A tension control method for parallel steel strand cables based on iterative backstepping

Abstract

The present invention provides a parallel steel strand cable tensioning control method based on iterative backstepping, which obtains the initial tensioning force vector of each steel strand by calculation; and obtains the first tensioning force vector by forward calculation according to the tensioning sequence. i After the steel strands are tensioned, the distance between the main beam anchor point and the main tower anchor point and the horizontal angle between the two points are calculated; the reduction in cable force of the remaining tensioned steel strands caused by the tensioning of each steel strand is calculated; the cable force difference vector is calculated between the cable force value vector and the average cable force; the tensioning force vector of each steel strand is calculated again according to the inverse method; when the cable force difference vector meets the set iterative convergence criterion, the final steel strand tensioning force vector can be obtained, which takes into account the influence of the deformation caused by the tensioning of each steel strand on the initial length and inclination, and determines the construction tension of each steel strand through the iterative inverse method, ensuring that the cable force of the entire bundle reaches the target value after the tensioning of multiple parallel steel strands is completed, and ensuring the uniformity of the steel strand tension in the cable body.

Description

Technical Field

[0001] The invention belongs to a control method for cable tensioning, involves a back-calculation method, an iteration method, a cable force calculation method and the like, and is applied to the tensioning construction control of parallel steel strand cables. Background Art

[0002] Most stay cables or cable-stayed cables in civil engineering use multiple parallel steel strands as the cable body, and the main construction method is to tension each strand one by one. However, the tensioning construction requires ensuring the uniformity of the tension of each steel strand and the accuracy of the tension of the entire cable bundle after all the steel strands in the cable body are tensioned. Therefore, it is necessary to accurately control the tensioning force for the parallel steel strand cable tensioning construction.

[0003] In the past, the reverse method was mostly used to calculate the tension of multiple steel strands in the cable body through backward calculation. However, this method assumes that the initial length and initial inclination of each steel strand are the same constants during the calculation, and does not consider the impact of the tensioning deformation of each steel strand on the initial length and inclination, which will lead to certain errors in the calculated construction tension. Summary of the Invention

[0004] The present invention aims to invent a parallel steel strand cable tensioning control method based on iterative backstepping. Through the iterative backstepping method, the influence of the different initial lengths and initial inclinations of each steel strand is taken into account, and the construction tensioning force of each steel strand is calculated so that the cable force of the entire bundle reaches the target value.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] A parallel steel strand cable tensioning control method based on iterative backstepping includes:

[0007] Step 1: Take the initial length L and initial horizontal inclination α of the first steel strand as the initial length and horizontal inclination of each steel strand and calculate the initial tension force vector [X 0 ];

[0008] Step 2: Take the initial length L and initial horizontal inclination angle α of the first strand as the distance L1 between the main beam anchor point and the main tower anchor point and the initial value α1 of the horizontal inclination angle of the line connecting the two points, L1 = L; α1 = α, and use the tension force vector [X 0 ], the distance L between the anchor point of the main beam and the anchor point of the main tower after the i-th steel strand is tensioned is calculated according to the tensioning sequence method. i+1 , the horizontal angle α of the line connecting the two points is obtained by calculation i+1 , and are used as the initial length L of the i+1th strand i+1 and the initial horizontal inclination angle α i+1 ;

[0009] Step 3: The initial length of each steel strand calculated in step 2 is [L] = {L1, L2, L3, ... L i} and horizontal inclination [α] = {α1, α2, α3, ... α i}, calculate the reduction in cable force of the remaining tensioned steel strands caused by the tensioning of each steel strand [ΔX];

[0010] Step 4: Obtain the cable force vector [F] of each steel strand after the last steel strand is tensioned by forward calculation, calculate the cable force difference vector [ΔF] between the cable force vector [F] and the average cable force Fa, and use the cable force difference vector [ΔF] as the convergence residual;

[0011] Step 5: Using the initial length [L] and horizontal inclination angle [α] of each steel strand calculated in step 2 as calculation parameters, calculate the tension vector [X] of each steel strand again according to the reverse calculation method described in step 1. 1 ];

[0012] Step 6: Use the tensile force vector [X 1 ] to perform forward calculation and repeat steps 2 to 5 until the cable force difference vector [ΔF] meets the set iterative convergence criterion, and the tension force vector [X m ].

[0013] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative back-stepping, in step 1, the back-stepping method is calculated by formulas 1 to 4 to calculate the tensioning force vector [X 0 ],

[0014] X n =F a =F / n Formula 1

[0015] X n-1 =F a +Δx n Formula 2

[0016]

[0017]

[0018] Where: X n -The tension of the nth strand, i.e. the tension of the last strand; X n-1 - the tension of the n-1th strand; F a - average cable tension; F - cable tension, i.e. the sum of all strand tensions; n - the total number of strands in the cable, which is a natural number greater than 1; Δln -The length change caused by the tensioning of the nth strand; Δx n - the reduction in the tension of the remaining steel strands caused by the tensioning of the nth steel strand; [X 0 ]-tension force vector of steel strand; X1 0 - Tensile force of the first strand; X n 0 - the tension of the nth steel strand; L- the initial length of the steel strand; E- the elastic modulus of the steel strand; A- the cross-sectional area of ​​the steel strand.

[0019] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 2, the distance L between the main beam anchor point and the main tower anchor point after the i-th steel strand is tensioned is calculated by the forward method according to the tensioning sequence using formula 5. i+1 , the horizontal angle α between the two points is calculated by formula 6 i+1 ,

[0020]

[0021]

[0022] Where: L i - the initial length of the i-th strand; α i - horizontal inclination angle of the i-th steel strand; k x - longitudinal stiffness of the main beam; k z - Vertical stiffness of main beam; k t - Vertical stiffness of the main tower.

[0023] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 3, the reduction value [ΔX] of the cable force of the remaining tensioned steel strands caused by the tensioning of each steel strand is calculated according to formulas 7 to 9.

[0024] Δl i =L i -L i+1 Formula 7

[0025]

[0026]

[0027] Where: Δl i - length change of the i-th strand caused by tensioning; Δx ij - the reduction in tension of the j-th steel strand caused by the tensioning of the i-th steel strand; [ΔX] - the steel strand tension reduction matrix, which is a lower triangular matrix with diagonal elements Δx nn Both are 0.

[0028] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 4, the cable force value vector [F] of each steel strand after the last steel strand is tensioned is calculated by forward calculation using formula 10, the cable force difference vector [ΔF] between the cable force value vector [F] and the average cable force Fa is calculated using formula 11, and the cable force difference vector [ΔF] is used as the convergence residual;

[0029] [F] = sum([ΔX], 1) + [X 0 ] Formula 10

[0030] Where sum([ΔX], 1) represents the sum of column vectors;

[0031] [ΔF]=[F]-F a Formula 11.

[0032] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, the iterative convergence criterion is that the cable force difference is less than 0.001.

[0033] It can be seen from the technical solutions disclosed above that, compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] The parallel steel strand cable tensioning control method based on iterative back-calculation provided by the present invention takes into account the influence of the deformation caused by tensioning each steel strand on the initial length and inclination, and determines the construction tensioning force of each steel strand through the iterative back-calculation method, ensuring that the tension of the entire bundle of cables reaches the target value after the tensioning of multiple parallel steel strands is completed, thereby ensuring the uniformity of the steel strand tension within the cable body. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of cable length change.

[0036] In the figure: 1-main tower, 2-main beam, 3-steel strand before tensioning, 4-steel strand after tensioning. DETAILED DESCRIPTION

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following examples, combined with the accompanying drawings, will provide a detailed description of the technical content and features of the present invention. It should be noted that the drawings are all in a very simplified form and are not precisely proportioned, and are only used to conveniently and clearly assist in illustrating the purpose of the embodiments of the present invention. For ease of description, the "upper" and "lower" described below are consistent with the upper and lower directions in the accompanying drawings, but this does not constitute a limitation of the technical solution of the present invention.

[0038] See also Figure 1In the figure, 1 is the main tower, 2 is the main beam, 3 is the steel strand before tensioning, and 4 is the steel strand after tensioning. This embodiment discloses a parallel steel strand cable tensioning control method based on iterative backstepping, including:

[0039] Step 1: Take the initial length L and initial horizontal inclination α of the first steel strand as the initial length and horizontal inclination of each steel strand and calculate the initial tension force vector [X 0 ];

[0040] Step 2: Take the initial length L and initial horizontal inclination angle α of the first strand as the distance L1 between the anchor point of the main beam 2 and the anchor point of the main tower 1 and the initial value α1 of the horizontal inclination angle of the line connecting the two points, L1 = L; α1 = α, and use the tension force vector [X 0 ], the distance L between the anchor point of the main beam and the anchor point of the main tower after the i-th steel strand is tensioned is calculated according to the tensioning sequence method. i+1 The horizontal angle α between the two connecting lines (i.e. the connecting line between the anchor point of the main beam and the anchor point of the main tower after the i-th steel strand is tensioned) is obtained by calculation. i+1 , and are used as the initial length L of the i+1th strand i+1 and the initial horizontal inclination angle α i+1 ;

[0041] Step 3: The initial length of each steel strand calculated in step 2 is [L] = {L1, L2, L3, ... L i} and horizontal inclination [α] = {α1, α2, α3, ... α i}, calculate the reduction in cable force of the remaining tensioned steel strands caused by the tensioning of each steel strand [ΔX];

[0042] Step 4: Obtain the cable force vector [F] of each steel strand after the last steel strand is tensioned by forward calculation, and calculate the cable force vector [F] and the average cable force F a The cable force difference vector [ΔF] is calculated and the cable force difference vector [ΔF] is used as the convergence residual;

[0043] Step 5: Using the initial length [L] and horizontal inclination angle [α] of each steel strand calculated in step 2 as calculation parameters, calculate the tension vector [X] of each steel strand again according to the reverse calculation method described in step 1. 1 ];

[0044] Step 6: Use the tensile force vector [X 1 ] to perform forward calculation and repeat steps 2 to 5 until the cable force difference vector [ΔF] meets the set iterative convergence criterion, and then the accurate steel strand tension force vector [X m ].

[0045] The parallel steel strand cable tensioning control method based on iterative back-calculation provided by the present invention takes into account the influence of the deformation caused by tensioning each steel strand on the initial length and inclination, and determines the construction tensioning force of each steel strand through the iterative back-calculation method, ensuring that the tension of the entire bundle of cables reaches the target value after the tensioning of multiple parallel steel strands is completed, thereby ensuring the uniformity of the steel strand tension within the cable body.

[0046] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative back-stepping, in step 1, the back-stepping method is calculated by formulas 1 to 4 to calculate the tensioning force vector [X 0 ],

[0047] X n =F a =F / n Formula 3

[0048] X n-1 =F a +Δx n Formula 4

[0049]

[0050]

[0051] Where: X n -The tension of the nth strand, i.e. the tension of the last strand; X n-1 - the tension of the n-1th strand; F a - average cable tension; F - cable tension, i.e. the sum of all strand tensions; n - the total number of strands in the cable, which is a natural number greater than 1; Δl n -The length change caused by the tensioning of the nth strand; Δx n - the reduction in the tension of the remaining steel strands caused by the tensioning of the nth steel strand; [X 0 ]-tension force vector of steel strand; X1 0 - Tensile force of the first strand; X n 0 - the tension of the nth steel strand; L- the initial length of the steel strand; E- the elastic modulus of the steel strand; A- the cross-sectional area of ​​the steel strand.

[0052] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 2, the distance L between the main beam anchor point and the main tower anchor point after the i-th steel strand is tensioned is calculated by the forward method according to the tensioning sequence using formula 5. i+1 The horizontal angle α between the two points (i.e., the line connecting the anchor point of the main beam and the anchor point of the main tower after the i-th steel strand is tensioned) is calculated by formula 6. i+1 ,

[0053]

[0054]

[0055] Where: L i - the initial length of the i-th strand; α i - horizontal inclination angle of the i-th steel strand; k x - longitudinal stiffness of the main beam; k z - Vertical stiffness of main beam; k t - Vertical stiffness of the main tower.

[0056] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 3, the reduction value [ΔX] of the cable force of the remaining tensioned steel strands caused by the tensioning of each steel strand is calculated according to formulas 7 to 9.

[0057] Δl i =L i -L i+1 Formula 7

[0058]

[0059]

[0060] Where: Δl i - length change of the i-th strand caused by tensioning; Δx ij - the reduction in tension of the j-th steel strand caused by the tensioning of the i-th steel strand; [ΔX] - the steel strand tension reduction matrix, which is a lower triangular matrix with diagonal elements Δx nn Both are 0.

[0061] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, in step 4, the cable force value vector [F] of each steel strand after the last steel strand is tensioned is calculated by forward calculation using formula 10, and the cable force value vector [F] and the average cable force F are calculated using formula 11. a The cable force difference vector [ΔF] is calculated and the cable force difference vector [ΔF] is used as the convergence residual;

[0062] [F] = sum([ΔX], 1) + [X 0 ] Formula 10

[0063] Where sum([ΔX], 1) represents the sum of column vectors;

[0064] [ΔF]=[F]-F a Formula 11.

[0065] Preferably, in the above-mentioned parallel steel strand cable tensioning control method based on iterative backstepping, the iterative convergence criterion is that the cable force difference is less than 0.001.

[0066] The parallel steel strand cable tensioning control method based on iterative back-calculation provided by the present invention takes into account the influence of the deformation caused by tensioning each steel strand on the initial length and inclination, and determines the construction tensioning force of each steel strand through the iterative back-calculation method, ensuring that the tension of the entire bundle of cables reaches the target value after the tensioning of multiple parallel steel strands is completed, thereby ensuring the uniformity of the steel strand tension within the cable body.

[0067] The above description is only a description of the preferred embodiments of the present invention and does not limit the scope of the present invention. Any changes and modifications made by ordinary technicians in the field of the present invention based on the above disclosure shall fall within the scope of protection of the claims.

Claims

1. A parallel steel strand cable tensioning control method based on iterative backstepping, characterized in that: include: Step 1: Take the initial length L and initial horizontal inclination α of the first steel strand as the initial length and horizontal inclination of each steel strand and calculate the initial tension force vector [X 0 ]; Step 2: Take the initial length L and initial horizontal inclination angle α of the first strand as the distance L1 between the main beam anchor point and the main tower anchor point and the initial value α1 of the horizontal inclination angle of the line connecting the two points, L1 = L; α1 = α, and use the tension force vector [X 0 ], the distance L between the anchor point of the main beam and the anchor point of the main tower after the i-th steel strand is tensioned is calculated according to the tensioning sequence method. i+1 , the horizontal angle α of the line connecting the two points is obtained by calculation i+1 , and are used as the initial length L of the i+1th strand i+1 and the initial horizontal inclination angle α i+1 ; Step 3: The initial length of each steel strand calculated in step 2 is [L] = {L1, L2, L3, ... L i } and horizontal inclination angle [α] = {α1, α2, α3, ... α i }, calculate the reduction in cable force [△X] of the remaining tensioned steel strands caused by the tensioning of each steel strand; Step 4: Obtain the cable force vector [F] of each steel strand after the last steel strand is tensioned by forward calculation, and calculate the cable force vector [F] and the average cable force F a The cable force difference vector [△F] is used as the convergence residual; Step 5: Using the initial length [L] and horizontal inclination angle [α] of each steel strand calculated in step 2 as calculation parameters, calculate the tension vector [X] of each steel strand again according to the reverse calculation method described in step 1. 1 ]; Step 6: Use the tensile force vector [X 1 ] to perform forward calculation and repeat steps 2 to 5 until the cable force difference vector [△F] meets the set iterative convergence criterion, and the tension force vector [X m ]; In step 2, the distance L between the anchor point of the main beam and the anchor point of the main tower after the i-th strand is tensioned is calculated by the formula 5 according to the tensioning sequence. i+1 , the horizontal angle α between the two points is calculated by formula 6 i+1 , Where: L i —The initial length of the i-th strand; α i —horizontal inclination angle of the i-th steel strand; k x —Longitudinal stiffness of main beam; k z —Vertical stiffness of main beam; k t —vertical stiffness of main tower; In step 3, the reduction in cable force [△X] of the remaining tensioned steel strands caused by the tensioning of each steel strand is calculated according to formulas 7 to 9. Δl i =L i -L i+1 Formula 7 Where: Δl i — length change of the i-th strand caused by tensioning; △x ij —The tension reduction value of the j-th steel strand caused by the tensioning of the i-th steel strand; [△X]—The steel strand tension reduction value matrix, which is a lower triangular matrix with diagonal elements △x nn Both are 0.

2. The parallel steel strand cable tensioning control method based on iterative backstepping according to claim 1, characterized in that: In step 1, the reverse method is used to calculate the tension vector of each steel strand [X 0 ], X n =F a =F / n Formula 1 X n-1 =F a +Δx n Formula 2 Where: X n —The tension of the nth steel strand, that is, the tension of the last steel strand; X n-1 —Tension force of the n-1th strand; F a —Average cable tension; F—stay cable tension, i.e., the sum of all strand tensions; n—the total number of strands in the stay cable, which is a natural number greater than 1; △l n —The length change caused by the tensioning of the nth strand; △x n —The reduction in the cable force of the remaining steel strands caused by the tensioning of the nth steel strand; [X 0 ]—tension force vector of steel strand; X1 0 —Tension force of the first strand; X n 0 —Tensioning force of the nth steel strand; L—initial length of the steel strand; E—elastic modulus of the steel strand; A—cross-sectional area of ​​the steel strand.

3. The parallel steel strand cable tensioning control method based on iterative backstepping according to claim 1, characterized in that: In step 4, the cable force vector [F] of each steel strand after the last steel strand is tensioned is calculated by using formula 10, and the cable force vector [F] and the average cable force F are calculated by using formula 11. a The cable force difference vector [△F] is used as the convergence residual; [F]=sum([ΔX],1)+[X 0 ] Formula 10 Among them, sum([ΔX],1) represents the sum of column vectors; [ΔF]=[F]-F a Formula 11.

4. The parallel steel strand cable tensioning control method based on iterative backstepping according to claim 1, characterized in that: The iterative convergence criterion is that the cable tension difference is less than 0.001.

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