CN104175831A - Design method for inner round sleeve thickness of suspension stabilizer bar rubber bushing - Google Patents

Abstract

The invention relates to a design method for the inner round sleeve thickness of a suspension stabilizer bar rubber bushing, and belongs to the technical field of vehicle suspensions. A reliable analysis and design method can not be provided always at home and abroad. The design method is characterized in that the inner round sleeve thickness serves as a parameter to be designed, an optimization design mathematical model of the inner round sleeve thickness of the rubber bushing is built according to the required roll angle rigidity design value of a stabilizer bar system, the vehicle tread and the structure and material characteristic parameters of a stabilizer bar and the rubber bushing, and the optimization design value of the inner round sleeve thickness can be obtained through a Matlab program. By means of the method, the accurate and reliable optimization design value of the inner round sleeve thickness can be obtained, and the design level of the stabilizer bar is improved, namely the stabilizer bar system can meet the roll angle rigidity design requirement only by optimization design of the inner round sleeve thickness. Meanwhile, by means of the method, design and testing expenses can be reduced, and vehicle running smoothness and control safety are improved.

Description

The method of designing of the inner circle sleeve thickness of suspension stabilizer rod rubber bush

Technical field

The present invention relates to vehicle suspension stabilizer rod, particularly the method for designing of the inner circle sleeve thickness of suspension stabilizer rod rubber bush.

Background technology

The roll angular rigidity of suspension system is not only subject to the structure of stabilizer rod, the impact of diameter, also be subject to the impact of the factors such as the length of rubber bush, interior radius of circle, exradius, material behavior and installation displacement simultaneously, wherein, the interior radius of circle of rubber bush is that the inner circle sleeve thickness by stabilizer rod diameter and rubber bush determines.Yet, owing to being subject to the restriction of rubber bush radial deformation and the end part of stabilizer rod vertical deviation Deformation analyses theory of computation and the key issues such as affecting that intercouples, radius outside given stabilizator rod structure and material characteristic parameter and rubber bush, axial length and installation site situation, design to the inner circle sleeve thickness of stabilizer rod rubber bush, failure-free resolution design method is failed to provide in home and abroad always at present.Home and abroad scholar utilizes simulation analysis software at present, to Panhard rod system variant and rigidity under fixed structure and load condition, carrying out Numerical Simulation Analysis, but, the method can only be to carrying out simulating, verifying to stabilizer rod system variant and rigidity under fixed structure and load condition, without analytical formula, can not meet the requirement of the design of stabilizer rod system analysis and modernization CAD design.

Along with the fast development of Vehicle Industry and the raising of moving velocity, the design of suspension stabilizer rod system has been proposed to higher designing requirement.How in structure, diameter and the material behavior of given stabilizer rod, and in the constant situation in the material behavior of rubber bush, exradius and two rubber bush installation sites, do not increasing under the prerequisite of design and productive costs, only by the optimal design to the inner circle sleeve thickness of rubber bush, just can make stabilizer rod system reach the designing requirement of roll angular rigidity, be current enterprise technical matters in the urgent need to address.Therefore, must set up a kind of accurately, the method for designing of the inner circle sleeve thickness of failure-free suspension stabilizer rod rubber bush, improve vehicle suspension design level, do not increasing under the prerequisite of productive costs, only pass through the optimal design of the inner circle sleeve thickness of stabilizer rod rubber bush, make stabilizer rod system reach the designing requirement of roll angular rigidity, improve Vehicle Driving Cycle ride comfort and handling safety.

Summary of the invention

For the defect existing in above-mentioned prior art, technical matters to be solved by this invention is to provide a kind of method of designing of inner circle sleeve thickness of easy, failure-free vehicle suspension stabilizer rod rubber bush, as shown in Figure 1, stabilizator rod structure schematic diagram as shown in Figure 2 for its design flow diagram.

For solving the problems of the technologies described above, the method for designing of the inner circle sleeve thickness of suspension stabilizer rod rubber bush provided by the present invention, is characterized in that adopting following steps:

(1) the vertical deviation deformation coefficient G of calculation stability boom end _w:

According to the total length l of Panhard rod _c, brachium l ₁, the mounting distance l between two rubber bushs ₀transition arc radius R, the central angle θ of transition arc, elastic properties of materials model E and Poisson's ratio μ, the vertical deviation deformation coefficient G to end part of stabilizer rod _wcalculate, that is:

$G_w=\frac{G_1+G_2+G_3+G_4+G_5+G_6}{\mathrm{\πE}};$

In formula, $G_1=\frac{64l_1^3}{3},G_2=-\frac{64[{(l_1\cos \mathrm{\θ}+R\sin \mathrm{\θ})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3},$

$G_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\θ}+\frac{\sin 2\mathrm{\θ}}{2})+\frac{1}{2}{R}^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+l_{1}R{\sin }^2\mathrm{\θ}],G_4=\frac{8l_0{(l_0-l_c)}^2}{3},$

$G_5=64R(\mathrm{\μ}+1)[R^2(\frac{3\mathrm{\θ}}{2}+\frac{\sin 2\mathrm{\θ}}{4}-2\sin \mathrm{\θ})+\frac{1}{2}{l}_1^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+4l_{1}R{\sin }^4\frac{\mathrm{\θ}}{2}],$

G ₆＝-32(μ+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _cf+2R _fsinθ _f]；

(2) set up rubber bush omnibearing line stiffness K _xexpression formula:

According to the diameter d of stabilizer rod, the axial length L of rubber bush, elastic modulus E _x, Poisson's ratio μ _x, exradius r _b, inner circle radius r _a=d/2+ δ, wherein, δ is the design parameter of the inner circle sleeve thickness of rubber bush, usings δ as parameter to be designed, sets up rubber bush omnibearing line stiffness K _xexpression formula,

$K_x\left(\mathrm{\δ}\right)=\frac{1}{u\left(\mathrm{\δ}\right)+y\left(\mathrm{\δ}\right)};$

Wherein, K _x(δ) be the expression formula about inner circle sleeve thickness δ;

$u\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)}{2\mathrm{\π}{E}_{x}L}[\ln \frac{r_b}{d/2+\mathrm{\δ}}-\frac{{r_b}^2-{(d/2+\mathrm{\δ})}^2}{{(d/2+\mathrm{\δ})}^2+{r_b}^2}],$

$y\left(\mathrm{\δ}\right)=a_1\left(\mathrm{\δ}\right)I(0,{\mathrm{\α}}_{\mathrm{hb}})+a_2\left(\mathrm{\δ}\right)K(0,{\mathrm{\α}}_{\mathrm{hb}})+a_3\left(\mathrm{\δ}\right)+\frac{(1+{\mathrm{\μ}}_x)}{5\mathrm{\π}{E}_{x}L}[\ln r_b+\frac{{r_b}^2}{r_b^2+{(d/2+\mathrm{\δ})}^2}],$

α _hb＝αr _b,α _a＝α(d/2+δ)，

$a_1\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)[K(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+{{3r}_b}^2)-K(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_x{\mathrm{L\α}}_{\mathrm{hb}}(d/2+\mathrm{\δ})[r_b^2+{(d/2+\mathrm{\δ})}^2][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_2\left(\mathrm{\δ}\right)=\frac{({\mathrm{\μ}}_x+1)[I(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+3r_b^2)-I(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_3\left(\mathrm{\δ}\right)=-\frac{(1+{\mathrm{\μ}}_x)[b_1\left(\mathrm{\δ}\right)+b_2\left(\mathrm{\δ}\right)+b_3\left(\mathrm{\δ}\right)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

b ₁(δ)＝(d/2+δ)((d/2+δ) ²+3r _b ²)[I(1,α _a)K(0,α _a)+K(1,α _a)I(0,α _a)]，

b ₂(δ)＝-r _b(r _b ²+3(d/2+δ) ²)[I(1,α _hb)K(0,α _a)+K(1,α _hb)I(0,α _a)]，

$b_3\left(\mathrm{\δ}\right)={\mathrm{\αr}}_b(d/2+\mathrm{\δ})[{(d/2+\mathrm{\δ})}^2+(r_b^2+{(d/2+\mathrm{\δ})}^2)\ln (d/2+\mathrm{\δ})][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})];$

Bessel correction function: I (0, α _hb), K (0, α _hb); I (1, α _hb), K (1, α _hb);

I(1,α _a)，K(1,α _a)；I(0,α _a)，K(0,α _a)；

(3) foundation and the design calculation of the inner circle sleeve thickness design mathematic model of rubber bush:

According to the wheelspan B of vehicle propons or back axle, the diameter d of stabilizer rod, total length l _c, the designing requirement value of stabilizer rod system roll angular rigidity , the vertical deviation deformation coefficient G of the resulting end part of stabilizer rod of calculating in step (1) _w, and the rubber bush omnibearing line rigidity expression formula K setting up in step (2) _x(δ), set up the mathematical model of optimizing design of rubber bush inner circle sleeve thickness δ, that is:

Utilize Matlab calculation procedure, solve above-mentioned math modeling, just can obtain under stabilizator rod structure and rubber bush installation site permanence condition, meet the design value of the inner circle thickness δ of the rubber bush that stabilizer rod system side inclination angle rigidity Design requires.

The present invention has advantages of than prior art:

Owing to being subject to the restriction of rubber bush radial deformation and the end part of stabilizer rod vertical deviation Deformation analyses theory of computation and the key issues such as affecting that intercouples, domestic at present, the outer inner circle sleeve thickness for stabilizer rod rubber bush, fail to provide failure-free resolution design method always, mostly to utilize finite simulation element analysis software, stabilizer rod system variant and rigidity are carried out to Numerical Simulation Analysis, but, the method can only be to carrying out simulating, verifying to distortion and the rigidity of the stabilizer rod system under fixed structure and load condition, without analytical formula, can not meet the requirement of the design of stabilizer rod system analysis and modernization CAD design.

The present invention can be according to the wheelspan of vehicle, the structure of stabilizer rod and material characteristic parameter, the exradius of rubber bush, axial length, and the roll angular rigidity designing requirement value of stabilizer rod system, the radial rigidity expression formula of deformation coefficient and rubber bush by end part of stabilizer rod, has set up the mathematical model of optimizing design of the inner circle sleeve thickness of stabilizer rod rubber bush, utilizes Matlab program just can obtain the optimal design value of the inner circle sleeve thickness of rubber bush.Utilize that the method can obtain accurately, the optimal design value of the inner circle sleeve thickness of failure-free rubber bush, do not increasing under the prerequisite of design and productive costs, only by the optimal design to the inner circle sleeve thickness of rubber bush, just can make stabilizer rod system reach the designing requirement of roll angular rigidity, improve vehicle suspension design level, improve Vehicle Driving Cycle ride comfort and handling safety; Meanwhile, utilize the method also can reduce design and testing expenses, improve the economic benefit of enterprise.

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

Fig. 1 is the design flow diagram of suspension stabilizer rod rubber bush installing space;

Fig. 2 is the structural representation of lateral stability lever system;

Fig. 3 is the structural representation of rubber bush;

Fig. 4 is that the stabilizer rod system roll angular rigidity of embodiment mono-is with the change curve of rubber bush installing space;

Fig. 5 is that the stabilizer rod system roll angular rigidity of embodiment tri-is with the change curve of rubber bush installing space.

Specific embodiments

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

Embodiment mono-: the wheelspan B=1600mm of certain automobile front-axle, and the structure of the stabilizer rod that adopts, as shown in Figure 2, and wherein, l _cfor the total length of stabilizer rod, l _c=800mm; l ₁for brachium, l ₁=150mm; l ₀for the mounting distance between rubber bush, l ₀=400mm; R is transition arc radius, R=50mm; θ is transition arc central angle, θ=60 °; Elastic modulus E=the 210GPa of stabilizer rod material, Poisson's ratio μ=0.3.The structure of rubber bush as shown in Figure 3, wherein, stabilizer rod 1, interior steel cylinder 2, rubber bush 3, outer steel cylinder 4, the diameter d=20mm of stabilizer rod 1, the elastic modulus E of rubber bush 3 _x=7.84MPa, Poisson's ratio μ _x=0.47, axial length L=25mm, exradius r _b=30mm, inner circle radius r _a=(10+ δ) mm, wherein, δ is the parameter of rubber bush inner circle sleeve wall thickness δ to be designed.The designing requirement value of the roll angular rigidity of this vehicle front suspension stabilizer rod system , the in the situation that of given stabilizer rod and rubber bush installation site, to rubber bush inner circle sleeve wall thickness, δ designs.

The method of designing of the inner circle sleeve thickness of the suspension stabilizer rod rubber bush that example of the present invention provides, as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) the vertical deviation deformation coefficient G of calculation stability boom end _w:

According to the total length l of Panhard rod _c=800mm, brachium l ₁=150mm, transition arc radius R=50mm, central angle θ=60 ° of transition arc, elastic modulus E=210GPa, Poisson's ratio μ=0.3, and the mounting distance l between two rubber bushs ₀=400mm, the vertical deviation deformation coefficient G to end part of stabilizer rod _wcalculate, that is:

$G_w=\frac{G_1+G_2+G_3+G_4+G_5+G_6}{\mathrm{\πE}}=1.5935\×{10}^{-12}{m}^5/N;$

In formula, $G_1=\frac{64l_1^3}{3}=0.0720;G_2=-\frac{64[{(l_1\cos \mathrm{\θ}+R\sin \mathrm{\θ})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3}=-0.1353,$

$G_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\θ}+\frac{\sin 2\mathrm{\θ}}{2})+\frac{1}{2}{R}^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+l_{1}R{\sin }^2\mathrm{\θ}]=0.0737,$

$G_4=\frac{8l_0{(l_0-l_c)}^2}{3}=0.1707,$

$G_5=64R(\mathrm{\μ}+1)[R^2(\frac{3\mathrm{\θ}}{2}+\frac{\sin 2\mathrm{\θ}}{4}-2\sin \mathrm{\θ})+\frac{1}{2}{l}_1^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+4l_{1}R{\sin }^4\frac{\mathrm{\θ}}{2}]=0.0371,$

G ₆＝-32(μ+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _cf+2R _fsinθ _f]＝－0.5624；

(2) set up rubber bush omnibearing line stiffness K _xexpression formula:

According to stabilizer rod diameter d=20mm, the axial length L=25mm of rubber bush, elastic modulus E _x=7.84Mpa, Poisson's ratio μ _x=0.47, exradius r _b, inner circle radius r _a=d/2+ δ, wherein, δ is the design parameter of the inner circle sleeve thickness of rubber bush, usings δ as parameter to be designed, sets up rubber bush omnibearing line stiffness K _xcalculation expression,

$K_x\left(\mathrm{\δ}\right)=\frac{1}{u\left(\mathrm{\δ}\right)+y\left(\mathrm{\δ}\right)};$

Wherein, K _x(δ) be the expression formula about inner circle sleeve thickness δ;

$u\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)}{2\mathrm{\π}{E}_{x}L}[\ln \frac{r_b}{d/2+\mathrm{\δ}}-\frac{{r_b}^2-{(d/2+\mathrm{\δ})}^2}{{(d/2+\mathrm{\δ})}^2+{r_b}^2}\text{],}$

$y\left(\mathrm{\δ}\right)=a_1\left(\mathrm{\δ}\right)I(0,{\mathrm{\α}}_{\mathrm{hb}})+a_2\left(\mathrm{\δ}\right)K(0,{\mathrm{\α}}_{\mathrm{hb}})+a_3\left(\mathrm{\δ}\right)+\frac{(1+{\mathrm{\μ}}_x)}{5\mathrm{\π}{E}_{x}L}[\ln r_b+\frac{{r_b}^2}{r_b^2+{(d/2+\mathrm{\δ})}^2}],$

α _hb＝αr _b＝9.2952,α _a＝α(d/2+δ)，

$a_1\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)[K(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+{{3r}_b}^2)-K(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_x{\mathrm{L\α}}_{\mathrm{hb}}(d/2+\mathrm{\δ})[r_b^2+{(d/2+\mathrm{\δ})}^2][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_2\left(\mathrm{\δ}\right)=\frac{({\mathrm{\μ}}_x+1)[I(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+3r_b^2)-I(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_3\left(\mathrm{\δ}\right)=-\frac{(1+{\mathrm{\μ}}_x)[b_1\left(\mathrm{\δ}\right)+b_2\left(\mathrm{\δ}\right)+b_3\left(\mathrm{\δ}\right)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

b ₁(δ)＝(d/2+δ)((d/2+δ) ²+3r _b ²)[I(1,α _a)K(0,α _a)+K(1,α _a)I(0,α _a)]，

b ₂(δ)＝-r _b(r _b ²+3(d/2+δ) ²)[I(1,α _hb)K(0,α _a)+K(1,α _hb)I(0,α _a)]，

$b_3\left(\mathrm{\δ}\right)={\mathrm{\αr}}_b(d/2+\mathrm{\δ})[{(d/2+\mathrm{\δ})}^2+(r_b^2+{(d/2+\mathrm{\δ})}^2)\ln (d/2+\mathrm{\δ})][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})];$

Bessel correction function: I (1, α _a), K (1, α _a); I (0, α _a), K (0, α _a);

I(0,α _hb)＝1444.8，K(0,α _hb)＝3.7285×10 ^-5；I(1,α _hb)＝1364.7，K(1,α _hb)＝3.9242×10 ^-5；

(3) foundation and the design calculation of the inner circle sleeve thickness design mathematic model of rubber bush:

According to the wheelspan B=1600mm of stabilizer rod place suspension, the diameter d=20mm of stabilizer rod, total length l _c=800mm, the designing requirement value of stabilizer rod system roll angular rigidity in step (1), calculate the vertical deviation deformation coefficient G of resulting end part of stabilizer rod _w=1.5935 * 10 ^-12m ⁵/ N, and the rubber bush omnibearing line rigidity expression formula K setting up in step (2) _x(δ), set up the design mathematic model of the inner circle sleeve thickness δ of rubber bush, that is:

Utilize Matlab calculation procedure, solve above-mentioned math modeling, just can obtain under stabilizator rod structure and rubber bush installation site permanence condition, meet the design value of the inner circle sleeve thickness of the rubber bush that stabilizer rod system side inclination angle rigidity Design requires, δ=4mm.

Wherein, in the situation that other structure and parameter is constant, this stabilizer rod system side inclination angle rigidity Design required value, with the change curve of the inner circle sleeve thickness δ of rubber bush, as shown in Figure 4.

Embodiment bis-: radius of circle and material characteristic parameter in the construction parameter of certain vehicle front suspension, the construction parameter of stabilizer rod and suspension lining, identical with embodiment mono-all, just the desired roll angular rigidity designing requirement of front suspension stabilizer rod system value is different, to under this roll angular rigidity designing requirement, the inner circle sleeve thickness δ of rubber bush is designed.

The design procedure that adopts embodiment mono-, designs the inner circle sleeve thickness δ of this car front suspension stabilizer rod rubber bush.Due to the construction parameter of this vehicle front suspension, the construction parameter of stabilizer rod and rubber bush exradius and material characteristic parameter, identical with embodiment mono-all, just roll angular rigidity designing requirement value is different.Therefore, design the inner circle sleeve thickness δ=8mm of resulting this vehicle front suspension rubber bush.

More known with embodiment mono-, due to roll angular rigidity designing requirement value increase 10kN.m/rad,, as long as the inner circle sleeve thickness δ of rubber bush is increased to 4mm, by previous 4mm, be increased to 8mm, just can, in the situation that not changing other construction parameter, be met the stabilizer rod system of roll angular rigidity designing requirement.

Embodiment tri-: the wheelspan B=1600mm of certain automobile front-axle, and the structure and material of the stabilizer rod that adopts is identical with embodiment's mono-, the diameter d=21mm of stabilizer rod; Installing space l between two rubber bushs ₀=400mm, the exradius r of rubber bush _b=30.5mm, axial length L=25mm; The elastic modulus E of rubber bush _x=7.84MPa, Poisson's ratio μ _x=0.47.The designing requirement value of the roll angular rigidity of this vehicle front suspension stabilizer rod system in given stabilizer rod and rubber bush installation site situation, the inner circle sleeve thickness δ of rubber bush is designed.

The design procedure that adopts embodiment mono-, designs the inner circle sleeve thickness δ of this car front suspension stabilizer rod rubber bush:

(1) the vertical deviation deformation coefficient G of calculation stability boom end _w:

Due to the mounting distance l between stabilizator rod structure parameter, material characteristic parameter and two rubber bushs ₀, all with execute the identical of example one, therefore, the vertical deviation deformation coefficient G of end part of stabilizer rod _walso with execute the identical of example one, that is:

$G_w=\frac{G_1+G_2+G_3+G_4+G_5+G_6}{\mathrm{\πE}}=1.5935\×{10}^{-12}{m}^5/N;$

(2) set up rubber bush omnibearing line stiffness K _xexpression formula:

According to the diameter d=21mm of stabilizer rod, the axial length L=25mm of rubber bush, elastic modulus E _x=7.84Mpa, Poisson's ratio μ _x=0.47, exradius r _b=30.5mm, inner circle radius r _a=d/2+ δ=(10.5+ δ) mm, wherein, δ is the inner circle sleeve thickness of rubber bush, usings δ as parameter to be designed, sets up rubber bush omnibearing line stiffness K _xcalculation expression,

$K_x\left(\mathrm{\δ}\right)=\frac{1}{u\left(\mathrm{\δ}\right)+y\left(\mathrm{\δ}\right)};$

Wherein, K _x(δ) be the expression formula about inner circle sleeve thickness δ;

$u\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)}{2\mathrm{\π}{E}_{x}L}[\ln \frac{r_b}{d/2+\mathrm{\δ}}-\frac{{r_b}^2-{(d/2+\mathrm{\δ})}^2}{{(d/2+\mathrm{\δ})}^2+{r_b}^2}\text{],}$

$y\left(\mathrm{\δ}\right)=a_1\left(\mathrm{\δ}\right)I(0,{\mathrm{\α}}_{\mathrm{hb}})+a_2\left(\mathrm{\δ}\right)K(0,{\mathrm{\α}}_{\mathrm{hb}})+a_3\left(\mathrm{\δ}\right)+\frac{(1+{\mathrm{\μ}}_x)}{5\mathrm{\π}{E}_{x}L}[\ln r_b+\frac{{r_b}^2}{r_b^2+{(d/2+\mathrm{\δ})}^2}],$

α _hb＝αr _b＝9.4501,α _a＝α(d/2+δ)，

$a_1\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)[K(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+{{3r}_b}^2)-K(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_x{\mathrm{L\α}}_{\mathrm{hb}}(d/2+\mathrm{\δ})[r_b^2+{(d/2+\mathrm{\δ})}^2][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_2\left(\mathrm{\δ}\right)=\frac{({\mathrm{\μ}}_x+1)[I(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+3r_b^2)-I(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_3\left(\mathrm{\δ}\right)=-\frac{(1+{\mathrm{\μ}}_x)[b_1\left(\mathrm{\δ}\right)+b_2\left(\mathrm{\δ}\right)+b_3\left(\mathrm{\δ}\right)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

b ₁(δ)＝(d/2+δ)((d/2+δ) ²+3r _b ²)[I(1,α _a)K(0,α _a)+K(1,α _a)I(0,α _a)]，

b ₂(δ)＝-r _b(r _b ²+3(d/2+δ) ²)[I(1,α _hb)K(0,α _a)+K(1,α _hb)I(0,α _a)]，

$b_3\left(\mathrm{\δ}\right)={\mathrm{\αr}}_b(d/2+\mathrm{\δ})[{(d/2+\mathrm{\δ})}^2+(r_b^2+{(d/2+\mathrm{\δ})}^2)\ln (d/2+\mathrm{\δ})][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})];$

Bessel correction function: I (1, α _a), K (1, α _a); I (0, α _a), K (0, α _a);

I(0,α _hb)＝1444.8，K(0,α _hb)＝3.7285×10 ^-5；I(1,α _hb)＝1364.7，K(1,α _hb)＝3.9242×10 ^-5；

(3) foundation and the design calculation of the inner circle sleeve thickness design mathematic model of rubber bush:

According to the wheelspan B=1600mm of stabilizer rod place suspension, the diameter d=21mm of stabilizer rod, total length l _c=800mm, the designing requirement value of stabilizer rod system roll angular rigidity in step (1), calculate the vertical deviation deformation coefficient G of resulting end part of stabilizer rod _w=1.5935 * 10 ^-12m ⁵/ N, and the rubber bush omnibearing line rigidity expression formula K setting up in step (2) _x(δ), set up the design mathematic model of the inner circle sleeve thickness δ of rubber bush, that is:

Utilize Matlab calculation procedure, solve above-mentioned math modeling, just can obtain under stabilizator rod structure and rubber bush installation site permanence condition, meet the design value of the inner circle sleeve thickness of the rubber bush that stabilizer rod system side inclination angle rigidity Design requires, δ=3mm.

Wherein, in the situation that other structure and parameter is constant, the roll angular rigidity designing requirement value of this vehicle stabilization lever system, with the change curve of the inner circle sleeve thickness δ of rubber bush, as shown in Figure 5.

Claims (1)

1. the method for designing of the inner circle sleeve thickness of suspension stabilizer rod rubber bush, its concrete steps are as follows:

(1) the vertical deviation deformation coefficient G of calculation stability boom end _w:

According to the total length l of Panhard rod _c, brachium l ₁, the mounting distance l between two rubber bushs ₀transition arc radius R, the central angle θ of transition arc, elastic properties of materials model E and Poisson's ratio μ, the vertical deviation deformation coefficient G to end part of stabilizer rod _wcalculate, that is:

$G_w=\frac{G_1+G_2+G_3+G_4+G_5+G_6}{\mathrm{\πE}};$

In formula, $G_1=\frac{64l_1^3}{3},G_2=-\frac{64[{(l_1\cos \mathrm{\θ}+R\sin \mathrm{\θ})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3},$

$G_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\θ}+\frac{\sin 2\mathrm{\θ}}{2})+\frac{1}{2}{R}^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+l_{1}R{\sin }^2\mathrm{\θ}],G_4=\frac{8l_0{(l_0-l_c)}^2}{3},$

$G_5=64R(\mathrm{\μ}+1)[R^2(\frac{3\mathrm{\θ}}{2}+\frac{\sin 2\mathrm{\θ}}{4}-2\sin \mathrm{\θ})+\frac{1}{2}{l}_1^2(\mathrm{\θ}-\frac{\sin 2\mathrm{\θ}}{2})+4l_{1}R{\sin }^4\frac{\mathrm{\θ}}{2}],$

G ₆＝-32(μ+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _cf+2R _fsinθ _f]；

(2) set up rubber bush omnibearing line stiffness K _xexpression formula:

According to stabilizer rod diameter d, the axial length L of rubber bush, elastic modulus E _x, Poisson's ratio μ _x, exradius r _b, inner circle radius r _a=d/2+ δ, wherein, δ is the design parameter of the inner circle sleeve thickness of rubber bush, usings δ as parameter to be designed, sets up rubber bush omnibearing line stiffness K _xcalculation expression,

$K_x\left(\mathrm{\δ}\right)=\frac{1}{u\left(\mathrm{\δ}\right)+y\left(\mathrm{\δ}\right)};$

Wherein, K _x(δ) be the expression formula about inner circle sleeve thickness δ;

$u\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)}{2\mathrm{\π}{E}_{x}L}[\ln \frac{r_b}{d/2+\mathrm{\δ}}-\frac{{r_b}^2-{(d/2+\mathrm{\δ})}^2}{{(d/2+\mathrm{\δ})}^2+{r_b}^2}],$

$y\left(\mathrm{\δ}\right)=a_1\left(\mathrm{\δ}\right)I(0,{\mathrm{\α}}_{\mathrm{hb}})+a_2\left(\mathrm{\δ}\right)K(0,{\mathrm{\α}}_{\mathrm{hb}})+a_3\left(\mathrm{\δ}\right)+\frac{(1+{\mathrm{\μ}}_x)}{5\mathrm{\π}{E}_{x}L}[\ln r_b+\frac{{r_b}^2}{r_b^2+{(d/2+\mathrm{\δ})}^2}],$

α _hb＝αr _b,α _a＝α(d/2+δ)，

$a_1\left(\mathrm{\δ}\right)=\frac{(1+{\mathrm{\μ}}_x)[K(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+{{3r}_b}^2)-K(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_x{\mathrm{L\α}}_{\mathrm{hb}}(d/2+\mathrm{\δ})[r_b^2+{(d/2+\mathrm{\δ})}^2][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_2\left(\mathrm{\δ}\right)=\frac{({\mathrm{\μ}}_x+1)[I(1,{\mathrm{\α}}_a)(d/2+\mathrm{\δ})({(d/2+\mathrm{\δ})}^2+3r_b^2)-I(1,{\mathrm{\α}}_{\mathrm{hb}})r_b(3{(d/2+\mathrm{\δ})}^2+{r_b}^2)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

$a_3\left(\mathrm{\δ}\right)=-\frac{(1+{\mathrm{\μ}}_x)[b_1\left(\mathrm{\δ}\right)+b_2\left(\mathrm{\δ}\right)+b_3\left(\mathrm{\δ}\right)]}{5\mathrm{\π}{E}_{x}L(d/2+\mathrm{\δ}){\mathrm{\α}}_{\mathrm{hb}}(r_b^2+{(d/2+\mathrm{\δ})}^2)[I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})]},$

b ₁(δ)＝(d/2+δ)((d/2+δ) ²+3r _b ²)[I(1,α _a)K(0,α _a)+K(1,α _a)I(0,α _a)]，

b ₂(δ)＝-r _b(r _b ²+3(d/2+δ) ²)[I(1,α _hb)K(0,α _a)+K(1,α _hb)I(0,α _a)]，

$b_3\left(\mathrm{\δ}\right)={\mathrm{\αr}}_b(d/2+\mathrm{\δ})[{(d/2+\mathrm{\δ})}^2+(r_b^2+{(d/2+\mathrm{\δ})}^2)\ln (d/2+\mathrm{\δ})][I(1,{\mathrm{\α}}_a)K(1,{\mathrm{\α}}_{\mathrm{hb}})-K(1,{\mathrm{\α}}_a)I(1,{\mathrm{\α}}_{\mathrm{hb}})];$

Bessel correction function: I (0, α _hb), K (0, α _hb); I (1, α _hb), K (1, α _hb);

I(1,α _a)，K(1,α _a)；I(0,α _a)，K(0,α _a)；

(3) foundation and the design calculation of the inner circle sleeve thickness design mathematic model of rubber bush:

According to the wheelspan B of stabilizer rod place suspension, the diameter d of stabilizer rod, total length l _c, the designing requirement value of stabilizer rod system roll angular rigidity , the vertical deviation deformation coefficient G of the resulting end part of stabilizer rod of calculating in step (1) _w, and the rubber bush omnibearing line rigidity expression formula K being set up in step (2) _x(δ), set up the design mathematic model of the inner circle sleeve thickness δ of rubber bush, that is:

Utilize Matlab calculation procedure, solve above-mentioned math modeling, just can obtain under stabilizator rod structure and rubber bush installation site permanence condition, meet the design value of the inner circle thickness δ of the rubber bush that stabilizer rod system side inclination angle rigidity Design requires.