Calculation method of the conductor height of the intermediate joint of rigid catenary based on the absolute node coordinate method

Abstract

The present invention discloses a method for calculating the height conductance of the middle joint of a rigid contact network based on an absolute node coordinate method, specifically: according to the design parameters of the rigid contact network, a finite element model of the rigid contact network without the middle joint is established by using an absolute node coordinate beam unit and a spring unit; according to the arrangement position of the middle joint along the line, the additional gravity load vector caused by the middle joint is calculated; the rigid contact network static equilibrium equation is solved by using the Newton iteration method to obtain an accurate rigid contact network height conductance curve; and the height conductance at the middle joint is extracted. The present invention can accurately solve the rigid contact network height conductance curve considering the middle joint, and can obtain the accurate value of the height conductance at the middle joint, providing an accurate numerical calculation method for the rigid contact network morphology calculation.

Description

Technical Field

[0001] The invention belongs to the technical field of rigid contact network simulation, and in particular relates to a method for calculating the height of a rigid contact network intermediate joint based on an absolute node coordinate method. Background Art

[0002] The rigid contact network busbar is generally 12m long, and the busbars are connected by intermediate joints. Compared with other ordinary sections, there is extra mass at the intermediate joint. Under the action of gravity, the rigid contact network may have extra sag here. Limited by the high cost of line trial hanging tests, it is impossible to conduct large-scale trial hanging tests to evaluate the change of the intermediate joint height and the rigid contact network height. In the field of dynamic and static performance research of rigid contact networks, numerical simulation has always been the mainstream research method. The absolute nodal coordinate method (ANCF) was proposed by Shabana et al. (AA. Shabana. An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. No. MBS96-1-UIC, 1996.) to deal with large rotation and large deformation problems of flexible bodies. This method introduces node slope coordinates as node degrees of freedom. The generalized mass matrix of the established multi-body dynamics equation is a constant matrix, which does not contain Coriolis and centrifugal inertia terms, and can accurately describe the rigid body motion of the structure. L. Chen et al. (Chen L, Liu Z, Zhang J, Hu Z. Influence of key parameters on high speed overhead conductor rail and pantograph system. In: Klomp M., Bruzelius F., Nielsen J., Hillemyr A. (Eds.) Advances in Dynamics of Vehicles on Roads and Tracks. IAVSD 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https: / / doi.org / 10.1007 / 978-3-030-38077-9_25.) established a finite element model of the general section of the rigid contact network using the absolute node coordinate method, and performed a dynamic simulation of the pantograph, but did not consider the problem of conductor height changes caused by the intermediate joint. Summary of the invention

[0003] In order to accurately calculate the height conduction curve of the rigid contact network after the introduction of the intermediate joint and the height conduction value at the intermediate joint, the present invention provides a method for calculating the height conduction of the intermediate joint of the rigid contact network based on the absolute node coordinate method.

[0004] A method for calculating the height of a rigid contact network intermediate joint based on an absolute node coordinate method of the present invention is characterized by comprising the following steps:

[0005] Step 1: According to the design parameters of the rigid contact network, the finite element model of the rigid contact network without the intermediate joint is established using the absolute node coordinate beam unit and the spring unit.

[0006] S11: According to the actual layout space of the rigid contact network, the ANCF beam unit is used to discretize the rigid contact network busbar and contact wire, and the spring unit is used to discretize the suspension structure. According to the unit connection relationship, the model stiffness matrix K and tangent stiffness matrix K of the rigid contact network without the intermediate joint are assembled. T .

[0007] S12: Gravity load vector P0 when assembling rigid contact network without intermediate joints.

[0008] Step 2: Calculate the additional gravity load vector caused by the intermediate joint according to the position of the intermediate joint along the line.

[0009] S21: According to the arrangement position of the intermediate joint along the line, determine the unit where the intermediate joint is located in the model.

[0010] S22: Calculate the additional gravity load caused by the intermediate joints one by one. The calculation method is:

[0011]

[0012] Among them, P s is the gravity load vector caused by a single intermediate joint, m s is the mass of a single intermediate joint, g is the acceleration due to gravity, is the transpose of the shape function of the intermediate joint at its location on the ANCF unit.

[0013] S23: According to the unit position of the intermediate joint in the model, the additional gravity load caused by the intermediate joint is assembled one by one into the gravity load vector P0 without the intermediate joint, so as to obtain the complete load vector P of the rigid contact network.

[0014] Step 3: Use Newton iteration method to solve the rigid contact network static equilibrium equation and obtain accurate rigid contact network conductivity curve.

[0015] S31: Construct the static balance incremental equation of the rigid contact network system including the intermediate joint, as follows

[0016] K T，i Δe i =PQ i (2)

[0017] Where Δe is the system coordinate increment, Q is the system elastic internal force vector, and i is the Newton iteration step index.

[0018] S32: According to the constraints on the rigid overhead wire suspension structure, delete K T Replace the rows and columns in P and Q that correspond to the constrained degrees of freedom, and delete the rows in P and Q that correspond to the constrained degrees of freedom.

[0019] S33: Calculate Δe according to formula (2) i , to determine whether the convergence condition max(Δe i )≤c, c is the convergence tolerance, if the convergence condition is met, then output e i , complete the solution and exit; otherwise, go to step S34.

[0020] S34: Calculate e i+1 =e i +Δe i , and update the Newton iteration index i, and update the rigid contact network system tangent stiffness matrix K according to the updated system coordinates T，i and the system elastic internal force Q i , and return to step S32.

[0021] S35: The vertical coordinates of each node in the calculation results can be extracted to obtain the rigid contact network height curve considering the intermediate joint.

[0022] Step 4: Extract the height guide at the middle joint.

[0023] S41: Determine the unit where the intermediate joint is located according to its position along the line.

[0024] S42: Calculate the rigid contact network conductor height at the intermediate joints one by one. The calculation formula is:

[0025] H=S s ·e s (3)

[0026] Among them, S s is the shape function of the intermediate joint at the location on the ANCF unit, e s is the coordinate vector of the ANCF unit where the intermediate joint is located.

[0027] The beneficial technical effects of the present invention are:

[0028] 1. The present invention can accurately solve the rigid contact network conductivity curve considering the intermediate joint;

[0029] 2. The present invention can accurately solve the conductance value at the middle joint. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a schematic diagram of the arrangement of intermediate joints on the rigid contact network in Example 1 of the present invention.

[0031] Figure 2 This is a schematic diagram of the arrangement of intermediate joints on the rigid contact network in Example 2 of the present invention.

[0032] Figure 3 This is the rigid contact network conductivity curve obtained in Example 1 of the present invention.

[0033] Figure 4 This is the rigid contact network conductivity curve obtained in Example 2 of the present invention. DETAILED DESCRIPTION

[0034] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] In both embodiments, a straight-line rigid contact network with one anchor section is used, and the busbars are arranged in a sinusoidal manner along the line. The calculation formula for the pull-out value is:

[0036]

[0037] Among them, A p is the maximum pull-out value, l is the position along the line, and λ is the wavelength of the sinusoidal arrangement. The specific parameters of the rigid contact network in the two embodiments are the same, as shown in Table 1.

[0038] Table 1 Parameters of rigid contact network in the embodiment

[0039] parameter value parameter value Span(m) 8 Busbar-contact line density (kg / m) 7.3 Number of spans 30 Suspension spring X-axis stiffness (N / m) 1E7 Maximum pull-out value (m) 0.2 Suspension spring Y-axis stiffness (N / m) 1E7 Pull-out value arrangement wavelength (m) 160 Suspension spring Z-axis stiffness (N / m) 1E7 Busbar-contact line tensile stiffness (N) 1.68E8 Equivalent mass of suspension device (kg) 10 Busbar-contact line bending stiffness () 2.87E5 Middle joint mass (kg) 2.9

[0040] The position of the intermediate joint in Example 1 is as follows Figure 1 As shown in Table 2, the position of the intermediate joint in Example 2 is as follows Figure 2 And as shown in Table 3.

[0041] Table 2 Location of intermediate joints along the line in Example 1

[0042] serial number 1 2 3 4 5 6 7 8 9 10 Position along the line (m) 12 24 36 48 60 72 84 96 108 120 serial number 11 12 13 14 15 16 17 18 19 -- Position along the line (m) 132 144 156 168 180 192 204 216 228 --

[0043] Table 3 Positions of intermediate joints along the line in Example 2

[0044]

[0045]

[0046] The specific implementation process of the two embodiments is the same, and the specific implementation process is as follows:

[0047] Step 1: According to the rigid contact network parameters in Table 1, the finite element model of the rigid contact network without the intermediate joint is established using the absolute node coordinate beam unit and the spring unit. The specific implementation steps are as follows:

[0048] S11: According to the rigid contact network parameters, the rigid contact network busbar and contact wire are discretized using ANCF beam units, the suspension structure is discretized using spring units, and the model stiffness matrix K and tangent stiffness matrix K of the rigid contact network without intermediate joints are assembled according to the unit connection relationship. T The stiffness matrix of the ANCF element is

[0049] K A =K l +K t (5)

[0050] in

[0051]

[0052]

[0053] Where E is Young's elastic modulus, A0 is the cross-sectional area of ​​the ANCF beam unit, I is the section moment of inertia of the ANCF beam unit, ε is the axial strain of the beam unit, and L0 is the original length of the unit.

[0054] The spring element stiffness matrix is

[0055]

[0056] where k x , k y , k z They are the stiffness coefficients of the spring unit in the three directions of X, Y and Z. The tangent stiffness matrix of the spring unit is the same as its own stiffness matrix.

[0057] The calculation formula of the tangent stiffness matrix of the ANCF element is:

[0058]

[0059] Where e A is the ANCF unit coordinate vector.

[0060] S12: Gravity load vector P0 when assembling rigid contact network without intermediate joints. The calculation formula for the node load caused by gravity on the busbar and contact line is:

[0061]

[0062] Where g is the gravity constant, ρ is the material density, A is the cross-sectional area of ​​the busbar contact line, L0 is the original length of the unit, and S is the ANCF unit type function matrix, which is in the form of

[0063] S=[(1-3ξ 2 +2ξ 3 )I3 L0(ξ-2ξ 2 +ξ 3 )I3 (3ξ 2 -2ξ 3 )I 3 L0(ξ 3 -ξ 2 )I3] (11)

[0064] Where I3 is the third-order unit matrix, x is the distance between the suspension point and the node on the unit. The mass of the suspension device is equivalent to a concentrated mass point, and its gravity equivalent load is

[0065]

[0066] In the formula, is the transpose of the shape function of the location of the suspension anchor point on the ANCF unit, m h is the equivalent mass of the suspension device, and g is the acceleration due to gravity.

[0067] Step 2: Calculate the additional gravity load vector caused by the intermediate joint according to the position of the intermediate joint along the line shown in Table 2. The specific implementation method is:

[0068] S21: judging the unit where the intermediate joint is located in the model according to the arrangement position of the intermediate joint along the line;

[0069] S22: Calculate the additional gravity load caused by the intermediate joints one by one, and the calculation formula is

[0070]

[0071] Among them, P s is the gravity load vector caused by a single intermediate joint, m s is the mass of a single intermediate joint, g is the acceleration due to gravity, is the transpose of the shape function of the intermediate joint at the position on the ANCF unit, and its calculation method is shown in formula (11).

[0072] S23: According to the unit position of the intermediate joint in the model, the additional gravity load caused by the intermediate joint is assembled one by one into the gravity load vector without the intermediate joint obtained in S12 to obtain the complete load vector P of the rigid contact network.

[0073] Step 3: Use Newton iteration method to solve the rigid contact network static balance equation and obtain accurate rigid contact network conductivity curve. The specific implementation steps are as follows:

[0074] S31: Construct the static balance incremental equation of the rigid contact network system including the intermediate joint, as follows

[0075] K T，i Δe i =PQ i (14)

[0076] Where Δe is the system coordinate increment, Q is the system elastic internal force vector, and i is the Newton iteration step index.

[0077] S32: According to the constraints on the rigid overhead wire suspension structure, delete K T Delete the rows and columns corresponding to the constrained degrees of freedom in P and Q;

[0078] S33: Calculate Δe according to formula (2) i , to determine whether the convergence condition max(Δe i )≤c, c is the convergence tolerance. If the convergence condition is met, then output e i , complete the solution and exit; otherwise, go to step S34.

[0079] S34: Calculate e i+1 =e i +Δe i , Update the Newton iteration index i. According to the updated system coordinates, update the rigid contact network system tangent stiffness matrix K T，i and the system elastic internal force Q i , and return to step S32.

[0080] S35: The vertical coordinates of each node in the calculation results can be extracted to obtain the rigid contact network height curve considering the intermediate joint.

[0081] Step 4: Extract the height of the middle joint. The specific implementation method is:

[0082] S41: judging the unit where the middle joint is located according to the position of the middle joint along the line;

[0083] S42: Calculate the rigid contact network conductor height at the intermediate joints one by one. The calculation formula is:

[0084] H=S s ·e s (15)

[0085] Among them, S s is the shape function of the intermediate joint at the location on the ANCF unit, e s is the coordinate vector of the ANCF unit where the intermediate joint is located.

[0086] The rigid contact network conductivity curve obtained in Example 1 is as follows Figure 3The calculation results of the height of each intermediate joint are shown in Table 4.

[0087] Table 4 Conductivity of each intermediate joint obtained in Example 1

[0088] serial number 1 2 3 4 5 6 7 8 9 10 Position along the line (m) 12 24 36 48 60 72 84 96 108 120 Conductive height (m) 5.29782 5.3 5.29680 5.3 5.29681 5.3 5.29681 5.3 5.29681 5.3 serial number 11 12 13 14 15 16 17 18 19 -- Position along the line (m) 132 144 156 168 180 192 204 216 228 -- Conductive height (m) 5.29681 5.3 5.29681 5.3 5.29681 5.3 5.29680 5.3 5.29782 --

[0089] The rigid contact network conductivity curve obtained in Example 2 is as follows Figure 4 The calculation results of the height of each intermediate joint are shown in Table 5.

[0090] Table 5 Conductivity of each intermediate joint obtained in Example 2

[0091] serial number 1 2 3 4 5 6 7 8 Position along the line (m) 10 20 30 40 50 60 70 80 Conductive height (m) 5.29928 5.29671 5.29834 5.3 5.29830 5.29698 5.29830 5.3 serial number 9 10 11 12 13 14 15 16 Position along the line (m) 90 100 110 120 130 140 150 160 Conductive height (m) 5.29830 5.29698 5.29830 5.3 5.29830 5.29698 5.29830 5.3 serial number 17 18 19 20 21 22 23 -- Position along the line (m) 170 180 190 200 210 220 230 -- Conductive height (m) 5.29830 5.29698 5.29830 5.3 5.29834 5.29671 5.29928 --

[0092] Both embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation processes are given, but the protection scope of the present invention is not limited to these two embodiments.

Claims

1. A method for calculating the height of the intermediate joint of a rigid contact network based on the absolute node coordinate method, characterized in that: The following steps are involved: Step 1: According to the design parameters of the rigid contact network, a finite element model of the rigid contact network without intermediate joints is established using absolute node coordinate beam units and spring units; Step 2: Calculate the additional gravity load vector caused by the intermediate joint according to the arrangement position of the intermediate joint along the line; S21: judging the unit where the intermediate joint is located in the model according to the arrangement position of the intermediate joint along the line; S22: Calculate the additional gravity load caused by the intermediate joints one by one. The calculation method is: Among them, P s is the gravity load vector caused by a single intermediate joint, m s is the mass of a single intermediate joint, g is the acceleration due to gravity, is the transpose of the shape function of the intermediate joint at the location on the ANCF unit; S23: according to the unit position of the intermediate joint in the model, the additional gravity load caused by the intermediate joint is assembled one by one into the gravity load vector P0 without the intermediate joint, so as to obtain the complete load vector P of the rigid contact network; Step 3: Use Newton iteration method to solve the rigid contact network static balance equation and obtain accurate rigid contact network conductor height curve; S31: Construct the static balance incremental equation of the rigid contact network system including the intermediate joint as follows: K T,i Δei=P-Qi(2)where Δe is the system coordinate increment, Q is the system elastic internal force vector, and i is the Newton iteration step index; S32: According to the constraints on the rigid catenary suspension structure, delete the tangent stiffness matrix K T Delete the rows and columns corresponding to the constrained degrees of freedom in P and Q; S33: Calculate Δe according to formula (2) i , to determine whether the convergence condition max(Δe i )≤c, c is the convergence tolerance, if the convergence condition is met, then output e i , complete the solution and exit; otherwise, go to step S34; S34: Calculate e i+1 =e i +Δe i , and update the Newton iteration index i, and update the rigid contact network system tangent stiffness matrix K according to the updated system coordinates T ,i and the system elastic internal force Qi, and return to step S32; S35: extracting the vertical coordinates of each node in the calculation result can obtain the rigid contact network height curve considering the intermediate joint; Step 4: Extract the height guide at the middle joint.

2. The method for calculating the height of the intermediate joint of a rigid contact network based on the absolute node coordinate method according to claim 1 is characterized in that: The step 4 is specifically as follows: S41: judging the unit where the middle joint is located according to the position of the middle joint along the line; S42: Calculate the rigid contact network conductor height at the intermediate joints one by one. The calculation formula is: H=S s ·e s (3) Among them, S s is the shape function of the intermediate joint at the location on the ANCF unit, e s is the coordinate vector of the ANCF unit where the intermediate joint is located.

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