CN106585709A - Automotive chassis integrated system and optimizing method thereof - Google Patents

Abstract

The invention discloses an automotive chassis integrated system and an optimizing method thereof. The automotive chassis integrated system comprises a differential power-assisted steering module, a motor braking module and a semi-active suspension module. During optimizing, parameters of part of structures of the differential power-assisted steering module, the motor braking module and the semi-active suspension module are used as root hairs, the differential power-assisted steering module, the motor braking module and the semi-active suspension module are used as a tree root, comprehensive performance indexes of an automobile are used as a tree trunk, steering performance, braking efficiency and smoothness of a suspension are used as tree branches, and steering road feeling, steering sensitivity, braking deceleration, automobile body accelerated speed, suspension dynamic deflection and wheel relative dynamic load are used as leaves to establish an automotive chassis integrated system optimized module with a tree-shaped structure; and based on the optimized module, the chassis integrated system is optimally designed by an Evol algorithm.

Description

A kind of automobile chassis integrated system and its optimization method

Technical field

The present invention relates to steering, brakes and suspension system, refer specifically to a kind of automobile chassis integrated system and its Optimization method.

Background technology

Used as the system of a complexity, it mainly includes the subsystems such as braking, steering and suspension to automobile chassis.Steering Input instruction according to driver deflects deflecting roller, to obtain the control of vehicle traveling direction, the quality of steering performance Determine steering sensitivity, portability and the control stability of automobile；The effect of brakes be make traveling car deceleration or Stop, the car speed of descent run keeps stable and stagnation of movement automobile to keep as you were, the braking effect of brakes Directional stability when can and brake directly affects the travel safety of automobile；Automotive suspension is used as connection vehicle body and the bridge of wheel Beam, its effect is vertical counter-force, longitudinal counter-force and the lateral reaction for road surface being acted on wheel, and these counter-forces are produced Torque is delivered on vehicle body, and to ensure the normally travel of automobile, the quality of suspension system performance directly affects the ride comfort of automobile.

In fact, under different driving cycles, the motion in automobile chassis system between each subsystem influences each other, phase interaction With.Look up from vertical, the motion of single subsystem is inherently impacted to many performances of automobile.It is multiple from transversely Subsystem and when depositing, certainly exists the interactional problem of movement relation between them.In optimization process, due to integrated system System optimization aim diversity, so need to design suitable optimization method that design is optimized to integrated system.

When parameter optimization is carried out by different performance indications to multiple subsystems, a certain subsystem performance index is changed Certain impact must be produced to other systems, the simple superposition of these subsystem optimizations can not obtain optimum while kind Chassis system combination property, so set up a kind of suitable Optimized model and be optimized to chassis integrated system seeming particularly heavy Will.

The content of the invention

The technical problem to be solved is for defect involved in background technology, there is provided a kind of automobile bottom Disk integrated system and its optimization method.

The present invention is employed the following technical solutions to solve above-mentioned technical problem：

A kind of automobile chassis integrated system, including differential power-assisted steering module, motor braking module and semi-active suspension mould Block；

The differential power-assisted steering module includes steering wheel torque rotary angle transmitter, rack and pinion steering gear, two wheel hubs Motor, vehicle speed sensor, two wheel speed sensors, yaw-rate sensor and differential power-assisted steering control ECU；

The steering wheel assembly of automobile is connected by steering column with rack and pinion steering gear, and rack and pinion steering gear is by turning to Drag link is connected with the axletree of vehicle front；

The steering wheel torque rotary angle transmitter is arranged on steering column, for obtaining the torque of vehicle steering and turning Angle；

Described two wheel hub motors are respectively used to the driving and braking of two front-wheels；

The vehicle speed sensor is used to obtain the speed of automobile；

Described two wheel speed sensors are separately positioned on two front-wheels, are respectively used to obtain the angular speed of two front-wheels；

The yaw-rate sensor is used to obtain the yaw velocity of automobile；

The differential power-assisted steering control ECU is passed respectively with steering wheel torque rotary angle transmitter, two wheel hub motors, speeds Sensor, two wheel speed sensors, yaw-rate sensors are electrically connected, the torque and corner, yaw according to vehicle steering The angular speed of angular speed, speed and two front-wheels sends current signal to left and right wheel hub motor so that left and right wheel hub motor is exported Different driving moment, to realize differential power-assisted steering；

The motor braking module includes brake pedal position sensor and motor braking control ECU；

The brake pedal position sensor is used to obtain automobile brake pedal positional information；

Motor braking control ECU respectively with brake pedal position sensor, two wheel hub motors, vehicle speed sensor, Two wheel speed sensors, yaw-rate sensors are electrically connected, for according to brake pedal position, speed, two front-wheels Angular speed, yaw velocity are adjusted realizing motor braking to the braking moment of wheel hub motor；

The semi-active suspension module includes flexible member and continuously adjustabe shock absorber；

The flexible member and continuously adjustabe shock absorber are set up in parallel, and the vehicle body of automobile is connected with vehicle frame.

The invention also discloses a kind of optimization method based on the automobile chassis integrated system, comprises the steps of：

Step 1), set up car load Three Degree Of Freedom model；

Step 2), set up differential power-assisted steering module, motor braking module and semi-active suspension modular power model；

Step 3), derive the quantitative formula of steering behaviour, brake efficiency and suspension ride comfort performance indications；

Step 4), optimized variable is chosen, Optimized model object function is set up, constraints is set, set up tree structure Chassis integrated system Optimized model；

Step 4.1), to turn to the rotary inertia of output shaft and little gear, turn to the equivalent damping of output shaft and little gear Coefficient, rack mass, tooth bar Equivalent damping coefficient, rack displacement, the equivalent moment of inertia of the tire comprising wheel hub motor, The Equivalent damping coefficient of the tire comprising wheel hub motor, front suspension equivalent stiffness, rear suspension equivalent stiffness, front suspension are equivalent Damped coefficient, rear suspension Equivalent damping coefficient are used as optimized variable；

Step 4.2), optimization mould is drawn by the quantitative formula of steering behaviour, brake efficiency and suspension ride comfort performance indications Type object function；

Step 4.3), the constraints that Optimized model object function needs to meet is set；

Step 4.4), with the optimized variable as coring, with differential power-assisted steering module, motor braking module and half actively On Suspension Module is tree root, with comprehensive vehicle performance as trunk, with steering behaviour, brake efficiency and suspension ride comfort as branch, with Steering response, steering sensitivity, braking deceleration, vehicle body acceleration, suspension dynamic deflection and wheel are leaf with respect to dynamic load, are set up The automobile chassis integrated system Optimized model of tree structure；

Step 5), based on automobile chassis integrated system Optimized model, it is optimized using Evol algorithms, obtain optimized variable Optimal value.

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 1) described in car load three Degrees of Freedom Model is：

Wherein, Y₁=-k_f-k_r；Y₂=-(ak_f-bk_r)/V；Y₃=-E₁k_f-E₂k_r-k_cf-k_cr；Y₄=k_f；

L₁=-ak_f+bk_r；L₂=(2 μ_rhmV²-a²k_f-b²k_r)/V；L₃=-aE₁k_f+bE₂k_r-ak_cf+bk_cr；

L₄=ak_f；L₅=2 μ_rhmV；

N₁=(k_f+k_r)h；N₂=(ak_f-bk_r)h/V；

N₃=mgh+2d (dK_2f-dK_2r2-K_a1-K_a2)+h(E₁k_f+E₂k_r+k_cf+k_cr)；

N₄=-k_fh；N₅=2d (dK_2f-dK_2r-K_a1-K_a2)；

M is complete vehicle quality；V is car speed；G is acceleration of gravity；H is bodywork height；ω_rFor yaw velocity；β is Side slip angle；For angle of heel；δ is front wheel angle；I_xFor rotary inertia of the car mass to x-axis；I_zIt is car mass to z The rotary inertia of axle；I_xzIt is car mass to x, the product of inertia of z-axis；A, b are respectively automobile barycenter to wheel base distance；k_f、 k_rCornering stiffness before and after respectively；E₁、E₂Roll steer coefficient before and after respectively；k_cf、k_crLateral thrust coefficient before and after respectively； K_a1、K_a2Respectively fore suspension and rear suspension roll angular rigidity；μ_rFor ground friction coefficient；D is the half of wheelspan；K_2f、K_2rBefore and after respectively Suspension rate.

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 3) described in lead steering The quantitative formula of energy index includes the quantitative formula of steering response and the quantitative formula of steering sensitivity, the amount of the steering response Changing formula is：

The quantitative formula of the steering sensitivity is：

Wherein,

P₃=XA₃；P₂=XA₂；P₁=XA₁；P₀=XA₀；

Q₆=X₂B₄；Q₅=X₁B₄+X₂B₃；Q₄=X₀B₄+X₁B₃+X₂B₂；Q₃=X₀B₃+X₁B₂+X₂B₁；

Q₂=X₀B₂+X₁B₁+X₂B₀；Q₁=X₀B₁+X₁B₀；Q₀=X₀B₀；

A₃=L₄Vh²m²-I_xL₅Y₄-I_xL₄Vm-I_xzN₄Vm-L₅N₄hm-I_xzVY₄hm；

A₂=I_xL₄Y₁-I_xL₁Y₄-I_xzN₁Y₄+I_xzN₄Y₁+L₅N₅Y₄+L₄N₅Vm-L₁N₄hm+L₄N₁hm；

A₁=L₁N₅Y₄-L₄N₅Y₁+L₅N₃Y₄-L₅N₄Y₃-L₃N₄Vm+L₄N₃Vm-L₃VY₄hm+L₄VY₃hm；

A₀=L₁N₃Y₄-L₁N₄Y₃-L₃N₁Y₄+L₃N₄Y₁+L₄N₁Y₃-L₄N₃Y₁；

B₄=I_zVh²m²-I_xI_zVm；

Direction is acted on for torque of the road excitation by wheel in steering gear transmission is in one's hands to driver The transmission function of disk equivalent moment；For the transmission function of steering wheel angle to yaw velocity, s be frequency-region signal, T_hS () is that driver acts on steering wheel equivalent moment under frequency domain；T_s' (s) for information of road surface under frequency domain by wheel through steering gear Torque during transmission is in one's hands；ω_r(s)、θ_sS () and δ (s) represent respectively yaw velocity under frequency domain, steering wheel angle and front rotation Angle, K_sFor steering wheel torque rotary angle transmitter equivalent stiffness；n₂For the gearratio of steering screw to front-wheel；J_e、B_eRespectively turn to The equivalent moment of inertia and Equivalent damping coefficient of output shaft and rack and pinion steering gear gear structure；m_rFor the equivalent matter of tooth bar Amount；b_rFor the Equivalent damping coefficient of tooth bar；k_rFor the equivalent stiffness of tooth bar；x_rFor the displacement of tooth bar；r_δFor left and right two front steering The stub lateral offset of wheel；r_pFor little gear radius；R is radius of wheel；N_lFor distance between track rod and axletree；G is Wheel hub motor reducing gear speed reducing ratio；J_eq、B_eqThe respectively equivalent moment of inertia of tire (include wheel hub motor) and equivalent Damped coefficient；K_aFor wheel hub motor moment coefficient；K_m1And K_m2Respectively left and right wheel hub motor power-assisted gain.

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 3) described in brake efficiency Quantitative formula including braking deceleration quantitative formula, be specifically expressed as：

In formula：For the transmission function of steering wheel angle to braking deceleration, a (s) is braking deceleration under frequency domain Degree,

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 3) described in suspension smooth-going Property performance quantification of targets formula include before and after body vibrations acceleration quantitative formula, the quantitative formula of fore suspension and rear suspension dynamic deflection The quantitative formula of dynamic load relative with front and back wheel, respectively：

In formula：WithBody vibrations acceleration transmission function before and after representing respectively；WithFore suspension and rear suspension dynamic deflection transmission function is represented respectively；WithFront and back wheel is represented respectively With respect to dynamic load transmission function；Q represents road excitation；Z_2fAnd Z_2rVehicle body displacement before and after representing respectively；Z_1fAnd Z_1rBefore and after representing respectively Wheel displacements；f_dfAnd f_drFore suspension and rear suspension dynamic deflection is represented respectively；WithRelative dynamic load before and after representing respectively, in formula, G_f= (m_1f+m_2f) g, G_r=(m_1r+m_2r)g；m_1fAnd m_1rNonspring carried mass before and after representing respectively；m_2fAnd m_2rSpring charge material before and after representing respectively Amount；K_tFor tire equivalent stiffness；K_2fAnd K_2rFore suspension and rear suspension rigidity is represented respectively；C_2fAnd C_2rFore suspension and rear suspension damping is represented respectively；g For acceleration of gravity.

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 4.2) described in optimize mould Type object function f (X) is：

F (X)=W₁f₁(X)+W₂f₂(X)+W₃f₃(X)

In formula：

Frequency in formula, when f is input into for road excitation；For Road Surface Power Spectrum Density；w_iFor weight coefficient；W_iFor Sub-goal function weight coefficient.

As the further prioritization scheme of optimization method of the automobile chassis integrated system, step 4.3) described in optimize mould Type object function need meet constraints be：

The denominator of steering sensitivity quantitative formula meet Routh Criterion, braking deceleration meet a≤g, suspension dynamic deflection expire Sufficient f_cr=(0.6～0.8) f_cf, relative damping factor meet ξ_f∈[0.2,0.4]、ξ_r∈[0.2,0.4]；

Wherein, f_cf=(m_1f+m_2f)g/k_2f；f_cr=(m_1r+m_2r)g/k_2r；

The present invention adopts above technical scheme compared with prior art, with following technique effect：

The Optimized model that the present invention is set up actively hangs while taking into account differential power-assisted steering module, motor braking module and half Impact of the frame module to comprehensive vehicle performance, can effective coordination three subsystems optimization when the multifarious problem of target, and And calculating is optimized using three subsystems as different branches, computational efficiency can be effectively improved.

Description of the drawings

Fig. 1 is electric power steering of the present invention and motor braking module arrangement schematic diagram；

Fig. 2 is semi-active suspension module arrangement schematic diagram of the present invention；

Fig. 3 is the Optimized model structural representation of the present invention；

Fig. 4 is the optimization method flow chart of the present invention.

In figure, 1- turns to output shaft and pinion rotation inertia, and 2- turns to output shaft and little gear Equivalent damping coefficient, 3- Rack mass, 4- tooth bar Equivalent damping coefficients, 5- rack displacements, 6- includes equivalent moment of inertia of the wheel hub motor in interior tire, 7- includes Equivalent damping coefficient of the wheel hub motor in interior tire, 8- front suspension equivalent stiffness, 9- rear suspension equivalent stiffness, before 10- Suspension Equivalent damping coefficient, 11- rear suspension Equivalent damping coefficients, 12- steering wheel torque rotary angle transmitters, 13- rack-and-pinion turns To device, 14- wheel hub motors.

Specific embodiment

Technical scheme is described in further detail below in conjunction with the accompanying drawings：

The invention discloses a kind of automobile chassis integrated system and its optimization method, as shown in figure 1, the invention discloses one Plant automobile chassis integrated system, including differential power-assisted steering module, motor braking module and semi-active suspension module.

The differential power-assisted steering module includes steering wheel torque rotary angle transmitter, rack and pinion steering gear, two wheel hubs Motor, vehicle speed sensor, two wheel speed sensors, yaw-rate sensor and differential power-assisted steering control ECU；The side of automobile It is connected with rack and pinion steering gear by steering column to disc assembly, rack and pinion steering gear is by track rod and vehicle front Axletree connection；The steering wheel torque rotary angle transmitter is arranged on steering column, for obtain vehicle steering torque and Corner；Described two wheel hub motors are respectively used to the driving and braking of two front-wheels；The vehicle speed sensor is used to obtain automobile Speed；Described two wheel speed sensors are separately positioned on two front-wheels, are respectively used to obtain the angular speed of two front-wheels；Institute Stating yaw-rate sensor is used for the yaw velocity of automobile；The differential power-assisted steering control ECU turns respectively with steering wheel Square rotary angle transmitter, two wheel hub motors, vehicle speed sensor, two wheel speed sensors, yaw-rate sensors are electrically connected, Left and right wheel hub motor is sent out according to the torque of vehicle steering and the angular speed of corner, yaw velocity, speed and two front-wheels Go out current signal so that left and right wheel hub motor exports different driving moments, to realize differential power-assisted steering.

The motor braking module includes brake pedal position sensor and motor braking control ECU；The brake pedal Position sensor is used to obtain automobile brake pedal positional information；The motor braking controls ECU respectively and brake pedal position Sensor, two wheel hub motors, vehicle speed sensor, two wheel speed sensors, yaw-rate sensors are electrically connected, for root According to brake pedal position, speed, the angular speed of two front-wheels, yaw velocity the braking moment of wheel hub motor is adjusted with Realize motor braking.

As shown in Fig. 2 the semi-active suspension module includes flexible member and continuously adjustabe shock absorber；The flexible member It is set up in parallel with continuously adjustabe shock absorber, the vehicle body of automobile is connected with vehicle frame.

As shown in figure 3, being joined with the part-structure of differential power-assisted steering module, motor braking module and semi-active suspension module Number is coring, with differential power-assisted steering module, motor braking module and semi-active suspension module as tree root, with comprehensive vehicle performance Index is trunk, with steering behaviour, brake efficiency and suspension ride comfort as branch, is subtracted with steering response, steering sensitivity, braking Speed, vehicle body acceleration, suspension dynamic deflection and wheel set up the automobile chassis integrated system of tree structure with respect to dynamic load for leaf Optimized model.

As shown in figure 4, the invention discloses a kind of optimization method based on the automobile chassis integrated system, including following step Suddenly：

Step 1), set up car load Three Degree Of Freedom model：

Wherein, Y₁=-k_f-k_r；Y₂=-(ak_f-bk_r)/V；Y₃=-E₁k_f-E₂k_r-k_cf-k_cr；Y₄=k_f；

L₁=-ak_f+bk_r；L₂=(2 μ_rhmV²-a²k_f-b²k_r)/V；L₃=-aE₁k_f+bE₂k_r-ak_cf+bk_cr；

L₄=ak_f；L₅=2 μ_rhmV；

N₁=(k_f+k_r)h；N₂=(ak_f-bk_r)h/V；

N₃=mgh+2d (dK_2f-dK_2r2-K_a1-K_a2)+h(E₁k_f+E₂k_r+k_cf+k_cr)；

N₄=-k_fh；N₅=2d (dK_2f-dK_2r-K_a1-K_a2)；

M is complete vehicle quality；V is car speed；G is acceleration of gravity；H is bodywork height；ω_rFor yaw velocity；β is Side slip angle；For angle of heel；δ is front wheel angle；I_xFor rotary inertia of the car mass to x-axis；I_zIt is car mass to z The rotary inertia of axle；I_xzIt is car mass to x, the product of inertia of z-axis；A, b are respectively automobile barycenter to wheel base distance；k_f、 k_rCornering stiffness before and after respectively；E₁、E₂Roll steer coefficient before and after respectively；k_cf、k_crLateral thrust coefficient before and after respectively； K_a1、K_a2Respectively fore suspension and rear suspension roll angular rigidity；μ_rFor ground friction coefficient；D is the half of wheelspan；K_2f、K_2rBefore and after respectively Suspension rate.

Step 2), set up differential power-assisted steering module, motor braking module and semi-active suspension modular power model.

Step 3), steering behaviour, brake efficiency and suspension ride comfort performance indications quantitative formula are derived successively.

Steering behaviour index, including steering response and steering sensitivity are derived first, and its quantitative formula is as follows：

Steering response quantitative formula is：

In formula：

To derive steering sensitivity quantitative formula, yaw velocity and front wheel angle relation are first derived：

In formula：A₃=L₄Vh²m²-I_xL₅Y₄-I_xL₄Vm-I_xzN₄Vm-L₅N₄hm-I_xzVY₄hm；

A₂=I_xL₄Y₁-I_xL₁Y₄-I_xzN₁Y₄+I_xzN₄Y₁+L₅N₅Y₄+L₄N₅Vm-L₁N₄hm+L₄N₁hm；

A₁=L₁N₅Y₄-L₄N₅Y₁+L₅N₃Y₄-L₅N₄Y₃-L₃N₄Vm+L₄N₃Vm-L₃VY₄hm+L₄VY₃hm；

A₀=L₁N₃Y₄-L₁N₄Y₃-L₃N₁Y₄+L₃N₄Y₁+L₄N₁Y₃-L₄N₃Y₁；

B₄=I_zVh²m²-I_xI_zVm；

Then front wheel angle and little gear angle relation are derived：

In formula：

The quantitative formula for being finally derived from steering sensitivity is：

In formula：P₃=XA₃；P₂=XA₂；P₁=XA₁；P₀=XA₀；

Q₆=X₂B₄；Q₅=X₁B₄+X₂B₃；Q₄=X₀B₄+X₁B₃+X₂B₂；Q₃=X₀B₃+X₁B₂+X₂B₁；

Q₂=X₀B₂+X₁B₁+X₂B₀；Q₁=X₀B₁+X₁B₀；Q₀=X₀B₀；

Direction is acted on for torque of the road excitation by wheel in steering gear transmission is in one's hands to driver The transmission function of disk equivalent moment；It is frequency-region signal, T for the transmission function of steering wheel angle to yaw velocity, s_h S () is that driver acts on steering wheel equivalent moment under frequency domain；T_s' (s) for information of road surface under frequency domain by wheel through steering gear Torque during transmission is in one's hands；ω_r(s)、θ_sS () and δ (s) represent respectively yaw velocity under frequency domain, steering wheel angle and front rotation Angle, K_sFor steering wheel torque rotary angle transmitter equivalent stiffness；n₂For the gearratio of steering screw to front-wheel；J_e、B_eRespectively turn to The equivalent moment of inertia and Equivalent damping coefficient of output shaft and rack and pinion steering gear gear structure；m_rFor the equivalent matter of tooth bar Amount；b_rFor the Equivalent damping coefficient of tooth bar；k_rFor the equivalent stiffness of tooth bar；x_rFor the displacement of tooth bar；R δ are left and right two front steering The stub lateral offset of wheel；r_pFor little gear radius；R is radius of wheel；N_lFor distance between track rod and axletree；G is Wheel hub motor reducing gear speed reducing ratio；J_eq、B_eqThe respectively equivalent moment of inertia of tire (include wheel hub motor) and equivalent Damped coefficient；K_aFor wheel hub motor moment coefficient；K_m1And K_m2Respectively left and right wheel hub motor power-assisted gain.

Secondly brake efficiency index, including braking deceleration are derived, its quantitative formula is：

In formula,For the transmission function of steering wheel angle to braking deceleration, a (s) is braking deceleration under frequency domain Degree,

Suspension flexibility index is finally derived, including Qian Hou body vibrations acceleration, fore suspension and rear suspension dynamic deflection and car in front and back The relative dynamic load of wheel, its quantitative formula is respectively：

In formula：WithBody vibrations acceleration transmission function before and after representing respectively；WithFore suspension and rear suspension dynamic deflection transmission function is represented respectively；WithFront and back wheel phase is represented respectively To dynamic load transmission function；Q represents road excitation；Z_2fAnd Z_2rVehicle body displacement before and after representing respectively；Z_1fAnd Z_1rCar before and after representing respectively Wheel displacement；f_dfAnd f_drFore suspension and rear suspension dynamic deflection is represented respectively；WithRelative dynamic load before and after representing respectively, in formula, G_f= (m_1f+m_2f) g, G_r=(m_1r+m_2r)g；m_1fAnd m_1rNonspring carried mass before and after representing respectively；m_2fAnd m_2rSpring charge material before and after representing respectively Amount；K_tFor tire equivalent stiffness；K_2fAnd K_2rFore suspension and rear suspension rigidity is represented respectively；C_2fAnd C_2rFore suspension and rear suspension damping is represented respectively；g For acceleration of gravity.

Step 4), Optimized model optimized variable is chosen, Optimized model object function is set up, constraints is set, set up tree The chassis integrated system Optimized model of shape structure；

(1) differential power-assisted steering module, motor braking module and semi-active suspension module are chosen and turns to output shaft and little tooth Wheel rotary inertia, turn to output shaft and little gear Equivalent damping coefficient, rack mass, tooth bar Equivalent damping coefficient rack displacement, Equivalent moment of inertia, Equivalent damping coefficient, front suspension comprising wheel hub motor in interior tire comprising wheel hub motor in interior tire Equivalent stiffness, rear suspension equivalent stiffness, front suspension Equivalent damping coefficient, rear suspension Equivalent damping coefficient are used as optimized variable；

(2) Optimized model target letter is drawn by steering behaviour, brake efficiency and suspension ride comfort performance indications quantitative formula Number；

Steering behaviour object function：

Brake efficiency object function：

Suspension ride comfort object function：

In formula：Frequency when f is input into for road roughness；For Road Surface Power Spectrum Density；w_iFor weight coefficient.

Comprehensive three above subsystem performance target goals function, draws Optimized model target object function：

F (X)=W₁f₁(X)+W₂f₂(X)+W₃f₃(X)

In formula：W_iFor sub-goal function weight coefficient.

(3) in optimization process, following constraints is set：The denominator of steering sensitivity quantitative formula should meet Louth and sentence Meet a≤g, suspension dynamic deflection and meet f according to, braking deceleration_cr=(0.6～0.8) f_cfMeet ξ with relative damping factor_f∈ [0.2,0.4]、ξ_r∈[0.2,0.4]。

In formula：f_cf=(m_1f+m_2f)g/k_2f；f_cr=(m_1r+m_2r)g/k_2r；

(4) according to tree structure, with the part of differential power-assisted steering module, motor braking module and semi-active suspension module Structural parameters are coring, comprehensive with automobile with differential power-assisted steering module, motor braking module and semi-active suspension module as tree root Conjunction performance indications be trunk, with steering behaviour, brake efficiency and suspension ride comfort as branch, with steering response, steering sensitivity, Braking deceleration, vehicle body acceleration, suspension dynamic deflection and wheel set up the automobile chassis collection of tree structure with respect to dynamic load for leaf Into system optimization model；

Step 5), based on automobile chassis integrated system Optimized model, it is optimized using Evol algorithms, obtain optimized variable Optimal value.

Concrete Evol algorithms realize that flow process is as follows：

Step1：Determine optimized variable collection, and it is encoded；

Step2：Determine Evol control parameter of algorithm and the specific strategy for being adopted, Evol control parameter of algorithm includes：Kind Group's quantity, mutation operator, crossover operator, maximum evolutionary generation, end condition etc.；

Step3：Randomly generate initial population, evolutionary generation t=1；

Step4：Initial population is evaluated, that is, calculates each individual fitness value in initial population；

Step5：Judge whether that reaching end condition or evolutionary generation reaches minimum, if so, then evolving terminates, by now Optimized individual is used as solution output；If it is not, then continuing；

Step6：Enter row variation and crossover operation, boundary condition is processed, obtain interim population；

Step7：Interim population is evaluated, each individual fitness value in interim population is calculated；

Step8：Selection operation is carried out, new population is obtained；

Step9:Evolutionary generation t=t+1, goes to step 4.

During actual optimization, as same big tree growth, when coring absorbs nutrient from soil, entered tree root Nutrient is conveyed to into trunk, branch and leaf；When leaf carries out photosynthesis, photosynthate is sent to branch And trunk.In the automobile chassis integrated system Optimized model of tree structure, the value of each optimized variable by changing coring, from And each subsystem of impact tree root, after tree root is affected, change as the comprehensive vehicle performance index of trunk, as tree Each system performance index of branch and each sub- index as leaf all change；When each sub-goal as leaf changes When, each system performance index as branch and the comprehensive vehicle performance index as trunk all will change.

It is understood that unless otherwise defined, all terms used herein are (including skill for those skilled in the art of the present technique Art term and scientific terminology) have with art of the present invention in those of ordinary skill general understanding identical meaning.Also It should be understood that those terms defined in such as general dictionary should be understood that with the context of prior art in The consistent meaning of meaning, and unless defined as here, will not be explained with idealization or excessively formal implication.

Above-described specific embodiment, has been carried out further to the purpose of the present invention, technical scheme and beneficial effect Describe in detail, should be understood that the specific embodiment that the foregoing is only the present invention, be not limited to this Bright, all any modification, equivalent substitution and improvements within the spirit and principles in the present invention, done etc. should be included in the present invention Protection domain within.

Claims (8)

1. a kind of automobile chassis integrated system, it is characterised in that main including differential power-assisted steering module, motor braking module and half Dynamic On Suspension Module；

The differential power-assisted steering module include steering wheel torque rotary angle transmitter, rack and pinion steering gear, two wheel hub motors, Vehicle speed sensor, two wheel speed sensors, yaw-rate sensor and differential power-assisted steering control ECU；

The steering wheel assembly of automobile is connected by steering column with rack and pinion steering gear, and rack and pinion steering gear is by turning to horizontal drawing Bar is connected with the axletree of vehicle front；

The steering wheel torque rotary angle transmitter is arranged on steering column, for obtaining torque and the corner of vehicle steering；

Described two wheel hub motors are respectively used to the driving and braking of two front-wheels；

The vehicle speed sensor is used to obtain the speed of automobile；

Described two wheel speed sensors are separately positioned on two front-wheels, are respectively used to obtain the angular speed of two front-wheels；

The yaw-rate sensor is used to obtain the yaw velocity of automobile；

The differential power-assisted steering control ECU is sensed respectively with steering wheel torque rotary angle transmitter, two wheel hub motors, speeds Device, two wheel speed sensors, yaw-rate sensors are electrically connected, the torque and corner, yaw angle according to vehicle steering The angular speed of speed, speed and two front-wheels sends current signal to left and right wheel hub motor so that left and right wheel hub motor is exported not Same driving moment, to realize differential power-assisted steering；

The motor braking module includes brake pedal position sensor and motor braking control ECU；

The brake pedal position sensor is used to obtain automobile brake pedal positional information；

Motor braking control ECU respectively with brake pedal position sensor, two wheel hub motors, vehicle speed sensor, two Wheel speed sensors, yaw-rate sensor are electrically connected, for fast according to the angle of brake pedal position, speed, two front-wheels Degree, yaw velocity are adjusted realizing motor braking to the braking moment of wheel hub motor；

The semi-active suspension module includes flexible member and continuously adjustabe shock absorber；

The flexible member and continuously adjustabe shock absorber are set up in parallel, and the vehicle body of automobile is connected with vehicle frame.

2. the optimization method of the automobile chassis integrated system being based on described in claim 1, it is characterised in that comprise the steps of：

Step 1), set up car load Three Degree Of Freedom model；

Step 2), set up differential power-assisted steering module, motor braking module and semi-active suspension modular power model；

Step 3), derive the quantitative formula of steering behaviour, brake efficiency and suspension ride comfort performance indications；

Step 4), optimized variable is chosen, Optimized model object function is set up, constraints is set, set up the chassis of tree structure Integrated system Optimized model；

Step 4.1), with turn to output shaft and little gear rotary inertia, turn to output shaft and little gear Equivalent damping coefficient, Rack mass, tooth bar Equivalent damping coefficient, rack displacement, the equivalent moment of inertia of the tire comprising wheel hub motor, include Equivalent damping coefficient, front suspension equivalent stiffness, rear suspension equivalent stiffness, front suspension equivalent damping of the wheel hub motor in interior tire Coefficient, rear suspension Equivalent damping coefficient are used as optimized variable；

Step 4.2), Optimized model mesh is drawn by the quantitative formula of steering behaviour, brake efficiency and suspension ride comfort performance indications Scalar functions；

Step 4.3), the constraints that Optimized model object function needs to meet is set；

Step 4.4), with the optimized variable as coring, with differential power-assisted steering module, motor braking module and semi-active suspension Module is tree root, with comprehensive vehicle performance as trunk, with steering behaviour, brake efficiency and suspension ride comfort as branch, to turn to Road feel, steering sensitivity, braking deceleration, vehicle body acceleration, suspension dynamic deflection and wheel are leaf with respect to dynamic load, set up tree-like The automobile chassis integrated system Optimized model of structure；

Step 5), based on automobile chassis integrated system Optimized model, it is optimized using Evol algorithms, obtain optimized variable most The figure of merit.

3. the optimization method of automobile chassis integrated system according to claim 2, it is characterised in that step 1) described in Car load Three Degree Of Freedom model is：

Wherein, Y₁=-k_f-k_r；Y₂=-(ak_f-bk_r)/V；Y₃=-E₁k_f-E₂k_r-k_cf-k_cr；Y₄=k_f；

L₁=-ak_f+bk_r；L₂=(2 μ_rhmV²-a²k_f-b²k_r)/V；L₃=-aE₁k_f+bE₂k_r-ak_cf+bk_cr；

L₄=ak_f；L₅=2 μ_rhmV；

N₁=(k_f+k_r)h；N₂=(ak_f-bk_r)h/V；

N₃=mgh+2d (dK_2f-dK_2r2-K_a1-K_a2)+h(E₁k_f+E₂k_r+k_cf+k_cr)；

N₄=-k_fh；N₅=2d (dK_2f-dK_2r-K_a1-K_a2)；

M is complete vehicle quality；V is car speed；G is acceleration of gravity；H is bodywork height；ω_rFor yaw velocity；β is barycenter Side drift angle；For angle of heel；δ is front wheel angle；I_xFor rotary inertia of the car mass to x-axis；I_zIt is car mass to z-axis Rotary inertia；I_xzIt is car mass to x, the product of inertia of z-axis；A, b are respectively automobile barycenter to wheel base distance；k_f、k_rPoint Not Wei before and after cornering stiffness；E₁、E₂Roll steer coefficient before and after respectively；k_cf、k_crLateral thrust coefficient before and after respectively；K_a1、 K_a2Respectively fore suspension and rear suspension roll angular rigidity；μ_rFor ground friction coefficient；D is the half of wheelspan；K_2f、K_2rIt is outstanding before and after respectively Frame rigidity.

4. the optimization method of automobile chassis integrated system according to claim 3, it is characterised in that step 3) described in The quantitative formula of the quantification of targets formula of steering behaviour index including steering response and the quantitative formula of steering sensitivity, described turn It is to the quantitative formula of road feel：

$|H\left(s\right){|}_{T_h~T_s^{\′}}=|\frac{T_h\left(s\right)}{{T_s}^{\′}\left(s\right)}|=\frac{K_s}{X_2{s}^2+X_{1}s+X_0}$

The quantitative formula of the steering sensitivity is：

$|H\left(s\right){|}_{{\mathrm{\ω}}_r~{\mathrm{\θ}}_s}=|\frac{{\mathrm{\ω}}_r\left(s\right)}{{\mathrm{\θ}}_s\left(s\right)}|=|\frac{{\mathrm{\ω}}_r\left(s\right)}{\mathrm{\δ}\left(s\right)}\frac{\mathrm{\δ}\left(s\right)}{{\mathrm{\θ}}_s\left(s\right)}|=\frac{P_3{s}^3+P_2{s}^2+P_{1}s+P_0}{Q_6{s}^6+Q_5{s}^5+Q_4{s}^4+Q_3{s}^3+Q_2{s}^2+Q_1{s}^1+Q_0}$

Wherein,

$X_1=n_2{B}_e+n_2{b}_r{r_p}^2+\frac{2{\mathrm{dr}}_{\mathrm{\δ}}{r}_p}{r^2{N}_l}\frac{G}{n_2}{B}_{eq};$

$X_0=n_2{K}_s+n_2{k}_r{r_p}^2+\frac{r_{\mathrm{\δ}}{r}_p}{{\mathrm{rN}}_l}{K}_a{K}_s(K_{m2}-K_{m1});$

P₃=XA₃；P₂=XA₂；P₁=XA₁；P₀=XA₀；

Q₆=X₂B₄；Q₅=X₁B₄+X₂B₃；Q₄=X₀B₄+X₁B₃+X₂B₂；Q₃=X₀B₃+X₁B₂+X₂B₁；

Q₂=X₀B₂+X₁B₁+X₂B₀；Q₁=X₀B₁+X₁B₀；Q₀=X₀B₀；

A₃=L₄Vh²m²-I_xL₅Y₄-I_xL₄Vm-I_xzN₄Vm-L₅N₄hm-I_xzVY₄hm；

A₂=I_xL₄Y₁-I_xL₁Y₄-I_xzN₁Y₄+I_xzN₄Y₁+L₅N₅Y₄+L₄N₅Vm-L₁N₄hm+L₄N₁hm；

A₁=L₁N₅Y₄-L₄N₅Y₁+L₅N₃Y₄-L₅N₄Y₃-L₃N₄Vm+L₄N₃Vm-L₃VY₄hm+L₄VY₃hm；

A₀=L₁N₃Y₄-L₁N₄Y₃-L₃N₁Y₄+L₃N₄Y₁+L₄N₁Y₃-L₄N₃Y₁；

B₄=I_zVh²m²-I_xI_zVm；

$\begin{array}{c}{B}_3=I_x{I}_z{Y}_1+I_x{L}_5{Y}_2+{I_{xz}}^{2}Vm-L_2{\mathrm{Vh}}^2{m}^2+L_5{\mathrm{Vh}}^2{m}^2+I_x{L}_{2}Vm-I_x{L}_{5}Vm+I_{xz}{N}_{2}Vm\\ +I_z{N}_{5}Vm+I_{xz}{L}_{5}hm+I_z{N}_{1}hm+L_5{N}_{2}hm+I_{xz}{\mathrm{VY}}_{2}hm\end{array};$

$\begin{array}{c}{B}_2=I_x{L}_1{Y}_2-I_{xz}{Y_2}_1-I_x{L}_2{Y}_1+I_{xz}{N}_1{Y}_2-I_{xz}{N}_2{Y}_1-I_z{N}_5{Y}_1-L_5{N}_5{Y}_2+L_1{\mathrm{Vh}}^2{m}^2\\ -I_x{L}_{1}Vm-I_{xz}{N}_{1}Vm+I_z{N}_{3}Vm-L_2{N}_{5}Vm+L_5{N}_{5}Vm+I_{xz}{L}_{1}hm+L_1{N}_{2}hm\\ -L_2{N}_{1}hm-I_{xz}{\mathrm{VY}}_{1}hm+I_z{\mathrm{VY}}_{3}hm\end{array};$

$\begin{array}{c}{B}_1=I_{xz}{L}_5{Y}_3+I_z{N}_1{Y}_3-I_z{N}_3{Y}_1-L_1{N}_5{Y}_2+L_2{N}_5{Y}_1+L_5{N}_2{Y}_3-L_5{N}_3{Y}_2+I_{xz}{L}_{3}Vm\\ -L_2{N}_{3}Vm+L_3{N}_{2}Vm+L_1{N}_{5}Vm-L_5{N}_3{Y}_2+I_{xz}{L}_{3}Vm-L_2{N}_{3}Vm+L_3{N}_{2}Vm\\ +L_1{N}_{5}Vm\end{array};$

$\begin{array}{c}{B}_0=I_{xz}{L}_1{Y}_3-I_{xz}{L}_3{Y}_1+L_1{N}_2{Y}_3-L_1{N}_3{Y}_2-L_2{N}_1{Y}_3+L_2{N}_3{Y}_1+L_3{N}_1{Y}_2-L_3{N}_2{Y}_1\\ +L_1{N}_{3}Vm-L_3{N}_{1}Vm+L_1{\mathrm{VY}}_{3}hm-L_3{\mathrm{VY}}_{1}hm\end{array};$

It is equivalent steering wheel to be acted on for torque of the road excitation by wheel in steering gear transmission is in one's hands to driver The transmission function of torque；It is frequency-region signal, T for the transmission function of steering wheel angle to yaw velocity, s_hS () is Driver acts on steering wheel equivalent moment under frequency domain；T_s' (s) be delivered to through steering gear by wheel for information of road surface under frequency domain Torque in hand；ω_r(s)、θ_sS () and δ (s) represent respectively yaw velocity, steering wheel angle and front wheel angle, K under frequency domain_s For steering wheel torque rotary angle transmitter equivalent stiffness；n₂For the gearratio of steering screw to front-wheel；J_e、B_eRespectively turn to output The equivalent moment of inertia and Equivalent damping coefficient of axle and rack and pinion steering gear gear structure；m_rFor the equivalent mass of tooth bar；b_rFor The Equivalent damping coefficient of tooth bar；k_rFor the equivalent stiffness of tooth bar；x_rFor the displacement of tooth bar；r_δFor the stub of left and right two steering front wheel Lateral offset；r_pFor little gear radius；R is radius of wheel；N_lFor distance between track rod and axletree；G is wheel hub motor Reducing gear speed reducing ratio；J_eq、B_eqThe respectively equivalent moment of inertia of tire (include wheel hub motor) and equivalent damping system Number；K_aFor wheel hub motor moment coefficient；K_m1And K_m2Respectively left and right wheel hub motor power-assisted gain.

5. the optimization method of automobile chassis integrated system according to claim 4, it is characterised in that step 3) described in make The quantitative formula of dynamic efficiency includes the quantitative formula of braking deceleration, is specifically expressed as：

$|H\left(s\right){|}_{a~{\mathrm{\θ}}_s}=|\frac{a\left(s\right)}{{\mathrm{\θ}}_s\left(s\right)}|=\frac{X_2{\mathrm{Ys}}^3+X_1{\mathrm{Ys}}^2+(n_{2}X-X_0)Ys}{X_2{Y}_1{s}^3+(X_2{Y}_0+X_1{Y}_1)s^2+(X_1{Y}_0+X_0{Y}_1)s+X_0{Y}_0}$

In formula：For the transmission function of steering wheel angle to braking deceleration, a (s) is braking deceleration under frequency domain,

6. the optimization method of automobile chassis integrated system according to claim 5, it is characterised in that step 3) described in hang The quantitative formula of frame ride comfort performance includes the quantization public affairs of the quantitative formula of body vibrations acceleration, fore suspension and rear suspension dynamic deflection in front and back Formula and front and back wheel with respect to dynamic load quantitative formula, respectively：

$|H\left(s\right){|}_{{\stackrel{\·\·}{Z}}_{2f}~\stackrel{\·}{q}}=|\frac{{\stackrel{\·\·}{Z}}_{2f}}{\stackrel{\·}{q}}|=\frac{K_t{C}_{2f}{s}^2+K_t{K}_{2f}s}{m_{1f}{m}_{2f}{s}^4+(m_{1f}+m_{2f})C_{2f}{s}^3+(K_t{m}_{2f}+K_{2f}{m}_{1f}+K_{2f}{m}_{2f})s^2+K_t{C}_{2f}s+K_t{K}_{2f}}$

$|H\left(s\right){|}_{{\stackrel{\·\·}{Z}}_{2r}~\stackrel{\·}{q}}=|\frac{{\stackrel{\·\·}{Z}}_{2r}}{\stackrel{\·}{q}}|=\frac{K_t{C}_{2r}{s}^2+K_t{K}_{2r}s}{m_{1r}{m}_{2r}{s}^4+(m_{1r}+m_{2r})C_{2r}{s}^3+(K_t{m}_{2r}+K_{2r}{m}_{1r}+K_{2r}{m}_{2r})s^2+{\mathrm{KC}}_{2r}s+K_t{K}_{2r}}$

$|H\left(s\right){|}_{f_{df}~q}=|\frac{f_{df}}{\stackrel{\·}{q}}|=|\frac{Z_{2f}-Z_{1f}}{\stackrel{\·}{q}}|=\frac{K_t{m}_{2f}s}{m_{1f}{m}_{2f}{s}^4+(m_{1f}+m_{2f})C_{2f}{s}^3+(K_t{m}_{2f}+K_{2f}{m}_{1f}+K_{2f}{m}_{2f})s^2+K_t{C}_{2f}s+K_t{K}_{2f}}$

$|H\left(s\right){|}_{f_{dr}~q}=|\frac{f_{dr}}{\stackrel{\·}{q}}|=|\frac{Z_{2r}-Z_{1r}}{\stackrel{\·}{q}}|=\frac{K_t{m}_{2r}s}{m_{1r}{m}_{2i}{s}^4+(m_{1r}+m_{2r})C_{2i}{s}^3+(K_t{m}_{2r}+K_{2r}{m}_{1r}+K_{2r}{m}_{2r})s^2+K_t{C}_{2r}s+K_t{K}_{2r}}$

$\begin{array}{c}|H\left(s\right){|}_{F_{df}/G_f~q}=|\frac{F_{df}}{G_f}\frac{1}{\stackrel{\·}{q}}|=|\frac{K_t(Z_{1f}-q_f)}{(m_{1f}+m_{2f})g\stackrel{\·}{q}}|\\ =\frac{K_t}{(m_{1f}+m_{2f})g}\frac{m_{1f}{m}_{2f}{s}^3+(m_{1f}+m_{2f})C_{2f}{s}^2+(m_{1f}+m_{2f})K_{2f}s}{m_{1f}{m}_{2f}{s}^4+(m_{1f}+m_{2f})C_{2f}{s}^3+(K_t{m}_{2f}+K_{2f}{m}_{1f}+K_{2f}{m}_{2f})s^2+K_t{C}_{2f}s+K_t{K}_{2f}}\end{array}$

$\begin{array}{c}|H\left(s\right){|}_{F_{dr}/G_r~q}=|\frac{F_{dr}}{G_r}\frac{1}{\stackrel{\·}{q}}|=|\frac{K_t(Z_{1r}-q)}{(m_{1r}+m_{2r})g\stackrel{\·}{q}}|\\ =\frac{K_t}{(m_{1r}+m_{2r})g}\frac{m_{1r}{m}_{2r}{s}^3+(m_{1r}+m_{2r})C_{2r}{s}^2+(m_{1r}+m_{2r})K_{2r}s}{m_{1i}{m}_{2i}{s}^4+(m_{1r}+m_{2r})C_{2r}{s}^3+(K_t{m}_{2i}+K_{2r}{m}_{1r}+K_{2r}{m}_{2r})s^2+K_t{C}_{2r}s+K_t{K}_{2r}}\end{array}$

In formula：WithBody vibrations acceleration transmission function before and after representing respectively；With Fore suspension and rear suspension dynamic deflection transmission function is represented respectively；WithRepresent front and back wheel with respect to dynamic load respectively Transmission function；Q represents road excitation；Z_2fAnd Z_2rVehicle body displacement before and after representing respectively；Z_1fAnd Z_1rFront and back wheel position is represented respectively Move；f_dfAnd f_drFore suspension and rear suspension dynamic deflection is represented respectively；WithRelative dynamic load before and after representing respectively, in formula, G_f=(m_1f+ m_2f) g, G_r=(m_1r+m_2r)g；m_1fAnd m_1rNonspring carried mass before and after representing respectively；m_2fAnd m_2rSpring carried mass before and after representing respectively； K_tFor tire equivalent stiffness；K_2fAnd K_2rFore suspension and rear suspension rigidity is represented respectively；C_2fAnd C_2rFore suspension and rear suspension damping is represented respectively；G attaches most importance to Power acceleration.

7. the optimization method of automobile chassis integrated system according to claim 6, it is characterised in that step 4.2) described in Optimized model object function f (X) is：

F (X)=W₁f₁(X)+W₂f₂(X)+W₃f₃(X)

In formula：

$f_2\left(X\right)=w_3{\∫}_0^{\mathrm{\∞}}\left|\right|H\left(s\right){|}_{a~{\mathrm{\θ}}_s}{|}_{s=f}^{2}df;$

$\begin{array}{c}{f}_3\left(X\right)=w_4{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{{\stackrel{\·\·}{Z}}_{2f}~\stackrel{\·}{q}}|}_{s=f}^{2}df+w_5{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{{\stackrel{\·\·}{Z}}_{2r}~\stackrel{\·}{q}}|}_{s=f}^{2}df+w_6{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{f_{df}~q}|}_{s=f}^{2}df\\ +w_7{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{f_{dr}~q}|}_{s=f}^{2}df+w_8{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{F_{fi}/G_f~q}|}_{s=f}^{2}df+w_9{\∫}_0^{\mathrm{\∞}}{G}_{\stackrel{\·}{q}}\left(f\right){\left|\right|H\left(s\right){|}_{F_{dr}/G_r~q}|}_{s=f}^{2}df\end{array};$

Frequency in formula, when f is input into for road excitation；For Road Surface Power Spectrum Density；w_iFor weight coefficient；W_iFor sub-goal Function weight coefficient.

8. the optimization method of automobile chassis integrated system according to claim 7, it is characterised in that step 4.3) described in Optimized model object function need meet constraints be：

The denominator of steering sensitivity quantitative formula meets Routh Criterion, braking deceleration and meets a≤g, suspension dynamic deflection and meets f_cr =(0.6～0.8) f_cf, relative damping factor meet ξ_f∈[0.2,0.4]、ξ_r∈[0.2,0.4]；

Wherein, f_cf=(m_1f+m_2f)g/K_2f；f_cr=(m_1r+m_2r)g/K_2r；