CN105825008A - Load checking calculation method when auxiliary spring of non-end-contact type few-piece variable cross section master and auxiliary springs works - Google Patents

Abstract

The invention relates to a load checking calculation method when an auxiliary spring of non-end-contact type few-piece variable cross section master and auxiliary springs works, and belongs to the technical field of suspension steel plate springs. The load checking calculation method comprises the following steps: according to the structure size and the elasticity modulus of each parabolic type variable cross section master spring piece with a flat end section and a non-equal structure, firstly determining the deformation coefficient and the half rigidity of an end point of each master spring piece, and the deformation coefficient Gx-BC of the Nth master spring piece at the contact point of a parabolic segment and the auxiliary spring; finally, according to the thickness of a flat section of the root of the master spring, the half rigidity of the master spring piece, the Gx-BC of the Nth master spring piece, and the gap design value of the master and auxiliary springs, performing checking calculation on the load when the auxiliary spring works. Through deformation simulation verification, accurate checking calculation on the load when the auxiliary spring of the non-end-contact type few-sheet variable cross section master and auxiliary springs works can be performed according to the method, so that the design level and the properties of products are improved, and the ride comfort of a vehicle is improved; besides, the weight and the cost of the springs are reduced, the design and experiment expenses are reduced, and the product development speed is accelerated.

Description

The auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load Method for Checking

Technical field

The present invention relates to vehicle suspension leaf spring, be that the auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load especially Lotus Method for Checking.

Background technology

In order to meet the vehicle suspension variation rigidity design requirement under different loads, generally few sheet variable-section steel sheet spring is designed as Major and minor spring, wherein, is provided with certain major-minor spring gap between main spring and auxiliary spring contact, auxiliary spring work load design want Ask.Owing to the 1st its stress of few main spring of sheet variable cross-section is complicated, be subjected to vertical load, simultaneously also subject to torsional load and Longitudinal loading, therefore, the end thickness of the 1st leaf spring designed by reality, generally than other each the thickest one A bit, the non-few sheet variable-section steel sheet spring waiting structure in end is the most mostly used；Simultaneously in order to meet setting of major-minor spring different composite rigidity Meter requirement, generally uses the auxiliary spring of different length, i.e. auxiliary spring contact is the most different from the contact position of main spring, therefore, can be divided into end Portion's contact and non-ends contact formula i.e. parabolic segment contact two kinds.When load works load more than auxiliary spring, major-minor spring connects Touching and concur, wherein, auxiliary spring works the size of load, and vehicle ride performance is had material impact.But, The deformation waiting few sheet parabolic type variable-section steel sheet spring of structure to locate at an arbitrary position owing to end is non-calculates extremely complex, therefore, Previously fail to provide the reliable Method for Checking of the auxiliary spring used load of the few sheet variable cross-section major-minor spring of non-ends contact formula always.Although first Before once someone gave the method for designing of few sheet variable-section steel sheet spring, such as, Peng Mo, high army once in " automobile engineering ", (volume 14) the 3rd phase in 1992, it is proposed that the design and calculation method of Varied section leaf spring, the method is primarily directed to end Being designed Deng few sheet parabolic type variable-section steel sheet spring of structure and calculate, its weak point is to meet that end is non-waits lacking of structure The design of sheet parabolic type variable-section steel sheet spring and the requirement calculated, more can not meet the few sheet parabolic type change of non-ends contact formula and cut The checking computations requirement of the auxiliary spring used load of face major-minor spring.

Therefore, it is necessary to set up the auxiliary spring effect of the few sheet parabolic type variable cross-section major-minor spring of a kind of non-ends contact formula accurate, reliable The Method for Checking of load, meets Vehicle Industry fast development and the careful design to few sheet parabolic type variable cross-section major-minor leaf spring And auxiliary spring works the requirement of load checking computations, improve design level, product quality and the property of few sheet parabolic type variable cross-section major-minor spring Can, meet auxiliary spring and work the design requirement of load, improve vehicle ride performance；Meanwhile, reduce design and testing expenses, Accelerate product development speed.

Summary of the invention

For defect present in above-mentioned prior art, the technical problem to be solved is to provide a kind of easy, reliably The auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load Method for Checking, design flow diagram, as shown in Figure 1.Few Sheet parabolic type variable cross-section major-minor spring is symmetrical structure, and the half symmetrical structure of spring can see Cantilever Beams of Variable Cross Section as, i.e. symmetrical Centrage sees the fixing end of root of half spring as, and spring end stress point sees end points as.Few sheet parabolic type variable cross-section master The half symmetrical structure schematic diagram of auxiliary spring, as in figure 2 it is shown, including, main spring 1, root shim 2, auxiliary spring 3, end Pad 4.The a length of L of half of each of main spring 1, is by root flat segments, parabolic segment and three sections of institute's structures of end flat segments Becoming, the thickness of every root flat segments is h₂, the half of installing space is l₃；The end flat segments of each of main spring 1 is non-waits structure, The thickness of the end flat segments of i.e. the 1st and length, more than other thickness of each and length, the thickness of each end flat segments It is respectively h with length_1iAnd l_1i, i=1,2 ..., N, N are the sheet number of few main spring of sheet variable cross-section, and its span is 2～4；Middle Variable cross-section is parabolic segment, and the thickness of each parabolic segment compares β_i, the distance of the root of parabolic segment to main spring end points is l₂=L- l₃.Between the root flat segments of each of main spring 1 and and the root flat segments of auxiliary spring 3 between be provided with root shim 2, main spring 1 Being provided with end pad 4 between the flat segments of end, the material of end pad is carbon fibre composite, is produced reducing spring works Raw frictional noise.The a length of L of half of auxiliary spring 3_A, i.e. auxiliary spring ends points is l to the horizontal range of main spring end points₀=L- L_A, between the parabolic segment and the ends points of auxiliary spring 3 of the main spring of N sheet, it is provided with certain major and minor spring gap delta, to meet Auxiliary spring work load design want.In each chip architecture parameter of main spring, material characteristic parameter, auxiliary spring length, major-minor spring gap In the case of Gei Ding, the auxiliary spring of sheet variable cross-section major-minor spring few to the end contact load that works checks.

For solving above-mentioned technical problem, the auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula provided by the present invention works load Lotus Method for Checking, it is characterised in that use following design procedure:

(1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section_x-DiCalculate:

According to half length L of few sheet main spring of parabolic type variable cross-section, width b, elastic modulus E, half l of installing space₃, throw The root of thing line segment is to distance l of main spring end points₂=L-l₃, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1, 2 ..., N, N are main reed number, the end points deformation coefficient G to each main spring of parabolic type variable cross-section_x-DiCalculate, i.e.

$G_{x-Di}=\frac{4\[l_2^3(1-{\mathrm{\β}}_i^3)+L^3\]}{Eb},i=1,2,...,N;$

(2) the N sheet main springs of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate:

According to half length L of few sheet main spring of parabolic type variable cross-section, width b, elastic modulus E, the root of parabolic segment is to main spring Distance l of end points₂, auxiliary spring contact and horizontal range l of main spring end points₀, to the N sheet main spring of parabolic type variable cross-section at parabola Section with auxiliary spring contact point at deformation coefficient G_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_2^{3/2}{l}_0^{3/2}-(9l_2^2+3L^2)l_0+2l_2^3+2L^3\];$

(3) the half stiffness K of each main spring of parabolic type variable cross-section_MiCalculate:

The thickness h of the root flat segments according to few sheet main spring of parabolic type variable cross-section₂, and calculated each main spring in step (1) End points deformation coefficient G_x-Di, half stiffness K to each main spring of parabolic type variable cross-section_MiCalculate, i.e.

$K_{Mi}=\frac{h_2^3}{G_{x-Di}},i=1,2,...,N;$

(4) auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load p_KChecking computations:

The thickness h of the root flat segments according to the main spring of parabolic type variable cross-section₂, major-minor spring gap design load δ, step is calculated in (2) G_x-BC, and the stiffness K of calculated each main spring half in step (3)_Mi, sheet variable cross-section few to non-ends contact formula The load p when auxiliary spring of major-minor spring works_KCheck, i.e.

$P_K=\frac{2{\mathrm{\δh}}_2^3\underset{i=1}{\overset{N}{\Σ}}{K}_{Mi}}{K_{MN}{G}_{x-BC}};$

In formula, K_MNIt is the half rigidity of the main spring of N sheet.

The present invention has the advantage that than prior art

It is extremely complex, therefore, the most always that the few sheet variable-section steel sheet spring waiting structure owing to end is non-deforms calculating at an arbitrary position Fail to provide the auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula to work load calculation method.The present invention can throw according to few sheet The physical dimension of the main spring of thing line style variable cross-section, elastic modelling quantity, it is first determined go out the non-each main spring change at end points waiting structure in end Shape coefficient, and the deformation coefficient that the main spring of N is at parabolic segment with auxiliary spring contact point；Then, utilize each main spring at end points Deformation coefficient, the half rigidity of each main spring is calculated；Finally, according to the root thickness of main spring, main spring parabolic segment And the gap delta between auxiliary spring ends points, N main spring deformation coefficient at parabolic segment with auxiliary spring contact point, and each main spring Rigidity, the auxiliary spring used load of sheet parabolic type variable cross-section major-minor spring few to non-ends contact formula checks.

By design example and ANSYS simulating, verifying, the method is utilized to can get non-ends contact formula accurate, reliable The checking computations value of the auxiliary spring used load of few sheet variable cross-section major-minor spring, for the non-few sheet parabolic type variable cross-section major-minor spring waiting structure in end Auxiliary spring works load checking computations, it is provided that reliably computational methods, and for the CAD of few sheet parabolic type variable cross-section major-minor spring And the exploitation of characteristic Simulation software established reliable technical foundation.Utilize the method can improve setting of few major and minor spring of sheet variable cross-section Meter level and performance, it is ensured that meet auxiliary spring and work the design requirement of load, improve vehicle ride performance；Meanwhile, also can drop Low bearing spring weight and cost, reduce design, exploitation and testing expenses, accelerate product development speed.

Accompanying drawing explanation

In order to be more fully understood that the present invention, it is described further below in conjunction with the accompanying drawings.

Fig. 1 is the checking computations flow chart of the auxiliary spring used load of the few sheet variable cross-section major-minor spring of non-ends contact formula；

Fig. 2 is the half symmetrical structure schematic diagram of the few sheet variable cross-section major-minor spring of non-ends contact formula；

Fig. 3 is the deformation simulation cloud atlas of the non-ends contact formula main spring of parabolic type variable cross-section of embodiment one；

Fig. 4 is the deformation simulation cloud atlas of the non-ends contact formula main spring of parabolic type variable cross-section of embodiment two.

Specific embodiments

Below by embodiment, the present invention is described in further detail.

Embodiment one: the sheet number N=2 of the few sheet main spring of parabolic type variable cross-section of certain non-ends contact formula, wherein, the one of each main spring Half length L=575mm, width b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments₂=11mm, installs Half l of spacing₃=55mm, the root of parabolic segment is to distance l of main spring end points₂=L-l₃=520mm；The end of the 1st main spring The thickness h of portion's flat segments₁₁=7mm, the thickness of the parabolic segment of the 1st main spring compares β₁=h₁₁/h₂=0.64, the 2nd main spring h₁₂=6mm, the thickness of the parabolic segment of the 2nd main spring compares β₂=h₁₂/h₂=0.55.Half length L of auxiliary spring_A=365mm, secondary Spring contact is to horizontal range l of main spring end points₀=210mm, the major-minor spring gap design between auxiliary spring contact and main spring parabolic segment Value δ=16.95mm.The auxiliary spring of sheet parabolic type variable cross-section major-minor spring few to this non-ends contact formula works load p_KTest Calculate.

The auxiliary spring of the few sheet variable cross-section major-minor spring of the non-ends contact formula that present example is provided works load Method for Checking, and it is tested Calculate flow process as it is shown in figure 1, concrete checking computations step is as follows:

(1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section_x-DiCalculate:

According to half length L=575mm of few sheet main spring of parabolic type variable cross-section, width b=60mm, elastic modulus E=200GPa, Half l of installing space₃=55mm, the root of parabolic segment is to distance l of main spring end points₂=520mm, the throwing of the 1st main spring The thickness of thing line segment compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂=0.55, to the 1st, the 2nd parabolic The end points deformation coefficient G of the main spring of line style variable cross-section_x-D1、G_x-D2It is respectively calculated, i.e.

$G_{x-D1}=\frac{4\[l_2^3(1-{\mathrm{\β}}_1^3)+L^3\]}{Eb}=98.16{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4\[l_2^3(1-{\mathrm{\β}}_2^3)+L^3\]}{Eb}=102.63{\mathrm{mm}}^4/N;$

(2) the 2nd main springs of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate:

According to half length L=575mm of few sheet main spring of parabolic type variable cross-section, width b=60mm, elastic modulus E=200GPa, The root of parabolic segment is to distance l of main spring end points₂Horizontal range l of=520mm, auxiliary spring contact and main spring end points₀=210mm, To the 2nd main spring of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_2^{3/2}{l}_0^{3/2}-(9l_2^2+3L^2)l_0+2l_2^3+2L^3\]=38.46{\mathrm{mm}}^4/N;$

(3) the half stiffness K of each main spring of parabolic type variable cross-section_MiCalculate:

I step: according to the thickness h of the root flat segments of the main spring of parabolic type variable cross-section₂In=11mm, and step (1) calculated G_x-D1=98.16mm⁴/ N and G_x-D2=102.63mm⁴/ N is firm to the half of the 1st, the 2nd main spring of parabolic type variable cross-section Degree K_M1And K_M2It is respectively calculated, i.e.

$K_{M1}=\frac{h_2^3}{G_{x-D1}}=13.56N/mm,$

$K_{M2}=\frac{h_2^3}{G_{x-D2}}=12.97N/mm;$

(4) auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load p_KChecking computations:

The thickness h of the root flat segments according to the main spring of parabolic type variable cross-section₂=11mm, major-minor spring gap delta=16.95mm, step (2) G obtained by middle calculating_x-BC, and the half rigidity of calculated 1st, the 2nd main spring in step (3) K_M1=13.56N/mm and K_M2=12.97N/mm, the auxiliary spring of sheet variable cross-section major-minor spring few to this non-ends contact formula works load Lotus P_KCalculate, i.e.

$P_K=\frac{2{\mathrm{\δh}}_2^3\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}{K_{MN}{G}_{x-BC}}=2400N;$

Utilize ANSYS finite element emulation software, according to each chip architecture parameter and the material behavior of this few sheet main spring of parabolic type variable cross-section Parameter, sets up the ANSYS phantom of the half symmetrical structure of this few sheet main spring of parabolic type variable cross-section, grid division, and Root at phantom applies fixed constraint, the auxiliary spring obtained by end points applies checking computations work load half i.e. P=1200N, the deformation to this few sheet main spring of parabolic type variable-section steel sheet spring carries out ANSYS emulation, obtained deformation Emulation cloud atlas, as it is shown on figure 3, wherein, this main spring deflection δ=17.11mm at distance end position 210mm.

Understanding, in the case of same load, the ANSYS simulating, verifying value δ=17.11mm of this leaf spring main spring deflection, with master Auxiliary spring gap design load δ=16.95mm matches, and relative deviation is only 0.94%；Result shows the non-end that this invention is provided The auxiliary spring of the few sheet variable cross-section major-minor spring of the portion's contact load Method for Checking that works is correct, and auxiliary spring works the checking computations value of load It is accurately and reliably.

Embodiment two: the sheet number N=2 of the few main spring of sheet parabolic type of certain non-ends contact formula, wherein, the half length of each main spring L=600mm, width b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments₂=14mm, installing space Half l₃=60mm, the root of parabolic segment is to distance l of main spring end points₂=L-l₃=540mm；The end of the 1st main spring is straight The thickness h of section₁₁=9mm, the thickness of the parabolic segment of the 1st main spring compares β₁=h₁₁/h₂=0.64；The end of the 2nd main spring is put down The thickness h of straight section₁₂=8mm, the thickness of the parabolic segment of the 2nd main spring compares β₂=h₁₂/h₂=0.57.The half length of auxiliary spring L_AHorizontal range l of=380mm, auxiliary spring contact and main spring end points₀=L-L_A=220mm, auxiliary spring contact and main spring parabolic segment it Between major-minor spring gap delta=23.21mm.The auxiliary spring of sheet parabolic type major-minor spring few to this non-ends contact formula load that works is carried out Checking computations.

Use the Method for Checking identical with embodiment one and step, sheet parabolic type variable cross-section main spring few to this non-ends contact formula The auxiliary spring load that works check, specifically comprise the following steps that

(1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section_x-DiCalculate:

According to half length L=600mm of few sheet main spring of parabolic type variable cross-section, width b=60mm, elastic modulus E=200GPa, Half l of installing space₃=60mm, the root of parabolic segment is to distance l of main spring end points₂=540mm, the throwing of the 1st main spring The thickness of thing line segment compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂=0.57, to the 1st, the 2nd parabolic The end points deformation coefficient G of the main spring of line style variable cross-section_x-D1、G_x-D2It is respectively calculated, i.e.

$G_{x-D1}=\frac{4\[l_2^3(1-{\mathrm{\β}}_1^3)+L^3\]}{Eb}=110.54{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4\[l_2^3(1-{\mathrm{\β}}_2^3)+L^3\]}{Eb}=114.69{\mathrm{mm}}^4/N;$

(2) the 2nd main springs of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate:

According to half length L=600mm of few sheet main spring of parabolic type variable cross-section, width b=60mm, elastic modulus E=200GPa, The root of parabolic segment is to distance l of main spring end points₂Horizontal range l of=540mm, auxiliary spring contact and main spring end points₀=220mm, To the 2nd main spring of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_2^{3/2}{l}_0^{3/2}-(9l_2^2+3L^2)l_0+2l_2^3+2L^3\]=43.26{\mathrm{mm}}^4/N;$

(3) the half stiffness K of each main spring of parabolic type variable cross-section_MiCalculate:

The thickness h of the root flat segments according to each main spring of parabolic type variable cross-section₂Obtained by calculating in=14mm, and step (1) the 1st Sheet, the end points deformation coefficient G of the 2nd main spring of variable cross-section_x-D1=110.54mm⁴/ N and G_x-D2=114.69mm⁴/ N, to the 1st Sheet, the half stiffness K of the 2nd main spring of parabolic type variable cross-section_M1And K_M2It is respectively calculated, i.e.

$K_{M1}=\frac{h_2^3}{G_{x-D1}}=24.82N/mm,$

$K_{M2}=\frac{h_2^3}{G_{x-D2}}=23.92N/mm;$

(4) auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load p_KChecking computations:

The thickness h of the root flat segments according to the main spring of parabolic type variable cross-section₂=14mm, major-minor spring gap delta=23.21mm, step (2) G obtained by middle calculating_x-BC=43.26mm⁴The half rigidity of each main spring obtained by calculating in/N, and step (3) K_M1=24.82N/mm, K_M2=23.92N/mm, the auxiliary spring of sheet variable cross-section major-minor spring few to non-ends contact formula works load P_KCheck, i.e.

$P_K=\frac{2{\mathrm{\δh}}_2^3\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{M2}}=6000N;$

Utilize ANSYS finite element emulation software, according to each chip architecture parameter and the material behavior of this few sheet main spring of parabolic type variable cross-section Parameter, the ANSYS phantom of the half symmetrical structure of the few sheet main spring of parabolic type variable cross-section of foundation, grid division, and The root of phantom applies fixed constraint, the auxiliary spring obtained by end points applies checking computations work load half i.e. P=3000N, the deformation to this few sheet main spring of parabolic type variable-section steel sheet spring carries out ANSYS emulation, obtained deformation Emulation cloud atlas, as shown in Figure 4, wherein, this main spring deflection δ=23.25mm at distance end position 220mm.

Understanding, in the case of same load, the ANSYS simulating, verifying value δ=23.25mm of this leaf spring main spring deflection, with master Auxiliary spring gap design load δ=23.21mm matches, and relative deviation is only 0.17%；Result shows the non-end that this invention is provided The auxiliary spring of the few sheet variable cross-section major-minor spring of the portion's contact load Method for Checking that works is correct.

Claims (1)

1. The auxiliary spring of the few sheet variable cross-section major-minor spring of the most non-ends contact formula works load Method for Checking, and wherein, few sheet parabolic type becomes and cuts The half symmetrical structure of the main spring in face is made up of root flat segments, parabolic segment, end flat segments three sections, and the end of each main spring is put down Straight section is non-isomorphic, i.e. the thickness of the end flat segments of the 1st main spring and length, more than other thickness of each and length；Auxiliary spring Length is less than main spring length, is provided with certain major-minor spring gap between auxiliary spring contact and main spring parabolic segment, when load reaches secondary Spring work load time, in auxiliary spring contact and main spring parabolic segment, certain point contacts；Special at each chip architecture parameter, the material of main spring Property parameter, auxiliary spring length, major-minor spring gap given in the case of, the auxiliary spring of sheet variable cross-section major-minor spring few to non-ends contact formula acts as Checking by load, concrete checking computations step is as follows:

   (1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section_x-DiCalculate:

   According to half length L of few sheet main spring of parabolic type variable cross-section, width b, elastic modulus E, half l of installing space₃, throw The root of thing line segment is to distance l of main spring end points₂=L-l₃, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1, 2 ..., N, N are main reed number, the end points deformation coefficient G to each main spring of parabolic type variable cross-section_x-DiCalculate, i.e.

   $G_{x-Di}=\frac{4\[l_2^3(1-{\mathrm{\β}}_i^3)+L^3\]}{Eb},i=1,2,...,N;$

   (2) the N sheet main springs of parabolic type variable cross-section deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate:

   According to half length L of few sheet main spring of parabolic type variable cross-section, width b, elastic modulus E, the root of parabolic segment is to main spring Distance l of end points₂, auxiliary spring contact and horizontal range l of main spring end points₀, to the N sheet main spring of parabolic type variable cross-section at parabola Section with auxiliary spring contact point at deformation coefficient G_x-BCCalculate, i.e.

   $G_{x-BC}=\frac{2}{Eb}\[8l_2^{3/2}{l}_0^{3/2}-(9l_2^2+3L^2)l_0+2l_2^3+2L^3\];$

   (3) the half stiffness K of each main spring of parabolic type variable cross-section_MiCalculate:

   The thickness h of the root flat segments according to few sheet main spring of parabolic type variable cross-section₂, and calculated each main spring in step (1) End points deformation coefficient G_x-Di, half stiffness K to each main spring of parabolic type variable cross-section_MiCalculate, i.e.

   $K_{Mi}=\frac{h_2^3}{G_{x-Di}},i=1,2,...,N;$

   (4) auxiliary spring of the few sheet variable cross-section major-minor spring of non-ends contact formula works load p_KChecking computations:

   The thickness h of the root flat segments according to the main spring of parabolic type variable cross-section₂, major-minor spring gap design load δ, step is calculated in (2) G_x-BC, and the stiffness K of calculated each main spring half in step (3)_Mi, sheet variable cross-section few to non-ends contact formula The load p when auxiliary spring of major-minor spring works_KCheck, i.e.

   $P_K=\frac{2{\mathrm{\δh}}_2^3\underset{i=1}{\overset{N}{\Σ}}{K}_{Mi}}{K_{MN}{G}_{x-BC}};$

   In formula, K_MNIt is the half rigidity of the main spring of N sheet.