A numerical calculation method for fluid-structure coupling of high-speed pantograph

Abstract

The application discloses a kind of high-speed pantograph fluid-solid coupling simulation method, it is related to information technology service technical field.The method includes the following steps: pantograph working model is established in Fluent, and it is meshed;The relationship between catenary stiffness and position is obtained, and then the pantograph-catenary contact force is obtained according to penalty function method;Based on mechanical vibration theory, the differential equation of pantograph reduction mass block motion is constructed, and the Newmark-Beta method is used to solve the differential equation, to calculate the displacement, velocity and acceleration of each component of pantograph;The pantograph posture at time t+△t is solved based on motion constraint equation;Fluent is used as the CFD calculation model of pantograph;The grid is updated until the preset time step is reached.The application realizes the coupling of aerodynamics and structural dynamics of pantograph in a single simulation software, greatly improves the fluid-solid coupling simulation efficiency, and has higher accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of information technology services, in particular to a numerical calculation method for fluid-structure coupling of a high-speed pantograph. BACKGROUND

[0002] The pantograph is one of the important components on the roof of the train, responsible for obtaining electrical energy to ensure the safe operation of the train. When traveling at low speed, the displacement of the pantograph in the vertical direction is small, and its nonlinear factors and dynamic effects can usually be ignored. However, as the train speed increases, the flow field near the pantograph becomes increasingly severe, and the pantograph is subjected to increasingly intense aerodynamic excitation, which in turn triggers the flow-induced vibration of the pantograph, and the vibration of the pantograph exacerbates the vibration of the airflow, thereby worsening the working environment of the pantograph.

[0003] The dynamic system formed by the catenary and the pantograph cannot effectively suppress the flow-induced vibration of the pantograph, resulting in a dramatic change in the pantograph-catenary contact force. Excessive or insufficient contact force will affect the current collection quality of the pantograph: excessive pantograph-catenary contact force will increase the friction between the pantograph and the catenary, exacerbating wear; and insufficient pantograph-catenary contact force will increase the contact resistance, affecting current collection, and may cause the pantograph carbon slide to separate from the catenary, resulting in an arc, causing irreversible damage to the catenary and the pantograph, and seriously affecting current collection.

[0004] Therefore, it is of great practical significance to study the flow-induced vibration of the high-speed train pantograph, which involves phenomena such as vortex-induced vibration and turbulent excitation. The flow-induced vibration of the high-speed pantograph involves the interaction between fluid and solid, and requires fluid-structure coupling research. The research methods for fluid-structure coupling include real vehicle tests and numerical simulations. Currently, the research on pantograph flow-induced vibration mainly relies on real vehicle tests, which are long in cycle, costly, and have complex external variables, making it difficult to achieve accurate research. One-way coupling has a certain reliability in the low-speed operation stage of the pantograph, but as the train speed increases, the pantograph vibration intensifies, making it difficult to ensure its authenticity. At present, there are few studies on the coupling effect between aerodynamics and structural dynamics of high-speed pantographs using two-way coupling, and the existing two-way coupling methods all rely on joint simulation between multiple platforms, which is low in calculation efficiency and long in simulation cycle. SUMMARY

[0005] To solve at least one of the above problems, the present application proposes a numerical calculation method for fluid-structure coupling of a high-speed pantograph.

[0006] The technical solution of the present application is: a simulation method for fluid-structure coupling of a high-speed pantograph, comprising the following steps:

[0007] S1, establish the pantograph working model in Fluent and divide the grid to obtain the pantograph overlapping grid fluid area, the pantograph comprising a pull-down rod, a lower arm rod, an upper frame, a pantograph head and a carbon slide plate;

[0008] S2, obtain the relationship between the catenary stiffness and position, and then obtain the pantograph-catenary contact force according to the penalty function method: In the formula, F c is the pantograph-catenary contact force; y h and y c are the carbon slide plate height and the catenary height respectively; k(t) is the relationship function between the catenary stiffness and time; k0 represents the average stiffness coefficient; k1, k2, k3, k4 and k5 represent the stiffness change coefficients; L is the catenary span; L1 represents the distance between adjacent droppers; v represents the vehicle speed; and t represents the time.

[0009] S3, construct the differential equation of the pantograph reduced mass motion based on the mechanical vibration theory, and solve the differential equation by using the Newmark-Beta method to calculate the displacement, velocity and acceleration of each component of the pantograph:

[0010] S4, solve the pantograph posture at t+△t based on the motion constraint equation:

[0011] The constraint relationship between the pantograph head and the lower arm rod base is:

[0012] The constraint relationship between the lower arm rod and the pull-down rod is: In the formula, respectively represent the upper frame length, the lengths of points D and F, the lower arm rod length and the pull-down rod length, wherein point D is a hinge point on the pull-down rod, and point F is a hinge point between the pull-down rod and the upper frame; CD is the distance between point D and point C, wherein point C is a hinge point between the pull-down rod and the upper frame; α, β, γ and δ are respectively the pull-down rod, the upper frame, the included angle between the lower arm rod and the horizontal direction, is the length between point C and point F; x and y are respectively the horizontal and vertical distances of point A and hinge point B, point A is a hinge point between the lower arm rod and the base, and point B is a hinge point between the pull-down rod and the base; x A and y A are respectively the horizontal and vertical coordinates of point A; x E and y E are respectively the horizontal and vertical coordinates of point E, and E is a hinge point between the upper frame and the pantograph head;

[0013] S5, assigning a velocity to the overlapped grid fluid region based on the results of S2-S4, updating the displacement, velocity and pantograph-catenary contact force of the pantograph in the model at t+△t;

[0014] S6, using Fluent as a CFD calculation model of the pantograph;

[0015] S7, repeating S2-S6 until a preset time step is reached.

[0016] Beneficial effects: 1. The present application realizes the coupling of pantograph aerodynamics and structural dynamics in a single simulation software, greatly improving the fluid-structure coupling simulation efficiency.

[0017] 2. The overlapped grid used in the pantograph aerodynamics calculation of the present application can adapt to complex flow changes and provide higher grid resolution.

[0018] 3. The pantograph structural dynamics calculation of the present application uses a pantograph lumped mass equivalent model, which can greatly reduce the coupling calculation time and has high calculation accuracy. The vibration of the carbon slide plate is also considered, which is more in line with the actual situation and can accurately capture the contact between the carbon slide plate and the catenary.

[0019] 4. The high-speed pantograph fluid-structure coupling method provided by the present application can be applied to different specifications of pantographs by modifying the pantograph parameter values set in the UDF. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a diagram of the pantograph;

[0021] Figure 2 is a diagram of the pantograph lumped mass model. DETAILED DESCRIPTION

[0022] The specific embodiments of the present application will be described below in conjunction with examples and drawings, it is obvious that the described examples are only part of the embodiments of the present application, not all embodiments.

[0023] A numerical calculation method for high-speed pantograph fluid-structure coupling, comprising the following steps:

[0024] S1, establishing a pantograph working model in Fluent and performing grid division to obtain a pantograph overlapped grid fluid region, the pantograph comprising a pull-down rod, a lower arm rod, an upper frame, a pantograph head and a carbon slide plate;

[0025] Specifically as Figure 1 shown, it is a diagram of the pantograph established in the embodiment, in Figure 1In the embodiment, the structure of the conventional pantograph is simplified, and a driven rod is arranged at the hinge point D between the actual pantograph and the head, but the driven rod is integrated with the upper frame because the driven rod and the upper frame have the same action process.

[0026] Figure 1 In the embodiment, the meanings of the parts are as follows: A and B respectively represent the hinge points of the lower arm rod and the lower pull rod with the base, AD represents the lower arm rod, BC represents the lower pull rod, FE represents the upper frame, D represents a hinge point on the lower arm rod, H, G and I respectively represent the aerodynamic force action points of the upper frame, the lower arm rod and the lower pull rod, β is the included angle between the upper frame and the horizontal direction, γ is the included angle between the CF segment and the horizontal direction, α is the included angle between the lower pull rod and the horizontal direction, and δ is the included angle between the lower arm rod and the horizontal direction.

[0027] In the process of dividing the grid, the grid is divided into a background grid and a pantograph grid, and the pantograph grid is taken as an overlapping grid fluid region so as to facilitate subsequent calculation and simulation.

[0028] S2, the relationship between the catenary stiffness and the position is obtained, and the pantograph-catenary contact force is obtained according to the penalty function method: In the formula, F c is the pantograph-catenary contact force; y h and y c are the height of the carbon slide plate and the height of the catenary respectively; k(t) is the relationship function between the catenary stiffness and time; k0 represents the average stiffness coefficient; k1, k2, k3, k4 and k5 represent the stiffness change coefficients; L is the span of the catenary; L1 represents the distance between adjacent droppers; v represents the vehicle speed; and t represents time.

[0029] In this step, the catenary stiffness is calculated by the finite element method, and the calculation result is fitted by the least square method, so as to obtain the relationship between the catenary stiffness and time.

[0030] S3, the differential equation of the pantograph reduced mass block motion is constructed based on the mechanical vibration theory, and the Newmark-Beta method is used to solve the differential equation, so as to calculate the displacement, velocity and acceleration of each component of the pantograph: when the calculation of the pantograph reduced mass block is performed, the pantograph reduced mass block needs to be constructed first, as shown in the following formula: Figure 2 In the formula, m1 represents the mass block of the lower arm rod, m2 represents the mass block of the upper frame, m3 represents the mass block of the head, and m4 represents the mass block of the carbon slide plate.

[0031] In this step, it specifically includes the following sub-steps:

[0032] S31. Initialize the model to obtain the displacement vector q(t) and load vector F(t) at time t; simultaneously obtain the mass matrix, stiffness matrix, and damping matrix of the pantograph reduced mass block model: In the formula, M, K, and C are the mass matrix, stiffness matrix, and damping matrix, respectively; m i k i c i (i = 1, 2, 3, 4) represent the equivalent mass, stiffness, and damping of the lower arm, upper frame, and bow head, respectively; m4, k4, and c4 represent the mass, suspension stiffness, and damping of the carbon slide plate, respectively.

[0033] S32. Based on mechanical vibration theory, obtain the differential equations of motion, displacement vector, and load vector of the pantograph's reduced mass block: q(t) = {x1(t)x2(t)x3(t)x4(t)} T F(t)={F L1 (t)+F t F L2 (t)F L3 (t)F L4 (t)-F c} T In the formula, xi(t) (i=1,2,3,4) represent the displacements of the lower arm, upper frame, bow head, and carbon slide plate at time t, respectively; F Li (t)(i=1,2,3,4) represents the aerodynamic lifting force on the lower boom, upper frame, bow head, and carbon slide plate at time t; F t The static lift force provided to the pantograph airbag;

[0034] S33. According to torque balance and the relationship between action and reaction forces, we can obtain: F L4 (t)=F Jy , In the formula, A j (j=1,2,3…7,8) are the equivalent coefficients of aerodynamic lift force; F Ex F Ey These are the horizontal and vertical aerodynamic forces acting at the point of application of the aerodynamic force, E, respectively; F Jx F Jy These are the horizontal and vertical aerodynamic forces acting at the point of application J, respectively; F Hx F Hy These are the horizontal and vertical aerodynamic forces acting at the point of application H, respectively; F Gx F Gy These are the horizontal and vertical aerodynamic forces acting at the point of application of the aerodynamic force, G, respectively; F Ix F Iy These are the horizontal and vertical aerodynamic forces acting at point I, respectively.

[0035] S34. Solve the differential equation using Newmark-Beta to obtain the effective stiffness matrix and effective load within the time interval Δt.

[0036]

[0037] In the formula, For the effective stiffness matrix, For the effective load, λ and ρ are constants, K is the stiffness matrix, C is the damping matrix, and M is the mass matrix;

[0038] S35. Calculate the displacement, velocity, and acceleration at time t+Δt:

[0039] S4. Solve for the pantograph attitude at time t+Δt based on the motion constraint equations:

[0040] The constraint relationship between the bow head and the lower boom base is as follows:

[0041] The constraint relationship between the lower boom and the pull rod is as follows: In the formula, Let α, β, γ, and δ represent the lengths of the upper frame, points D and F, the lower arm, and the pull rod, respectively. Point D is a hinge point on the pull rod, and point F is the hinge point between the pull rod and the upper frame. CD is the distance between point D and point C, where point C is the hinge point between the pull rod and the upper frame. α, β, γ, and δ represent the lengths of the pull rod, upper frame, and lower arm, respectively. The angle between the lower boom and the horizontal direction. Let x be the length between points C and F; x and y are the horizontal and vertical distances between points A and hinge point B, respectively. Point A is the hinge point between the lower arm and the base, and point B is the hinge point between the pull rod and the base; x A y A Let x and y be the x and y coordinates of point A, respectively. E y E Let x and y be the x and y coordinates of point E, where E is the hinge point between the upper frame and the bow head;

[0042] S5. Based on the results of S2 to S4, velocity is assigned to the fluid region of the overlapping grid, and the displacement, velocity, and pantograph-catenary contact force of the pantograph at time t+Δt in the model are updated.

[0043] S6. CFD calculation model based on Fluent as pantograph;

[0044] When performing CFD calculations on the pantograph, different CFD calculation models can be used depending on the situation. For example, in the turbulence model, SST k-ω is used as the CFD calculation module, the pressure basis is selected to solve the flow, the velocity and pressure are coupled and solved using the SIMPLEC algorithm, the convection term is processed using the second-order upwind scheme, the dissipation term is processed using the QUICK scheme, and the time term is processed using the second-order precision central difference scheme.

[0045] S7. Repeat S2 to S6 until the preset time step is reached.

[0046] In the above steps, the pantograph-catenary contact force at different times is obtained through S2, the displacement, velocity and acceleration of different parts of the pantograph at different times are obtained through S3, and the angles of different parts of the pantograph with the horizontal plane at different times are obtained through S4. The attitude of the pantograph at different times can be obtained through this angle. Finally, the flow field distribution of the pantograph at different times can be obtained through Fluent's built-in CFD calculation model.

[0047] Therefore, the method of this embodiment can simulate and predict the pantograph-catenary contact force, displacement, velocity, acceleration, attitude, and flow field distribution during the entire pantograph movement process. Furthermore, all of the above operations are implemented within the Fulent software, enabling this embodiment of the invention to simulate pantograph-fluid-structure interaction using only one software, making the operation more convenient, simpler, and easier to promote and use.

[0048] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A simulation method for high-speed pantograph fluid-structure interaction, characterized in that, Includes the following steps: S1. Establish a working model of the pantograph in Fluent and mesh it to obtain the overlapping mesh fluid region of the pantograph. The pantograph includes a pull rod, a lower arm, an upper frame, a bow head, and a carbon sliding plate. S2. Obtain the relationship between the stiffness of the overhead contact line and time, and then obtain the contact force between the pantograph and the contact line using the penalty function method: , In the formula, F c For the contact force between the bow and the firebox; y h and y c These refer to the height of the carbon sliding plate and the height of the overhead contact line, respectively. k ( t ) is the function relating the stiffness of the overhead contact line to time; k 0 indicates the average stiffness coefficient; k 1, k 2, k 3, k 4, k 5 represents the stiffness variation coefficient; L The span of the overhead contact line; L 1 indicates the distance between adjacent hangers; v Indicates vehicle speed; t Indicates time; S3. Based on mechanical vibration theory, construct the differential equations for the motion of the pantograph's reduced mass block, and use the Newmark-Beta method to solve the differential equations, calculating the displacement, velocity, and acceleration of each component of the pantograph: S4. Solve for the pantograph attitude at time t+Δt based on the motion constraint equations: The constraint relationship between the bow head and the lower boom base is as follows: , , The constraint relationship between the lower boom and the pull rod is as follows: In the formula, , , , Let α, β, γ, and δ represent the lengths of the upper frame, the distance between points D and F, the lower arm, and the pull rod, respectively. Point D is a hinge point on the pull rod, and point F is a hinge point between the pull rod and the upper frame. CD is the distance between points D and C, where point C is the hinge point between the pull rod and the upper frame. α, β, γ, and δ represent the lengths of the pull rod, upper frame, and lower arm, respectively. The angle between the lower boom and the horizontal direction. Let x be the length between points C and F; x and y are the horizontal and vertical distances between points A and hinge point B, respectively. Point A is the hinge point between the lower arm and the base, and point B is the hinge point between the pull rod and the base. x A , y A Let A be the x and y coordinates of point A respectively. x E , y E Let x and y be the x and y coordinates of point E, where E is the hinge point between the upper frame and the bow head; S5. Based on the results of S2~S4, velocity is assigned to the fluid region of the overlapping grid, and the displacement, velocity, and pantograph-catenary contact force of the pantograph at time t+Δt in the model are updated. S6. Use Fluent as the CFD calculation model for the pantograph; S7. Repeat S2~S6 until the preset time step is reached.

2. The method according to claim 1, characterized in that, In S1, the overlapping mesh fluid region refers to the pantograph model mesh.

3. The method according to claim 1, characterized in that, In S2, the stiffness of the contact wire is calculated using the finite element method, and the calculation results are fitted using the least squares method to obtain the relationship between the stiffness of the contact wire and time.

4. The method according to claim 1, characterized in that, S3 includes the following steps: S31. Initialize the model and obtain the displacement vector of the model at time t. q ( t ) and load vector F ( t Simultaneously, the mass matrix, stiffness matrix, and damping matrix of the pantograph's reduced mass block are obtained: , , In the formula, M , K , C These are the mass matrix, stiffness matrix, and damping matrix, respectively. m i , k i , c i The equivalent mass, stiffness, and damping of the lower boom, upper frame, and bow head are respectively, i=1,2,3,4; S32. Based on mechanical vibration theory, obtain the differential equations of motion, displacement vector, and load vector of the pantograph's reduced mass block: , , In the formula, x i ( t () represent the displacements of the lower arm, upper frame, bow head, and carbon slide plate at time t; F Li ( t ) represents the aerodynamic lifting force exerted on the lower boom, upper frame, bow head, and carbon slide plate at time t; F t The static lift force provided to the pantograph airbag; S33. According to torque balance and the relationship between action and reaction forces, we can obtain: , , , In the formula, A j , where j = 1, 2, 3…7, 8; F Ex , F Ey These are the horizontal and vertical aerodynamic forces acting at the point of application of the aerodynamic force, E, respectively. F Jx , F Jy These are the horizontal and vertical aerodynamic forces acting at the point of application of the aerodynamic force, J, respectively. F Hx , F Hy These are the horizontal and vertical aerodynamic forces acting at the point of application H, respectively. F Gx , F Gy These are the horizontal and vertical aerodynamic forces acting at the point of application of the aerodynamic force, G, respectively. F Ix , F Iy These are the horizontal and vertical aerodynamic forces acting at point I, respectively. S34. Solve the differential equation using Newmark-Beta to obtain the effective stiffness matrix and effective load within the time interval Δt. , In the formula, For the effective stiffness matrix, For the payload, λ , ρ It is a constant. K Here is the stiffness matrix. C Here is the damping matrix. M This is the quality matrix; S35. Calculate the displacement, velocity, and acceleration at time t+Δt: , , .

5. The method according to claim 1, characterized in that, In S6, SST k-ω is used as the CFD calculation module in the turbulence model. The pressure basis is selected to solve the flow field. The velocity and pressure coupled solution adopts the SIMPLEC algorithm. The convection term adopts the second-order upwind scheme, the dissipation term adopts the QUICK scheme, and the time term adopts the second-order accurate central difference scheme.

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