CN105160105B

CN105160105B - High ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient

Info

Publication number: CN105160105B
Application number: CN201510559978.6A
Authority: CN
Inventors: 周长城; 于曰伟
Original assignee: Shandong University of Technology
Current assignee: Shandong University of Technology
Priority date: 2015-09-06
Filing date: 2015-09-06
Publication date: 2018-02-13
Anticipated expiration: 2035-09-06
Also published as: CN105160105A

Abstract

The present invention relates to high ferro two it is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient, belongs to high speed railway car suspension technical field.The present invention cooperates with optimization Simulation model by establishing high ferro vehicle 6DOF vertical vibration, using track transition as input stimulus, with the minimum design object of vibration root mean square of weighed acceleration of car body catenary motion, it is vertical and body end portion longitudinal shock absorber optimal damping constant that optimization design, which obtains high ferro two,.By designing example and SIMPACK simulating, verifyings, this method it is available accurately and reliably two be vertical damper and body end portion longitudinal shock absorber damping coefficient, for high ferro two be vertical and the design of body end portion longitudinal shock absorber damped coefficient provides reliable design method.Using this method, the design level of high ferro suspension system can be not only improved, improves vehicle safety and stationarity, can also reduce product design and testing expenses, strengthens the competitiveness in the international market of China's rail vehicle.

Description

High ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient

Technical field

The present invention relates to high speed railway car suspension, particularly high ferro two it is vertical and end longitudinal shock absorber damped coefficient Cooperative optimization method.

Background technology

Two to be that vertical damper and body end portion longitudinal shock absorber have to the riding comfort and security of high ferro important Influence.However, being understood according to institute's inspection information, because high ferro belongs to Mdof Vibration System, dynamic analysis is carried out to it Calculate extremely difficult, be both at home and abroad at present vertical for high ferro two and the design of body end portion longitudinal shock absorber damped coefficient, one The straight theoretical design method for not providing system, it is that vertical damper and body end portion longitudinal shock absorber are single respectively to two to be mostly Solely studied, and by computer technology, using Dynamics Simulation soft sim PACK or ADAMS/Rail, led to respectively Solid modelling is crossed to optimize and determine its size, although this method can obtain reliable simulation numerical, there is vehicle Preferable power performance, however, due to two be vertical damper and body end portion longitudinal shock absorber be one intercouple answer Miscellaneous system, it is this at present individually to model the method being designed to its shock absorber damping, it is difficult to the system of high ferro two is hung down To and the damped coefficient of body end portion longitudinal shock absorber reach best match, and with the continuous improvement of high ferro travel speed, people Be vertical to two and the design of body end portion longitudinal shock absorber damped coefficient proposes higher requirement, the system of high ferro two hangs down at present To and the method for body end portion longitudinal shock absorber damped coefficient design can not provide the innovation theory with directive significance, it is impossible to it is full Development in the case of the constantly speed-raising of sufficient rail vehicle to absorber designing requirement.Therefore, it is necessary to establish a kind of accurate, reliable high Iron two is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient, meets that rail vehicle is right in the case of constantly raising speed The requirement of absorber designing, the design level and product quality of high ferro suspension system are improved, improve vehicle riding comfort and peace Quan Xing；Meanwhile product design and testing expenses are reduced, shorten the product design cycle, strengthen the international market of China's rail vehicle Competitiveness.

The content of the invention

For defect present in above-mentioned prior art, the technical problems to be solved by the invention be to provide it is a kind of accurate, Reliable high ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient, its design flow diagram such as Fig. 1 institutes Show；The front view of high ferro vehicle 6DOF traveling vertical direction vibration model is as shown in Fig. 2 high ferro vehicle 6DOF travels vertical shake The left view of movable model is as shown in Figure 3.

In order to solve the above technical problems, high ferro two provided by the present invention is vertical and end longitudinal shock absorber damped coefficient Cooperative optimization method, it is characterised in that use following design procedure：

(1) the high ferro vehicle 6DOF traveling vertical vibration differential equation is established：

According to the quality m of the single-unit car body of high ferro₂, nod rotary inertia J_2φ；The quality m of every bogie frame₁, nod Rotary inertia J_1φ；Forecarriage one is the vertical equivalent stiffness K of front suspension_1zff, vertical equivalent damping C_d1ff, the system of forecarriage one The vertical equivalent stiffness K of rear suspension_1zfr, vertical equivalent damping C_d1fr；Trailing bogie one is the vertical equivalent stiffness of front suspension K_1zrf, vertical equivalent damping C_d1rf, trailing bogie one is the vertical equivalent stiffness K of rear suspension_1zrr, vertical equivalent damping C_d1rr；Before The vertical equivalent stiffness K of the system of bogie two suspension_2zf；The vertical equivalent stiffness K of the system of trailing bogie two suspension_2zr；Forward to be designed It is the Equivalent damping coefficient C of vertical damper to frame two_d2f, trailing bogie two to be designed be vertical damper equivalent damping system Number C_d2r；The Equivalent damping coefficient C of body end portion longitudinal shock absorber to be designed₃；Car body upper end end longitudinal shock absorber is to car body matter The height h of the heart₁, the height h of car body lower end longitudinal shock absorber to car body barycenter₂, the half a of length between truck centers, wheel-base bogie Half a₀；Distinguish the barycenter O of former, trailing bogie framework and car body₁、O₂、O₃For the origin of coordinates；Bogie frame in the past Drift along displacement z_1f, nod displacement φ_1f, the displacement z that drifts along of trailing bogie framework_1r, nod displacement φ_1rAnd the displacement of drifting along of car body z₂, nod displacement φ₂For coordinate；With the track transition at the forward and backward wheel of forecarriage and the forward and backward wheel of trailing bogie Input z₀₁(t)、z₀₂(t)、z₀₃(t)、z₀₄(t) it is input stimulus, wherein, t is time variable；Establish high ferro vehicle 6DOF row The vertical vibration differential equation is sailed, i.e.,：

(2) high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model is built：

The vertical vibration differential equation is travelled according to the high ferro vehicle 6DOF established in step (1), utilizes Matlab/ Simulink simulation softwares, structure high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model；

(3) it is vertical and the damping of end longitudinal shock absorber collaboration optimization object function J to establish high ferro two：

Optimization Simulation model is cooperateed with according to the high ferro vehicle 6DOF vertical vibration established in step (2), with front steering Frame two is that the Equivalent damping coefficient of vertical damper, trailing bogie two are the Equivalent damping coefficient and body end portion of vertical damper The Equivalent damping coefficient of longitudinal shock absorber is design variable, and the track transition stochastic inputs at place are swashed as input using each wheel Encourage, utilize the vibration frequency root mean square of weighed acceleration of the car body porpoising obtained by emulationAnd car body is nodded motion Vibration frequency root mean square of weighed accelerationEstablish high ferro two be vertical and the damping of end longitudinal shock absorber collaboration it is excellent Change object function J, i.e.,：

In formula, vibration frequency root mean square of weighed accelerationCoefficient 1,0.4, respectively car body drifts along fortune Move, put cephalomotor axle weight coefficient；Wherein, vibration frequency root mean square of weighed acceleration at different frequencies Frequency weight values, be respectively：

(4) high ferro two is vertical damper optimal damping constant C_of、C_orAnd body end portion longitudinal shock absorber optimal damping system Number C_o3Optimization design：

1. according to the half a of length between truck centers, the half a of wheel-base bogie₀, institute in Vehicle Speed v, and step (2) The high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model of foundation, it is random to the track transition at place with each wheel Input z₀₁(t)、z₀₂(t)、z₀₃(t)、z₀₄(t) it is input stimulus, is asked using optimized algorithm in step (3) and establish the system of high ferro two Vertical and end longitudinal shock absorber damping collaboration optimization object function J minimum value, corresponding design variable is forward It is the best equivalence damped coefficient C of vertical damper to frame two_d2f, trailing bogie two be vertical damper best equivalence damping Coefficient C_d2rWith the best equivalence damped coefficient C of body end portion longitudinal shock absorber₃；

Wherein, the relation between track transition stochastic inputs is：

2. it is the installation number n of vertical damper according to every bogie two₁, the installation branch of body end portion longitudinal shock absorber Number n₂, and 1. the forecarriage two in step obtained by optimization design is the best equivalence damped coefficient C of vertical damper_d2f, after Bogie two is the best equivalence damped coefficient C of vertical damper_d2rSystem is damped with the best equivalence of body end portion longitudinal shock absorber Number C₃, it is that vertical damper, trailing bogie two are vertical damper and body end portion longitudinal direction that single branch forecarriage two, which is calculated, The optimal damping constant of shock absorber, it is respectively：C_of=C_d2f/n₁, C_or=C_d2r/n₁, C_o3=C₃/n₂。

The present invention has the advantage that than prior art：

Because high ferro belongs to Mdof Vibration System, dynamic analysis is carried out to it and calculates extremely difficult, the current country It is outside vertical for high ferro two and the design of body end portion longitudinal shock absorber damped coefficient, the theory for never providing system are set Meter method, it is that vertical damper and body end portion longitudinal shock absorber are individually studied to two to be mostly, and by calculating Machine technology, using Dynamics Simulation soft sim PACK or ADAMS/Rail, optimize and determine by solid modelling respectively Its size, although this method can obtain reliable simulation numerical, make vehicle that there is preferable power performance, however, by Be vertical damper in two and body end portion longitudinal shock absorber be a complication system to intercouple, it is this at present individually Model the method that is designed to its shock absorber damping, it is difficult to make high ferro two be vertical and body end portion longitudinal shock absorber Damped coefficient reaches best match, and with the continuous improvement of high ferro travel speed, people are vertical to two and body end portion is indulged Design to shock absorber damping proposes higher requirement, and high ferro two is vertical at present and body end portion longitudinal shock absorber hinders The method of Buddhist nun's factor design can not provide the innovation theory with directive significance, it is impossible in the case of meeting that rail vehicle constantly raises speed Development to absorber designing requirement.

The present invention travels the vertical vibration differential equation by establishing high ferro vehicle 6DOF, utilizes MATLAB/Simulink Simulation software, high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model is constructed, and using track transition to be defeated Enter excitation, with the minimum design object of vibration root mean square of weighed acceleration of car body catenary motion, optimization design obtains high ferro Two be vertical and body end portion longitudinal shock absorber optimal damping constant.By designing example and SIMPACK simulating, verifyings, This method it is available accurately and reliably two be vertical damper and body end portion longitudinal shock absorber damping coefficient, be high ferro two It is vertical and the design of body end portion longitudinal shock absorber damped coefficient provides reliable design method.Using this method, not only The design level and product quality of high ferro suspension system can be improved, improves vehicle safety and stationarity；Meanwhile it can also drop Low product design and testing expenses, shorten the product design cycle, strengthen the competitiveness in the international market of China's rail vehicle.

Brief description of the drawings

It is described further below in conjunction with the accompanying drawings for a better understanding of the present invention.

Fig. 1 is that high ferro two is vertical and the design flow diagram of end longitudinal shock absorber damped coefficient cooperative optimization method；

Fig. 2 is the front view of high ferro vehicle 6DOF traveling vertical direction vibration model；

Fig. 3 is the left view of high ferro vehicle 6DOF traveling vertical direction vibration model；

Fig. 4 is the high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation illustraton of model of embodiment；

Fig. 5 is the German track transition random input stimuli z that embodiment is applied₀₁(t)；

Fig. 6 is the German track transition random input stimuli z that embodiment is applied₀₂(t)；

Fig. 7 is the German track transition random input stimuli z that embodiment is applied₀₃(t)；

Fig. 8 is the German track transition random input stimuli z that embodiment is applied₀₄(t)。

Specific embodiment

The present invention is described in further detail below by an embodiment.

It is vertical damper that two two are provided with every bogie of certain high ferro, and four cars are provided between two adjacent car bodies Body end portion longitudinal shock absorber, i.e. n₁=2, n₂=4；The quality m of its single-unit car body₂=63966kg, nod rotary inertia J_2φ= 2887500kg.m²；The quality m of every bogie frame₁=2758kg, nod rotary inertia J_1φ=2222kg.m²；Front steering Frame one is the vertical equivalent stiffness K of front suspension_1zff=2.74 × 10⁶N/m, vertical equivalent damping C_d1ff=28.3kN.s/m, forward It is the vertical equivalent stiffness K of rear suspension to frame one_1zfr=2.74 × 10⁶N/m, vertical equivalent damping C_d1fr=28.3kN.s/m；Afterwards The vertical equivalent stiffness K of bogie primary front suspension_1zrf=2.74 × 10⁶N/m, vertical equivalent damping C_d1rf=28.3kN.s/m, Trailing bogie one is the vertical equivalent stiffness K of rear suspension_1zrr=2.74 × 10⁶N/m, vertical equivalent damping C_d1rr=28.3kN.s/ m；The vertical equivalent stiffness K of the system of forecarriage two suspension_2zf=1136.8kN/m；The system of trailing bogie two suspends vertical equivalent firm Spend K_2zr=1136.8kN/m；Height h of the car body upper end end longitudinal shock absorber to car body barycenter₁=0.5m, car body lower end Height h of the longitudinal shock absorber to car body barycenter₂=0.5m, the half a=9.5m of length between truck centers, the half a of wheel-base bogie₀= 1.35m；Forecarriage two to be designed is that the Equivalent damping coefficient of vertical damper is C_d2f, trailing bogie two to be designed be vertical The Equivalent damping coefficient of shock absorber is C_d2r；The Equivalent damping coefficient of body end portion longitudinal shock absorber to be designed is C₃.The high ferro two It is vertical and Vehicle Speed v=300km/h that the design of body end portion longitudinal shock absorber damped coefficient is required, to the high ferro Two be vertical and the optimal damping constant of body end portion longitudinal shock absorber is designed.

The high ferro two that present example is provided is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient, Its design flow diagram is as shown in figure 1, high ferro vehicle 6DOF travels the front view of vertical direction vibration model as shown in Fig. 2 high ferro is whole The left view of car 6DOF traveling vertical direction vibration model is as shown in figure 3, comprise the following steps that：

According to the quality m of the single-unit car body of high ferro₂=63966kg, nod rotary inertia J_2φ=2887500kg.m²；Every The quality m of bogie frame₁=2758kg, nod rotary inertia J_1φ=2222kg.m²；Forecarriage one is the vertical of front suspension Equivalent stiffness K_1zff=2.74 × 10⁶N/m, vertical equivalent damping C_d1ff=28.3kN.s/m, forecarriage one are hanging down for rear suspension To equivalent stiffness K_1zfr=2.74 × 10⁶N/m, vertical equivalent damping C_d1fr=28.3kN.s/m；Trailing bogie one is front suspension Vertical equivalent stiffness K_1zrf=2.74 × 10⁶N/m, vertical equivalent damping C_d1rf=28.3kN.s/m, trailing bogie one are rear suspension Vertical equivalent stiffness K_1zrr=2.74 × 10⁶N/m, vertical equivalent damping C_d1rr=28.3kN.s/m；The system of forecarriage two suspends Vertical equivalent stiffness K_2zf=1136.8kN/m；The vertical equivalent stiffness K of the system of trailing bogie two suspension_2zr=1136.8kN/m； Forecarriage two to be designed is the Equivalent damping coefficient C of vertical damper_d2f, trailing bogie two to be designed be vertical damper Equivalent damping coefficient C_d2r；The Equivalent damping coefficient C of body end portion longitudinal shock absorber to be designed₃；Car body upper end end longitudinal damping Height h of the device to car body barycenter₁=0.5m, the height h of car body lower end longitudinal shock absorber to car body barycenter₂=0.5m, vehicle The half a=9.5m of spacing, the half a of wheel-base bogie₀=1.35m；Distinguish the barycenter of former, trailing bogie framework and car body O₁、O₂、O₃For the origin of coordinates；The displacement z that drifts along of bogie frame in the past_1f, nod displacement φ_1f, trailing bogie framework drifts along Displacement z_1r, nod displacement φ_1rAnd the displacement z that drifts along of car body₂, nod displacement φ₂For coordinate；With the forward and backward wheel of forecarriage and Track transition excitation z at the forward and backward wheel of trailing bogie₀₁(t)、z₀₂(t)、z₀₃(t)、z₀₄(t) it is input, wherein, t For time variable；The high ferro vehicle 6DOF traveling vertical vibration differential equation is established, i.e.,：

The vertical vibration differential equation is travelled according to the high ferro vehicle 6DOF established in step (1), utilizes Matlab/ Simulink simulation softwares, structure high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model, as shown in Figure 4；

1. according to the half a=9.5m of length between truck centers, the half a of wheel-base bogie₀=1.35m, Vehicle Speed v= The high ferro vehicle 6DOF vertical vibration collaboration optimization Simulation model established in 300km/h, and step (2), with each wheel to place Track transition stochastic inputs z₀₁(t)、z₀₂(t)、z₀₃(t)、z₀₄(t) it is input stimulus, step is sought using optimized algorithm (3) establish that high ferro two is vertical and the damping of end longitudinal shock absorber cooperates with optimization object function J minimum value in, optimization is set Meter obtains the best equivalence damped coefficient C that forecarriage two is vertical damper_d2f=113.5kN.s/m, the system of trailing bogie two hang down To the best equivalence damped coefficient C of shock absorber_d2r=116.3kN.s/m, the best equivalence damping system of body end portion longitudinal shock absorber C₃=2917.8kN.s/m；Wherein, the relation between track transition stochastic inputs is：z₀₂(t)=z₀₁(t- 0.0324s), z₀₃(t)=z₀₁(t-0.228s), z₀₄(t)=z₀₁(t-0.2604s)；During Vehicle Speed v=300km/h, The German track transition random input stimuli that each wheel applies to place, respectively as shown in Fig. 5, Fig. 6, Fig. 7, Fig. 8；

2. it is the installation number n of vertical damper according to every bogie two₁=2, the peace of body end portion longitudinal shock absorber Fill number n₂=4, and 1. the forecarriage two in step obtained by optimization design is the best equivalence damping system of vertical damper Number C_d2f=113.5kN.s/m, trailing bogie two are the best equivalence damped coefficient C of vertical damper_d2r=116.3kN.s/m, The best equivalence damped coefficient C of body end portion longitudinal shock absorber₃=2917.8kN.s/m, single system of branch forecarriage two is calculated Vertical damper, trailing bogie two are the optimal damping constant of vertical damper and body end portion longitudinal shock absorber, are respectively：C_of =C_d2f/n₁=56.75kN.s/m, C_or=C_d2r/n₁=58.15kN.s/m, C_o3=C₃/n₂=729.45kN.s/m.

The vehicle parameter provided according to embodiment, using rail vehicle special-purpose software SIMPACK, imitated by solid modelling True checking can obtain, and the high ferro forecarriage two is the optimal damping constant C of vertical damper_of=56.33kN.s/m, trailing bogie Two be the optimal damping constant C of vertical damper_or=58.31kN.s/m, the optimal damping constant of body end portion longitudinal shock absorber C_o3=729.17kN.s/m；Understand, using the high ferro forecarriage two obtained by cooperative optimization method be vertical damper most Good damped coefficient C_of=56.75kN.s/m, trailing bogie two are the optimal damping constant C of vertical damper_or=58.15kN.s/ M, the optimal damping constant C of body end portion longitudinal shock absorber_o3Obtained by=729.45kN.s/m, with SIMPACK simulating, verifyings Forecarriage two is the optimal damping constant C of vertical damper_of=56.33kN.s/m, trailing bogie two are vertical damper Optimal damping constant C_or=58.31kN.s/m, the optimal damping constant C of body end portion longitudinal shock absorber_o3=729.17kN.s/m Matching, both deviations are respectively 0.42kN.s/m, 0.16kN.s/m, 0.28kN.s/m, relative deviation is respectively 0.75%, 0.27%th, 0.038%, show that high ferro two provided by the present invention is vertical and the collaboration of end longitudinal shock absorber damped coefficient is excellent Change method is correct.

Claims

1. high ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber damped coefficient, its specific design step are as follows：

According to the quality m of the single-unit car body of high ferro₂, nod rotary inertia J_2φ；The quality m of every bogie frame₁, rotation of nodding Inertia J_1φ；Forecarriage one is the vertical equivalent stiffness K of front suspension_1zff, vertical equivalent damping C_d1ff, forecarriage one is rear overhang The vertical equivalent stiffness K of frame_1zfr, vertical equivalent damping C_d1fr；Trailing bogie one is the vertical equivalent stiffness K of front suspension_1zrf, hang down To equivalent damping C_d1rf, trailing bogie one is the vertical equivalent stiffness K of rear suspension_1zrr, vertical equivalent damping C_d1rr；Forecarriage The vertical equivalent stiffness K of two systems suspension_2zf；The vertical equivalent stiffness K of the system of trailing bogie two suspension_2zr；Forecarriage two to be designed It is the Equivalent damping coefficient C of vertical damper_d2f, trailing bogie two to be designed be vertical damper Equivalent damping coefficient C_d2r； The Equivalent damping coefficient C of body end portion longitudinal shock absorber to be designed₃；Height of the car body upper end end longitudinal shock absorber to car body barycenter Spend h₁, the height h of car body lower end longitudinal shock absorber to car body barycenter₂, the half a of length between truck centers, the half of wheel-base bogie a₀；Distinguish the barycenter O of former, trailing bogie framework and car body₁、O₂、O₃For the origin of coordinates；The position of drifting along of bogie frame in the past Move z_1f, nod displacement φ_1f, the displacement z that drifts along of trailing bogie framework_1r, nod displacement φ_1rAnd the displacement z that drifts along of car body₂, nod Displacement φ₂For coordinate；Z is inputted with the track transition at the forward and backward wheel of forecarriage and the forward and backward wheel of trailing bogie₀₁ (t)、z₀₂(t)、z₀₃(t)、z₀₄(t) it is input stimulus, wherein, t is time variable；It is vertical to establish high ferro vehicle 6DOF traveling Oscillatory differential equation, i.e.,：

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<mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <mrow> <mn>2</mn> <mi>&phi;</mi> </mrow> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <mi>a</mi> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mi>a</mi> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>f</mi> </mrow> </msub> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mn>3</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>C</mi> <mn>3</mn> </msub> <msub> <mi>h</mi> <mn>2</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>r</mi> </mrow> </msub> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <msub> <mover> <mi>z</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <mi>a</mi> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>01</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>02</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>01</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>02</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <mrow> <mn>1</mn> <mi>&phi;</mi> </mrow> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>f</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>01</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>f</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>02</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>01</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>02</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <msub> <mover> <mi>z</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>2</mn> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mi>a</mi> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>z</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a&phi;</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>r</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>03</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>04</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>r</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>03</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>04</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <mrow> <mn>1</mn> <mi>&phi;</mi> </mrow> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>r</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>03</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mn>1</mn> <mi>r</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>z</mi> <mo>&CenterDot;</mo> </mover> <mn>04</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>r</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>03</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>z</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>04</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msub> <mi>&phi;</mi> <mrow> <mn>1</mn> <mi>r</mi> </mrow> </msub> </mrow> <mo>&rsqb;</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

Optimization Simulation model is cooperateed with according to the high ferro vehicle 6DOF vertical vibration established in step (2), with forecarriage two Equivalent damping coefficient, the trailing bogie two for being vertical damper are Equivalent damping coefficient and the body end portion longitudinal direction of vertical damper The Equivalent damping coefficient of shock absorber is design variable, is taken turns using each to the track transition stochastic inputs at place as input stimulus, Utilize the vibration frequency root mean square of weighed acceleration of the car body porpoising obtained by emulationAnd car body point is cephalomotor shakes Dynamic frequency root mean square of weighed accelerationEstablish high ferro two be vertical and the damping of end longitudinal shock absorber collaboration optimization mesh Scalar functions J, i.e.,：

<mrow> <mi>J</mi> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>&sigma;</mi> <msub> <mover> <mi>z</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mn>0.4</mn> <msub> <mi>&sigma;</mi> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mn>2</mn> </msub> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>;</mo> </mrow>

In formula, vibration frequency root mean square of weighed accelerationCoefficient 1,0.4, respectively car body porpoising, point Cephalomotor axle weight coefficient；Wherein, vibration frequency root mean square of weighed acceleration at different frequenciesFrequency Weighted value, it is respectively：

<mrow> <msub> <mi>w</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>0.5</mn> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0.5</mn> <mo>,</mo> <mn>2</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>/</mo> <mn>4</mn> </mrow> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>(</mo> <mn>4</mn> <mo>,</mo> <mn>12.5</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>12.5</mn> <mo>/</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>(</mo> <mn>12.5</mn> <mo>,</mo> <mn>80</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

<mrow> <msub> <mi>w</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0.5</mn> <mo>,</mo> <mn>1</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>80</mn> <mo>&rsqb;</mo> <mi>H</mi> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

(4) high ferro two is vertical damper optimal damping constant C_of、C_orAnd body end portion longitudinal shock absorber optimal damping constant C_o3 Optimization design：

1. according to the half a of length between truck centers, the half a of wheel-base bogie₀, established in Vehicle Speed v, and step (2) High ferro vehicle 6DOF vertical vibration cooperates with optimization Simulation model, the track transition stochastic inputs z with each wheel to place₀₁ (t)、z₀₂(t)、z₀₃(t)、z₀₄(t) be input stimulus, asked using optimized algorithm establish in step (3) high ferro two be it is vertical and The damping collaboration optimization object function J of end longitudinal shock absorber minimum value, corresponding design variable is forecarriage two It is the best equivalence damped coefficient C of vertical damper_d2f, trailing bogie two be vertical damper best equivalence damped coefficient C_d2r With the best equivalence damped coefficient C of body end portion longitudinal shock absorber₃；

Wherein, the relation between track transition stochastic inputs is： <mrow> <msub> <mi>z</mi> <mn>04</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>z</mi> <mn>01</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>a</mi> <mo>+</mo> <mn>2</mn> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> <mi>v</mi> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow>

2. it is the installation number n of vertical damper according to every bogie two₁, the installation number n of body end portion longitudinal shock absorber₂, And 1. the forecarriage two in step obtained by optimization design is the best equivalence damped coefficient C of vertical damper_d2f, rear steering Frame two is the best equivalence damped coefficient C of vertical damper_d2rWith the best equivalence damped coefficient of body end portion longitudinal shock absorber C₃, it is that vertical damper, trailing bogie two are that vertical damper and body end portion longitudinally subtract that single branch forecarriage two, which is calculated, Shake the optimal damping constant of device, is respectively：C_of=C_d2f/n₁, C_or=C_d2r/n₁, C_o3=C₃/n₂。