CN103148146B - Method for designing curve shape of limiting check ring of rebound valve of shock absorber - Google Patents

Abstract

The invention relates to a method for designing the curve shape of a limiting check ring of a rebound valve of a shock absorber, and belongs to the technical field of shock absorbers. The method is characterized by comprising the following steps: 1) calculating the deformation coefficient Gr of the rebound valve sheet at any radius r; 2) determining the local throttle loss sum of the rebound valve and the equivalent length of a piston hole in the maximal valve opening state; 3) determining the throttle pressure and the flow quantity of a piston gap in the maximal valve opening state; 4) determining the flow quantity and the throttle pressure of the piston hole in the maximal valve opening state; 5) determining the pressure on a rebound valve sheet in the maximal valve opening state; 6) determining the equivalent height he of the rebound sandwich valve sheet of the shock absorber; and 7) designing the curve shape of the limiting check ring of the rebound valve. With the method, the accurate and reliable curve shape of the limiting check ring of the rebound valve can be obtained, the requirements of the maximal valve opening speed and the damping characteristics can be met, the shock absorber can be prevented being damaged due to breakdown, the stress state of the rebound valve sheet can be also improved at the same time, and the service life of the shock absorber can be prolonged.

Description

The design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber

Technical field

The present invention relates to dydraulic shock absorber, particularly the design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber.

Background technique

The spacing back-up ring of Rebuilt valve of shock absorber is designed to as curve form, is not only in order to meet rebuilt valve maximum limit interdigit gap designing requirement, when rebuilt valve reaches maximum opening, thereby prevent that vibration damper from puncturing, meet the designing requirement of vehicle ride comfort to resistance of shock absorber characteristic; , and reach after maximum opens valve speed when vibration damper movement velocity meanwhile, restore valve block and contact completely with the curved surface of spacing back-up ring, therefore, the accurate spacing back-up ring curve form of rebuilt valve can improve and restores valve block stress, raising vibration damper working life.Owing to being subject to the restriction of Throttle Slice of Shock Absorber Deformation analyses computational problem, it is at present domestic that for Rebuilt valve of shock absorber, spacing back-up ring curve form design does not also have reliable design method, be mostly by the method for repetition test and modification, finally determine the spacing back-up ring curved design of this Rebuilt valve of shock absorber shape.Because the spacing back-up ring curved design of Rebuilt valve of shock absorber shape is subject to normal open hole area a ₀, restore throttle slice thickness hand vibration damper maximum is opened valve damping force f _dk2etc. multifactorial impact, be difficult to obtain the spacing back-up ring curved design of accurate Rebuilt valve of shock absorber shape, once and also no longer require to change with type of vehicle, vehicle parameter, vibration-damper characterist after design shaping.Current China does not have reliable design method to the spacing back-up ring curve form of Rebuilt valve of shock absorber yet yet, much also just with reference to same type vibration damper, the spacing back-up ring curve form of rebuilt valve is designed, even some vibration damper does not adopt the spacing back-up ring with curved surface, and directly with the packing ring of same diameter, replace, therefore, can not bring into play at all spacing back-up ring and curved surface when maximum is driven valve to restoring the support of valve block effect and improving stress, the effect that improves the vibration damper life-span, more can not meet vehicle and vibration damper be opened to the designing requirement of valve damping characteristic.

The spacing back-up ring curve form of Rebuilt valve of shock absorber not only affects Vehicle Driving Cycle smoothness, but also the stress of valve block and the working life of vibration damper are restored in impact.Along with the fast development of automotive industry and improving constantly of Vehicle Speed, absorber designing is had higher requirement, therefore, must set up the design method of the spacing back-up ring curve form of a kind of Rebuilt valve of shock absorber accurately, meet the requirement of Vehicle Driving Cycle smoothness to resistance of shock absorber characteristic, improve vibration damper working life, accelerate product specification and development rate, reduce design and testing expenses.

Summary of the invention

For the defect existing in above-mentioned prior art, technical problem to be solved by this invention is to provide a kind of design method of accurate, the reliable spacing back-up ring curve form of Rebuilt valve of shock absorber.

In order to solve the problems of the technologies described above, the design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber provided by the present invention, as shown in Figure 1, its technological scheme implementation step is as follows for design flow diagram:

(1) restore valve block meaning radius in office rposition deformation coefficient g _r calculating:

According to the interior circle radius that restores valve block r _a, exradius r _b, valve port radius r _k, Young's modulus e, Poisson's ratio μ, calculates and restores valve block meaning radius in office rposition deformation coefficient g _r , that is:

；

Wherein, ;

，

；

, , ,

， ， ， ， ， ， ， ， ；

，

，

，

，

，

，

，

Wherein, ;

(2) determine rebuilt valve part throttle loss stack and piston hole equivalent length when maximum is driven valve :

According to damper piston assembly and restore the structural drawing of valve body, Rebuilt valve of shock absorber part throttle loss stack conversion, for the flow through friction loss of piston hole of fluid, is determined to the piston hole equivalent length when maximum is driven valve for:

；

In formula, physical length for piston hole; for piston hole diameter; piston hole loss factor while driving valve for maximum, , for fluid kinematical viscosity; the coefficient of partial resistance that piston elongated orifices is dwindled suddenly; for the coefficient of partial resistance of piston hole sudden enlargement, , for the gross area of piston hole, , , for the fixing radius that restores valve block base is installed in rebuilt valve inner chamber, for rebuilt valve inner chamber radius, i.e. valve port radius; for fluid is flowed through piston hole because changing the coefficient of partial resistance flowing to;

(3) determine piston crevice throttle pressure when maximum is driven valve and flow :

According to vibration damper maximum, open valve speed point and the corresponding absorber damping force requiring , the annulus area between piston bore and piston rod , determine that vibration damper opens valve speed in maximum piston gap pressure during point for:

；

In formula, for damper piston internal diameter of cylinder; for diameter of piston rod;

According to damper structure parameter and fluid parameter: piston bore internal diameter , piston mean gap , eccentricity , fluid kinetic viscosity , piston gap length , in maximum, open valve speed piston gap pressure during point , determine in maximum and open valve speed piston gap flow during point for:

；

(4) determine piston hole flow when maximum is driven valve and choke pressure :

According to vibration damper maximum, open valve speed annulus area between point and piston bore and piston rod , and in step (3) , determine piston hole flow when maximum is driven valve for:

；

According to fluid kinetic viscosity , piston hole number , piston hole diameter , piston hole flow and in step (2) , determine the piston hole choke pressure when maximum is driven valve for:

；

(5) determine and when maximum is driven valve, restore the suffered pressure of valve block :

When driving valve, maximum restores the suffered pressure of valve block equal the choke pressure in vibration damper normal open hole, according to maximum, open relation between valve rear oil duct figure and piston crevice throttle pressure and piston hole and normal open hole choke pressure, utilize in step (3) , and step (4) , determine and when maximum is driven valve, restore the suffered pressure of valve block for:

；

(6) determine the equivalent thickness of absorber stack valve block h _e:

According to the design thickness of absorber stack valve block and sheet number ( h ₁, n ₁; h ₂, n ₂; h _n , n _n), determine the equivalent thickness of absorber stack valve block h _e, that is:

；

(7) the spacing back-up ring curve form of design rebuilt valve :

According to the height at place, garden in spacing back-up ring , step (1) g _r , in step (5) , in step (6) h _e, to the spacing back-up ring curve form of rebuilt valve design, that is:

。

The present invention has advantages of than prior art:

Owing to being subject to the restriction of Throttle Slice of Shock Absorber Deformation analyses computational problem, it is at present domestic that for Rebuilt valve of shock absorber, spacing back-up ring curve form design does not also have reliable design method, be mostly by the method for repetition test and modification, finally determine the spacing back-up ring curved design of this Rebuilt valve of shock absorber shape.Because the spacing back-up ring curved design of Rebuilt valve of shock absorber shape is subject to normal open hole area a ₀, restore throttle slice thickness hand vibration damper maximum is opened valve damping force f _dk2etc. multifactorial impact, be difficult to obtain the spacing back-up ring curved design of accurate Rebuilt valve of shock absorber shape, once and also no longer require to change with type of vehicle, vehicle parameter, vibration-damper characterist after design shaping.Current China does not have reliable design method to the spacing back-up ring curve form of Rebuilt valve of shock absorber yet yet, much also just with reference to same type vibration damper, the spacing back-up ring curve form of rebuilt valve is designed, even some does not adopt the spacing back-up ring with curved surface, and directly with the packing ring of same diameter, replace, can not bring into play at all spacing back-up ring and curved surface when maximum is driven valve to restoring the support of valve block effect and improving stress, the effect that improves the vibration damper life-span, more can not meet vehicle and vibration damper be opened to the designing requirement of valve damping characteristic.

The design method of the spacing back-up ring curve form of this Rebuilt valve of shock absorber, according to damper structure parameter, oil circuit when fluid parameter and maximum are driven valve, by local pressure loss stack conversion, it is the equivalent length of piston hole, determine the suffered pressure of absorber valve block when maximum is driven valve, then according to the thickness and sheet number and the equivalent thickness that restore stack valve block, utilize the Deformation analyses calculating formula of vibration damper valve block meaning radius in office, the spacing back-up ring curve form of Rebuilt valve of shock absorber is resolved to design, therefore, the spacing back-up ring curve form of rebuilt valve design load is accurate, reliably, guarantee that vibration damper opens the damping characteristic requirement under valve speed in maximum, prevent vibration damper electrical breakdown, improve and restore the stress of valve block when opening valve speed, improve the life-span of vibration damper, simultaneously, avoid repetition test and modification, reduce design and testing expenses.

In order to understand better the present invention, below in conjunction with accompanying drawing, be further described.

Fig. 1 is the spacing back-up ring curve form of rebuilt valve design flow diagram;

Fig. 2 is damper piston assembly and rebuilt valve structural drawing;

Fig. 3 is the spacing back-up ring of rebuilt valve and curve form figure;

Fig. 4 is the oil circuit figure of Rebuilt valve of shock absorber maximum while driving valve;

Fig. 5 is embodiment one the desired speed characteristic curve of design vibration damper;

Fig. 6 is the deformation coefficient curve at embodiment one any radius r of design absorber valve block place;

Fig. 7 is the spacing back-up ring curved design of embodiment one rebuilt valve shape;

Fig. 8 is the speed characteristic curve that embodiment one design vibration damper test obtains;

Fig. 9 is embodiment two the desired speed characteristic curve of design vibration damper;

Figure 10 is the spacing back-up ring curved design of embodiment two rebuilt valve shape;

Figure 11 is the speed characteristic curve that embodiment two design vibration damper test obtains.

Specific embodiments

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

embodiment one: certain damper piston assembly and rebuilt valve structure, as shown in Figure 2, piston body 1, piston rod 2, piston hole 3, restore valve block 4, spacing back-up ring 5, tightening nut 6, wherein, the excessive vibration damper that makes of rebuilt valve opening punctures when preventing that vibration damper movement velocity is excessive, and that restores valve block 4 is equipped with spacing back-up ring 5 below, and is fixed with tightening nut 6.The surface of spacing back-up ring 5 becomes cambered surface, as shown in Figure 3, and to guarantee that vibration damper drives valve under normal circumstances, and when vibration damper movement velocity reaches certain numerical value, restore throttle valve plate bending deflection and contact with spacing back-up ring, rebuilt valve reaches maximum opening, thereby prevents that vibration damper from puncturing; Meanwhile, when vibration damper movement velocity reaches certain numerical value, restore throttle valve plate and contact completely with spacing back-up ring curved surface, improve the stress of restoring valve block, improve the working life of vibration damper.The structural parameter of vibration damper and valve body structure and fluid parameter are as follows: piston bore internal diameter , diameter of piston rod d _g=20mm, the annulus area between piston bore and piston rod ; Piston gap length ; Piston mean gap ; Eccentricity ; Fluid kinematical viscosity viscosity = m ²/ s, density , kinetic viscosity ; Piston hole diameter , number , direction angle ; Throttle valve exradius , interior diameter , valve port radius ,, Young's modulus e=200GPa, Poisson's ratio μ=0.3; Thickness and the sheet number of absorber stack valve block are respectively, ; ; ; Normal open hole area , normal open hole flow coefficient ; Valve block is in outer radius r _bdeformation coefficient m ⁶/ N; The desired speed characteristic curve of absorber designing, as shown in Figure 5, wherein, Rebuilt valve of shock absorber is opened valve speed for the first time , open for the first time valve damping force ; Maximum is opened valve speed , maximum is opened valve damping force ; The maximum height y of spacing back-up ring inner circle ₀=5mm, designs the curve form of spacing back-up ring.

The design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber that example of the present invention provides, as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) restore valve block meaning radius in office rposition deformation coefficient g _r calculating:

According to the interior circle radius that restores valve block r _a=5.5mm, exradius r _b=8.5mm, valve port radius r _k=8.0mm, Young's modulus e=200GPa, Poisson's ratio μ=0.3, calculates and restores valve block meaning radius in office rposition deformation coefficient g _r , that is:

；－

Wherein, ;

，

；

＝－5.78×10 ^－4, =－0.00246,

＝－1.925×10 ^－8,

=-1.17612×10 ^－7， =181.82，

=-0.05173， =0.011， =6.655×10 ^－7； =-9688.58， =-9.09599， =2.6， =9.537×10 ^－4；

=-3.8×10 ^－4，

=-6.558，

=-24.5565；

，

=0.0022679；

=0.0099，

=530.67，

=2479.81，

=0.06249，

Wherein, =5.7549 * 10 ^-8;

Calculate resulting absorber valve block meaning radius in office rdeformation coefficient Gr, as shown in Figure 6.

(2) determine rebuilt valve part throttle loss stack and piston hole equivalent length when maximum is driven valve :

According to damper piston assembly and rebuilt valve structural drawing 2, the physical length of piston hole =9.0mm; Piston hole diameter =2.0mm, opens valve speed in maximum when vibration damper fluid is flowed through piston hole during=1.0m/s, dwindle suddenly coefficient of partial resistance , sudden enlargement coefficient of partial resistance with change direction coefficient of partial resistance and friction loss , determine piston hole equivalent length while driving valve greatly for:

=140.1mm；

In formula, =0.0231, , , = m ²/ s; Table look-up, ; , , , , , , ; , , wherein, ;

(3) determine piston crevice throttle pressure when maximum is driven valve and flow :

According to the desired speed characteristic curve of absorber designing, as shown in Figure 5, maximum is opened valve speed the corresponding absorber damping force requiring of point , piston bore internal diameter , diameter of piston rod =20mm, and the annulus area between piston bore and piston rod = , determine that vibration damper opens valve speed in maximum time piston gap pressure for:

5.471 ；

According to damper structure parameter and fluid parameter: piston bore internal diameter =28mm, piston mean gap , eccentricity =1.0, fluid kinetic viscosity , piston gap length , and piston gap pressure =5.471 , determine in maximum and open valve speed time piston gap flow for:

8.0108 ；

(4) determine piston hole flow when maximum is driven valve and choke pressure :

Piston hole flow when definite maximum is driven valve : according to rebuilt valve maximum, open valve oil road Fig. 4 known: maximum is opened the recovery ring-shaped throttling gap of valve and connected with piston hole with after the parallel connection of normal open hole, and then in parallel with piston gap, according to vibration damper maximum, opens valve speed annulus area between=1.0m/s and piston bore and piston rod = , and in step (3) =8.0108 , determine piston hole flow when maximum is driven valve for:

2.2189 ；

According to fluid kinetic viscosity , piston hole diameter =2.0mm and number =4, piston hole flow =2.2189 and the piston hole equivalent length in step (1) =140.1mm, determines the piston hole choke pressure when maximum is driven valve for:

1.7618 ；

(5) determine and when maximum is driven valve, restore the suffered pressure of valve block :

According to Fig. 4 Rebuilt valve of shock absorber maximum, open valve rear oil duct figure, when maximum is driven valve, restore the suffered pressure of valve block equal the choke pressure in vibration damper normal open hole, utilize in step (3) =5.471 , and step (4) =1.7618 , determine and when maximum is driven valve, restore the suffered pressure of valve block for:

5.2948 ；

(6) determine the equivalent thickness of absorber stack valve block h _e:

According to design thickness and the sheet number of absorber stack valve block ; ; , determine the equivalent thickness of absorber stack valve block h _e, that is:

＝0.286mm；

(7) the spacing back-up ring curve form of design rebuilt valve y _r :

According to the height at place, garden in spacing back-up ring =5.0mm, in step (1) g _r , in step (5) =5.2948 , in step (6) h _e=0.286mm, to the spacing back-up ring curve form of rebuilt valve design, the spacing back-up ring curve form of Rebuilt valve of shock absorber that design obtains as shown in Figure 7.

Utilize the comprehensive performance test bed vibration damper to embodiment's one designed processing of electro-hydraulic servo vibration damper to carry out characteristic test, measured vibration damper speed characteristic curve as shown in Figure 8, open valve speed and be by vibration damper v _k2=1.01m/s, with the desired valve speed point of opening of design v _k2=1.0m/s matches, and shows that the design method of the spacing back-up ring curve form of this Rebuilt valve of shock absorber is correct.

embodiment two: certain hydraulic fluid pressure damper designs desired recovery speed characteristics, and as shown in Figure 9, maximum is opened valve speed , maximum is opened valve damping force ; Restore design thickness and the sheet number of stack valve block ; ; , equivalent thickness =0.2674mm, the structural parameter of vibration damper, fluid parameter are identical with example one, the height at place, garden in the spacing back-up ring of rebuilt valve =5.0mm.

Adopt embodiment one design procedure, to the spacing back-up ring curve form of this Rebuilt valve of shock absorber design; Due to the structural parameter of vibration damper, fluid parameter, restore the structural parameter of valve block, all identical with embodiment one, therefore, restores the deformation coefficient of valve block g _r identical with embodiment one, as shown in Figure 6; Just thickness and the sheet number of this absorber stack valve block and the maximum of restoring stroke are opened valve damping characteristic and are required different from embodiment one, wherein:

Restore the equivalent thickness of stack valve block h _e=0.2674mm;

When driving valve, maximum restores the suffered pressure of valve block =4.674 ;

Therefore the spacing back-up ring curve form of Rebuilt valve of shock absorber that, design obtains as shown in figure 10.

Utilize the comprehensive performance test bed vibration damper to embodiment's two designed processing of electro-hydraulic servo vibration damper to carry out characteristic test, measured vibration damper speed characteristic curve as shown in figure 11, open valve speed and be by vibration damper v _k2=1.02m/s, with the desired valve speed point of opening of design v _k2=1.0m/s matches, and shows that the design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber is correct.

Claims (1)

1. the design method of the spacing back-up ring curve form of Rebuilt valve of shock absorber, its concrete steps are as follows:

(1) restore valve block meaning radius r in office position deformation coefficient G _rcalculating:

According to the inner circle radius r of restoring valve block _a, exradius r _b, valve port radius r _k, elastic modulus E, Poisson's ratio μ, calculates and restores valve block meaning radius r in office position deformation coefficient G _r, that is:

$G_r=\left\{\begin{array}{cc}{G}_{r1}-G_{r21}& (r_a\&le;r\&le;r_k)\\ G_{r1}-G_{r22}& (r_k<r\&le;r_b)\end{array}\right.;$

Wherein, $G_{r1}=\frac{3(1-{\mathrm{\&mu;}}^2)[E_1\log \left(r\right)+E_2{r}^2\log \left(r\right)+E_3{r}^2+E_4+r^4]}{16E};$

G _r21＝b ₁log(r)+b ₂r ²log(r)+b ₃r ²+b ₄(r _a≤r≤r _k)，

G _r22＝c ₁log(r)+c ₂r ²log(r)+c ₃r ²+c ₄(r _k<r≤r _b)；

$E_2=-8r_b^2,E_3=\frac{(A_1{E}_2{B}_2+A_1{B}_4-B_1{E}_2{A}_2-B_1{A}_4)}{B_1{A}_3-A_1{B}_3},E_1=-\frac{A_4+E_2{A}_2+E_3{A}_3}{A_1},$

$E_4=-(r_a^4-E_1\log \left(r_a\right)+E_2{r}_a^2\log \left(r_a\right)+E_3{r}_a^2),A_1=\frac{1}{r_a},A_2=2r_a\log \left(r_a\right)+r_a,A_3=2r_a,$

$A_4=4r_a^2,B_1=\frac{(\mathrm{\&mu;}-1)}{r_b^2},B_2=2(\mathrm{\&mu;}+1)\ln r_b+\mathrm{\&mu;}+3,B_3=2(\mathrm{\&mu;}+1),B_4=4r_b^2(3+\mathrm{\&mu;});$

$\begin{array}{c}{b}_1=\frac{12(1-{\mathrm{\&mu;}}^2)r_a^2}{720\mathrm{EK}}(20r_k^3{r}_b^2\mathrm{\&mu;}-180r_b^4{r}_k\ln r_a+9r_k^5\mathrm{\&mu;}+20r_k^3{r}_b^2+45r_b^4{r}_k+16r_b^5\mathrm{\&mu;}-60r_k^3{r}_b^2\mathrm{\&mu;}\ln r_k+180r_b^4{r}_k\mathrm{\&mu;}\ln r_b\\ +60r_k^3{r}_b^2\mathrm{\&mu;}\ln r_a-180r_b^4\mathrm{\&mu;}\ln r_a-45r_b^4{r}_k\mathrm{\&mu;}-120r_b^5\ln r_b+60r_k^3{r}_b^2\ln r_a+120r_b^5\mathrm{\&mu;}\ln r_a+120r_b^5\ln r_a-9r_k^5\\ -60r_k^3{r}_b^2\ln r_k+180r_b^4{r}_k\ln r_b-120r_b^5\mathrm{\&mu;}\ln r_b-56r_b^5),\end{array}$

$b_2=\frac{(1-{\mathrm{\&mu;}}^2)(r_k^2+r_k{r}_b-r_b^2)}{2E},$

$\begin{array}{c}{b}_3=-\frac{12(1-{\mathrm{\&mu;}}^2)}{1440\mathrm{EK}}(-120r_a^2{r}_b^3\ln r_a-10r_k^3{r}_b^2\mathrm{\&mu;}-60r_k^3{r}_b^2\mathrm{\&mu;}\ln r_k+180r_b^4{r}_k\mathrm{\&mu;}\ln r_b+60r_k^3{r}_b^2\mathrm{\&mu;}\ln r_a\\ +180r_k{r}_a^2{r}_b^2\ln r_a+120r_a^2{r}_b^3\mathrm{\&mu;}\ln r_a+9r_k^5\mathrm{\&mu;}-10r_k^3{r}_b^2+135r_b^4{r}_k-44r_b^5\mathrm{\&mu;}-60r_a^2{r}_b^2-30r_k^3{r}_a^2+45r_b^4\\ -180r_k{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_a-9r_k^5+90r_k{r}_a^2{r}_b^2+60r_a^2{r}_b^3\mathrm{\&mu;}+30r_k^3{r}_a^2\mathrm{\&mu;}-90r_k{r}_a^2{r}_b^2\mathrm{\&mu;}\\ -116r_b^5-120r_b^5\ln r_b-60r_k^3{r}_b^2\ln r_k+180r_b^4{r}_k\ln r_b-120r_b^5\mathrm{\&mu;}\ln r_b-60r_k^3{r}_a^2\ln r_a),\end{array},r_k\mathrm{\&mu;}$

$\begin{array}{c}{b}_4=\frac{r_a^{2}12(1-{\mathrm{\&mu;}}^2)}{1440\mathrm{EK}}[-10r_k^3{r}_b^2\mathrm{\&mu;}+120r_k^3{r}_b^2\mathrm{\&mu;}\ln r_a\ln r_k-60r_k^3{r}_b^2\mathrm{\&mu;}\ln r_k+180r_b^4{r}_k\mathrm{\&mu;}\ln r_b-270r_b^4{r}_k\ln r_a\\ +20r_k^3{r}_b^2\ln r_a+88r_b^5\mathrm{\&mu;}\ln r_a+9r_k^5\mathrm{\&mu;}-10r_k^3{r}_b^2+135r_b^4{r}_k-44r_k^5\mathrm{\&mu;}-60r_a^2{r}_b^3-30r_k^3{r}_a^2+45r_b^4{r}_k\mathrm{\&mu;}\\ +18r_k^5\ln r_a+360r_b^4{r}_k{\left(\ln r_a\right)}^2-120r_k^3{r}_b^2{\left(\ln r_a\right)}^2-240r_b^5\mathrm{\&mu;}{\left(\ln r_a\right)}^2-18r_k^5\mathrm{\&mu;}\ln r_a+240r_b^5\ln r_a\ln r_b\\ -120r_k^3{r}_a^2\mathrm{\&mu;}{\left(\ln r_a\right)}^2+360r_b^4{r}_k\mathrm{\&mu;}{\left(\ln r_a\right)}^2+120r_k^3{r}_b^2\ln r_a\ln r_k-360r_b^4{r}_k\ln r_a\ln r_b+240r_b^5\mathrm{\&mu;}\ln r_a\ln r_b\\ +232r_b^5\ln r_a+20r_k^3{r}_b^2\mathrm{\&mu;}\ln r_a-90r_b^4{r}_k\mathrm{\&mu;}\ln r_a-240r_b^5{\left(\ln r_a\right)}^2-360r_b^4{r}_k\mathrm{\&mu;}\ln r_a\ln r_b-9r_k^5+90r_a^2{r}_b^2{r}_k\end{array}$

$+60r_a^2{r}_b^3\mathrm{\&mu;}+30r_k^3{r}_a^2\mathrm{\&mu;}-90r_a^2{r}_b^2{r}_k\mathrm{\&mu;}-116r_b^5-120r_b^5\ln r_b-60r_k^3{r}_b^2\ln r_k+180r_b^4{r}_k\ln r_b-120r_b^5\mathrm{\&mu;}\ln r_b],$

$\begin{array}{c}{c}_1=\frac{12r_b^2(1-{\mathrm{\&mu;}}^2)}{720\mathrm{EK}}(9r_k^5\mathrm{\&mu;}+9r_k^5+60r_k^3{r}_a^2\ln r_a-60r_k^3{r}_a^2\ln r_k+20r_k^3{r}_a^2+20r_k^3{r}_a^2\mathrm{\&mu;}-60\mathrm{\&mu;}{r}_k^3{r}_a^2\ln r_k\\ +60\mathrm{\&mu;}{r}_k^3{r}_a^2\ln r_a+45r_k{r}_a^2{r}_b^2+180r_k{r}_a^2{r}_b^2\ln r_b-180r_k{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_a+180r_k{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_b-180r_k{r}_a^2{r}_b^2\ln r_a\\ -45r_k{r}_a^2{r}_b^2\mathrm{\&mu;}-56r_a^2{r}_b^3-120r_a^2{r}_b^3\ln r_b+120r_a^2{r}_b^3\mathrm{\&mu;}\ln r_a+16r_a^2{r}_b^3\mathrm{\&mu;}+120r_a^2{r}_b^3\ln r_a-120r_a^2{r}_b^3\mathrm{\&mu;}\ln r_b),\end{array}$

$c_2=-\frac{r_b^2}{E(r_k-r_b)}(\frac{r_k}{8}-\frac{r_b}{12}),$

$\begin{array}{c}{c}_3=-\frac{12(1-{\mathrm{\&mu;}}^2)}{1440\mathrm{EK}}(-44r_b^5\mathrm{\&mu;}-120r_b^5\ln r_b+135r_k{r}_b^4-120r_a^2{r}_b^3\ln r_a+180r_b^4{r}_k{\mathrm{\&mu;}}_k\ln r_b-60r_a^2{r}_k^3\mathrm{\&mu;}\ln r_k\\ -60r_a^2{r}_k^3\ln r_a+90r_a^2{r}_b^2{r}_k+60r_a^2{r}_k^3\ln r_k-60r_a^2{r}_b^3-20r_a^2{r}_k^3-180r_a^2{r}_b^2\mathrm{\&mu;}\ln r_a+60r_a^2{r}_b^3\mathrm{\&mu;}\\ 180r_b^4{r}_k\ln r_b+20r_a^2{r}_k^3\mathrm{\&mu;}-116r_b^5+120r_a^2{r}_b^3\mathrm{\&mu;}\ln r_a-90r_a^2{r}_b^2{r}_k\mathrm{\&mu;}-120r_b^5\mathrm{\&mu;}\ln r_b+180r_a^2{r}_b^2{r}_k\ln r_a\\ +60r_a^2{r}_k^3\mathrm{\&mu;}\ln r_a-9r_k^5+9r_k^5\mathrm{\&mu;}+45r_b^4{r}_k\mathrm{\&mu;}),\end{array}$

$\begin{array}{c}{c}_4=-\frac{12(1-{\mathrm{\&mu;}}^2)}{1440\mathrm{EK}}[-1350r_k{r}_a^2{r}_b^4+171r_k^5{r}_a^2\mathrm{\&mu;}-180r_k^5{r}_a^2\ln r_a+180r_k^5{r}_b^2\ln r_k-900r_k{r}_a^4{r}_b^2-300r_k^3{r}_a^4\mathrm{\&mu;}\\ -180r_k^5{r}_a^2\mathrm{\&mu;}\ln r_k+600r_k^3{r}_a^2{r}_b^2\ln r_k+1200r_a^2{r}_b^5\mathrm{\&mu;}\ln r_b-1800r_k{r}_a^2{r}_b^4\ln r_b-2400r_a^2{r}_b^5\ln r_a\ln r_b\\ +2400r_a^2{r}_b^5\mathrm{\&mu;}{\left(\ln r_a\right)}^2-880r_a^2{r}_b^5\mathrm{\&mu;}\ln r_a+180r_k^5{r}_a^2\mathrm{\&mu;}\ln r_a-200r_k^3{r}_a^2{r}_b^2\ln r_a+1200r_k^3{r}_a^2{r}_b^2{\left(\ln r_a\right)}^2\\ +2700r_k{r}_a^2{r}_b^4\ln r_a-3600r_k{r}_a^2{r}_b^4{\left(\ln r_a\right)}^2+1160r_a^2{r}_b^5+600r_a^4{r}_b^3-171r_k^5{r}_a^2-261r_k^5{r}_b^2+300r_k^3{r}_a^4\\ -600r_a^4{r}_b^3\mathrm{\&mu;}+900r_k{r}_a^2{r}_b^4\mathrm{\&mu;}\ln r_a-3600r_k{r}_a^2{r}_b^4\mathrm{\&mu;}{\left(\ln r_a\right)}^2-2400r_a^2{r}_b^5\mathrm{\&mu;}\ln r_a\ln r_b\\ +3600r_k{r}_a^2{r}_b^4\ln r_a\ln r_b+600r_k^3{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_k+1200r_a^2{r}_b^5\ln r_b+1200r_k^3{r}_a^2{r}_b^2\mathrm{\&mu;}{\left(\ln r_a\right)}^2\\ -200r_k^3{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_a+3600r_k{r}_a^2{r}_b^4\mathrm{\&mu;}\ln r_a\ln r_b+440r_a^2{r}_b^5\mathrm{\&mu;}+100r_k^3{r}_a^2{r}_b^2-261r_k^5{r}_b^2\mathrm{\&mu;}\\ -1800r_k{r}_a^2{r}_b^4\mathrm{\&mu;}\ln r_b-1200r_k^3{r}_a^2{r}_b^2\mathrm{\&mu;}\ln r_a\ln r_k-1200r_k^3{r}_a^2{r}_b^2\ln r_a\ln r_k+180r_k^5{r}_b^2\mathrm{\&mu;}\ln r_k\\ +180r_k^5{r}_a^2\ln r_k+2400r_a^2{r}_b^5{\left(\ln r_a\right)}^2-2320r_a^2{r}_b^5\ln r_a+100r_k^3{r}_a^2{r}_b^2\mathrm{\&mu;}+900r_k{r}_a^4{r}_b^2-450r_k{r}_a^2{r}_b^4\mathrm{\&mu;}],\end{array}$

Wherein, $K=r_b^3+r_k{r}_a^2\mathrm{\&mu;}-r_b{r}_a^2\mathrm{\&mu;}+r_k{r}_a^2+r_b{r}_a^2+r_b^3\mathrm{\&mu;}-r_b^2{r}_k-r_b^2{r}_k\mathrm{\&mu;};$

(2) determine rebuilt valve part throttle loss stack and piston hole equivalent length L when maximum is driven valve _hek2:

According to damper piston assembly and restore the structural drawing of valve body, Rebuilt valve of shock absorber part throttle loss stack conversion, for the flow through friction loss of piston hole of fluid, is determined to the piston hole equivalent length L when maximum is driven valve _hek2for:

$L_{\mathrm{hek}2}=L_h+({\mathrm{\&zeta;}}_{h1}+{\mathrm{\&zeta;}}_{h2}+{\mathrm{\&zeta;}}_{h3})\frac{{\mathrm{\&lambda;}}_{\mathrm{hk}2}}{d_h};$

In formula, L _hphysical length for piston hole; d _hfor piston hole diameter; λ _hk2piston hole loss factor while driving valve for maximum, ν is fluid kinematical viscosity; ζ _h1the coefficient of partial resistance that piston elongated orifices is dwindled suddenly; ζ _h2for the coefficient of partial resistance of piston hole sudden enlargement, ζ _h2=[1-A _h/ S _f] ², A _hfor the gross area of piston hole, r _afor the fixing radius that restores valve block base, r are installed in rebuilt valve inner chamber _kfor rebuilt valve inner chamber radius, i.e. valve port radius; ζ _h3for fluid is flowed through piston hole because changing the coefficient of partial resistance flowing to;

(3) determine piston crevice throttle pressure when maximum is driven valve _pHk2with flow Q _hk2:

According to vibration damper maximum, open valve speed V _k2point and the corresponding absorber damping force F requiring _dk2, the annulus area between piston bore and piston rod determine that vibration damper opens valve speed V in maximum _k2piston gap pressure p during point _hk2for:

p _Hk2＝F _dk2/S _H；

In formula, D _hfor damper piston internal diameter of cylinder; d _gfor diameter of piston rod;

According to damper structure parameter and fluid parameter: piston bore inside diameter D _h, piston mean gap δ _h, eccentric ratio e, fluid kinetic viscosity μ _t, piston gap length L _h, in maximum, open valve speed V _k2piston gap pressure p during point _hk2, determine in maximum and open valve speed V _k2piston gap flow Q during point _hk2for:

$Q_{\mathrm{Hk}2}=\frac{\mathrm{\&pi;}{D}_H{{\mathrm{\&delta;}}_H}^3(1+1.5e^2)p_{\mathrm{Hk}2}}{12{\mathrm{\&mu;}}_t{L}_H};$

(4) determine piston hole flow Q when maximum is driven valve _hk2and choke pressure p _hk2:

According to vibration damper maximum, open valve speed V _k2annulus area S between point and piston bore and piston rod _h, and the Q in step (3) _hk2, determine piston hole flow Q when maximum is driven valve _hk2for:

Q _hk2＝V _k2S _H-Q _Hk2；

According to fluid kinetic viscosity μ _t, piston hole number n _h, piston hole diameter d _h, piston hole flow Q _hk2and the L in step (2) _hek2, determine the piston hole choke pressure p when maximum is driven valve _hk2for:

$p_{\mathrm{hk}2}=\frac{128{\mathrm{\&mu;}}_t{L}_{\mathrm{hek}2}{Q}_{\mathrm{hk}2}}{\mathrm{\&pi;}{n}_h{d_h}^4};$

(5) determine and when maximum is driven valve, restore the suffered pressure p of valve block _fk2:

When driving valve, maximum restores the suffered pressure p of valve block _fk2equal the choke pressure in vibration damper normal open hole, according to maximum, open relation between valve rear oil duct figure and piston crevice throttle pressure and piston hole and normal open hole choke pressure, utilize the p in step (3) _hk2, and the p of step (4) _hk2, determine and when maximum is driven valve, restore the suffered pressure p of valve block _fk2for:

p _fk2＝p _Hk2-p _hk2；

(6) determine the equivalent thickness h of absorber stack valve block _e:

According to design thickness and the sheet number (h of absorber stack valve block ₁, n ₁; h ₂, n ₂; h _n, n _n), determine the equivalent thickness h of absorber stack valve block _e, that is:

$h_e=\sqrt[3]{n_1{h}_1^3+n_2{h}_2^3+\&CenterDot;\&CenterDot;\&CenterDot;+n_n{h}_n^3};$

(7) the spacing back-up ring curve form of design rebuilt valve y _r:

According to the height y at place, garden in spacing back-up ring ₀, the G of step (1) _r, the p in step (5) _fk2, the h in step (6) _e, to the spacing back-up ring curve form of rebuilt valve y _rdesign, that is:

$y_r=y_0-G_r\frac{p_{\mathrm{fk}2}}{h_e}.$