High-speed rail contact line fluctuation propagation speed calculation method based on analytical model

Abstract

The invention discloses a high-speed rail contact line fluctuation propagation velocity calculation method based on an analytical model, and the method specifically comprises the steps: firstly, determining a vertical motion differential equation of a contact line, and solving the differential equation of the contact line through a residue theorem; analyzing an exponential term of the solution of the contact line, determining the wavelength of the wave on the contact line, and obtaining the fluctuation propagation speed of the contact line according to the harmonic frequency and the corresponding wavelength; then establishing an analytical model of the infinitely long viscoelastic layer, and solving the analytical model to obtain the vertical displacement of the contact line; adjusting the damping value of the contact line, enabling the attenuation coefficient of the analytical model to be matched with the attenuation coefficient of the contact line, obtaining the damping value of the contact line, and solving the fluctuation propagation speed through damping; and finally, adjusting the harmonic frequency, calculating the damping values of the contact line under different frequencies, determining the main vibration frequency of pantograph-catenary coupling, and solving the fluctuation propagation speed of the contact line under the frequency. The method has higher calculation efficiency, and the calculation precision of the contact line fluctuation propagation speed is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of contact network wave behavior simulation, and in particular relates to a method for calculating the wave propagation speed of a high-speed railway contact line based on an analytical model. Background Art

[0002] Overhead contact network, commonly known as catenary, is a system that provides power to high-speed railway vehicles through sliding contact with the pantograph. Good dynamic performance of the pantograph is an important guarantee for the safe operation of high-speed trains. The fluctuation performance of the contact line is a key issue in the field of high-speed pantograph and catenary research, and the fluctuation speed is the main indicator to measure the fluctuation performance of the contact line.

[0003] At present, the generally accepted wave propagation velocity calculation formula comes from the European standard EN50119, which is completed on the basis of mathematical derivation, field tests and engineering experience. Zou Dong et al. used a set of non-contact photogrammetry devices to measure and verify the wave group velocity of the contact line. The results showed that the wave velocity obtained by the traditional wave propagation velocity calculation method was different from the test results. As an important influencing factor of the contact network dynamics, the contact line damping has not been considered in most studies on the calculation of wave propagation velocity. Liu Zhigang et al. considered the influence of air damping and revised the calculation method of the contact line wave propagation velocity. Since the air damping caused by static wind load is small, it will not have a significant impact on the calculation of the contact line wave propagation velocity. Park et al. analyzed the test signal of the contact network vibration, explored the dispersion problem of the wave on the contact network, and gave the relationship between the wave propagation velocity and the wave frequency on the contact network. Li Fuzhong et al. used numerical analysis methods to analyze the relationship between wavelength and wave propagation velocity, and proposed a method to improve the utilization rate of the contact network wave velocity.

[0004] In summary, in the study of high-speed railway contact line wave propagation velocity, most of the existing research focuses on analytical model calculation, numerical simulation and line test. However, the traditional contact line wave propagation velocity calculation method cannot complete the accurate calculation of the wave propagation velocity, and the finite element simulation method has the problem of low calculation efficiency. The physical test also faces the problem of field conditions and high test costs. Therefore, a new method for accurately and efficiently calculating the contact line wave propagation velocity is urgently needed. Summary of the invention

[0005] In view of the above problems, the present invention provides a method for calculating the wave propagation velocity of high-speed railway contact line based on an analytical model.

[0006] The present invention provides a method for calculating the wave propagation velocity of a high-speed railway contact line based on an analytical model. Based on the wave attenuation law and the contact network analytical model, the damping of the contact line is obtained, the influence of the contact line damping is considered, and the wave propagation law and residue theorem are used to complete the accurate calculation of the wave propagation velocity of the contact line. Specifically, the following steps are included:

[0007] Step 1: Determine the vertical motion differential equation of the contact line, as shown in formula (1):

[0008]

[0009] Where: μ c and c m They represent the mass and damping per unit length, T represents the contact line tension, and F 0 represents the contact force, δ represents the Dirac function, w represents the vertical displacement of the contact line, x represents the longitudinal position of the contact line, Ω represents the frequency, v represents the operating speed of the pantograph, t represents the time, and i represents the imaginary unit.

[0010] Step 2: Use the residue theorem to solve the differential equation of the contact line, and the result is shown in formula (2):

[0011]

[0012] in:

[0013]

[0014] μ represents the mass per unit length, and the subscripts c and c represent the contact line.

[0015] in:

[0016]

[0017] Step 3: Assuming that the operating speed of the pantograph is 0, the solution of the contact line is obtained, as shown in equation (5):

[0018]

[0019] Step 4: Analyze the exponential term of formula (5) and determine the wavelength of the wave on the contact line:

[0020]

[0021] in: represent The real part of .

[0022] According to the harmonic frequency and its corresponding wavelength, the wave propagation velocity of the contact line is obtained as:

[0023]

[0024] Step 5: Establish an analytical model of an infinitely long viscoelastic layer, complete the solution of the analytical model, and obtain the vertical displacement expression of the contact line:

[0025]

[0026] p and q represent positive and negative numbers respectively, and r refers to the pole that does not have the same sign as p or q in the formula. p represents the pole whose imaginary part is positive, k q Indicates the poles where the imaginary part is negative.

[0027] in:

[0028]

[0029] in:

[0030]

[0031] in:

[0032]

[0033] α and β refer to the proportional damping coefficients, Refers to the average stiffness of the analytical model.

[0034] Step 6: Determine the proportional attenuation coefficient in the contact line model as The wave will be in the positive x direction. Proportional attenuation, yes The imaginary part of k 1I is the proportional attenuation coefficient, k 1I It is k 1 The imaginary part of .

[0035] Step 7: Adjust the contact line damping value c m The size is adjusted so that the attenuation coefficient of the analytical model matches the attenuation coefficient of the contact line, the contact line damping value is obtained, and the damping is used to solve the wave propagation velocity.

[0036] Step 8: Adjust the harmonic frequency and repeat step 7 to calculate the damping value of the contact line at different frequencies.

[0037] Step 9: Determine the main vibration frequency of the bow-catenary coupling, and solve the contact line wave propagation velocity at this frequency based on the main vibration frequency of the bow-catenary coupling.

[0038] The beneficial technical effects of the present invention are:

[0039] The method for calculating the wave propagation velocity of the high-speed rail contact line proposed in the present invention adopts the contact network analytical model to complete the calculation of the wave propagation velocity of the contact line, which can avoid the field condition restrictions and high test costs faced by physical tests, and has higher calculation efficiency than finite element simulation. Compared with previous studies that ignored or roughly estimated damping, the present invention combines the analytical model with the wave attenuation theory to accurately solve the contact line damping at different frequencies. Compared with the traditional method for calculating the wave propagation velocity of the contact line, the calculation accuracy of the wave propagation velocity of the contact line is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a method for calculating the wave propagation velocity of a high-speed railway contact line based on an analytical model of the present invention.

[0041] Figure 2 These are the contact line wave velocity calculation results using the traditional wave propagation velocity calculation method and the wave propagation velocity calculation method proposed in this invention ((a) is the Beijing-Tianjin Line; (b) is EN50318:2018).

[0042] Figure 3 is the damping value of the contact line at different frequencies. Method 1 is the damping value obtained by analyzing the attenuation of the wave, and method 2 is the damping obtained using the proportional damping formula.

[0043] Figure 4 is the main vibration frequency of the bow-catenary coupling ((a) is the Beijing-Tianjin line; (b) is EN50318:2018).

[0044] Figure 5 It is the contact line displacement contour diagram ((a) is the Beijing-Tianjin Line; (b) is EN50318:2018). DETAILED DESCRIPTION

[0045] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] The embodiment uses the line data of the Beijing-Tianjin line and the standard data of EN50318:2018 to verify the proposed method for calculating the wave propagation velocity of the high-speed railway contact line based on the analytical model.

[0047] The process of the method for calculating the wave propagation velocity of high-speed railway contact line based on the analytical model of the present invention is as follows: Figure 1 As shown in the figure, based on the wave attenuation law and the contact network analytical model, the damping of the contact line is obtained, the influence of the contact line damping is considered, and the wave propagation law and residue theorem are used to complete the accurate calculation of the contact line wave propagation speed. Specifically, the following steps are included:

[0048] Step 1: Based on the nonlinear finite element theory, nonlinear cable and rod units are used to establish a three-dimensional model of the contact network. Combined with the three-dimensional mass pantograph model, the dynamic simulation of the pantograph network is realized. The data of EN50318:2018 is used to verify the effectiveness of the dynamic solution.

[0049] Step 2: Determine the vertical motion differential equation of the contact line, as shown in formula (1):

[0050]

[0051] Where: μ c and c m They represent the mass and damping per unit length, T represents the contact line tension, and F 0 represents the contact force, δ represents the Dirac function, w represents the vertical displacement of the contact line, x represents the longitudinal position of the contact line, Ω represents the frequency, v represents the operating speed of the pantograph, t represents the time, and i represents the imaginary unit.

[0052] Step 3: Use the residue theorem to solve the differential equation of the contact line, and the result is shown in formula (2):

[0053]

[0054] in:

[0055]

[0056] μ represents the mass per unit length, and the subscripts c and c represent the contact line.

[0057] in:

[0058]

[0059] Step 4: Assuming that the operating speed of the pantograph is 0, the solution of the contact line is obtained, as shown in equation (5):

[0060]

[0061] Step 5: Analyze the exponential term of formula (5) to determine the wavelength of the wave on the contact line:

[0062]

[0063] in: represent The real part of .

[0064] According to the harmonic frequency and its corresponding wavelength, the wave propagation velocity of the contact line is obtained as:

[0065]

[0066] The contact line wave propagation velocity obtained by the conventional contact line wave propagation velocity calculation method and the contact line wave propagation velocity calculation method proposed in the present invention is as follows: Figure 2 shown.

[0067] Step 6: Establish an analytical model of an infinitely long viscoelastic layer, complete the solution of the analytical model, and obtain the vertical displacement expression of the contact line:

[0068]

[0069] p and q represent positive and negative numbers respectively, r refers to the pole that does not have the same sign as p or q in the formula, k p represents the pole whose imaginary part is positive, k q Indicates the poles where the imaginary part is negative.

[0070] in:

[0071]

[0072] in:

[0073]

[0074] in:

[0075]

[0076] α and β refer to the proportional damping coefficients, Refers to the average stiffness of the analytical model.

[0077] Step 7: Determine the proportional attenuation coefficient in the contact line model as The wave will be in the positive x direction. Proportional attenuation, yes The imaginary part of k 1I is the proportional attenuation coefficient, k 1I It is k 1 The imaginary part of .

[0078] Step 8: Adjust the contact line damping value c m The size is adjusted so that the attenuation coefficient of the analytical model matches the attenuation coefficient of the contact line, the contact line damping value is obtained, and the damping is used to solve the wave propagation velocity.

[0079] Step 9: Adjust the harmonic frequency and repeat step 8 to calculate the damping value of the contact line at different frequencies, such as Figure 3 As shown in the figure, when the system frequency is small, the damping value obtained by method 1 is significantly greater than that by method 2.

[0080] Step 10: Using the model established in step 1, obtain the main vibration frequency of the bow-catenary coupling as follows: Figure 4As shown, the main vibration frequency of the Beijing-Tianjin line is 1.3Hz, and the main vibration frequency of EN50318:2018 is 0.9Hz.

[0081] Step 11: Use the obtained main vibration frequency of the bow-catenary coupling to calculate the contact line wave propagation velocity at this frequency, such as Figure 2 shown.

[0082] Step 12: Use the pantograph-catenary coupling model established in step 1 to obtain the contact line displacement contour map as shown in Figure 5 The slope in the contour plot is determined as the wave propagation velocity, and the average of the wave propagation velocities of the waves propagating forward and backward is taken as the measured value of the wave propagation velocity. The calculated and measured values ​​of the wave propagation velocity are shown in Table 1.

[0083] Table 1 Calculated and measured values ​​of wave propagation velocity in the embodiment

[0084]

[0085] The maximum relative error of the method proposed in the present invention is 2.71%, while the minimum relative error of the traditional calculation method is 7.05% and the maximum is 12.18%. In summary, compared with the traditional calculation method, the proposed method for calculating the wave propagation velocity of the high-speed rail contact line based on the analytical model has a smaller relative error and the obtained wave propagation velocity is more accurate.

Claims

1. A method for calculating the wave propagation velocity of high-speed railway contact line based on an analytical model, characterized in that: The following steps are involved: Step 1: Determine the vertical motion differential equation of the contact line, as shown in formula (1): Where: μ c and c m They represent the mass and damping per unit length, T represents the contact line tension, F0 represents the contact force, δ represents the Dirac function, w represents the vertical displacement of the contact line, x represents the longitudinal position of the contact line, Ω represents the frequency, v represents the operating speed of the pantograph, t represents the time, and i represents the imaginary unit; Step 2: Use the residue theorem to solve the differential equation of the contact line, and the result is shown in formula (2): in: μ represents the mass per unit length, and the subscripts c and c represent the contact line; in: Step 3: Assuming that the operating speed of the pantograph is 0, the solution of the contact line is obtained, as shown in equation (5): Step 4: Analyze the exponential term of formula (5) and determine the wavelength of the wave on the contact line: in: represent The real part of According to the harmonic frequency and its corresponding wavelength, the wave propagation velocity of the contact line is obtained as: Step 5: Establish an analytical model of an infinitely long viscoelastic layer, complete the solution of the analytical model, and obtain the vertical displacement expression of the contact line: p and q represent positive and negative numbers respectively, r refers to the pole that does not have the same sign as p or q in the formula, k p represents the pole whose imaginary part is positive, k q represents the poles where the imaginary part is negative; in: in: in: α and β refer to the proportional damping coefficients, Refers to the average stiffness of the analytical model; Step 6: Determine the proportional attenuation coefficient in the contact line model as The wave will be in the positive x direction. Proportional attenuation, yes The imaginary part of k 1I is the proportional attenuation coefficient, k 1I is the imaginary part of k1; Step 7: Adjust the contact line damping value c m The size is adjusted so that the attenuation coefficient of the analytical model matches the attenuation coefficient of the contact line, the contact line damping value is obtained, and the damping is used to solve the wave propagation velocity; Step 8: Adjust the harmonic frequency, repeat step 7, and calculate the damping value of the contact line at different frequencies; Step 9: Determine the main vibration frequency of the bow-catenary coupling, and solve the contact line wave propagation velocity at this frequency based on the main vibration frequency of the bow-catenary coupling.

Images