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

Abstract

The invention relates to a railway vehicle system structure modal force acquisition method and a resonance control method. The modal force acquisition method comprises the following steps: constructing a system oscillatory differential equation; converting the system oscillatory differential equation to obtain a decoupling equation set about the modal force, and converting the decoupling equation set into a component form to obtain a general form of the modal force; and based on the general form of the modal force, according to the dynamic parameters of the railway vehicle system, determining the order of the modal force of the vehicle system, calculating the total ith-order modal force jointly acted on the vehicle body by all suspension elements in the railway vehicle system, and calculating the component form based on the dynamic parameters to obtain the final modal force. Compared with the prior art, the method has the advantages of clear principle, convenience in implementation, low cost and the like.

Description

Technical Field

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

[0002] With the increase of rail train operating mileage and the increase of running speed, train vibration has intensified, resulting in a decrease in train running stability. The main reasons include two aspects:

[0003] On the one hand, most train bodies currently adopt a lightweight design. The body design is a hollow aluminum welded structure. Compared with the traditional steel structure body, it can reduce the weight by about 40%, and at the same time reduce air resistance, thereby achieving the purpose of improving traction acceleration capability and reducing energy consumption. However, at the same time, the body made of this aluminum alloy material usually leads to insufficient structural rigidity and aggravated structural vibration.

[0004] On the other hand, although the lightweight design of the car body helps to reduce the axle weight, improve the wheel-rail interaction relationship of the vehicle and the service conditions of related components, the significant reduction in the car body stiffness leads to a decrease in the car body modal frequency, which is easy to approach the excitation frequency from other structures and stimulate the elastic mode of the car body, thereby aggravating the vibration of the car body. In more and more cases, it is found that the elastic vibration of the car body has become an important factor affecting the passenger riding comfort.

[0005] Patent CN106570264B discloses a method for quickly adjusting the exciting force in a pure modal test. In this method, an exciter is used to apply the exciting force, and the modal force is solved by solving the exciting force. The calculation process is complicated and difficult to implement. Summary of the invention

[0006] The purpose of the present invention is to provide a rail vehicle system structure modal force acquisition method and a resonance control method for improving the modal force calculation accuracy.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

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

[0009] Construct differential equations for system vibrations;

[0010] Transforming the vibration differential equation of the system to obtain a set of decoupled equations about the modal force, and transforming the set of decoupled equations into a component form to obtain a general form of the modal force;

[0011] Based on the general form of the modal force, according to the dynamic parameters of the rail vehicle system, the modal force order of the vehicle system is determined, the overall i-th order modal force of all suspension elements in the rail vehicle system acting on the vehicle body is calculated, and the component form is calculated based on the dynamic parameters to obtain the final modal force.

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

[0013]

[0014] Where M is the mass matrix, is the acceleration, u is the modal vector, e jωt is the complex coordinate expression of the periodic excitation force, K is the stiffness matrix, G is the structural damping matrix, j is the jth sampling point, and F is the set of external forces on the structure.

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

[0016] G=αM+βK

[0017] Where α and β are proportional coefficients.

[0018] Furthermore, the expression of the modal vector u is:

[0019]

[0020] In the formula, represents the set of i-th order mode shapes of each point, q i (i=1,2,…,n) are the modal coordinates of n modal vectors in the modal coordinate system, Φ is the modal vibration shape, and q is the modal coordinate column vector.

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

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

[0023]

[0024] The orthogonal relationships are:

[0025] Φ T MΦ=diag[m i ]

[0026] Φ T KΦ=diag[k i ]

[0027] Φ T GΦ=diag[αm i+βk i ]=diag[g i ]

[0028] Combining the orthogonal relationship, the decoupling equations for the modal force are obtained:

[0029]

[0030] In the formula, the orthogonal relationship represents the modal mass matrix, the modal primary stiffness matrix, and the modal structural proportional damping matrix, Φ T is the transpose of the vibration matrix, M is the mass matrix, Φ is the modal vibration, K is the stiffness matrix, G is the structural damping matrix, j is the jth sampling point, F is the set of external forces on the structure, e jωt is the complex coordinate expression of the periodic excitation force, diag represents the diagonal matrix, k i is the modal stiffness of the i-th order natural vibration mode, m i is the modal mass of the i-th order natural vibration mode, g i is the modal structural proportional damping coefficient of the i-th order natural vibration mode, and q is the modal coordinate column vector.

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

[0032] q=Qe jωt

[0033] Where Q is the amplitude.

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

[0035]

[0036] Order The above formula can be further expressed in component form as follows:

[0037]

[0038] In the formula, Q i represents the amplitude of the i-th modal coordinate, j is the j-th sampling point, F is the set of external forces on the structure, ω represents the excitation frequency, ω 0i represents the modal frequency of the i-th mode of the system, for The transpose of represents the set of i-th order mode shapes of each point, g i is the modal structural proportional damping coefficient of the i-th order natural vibration mode, m i is the modal mass of the i-th order natural vibration mode, is the overall i-th-order modal force acting on the vehicle body by all suspension components.

[0039] Furthermore, the calculation expression of the overall i-th order modal force of all the suspension elements acting on the vehicle body is:

[0040]

[0041] Where P i is the overall i-th order modal force, for The transpose of represents the set of i-th order modal vibration shapes of each point, F is the set of external forces on the structure, and F 悬挂元件x It represents the force amplitude of the x-th suspension element acting on the vehicle body, s represents the total number of suspension elements, and 0 represents the amplitude at the point where no force is applied.

[0042] Furthermore, the suspension elements include an air spring, a secondary vertical shock absorber, a secondary lateral shock absorber, an anti-snaking shock absorber and a traction rod.

[0043] This embodiment also provides a resonance control method according to the above-mentioned rail vehicle system structure modal force acquisition method, comprising the following steps:

[0044] Calculate the contribution of each modal force to the vehicle body vibration, optimize the suspension system design to reduce the modal force that contributes most to the vehicle body vibration, reduce resonance, and achieve resonance control process.

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

[0046] (1) The present invention maps and decomposes the forces acting on the vehicle body by the suspension components, effectively decoupling them into modal forces of various orders, and combines the system modal vibration to better calculate the system modal forces, thereby improving the accuracy of modal force calculation.

[0047] (2) The present invention performs modal force mapping decomposition on the external excitation force acting on the vehicle body based on the modal space, providing a theoretical basis for the vehicle body elastic resonance control measures, thereby improving the vehicle running stability and the vehicle riding comfort, and is suitable for the control of the elastic modal vibration of the high-speed EMU vehicle body.

[0048] (3) The present invention has clear principles, is easy to implement and has low cost. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0050] Figure 2 The overall modal forces of all suspension elements of the present invention acting together on the lateral direction of the vehicle body;

[0051] Figure 3 It is the overall modal forces of all orders acting on the vehicle body in the vertical direction by all the suspension elements of the present invention;

[0052] Figure 4 1 and 2 are the rhombus modal force contributions of the suspension elements of the present invention acting on the vehicle body, wherein (a) is the lateral rhombus modal force contribution, and (b) is the vertical rhombus modal force contribution. DETAILED DESCRIPTION

[0053] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope 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 force of a rail vehicle system. Figure 1 As shown, the method comprises the following steps:

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

[0057] Modal force refers to the force applied to each vibration mode after considering the vibration mode of the structure, which reflects the contribution of the excitation force to the modal excitation. By calculating the modal force, we can understand the influence of different modal forces on the structural response. At the same time, the modal force is the direct source of modal vibration. For an n-degree-of-freedom system with structural damping, the vibration differential equation is:

[0058]

[0059] Where M is the mass matrix, K is the stiffness matrix, and G is the structural damping matrix.

[0060] if

[0061] G=αM+βK (2)

[0062] This is called structural proportional damping.

[0063] According to the orthogonality of eigenvectors, n linearly independent eigenvectors Form a complete orthogonal basis of an n-dimensional vector space, which is called a modal space. For a real modal system, the modal space constructed with n modal vectors is a real linear space. Let the modal coordinates of the vector u in the physical coordinate system be q i (i=1,2,…,n), then

[0064]

[0065] Where q is the modal coordinate column vector and Φ is the modal vibration shape.

[0066] Substitute the coordinate transformation formula (3) into (1) and multiply Φ on the left T have to:

[0067]

[0068] in

[0069] Φ T MΦ=diag[m i ] (5)

[0070] Φ T KΦ=diag[k i ] (6)

[0071] Φ T GΦ=diag[αm i +βk i ]=diag[g i ] (7)

[0072] The above three equations represent the modal (primary) mass matrix, modal (primary) stiffness matrix, and modal structural proportional damping matrix. diag represents a diagonal matrix, k i is the modal (main) stiffness of the i-th order natural vibration mode, m i is the modal (primary) mass of the ith order natural vibration mode, g i is the modal structural proportional damping coefficient of the i-th order natural vibration mode.

[0073] Combining the orthogonal relations (5), (6), and (7), we get the decoupled equations:

[0074]

[0075] Without loss of generality, let the steady-state displacement response q = Qe jωt Substituting in:

[0076] diag[k i -ω 2 m i +jg i ]Q=Φ T F (9)

[0077] Write the above formula in its component form, then:

[0078]

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

[0080]

[0081] Where ω represents the excitation frequency, ω 0irepresents the modal frequency of the i-th mode of the system, Q i represents the amplitude of the i-th order modal coordinate, Represents the set of i-th order mode shapes at each point.

[0082] The motion equations of the physical space are decoupled by the modal vector. At the same time, the excitation force needs to be multiplied by the transpose of the vibration matrix on the left, and Φ T F is the modal force. It can be seen that the transpose of the vibration matrix Φ T Contains information about different vibration modes, and F represents the set of external forces on the structure.

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

[0084] Once the vehicle system dynamics parameters are determined, the modal parameter part of the denominator in equation (10) is a constant, so Q i It depends only on the numerator, that is, the total i-th modal force of all suspension elements acting on the vehicle body, defined as P i :

[0085]

[0086] In the formula, F 悬挂元件x represents the force amplitude of the x-th suspension element acting on the vehicle body, s represents the total number of suspension elements, and the amplitude of the point where no force is applied is 0.

[0087] The total i-th modal force P acting on the vehicle body by all suspension components i , is actually the superposition of the i-th order modal forces of the suspension components acting on the vehicle body. i When the minimum, Q i The corresponding value reaches the minimum, which also means that the vibration of this mode reaches the minimum.

[0088] S3. Analysis of modal force contribution acting on the rail vehicle system structure.

[0089] In order to more intuitively reflect the participation degree of a certain order modal force of the x-th suspension element acting on the vehicle body relative to the overall certain order modal force of all s suspension elements acting on the vehicle body, the energy of a certain order modal force of the x-th suspension element acting on the vehicle body is defined as:

[0090]

[0091] In the formula, h x (j) is the force amplitude of the jth sampling point of a certain modal force of the xth suspension element acting on the vehicle body, and K is the total number of sampling points.

[0092] Therefore, the modal force energy G acting on the vehicle body by the x-th suspension element isx The ratio of the total modal force energy of all s suspension elements acting on the vehicle body to a certain order η x Represents the modal force contribution of the suspension element acting on the vehicle body, which can be calculated as:

[0093]

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

[0095] 1. Extract the forces acting on the vehicle body by the air spring, secondary vertical shock absorber, secondary lateral shock absorber, anti-snaking shock absorber and traction rod in the dynamics software SIMPACK.

[0096] 2. Combined with the vehicle body modal vibration matrix information extracted by polycondensation calculation, the modal force of each suspension element acting on the vehicle body and the overall modal force of all suspension elements acting on the vehicle body are calculated, taking the empty spring as an example.

[0097] The modal force of the empty spring acting on the vehicle body is extracted by the rigid-flexible coupling dynamics model of the vehicle. The component values ​​of each order vibration mode vector at the connection position of the four empty springs on the vehicle body are extracted by the condensation calculation to calculate the lateral and vertical forces of all the empty springs acting on the vehicle body ( Figure 2 ) and vertical ( Figure 3 ) of the modal force.

[0098] It can be seen from the analysis and calculation results that the forces acting on the vehicle body by all air springs can be mapped and decomposed in the modal space, which can effectively decouple them into modal forces of various orders.

[0099] S3. Based on the modal force of each suspension element acting on the vehicle body, the magnitude and contribution of the modal force of each suspension element acting on the vehicle body are further analyzed.

[0100] This experiment obtained the following through analysis: Figure 4 The lateral and vertical diamond modal force contributions are shown in (a) and (b).

[0101] Example 2

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

[0103] Calculate the contribution of each modal force to the vehicle body vibration, optimize the suspension system design to reduce the modal force that contributes most to the vehicle body vibration, reduce resonance, and achieve resonance control process.

[0104] That is, under the premise that the position of the analysis point remains unchanged, that is, the component values ​​of the modal vibration vectors of each order at the analysis point remain unchanged, the factors affecting the elastic modal vibration of the vehicle body include the denominator m of the modal order. i (ω0 2 i -ω 2 )+jg i In addition, once the dynamic parameters of the vehicle system are determined, the part of the denominator about the modal parameters is fixed, so the modal vibration depends only on the numerator, that is, the modal force. That is, by optimizing the suspension component parameters, adjusting the position of the empty spring, and performing wheel repair, from the perspective of reducing the modal force that contributes most to the vehicle vibration, the optimization effect of the above measures on the modal force and modal vibration can be analyzed, thereby solving the problem of vehicle body elastic resonance.

[0105] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0106] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for obtaining structural modal force of a rail vehicle system, characterized in that: The following steps are involved: Construct differential equations for system vibrations; Transforming the vibration differential equation of the system to obtain a set of decoupled equations about the modal force, and transforming the set of decoupled equations into a component form to obtain a general form of the modal force; Based on the general form of the modal force, according to the dynamic parameters of the rail vehicle system, the modal force order of the vehicle system is determined, the overall i-th order modal force of all suspension elements in the rail vehicle system acting on the vehicle body is calculated, and the component form is calculated based on the dynamic parameters to obtain the final modal force.

2. A method for obtaining structural modal force of a rail vehicle system according to claim 1, characterized in that: The expression of the vibration differential equation of the system is: Where M is the mass matrix, is the acceleration, u is the modal vector, e jωt is the complex coordinate expression of the periodic excitation force, K is the stiffness matrix, G is the structural damping matrix, j is the jth sampling point, and F is the set of external forces on the structure.

3. A method for obtaining structural modal force of a rail vehicle system according to claim 2, characterized in that: The expression of the structural damping matrix G is: G=αM+βK Where α and β are proportional coefficients.

4. A method for obtaining structural modal force of a rail vehicle system according to claim 2, characterized in that: The expression of the modal vector u is: In the formula, represents the set of i-th order mode shapes of each point, q i (i=1,2,…,n) are the modal coordinates of n modal vectors in the modal coordinate system, Φ is the modal vibration shape, and q is the modal coordinate column vector.

5. A method for obtaining structural modal force of a rail vehicle system according to claim 1, characterized in that: The step of obtaining the decoupling equations for the modal force comprises: By multiplying the vibration differential equation of the system by the transpose of the vibration mode matrix on the left, we get: The orthogonal relationships are: F T MΦ=diag[m i ] Φ T kΦ=diag[k i ] F T GΦ=diag[αm i +βk i ]=diag[g i ] Combining the orthogonal relationship, the decoupling equations for the modal force are obtained: In the formula, the orthogonal relationship represents the modal mass matrix, the modal primary stiffness matrix, and the modal structural proportional damping matrix, Φ T is the transpose of the vibration matrix, M is the mass matrix, Φ is the modal vibration, K is the stiffness matrix, G is the structural damping matrix, j is the jth sampling point, F is the set of external forces on the structure, and e jωt is the complex coordinate expression of the periodic excitation force, diag represents the diagonal matrix, k i is the modal stiffness of the i-th order natural vibration mode, m i is the modal mass of the i-th order natural vibration mode, g i is the modal structural proportional damping coefficient of the i-th order natural vibration mode, and q is the modal coordinate column vector.

6. A method for obtaining structural modal force of a rail vehicle system according to claim 5, characterized in that: The expression of the modal coordinate column vector q is: q=Qe jωt Where Q is the amplitude.

7. A method for obtaining structural modal force of a rail vehicle system according to claim 1, characterized in that: The expression in component form is: make The above formula can be further expressed in component form as follows: In the formula, Q i represents the amplitude of the i-th modal coordinate, j is the j-th sampling point, F is the set of external forces on the structure, ω represents the excitation frequency, ω 0i represents the modal frequency of the i-th mode of the system, for The transpose of represents the set of i-th order mode shapes of each point, g i is the modal structural proportional damping coefficient of the i-th order natural vibration mode, m i is the modal mass of the i-th order natural vibration mode, is the overall i-th-order modal force acting on the vehicle body by all suspension components.

8. A method for obtaining structural modal force of a rail vehicle system according to claim 1, characterized in that: The calculation expression of the overall i-th order modal force acting on the vehicle body by all the suspension elements is: Where P i is the overall i-th order modal force, for The transpose of represents the set of i-th order modal vibration shapes of each point, F is the set of external forces on the structure, and F 悬挂元件x It represents the force amplitude of the x-th suspension element acting on the vehicle body, s represents the total number of suspension elements, and 0 represents the amplitude at the point where no force is applied.

9. A method for obtaining structural modal force of a rail vehicle system according to claim 1, characterized in that: The suspension elements include an air spring, a secondary vertical shock absorber, a secondary lateral shock absorber, an anti-snaking shock absorber and a traction rod.

10. A resonance control method for obtaining the structural modal force of a rail vehicle system according to any one of claims 1 to 9, characterized in that: The following steps are involved: Calculate the contribution of each modal force to the vehicle body vibration, optimize the suspension system design to reduce the modal force that contributes most to the vehicle body vibration, reduce resonance, and achieve resonance control process.

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