CN105160105A - Collaborative optimization method of two-line vertical and end part longitudinal damper damping coefficient of high-speed railway - Google Patents

Abstract

The invention relates to a collaborative optimization method of a two-line vertical and end part longitudinal damper damping coefficient of a high-speed railway, and belongs to the technical field of high-speed railway suspension. A complete railway six-degree-of-freedom vertical vibration collaborative optimization simulation model of the high-speed railway is established, the uneven random input of the railway is used as input stimulation, the minimum of the vibration acceleration root-mean-square value of vehicle body vertical movement is taken as a design target, and optimal design is carried out to obtain an optimal damping coefficient of the two-line vertical and vehicle body end part longitudinal damper damping coefficient of the high-speed railway. Through a design example and SIMPACK simulation verification, the method can obtain the accurate and reliable two-line vertical and vehicle body end part longitudinal damper damping coefficient value, and provides a reliable design method for the design of the two-line vertical and vehicle body end part longitudinal damper damping coefficient of the high-speed railway. The method can improve the design level of the suspension system of the high-speed railway, improves vehicle driving safety and stability, can lower product design and experiment cost and enhances the international market competitiveness of the railway vehicle in China.

Description

High ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping

Technical field

The present invention relates to high speed railway car suspension, particularly high ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping.

Background technology

Two is that vertical damper and car body end longitudinal shock absorber have important impact to the riding comfort of high ferro and security.But, known according to institute's inspection information, because high ferro belongs to Mdof Vibration System, carrying out dynamic analysis to it calculates very difficult, domestic and international is at present vertical for high ferro two and the design of car body end longitudinal shock absorber ratio of damping, never provide the theoretical design method of system, mostly be that vertical damper and car body end longitudinal shock absorber are individually studied to two, and computer technology, utilize Dynamics Simulation soft sim PACK or ADAMS/Rail, optimize respectively by solid modelling and determine its size, although the method can obtain reliable simulation numerical, vehicle is made to have good power performance, but, because two be vertical damper and car body end longitudinal shock absorber is a complication system intercoupled, the method that this individually modeling at present designs its shock absorber damping, be difficult to make high ferro two be vertical and the ratio of damping of car body end longitudinal shock absorber reaches optimum matching, and improving constantly along with high ferro travel speed, people are vertical to two and the design of car body end longitudinal shock absorber ratio of damping is had higher requirement, current high ferro two is vertical and the method for car body end longitudinal shock absorber ratio of damping design can not provide the innovation theory with directive significance, the development to absorber designing requirement in rail vehicle constantly speed-raising situation can not be met.Therefore, must set up a kind of accurate, reliable high ferro two is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping, meet the requirement to absorber designing in rail vehicle constantly speed-raising situation, improve design level and the product quality of high ferro suspension system, improve vehicle riding comfort and security; Meanwhile, reduce product design and testing expenses, shorten the product design cycle, strengthen the competitiveness in the international market of China's rail vehicle.

Summary of the invention

For the defect existed in above-mentioned prior art, it is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping that technical matters to be solved by this invention is to provide a kind of accurate, reliable high ferro two, and its design flow diagram as shown in Figure 1; High ferro car load 6DOF travels the front view of vertical direction vibration model as shown in Figure 2, and high ferro car load 6DOF travels the left view of vertical direction vibration model as shown in Figure 3.

For solving the problems of the technologies described above, high ferro two provided by the present invention is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping, it is characterized in that adopting following design procedure:

(1) set up high ferro car load 6DOF and travel the vertical vibration differential equation:

According to the quality m of the single-unit car body of high ferro ₂, nod moment of inertia J _{2 φ}; The quality m of every platform bogie frame ₁, nod moment of inertia J _{1 φ}; Forecarriage one is the vertical equivalent stiffness K of front suspension _1zff, vertical equivalent damping C _d1ff, forecarriage one is the vertical equivalent stiffness K of rear suspension _1zfr, vertical equivalent damping C _d1fr; Trailing bogie one is the vertical equivalent stiffness K of front suspension _1zrf, vertical equivalent damping C _d1rf, trailing bogie one is the vertical equivalent stiffness K of rear suspension _1zrr, vertical equivalent damping C _d1rr; Forecarriage two is the vertical equivalent stiffness K of suspension _2zf; Trailing bogie two is the vertical equivalent stiffness K of suspension _2zr; Forecarriage two to be designed is the Equivalent damping coefficient C of vertical damper _d2f, trailing bogie two to be designed is the Equivalent damping coefficient C of vertical damper _d2r; The Equivalent damping coefficient C of car body end to be designed longitudinal shock absorber ₃; End, car body upper end longitudinal shock absorber is to the height h of car body barycenter ₁, car body lower end longitudinal shock absorber is to the height h of car body barycenter ₂, the half a of length between truck centers, the half a of wheel-base bogie ₀; Respectively in the past, the barycenter O of trailing bogie framework and car body ₁, O ₂, O ₃for true origin; The displacement z that drifts along of bogie frame in the past _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 body ₂, nod displacement φ ₂for coordinate; Z is inputted with the track transition at the forward and backward wheel of forecarriage and the forward and backward wheel place of trailing bogie ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input stimulus, wherein, t is time variable; Set up high ferro car load 6DOF and travel the vertical vibration differential equation, that is:

$\left\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+K_{2zr}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)=0\\ J_{2\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_2-C_{d2f}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}a\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_3{h}_1{\stackrel{\·}{\mathrm{\φ}}}_2+C_3{h}_2{\stackrel{\·}{\mathrm{\φ}}}_2\\ +K_{2zr}a\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)=0\\ m_1{\stackrel{\·\·}{z}}_{1f}-C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_{d1ff}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]\\ +K_{1zff}\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]+K_{1zfr}\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1f}-C_{d1ff}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]-K_{1zff}{a}_0\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]\\ +K_{1zfr}{a}_0\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ m_1{\stackrel{\·\·}{z}}_{1r}-C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zr}\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)+C_{d1rf}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]\\ +K_{1zrf}\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]+K_{1zrr}\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1r}-C_{d1rf}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]-K_{1zrf}{a}_0\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]\\ +K_{1zrr}{a}_0\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\end{array}\right.;$

(2) high ferro car load 6DOF vertical vibration cooperate optimization realistic model is built:

Travel the vertical vibration differential equation according to the high ferro car load 6DOF set up in step (1), utilize Matlab/Simulink simulation software, build high ferro car load 6DOF vertical vibration cooperate optimization realistic model;

(3) setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber:

According to the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with forecarriage two be the Equivalent damping coefficient of vertical damper, trailing bogie two is that the Equivalent damping coefficient of the Equivalent damping coefficient of vertical damper and car body end longitudinal shock absorber is for design variable, take turns to the track transition stochastic inputs located for input stimulus with each, utilize the vibration frequency root mean square of weighed acceleration emulating the car body porpoising obtained and the cephalomotor vibration frequency root mean square of weighed acceleration of car body point setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber, that is:

$J=\sqrt{{\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2}^2+{\left(0.4{\mathrm{\σ}}_{{\stackrel{\·\·}{\mathrm{\φ}}}_2}\right)}^2};$

In formula, vibration frequency root mean square of weighed acceleration coefficient 1,0.4, be respectively car body porpoising, put cephalomotor axle weighting coefficient; Wherein, vibration frequency root mean square of weighed acceleration at different frequencies frequency weight values, be respectively:

$w_k\left(f_i\right)=\left\{\begin{array}{cc}0.5& f_i\∈\[0.5,2\]Hz\\ f_i/4& f_i\∈(2,4\]Hz\\ 1& f_i\∈(4,12.5\]Hz\\ 12.5/f_i& f_i\∈(12.5,80\]Hz\end{array}\right.;$

$w_e\left(f_i\right)=\left\{\begin{array}{cc}1& f_i\∈\[0.5,1\]Hz\\ 1/f_i& f_i\∈(1,80\]Hz\end{array}\right.;$

(4) high ferro two is vertical damper optimal damping constant C _of, C _orand car body end longitudinal shock absorber optimal damping constant C _o3optimal design:

1. according to the half a of length between truck centers, the half a of wheel-base bogie ₀, Vehicle Speed v, and the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with each track transition stochastic inputs z taken turns place ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input stimulus, utilize optimized algorithm to ask in step (3) to set up high ferro two be vertical and the minimum value of the damping cooperate optimization objective function J of end longitudinal shock absorber, corresponding design variable is the best equivalence ratio of damping C that forecarriage two is vertical damper _d2f, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2rwith the best equivalence ratio of damping C of car body end longitudinal shock absorber ₃;

Wherein, the pass between track transition stochastic inputs is: $z_{04}\left(t\right)=z_{01}(t-\frac{2a+2a_0}{v});$

2. be the installation number n of vertical damper according to every platform bogie two ₁, the installation number n of car body end longitudinal shock absorber ₂, and the forecarriage two that 1. optimal design obtains in step is the best equivalence ratio of damping C of vertical damper _d2f, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2rwith the best equivalence ratio of damping C of car body end longitudinal shock absorber ₃, calculate that single forecarriage two is vertical damper, trailing bogie two is vertical damper and the optimal damping constant of car body end longitudinal shock absorber, be respectively: C _of=C _d2f/ n ₁, C _or=C _d2r/ n ₁, C _o3=C ₃/ n ₂.

The advantage that the present invention has than prior art:

Because high ferro belongs to Mdof Vibration System, carrying out dynamic analysis to it calculates very difficult, domestic and international is at present vertical for high ferro two and the design of car body end longitudinal shock absorber ratio of damping, never provide the theoretical design method of system, mostly be that vertical damper and car body end longitudinal shock absorber are individually studied to two, and computer technology, utilize Dynamics Simulation soft sim PACK or ADAMS/Rail, optimize respectively by solid modelling and determine its size, although the method can obtain reliable simulation numerical, vehicle is made to have good power performance, but, because two be vertical damper and car body end longitudinal shock absorber is a complication system intercoupled, the method that this individually modeling at present designs its shock absorber damping, be difficult to make high ferro two be vertical and the ratio of damping of car body end longitudinal shock absorber reaches optimum matching, and improving constantly along with high ferro travel speed, people are vertical to two and the design of car body end longitudinal shock absorber ratio of damping is had higher requirement, current high ferro two is vertical and the method for car body end longitudinal shock absorber ratio of damping design can not provide the innovation theory with directive significance, the development to absorber designing requirement in rail vehicle constantly speed-raising situation can not be met.

The present invention travels the vertical vibration differential equation by setting up high ferro car load 6DOF, utilize MATLAB/Simulink simulation software, construct high ferro car load 6DOF vertical vibration cooperate optimization realistic model, and be input stimulus with track transition, minimum for design object with the vibration root mean square of weighed acceleration of car body catenary motion, it is vertical and optimal damping constant that is car body end longitudinal shock absorber that optimal design obtains high ferro two.By design example and SIMPACK simulating, verifying known, the method can obtain two being the damping coefficient of vertical damper and car body end longitudinal shock absorber accurately and reliably, and for high ferro two be vertical and the design of car body end longitudinal shock absorber ratio of damping provides reliable method for designing.Utilize the method, not only can improve design level and the product quality of high ferro suspension system, improve vehicle safety and stationarity; Meanwhile, also can reduce product design and testing expenses, shorten the product design cycle, strengthen the competitiveness in the international market of China's rail vehicle.

Accompanying drawing explanation

Be described further below in conjunction with accompanying drawing to understand the present invention better.

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

Fig. 2 is the front view that high ferro car load 6DOF travels vertical direction vibration model;

Fig. 3 is the left view that high ferro car load 6DOF travels vertical direction vibration model;

Fig. 4 is the high ferro car load 6DOF vertical vibration cooperate optimization realistic model figure of embodiment;

Fig. 5 is the German track transition random input stimuli z that embodiment applies ₀₁(t);

Fig. 6 is the German track transition random input stimuli z that embodiment applies ₀₂(t);

Fig. 7 is the German track transition random input stimuli z that embodiment applies ₀₃(t);

Fig. 8 is the German track transition random input stimuli z that embodiment applies ₀₄(t).

Specific embodiments

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

It is vertical damper that every platform bogie of certain high ferro is provided with two two, is provided with four car body end longitudinal shock absorbers, i.e. n between two adjacent car bodies ₁=2, n ₂=4; The quality m of its single-unit car body ₂=63966kg, nod moment of inertia J _{2 φ}=2887500kg.m ²; The quality m of every platform bogie frame ₁=2758kg, nod moment of inertia J _{1 φ}=2222kg.m ²; Forecarriage one is the vertical equivalent stiffness K of front suspension _1zff=2.74 × 10 ⁶n/m, vertical equivalent damping C _d1ff=28.3kN.s/m, forecarriage one is the vertical equivalent stiffness K of rear suspension _1zfr=2.74 × 10 ⁶n/m, vertical equivalent damping C _d1fr=28.3kN.s/m; Trailing bogie one is the vertical equivalent stiffness K of front suspension _1zrf=2.74 × 10 ⁶n/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 × 10 ⁶n/m, vertical equivalent damping C _d1rr=28.3kN.s/m; Forecarriage two is the vertical equivalent stiffness K of suspension _2zf=1136.8kN/m; Trailing bogie two is the vertical equivalent stiffness K of suspension _2zr=1136.8kN/m; End, car body upper end longitudinal shock absorber is to the height h of car body barycenter ₁=0.5m, car body lower end longitudinal shock absorber is to the height h of car body barycenter ₂=0.5m, the half a=9.5m of length between truck centers, the half a of wheel-base bogie ₀=1.35m; Forecarriage two to be designed is the Equivalent damping coefficient of vertical damper is C _d2f, trailing bogie two to be designed be the Equivalent damping coefficient of vertical damper is C _d2r; The Equivalent damping coefficient of car body end to be designed longitudinal shock absorber is C ₃.This high ferro two be vertical and car body end longitudinal shock absorber ratio of damping design required by Vehicle Speed v=300km/h, to this high ferro two be vertical and the optimal damping constant of car body end longitudinal shock absorber designs.

The high ferro two that example of the present invention provides is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping, its design flow diagram as shown in Figure 1, high ferro car load 6DOF travels the front view of vertical direction vibration model as shown in Figure 2, high ferro car load 6DOF travels the left view of vertical direction vibration model as shown in Figure 3, and concrete steps are as follows:

(1) set up high ferro car load 6DOF and travel the vertical vibration differential equation:

According to the quality m of the single-unit car body of high ferro ₂=63966kg, nod moment of inertia J _{2 φ}=2887500kg.m ²; The quality m of every platform bogie frame ₁=2758kg, nod moment of inertia J _{1 φ}=2222kg.m ²; Forecarriage one is the vertical equivalent stiffness K of front suspension _1zff=2.74 × 10 ⁶n/m, vertical equivalent damping C _d1ff=28.3kN.s/m, forecarriage one is the vertical equivalent stiffness K of rear suspension _1zfr=2.74 × 10 ⁶n/m, vertical equivalent damping C _d1fr=28.3kN.s/m; Trailing bogie one is the vertical equivalent stiffness K of front suspension _1zrf=2.74 × 10 ⁶n/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 × 10 ⁶n/m, vertical equivalent damping C _d1rr=28.3kN.s/m; Forecarriage two is the vertical equivalent stiffness K of suspension _2zf=1136.8kN/m; Trailing bogie two is the vertical equivalent stiffness K of 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 is the Equivalent damping coefficient C of vertical damper _d2r; The Equivalent damping coefficient C of car body end to be designed longitudinal shock absorber ₃; End, car body upper end longitudinal shock absorber is to the height h of car body barycenter ₁=0.5m, car body lower end longitudinal shock absorber is to the height h of car body barycenter ₂=0.5m, the half a=9.5m of length between truck centers, the half a of wheel-base bogie ₀=1.35m; Respectively in the past, the barycenter O of trailing bogie framework and car body ₁, O ₂, O ₃for true origin; The displacement z that drifts along of bogie frame in the past _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 body ₂, nod displacement φ ₂for coordinate; Z is encouraged with the track transition at the forward and backward wheel of forecarriage and the forward and backward wheel place of trailing bogie ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input, wherein, t is time variable; Set up high ferro car load 6DOF and travel the vertical vibration differential equation, that is:

$\left\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+K_{2zr}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)=0\\ J_{2\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_2-C_{d2f}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}a\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_3{h}_1{\stackrel{\·}{\mathrm{\φ}}}_2+C_3{h}_2{\stackrel{\·}{\mathrm{\φ}}}_2\\ +K_{2zr}a\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)=0\\ m_1{\stackrel{\·\·}{z}}_{1f}-C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_{d1ff}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]\\ +K_{1zff}\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]+K_{1zfr}\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1f}-C_{d1ff}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]-K_{1zff}{a}_0\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]\\ +K_{1zfr}{a}_0\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ m_1{\stackrel{\·\·}{z}}_{1r}-C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zr}\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)+C_{d1rf}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]\\ +K_{1zrf}\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]+K_{1zrr}\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1r}-C_{d1rf}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]-K_{1zrf}{a}_0\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]\\ +K_{1zrr}{a}_0\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\end{array}\right.;$

(2) high ferro car load 6DOF vertical vibration cooperate optimization realistic model is built:

Travel the vertical vibration differential equation according to the high ferro car load 6DOF set up in step (1), utilize Matlab/Simulink simulation software, build high ferro car load 6DOF vertical vibration cooperate optimization realistic model, as shown in Figure 4;

(3) setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber:

According to the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with forecarriage two be the Equivalent damping coefficient of vertical damper, trailing bogie two is that the Equivalent damping coefficient of the Equivalent damping coefficient of vertical damper and car body end longitudinal shock absorber is for design variable, take turns to the track transition stochastic inputs located for input stimulus with each, utilize the vibration frequency root mean square of weighed acceleration emulating the car body porpoising obtained and the cephalomotor vibration frequency root mean square of weighed acceleration of car body point setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber, that is:

$J=\sqrt{{\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2}^2+{\left(0.4{\mathrm{\σ}}_{{\stackrel{\·\·}{\mathrm{\φ}}}_2}\right)}^2};$

In formula, vibration frequency root mean square of weighed acceleration coefficient 1,0.4, be respectively car body porpoising, put cephalomotor axle weighting coefficient; Wherein, vibration frequency root mean square of weighed acceleration at different frequencies frequency weight values, be respectively:

$w_k\left(f_i\right)=\left\{\begin{array}{cc}0.5& f_i\∈\[0.5,2\]Hz\\ f_i/4& f_i\∈(2,4\]Hz\\ 1& f_i\∈(4,12.5\]Hz\\ 12.5/f_i& f_i\∈(12.5,80\]Hz\end{array}\right.;$

$w_e\left(f_i\right)=\left\{\begin{array}{cc}1& f_i\∈\[0.5,1\]Hz\\ 1/f_i& f_i\∈(1,80\]Hz\end{array}\right.;$

(4) high ferro two is vertical damper optimal damping constant C _of, C _orand car body end longitudinal shock absorber optimal damping constant C _o3optimal design:

1. according to the half a=9.5m of length between truck centers, the half a of wheel-base bogie ₀=1.35m, Vehicle Speed v=300km/h, and the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with each track transition stochastic inputs z taken turns place ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input stimulus, utilize optimized algorithm to ask in step (3) to set up high ferro two be vertical and the minimum value of the damping cooperate optimization objective function J of end longitudinal shock absorber, optimal design obtains the best equivalence ratio of damping C that forecarriage two is vertical damper _d2f=113.5kN.s/m, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2r=116.3kN.s/m, the best equivalence damping system C of car body end longitudinal shock absorber ₃=2917.8kN.s/m; Wherein, the pass between track transition stochastic inputs is: z ₀₂(t)=z ₀₁(t-0.0324s), z ₀₃(t)=z ₀₁(t-0.228s), z ₀₄(t)=z ₀₁(t-0.2604s); During Vehicle Speed v=300km/h, the German track transition random input stimuli that each wheel applies place, respectively as shown in Fig. 5, Fig. 6, Fig. 7, Fig. 8;

2. be the installation number n of vertical damper according to every platform bogie two ₁=2, the installation number n of car body end longitudinal shock absorber ₂=4, and the forecarriage two that 1. optimal design obtains in step is the best equivalence ratio of damping C of vertical damper _d2f=113.5kN.s/m, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2r=116.3kN.s/m, the best equivalence ratio of damping C of car body end longitudinal shock absorber ₃=2917.8kN.s/m, calculates that single forecarriage two is vertical damper, trailing bogie two is vertical damper and the optimal damping constant of car body end longitudinal shock absorber, is respectively: C _of=C _d2f/ n ₁=56.75kN.s/m, C _or=C _d2r/ n ₁=58.15kN.s/m, C _o3=C ₃/ n ₂=729.45kN.s/m.

According to the vehicle parameter that embodiment provides, utilize rail vehicle special software SIMPACK, can be obtained by solid modelling simulating, verifying, this high ferro forecarriage two is the optimal damping constant C of vertical damper _of=56.33kN.s/m, trailing bogie two is the optimal damping constant C of vertical damper _or=58.31kN.s/m, the optimal damping constant C of car body end longitudinal shock absorber _o3=729.17kN.s/m; Known, the high ferro forecarriage two utilizing cooperative optimization method to obtain is the optimal damping constant C of vertical damper _of=56.75kN.s/m, trailing bogie two is the optimal damping constant C of vertical damper _or=58.15kN.s/m, the optimal damping constant C of car body end longitudinal shock absorber _o3=729.45kN.s/m, the forecarriage two obtained with SIMPACK simulating, verifying is the optimal damping constant C of vertical damper _of=56.33kN.s/m, trailing bogie two is the optimal damping constant C of vertical damper _or=58.31kN.s/m, the optimal damping constant C of car body end longitudinal shock absorber _o3=729.17kN.s/m matches, both are respectively 0.42kN.s/m, 0.16kN.s/m, 0.28kN.s/m at deviation, relative deviation is respectively 0.75%, 0.27%, 0.038%, shows that high ferro two provided by the present invention is vertical and the cooperative optimization method of end longitudinal shock absorber ratio of damping is correct.

Claims (1)

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

(1) set up high ferro car load 6DOF and travel the vertical vibration differential equation:

According to the quality m of the single-unit car body of high ferro ₂, nod moment of inertia J _{2 φ}; The quality m of every platform bogie frame ₁, nod moment of inertia J _{1 φ}; Forecarriage one is the vertical equivalent stiffness K of front suspension _1zff, vertical equivalent damping C _d1ff, forecarriage one is the vertical equivalent stiffness K of rear suspension _1zfr, vertical equivalent damping C _d1fr; Trailing bogie one is the vertical equivalent stiffness K of front suspension _1zrf, vertical equivalent damping C _d1rf, trailing bogie one is the vertical equivalent stiffness K of rear suspension _1zrr, vertical equivalent damping C _d1rr; Forecarriage two is the vertical equivalent stiffness K of suspension _2zf; Trailing bogie two is the vertical equivalent stiffness K of suspension _2zr; Forecarriage two to be designed is the Equivalent damping coefficient C of vertical damper _d2f, trailing bogie two to be designed is the Equivalent damping coefficient C of vertical damper _d2r; The Equivalent damping coefficient C of car body end to be designed longitudinal shock absorber ₃; End, car body upper end longitudinal shock absorber is to the height h of car body barycenter ₁, car body lower end longitudinal shock absorber is to the height h of car body barycenter ₂, the half a of length between truck centers, the half a of wheel-base bogie ₀; Respectively in the past, the barycenter O of trailing bogie framework and car body ₁, O ₂, O ₃for true origin; The displacement z that drifts along of bogie frame in the past _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 body ₂, nod displacement φ ₂for coordinate; Z is inputted with the track transition at the forward and backward wheel of forecarriage and the forward and backward wheel place of trailing bogie ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input stimulus, wherein, t is time variable; Set up high ferro car load 6DOF and travel the vertical vibration differential equation, that is:

$\left\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+K_{2zr}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)=0\\ J_{2\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_2-C_{d2f}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)+C_{d2r}a\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}a\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_3{h}_1{\stackrel{\·}{\mathrm{\φ}}}_2+C_3{h}_2{\stackrel{\·}{\mathrm{\φ}}}_2\\ +K_{2zr}a\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)=0\\ m_1{\stackrel{\·\·}{z}}_{1f}-C_{d2f}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1f}-a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zf}\left(z_2-z_{1f}-{\mathrm{a\φ}}_2\right)+C_{d1ff}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]\\ +K_{1zff}\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]+K_{1zfr}\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1f}-C_{d1ff}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{01}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]+C_{d1fr}{a}_0\[{\stackrel{\·}{z}}_{1f}-{\stackrel{\·}{z}}_{02}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1f}\]-K_{1zff}{a}_0\[z_{1f}-z_{01}\left(t\right)-a_0{\mathrm{\φ}}_{1f}\]\\ +K_{1zfr}{a}_0\[z_{1f}-z_{02}\left(t\right)+a_0{\mathrm{\φ}}_{1f}\]=0\\ m_1{\stackrel{\·\·}{z}}_{1r}-C_{d2r}\left({\stackrel{\·}{z}}_2-{\stackrel{\·}{z}}_{1r}+a{\stackrel{\·}{\mathrm{\φ}}}_2\right)-K_{2zr}\left(z_2-z_{1r}+{\mathrm{a\φ}}_2\right)+C_{d1rf}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]\\ +K_{1zrf}\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]+K_{1zrr}\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\\ J_{1\mathrm{\φ}}{\stackrel{\·\·}{\mathrm{\φ}}}_{1r}-C_{d1rf}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{03}\left(t\right)-a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]+C_{d1rr}{a}_0\[{\stackrel{\·}{z}}_{1r}-{\stackrel{\·}{z}}_{04}\left(t\right)+a_0{\stackrel{\·}{\mathrm{\φ}}}_{1r}\]-K_{1zrf}{a}_0\[z_{1r}-z_{03}\left(t\right)-a_0{\mathrm{\φ}}_{1r}\]\\ +K_{1zrr}{a}_0\[z_{1r}-z_{04}\left(t\right)+a_0{\mathrm{\φ}}_{1r}\]=0\end{array}\right.;$

(2) high ferro car load 6DOF vertical vibration cooperate optimization realistic model is built:

Travel the vertical vibration differential equation according to the high ferro car load 6DOF set up in step (1), utilize Matlab/Simulink simulation software, build high ferro car load 6DOF vertical vibration cooperate optimization realistic model;

(3) setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber:

According to the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with forecarriage two be the Equivalent damping coefficient of vertical damper, trailing bogie two is that the Equivalent damping coefficient of the Equivalent damping coefficient of vertical damper and car body end longitudinal shock absorber is for design variable, take turns to the track transition stochastic inputs located for input stimulus with each, utilize the vibration frequency root mean square of weighed acceleration emulating the car body porpoising obtained and the cephalomotor vibration frequency root mean square of weighed acceleration of car body point setting up high ferro two is vertical and the damping cooperate optimization objective function J of end longitudinal shock absorber, that is:

$J=\sqrt{{\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2}^2+{\left(0.4{\mathrm{\σ}}_{{\stackrel{\·\·}{\mathrm{\φ}}}_2}\right)}^2};$

In formula, vibration frequency root mean square of weighed acceleration coefficient 1,0.4, be respectively car body porpoising, put cephalomotor axle weighting coefficient; Wherein, vibration frequency root mean square of weighed acceleration at different frequencies frequency weight values, be respectively:

$w_k\left(f_i\right)=\left\{\begin{array}{cc}0.5& f_i\∈\[0.5,2\]Hz\\ f_i/4& f_i\∈(2,4\]Hz\\ 1& f_i\∈(4,12.5\]Hz\\ 12.5/f_i& f_i\∈(12.5,80\]Hz\end{array}\right.;$

$w_e\left(f_i\right)=\left\{\begin{array}{cc}1& f_i\∈\[0.5,1\]Hz\\ 1/f_i& f_i\∈(1,80\]Hz\end{array}\right.;$

(4) high ferro two is vertical damper optimal damping constant C _of, C _orand car body end longitudinal shock absorber optimal damping constant C _o3optimal design:

1. according to the half a of length between truck centers, the half a of wheel-base bogie ₀, Vehicle Speed v, and the high ferro car load 6DOF vertical vibration cooperate optimization realistic model set up in step (2), with each track transition stochastic inputs z taken turns place ₀₁(t), z ₀₂(t), z ₀₃(t), z ₀₄t () is input stimulus, utilize optimized algorithm to ask in step (3) to set up high ferro two be vertical and the minimum value of the damping cooperate optimization objective function J of end longitudinal shock absorber, corresponding design variable is the best equivalence ratio of damping C that forecarriage two is vertical damper _d2f, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2rwith the best equivalence ratio of damping C of car body end longitudinal shock absorber ₃;

Wherein, the pass between track transition stochastic inputs is: $z_{04}\left(t\right)=z_{01}(t-\frac{2a+2a_0}{v});$

2. be the installation number n of vertical damper according to every platform bogie two ₁, the installation number n of car body end longitudinal shock absorber ₂, and the forecarriage two that 1. optimal design obtains in step is the best equivalence ratio of damping C of vertical damper _d2f, trailing bogie two is the best equivalence ratio of damping C of vertical damper _d2rwith the best equivalence ratio of damping C of car body end longitudinal shock absorber ₃, calculate that single forecarriage two is vertical damper, trailing bogie two is vertical damper and the optimal damping constant of car body end longitudinal shock absorber, be respectively: C _of=C _d2f/ n ₁, C _or=C _d2r/ n ₁, C _o3=C ₃/ n ₂.