Railway vehicle system structure modal force acquisition method and resonance control method

Abstract

The application relates to a rail vehicle system structure modal force acquisition method and a resonance control method. The modal force acquisition method comprises the following steps: constructing a system vibration differential equation; transforming the system vibration differential equation to obtain a decoupling equation group about a modal force, and transforming the decoupling equation group into a component form to obtain a general form of the modal force; based on the general form of the modal force, determining a vehicle system modal force order according to rail vehicle system dynamics parameters, calculating a total i-order modal force of all suspension elements in the rail vehicle system acting on a vehicle body, and calculating the component form based on the dynamics parameters to obtain a final modal force. Compared with the prior art, the application has the advantages of clear principle, convenient implementation, low cost and the like.

Description

Technical Field

[0001] This invention relates to the field of vibration control technology, and in particular to a method for obtaining structural modal forces and a resonance control method for a rail vehicle system. Background Technology

[0002] As the operating mileage and speed of rail trains increase, train vibration intensifies, leading to a decrease in train running stability. The main reasons for this include two aspects:

[0003] On the one hand, most train bodies currently adopt lightweight design, with the body designed as a hollow aluminum welded structure. Compared with the traditional steel structure body, it can reduce the weight by about 40%, while reducing air resistance, thereby improving traction acceleration and reducing energy consumption. However, the aluminum alloy body usually leads to insufficient structural rigidity and increased structural vibration.

[0004] On the other hand, while lightweight vehicle design helps reduce axle load and improves wheel-rail interaction and service conditions of related components, the significant reduction in vehicle stiffness leads to a decrease in vehicle modal frequencies. These frequencies are more likely to approach the excitation frequencies from other structures, thus exciting the vehicle's elastic modes and exacerbating vibrations. In an increasing number of cases, vehicle elastic vibration has become a significant factor affecting passenger comfort.

[0005] Patent CN106570264B discloses a method for rapidly adapting the excitation force in pure modal testing. In this method, an exciter is used to apply the excitation force, and the modal force is then solved by solving the excitation force. The calculation process is complex and not easy to implement. Summary of the Invention

[0006] The purpose of this invention is to provide a method for obtaining modal forces and a resonance control method for rail vehicle system structures that improves the accuracy of modal force calculation.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A method for obtaining the structural modal forces of a rail vehicle system includes the following steps:

[0009] Construct the system vibration differential equation;

[0010] The vibration differential equation of the system is transformed to obtain a set of decoupled equations for modal forces, and the set of decoupled equations is transformed into component form to obtain the general form of modal forces;

[0011] Based on the general form of the modal forces, and according to the dynamic parameters of the rail vehicle system, the modal force order of the vehicle system is determined, and the overall modal force order of all suspension components acting on the car body in the rail vehicle system is calculated. The first modal force is calculated, and the component form is calculated based on the dynamic parameters to obtain the final modal force.

[0012] Furthermore, the expression for the system vibration differential equation is:

[0013]

[0014] In the formula, For the quality matrix, For acceleration, For modal vectors, The complex coordinate expression of periodic excitation force. Here is the stiffness matrix. Here is the structural damping matrix. The imaginary unit, It is the collection of external forces acting on the structure.

[0015] Furthermore, the structural damping matrix The expression is:

[0016]

[0017] In the formula, , This is the proportionality coefficient.

[0018] Furthermore, the mode vector The expression is:

[0019]

[0020] In the formula, The first representing each point A set of first-order mode shapes. ( )for n Modal coordinates of a modal vector in the modal coordinate system For modal vibration modes, This is a column vector of modal coordinates.

[0021] Furthermore, the step of obtaining the decoupling equations for modal forces includes:

[0022] Multiplying the vibration differential equation of the system by the transpose of the mode shape matrix on the left, we get:

[0023]

[0024] The orthogonal relations are as follows:

[0025]

[0026]

[0027]

[0028] Combining the orthogonal relation, we obtain the decoupling equations for modal forces:

[0029]

[0030] In the formula, the orthogonal relations represent the modal mass matrix, the modal principal stiffness matrix, and the modal structural proportional damping matrix, respectively. For the transpose of the mode shape matrix, For the quality matrix, For modal vibration modes, Here is the stiffness matrix. Here is the structural damping matrix. The imaginary unit, It is the collection of external forces acting on the structure. This represents the complex coordinate representation of the periodic excitation force, where diag denotes a diagonal matrix. For the first Modal stiffness of the first natural mode shape, For the first Modal mass of the first natural mode shape, For the first The modal structure proportional damping coefficient of the first natural vibration mode. This is a column vector of modal coordinates.

[0031] Furthermore, the modal coordinate column vector The expression is:

[0032]

[0033] In the formula, This refers to the amplitude.

[0034] Furthermore, the expression in component form is:

[0035]

[0036] make The above expression can be further expressed in component form as follows:

[0037]

[0038] In the formula, Representing the The magnitude of the first modal coordinates, The imaginary unit, It is the collection of external forces acting on the structure. Represents the excitation frequency, Representing the system's number The modal frequencies of the first mode. for transpose, The first representing each point A set of first-order mode shapes. For the first The modal structure proportional damping coefficient of the first natural vibration mode. For the first Modal mass of the first natural mode shape, The overall effect of all suspension components acting together on the vehicle body First-order modal forces.

[0039] Furthermore, all the aforementioned suspension elements work together to affect the overall structure of the vehicle body. The expression for calculating the first modal force is:

[0040]

[0041] In the formula, For the overall first First-order modal forces, for transpose, The first representing each point A set of first-order mode shapes. It is the collection of external forces acting on the structure. Indicates the first The force amplitude of each suspension element acting on the vehicle body This indicates the total number of suspension elements, with 0 representing the amplitude of the point where no force is applied.

[0042] Furthermore, the suspension components include air springs, secondary vertical dampers, secondary lateral dampers, anti-hunting dampers, and traction rods.

[0043] This embodiment also provides a resonance control method based on the above-described method for obtaining the structural modal forces of a rail vehicle system, comprising the following steps:

[0044] The contribution of each modal force to vehicle vibration is calculated, and the suspension system design is optimized to reduce the modal forces that contribute significantly to vehicle vibration, thereby reducing resonance and achieving resonance control.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] (1) This invention effectively decouples the forces acting on the vehicle body by mapping and decomposing the forces of the suspension components into modal forces of various orders. Combined with the system modal vibration, the system modal forces can be calculated better, thus improving the accuracy of modal force calculation.

[0047] (2) Based on the modal space, the present invention performs modal force mapping decomposition on the external excitation force acting on the car body, providing a theoretical basis for the control measures of elastic resonance of the car body, thereby improving the stability of vehicle operation and improving the ride comfort of the vehicle, and is applicable to the control of elastic modal vibration of high-speed train car body.

[0048] (3) The principle of this invention is clear, easy to implement and low in cost. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0050] Figure 2 The total modal forces of all suspension elements acting together on the lateral side of the vehicle body in this invention;

[0051] Figure 3 The total modal forces of all suspension elements acting together on the vehicle body in the vertical direction are the total modal forces of all orders.

[0052] Figure 4 The figures show the contribution of each suspension element of the present invention to the rhomboid modal force acting on the vehicle body, wherein (a) shows the contribution of the rhomboid modal force in the lateral direction, and (b) shows the contribution of the rhomboid modal force in the vertical direction. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0054] Example 1

[0055] This embodiment provides a method for obtaining the structural modal forces of a rail vehicle system, such as... Figure 1 As shown, the method includes the following steps:

[0056] S1. Definition of structural modal forces in rail vehicle systems.

[0057] Modal force refers to the force applied to each vibration mode after considering the vibration modes of the structure. It reflects the contribution of the excitation force to modal excitation. By calculating modal forces, the influence of different modal forces on the structural response can be understood. Furthermore, modal forces are the direct source of modal vibrations. For structures containing structural damping... The vibration differential equation of the system with degrees of freedom is:

[0058] (1)

[0059] In the formula, For the quality matrix, Here is the stiffness matrix. Here is the structural damping matrix.

[0060] if

[0061] (2)

[0062] This is called structural proportional damping.

[0063] Based on the orthogonality of eigenvectors, linearly independent eigenvectors , forming a A complete orthogonal basis for a dimensional vector space, this The 1-dimensional space is called the modal space. For real modal systems, the modal space is... The modal space constructed from modal vectors is a real linear space. Let the vectors in the physical coordinate system... The modal coordinates in the modal coordinate system are: ( ),but

[0064] (3)

[0065] In the formula, The modal coordinate column vector, It is a mode shape.

[0066] Substitute coordinate transformation equation (3) into (1) and multiply by the left side. have to:

[0067] (4)

[0068] in

[0069] (5)

[0070] (6)

[0071] (7)

[0072] The above three equations represent the modal (principal) mass matrix, modal (principal) stiffness matrix, and modal structure proportional damping matrix, respectively. `diag` represents a diagonal matrix. For the first Modal (principal) stiffness of the first-order natural vibration mode. For the first Modal (principal) mass of the first natural mode shape, For the first The modal structure proportional damping coefficient of the first natural vibration mode.

[0073] Combining the orthogonality relation (5), (6), and (7), we obtain the decoupling equation system.

[0074] (8)

[0075] Without loss of generality, let the steady-state displacement response be expressed as... Substituting, we get:

[0076] (9)

[0077] Rewriting the above expression in component form, we get:

[0078] (10)

[0079] make Equation (10) can be further written as:

[0080] (11)

[0081] In the formula, Represents the excitation frequency, Representing the system's number The modal frequencies of the first mode. Representing the The magnitude of the first modal coordinates, The first representing each point A set of mode shapes.

[0082] The motion equations in physical space are decoupled through modal vectors, while the excitation force needs to be multiplied by the transpose of the mode shape matrix. It refers to modal forces. It can be seen that the transpose of the mode shape matrix... It contains information about different vibration modes. This represents the collection of external forces acting on the structure.

[0083] S2. Extraction of modal forces acting on the structure of the rail vehicle system.

[0084] Once the vehicle system dynamic parameters are determined, the modal parameter part in the denominator of equation (10) is a constant. It depends only on the molecular part, that is, the overall effect of all suspension elements on the vehicle body. First-order modal force, defined as :

[0085] (12)

[0086] In the formula, Indicates the first The force amplitude of each suspension element acting on the vehicle body This represents the total number of suspension elements, where the amplitude of the unforced points is 0.

[0087] All suspension components work together to affect the overall structure of the vehicle body. First-order modal forces In reality, it is the first action of each suspension element on the vehicle body. It is formed by the superposition of modal forces. When At its minimum, The corresponding value reaches its minimum, which also means that the vibration of this mode reaches its minimum.

[0088] S3. Modal force contribution analysis of the rail vehicle system structure.

[0089] To more intuitively illustrate the first A certain modal force exerted by a suspension element on the vehicle body relative to all other suspension elements. s The degree of participation of each suspension element in the overall modal force of the vehicle body at a certain order will be determined by the number of suspension elements. The energy of a certain modal force exerted on the vehicle body by a suspension element is defined as follows:

[0090] (13)

[0091] In the formula, For the first The first modal force of a suspension element acting on the vehicle body is... Force amplitude at each sampling point This represents the total number of sampling points.

[0092] Therefore, the first A suspension element exerts a certain modal force energy on the vehicle body. G x account for all s The ratio of the total modal force energy of a certain order exerted by all suspension components on the vehicle body The contribution of a certain modal force exerted by the suspension element on the vehicle body can be calculated as follows:

[0093] (14)

[0094] To verify the effectiveness of the above method, the following experiments were conducted in this embodiment:

[0095] 1. Extract the forces acting on the vehicle body from the air spring, secondary vertical damper, secondary lateral damper, anti-hunting damper, and traction rod in the dynamics software SIMPACK.

[0096] 2. Based on the vehicle body modal shape matrix information extracted by condensation calculation, the modal forces of each suspension element acting on the vehicle body and the total modal forces of all suspension elements acting on the vehicle body are calculated, taking the air spring as an example.

[0097] Modal forces acting on the vehicle body by the air springs are extracted from the vehicle rigid-flexible coupling dynamics model. The forces acting on the vehicle body by the air springs in the lateral and vertical directions are extracted, and the component values ​​of the mode shape vectors at the connection points of the four air springs on the vehicle body are extracted by condensation calculation. The combined force of all air springs acting on the lateral direction of the vehicle body is calculated. Figure 2 ) and vertical ( Figure 3 Modal forces.

[0098] The analysis and calculation results show that by mapping and decomposing the forces acting on the vehicle body by all the air springs in the modal space, they can be effectively decoupled into modal forces of various orders.

[0099] S3. Based on the modal forces exerted on the vehicle body by each suspension element, further analyze the magnitude and contribution of the modal forces exerted on the vehicle body by each suspension element.

[0100] This experiment obtained the following results through analysis: Figure 3 The horizontal and vertical contributions of the rhomboid modal forces are shown in Figures (a) and (b).

[0101] Example 2

[0102] This embodiment provides a resonance control method based on the modal force acquisition method for a rail vehicle system structure described in Embodiment 1, comprising the following steps:

[0103] The contribution of each modal force to vehicle vibration is calculated, and the suspension system design is optimized to reduce the modal forces that contribute significantly to vehicle vibration, thereby reducing resonance and achieving resonance control.

[0104] That is, under the premise that the position of the analysis measurement point remains unchanged, i.e., the component values ​​of the mode shape vectors at each analysis measurement point remain unchanged, the factors affecting the elastic modal vibration of the vehicle body include the denominator of that mode. The section concerning modal parameters and modal forces of that order is discussed. Furthermore, once the dynamic parameters of the vehicle system are determined, the portion of the denominator concerning modal parameters is fixed; therefore, modal vibration depends only on the numerator, i.e., the modal forces. Thus, by optimizing suspension component parameters, adjusting air spring positions, and performing wheel resurfacing, the optimization effects of these measures on modal forces and modal vibrations can be analyzed, focusing on reducing the modal forces that significantly contribute to vehicle vibration, thereby resolving the problem of vehicle body elastic resonance.

[0105] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0106] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for obtaining the structural modal forces of a rail vehicle system, characterized in that, Includes the following steps: Construct the system vibration differential equation; The vibration differential equation of the system is transformed to obtain a set of decoupled equations for modal forces, and the set of decoupled equations is transformed into component form to obtain the general form of modal forces; Based on the general form of the modal forces, and according to the dynamic parameters of the rail vehicle system, the modal force order of the vehicle system is determined, and the overall modal force order of all suspension components acting on the car body in the rail vehicle system is calculated. The first modal force is calculated, and the component form is calculated based on the dynamic parameters to obtain the final modal force. All suspension elements act together on the overall first modal force of the vehicle body. The expression for calculating the first modal force is: In the formula, For the overall first First-order modal forces, for transpose, The first representing each point A set of first-order mode shapes. It is the collection of external forces acting on the structure. Indicates the first The force amplitude of each suspension element acting on the vehicle body This indicates the total number of suspension elements; 0 represents the amplitude of a point where no force is applied. The expression in component form is: make The above expression can be further expressed in component form as follows: In the formula, Representing the The magnitude of the first modal coordinates, The imaginary unit, It is the collection of external forces acting on the structure. Represents the excitation frequency, Representing the system's number The modal frequencies of the first mode. for transpose, The first representing each point A set of first-order mode shapes. For the first The modal structure proportional damping coefficient of the first natural vibration mode. For the first Modal mass of the first natural mode shape, The overall effect of all suspension components acting together on the vehicle body First-order modal forces.

2. The method for obtaining the structural modal forces of a rail vehicle system according to claim 1, characterized in that, The expression for the system's vibration differential equation is: In the formula, For the quality matrix, For acceleration, For modal vectors, The complex coordinate expression of periodic excitation force. Here is the stiffness matrix. Here is the structural damping matrix. The imaginary unit, It is the collection of external forces acting on the structure.

3. The method for obtaining the structural modal forces of a rail vehicle system according to claim 2, characterized in that, The structural damping matrix The expression is: In the formula, , This is the proportionality coefficient.

4. The method for obtaining the structural modal forces of a rail vehicle system according to claim 2, characterized in that, The mode vector The expression is: In the formula, The first representing each point A set of first-order mode shapes. ( )for n Modal coordinates of a modal vector in the modal coordinate system For modal vibration modes, This is a column vector of modal coordinates.

5. The method for obtaining the structural modal forces of a rail vehicle system according to claim 1, characterized in that, The steps for obtaining the decoupling equations for modal forces include: Multiplying the vibration differential equation of the system by the transpose of the mode shape matrix on the left, we get: The orthogonal relations are as follows: Combining the orthogonal relation, we obtain the decoupling equations for modal forces: In the formula, the orthogonal relations represent the modal mass matrix, the modal principal stiffness matrix, and the modal structural proportional damping matrix, respectively. For the transpose of the mode shape matrix, For the quality matrix, For modal vibration modes, Here is the stiffness matrix. Here is the structural damping matrix. The imaginary unit, It is the collection of external forces acting on the structure. This represents the complex coordinate representation of the periodic excitation force, where diag denotes a diagonal matrix. For the first Modal stiffness of the first natural mode shape, For the first Modal mass of the first natural mode shape, For the first The modal structure proportional damping coefficient of the first natural vibration mode. This is a column vector of modal coordinates.

6. The method for obtaining the structural modal forces of a rail vehicle system according to claim 5, characterized in that, The modal coordinate column vector The expression is: In the formula, This refers to the amplitude.

7. The method for obtaining the structural modal forces of a rail vehicle system according to claim 1, characterized in that, The suspension components include air springs, secondary vertical dampers, secondary lateral dampers, anti-hunting dampers, and traction rods.

8. A resonance control method for obtaining the structural modal forces of a rail vehicle system according to any one of claims 1-7, characterized in that, Includes the following steps: The contribution of each modal force to vehicle vibration is calculated, and the suspension system design is optimized to reduce the modal forces that contribute significantly to vehicle vibration, thereby reducing resonance and achieving resonance control.

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