwDesign:
I steps:According to the K being calculated in step (2)M1, and identified F in step (3)max, under maximum load The Leading Edge Deformation f of leaf springmCalculated, i.e.,
II steps:According to the drift L of limited blockxw, and the f being calculated in I stepsm, determine the non-grade structure in end The spacing amount of deflection of few piece end Enhanced type band spring, i.e.,
The present invention has the advantage that than prior art
Because the structure type of the few piece variable-section steel sheet spring of reinforcement end is complex, it is non-that analysis calculating is carried out to it It is often difficult, understood according to consulting reference materials, do not provided that reliable end is non-to wait the few piece reinforcement end plate of structure always both at home and abroad at present The design method of the spacing amount of deflection of spring.The present invention can be according to the structural parameters of each flat spring, modulus of elasticity, maximum allowable safe stress And limited block drift, the spacing amount of deflection of few piece end Enhanced type band spring of grade structure non-to end are designed.Pass through Knowable to model machine deformation under load test test, the spacing amounts of deflection of the few piece end reinforced type leaf spring of structure such as end provided by the present invention is non- Design method is correct, can obtain accurately and reliably spacing amount of deflection design load, is the non-few piece reinforcement end for waiting structure in end Reliable technical foundation has been established in design and the CAD software exploitation of leaf spring;Meanwhile using this method, product can be improved and set Meter level, product quality and vehicle ride performance;Meanwhile design and experimental test expense can be also reduced, accelerate product development Speed.
Brief description of the drawings
For a better understanding of the present invention, it is described further below in conjunction with the accompanying drawings.
Fig. 1 is the non-design flow diagram for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end;
Fig. 2 is the structural representation of the half of the few piece reinforcement end variable-section steel sheet spring of the non-grade structure in end.
Specific embodiment
The present invention is described in further detail below by embodiment.
Embodiment one:The half length L of certain each flat spring of few piece reinforcement end variable-section steel sheet springM=575mm, it is wide Spend b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments2M=11mm, clipping room away from half l3=55mm, The length Δ l=30mm of oblique line section, the distance l of the root of parabolic segment to spring end points2M=LM-l3=520mm;First flat spring Parabolic segment end thickness h1Mp1=6mm, i.e. parabolic segment thickness ratio β1=h1Mp1/h2M=0.55, the end of parabolic segment Distance l of the portion to spring end points1Mp1=l2Mβ1 2=157.30mm, the thickness h of end flat segments1M1=7mm, i.e. oblique line section thickness Degree compares γM1=h1M1/h1Mp1=1.17, the length l of end flat segments1M1=l1Mp1- Δ l=127.30mm, the freedom of limited block Length Lxw=15mm.Maximum allowable safe stress [σ]=900MPa of the spring, the few piece end for waiting structure non-to the end are strengthened The spacing amount of deflection of steel plate spring is designed.
The non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end that present example is provided, it sets Flow is counted as shown in figure 1, comprising the following steps that:
(1) the reinforcement end leaf spring head flat spring end points deformation coefficients G under end points stressing conditionsx-E1Calculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM=575mm, width b=60mm, installation The half l of spacing3=55mm, the length Δ l=30mm of oblique line section, elastic modulus E=200GPa, the root of parabolic segment to bullet The distance l of spring end points2M=520mm, the thickness ratio β of the parabolic segment of first flat spring1=0.55, the thickness of the oblique line section of first flat spring Degree compares γM1=1.17, the distance l of the root of the oblique line section of first flat spring to spring end points1Mp1=157.30mm, first flat spring Distance l of the end of oblique line section to spring end points1M1=127.30mm, to the first flat spring under end points stressing conditions at end points Deformation coefficient Gx-E1Calculated, i.e.,
(2) the half stiffness K of reinforcement end leaf spring head flat springs in the clamp stateM1Calculating:
According to the root thickness h of few piece reinforcement end variable-section steel sheet spring2MCalculated in=11mm, and step (1) The G arrivedx-E1=91.51mm4/ N, it is determined that the half stiffness K of first flat spring in the clamp stateM1, i.e.,
(3) based on the half maximum load F suffered by the first flat spring of maximum allowable safe stressmaxCalculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM=575mm, width b=60mm, installation The half l of spacing3=55mm, root thickness h2M=11mm, and maximum allowable safe stress [σ]=900MPa, it is determined that based on most Half maximum load F suffered by the first flat spring of big safe stress allowablemax, i.e.,
(4) the non-spacing amount of deflection h of few piece end Enhanced type band spring for waiting structure in endxwDesign:
I steps:According to the K being calculated in step (2)M1Identified F in=14.54N/mm, and step (3)max= 1989N, to the Leading Edge Deformation f of the leaf spring under maximum loadmCalculated, i.e.,
II steps:According to the drift L of limited blockxwThe f being calculated in=15mm, and I stepsm=136.80mm, The spacing amount of deflection of few piece end Enhanced type band spring of the non-grade structure in end is determined, i.e.,
Tested by prototype test, the spacing amount of deflection design load of spring is reliable, can meet the non-grade structure in end Lack the design requirement of the spacing amount of deflection of piece end Enhanced type band spring, the results showed that the few piece of the non-grade structure in end that the invention is provided The design method of the spacing amount of deflection of reinforcement end leaf spring is correct, and parameter design value is accurately and reliably.
Embodiment two:The half length L of certain each flat spring of few piece reinforcement end variable-section steel sheet springM=600mm, it is wide Spend b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments2M=12mm, clipping room away from half l3=60mm, The length Δ l=30mm of oblique line section, the distance l of the root of parabolic segment to spring end points2M=LM-l3=540mm;First flat spring Parabolic segment end thickness h1Mp1=7mm, i.e. parabolic segment thickness ratio β1=h1Mp1/h2M=0.58, the end of parabolic segment Distance l of the portion to spring end points1Mp1=l2Mβ1 2=181.66mm, the thickness h of end flat segments1M1=8mm, i.e. oblique line section thickness Degree compares γM1=h1M1/h1Mp1=1.14, the length l of end flat segments1M1=l1Mp1- Δ l=151.66mm, the freedom of limited block Length Lxw=12mm.Maximum allowable safe stress [σ]=900MPa of the spring, the few piece end for waiting structure non-to the end are strengthened The spacing amount of deflection of steel plate spring is designed.
Using with the identical design method of embodiment one and step, piece reinforcement end variable-section steel sheet spring is lacked to this Spacing amount of deflection is designed, and is comprised the following steps that:
(1) the reinforcement end leaf spring head flat spring end points deformation coefficients G under end points stressing conditionsx-E1Calculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM=600mm, width b=60mm, installation The half l of spacing3=60mm, the length Δ l=30mm of oblique line section, elastic modulus E=200GPa, the root of parabolic segment to bullet The distance l of spring end points2M=540mm, the thickness ratio β of the parabolic segment of first flat spring1=0.58, the thickness of the oblique line section of first flat spring Degree compares γM1=1.14, the distance l of the root of the oblique line section of first flat spring to spring end points1Mp1=181.66mm, first flat spring Oblique line section end to spring end points distance l1M1=151.66mm, to the first flat spring under end points stressing conditions in end points The deformation coefficient G at placex-E1Calculated, i.e.,
(2) the half stiffness K of reinforcement end leaf spring head flat springs in the clamp stateM1Calculating:
According to the root thickness h of few piece reinforcement end variable-section steel sheet spring2MCalculated in=12mm, and step (1) The G arrivedx-E1=101.33mm4/ N, it is determined that the half stiffness K of first flat spring in the clamp stateM1, i.e.,
(3) based on the half maximum load F suffered by the first flat spring of maximum allowable safe stressmaxCalculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM=600mm, width b=60mm, installation The half l of spacing3=60mm, root thickness h2M=12mm, and maximum allowable safe stress [σ]=900MPa, it is determined that based on most Half maximum load F suffered by the first flat spring of big safe stress allowablemax, i.e.,
(4) the non-spacing amount of deflection h of few piece end Enhanced type band spring for waiting structure in endxwDesign:
I steps:According to the K being calculated in step (2)M1Identified F in=17.05N/mm, and step (3)max= 2273.70N, to the Leading Edge Deformation f of the leaf spring under maximum loadmCalculated, i.e.,
II steps:According to the drift L of limited blockxwThe f being calculated in=12mm, and I stepsm=133.35mm, The spacing amount of deflection of few piece end Enhanced type band spring of the non-grade structure in end is determined, i.e.,
Tested by prototype test, the spacing amount of deflection design load of spring is reliable, can meet the non-grade structure in end Lack the design requirement of the spacing amount of deflection of piece end Enhanced type band spring, the results showed that the few piece of the non-grade structure in end that the invention is provided The design method of the spacing amount of deflection of reinforcement end leaf spring is correct, and parameter design value is accurately and reliably.

Claims (1)

1. the non-design method for waiting the spacing amount of deflection of the few piece end reinforced type leaf spring of structure in end, wherein, the non-few bit end for waiting structure in end The half symmetrical structure of the reinforced variable-section steel sheet spring in portion is by root flat segments, parabolic segment, oblique line section and end flat segments 4 Section is formed, and an oblique line section is provided between parabolic segment and end flat segments, and booster action is played to the end of variable-section steel sheet spring; The end of each flat spring is non-to wait structure, i.e., the thickness and length of first flat spring end flat segments, thickness and length of each more than other Degree, to meet the requirement of first flat spring complicated applied force;Safely should in the structural parameters, modulus of elasticity, maximum allowable of each flat spring In the case of power and limited block drift are given, the spacing amount of deflection of few piece end Enhanced type band spring of the structure such as non-to end is entered Row design, it is characterised in that using design procedure in detail below:
(1) the reinforcement end leaf spring head flat spring end points deformation coefficients G under end points stressing conditionsx-E1Calculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM, width b, clipping room away from half l3, oblique line section Length Δ l, elastic modulus E, the distance l of the root of parabolic segment to spring end points2M, the thickness of the parabolic segment of first flat spring Compare β1, the thickness ratio γ of the oblique line section of first flat springM1, the distance l of the root of the oblique line section of first flat spring to spring end points1Mp1, Distance l of the end of the oblique line section of first flat spring to spring end points1M1, to the first flat spring under end points stressing conditions at end points Deformation coefficient Gx-E1Calculated, i.e.,
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>G</mi> <mrow> <mi>x</mi> <mo>-</mo> <mi>E</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>-</mo> <msubsup> <mi>l</mi> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mn>3</mn> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>E</mi> <mi>b</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mn>8</mn> <msubsup> <mi>l</mi> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>l</mi> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>E</mi> <mi>b</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>4</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> </mrow> <mrow> <msubsup> <mi>Eb&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <msubsup> <mi>&amp;beta;</mi> <mn>1</mn> <mn>3</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>6</mn> <mi>&amp;Delta;</mi> <mi>l</mi> <mrow> <mo>(</mo> <mn>4</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>3</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mi>Eb&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <msubsup> <mi>&amp;beta;</mi> <mn>1</mn> <mn>3</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </mfrac> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mn>6</mn> <mi>&amp;Delta;</mi> <mi>l</mi> <mrow> <mo>(</mo> <mn>4</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <mo>-</mo> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <mo>-</mo> <mn>2</mn> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>ln&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>ln&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> </msub> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <mo>-</mo> <mn>4</mn> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>M</mi> <mi>p</mi> <mn>1</mn> </mrow> </msub> <msubsup> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>ln&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mi>Eb&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;beta;</mi> <mn>1</mn> <mn>3</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </mfrac> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
(2) the half stiffness K of reinforcement end leaf spring head flat springs in the clamp stateM1Calculating:
According to the root thickness h of few piece reinforcement end variable-section steel sheet spring2M, and the G being calculated in step (1)x-E1, really The fixed half stiffness K of first flat spring in the clamp stateM1, i.e.,
<mrow> <msub> <mi>K</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>h</mi> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mn>3</mn> </msubsup> <msub> <mi>G</mi> <mrow> <mi>x</mi> <mo>-</mo> <mi>E</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>;</mo> </mrow>
(3) based on the half maximum load F suffered by the first flat spring of maximum allowable safe stressmaxCalculating:
According to the half length L of few piece reinforcement end variable-section steel sheet springM, width b, clipping room away from half l3, root thickness Spend h2M, and maximum allowable safe stress [σ], it is determined that based on the maximum load of half suffered by the first flat spring of maximum allowable safe stress Lotus Fmax, i.e.,
<mrow> <msub> <mi>F</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>bh</mi> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mn>2</mn> </msubsup> <mo>&amp;lsqb;</mo> <mi>&amp;sigma;</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>6</mn> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>
(4) the non-spacing amount of deflection h of few piece end Enhanced type band spring for waiting structure in endxwDesign:
I steps:According to the K being calculated in step (2)M1, and identified F in step (3)max, to the steel plate under maximum load The Leading Edge Deformation f of springmCalculated, i.e.,
<mrow> <msub> <mi>f</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>F</mi> <mi>max</mi> </msub> <msub> <mi>K</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> </mfrac> <mo>;</mo> </mrow>
II steps:According to the drift L of limited blockxw, and the f being calculated in I stepsm, determine the non-few piece for waiting structure in end The spacing amount of deflection of reinforcement end leaf spring, i.e.,
<mrow> <msub> <mi>h</mi> <mrow> <mi>x</mi> <mi>w</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mi>m</mi> </msub> <mo>-</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msub> <mi>L</mi> <mrow> <mi>x</mi> <mi>w</mi> </mrow> </msub> <mo>.</mo> </mrow>
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CN105550487A (en) * 2016-03-13 2016-05-04 周长城 Method for designing few-leaf oblique line type variable-section main springs in gaps between oblique line segments and auxiliary spring
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