CN105069261B - Low speed rail vehicle two is the design method of lateral damper optimum damping coefficient - Google Patents

Abstract

The invention relates to a design method for an optimal damping coefficient of a secondary transverse shock absorber of a low-speed rail vehicle, and belongs to the technical field of low-speed rail vehicle suspension. The present invention builds the 17-degree-of-freedom lateral vibration optimization design simulation model of the low-speed rail vehicle vehicle through the establishment of the 17-degree-of-freedom lateral vibration differential equation of the low-speed rail vehicle vehicle, and uses the MATLAB/Simulink simulation software. Irregularity is used as the input excitation, and the minimum root mean square value of the vibration-weighted acceleration of the lateral movement of the car body is the design goal, and the optimal damping coefficient of the secondary lateral shock absorber of the low-speed rail vehicle is obtained through optimization design. Through design examples and SIMPACK simulation verification, it can be known that this method can obtain accurate and reliable optimal damping coefficient values of secondary lateral shock absorbers, and provides a reliable design method for the design of optimal damping coefficients of secondary lateral shock absorbers for low-speed rail vehicles . By using the method, the design level of the suspension system of the low-speed rail vehicle and the safety and stability of the vehicle can be significantly improved.

Description

Design method for optimal damping coefficient of secondary transverse shock absorbers of low-speed rail vehicles

technical field

The invention relates to a low-speed rail vehicle mount, in particular to a design method for an optimal damping coefficient of a secondary transverse shock absorber of a low-speed rail vehicle.

Background technique

Secondary transverse shock absorbers have an important impact on the ride comfort and safety of low-speed rail vehicles. However, according to the available information, it is very difficult to analyze and calculate the dynamics of low-speed rail vehicles because they belong to multi-degree-of-freedom vibration systems. Most of the theoretical design methods rely on computer technology, using multi-body dynamics simulation software SIMPACK or ADAMS/Rail, to optimize and determine its size through solid modeling, although this method can obtain relatively reliable simulation values, so that the vehicle has better performance However, with the continuous development of the rail vehicle industry, people put forward higher requirements for the design of the damping coefficient of the secondary transverse shock absorber. The current method of designing the damping coefficient of the secondary transverse shock absorber cannot give a The innovative theory of guiding significance cannot meet the development of shock absorber design requirements under the rapid development of rail vehicles. Therefore, it is necessary to establish an accurate and reliable design method for the optimal damping coefficient of the secondary transverse shock absorber of low-speed rail vehicles, to meet the requirements of shock absorber design under the rapid development of rail vehicles, and to improve the performance of the suspension system of low-speed rail vehicles. Improve the design level and product quality, improve the comfort and safety of vehicles; at the same time, reduce product design and test costs, shorten product design cycles, and enhance the international market competitiveness of my country's rail vehicles.

Contents of the invention

In view of the above-mentioned defects in the prior art, the technical problem to be solved by the present invention is to provide an accurate and reliable design method for the optimal damping coefficient of the secondary lateral shock absorber of low-speed rail vehicles, and its design flow chart is shown in Figure 1 Figure 2 shows the left view of the 17-degree-of-freedom running lateral vibration model of the low-speed rail vehicle, and the top view of the 17-degree-of-freedom running lateral vibration model of the low-speed rail vehicle is shown in Figure 3.

In order to solve the problems of the technologies described above, the design method of the optimal damping coefficient of the secondary transverse shock absorber of the low-speed rail vehicle provided by the present invention is characterized in that the following design steps are adopted:

(1) Establish the differential equation of the lateral vibration of the low-speed rail vehicle with 17 degrees of freedom:

According to the mass m ₃ of the single car body of the rail vehicle and the moment of inertia of the shaking head Rolling moment of inertia J _3θ ; mass m ₂ of each bogie frame, moment of inertia of shaking head Rolling moment of inertia J _2θ ; mass m ₁ of each wheel pair, moment of inertia of shaking head Axle weight W of each wheel; transverse creep coefficient f ₁ and longitudinal creep coefficient f ₂ of each wheel pair; longitudinal stiffness K _1x , transverse stiffness K _1y , and vertical stiffness K _1z of each axle box positioning device; each steering The longitudinal stiffness K _2x and lateral positioning stiffness K _2y of the central spring of the frame; the vertical equivalent stiffness K _2z and vertical equivalent damping C _d2 of the secondary suspension of each bogie; the torsional stiffness K of a single anti-roll torsion bar _θ ; equivalent damping coefficient C ₂ of secondary lateral shock absorber to be designed for each bogie; wheel rolling radius r, wheel tread slope λ; vehicle running speed v; half b ₁ of the lateral installation distance of the positioning spring, half b ₂ of the lateral installation distance of the central spring of the bogie, half a of the fixed distance of the vehicle, half a ₀ of the wheelbase of the bogie, the height h ₀ from the center line of the axle to the plane of the track, The height h ₁ from the center of mass of the body to the upper plane of the central spring, the height h 2 from the center of mass of the car body to the secondary transverse shock absorber, the height h ₃ from the upper plane of the central spring to the center of mass of the frame, and the height h from the center of mass _of the bogie frame to the center line of the axle ₄ , the height h ₅ from the secondary transverse shock absorber to the center of mass of the frame; the center of mass O _1ff , O _1fr of the front bogie wheel set, the center of mass O _1rf , O _1rr of the rear bogie wheel set, and the center of mass of the front and rear bogie frames The center of mass O _2f , O _2r and the center of mass O ₃ of the vehicle body are the origin of coordinates; the yaw displacement y _1ff and the shaking head displacement of the former bogie front wheel set The yaw displacement y _1fr of the front bogie and the rear wheel set, the shaking head displacement The yaw displacement y _1rf of the front wheel set of the rear bogie and the head displacement The yaw displacement y _1rr of the rear wheel set of the rear bogie and the head displacement The yaw displacement y _2f of the front bogie frame and the shaking head displacement The roll displacement θ _2f , the yaw displacement y _2r of the rear bogie frame, and the shaking head displacement The roll displacement θ _2r , and the yaw displacement y ₃ of the car body and the shaking head displacement Rolling displacement θ ₃ is the coordinate; input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 of the track direction irregularity at the front and rear wheels of the front bogie and the front and rear wheels of the rear bogie (t) and horizontal irregularity input z _θ1 (t), z _θ2 (t), z _θ3 (t), z _θ4 (t) are the input excitations, where t is the time variable; establish a low-speed rail vehicle 17 free The differential equation of lateral vibration during driving at 100°C is:

①The yaw vibration equation of the front wheel set of the front bogie:

②The head shaking vibration equation of the front wheel set of the front bogie:

③The yaw vibration equation of the front bogie and the rear wheel set:

④ Head shaking vibration equation of front bogie and rear wheel set:

⑤ The yaw vibration equation of the front wheel set of the rear bogie:

⑥Shaking vibration equation of the front wheel set of the rear bogie:

⑦The yaw vibration equation of the rear wheel set of the rear bogie:

⑧ Shaking vibration equation of the rear wheel set of the rear bogie:

⑨The yaw vibration equation of the front bogie frame:

⑩Rolling vibration equation of the front bogie frame:

The shake head vibration equation of the front bogie frame:

The yaw vibration equation of the rear bogie frame:

The roll vibration equation of the rear bogie frame:

The shaking head vibration equation of the rear bogie frame:

The yaw vibration equation of the car body:

The rolling vibration equation of the car body:

Wherein, h=h ₀ +h ₁ +h ₃ +h ₄ ;

Shaking head vibration equation of the car body:

(2) Construct a 17-degree-of-freedom lateral vibration optimization design simulation model for a low-speed rail vehicle:

According to the low-speed rail vehicle vehicle 17 degrees of freedom driving lateral vibration differential equation established in the step (1), utilize Matlab/Simulink simulation software to construct the low-speed rail vehicle vehicle 17 degrees of freedom lateral vibration optimization design simulation model;

(3) Establish the damping optimization design objective function J of the secondary transverse shock absorber:

According to the low-speed rail vehicle 17-degree-of-freedom lateral vibration optimization design simulation model established in step (2), the equivalent damping coefficient of the secondary lateral shock absorber of each bogie is used as the design variable, and the The random input of the track direction irregularity and the horizontal irregularity random input are the input excitations, and the root mean square value of the vibration frequency weighted acceleration of the vehicle body yaw motion obtained by simulation The root mean square value of vibration frequency weighted acceleration of vehicle body roll motion and the root mean square value of the vibration frequency weighted acceleration of the shaking head of the car body The damping optimization design objective function J of the secondary transverse shock absorber is established, namely:

In the formula, the root mean square value of vibration frequency weighted acceleration The coefficients 1, 0.63, and 0.2 are the axis weighting coefficients of the yaw motion, roll motion, and shaking head motion of the car body respectively; among them, the root mean square value of the vibration frequency weighted acceleration at different frequencies The frequency weighted values of are respectively w _d (f _i ), w _e (f _i ), w _f (f _i ), that is:

(4) Optimal design of the optimal damping coefficient C of the secondary transverse shock absorber of low-speed rail vehicles:

①According to half a of the vehicle fixed distance, half a ₀ of the bogie wheelbase, vehicle speed v, and the 17-degree-of-freedom lateral vibration optimization design simulation model of the low-speed rail vehicle established in step (2), the Randomly input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 (t) for track direction irregularity and horizontal irregularity randomly input z _θ1 (t), z _θ2 (t), z _θ3 (t) and z _θ4 (t) are the input excitations, use the optimization algorithm to find the minimum value of the objective function J of the damping optimization design of the secondary transverse shock absorber established in step (3), and the corresponding design variables are The optimal equivalent damping coefficient C ₂ of the secondary transverse shock absorber of each bogie;

Among them, the relationship between the track direction irregularity random input is: The relationship between horizontally uneven random inputs is:

②According to the installed number n of the secondary transverse shock absorbers of each bogie, and the optimal equivalent damping coefficient C ₂ of the secondary transverse shock absorbers of each bogie obtained from the optimization design in step ① of step (4), The optimal damping coefficient C of the single secondary series transverse shock absorber is calculated, namely: C=C ₂ /n.

The present invention has the advantage over prior art:

Since the low-speed rail vehicle belongs to a multi-degree-of-freedom vibration system, it is very difficult to analyze and calculate its dynamics. At present, there is no systematic theoretical design method for the design of the damping coefficient of the secondary transverse shock absorber at home and abroad, and most of them rely on computers. Technology, using multi-body dynamics simulation software SIMPACK or ADAMS/Rail, through solid modeling to optimize and determine its size, although this method can get more reliable simulation values, so that the vehicle has better dynamic performance, however, with With the continuous development of the rail vehicle industry, people have put forward higher requirements for the design of the damping coefficient of the secondary transverse shock absorber. The current design method of the damping coefficient of the secondary transverse shock absorber cannot provide an innovative theory with guiding significance and cannot meet Development of shock absorber design requirements in the context of rapid development of rail vehicles.

The present invention builds the 17-degree-of-freedom lateral vibration optimization design simulation model of the low-speed rail vehicle vehicle by establishing the 17-degree-of-freedom lateral vibration differential equation of the low-speed rail vehicle vehicle, and uses the MATLAB/Simulink simulation software, and uses the track direction irregularity and level Irregularity is used as the input excitation, and the minimum root mean square value of the vibration-weighted acceleration of the lateral motion of the car body is the design goal, and the optimal damping coefficient of the secondary lateral shock absorber of the low-speed rail vehicle is obtained through optimization design. Through the design example and SIMPACK simulation verification, it can be seen that the method can obtain accurate and reliable damping coefficient value of the secondary transverse shock absorber, which provides a reliable design method for the design of the damping coefficient of the secondary transverse shock absorber of low-speed rail vehicles. This method can not only improve the design level and product quality of the suspension system of low-speed rail vehicles, but also improve the safety and stability of the vehicle; at the same time, it can also reduce product design and test costs, shorten the product design cycle, and enhance the quality of my country's rail vehicles. international market competitiveness.

Description of drawings

In order to better understand the present invention, further description will be made below in conjunction with the accompanying drawings.

Fig. 1 is the design flowchart of the optimal damping coefficient design method for the secondary transverse shock absorber of low-speed rail vehicles;

Fig. 2 is the left side view of the 17-degree-of-freedom running lateral vibration model of a low-speed rail vehicle;

Fig. 3 is a top view of a 17-degree-of-freedom vehicle running lateral vibration model of a low-speed rail vehicle;

Fig. 4 is the low-speed rail vehicle whole vehicle 17 degrees of freedom lateral vibration optimization design simulation model of embodiment;

Fig. 5 is the irregular random input excitation y _a1 (t) of the U.S. track direction imposed by the embodiment;

Fig. 6 is the U.S. track direction irregular random input excitation y _a2 (t) applied by the embodiment;

Fig. 7 is the U.S. track direction irregularity random input excitation y _a3 (t) applied by the embodiment;

Fig. 8 is the irregular random input excitation y _a4 (t) of the U.S. track direction imposed by the embodiment;

Fig. 9 is the random input excitation z _θ1 (t) of the U.S. track level irregularity applied by the embodiment;

Fig. 10 is the U.S. track horizontal irregularity random input excitation z _θ2 (t) applied by the embodiment;

Fig. 11 is the U.S. track level irregularity random input excitation z _θ3 (t) applied by the embodiment;

Figure 12 is the US track level irregularity random input excitation z _θ4 (t) applied by the embodiment.

specific implementation plan

The present invention will be further described in detail through an embodiment below.

Two secondary series transverse shock absorbers are installed on each bogie of a low-speed rail vehicle, that is, n=2; the mass of a single car body m ₃ =56910kg, the moment of inertia Rolling moment of inertia J _3θ = 159300kg.m ² ; mass of each bogie frame m ₂ = 2310kg, shaking head moment of inertia Rolling moment of inertia J _2θ = 2080kg.m ² ; mass of each wheel set m ₁ = 2080kg, oscillating moment of inertia The axle load of each wheel is W=160000N; the lateral creep coefficient _{f 1} of each wheel pair is 17250000N, the longitudinal creep coefficient f2 is 17250000N; the longitudinal stiffness K _1x of each axle box positioning device is 17×10 ⁶ N/m, Lateral stiffness K _1y = 1.48×10 ⁶ N/m, vertical stiffness K _1z = 1.48×10 ⁶ N/m; longitudinal stiffness K _2x = 0.165×10 ⁶ N/m of central spring of each bogie, K _2y ＝0.165×10 ⁶ N/m; the vertical equivalent stiffness K _2z ＝561.68kN/m, the vertical equivalent damping C _d2 ＝111.39kN.s/m of the secondary suspension of each bogie; The torsional rigidity of the roll torsion bar K _θ = 2.5×10 ⁶ Nm/rad; the wheel rolling radius r = 0.43m, the wheel tread slope λ = 0.15; the half of the lateral distance between the wheel and the rail contact point b = 0.7175m, the wheel axle positioning Half of the transverse installation distance of springs b ₁ =1.05m, half of the transverse installation distance of bogie central springs b ₂ =1.2m, half of vehicle fixed distance a=7.85m, half of bogie wheelbase a ₀ =1.25m, axle The height h ₀ from the center line to the track plane = 0.43m, the height h ₁ = 0.779m from the center of mass of the car body to the upper plane of the central spring, h ₂ = 0.616m from the center of mass of the car body to the secondary transverse shock absorber, and The height h ₃ = 0.216m from the plane to the center of mass of the frame, h _{4 = 0.075m from the center of mass of the bogie frame to the centerline of the axle, h 5 =} 0.379m from the secondary transverse shock absorber to the center of mass of the frame; The equivalent damping coefficient of the designed secondary transverse shock absorber is C ₂ . The vehicle speed v=100km/h required by the design of the damping coefficient of the second-series transverse shock absorber of the low-speed rail vehicle is designed for the optimal damping coefficient of the second-series transverse shock absorber of the low-speed rail vehicle.

The design method of the optimal damping coefficient of the second series lateral shock absorber of the low-speed rail vehicle provided by the example of the present invention, its design flow chart as shown in Figure 1, the left view of the 17-degree-of-freedom driving lateral vibration model of the low-speed rail vehicle vehicle 2. The top view of the 17-degree-of-freedom running lateral vibration model of a low-speed rail vehicle is shown in Figure 3, and the specific steps are as follows:

(1) Establish the differential equation of the lateral vibration of the low-speed rail vehicle with 17 degrees of freedom:

According to the mass m ₃ of a single car body of a rail vehicle = 56910kg, the moment of inertia of shaking the head Rolling moment of inertia J _3θ = 159300kg.m ² ; mass of each bogie frame m ₂ = 2310kg, shaking head moment of inertia Rolling moment of inertia J _2θ = 2080kg.m ² ; mass of each wheel set m ₁ = 2080kg, oscillating moment of inertia The axle load of each wheel is W=160000N; the lateral creep coefficient _{f 1} of each wheel pair is 17250000N, the longitudinal creep coefficient f2 is 17250000N; the longitudinal stiffness K _1x of each axle box positioning device is 17×10 ⁶ N/m, Lateral stiffness K _1y = 1.48×10 ⁶ N/m, vertical stiffness K _1z = 1.48×10 ⁶ N/m; longitudinal stiffness K _2x = 0.165×10 ⁶ N/m of central spring of each bogie, K _2y ＝0.165×10 ⁶ N/m; the vertical equivalent stiffness K _2z ＝561.68kN/m, the vertical equivalent damping C _d2 ＝111.39kN.s/m of the secondary suspension of each bogie; The torsional stiffness of the roll torsion bar K _θ = 2.5×10 ⁶ Nm/rad; the equivalent damping coefficient C ₂ of the secondary lateral shock absorber to be designed for each bogie; the wheel rolling radius r = 0.43m, the wheel tread slope λ=0.15; vehicle running speed v=100km/h; half of the lateral distance between the wheel and rail contact point b=0.7175m, half of the lateral installation distance of the axle positioning spring b ₁ =1.05m, half of the lateral installation distance of the central spring of the bogie b ₂ =1.2m, half of the fixed distance of the vehicle a=7.85m, half of the wheelbase of the bogie a ₀ =1.25m, the height h 0 from the center line of the axle to the track plane h ₀ =0.43m, the center of mass of the car body to the upper plane of the central spring The height h ₁ = 0.779m, the height h ₂ = 0.616m from the center of mass of the car body to the secondary transverse shock absorber, h ₃ = 0.216m from the upper plane of the central spring to the center of mass of the frame, and the distance from the center of mass of the bogie frame to the centerline of the axle Height h ₄ =0.075m, height h ₅ =0.379m from the secondary transverse shock absorber to the center of mass of the frame; the center of mass O _1ff , O _1fr of the front bogie wheel set, and the center of mass O _1rf , O _1rr of the rear bogie wheel set respectively , the center of mass O _2f , O _2r of the front and rear _bogies and the center of mass O ₃ of the car body are the coordinate origin; The yaw displacement y _1fr of the front bogie and the rear wheel set, the shaking head displacement The yaw displacement y _1rf of the front wheel set of the rear bogie and the head displacement The yaw displacement y _1rr of the rear wheel set of the rear bogie and the head displacement The yaw displacement y _2f of the front bogie frame and the shaking head displacement The roll displacement θ _2f , the yaw displacement y _2r of the rear bogie frame, and the shaking head displacement The roll displacement θ _2r , and the yaw displacement y ₃ of the car body and the shaking head displacement Rolling displacement θ ₃ is the coordinate; input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 of the track direction irregularity at the front and rear wheels of the front bogie and the front and rear wheels of the rear bogie (t) and horizontal irregularity input z _θ1 (t), z _θ2 (t), z _θ3 (t), z _θ4 (t) are the input excitations, where t is the time variable; establish a low-speed rail vehicle 17 free The differential equation of lateral vibration during driving at 100°C is:

①The yaw vibration equation of the front wheel set of the front bogie:

②The head shaking vibration equation of the front wheel set of the front bogie:

③The yaw vibration equation of the front bogie and the rear wheel set:

④ Head shaking vibration equation of front bogie and rear wheel set:

⑤ The yaw vibration equation of the front wheel set of the rear bogie:

⑥Shaking vibration equation of the front wheel set of the rear bogie:

⑦The yaw vibration equation of the rear wheel set of the rear bogie:

⑧ Shaking vibration equation of the rear wheel set of the rear bogie:

⑨The yaw vibration equation of the front bogie frame:

⑩Rolling vibration equation of the front bogie frame:

The shake head vibration equation of the front bogie frame:

The yaw vibration equation of the rear bogie frame:

The roll vibration equation of the rear bogie frame:

The shaking head vibration equation of the rear bogie frame:

The yaw vibration equation of the car body:

The rolling vibration equation of the car body:

Wherein, h=h ₀ +h ₁ +h ₃ +h ₄ ;

Shaking head vibration equation of the car body:

(2) Construct a 17-degree-of-freedom lateral vibration optimization design simulation model for a low-speed rail vehicle:

According to the 17-degree-of-freedom lateral vibration differential equation of the whole low-speed rail vehicle established in step (1), use Matlab/Simulink simulation software to construct the 17-degree-of-freedom lateral vibration optimization design simulation model of the low-speed rail vehicle, as shown in Figure 4 Show;

(3) Establish the damping optimization design objective function J of the secondary transverse shock absorber:

According to the low-speed rail vehicle 17-degree-of-freedom lateral vibration optimization design simulation model established in step (2), the equivalent damping coefficient of the secondary lateral shock absorber of each bogie is used as the design variable, and the The random input of the track direction irregularity and the horizontal irregularity random input are the input excitations, and the root mean square value of the vibration frequency weighted acceleration of the vehicle body yaw motion obtained by simulation The root mean square value of vibration frequency weighted acceleration of vehicle body roll motion and the root mean square value of the vibration frequency weighted acceleration of the shaking head of the car body The damping optimization design objective function J of the secondary transverse shock absorber is established, namely:

In the formula, the root mean square value of vibration frequency weighted acceleration The coefficients 1, 0.63, and 0.2 are the axis weighting coefficients of the yaw motion, roll motion, and shaking head motion of the car body respectively; among them, the root mean square value of the vibration frequency weighted acceleration at different frequencies The frequency weighted values of are respectively w _d (f _i ), w _e (f _i ), w _f (f _i ), that is:

(4) Optimal design of the optimal damping coefficient C of the secondary transverse shock absorber of low-speed rail vehicles:

①According to half of the vehicle fixed distance a = 7.85m, half of the bogie wheelbase a ₀ =1.25m, vehicle speed v = 100km/h, and the 17 degrees of freedom of the low-speed rail vehicle established in step (2) The simulation model of lateral vibration optimization design, randomly input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 (t) of track direction irregularity at each wheel set and random input of horizontal irregularity z _θ1 (t), z _θ2 (t), z _θ3 (t), z _θ4 (t) are the input excitations, use the optimization algorithm to find the damping optimization design objective function J of the secondary transverse shock absorber established in step (3) The minimum value, the optimized design obtains the optimal equivalent damping coefficient C ₂ =86.3kN.s/m of the secondary transverse shock absorber of each bogie;

Among them, the relationship between the track direction irregular random input is: y _a2 (t) = y _a1 (t-0.09s), y _a3 (t) = y _a1 (t-0.5652s), y _a4 (t) = y _a1 (t-0.6552s); the relationship between horizontal irregular random input excitations is: z _θ2 (t) = z _θ1 (t-0.09s), z _θ3 (t) = z _θ1 (t-0.5652s) , z _θ4 (t)=z _θ1 (t-0.6552s); when the vehicle speed v=100km/h, the random input excitation of the U.S. track direction irregularity applied to each wheel set is shown in Fig. 5, Fig. 6 and Fig. 7. As shown in Figure 8; the random input excitation of the US track level irregularity is shown in Figure 9, Figure 10, Figure 11, and Figure 12 respectively;

②According to the installation number n=2 of the secondary transverse shock absorber of each bogie, and the optimal equivalent damping coefficient C of the secondary transverse shock absorber of each bogie obtained by the optimization design in step (4) of step ① ₂ =86.3kN.s/m, and the optimal damping coefficient C of the single secondary series transverse shock absorber is calculated, namely: C=C ₂ /n=43.15kN.s/m.

According to the vehicle parameters provided in the embodiments, using the special software SIMPACK for rail vehicles, it can be obtained through solid modeling and simulation verification that the optimal damping coefficient of the secondary transverse shock absorber of the low-speed rail vehicle is C=43.17kN.s/m; It can be seen that the optimal damping coefficient C=43.15kN.s/m of the secondary transverse shock absorber of the low-speed rail vehicle obtained by the optimal design method is the same as the optimal damping coefficient C=43.17kN.s/m obtained by SIMPACK simulation verification. m coincides, the deviation between the two is only 0.02kN.s/m, and the relative deviation is only 0.046%, which shows that the design method of the optimal damping coefficient of the secondary transverse shock absorber for low-speed rail vehicles provided by the present invention is correct.

Claims (1)

1. The design method of the optimal damping coefficient of the secondary transverse shock absorber of low-speed rail vehicles, the specific design steps are as follows: (1) Establish the differential equation of the lateral vibration of the low-speed rail vehicle with 17 degrees of freedom: According to the mass m ₃ of the single car body of the rail vehicle and the moment of inertia of the shaking head Rolling moment of inertia J _3θ ; mass m ₂ of each bogie frame, moment of inertia of shaking head Rolling moment of inertia J _2θ ; mass m ₁ of each wheel pair, moment of inertia of shaking head Axle weight W of each wheel; transverse creep coefficient f ₁ and longitudinal creep coefficient f ₂ of each wheel pair; longitudinal stiffness K _1x , transverse stiffness K _1y , and vertical stiffness K _1z of each axle box positioning device; each steering The longitudinal stiffness K _2x and lateral positioning stiffness K _2y of the central spring of the frame; the vertical equivalent stiffness K _2z and vertical equivalent damping C _d2 of the secondary suspension of each bogie; the torsional stiffness K of a single anti-roll torsion bar _θ ; equivalent damping coefficient C ₂ of secondary lateral shock absorber to be designed for each bogie; wheel rolling radius r, wheel tread slope λ; vehicle running speed v; half b ₁ of the lateral installation distance of the positioning spring, half b ₂ of the lateral installation distance of the central spring of the bogie, half a of the fixed distance of the vehicle, half a ₀ of the wheelbase of the bogie, the height h ₀ from the center line of the axle to the plane of the track, The height h ₁ from the center of mass of the body to the upper plane of the central spring, the height h 2 from the center of mass of the car body to the secondary transverse shock absorber, the height h ₃ from the upper plane of the central spring to the center of mass of the frame, and the height h from the center of mass _of the bogie frame to the center line of the axle ₄ , the height h ₅ from the secondary transverse shock absorber to the center of mass of the frame; the center of mass O _1ff , O _1fr of the front bogie wheel set, the center of mass O _1rf , O _1rr of the rear bogie wheel set, and the center of mass of the front and rear bogie frames The center of mass O _2f , O _2r and the center of mass O ₃ of the vehicle body are the origin of coordinates; the yaw displacement y _1ff and the shaking head displacement of the former bogie front wheel set The yaw displacement y _1fr of the front bogie and the rear wheel set, the shaking head displacement The yaw displacement y _1rf of the front wheel set of the rear bogie and the head displacement The yaw displacement y _1rr of the rear wheel set of the rear bogie and the head displacement The yaw displacement y _2f of the front bogie frame and the shaking head displacement The roll displacement θ _2f , the yaw displacement y _2r of the rear bogie frame, and the shaking head displacement The roll displacement θ _2r , and the yaw displacement y ₃ of the car body and the shaking head displacement Rolling displacement θ ₃ is the coordinate; input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 of the track direction irregularity at the front and rear wheels of the front bogie and the front and rear wheels of the rear bogie (t) and horizontal irregularity input z _θ1 (t), z _θ2 (t), z _θ3 (t), z _θ4 (t) are the input excitations, where t is the time variable; establish a low-speed rail vehicle 17 free The differential equation of lateral vibration during driving at 100°C is: ①The yaw vibration equation of the front wheel set of the front bogie: ②The head shaking vibration equation of the front wheel set of the front bogie: ③The yaw vibration equation of the front bogie and the rear wheel set: ④ Head shaking vibration equation of front bogie and rear wheel set: ⑤ The yaw vibration equation of the front wheel set of the rear bogie: ⑥Shaking vibration equation of the front wheel set of the rear bogie: ⑦The yaw vibration equation of the rear wheel set of the rear bogie: ⑧ Shaking vibration equation of the rear wheel set of the rear bogie: ⑨The yaw vibration equation of the front bogie frame: ⑩Rolling vibration equation of the front bogie frame: The shake head vibration equation of the front bogie frame: The yaw vibration equation of the rear bogie frame: The roll vibration equation of the rear bogie frame: The shaking head vibration equation of the rear bogie frame: The yaw vibration equation of the car body: The rolling vibration equation of the car body: Wherein, h=h ₀ +h ₁ +h ₃ +h ₄ ; Shaking head vibration equation of the car body: (2) Construct a 17-degree-of-freedom lateral vibration optimization design simulation model for a low-speed rail vehicle: According to the low-speed rail vehicle vehicle 17 degrees of freedom driving lateral vibration differential equation established in the step (1), utilize Matlab/Simulink simulation software to construct the low-speed rail vehicle vehicle 17 degrees of freedom lateral vibration optimization design simulation model; (3) Establish the damping optimization design objective function J of the secondary transverse shock absorber: According to the low-speed rail vehicle 17-degree-of-freedom lateral vibration optimization design simulation model established in step (2), the equivalent damping coefficient of the secondary lateral shock absorber of each bogie is used as the design variable, and the The random input of the track direction irregularity and the horizontal irregularity random input are the input excitations, and the root mean square value of the vibration frequency weighted acceleration of the vehicle body yaw motion obtained by simulation The root mean square value of vibration frequency weighted acceleration of vehicle body roll motion and the root mean square value of the vibration frequency weighted acceleration of the shaking head of the car body The damping optimization design objective function J of the secondary transverse shock absorber is established, namely: In the formula, the root mean square value of vibration frequency weighted acceleration The coefficients 1, 0.63, and 0.2 are the axis weighting coefficients of the yaw motion, roll motion, and shaking head motion of the car body respectively; among them, the root mean square value of the vibration frequency weighted acceleration at different frequencies The frequency weighted values of are respectively w _d (f _i ), w _e (f _i ), w _f (f _i ), that is: <mrow><msub><mi>w</mi><mi>d</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>&amp;Element;</mo><mo>&amp;lsqb;</mo><mn>0.5</mn><mo>,</mo><mn>2</mn><mo>&amp;rsqb;</mo><mi>H</mi><mi>z</mi></mrow></mtd></mtr><mtr><mtd><mrow><mn>2</mn><mo>/</mo><msub><mi>f</mi><mi>i</mi></msub></mrow></mtd><mtd><mrow><msub><mi>f</mi><mi>i</mi></msub><mo>&amp;Element;</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>80</mn><mo>&amp;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>&amp;Element;</mo><mo>&amp;lsqb;</mo><mn>0.5</mn><mo>,</mo><mn>1</mn><mo>&amp;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>&amp;Element;</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>80</mn><mo>&amp;rsqb;</mo><mi>H</mi><mi>z</mi></mrow></mtd></mtr></mtable></mfenced><mo>;</mo></mrow> <mrow><msub><mi>w</mi><mi>f</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>&amp;Element;</mo><mo>&amp;lsqb;</mo><mn>0.5</mn><mo>,</mo><mn>1</mn><mo>&amp;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>&amp;Element;</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>80</mn><mo>&amp;rsqb;</mo><mi>H</mi><mi>z</mi></mrow></mtd></mtr></mtable></mfenced><mo>;</mo></mrow> (4) Optimal design of the optimal damping coefficient C of the secondary transverse shock absorber of low-speed rail vehicles: ①According to half a of the vehicle fixed distance, half a ₀ of the bogie wheelbase, vehicle speed v, and the 17-degree-of-freedom lateral vibration optimization design simulation model of the low-speed rail vehicle established in step (2), the Randomly input y _a1 (t), y _a2 (t), y _a3 (t), y _a4 (t) for track direction irregularity and horizontal irregularity randomly input z _θ1 (t), z _θ2 (t), z _θ3 (t) and z _θ4 (t) are the input excitations, use the optimization algorithm to find the minimum value of the objective function J of the damping optimization design of the secondary transverse shock absorber established in step (3), and the corresponding design variables are The optimal equivalent damping coefficient C ₂ of the secondary transverse shock absorber of each bogie; Among them, the relationship between the track direction irregularity random input is: The relationship between horizontally uneven random inputs is: ②According to the installed number n of the secondary transverse shock absorbers of each bogie, and the optimal equivalent damping coefficient C ₂ of the secondary transverse shock absorbers of each bogie obtained from the optimization design in step ① of step (4), The optimal damping coefficient C of the single secondary series transverse shock absorber is calculated, namely: C=C ₂ /n.