CN104182597B

CN104182597B - The check method of vehicle suspension roll angular rigidity

Info

Publication number: CN104182597B
Application number: CN201410476073.8A
Authority: CN
Inventors: 周长城; 郭剑; 提艳; 安艳; 高炳凯; 于曰伟
Original assignee: Shandong University of Technology
Current assignee: Shandong University of Technology
Priority date: 2014-09-18
Filing date: 2014-09-18
Publication date: 2018-04-10
Anticipated expiration: 2034-09-18
Also published as: CN104182597A

Abstract

The present invention relates to the check method of vehicle suspension roll angular rigidity, belongs to vehicle suspension technical field.Previously fail to provide the parsing calculation and check method of roll angular rigidity always.The present invention utilizes the deformation coefficient G of end part of stabilizer rod according to vehicle and suspension parameter, and the structure and material characterisitic parameter of designed stabiliser bar and rubber bushing_WAnd rubber bushing radial rigidity K_xAnalytical formula, calculation and check is carried out to forward and backward suspension roll angular rigidity and the total roll angular rigidity of vehicle.Using the calculation and check value of the available accurately and reliably vehicle roll angular rigidity of this method, vehicle suspension and the design level and quality of stabilizer bar system can be not only improved, improves the ride performance and security of vehicle；Meanwhile design and testing expenses can be reduced using this method, accelerate product development speed, and reliable technical support is improved for the exploitation of stabiliser bar CAD software.

Description

Method for checking vehicle suspension roll angle rigidity

Technical Field

The invention relates to a vehicle suspension, in particular to a method for checking the roll angle rigidity of the vehicle suspension.

Background

The design of the vehicle suspension and the stabilizer bar must meet the design requirement on the rigidity of the side inclination angle when the vehicle turns. However, due to the restriction of key problems of deformation analysis calculation of the stabilizer bar, deformation analysis calculation of the rubber bushing and mutual coupling, a reliable analysis calculation method cannot be provided for checking and calculating the vehicle roll angle rigidity. At present, most vehicle roll angle rigidity checking at home and abroad utilizes ANSYS simulation software to perform simulation analysis and verification on roll angle rigidity through entity modeling, and although a reliable simulation numerical value can be obtained by the method, the requirement of CAD software development of a suspension stabilizer bar system cannot be met because an accurate analytic calculation formula cannot be provided. With the rapid development of the vehicle industry and the continuous improvement of the vehicle running speed, higher requirements are put forward on the design of a vehicle suspension system and a stabilizer bar, and vehicle manufacturers urgently need the CAD software of the stabilizer bar system. Therefore, an accurate and reliable method for checking the vehicle suspension roll angle rigidity is required to be established, the design level and quality of products are improved, and the running smoothness and safety of vehicles are improved; meanwhile, the design and test cost is reduced, and the product development speed is accelerated.

Disclosure of Invention

In view of the above-mentioned drawbacks in the prior art, the present invention provides a simple and reliable method for checking the roll stiffness of a vehicle suspension, where a checking calculation flowchart is shown in fig. 1, a rolling motion model of the vehicle is shown in fig. 2, and a structure diagram of a stabilizer bar is shown in fig. 3.

In order to solve the technical problem, the method for checking the roll angle rigidity of the vehicle suspension is characterized by comprising the following calculation steps.

(1) Total roll stiffness required for vehicle suspensionThe calculation of (2):

according to vehicle body mass m_sDistance h between the center of mass of the vehicle body and the roll axis_sWheel radius r, lateral acceleration a_yAnd the maximum roll angle of the vehicle body required by the vehicle designCalculating the total roll stiffness required for the vehicle suspension, namely:

wherein g is the acceleration of gravity;

(2) roll stiffness of front and rear suspension springsAndthe calculation of (2):

according to the front track B of the vehicle_fAnd rear track B_rLength of front swing arm T_1fLength of rear swing arm T_1rDistance T between the mounting positions of the front and rear suspension springs and the hinge point of the swing arm_2fAnd T_2rAnd linear stiffness k of front and rear suspension springs_sfAnd k_srCalculating the roll angle stiffness of the front and rear suspension springs respectively, namely:

(3) deformation coefficient G of vertical displacement of end parts of front and rear suspension stabilizer bars_wfAnd G_wrThe calculation of (2):

according to the total length l of the front and rear suspension stabilizer bars_cfAnd l_crMounting distance l of two middle rubber bushings_0fAnd l_0rArm length l of front and rear stabilizer bars_1fAnd l_1rRadius of transition arc R of front and rear stabilizer bars_fAnd R_rCentral angle theta of transition arc_fAnd theta_rAnd the material elastic model E and Poisson's ratio mu, the deformation coefficient G to the vertical displacement of the front and rear suspension stabilizer bar ends_wfAnd G_wrThe calculation is carried out as follows:

in the formula,

Q_6f＝32(μ+1)[R_f(cosθ_f-1)-l_1fsinθ_f]²[2l_1fcosθ_f-l_cf+2R_fsinθ_f]；

Q_6r＝32(u+1)[R_r(cosθ_r-1)-l_1rsinθ_r]²[2l_1rcosθ_r-l_cr+2R_rsinθ_r]；

(4) radial linear rigidity K of rubber bushing of front stabilizer bar and rear stabilizer bar_xfAnd K_xrThe analytic calculation of (2):

according to the inner circle half of the front and rear rubber bushingsDiameter r_afAnd r_arOuter radius r_bfAnd r_brAxial length L_fAnd L_rAnd modulus of elasticity E of rubber bushing_xPoisson ratio μ_xAnd respectively calculating the radial linear rigidity of the front and rear suspension rubber bushings, namely:

wherein,

bessel correction function I (0, α)_fr_bf)，K(0,α_fr_bf)，I(1,α_fr_bf)，K(1,α_fr_bf)；

I(1,α_fr_af)，K(1,α_fr_af)，I(0,α_fr_af)，K(0,α_fr_af)；

Wherein,

bessel correction function I (0, α)_rr_br)，K(0,α_rr_br)，I(1,α_rr_br)，K(1,α_rr_br)；

I(1,α_rr_ar)，K(1,α_rr_ar)，I(0,α_rr_ar)，K(0,α_rr_ar)；

(5) Roll stiffness of front and rear stabilizer bar systemsAndchecking and calculating:

according to the wheel track B of the front and rear axles of the vehicle_fAnd B_rDiameter d of front and rear suspension stabilizer bars_fAnd d_rLength l of_cfAnd l_crAnd the installation distance length l of the rubber bushing of the front stabilizer bar and the rear stabilizer bar_0fAnd l_0rAnd (4) calculating the deformation coefficients G of the end points of the front and rear stabilizer bars obtained in the step (3)_wfAnd G_wrCalculating the radial rigidity K of the front and rear rubber bushings obtained in the step (4)_xfAnd K_xrRoll stiffness to front and rear stabilizer bar systemsAndrespectively carrying out check calculation, namely:

(6) vehicle total roll stiffnessChecking and calculating:

according to the roll angle stiffness of the front and rear suspension springs obtained in the step (2)Androll angle stiffness of the front and rear stabilizer bar systems obtained in step (5)Andchecking the stiffness of the total roll angle of the vehicle, i.e.

If the calculated value of the checking of the rigidity of the total roll angle of the vehicleGreater than or equal to the design value required for the vehicle calculated in step (1)Namely, it isThe vehicle roll angle rigidity meets the vehicle design requirements; otherwise, ifThe roll angle stiffness of the vehicle does not meet the vehicle design requirements and requires front and rear suspensionThe stabilizer bar system is designed to be adjustable.

Compared with the prior art, the invention has the advantages that:

at present, most of the vehicle suspension side inclination rigidity checking at home and abroad utilizes simulation software to check and analyze the vehicle side inclination rigidity through modeling simulation, but the method can not provide an analytic calculation formula, so that the requirement of CAD software development of a stabilizer bar system can not be met. The invention can utilize the roll angle rigidity of the front and rear suspension springs and the deformation coefficient G of the end part of the stabilizer bar according to vehicle parameters, suspension parameters, structural parameters and material characteristic parameters of the designed stabilizer bar and rubber bushing_wAnd radial stiffness K of the rubber bushing_xThe analysis calculation formula of (2) checks and calculates the front and rear suspension side inclination rigidity and the vehicle total side inclination rigidity. The method can obtain an accurate and reliable checking calculation value of the vehicle roll angle rigidity, provides a reliable roll angle rigidity checking calculation method for the design of a vehicle suspension and a stabilizer bar, and lays a technical foundation for the development of CAD software of the stabilizer bar. By using the method, the design level and quality of a vehicle suspension and a stabilizer bar system can be improved, and the driving smoothness and safety of a vehicle are improved; meanwhile, the method can reduce the design and test cost and accelerate the product development speed.

Drawings

For a better understanding of the invention, reference is made to the following further description taken in conjunction with the accompanying drawings.

FIG. 1 is a flow chart of a vehicle suspension roll stiffness check calculation;

FIG. 2 is a diagram of a model of a vehicle roll motion;

FIG. 3 is a schematic structural view of a stabilizer bar system;

fig. 4 is a schematic structural view of the rubber bushing.

Detailed Description

The present invention will be described in further detail by way of examples.

The first embodiment is as follows: body mass m of a vehicle_s4690kg, lateral acceleration a_y0.4g, the distance h between the center of mass of the vehicle body and the roll axis_s1069mm, design requirement value of vehicle body roll angleFront suspension swing arm length T_1f675mm, spring wire stiffness k_sf102.45N/mm, distance T between spring center and swing arm hinge point_2f430 mm; rear suspension swing arm length T_1r650mm, spring wire stiffness K_sr261N/mm, distance T between spring center and swing arm hinge point_2r400 mm; the front axle track B of the vehicle_f1650mm rear axle track B_r1485 mm; the vehicle is provided with a stabilizer bar system only at the front suspension, and the structure diagram is shown in figure 3, wherein, the diameter d of the stabilizer bar_f20mm, total length l_cf800mm, arm length l_1f150mm, transition arc radius R_f50mm, transition arc central angle theta_f60 degrees, the installation distance between the two rubber bushings l_0f400mm, the elastic modulus E of the stabilizer bar material is 210GPa, and the Poisson ratio mu is 0.3. The structure of the rubber bushing of the front stabilizer bar is as shown in fig. 4, a stabilizer bar 1, an inner circle sleeve 2, a rubber bushing 3, an outer circle sleeve 4, an inner circle sleeve 2 and a rubber bushing 3 are integrated, and are matched with the stabilizer bar 1 through the inner circle sleeve 2 and installed on the stabilizer bar 1, wherein the axial length L of the rubber bushing 1_f25mm, thickness h_f10mm, wall thickness Δ l of the inner sleeve 2_f2.0mm, i.e. the inner circle radius r of the rubber bushing_af12mm, outer radius r_bf22mm, modulus of elasticity E_x7.84MPa, Poisson ratio mu_x0.47. And checking and calculating the roll angle rigidity of the vehicle suspension system.

The method for checking the vehicle suspension roll angle stiffness provided by the embodiment of the invention has a checking calculation flow as shown in figure 1, and comprises the following specific steps:

(1) total roll stiffness required for vehicle suspensionThe calculation of (2):

according to vehicle body mass m_s4690kg, lateral acceleration a_y0.4g, the distance h between the center of mass of the vehicle body and the roll axis_s1069mm, body roll angleNeglecting unsprung mass m_uIn this case, the total roll stiffness required for the vehicle suspension is calculated, namely:

(2) roll stiffness of front and rear suspension springs for a vehicleAndthe calculation of (2):

according to the front track B of the vehicle_f1650mm and rear track B_r1485mm, forearm length T_1f675mm, rear swing arm length T_1r650mm, distance T between the mounting positions of the front and rear suspension springs and the hinge point of the swing arm_2f430mm and T_2r400mm, and linear stiffness k of front and rear suspension springs_sf102.45N/mm and k_srThe roll stiffness of the front and rear suspension springs were calculated, 261N/mm, respectively, as:

(3) coefficient of deformation G of front suspension stabilizer bar end_wfThe calculation of (2):

stabilizer bar total length l according to front suspension_cf800mm, the installation distance l of two middle rubber bushings_0f400mm, arm length l of the front stabilizer bar_1f150mm, radius of transition arc R of front stabilizer bar_f50mm, central angle theta of transition arc_fThe deformation coefficient of the front suspension stabilizer bar end is calculated as 60 °, the material elastic model E is 210GPa and the poisson ratio μ is 0.3, namely:

in the formula,

Q_6f＝32(u+1)[R_f(cosθ_f-1)-l_1fsinθ_f]²[2l_1fcosθ_f-l_cf+2R_fsinθ_f]＝-0.5624m³；

(4) radial linear rigidity K of rubber bushing of front suspension stabilizer bar_xfThe analytic calculation of (2):

according to the inner circle radius r of the rubber bushing of the front suspension stabilizer bar_af12mm, outer radius r_bf22mm, axial length L_f25mm and modulus of elasticity E of the rubber bushing_x7.84MPa, Poisson ratio mu_x0.47, radial line stiffness K to front suspension rubber bushing_xfThe calculation is carried out, namely:

wherein,

bessel's correction function:

I(0,α_fr_bf)＝25.0434，K(0,α_fr_bf)＝0.0041，

I(1,α_fr_bf)＝22.3175，K(1,α_fr_bf)＝0.0045，

I(1,α_fr_af)＝2.1439，K(1,α_fr_af)＝0.0922，

I(0,α_fr_af)＝2.8801，K(0,α_fr_af)＝0.0769；

(5) roll stiffness for a front stabilizer bar systemChecking and calculating:

according to the wheel track B of the front axle of the vehicle_f1650mm, diameter d of the stabilizer bar_f20mm, length l_cf800mm, the installation distance between two rubber bushings is l_0fCalculating the deformation coefficient G at the end point of the front stabilizer bar obtained in the step (3) when the diameter is 400mm_wf＝1.5935×10^-12m⁵/N, and calculating the radial stiffness K of the front rubber bushing obtained in the step (4)_xfRoll stiffness to front stabilizer bar system of 2106.8N/mmAnd (3) performing checking calculation, namely:

(6) vehicle total roll stiffnessChecking and calculating:

according to the roll angle rigidity of the front and rear suspension springs calculated in the step (2)And

calculating roll angle stiffness of the resulting front stabilizer bar system in step (5)Checking the stiffness of the total roll angle of the vehicle, i.e.

Checking calculation value of total roll angle rigidity of vehicleGreater than the design value required for the vehicle calculated in step (1)Namely, it isThe vehicle roll angle stiffness meets vehicle design requirements.

Example two: knowing the mass m of a vehicle body_s5000kg, lateral acceleration a_y0.4g, the distance h between the center of mass of the vehicle body and the roll axis_s1150mm vehicle body roll angleSpring wire stiffness k for vehicle front suspension_sf90.761N/mm, spring wire stiffness k of rear suspension_sr176.23N/mm; front track B_f1650mm, rear track B_r1600 mm; front suspension swing arm length T_1f660mm, distance T between the center of the front suspension spring and the hinge point of the swing arm at the same side_2f450 mm; length T of rear swing arm_1r650mm, distance T between the mounting center of the rear suspension spring and the hinge point of the cross arm at the same side_2r400 mm. The front and rear suspension stabilizer bars and the rubber bushing have the same parameters as in the first embodiment except for the difference in diameter, wherein the diameter d of the front stabilizer bar_f22mm, diameter d of rear stabilizer bar_r19 mm; inner radius r of front rubber bushing_af13mm, outer radius r_bf23mm, inner circle radius r of rear rubber bushing_ar11.5 mm. Radius of the outer circle r_br21.5 mm. And checking and calculating the roll angle rigidity of the vehicle suspension system.

By adopting the steps of the first embodiment, the roll angle rigidity of the vehicle suspension system is checked and calculated, namely:

(1) total roll stiffness required for vehicle suspensionThe calculation of (2):

according to vehicle body mass m_s5000kg, lateral acceleration a_y0.4g, the distance h between the center of mass of the vehicle body and the roll axis_s1150mm maximum roll angle required for vehicle body designCalculating the total roll stiffness required for the vehicle suspension, namely:

wherein g is the acceleration of gravity, g is 9.8m/s²；

according to the front track B of the vehicle_f1650mm and rear track B_r1600mm, front swing arm length T_1f660mm, rear swing arm length T_1r650mm, distance T between the mounting positions of the front and rear suspension springs and the hinge point of the swing arm_2f450mm and T_2r400mm, and linear stiffness k of front and rear suspension springs_sf90.761N/mm and k_srThe roll stiffness of the front and rear suspension springs were calculated as 176.23N/mm, respectively, i.e.:

(3) deformation coefficient G of front and rear suspension stabilizer bar ends_wfAnd G_wrThe calculation of (2):

since the parameters of the front and rear suspension stabilizer bars are identical to those of the first embodiment except for the diameter, the deformation coefficients of the end portions of the front and rear suspension stabilizer bars are also identical to those of the first embodiment, that is:

(4) radial linear rigidity K of rubber bushing of front and rear suspension stabilizer bars_xfAnd K_xrThe analytic calculation of (2):

because the diameters of the front and rear suspension stabilizer bars and the inner circle radius and the outer circle radius of the rubber bushing are different, the radial linear rigidity K of the rubber bushing_xfAnd K_xrAnd are also different. According to the inner radius r of the front rubber bushing_af13mm, outer radius r_bf23mm, inner circle radius r of rear rubber bushing_ar11.5mm, outer radius r_br21.5mm and the length L of the rubber bushing_f25mm, modulus of elasticity E_x7.84MPa, Poisson ratio mu_xThe calculation method of the first embodiment is adopted to calculate the radial linear stiffness K of the rubber bushing of the front and rear suspension stabilizer bars as 0.47_xfAnd K_xrThe calculations were performed separately, i.e.:

wherein,

according to the wheel track B of the front and rear axles of the vehicle_f1650mm and B_rDiameter d of front and rear stabilizer bars 1600mm_f22mm and d_r19mm, length l_cf＝l_cr800mm, the installation distance between two rubber bushings is l_0f＝l_0rCalculating the deformation coefficient G of the end points of the front and rear stabilizer bars obtained in the step (3) when the length is 400mm_wf＝G_wr＝1.5935×10^-12m⁵/N, and calculating the radial rigidity K of the front and rear rubber bushings obtained in the step (4)_xf2267.0N/mm and K_xrRoll stiffness to front and rear stabilizer bar systems of 2026.7N/mmAndrespectively carrying out check calculation, namely:

(6) vehicle total roll stiffnessChecking and calculating:

according to the roll angle rigidity of the front and rear suspension springs calculated in the step (2)Andcalculating the roll angle rigidity of the front and rear stabilizer bar systems obtained in the step (5)Andchecking the stiffness of the total roll angle of the vehicle, i.e.

Example three: stabilizer bar diameter d of some vehicle except front suspension_fAnd the inner circle radius r of the rubber bushing_afAnd the radius r of the outer circle_bfExcept for the difference, all other parameters were identical to those of the second embodiment, in which the diameter d of the front stabilizer bar_fAbout 21mm, the inner circle of the rubber bushing is halfDiameter r_af12.5mm, and outer radius r_bf22.5 mm. And checking and calculating the roll angle rigidity of the vehicle suspension system.

And checking and calculating the roll angle rigidity of the vehicle suspension system by adopting the step of the embodiment I:

(1) total roll stiffness required for vehicle suspensionThe calculation of (2):

since the vehicle parameters are exactly the same as those of the second embodiment, the total roll stiffness required for the vehicle suspension is also the same as that of the second embodiment, namely:

since the vehicle parameters and the suspension spring stiffness of the vehicle are exactly the same as those of the second embodiment, the roll angle stiffnesses of the front and rear suspension springs of the vehicle are also respectively the same as those of the second embodiment, that is:

since the parameters of the vehicle front and rear suspension stabilizer bars are exactly the same as those of the second embodiment except for the diameters thereof, the coefficients of deformation of the end portions of the vehicle front and rear suspension stabilizer bars are also exactly the same as those of the second embodiment, that is:

the diameter of the rear suspension stabilizer bar and the inner circle radius and the outer circle radius of the rubber bushing are completely the same as those of the second embodiment, so that the radial linear rigidity K of the rubber bushing of the rear suspension stabilizer bar is_xrAlso all are exactly the same as in example two, namely:

the diameter of the stabilizer bar of the front suspension of the vehicle and the inner circle radius and the outer circle radius of the rubber bushing are different from those of the second embodiment. According to the inner radius r of the front rubber bushing_af12.5mm, outer radius r_bf22.5mm, modulus of elasticity E_x7.84MPa, Poisson ratio mu_xWhen the linear stiffness K of the rubber bushing of the front suspension stabilizer bar is 0.47, the calculation method of the first embodiment is adopted_xfThe calculation is carried out, namely:

wherein,

since the vehicle rear suspension stabilizer bar diameter and the rubber bushing are completely the same as those of the second embodiment, the roll angle rigidity of the rear suspension stabilizer bar systemAlso the same as in example two, namely:

according to the wheel track B of the front axle of the vehicle_f1650mm, diameter d of the stabilizer bar_fLength l of 21mm_cf800mm, the installation distance between two rubber bushings is l_0fCalculating the deformation coefficient G at the end point of the front stabilizer bar obtained in the step (3) when the diameter is 400mm_wf＝1.5935×10^-12m⁵/N, and calculating the radial stiffness K of the front rubber bushing obtained in the step (4)_xfRoll stiffness to front stabilizer bar system of 2186.9N/mmAnd (3) performing checking calculation, namely:

(6) vehicle total roll stiffnessChecking and calculating:

Checking calculation value of total roll angle rigidity of vehicleLess than the design value required for the vehicle calculated in step (1)Namely, it isThe vehicle roll stiffness does not meet vehicle design requirements.

The diameter of the front suspension stabilizer bar is adjusted and designed, namely the diameter of the front suspension stabilizer bar is adjusted and designed to be d_fThe roll angle rigidity of the vehicle is increased to 22mmThe design requirement value of the vehicle roll angle rigidity is met; also hasThe mounting distance between the two rubber bushings of the front suspension stabilizer bar can be adjusted and designed, and the distance between the two rubber bushings is adjusted₀Is designed to adjust the installation distance₀The mounting distance is increased by 10mm when the vehicle is 420mm, so that the roll angle rigidity of the vehicle is increasedAnd the design requirement value of the vehicle roll angle rigidity is met.

Claims

1. The method for checking the roll angle rigidity of the vehicle suspension comprises the following specific steps:

(1) total roll stiffness required for vehicle suspensionThe calculation of (2):

wherein g is the acceleration of gravity;

in the formula,

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Q_6f＝32(μ+1)[R_f(cosθ_f-1)-l_1fsinθ_f]²[2l_1fcosθ_f-l_cf+2R_fsinθ_f]；

<mrow> <msub> <mi>Q</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>64</mn> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> <mn>3</mn> </msubsup> </mrow> <mn>3</mn> </mfrac> <mo>,</mo> <msub> <mi>Q</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>64</mn> <mo>&lsqb;</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <msub> <mi>cos&theta;</mi> <mi>r</mi> </msub> <mo>+</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <msub> <mi>sin&theta;</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>&rsqb;</mo> </mrow> <mn>3</mn> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>Q</mi> <mrow> <mn>3</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>64</mn> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>&lsqb;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>R</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <msub> <mi>R</mi> <mi>r</mi> </msub> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> <mo>&rsqb;</mo> <mo>,</mo> <msub> <mi>Q</mi> <mrow> <mn>4</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mi>r</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mn>3</mn> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>Q</mi> <mrow> <mn>5</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>64</mn> <msub> <mi>R</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>&mu;</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&lsqb;</mo> <msubsup> <mi>R</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>3</mn> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> </mrow> <mn>4</mn> </mfrac> <mo>-</mo> <mn>2</mn> <msub> <mi>sin&theta;</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> <msub> <mi>l</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <msub> <mi>R</mi> <mi>r</mi> </msub> <msup> <mi>sin</mi> <mn>4</mn> </msup> <mfrac> <msub> <mi>&theta;</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> <mo>&rsqb;</mo> <mo>,</mo> </mrow>

Q_6r＝32(u+1)[R_r(cosθ_r-1)-l_1rsinθ_r]²[2l_1rcosθ_r-l_cr+2R_rsinθ_r]；

according to the inner circle radius r of the front and rear rubber bushings_afAnd r_arOuter radius r_bfAnd r_brAxial length L_fAnd L_rAnd modulus of elasticity E of rubber bushing_xPoisson ratio μ_xAnd respectively calculating the radial linear rigidity of the front and rear suspension rubber bushings, namely:

wherein,

<mrow> <mi>y</mi> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>3</mn> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>f</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mi> </mi> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mfrac> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>)</mo> <mo>&lsqb;</mo> <mi>K</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mi>K</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>(</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>&rsqb;</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&lsqb;</mo> <mi>I</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>(</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>&rsqb;</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>3</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>)</mo> <mo>(</mo> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mn>3</mn> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>3</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> <mrow> <mo>&lsqb;</mo> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mi>ln</mi> <mi> </mi> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>2</mn> <msqrt> <mn>15</mn> </msqrt> <mo>/</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <mo>,</mo> </mrow>

I(1,α_fr_af)，K(1,α_fr_af)，I(0,α_fr_af)，K(0,α_fr_af)；

Wherein,

<mrow> <mi>y</mi> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mn>3</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mi> </mi> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mfrac> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>)</mo> <mo>&lsqb;</mo> <mi>K</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mi>K</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>&rsqb;</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&lsqb;</mo> <mi>I</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mi>I</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>&rsqb;</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mn>3</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>x</mi> </msub> <mo>)</mo> <mo>(</mo> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mn>3</mn> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mn>5</mn> <msub> <mi>&pi;E</mi> <mi>x</mi> </msub> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msub> <mi>b</mi> <mrow> <mn>3</mn> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>&lsqb;</mo> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>K</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>I</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>&lsqb;</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow> <mi>b</mi> <mi>r</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mi>ln</mi> <mi> </mi> <msub> <mi>r</mi> <mrow> <mi>a</mi> <mi>r</mi> </mrow> </msub> <mo>&rsqb;</mo> <mo>,</mo> </mrow>

<mrow> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>2</mn> <msqrt> <mn>15</mn> </msqrt> <mo>/</mo> <msub> <mi>L</mi> <mi>r</mi> </msub> <mo>;</mo> </mrow>

I(1,α_rr_ar)，K(1,α_rr_ar)，I(0,α_rr_ar)，K(0,α_rr_ar)；

(6) vehicle total roll stiffnessChecking and calculating:

If the calculated value of the checking of the rigidity of the total roll angle of the vehicleGreater than or equal to the design value required for the vehicle calculated in step (1)Namely, it isThe vehicle roll angle rigidity meets the vehicle design requirements; otherwise, ifThe roll angle stiffness of the vehicle does not meet the vehicle design requirements and the front and rear suspension stabilizer bar systems need to be adjusted and designed.