CN104200123A - Method for calculating rigidity of transverse stabilizer bar system on basis of radial deformation of rubber bushing - Google Patents

Abstract

The invention relates to a method for calculating rigidity of a transverse stabilizer bar system on basis of radial deformation of a rubber bushing and belongs to the technical field of vehicle suspensions. The method is characterized by including the steps of first, according to structural and material characteristics and mounting position parameters of a stabilizer bar and the rubber bushing, analytically calculating radial linear rigidity K<x> of the rubber bushing and vertical deformation coefficient G<w> of an end of the stabilizer bar; second, according to the structural parameters and mounting positions of the stabilizer bar and the rubber bushing and according to the radial linear rigidity K<x> and the vertical deformation coefficient G<w> obtained by calculation, analytically calculating the rigidity K<wle> of the transverse stabilizer bar system on basis of the radial deformation of the rubber bushing. Simulation and verification by the ANSYS software show that the method is accurate and reliable; by the application of the method, the design level and quality of the vehicle suspension stabilizer bar system can be increased, design and testing expenses are reduced, and the reliable rigidity calculation method is provided for the development of stabilizer bar CAD (computer aided design) software.

Description

The computing method of the QS system stiffness based on rubber bushing radial deformation

Technical field

The present invention relates to vehicle suspension, particularly the computing method of the QS system stiffness based on rubber bushing radial deformation.

Background technology

Lateral stability lever system is one of important spare part in vehicle suspension system.It not only can prevent that vehicle vehicle body when Turning travel from excessive inclination occurring, and also directly affects control stability and the driving safety of vehicle.Current home and abroad, owing to being subject to the restriction of rubber bushing radial deformation analytical Calculation, the stabilizer bar system global stiffness of failing to provide based on rubber bushing radial deformation carries out accurate Analytic Calculation Method, can only adopt tradition piecemeal integral method to not considering that QS self rigidity in rubber bushing situation calculates, and because stabilizator rod structure is complicated, there is transition arc part, in practical stability bar Rigidity Calculation process, is left in the basket.At present, home and abroad great majority are all to utilize ANSYS finite element software, by modeling, carry out numerical simulation, although can access reliable distortion and rigidity simulation numerical, but utilize finite element emulation software, can only, to carrying out simulating, verifying to distortion and the rigidity of the lateral stability lever system under fixed structure and load, can not provide reliable analytical formula, therefore, cannot meet the requirement of stabilizer bar computing machine CAD design.Along with the fast development of Vehicle Industry and the speed of Vehicle Driving Cycle improve constantly, stabilizer bar system is had higher requirement, many vehicles manufacturing enterprise is in the urgent need to stabilizer bar modernization CAD design and stiffness analysis software for calculation.Therefore, must set up a kind of accurately, the computing method of the QS system stiffness based on rubber bushing radial deformation reliably, to meet the requirement of stabilizer bar system.

Summary of the invention

The defect existing for above-mentioned prior art, technical matters to be solved by this invention is to provide a kind of easy, accurate, reliable computing method of the QS system stiffness based on rubber bushing radial deformation, its calculation flow chart as shown in Figure 1, the structural representation of lateral stability lever system, as shown in Figure 2.

In order to solve the problems of the technologies described above, the computing method of the QS system stiffness based on rubber bushing radial deformation provided by the present invention, is characterized in that adopting following steps:

(1) the radial line stiffness K of rubber bushing _xcalculating:

According to the inner circle radius r of rubber bushing _a, exradius r _b, axial length L, elastic modulus E _x, Poisson ratio μ _x, the radial line rigidity of rubber bushing is calculated, that is:

$K_x=\frac{1}{u_r\left(r_b\right)+y\left(r_b\right)};$

Wherein, $u_r\left(r_b\right)=\frac{1+{\mathrm{\&mu;}}_x}{2\mathrm{\&pi;}{E}_{x}L}(\ln \frac{r_b}{r_a}-\frac{r_b^2-r_a^2}{r_a^2+r_b^2}),$

$y\left(r_b\right)=a_{1}I(0,{\mathrm{\&alpha;r}}_b)+a_{2}K(0,{\mathrm{\&alpha;r}}_b)+a_3+\frac{1+{\mathrm{\&mu;}}_x}{5\mathrm{\&pi;}{E}_{x}L}(\ln r_b+\frac{r_b^2}{r_a^2+r_b^2}),$

$a_1=\frac{(1+{\mathrm{\&mu;}}_x)[K(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-K(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)},$

$a_2=\frac{({\mathrm{\&mu;}}_x+1)[I(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-I(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)},$

$a_3=\frac{(1+{\mathrm{\&mu;}}_x)(b_1-b_2+b_3)}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)};$

$b_1=[I(1,{\mathrm{\&alpha;r}}_a)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_a)I(0,{\mathrm{\&alpha;r}}_a)]r_a(r_a^2+{3r}_b^2),$

$b_2=[I(1,{\mathrm{\&alpha;r}}_b)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_b)I(0,{\mathrm{\&alpha;r}}_a)]r_b(r_b^2+{3r}_a^2),$

$b_3={\mathrm{\&alpha;r}}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)][r_a^2+(r_a^2+r_b^2)\ln r_a],$

$\mathrm{\&alpha;}=2\sqrt{15}/L,$

Bessel correction function I (0, α r _b), K (0, α r _b), I (1, α r _b), K (1, α r _b),

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

(2) the deformation coefficient G of QS end points vertical deviation _wcalculating:

According to the total length l of QS _c, brachium l ₁, transition arc radius R and central angle θ, elasticity modulus of materials E, Poisson ratio μ, and the mounting distance l of middle two rubber bushings of QS ₀, the deformation coefficient G to QS at the vertical deviation at end points place _wcalculate, that is:

$G_w=\frac{Q1-Q_2+Q_3+Q_4+Q_5-Q_6}{\mathrm{\&pi;E}};$

Wherein, $Q_1=\frac{{64l}_1^3}{3},$ $Q_2=\frac{64[{(l_1\cos \mathrm{\&theta;}+R\sin \mathrm{\&theta;})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3},$

$Q_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\&theta;}+\frac{\sin 2\mathrm{\&theta;}}{2})+\frac{1}{2}{R}^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+l_{1}R{\sin }^2\mathrm{\&theta;}],$

$Q_4=\frac{8l_0{(l_0-l_c)}^2}{3},$

$Q_5=64R(\mathrm{\&mu;}+1)[R^2(\frac{3\mathrm{\&theta;}}{2}+\frac{\sin 2\mathrm{\&theta;}}{4}-2\sin \mathrm{\&theta;})+\frac{1}{2}{l}_1^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+{4l}_{1}R{\sin }^4\frac{\mathrm{\&theta;}}{2}],$

Q ₆＝32(μ+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _c+2Rsinθ]；

(3) the QS system stiffness K based on rubber bushing radial deformation _wlecalculating:

According to stabilizer bar diameter d, total length l _c, and the installing space l between two rubber bushings ₀, the radial line stiffness K of resulting rubber bushing in step (1) _x, and in step (2) resulting QS at the deformation coefficient G of the vertical deviation at end points place _w, to the QS system stiffness K based on rubber bushing radial deformation _wlecalculate, that is:

$K_{\mathrm{wle}}=\frac{d^4{K}_x{l}_0^2}{d^4{l}_c^2+K_x{l}_0^2{G}_w};$

According to QS system stiffness K _wleand the stressed F at end points place, can be to lateral stability lever system the total deformation f at end points place _tcalculate, that is:

$f_T=\frac{F}{K_{\mathrm{wle}}}=\frac{F(d^4{l}_c^2+K_x{l}_0^2{G}_w)}{d^4{K}_x{l}_0^2}.$

The present invention has advantages of than prior art:

Previously, due to the restriction that calculated by rubber bushing distortion, for stabilizer bar system stiffness, fail to provide accurate Analytic Calculation Method always, can not meet the requirement of stabilizer bar modernization CAD design.The present invention is based on the computing method of the QS system stiffness of rubber bushing radial deformation, according to the structural parameters of rubber bushing, utilize rubber bushing elastic modulus E _xand Poisson ratio μ _x, obtain the radial line stiffness K of rubber bushing _x; According to the structural parameters of QS, determine the deformation coefficient G of QS _wand stiffness K _w; According to the diameter d of QS, the stressed F at two ends, utilize superposition principle, set up the computing method of QS system end points displacement, thereby obtain the Analytic Calculation Method of the QS system stiffness based on rubber bushing radial deformation, utilize the method can realize the QS system stiffness K based on rubber bushing radial deformation _wlecarry out accurate Analysis calculating, reduce design and testing expenses, and design and CAD software development provides reliable method for designing for stabilizer bar.

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

Fig. 1 is the calculation flow chart of the QS system stiffness based on rubber bushing radial deformation;

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

Fig. 3 is the structural representation of rubber bushing;

Fig. 4 is the distortion checking cloud atlas of the lateral stability lever system based on rubber bushing radial deformation of embodiment mono-;

Fig. 5 is the distortion checking cloud atlas of the lateral stability lever system based on rubber bushing radial deformation of embodiment bis-;

Fig. 6 is the distortion checking cloud atlas of the lateral stability lever system based on rubber bushing radial deformation of embodiment tri-.

Specific embodiments

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

Embodiment mono-: the diameter d=20mm of certain stabilizer bar system, total length l _c=800mm, brachium l ₁=150mm; Central angle θ=60 ° of transition arc, arc radius R=50mm, the mounting distance l between two rubber bushings ₀=4200mm; Elastic modulus E=the 210GPa of stabilizer bar material, Poisson ratio μ=0.3.The structure of rubber bushing as shown in Figure 3, stabilizer bar 1, interior round buss 2, rubber bushing 3, outer round buss 4, wherein, the inner circle radius r of rubber bushing 3 _a=12mm, exradius r _b=22mm, length L=25mm; The elastic modulus E of rubber bushing _x=7.84MPa, Poisson ratio μ _x=0.47.The stressed F=1000N at QS two-end-point place, calculates the rigidity of this stabilizer bar system.

The method for designing of the suspension stabilizer bar rubber bushing length that example of the present invention provides, as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) rubber bushing radial line stiffness K _xcalculating:

According to the inner circle radius r of rubber bushing _a=12mm, exradius r _b=22mm, axial length L=25mm, elastic modulus E _x=7.84MPa, Poisson ratio μ _x=0.47, the radial line stiffness K to rubber bushing _xcalculate, that is:

$K_x=\frac{1}{u_r\left(r_b\right)+y\left(r_b\right)}=2106.8N/\mathrm{mm};$

Wherein, $u_r\left(r_b\right)=\frac{1+{\mathrm{\&mu;}}_x}{2\mathrm{\&pi;}{E}_{x}L}(\ln \frac{r_b}{r_a}-\frac{r_b^2-r_a^2}{r_a^2+r_b^2})=7.7271\&times;{10}^{-5}\mathrm{mm}/N;$

$y\left(r_b\right)=a_{1}I(0,{\mathrm{ar}}_b)+a_{2}K(0,{\mathrm{ar}}_b)+a_3+\frac{1+{\mathrm{\&mu;}}_x}{5\mathrm{\&pi;}{E}_{x}L}(\ln r_b+\frac{r_b^2}{r_a^2+r_b^2})=3.9738\&times;{10}^{-4}\mathrm{mm}/N,$

$a_1=\frac{(1+{\mathrm{\&mu;}}_x)[K(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-K(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=-3.3642\&times;{10}^{-11},$

$a_2=\frac{({\mathrm{\&mu;}}_x+1)[I(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-I(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=3.3376\&times;{10}^{-12},$

$a_3=\frac{(1+{\mathrm{\&mu;}}_x)(b_1-b_2+b_3)}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=1.8565\&times;{10}^{-6},$

$b_1=[I(1,{\mathrm{\&alpha;r}}_a)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_a)I(0,{\mathrm{\&alpha;r}}_a)]r_a(r_a^2+{3r}_b^2)=5.1511\&times;{10}^{-6},$

$b_2=[I(1,{\mathrm{\&alpha;r}}_b)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_b)I(0,{\mathrm{\&alpha;r}}_a)]r_b(r_b^2+{3r}_a^2)=-4.065\&times;{10}^{-5},$

$b_3={\mathrm{\&alpha;r}}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)][r_a^2+(r_a^2+r_b^2)\ln r_a]=4.877\&times;{10}^{-4};$

Bessel correction function:

I(0,αr _b)＝25.0434，K(0,αr _b)＝0.0041，

I(1,αr _b)＝22.3175，K(1,αr _b)＝0.0045，

I(1,αr _a)＝2.1439，K(1,αr _a)＝0.0922，

I(0,αr _a)＝2.8801，K(0,αr _a)＝0.0769，

$\mathrm{\&alpha;}=2\sqrt{15}/L=309.8387;$

(2) the deformation coefficient G of stabilizer bar end points vertical deviation _wcalculating:

According to the total length l of QS _c=800mm, brachium l ₁=150mm, central angle θ=60 ° of transition arc, arc radius R=50mm, elasticity modulus of materials E=210GPa and Poisson ratio μ=0.3, the mounting distance l between two rubber bushings ₀=420mm, to the deformation coefficient G at end points vertical deviation _wcalculate, that is:

$G_w=\frac{Q1-Q_2+Q_3+Q_4+Q_5-Q_6}{\mathrm{\&pi;E}}=1543.0m{m}^5/N;$

Wherein, $Q_1=\frac{{64l}_1^3}{3}=0.0720m^3,$

$Q_2=\frac{64[{(l_1\cos \mathrm{\&theta;}+R\sin \mathrm{\&theta;})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3}=-0.111m^3,$

$Q_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\&theta;}+\frac{\sin 2\mathrm{\&theta;}}{2})+\frac{1}{2}{R}^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+l_{1}R{\sin }^2\mathrm{\&theta;}]=0.0737m^3,$

$Q_4=\frac{8l_0{(l_0-l_c)}^2}{3}=0.1617m^3,$

$Q_5=64R(\mathrm{\&mu;}+1)[R^2(\frac{3\mathrm{\&theta;}}{2}+\frac{\sin 2\mathrm{\&theta;}}{4}-2\sin \mathrm{\&theta;})+\frac{1}{2}{l}_1^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+{4l}_{1}R{\sin }^4\frac{\mathrm{\&theta;}}{2}]=0.0371m^3,$

Q ₆＝32(u+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _c+2Rsinθ]＝-0.5624m ³；

(3) the QS system stiffness K based on rubber bushing radial deformation _wlecalculating:

According to stabilizer bar diameter d=20mm, the total length l of stabilizer bar _c=800mm, the installing space l of rubber bushing ₀=420mm, the radial line stiffness K of resulting rubber bushing in step (1) _x=2106.8N/mm, and in step (2) resulting QS at the deformation coefficient G of the vertical deviation at end points place _w=1543.0mm ⁵/ N, to the QS system stiffness K based on rubber bushing radial deformation _wlecalculate, that is:

$K_{\mathrm{wle}}=\frac{d^4{K}_x{l}_0^2}{d^4{l}_c^2+K_x{l}_0^2{G}_w}=87.982N/\mathrm{mm};$

According to QS system stiffness K _wlethe power F=1000N that=87.982N/mm and end points place are subject to, can be to lateral stability lever system the total deformation f at the vertical deviation at end points place _tcalculate, that is:

$f_T=\frac{F}{K_{\mathrm{wle}}}=\frac{F(d^4{l}_c^2+K_x{l}_0^2{G}_w)}{d^4{K}_x{l}_0^2}=11.366\mathrm{mm}.$

Utilize ANSYS software to carry out modeling, the deformation simulation cloud atlas of the resulting lateral stability lever system of emulation, as shown in Figure 4.

Known, at two-end-point, be subject under reverse direction power F=1000N effect, the simulation value of this lateral stability lever system maximum distortion is f _t=11.20mm, the simulation value of rigidity is K _wle=89.2857N/mm.The calculated value that utilizes the resulting maximum distortion of the method is f _t=11.366mm, the analytical Calculation value of rigidity is K _wle=87.982N/mm.Relative deviation between them is only 1.5%, and the Analytic Calculation that shows the stabilizer bar system stiffness based on rubber bushing radial deformation that the present invention sets up is accurately, reliably, for the design of vehicle suspension system provides reliable theoretical foundation.

Embodiment bis-: the total length l of certain lateral stability lever system _c=700mm, diameter d=18mm, the mounting distance l of two rubber bushings in the middle of QS ₀=350mm, brachium l ₁=120mm, transition arc radius R=45mm, transition arc central angle θ=60 °, elastic modulus E=210GPa, Poisson ratio μ=0.3.The inner circle radius r of rubber bushing 3 _a=9mm, exradius r _b=19mm, axial length L=30mm, Poisson ratio μ _x=0.47, elastic modulus E _x=7.8MPa.The stressed F=1000N at two-end-point place, calculates the rigidity of this lateral stability lever system.

Adopt the calculation procedure of embodiment mono-, the rigidity of this stabilizer bar system is calculated, that is:

(1) the radial line stiffness K of rubber bushing _xcalculating:

According to the inner circle radius r of rubber bushing _a=9mm, exradius r _b=19mm, axial length L=30mm, elastic modulus E _x=7.8MPa, Poisson ratio μ _x=0.47, the radial line rigidity of rubber bushing is calculated, that is:

$K_x=\frac{1}{u_r\left(r_b\right)+y\left(r_b\right)}=3415.4N/\mathrm{mm};$

Wherein, $u_r\left(r_b\right)=\frac{1+{\mathrm{\&mu;}}_x}{2\mathrm{\&pi;}{E}_{x}L}(\ln \frac{r_b}{r_a}-\frac{r_b^2-r_a^2}{r_a^2+r_b^2})=1.1371\&times;{10}^{-7}m/N,$

$y\left(r_b\right)=a_{1}I(0,{\mathrm{ar}}_b)+a_{2}K(0,{\mathrm{ar}}_b)+a_3+\frac{1+{\mathrm{\&mu;}}_x}{5\mathrm{\&pi;}{E}_{x}L}(\ln r_b+\frac{r_b^2}{r_a^2+r_b^2})=1.7909\&times;{10}^{-7}m/N,$

$a_1=\frac{(1+{\mathrm{\&mu;}}_x)[K(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-K(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=-9.1489\&times;{10}^{-9}m/N,$

$a_2=\frac{({\mathrm{\&mu;}}_x+1)[I(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-I(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=2.3389\&times;{10}^{-6}m/N,$

$a_3=\frac{(1+{\mathrm{\&mu;}}_x)(b_1-b_2+b_3)}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=1.6570\&times;{10}^{-6}m/N,$

$b_1=[I(1,{\mathrm{\&alpha;r}}_a)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_a)I(0,{\mathrm{\&alpha;r}}_a)]r_a(r_a^2+{3r}_b^2)=4.5082\&times;{10}^{-6}{m}^3,$

$b_2=[I(1,{\mathrm{\&alpha;r}}_b)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_b)I(0,{\mathrm{\&alpha;r}}_a)]r_b(r_b^2+{3r}_a^2)=1.9847\&times;{10}^{-5}{m}^3,$

$b_3={\mathrm{\&alpha;r}}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)][r_a^2+(r_a^2+r_b^2)\ln r_a]=1.8087\&times;{10}^{-4}{m}^3;$

Bessel correction function I (0, α r _b)=25.0434, K (0, α r _b)=0.0041,

I(1,αr _b)＝22.3175，K(1,αr _b)＝0.0045，

I(1,αr _a)＝2.1439，K(1,αr _a)＝0.0922，

I(0,αr _a)＝2.8801，K(0,αr _a)＝0.0769，

$\mathrm{\&alpha;}=2\sqrt{15}/L=258.1989;$

(2) the deformation coefficient G of QS end points _wcalculating:

According to the total length l of QS _c=700mm, the mounting distance l of two rubber bushings in the middle of QS ₀=350mm, QS brachium l ₁=120mm, transition arc radius R=45mm, transition arc central angle θ=60 °, elastic modulus E=210GPa, Poisson ratio μ=0.3, the deformation coefficient G to QS end points place vertical deviation _wcalculate, that is:

$G_w=\frac{Q1-Q_2+Q_3+Q_4+Q_5-Q_6}{\mathrm{\&pi;E}}=977.42{\mathrm{mm}}^5/N;$

Wherein, $Q_1=\frac{{64l}_1^3}{3}=0.0369m^3,$

$Q_2=\frac{64[{(l_1\cos \mathrm{\&theta;}+R\sin \mathrm{\&theta;})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3}=-0.0937m^3,$

$Q_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\&theta;}+\frac{\sin 2\mathrm{\&theta;}}{2})+\frac{1}{2}{R}^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+l_{1}R{\sin }^2\mathrm{\&theta;}]=0.0441m^3,$

$Q_4=\frac{8l_0{(l_0-l_c)}^2}{3}=0.1143m^3,$

$Q_5=64R(\mathrm{\&mu;}+1)[R^2(\frac{3\mathrm{\&theta;}}{2}+\frac{\sin 2\mathrm{\&theta;}}{4}-2\sin \mathrm{\&theta;})+\frac{1}{2}{l}_1^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+{4l}_{1}R{\sin }^4\frac{\mathrm{\&theta;}}{2}]=0.0220m^3,$

Q ₆＝32(u+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _c+2Rsinθ]＝-0.3338m ³；

(3) the QS system stiffness K based on rubber bushing radial deformation _wlecalculating:

According to stabilizer bar diameter d=18mm, the total length l of stabilizer bar _c=700mm, the installing space l of rubber bushing ₀=350mm, the radial line stiffness K of resulting rubber bushing in step (1) _x=3415.4N/mm, and in step (2) resulting QS at the deformation coefficient G of the vertical deviation at end points place _w=977.42mm ⁵/ N, to the QS system stiffness K based on rubber bushing radial deformation _wlecalculate, that is:

$K_{\mathrm{wle}}=\frac{d^4{K}_x{l}_0^2}{d^4{l}_c^2+K_x{l}_0^2{G}_w}=86.2069N/\mathrm{mm};$

According to QS system stiffness K _wleand the stressed F in end points place, can be to lateral stability lever system the total deformation f at end points place _tcalculate, that is:

$f_T=\frac{F}{K_{\mathrm{wle}}}=\frac{F(d^4{l}_c^2+K_x{l}_0^2{G}_w)}{d^4{K}_x{l}_0^2}=11.6\mathrm{mm}.$

Utilize ANSYS software to carry out modeling, the deformation simulation cloud atlas of the resulting lateral stability lever system of emulation, as shown in Figure 5.Known, at two ends, be subject under reverse direction power F=1000N effect, the maximum distortion simulation value of this lateral stability lever system is 11.41mm, i.e. the simulation value K of rigidity _wle=87.6424N/mm.Utilize the resulting maximum distortion calculated value of the method 11.6mm, i.e. the analytical Calculation K of rigidity _wle=86.2069N/mm.Relative deviation between them is only 1.64%, and the computing method that shows the stabilizer bar system stiffness based on rubber bushing radial deformation that the present invention sets up is accurately, reliably, for the design of suspension stabilizer bar provides reliable method for designing.

Embodiment tri-: the total length l of certain lateral stability lever system _c=800mm, diameter d=20mm, the mounting distance l of two rubber bushings in the middle of QS ₀=400mm, brachium l ₁=150mm, transition arc radius R=50mm, transition arc central angle θ=60 °, elastic modulus E=210GPa, Poisson ratio μ=0.3.The inner circle radius r of rubber bushing _a=10mm, exradius r _b=20mm, axial length L=25mm, Poisson ratio μ _x=0.47, elastic modulus E _x=7.8MPa.The stressed F=900N at QS two-end-point place, calculates the rigidity of this stabilizer bar system.

Adopt the calculation procedure of embodiment mono-, the rigidity of this stabilizer bar system is calculated, that is:

(1) the radial line stiffness K of rubber bushing _xcalculating:

According to the inner circle radius r of rubber bushing _a=10mm, exradius r _b=20mm, axial length L=25mm, elastic modulus E _x=7.8MPa, Poisson ratio μ _x=0.47, the radial line rigidity of rubber bushing is calculated, that is:

$K_x=\frac{1}{u_r\left(r_b\right)+y\left(r_b\right)}2773.5N/\mathrm{mm};$

Wherein, $u_r\left(r_b\right)=\frac{1+{\mathrm{\&mu;}}_x}{2\mathrm{\&pi;}{E}_{x}L}(\ln \frac{r_b}{r_a}-\frac{r_b^2-r_a^2}{r_a^2+r_b^2})=1.1176\&times;{10}^{-7}m/N,$

$y\left(r_b\right)=a_{1}I(0,{\mathrm{ar}}_b)+a_{2}K(0,{\mathrm{ar}}_b)+a_3+\frac{1+{\mathrm{\&mu;}}_x}{5\mathrm{\&pi;}{E}_{x}L}(\ln r_b+\frac{r_b^2}{r_a^2+r_b^2})=2.4880\&times;{10}^{-7}m/N,$

$a_1=\frac{(1+{\mathrm{\&mu;}}_x)[K(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-K(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=-2.6488\&times;{10}^{-9}m/N,$

$a_2=\frac{({\mathrm{\&mu;}}_x+1)[I(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-I(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=5.7532\&times;{10}^{-6}m/N,$

$a_3=\frac{(1+{\mathrm{\&mu;}}_x)(b_1-b_2+b_3)}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)}=1.9497\&times;{10}^{-6}m/N;$

$b_1=[I(1,{\mathrm{\&alpha;r}}_a)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_a)I(0,{\mathrm{\&alpha;r}}_a)]r_a(r_a^2+{3r}_b^2)=4.1957\&times;{10}^{-6}{m}^3,$

$b_2=[I(1,{\mathrm{\&alpha;r}}_b)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_b)I(0,{\mathrm{\&alpha;r}}_a)]r_b(r_b^2+{3r}_a^2)=3.2063\&times;{10}^{-5}{m}^3,$

$b_3={\mathrm{\&alpha;r}}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)][r_a^2+(r_a^2+r_b^2)\ln r_a]=3.5833\&times;{10}^{-4}{m}^3,$

Bessel correction function: I (0, α r _b)=80.4799, K (0, α r _b)=0.0010;

I(1,αr _b)＝73.6642，K(1,αr _b)＝0.0011；

I(1,αr _a)＝4.3199，K(1,αr _a)＝0.0357；

I(0,αr _a)＝5.2875，K(0,αr _a)＝0.0310； $\mathrm{\&alpha;}=2\sqrt{15}/L=309.8387;$

(2) the deformation coefficient G of QS end points vertical deviation _wcalculating:

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

$G_w=\frac{Q1-Q_2+Q_3+Q_4+Q_5-Q_6}{\mathrm{\&pi;E}}=1593.5{\mathrm{mm}}^5/N;$

Wherein, $Q_1=\frac{{64l}_1^3}{3}=0.0720m^3,$

$Q_2=\frac{64[{(l_1\cos \mathrm{\&theta;}+R\sin \mathrm{\&theta;})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3}=-0.1353m^3,$

$Q_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\&theta;}+\frac{\sin 2\mathrm{\&theta;}}{2})+\frac{1}{2}{R}^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+l_{1}R{\sin }^2\mathrm{\&theta;}]=0.0737m^3,$

$Q_4=\frac{8l_0{(l_0-l_c)}^2}{3}=0.1707m^3,$

$Q_5=64R(\mathrm{\&mu;}+1)[R^2(\frac{3\mathrm{\&theta;}}{2}+\frac{\sin 2\mathrm{\&theta;}}{4}-2\sin \mathrm{\&theta;})+\frac{1}{2}{l}_1^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+{4l}_{1}R{\sin }^4\frac{\mathrm{\&theta;}}{2}]=0.0371m^3,$

Q ₆＝32(u+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _c+2Rsinθ]＝-0.5624m ³；

(3) the QS system stiffness K based on rubber bushing radial deformation _wlecalculating:

According to stabilizer bar diameter d=20mm, the total length l of stabilizer bar _c=800mm, the installing space l of rubber bushing ₀=400mm, the radial line stiffness K of resulting rubber bushing in step (1) _x=2773.5N/mm, and in step (2) resulting QS at the deformation coefficient G of the vertical deviation at end points place _w=1593.5mm ⁵/ N, to the QS system stiffness K based on rubber bushing radial deformation _wlecalculate, that is:

$K_{\mathrm{wle}}=\frac{d^4{K}_x{l}_0^2}{d^4{l}_c^2+K_x{l}_0^2{G}_w}=77.58N/\mathrm{mm};$

According to QS system stiffness K _wle=77.58N/mm and the stressed F=900N in end points place, can be to lateral stability lever system the total deformation f at end points place _tcalculate, that is:

$f_T=\frac{F}{K_{\mathrm{wle}}}=\frac{F(d^4{l}_c^2+K_x{l}_0^2{G}_w)}{d^4{K}_x{l}_0^2}=11.6009\mathrm{mm}.$

Utilize ANSYS software to carry out modeling, the resulting QS system variant of emulation emulation cloud atlas, as shown in Figure 6.Known, this lateral stability lever system is subject at two-end-point under the effect of reverse direction power F=900N, and the maximum distortion simulation value of QS is f _t=11.357mm, i.e. the simulation value K of rigidity _wle=79.2463N/mm.Utilizing the resulting maximum distortion calculated value of the method is f _t=11.6009mm, i.e. the analytical Calculation value K of rigidity _wle=77.58N/mm.Relative deviation between them is only 2.095%, and the Analytic Calculation that shows the stabilizer bar system stiffness based on rubber bushing radial deformation that the present invention sets up is accurately, reliably, for the design of vehicle suspension system provides reliable theoretical foundation.

Claims (1)

1. the computing method of the QS system stiffness based on rubber bushing radial deformation, its concrete calculation procedure is as follows:

(1) the radial line stiffness K of rubber bushing _xcalculating:

According to the inner circle radius r of rubber bushing _a, exradius r _b, axial length L, elastic modulus E _x, Poisson ratio μ _x, the radial line rigidity of rubber bushing is calculated, that is:

$K_x=\frac{1}{u_r\left(r_b\right)+y\left(r_b\right)};$

Wherein, $u_r\left(r_b\right)=\frac{1+{\mathrm{\&mu;}}_x}{2\mathrm{\&pi;}{E}_{x}L}(\ln \frac{r_b}{r_a}-\frac{r_b^2-r_a^2}{r_a^2+r_b^2}),$

$y\left(r_b\right)=a_{1}I(0,{\mathrm{\&alpha;r}}_b)+a_{2}K(0,{\mathrm{\&alpha;r}}_b)+a_3+\frac{1+{\mathrm{\&mu;}}_x}{5\mathrm{\&pi;}{E}_{x}L}(\ln r_b+\frac{r_b^2}{r_a^2+r_b^2}),$

$a_1=\frac{(1+{\mathrm{\&mu;}}_x)[K(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-K(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)},$

$a_2=\frac{({\mathrm{\&mu;}}_x+1)[I(1,{\mathrm{\&alpha;r}}_a)r_a(r_a^2+{3r}_b^2)-I(1,{\mathrm{\&alpha;r}}_b)r_b({3r}_a^2+r_b^2)]}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)},$

$a_3=\frac{(1+{\mathrm{\&mu;}}_x)(b_1-b_2+b_3)}{5\mathrm{\&pi;}{E}_x\mathrm{L\&alpha;}{r}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)](r_a^2+r_b^2)};$

$b_1=[I(1,{\mathrm{\&alpha;r}}_a)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_a)I(0,{\mathrm{\&alpha;r}}_a)]r_a(r_a^2+{3r}_b^2),$

$b_2=[I(1,{\mathrm{\&alpha;r}}_b)K(0,{\mathrm{\&alpha;r}}_a)+K(1,{\mathrm{\&alpha;r}}_b)I(0,{\mathrm{\&alpha;r}}_a)]r_b(r_b^2+{3r}_a^2),$

$b_3={\mathrm{\&alpha;r}}_a{r}_b[I(1,{\mathrm{\&alpha;r}}_a)K(1,{\mathrm{\&alpha;r}}_b)-K(1,{\mathrm{\&alpha;r}}_a)I(1,{\mathrm{\&alpha;r}}_b)][r_a^2+(r_a^2+r_b^2)\ln r_a],$

$\mathrm{\&alpha;}=2\sqrt{15}/L,$

Bessel correction function I (0, α r _b), K (0, α r _b), I (1, α r _b), K (1, α r _b),

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

(2) the deformation coefficient G of QS end points vertical deviation _wcalculating:

According to the total length l of QS _c, brachium l ₁, transition arc radius R and central angle θ, elasticity modulus of materials E, Poisson ratio μ, and the mounting distance l of middle two rubber bushings of QS ₀, the deformation coefficient G to QS at the vertical deviation at end points place _wcalculate, that is:

$G_w=\frac{Q1-Q_2+Q_3+Q_4+Q_5-Q_6}{\mathrm{\&pi;E}};$

Wherein, $Q_1=\frac{{64l}_1^3}{3},$ $Q_2=\frac{64[{(l_1\cos \mathrm{\&theta;}+R\sin \mathrm{\&theta;})}^3+\frac{1}{8}{(l_0-l_c)}^3]}{3},$

$Q_3=64R[\frac{1}{2}{l}_1^2(\mathrm{\&theta;}+\frac{\sin 2\mathrm{\&theta;}}{2})+\frac{1}{2}{R}^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+l_{1}R{\sin }^2\mathrm{\&theta;}],$

$Q_4=\frac{8l_0{(l_0-l_c)}^2}{3},$

$Q_5=64R(\mathrm{\&mu;}+1)[R^2(\frac{3\mathrm{\&theta;}}{2}+\frac{\sin 2\mathrm{\&theta;}}{4}-2\sin \mathrm{\&theta;})+\frac{1}{2}{l}_1^2(\mathrm{\&theta;}-\frac{\sin 2\mathrm{\&theta;}}{2})+{4l}_{1}R{\sin }^4\frac{\mathrm{\&theta;}}{2}],$

Q ₆＝32(μ+1)[R(cosθ-1)-l ₁sinθ] ²[2l ₁cosθ-l _c+2Rsinθ]；

(3) the QS system stiffness K based on rubber bushing radial deformation _wlecalculating:

According to stabilizer bar diameter d, total length l _c, and the installing space l between two rubber bushings ₀, the radial line stiffness K of resulting rubber bushing in step (1) _x, and in step (2) resulting QS at the deformation coefficient G of the vertical deviation at end points place _w, to the QS system stiffness K based on rubber bushing radial deformation _wlecalculate, that is:

$K_{\mathrm{wle}}=\frac{d^4{K}_x{l}_0^2}{d^4{l}_c^2+K_x{l}_0^2{G}_w};$

According to QS system stiffness K _wleand the stressed F at end points place, can be to lateral stability lever system the total deformation f at end points place _tcalculate, that is:

$f_T=\frac{F}{K_{\mathrm{wle}}}=\frac{F(d^4{l}_c^2+K_x{l}_0^2{G}_w)}{d^4{K}_x{l}_0^2}.$