CN109583024B - Overhead power transmission ground wire stranded wire contact effect analysis method and system - Google Patents
Overhead power transmission ground wire stranded wire contact effect analysis method and system Download PDFInfo
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Abstract
A method and a system for analyzing contact effect of overhead power transmission ground wires and stranded wires are provided, wherein the method comprises the steps of determining a total rigidity matrix of the overall analysis of the overhead ground wires, establishing a tension analysis method in the overall analysis of the overhead ground wires, determining stress conditions under the action of self weight and external load, establishing a fine rigidity matrix and an external load vector of the stranded wires, establishing a nonlinear contact analysis method of the stranded wires, determining contact force among the stranded wires, establishing a stranded wire contact force nonlinear iterative algorithm, determining a stress balance equation of the overall ground wires, and analyzing and calculating the contact force of the ground wires. The system comprises an overhead ground wire parameter analysis module, an overhead ground wire rigidity matrix analysis module, an overhead ground wire tension analysis module, a strand rigidity matrix and external load analysis module, a strand stress equation analysis module and a strand contact stress analysis module. The method provided by the invention can accurately and effectively analyze the contact stress of each strand of the overhead ground wire, and completely meets the fine requirement of practical engineering analysis.
Description
Technical Field
The invention relates to an overhead power transmission ground wire stranded wire contact effect analysis method and system, and belongs to the technical field of overhead ground wires.
Background
The transmission line is an important life line project and energy transmission infrastructure and is widely applied at home and abroad. Because the power transmission line is in service in the field for a long time and passes through a plurality of terrain and climate complex areas, the power transmission line is easy to damage and destroy under the action of strong external loads such as strong wind, earthquake, ice coating and the like, which can cause serious economic loss and secondary disasters. Therefore, by combining the reality of the transmission line engineering catastrophe in China, the corresponding work of disaster prevention and reduction and service performance evaluation is developed, and the method has important scientific significance and engineering value. The overhead ground wire is an important component in a transmission tower wire system and plays an important role in transmitting electric power, and the overhead ground wire is also an essential characteristic of the transmission tower wire system different from other various high-rise steel structures. The mechanical property and strength design of the overhead ground wire are related to the service safety of the power transmission line, so that the design and construction of the power transmission line are a key problem. However, the mechanical properties of different layers in the ground wire are not considered in the conventional overhead ground wire design, and the conventional ground wire design generally considers the ground wire as an isotropic suspension cable and directly performs bearing capacity analysis. The method does not consider the detailed mechanical property of each strand of steel strand in the overhead ground wire and the interaction effect between the strands of the ground wire, so that the method only can master the running tension and the axial stress of the ground wire in general, but cannot master the detailed stress characteristic of the overhead ground wire, and particularly cannot effectively master the characteristic of the nonlinear contact effect between the strands of the overhead ground wire.
At present, the overhead ground wire is widely applied to a power transmission line, but an analysis and calculation method for the contact effect of each strand of the ground wire is very deficient, and at present, only finite element software can be used for carrying out overall analysis on the ground wire, and the stress characteristic of each strand of the ground wire cannot be accurately evaluated. The common method is to establish an integral finite element model of the overhead ground wire by adopting a finite element method and calculate the bearing capacity of the overhead ground wire. However, since the overhead ground wire is actually composed of a plurality of strands, the current method cannot take into account the contact effect between the strands of the ground wire at all. How to establish an effective method and accurately and quantitatively analyze the contact effect of the overhead ground wire strands is a difficult problem troubling engineering technicians, and the work in the aspect is still blank. In the process of analyzing the ground wire contact effect, an accurate detail finite element model must be established for each strand, and then a stiffness matrix and a load vector of each strand are formed respectively. Therefore, the actual analysis process is complicated and complicated, and the analysis difficulty is high.
In general, the research on the overhead ground wire contact effect analysis method is still very deficient, and much work needs to be carried out. At present, the research mainly focuses on the analysis and research of the integral operation tension and the like of the overhead ground wire, and no relevant report exists on the research of the nonlinear contact effect between the strands of the ground wire. Methods that can accurately evaluate strand contact effects are still lacking and await further exploration and innovation. One of the key problems is that there is currently no method and system for analyzing the contact effect of the overhead ground wire strands.
Therefore, there is a need for systematic study of the characteristics of the contact effect of the overhead ground wire strands, and for establishing an accurate and effective analysis method of the contact force of the ground wire strands.
Disclosure of Invention
The invention aims to solve the problems in the aspect of overhead ground wire contact effect analysis methods, and provides an overhead power transmission ground wire stranded wire contact effect analysis method and system, which are used for effectively improving the stress calculation efficiency and analysis level of split ground wires and improving the analysis evaluation level and construction level of large power transmission lines.
The technical scheme of the invention is as follows: an overhead power transmission ground wire strand contact effect analysis method comprises the following steps:
(1) Determining coordinate information of the overall analysis of the overhead ground wire, and determining physical parameters and load parameters of the ground wire such as elastic modulus, dead weight, external load and the like;
(2) Determining a total rigidity matrix K of the overall analysis of the overhead ground wire;
(3) Establishing a tension analysis method during the integral analysis of the overhead ground wire, and determining the stress condition under the action of self weight and external load;
(4) Establishing a fine stiffness matrix of strands
And the external load vector
(5) Establishing a nonlinear contact analysis method of the strands, and determining the contact force between the strands;
(6) Establishing a strand contact force nonlinear iterative algorithm, and determining a stress balance equation of the whole ground wire;
(7) And analyzing and calculating the contact force of each strand of the ground wire.
The total rigidity matrix K of the overhead ground wire is as follows:
K＝K e +K g +K f
in the formula, K e Elastic stiffness matrix, K, for an overhead ground wire unit g Is a dead weight stress stiffness matrix of the ground wire; k f Is the external load stress rigidity matrix of the ground wire.
The stress conditions under the action of the dead weight and the external load are as follows:
Kx＝G+F
wherein x is the displacement response of the overhead ground wire; g is the dead weight load of the ground wire; f is equivalent node load of the ground wire caused by external load; k is the total stiffness matrix of the overhead ground wire.
Fine stiffness matrix of the strands
And the external load vector
Comprises the following steps:
in the formula, D is a strand unit elastic coefficient matrix; b is a geometric matrix of strand units; n is a folded yarn unit shape function matrix; b s To act on strand sheetsThe load volume force vector of the element; p is a radical of s Distributing force vectors for external loads acting on the strand units; omega is a strand unit integral area; a is the area division region of the external load action of the strand unit.
Contact force f between the strands n ：
In the formula, K n Is the contact stiffness between the strands; d is the distance between the strand contact areas.
The stress balance equation of the whole ground wire is as follows:
in the formula, x i,j Is the displacement of the jth strand of the ith layer; g i,j The ground wire is subjected to dead weight load; f i,j The equivalent node load of the ground wire caused by external load;
is the contact force vector acting on the strand.
The contact force of each strand of the air-ground wire is as follows:
in the formula, K t The rigidity of the contact surface during sliding is shown;
the contact force of the jth strand wire of the ith layer of ground wire in the x direction is obtained;
the contact force of the jth strand of the ith layer of ground wire in the y direction;
deformation of the ith layer of ground wire in the x direction of the contact point of the jth strand wire;
the contact point y direction deformation of the jth strand of the ith layer ground wire.
The invention discloses an overhead power transmission ground wire strand contact effect analysis system which comprises an overhead ground wire parameter analysis module, an overhead ground wire rigidity matrix analysis module, an overhead ground wire tension analysis module, a strand rigidity matrix and external load analysis module, a strand stress equation analysis module and a strand contact stress analysis module. Each module is in a logic relationship of forward and backward progression, and the function of the latter module can be realized based on the result of the former module only after the former module is finished.
The overhead ground wire parameter analysis module is used for determining node information, line type information and physical parameters of the overhead ground wire; the node information comprises node coordinates, the ground wire linear information is the length of a ground wire unit, and the physical parameters of the ground wire comprise elastic modulus, dead weight and external load;
the overhead ground wire rigidity matrix analysis module is used for firstly establishing a linear rigidity matrix, a self-weight stress rigidity matrix degree and an external load stress rigidity matrix of the ground wire in the ground wire integral analysis and then establishing a ground wire integral rigidity matrix under an integral coordinate system;
the overhead ground wire tension analysis module is used for establishing a stress balance equation of the overhead ground wire under the action of self weight and external load, and analyzing and determining the integral operation tension of the overhead ground wire;
the strand stiffness matrix and external load analysis module is used for establishing a strand fine analysis model to form a strand stiffness matrix and a load vector;
the strand stress equation analysis module firstly establishes deformation expressions of strands of the ground wire and then establishes a stress balance equation set of the strands of the overhead ground wire;
and the strand contact stress analysis module is used for establishing a nonlinear iterative algorithm of the strand contact force and analyzing and calculating the nonlinear contact force of the strand.
The method has the beneficial effects that the integral operation tension of the overhead ground wire is determined through integral analysis. Then establishing a strand refinement stress equation set and a nonlinear iteration convergence criterion; further determining the deformation of each strand of the ground wire through multiple iterations and determining the nonlinear contact force and the contact effect of the ground wire on the basis; the stress calculation efficiency and the analysis level of the split ground wire are effectively improved, and the analysis evaluation level and the construction level of the large-scale power transmission line are improved.
The overhead ground strand linear contact effect analysis method provided by the invention has the advantages of clear concept and accurate analysis and calculation. The analysis method and the system have applicability, and are suitable for analyzing and calculating the contact effect of the overhead ground wires with different spans, verticality and physical parameters. The method has wide application prospect in the performance evaluation of the overhead ground wire in the future and generates remarkable social and economic effects.
Drawings
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
fig. 2 is a schematic diagram of an overhead ground wire global analysis coordinate system;
fig. 3 is a schematic diagram of a fine analysis model of each strand of the overhead ground wire;
FIG. 4 is a schematic diagram of the contact effect of the strands of the ground wire;
fig. 5 is an identification diagram of each strand of overhead ground wire;
FIG. 6 is a comparison of contact stresses of strands of the second layer;
fig. 7 shows the variation of the contact stress of the second layer of strands at different pitches.
Detailed Description
A specific embodiment of the present invention is shown in fig. 1.
The embodiment analyzes the contact effect of the overhead ground wire, firstly determines the tension under the action of the service load through overall analysis, and then determines the contact force through fine analysis.
As shown in fig. 2, the present embodiment first determines information such as coordinates of the overhead ground wire. And further determining a rigidity matrix and a load vector of the overall analysis of the overhead ground wire. And establishing a tension analysis method during the integral analysis of the overhead ground wire, and determining the operation tension of the overhead ground wire. And further establishing a fine analysis model of the strand and determining a rigidity matrix and an external load vector of the strand. Establishing a nonlinear contact analysis method and a contact force nonlinear iterative algorithm of the strands, determining the deformation of the strands through multiple iterations and further solving the nonlinear contact force of the strands.
The overhead ground wire strand contact effect analysis method in the embodiment overcomes the defect of lack of the strand contact force analysis method at present, and can be effectively applied to analysis and evaluation of the actual overhead ground wire strand contact effect.
Specifically, the method and the system for analyzing the overhead ground strand linear contact effect are established through the following steps:
step 1: establishing an overhead ground wire coordinate system
As shown in fig. 2, the overall coordinate system of the overhead ground wire can be established as O-XYZ. And establishing a local coordinate system o-xi with o as a midpoint.
Defining coordinates (X) of each node on a three-node cable unit on an overhead ground wire unit 1 ,Y 1 ,Z 1 )、(X 2 ,Y 2 ,Z 2 )，(X 3 ,Y 3 ,Z 3 ) Defining the displacement (u) of each node of the three-node cable unit 1 ,v 1 ,w 1 )、(u 2 ,v 2 ,w 2 )、(u 3 ,v 3 ,w 3 ) Then the node displacement of the overhead ground wire unit can be expressed in vector form:
U＝[u v w] T (1)
the node displacement vector can be expressed as a shape function N and two-end node displacement U e The product of (a):
U＝NU e (2)
wherein:
U e ＝[u 1 v 1 w 1 u 2 v 2 w 2 u 3 v 3 w 3 ] T (3)
in the formula: n is a shape function matrix.
The coordinate interpolation function of any point on the overhead ground wire unit is the same as the displacement interpolation function:
X＝NX e (4)
in the formula: x is a coordinate value of any point on the overhead ground wire unit under the whole coordinate system; x e The coordinate vector of the upper node of the overhead ground wire unit under the whole coordinate system is as follows:
X e ＝[x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 ] T (5)
step 2: rigidity matrix for establishing overhead ground wire integral analysis
The tension of the overhead ground wire needs to be determined by overall analysis. The rigidity matrix of the overhead ground wire overall analysis needs to consider the influence of geometric nonlinear effect. Thus, its stiffness matrix can be expressed as a linear stiffness matrix K e Dead weight stress stiffness matrix degree K g And external load stress stiffness matrix K f And (3) the sum:
K＝K e +K g +K f (6)
the ground wire unit elastic stiffness matrix in the local coordinate system can be expressed as:
in the formula: e is the elastic modulus of the ground wire; a is the cross sectional area of the ground wire; l is the ground line unit length.
The elastic stiffness matrix of the overhead ground wire unit in the global coordinate system can be expressed as follows:
in the formula: and T is a coordinate transformation matrix of the local coordinate system and the whole coordinate system.
The overhead ground wire belongs to a flexible cable structure, and a stress rigidity matrix caused by self weight and external load is generated. Dead weight stress rigidity matrix K of overhead ground wire under action of dead weight load g Can be expressed as:
W＝AEε g (10)
in the formula: w is the internal force in the ground wire caused by the dead weight load; epsilon g Is the overhead ground wire strain induced by W; k 0 Is a matrix of coefficients. From this, the dead weight stress stiffness matrix K g Can be further expressed as:
stress stiffness matrix K of overhead ground wire under external load action f Can be expressed as:
f＝AEε f (13)
in the formula: f is the internal force in the ground wire caused by the external load; epsilon f Is the overhead ground wire strain induced by F. Stress stiffness matrix K under external load effect f Can be further expressed as:
and step 3: tension analysis method for establishing integral analysis of overhead ground wire
During integral analysis, the stress balance equation of the overhead ground wire under the action of self weight and external load can be expressed as follows:
Kx＝G+F (15)
in the formula: x is the displacement response of the overhead ground wire; g is the dead weight load of the ground wire; f is the equivalent node load of the ground wire caused by the external load.
The overhead ground wire is a typical strong geometric nonlinear system, the response of the overhead ground wire under the action of external load and dead weight load must be completed by adopting a nonlinear iteration method, and the balance equation can be expressed as follows:
Kx＝R-R s (16)
in the formula: r is a load vector formed by the overhead ground wire due to external load and dead load, R s And the vector is the initial stress equivalent node load vector.
And (4) carrying out nonlinear reaction analysis on the overhead ground wire by adopting a Newton-Rapshon iterative method. Firstly, the rigidity matrix of the overhead ground wire is assembled, so that the stress balance equation of the overhead ground wire can be obtained:
(K e +K g +K f )Δx-R＝0 (17)
the tangent stiffness matrix can be obtained again after the approximate displacement of the overhead ground wire is solved, the unbalance force of the structure can be calculated, and the displacement correction value of the overhead ground wire is further calculated. The overhead ground wire displacement of step j +1 can be expressed as:
x j+1 ＝x j +Δx j (18)
and according to the set convergence criterion, the imbalance force is considered to be calculated if the imbalance force is small enough. If the set convergence criterion is not satisfied, repeating the above steps until the convergence criterion is satisfied. On the basis of which the analytical calculation of the next time step is carried out. Therefore, the response of the overhead ground wire under the combined action of the external load and the dead weight load can be determined.
And 4, step 4: establishing a fine stiffness matrix and an external load vector for the strands
The overall model cannot take into account the interaction between the strands of the ground wire, so a fine strand model must be built to take into account the contact effects between the strands. Fig. 3 shows a schematic diagram of a fine analysis model of each strand of the overhead ground wire. A fine analysis model of each strand is built using multi-node solid units, where each node has 3 degrees of freedom. The strain epsilon of the strand unit is:
in the formula: u is a strand unit displacement vector; q. q.s e A strand node displacement vector is obtained; n is a folded yarn unit shape function matrix; b is a geometric matrix of strand units;
is an operator matrix of the geometric equation.
Strand unit stiffness matrix
Can be expressed as:
in the formula: d is a strand unit elastic coefficient matrix; Ω is the strand unit integral area.
Equivalent nodal loads acting on strand units
Can be expressed as:
in the formula: b is a mixture of s Is the load volume force vector acting on the strand unit; p is a radical of formula s Distributing force vectors for external loads acting on the strand units; a is the outer load action area subarea of the strand unit.
And 5: method for establishing nonlinear contact analysis of strand
The strands of each layer of the overhead ground wire will be strained and elongated under an external load. Because the outer layer strands are wound around the inner layer steel core, the outer layer strands will produce a squeezing action and a squeezing stress on the inner layer steel core under the action of a tensile force, and further form contact surfaces and contact stresses between the strands. As shown in fig. 4, the contact surface is the contact portion between two different strands, one of which is the target surface and the other of which is the contact surface. The target surface may be represented by target nodes I, J, K, and L. The node M on the contact surface contacts with the target surface, and the contact is represented by a distance d between the M point and the contact surface. The contact distance d must be greater than or equal to zero, which is referred to as a contact coordination condition. If the contact distance d is less than zero, it indicates that mutual penetration between the two contact surfaces occurs, and the contact coordination condition is violated.
In the analysis process of the contact effect, contact coordination conditions need to be met between contact surfaces. The analysis of the contact effect between the strands can adopt a penalty function method, and the contact force between the strands can be expressed as:
in the formula: k is n Is the contact stiffness between the strands; d is the distance between the strand contact areas.
The deformation η at a point on the strand interface can be expressed as:
in the formula: eta x And η y Respectively, the displacement of the contact point in two orthogonal directions x and y in the local coordinate system. The deformation of the contact point can be expressed as an elastic deformation η e And sliding deformation η s The sum of the two:
the component of the contact force at the point of contact can be expressed as:
in the formula: k is t The stiffness of the contact surface when it is slippery.
And 6: nonlinear iterative algorithm for establishing strand contact force
The interaction between the strands of the overhead ground wire is a very complex nonlinear contact process, so the analysis of the nonlinear contact effect must be completed through multiple iterations.
For the jth strand of the ith layer of the overhead ground wire, the force balance equation can be expressed as:
in the formula: x is a radical of a fluorine atom i,j Is the displacement of the jth strand of the ith layer; g i,j The dead load of the ground wire is obtained; f i,j The equivalent node load of the ground wire caused by the external load;
is the contact force vector acting on the strand.
And solving a stress equation of the strand by adopting a mode of combining a Newton-Raphson method and an incremental method. The iterative process uses a displacement convergence criterion. Assuming an initial displacement of the structure of
Solving the unbalanced node force and integral rigidity matrix at the moment
According to aboveThe imbalance found in one step seeks to find the strand displacement correction:
the nodal displacement of the strand in the new contact equilibrium configuration is:
according to the ground wire displacement under the new balanced form obtained by solving, the unbalanced force vector delta psi of the strand can be reformed i,j . Repeating the steps until the obtained strand displacement difference norm meets the set convergence tolerance, and ending the iterative solution process of the jth strand of the ith layer:
in the formula: tol is a predetermined convergence tolerance greater than zero.
For the overhead ground wire, all the strands of the overhead ground wire have to meet the contact iteration convergence condition, and then the contact effect analysis of the whole ground wire is completed. The force balance equation for the entire ground is therefore effectively a series of equations:
in the formula: m is the number of layers of ground wire strands; n is the number of strands in each layer.
For a conventionally used GJ-50 two-layer ground wire, the inner part is a single-layer steel strand, and the outer layer is 6 aluminum strands, so that the stress balance equation is as follows:
and uniformly solving the stress balance equations of the plurality of ground wire strands, and ending the analysis and calculation when each equation reaches a convergence condition after k iterations.
The deformation of each strand of the ground wire under the action of self weight and external load can be determined through calculation.
And 7: analyzing and calculating the contact force of each strand of the ground wire
After determining the deformation of each strand, the deformation of the contact point of each strand, and thus the deformation of the contact point of the jth strand of the ith layer, can be determined:
the contact force of the jth strand of the ith layer may be expressed as:
an overhead power transmission ground wire strand contact effect analysis system comprises an overhead ground wire parameter analysis module, an overhead ground wire rigidity matrix analysis module, an overhead ground wire tension analysis module, a strand rigidity matrix and external load analysis module, a strand stress equation analysis module and a strand contact stress analysis module.
The overhead ground wire parameter analysis module is used for determining node information, line type information and physical parameters of the overhead ground wire; the node information comprises node coordinates, the ground wire linear information is the length of a ground wire unit, and the physical parameters of the ground wire comprise elastic modulus, dead weight, external load and the like.
The overhead ground wire rigidity matrix analysis module is used for firstly establishing a linear rigidity matrix, a self-weight stress rigidity matrix degree and an external load stress rigidity matrix of the ground wire in the ground wire integral analysis and then establishing a ground wire integral rigidity matrix under an integral coordinate system.
And the overhead ground wire tension analysis module is used for establishing a stress balance equation of the overhead ground wire under the action of self weight and external load, and analyzing and determining the integral operation tension of the overhead ground wire.
And the strand stiffness matrix and external load analysis module is used for forming a strand stiffness matrix and a load vector by establishing a strand fine analysis model.
The stranded wire stress equation analysis module firstly establishes a deformation expression of each stranded wire of the ground wire and then establishes an overhead ground wire stranded wire stress balance equation set.
And the strand contact stress analysis module is used for establishing a strand contact force nonlinear iterative algorithm and analyzing and calculating the nonlinear contact force of the strand.
The following describes a specific implementation of the present invention in the case of an actual overhead ground wire:
the ground wire span of a certain practical power transmission line is 300m, the ground wire model is GJ-80, the ground wire comprises three layers of 19 strand wires in total, the third layer comprises 12 strand wires, the second layer comprises 6 strand wires, the diameter of each strand of the ground wire is 2.3mm, the total diameter of the ground wire is 11.5mm, and the calculated sectional area is 78.94mm 2 . The ground wire has an elastic modulus of 185GPa, a weight per unit length of 628.4kg/m and a linear expansion coefficient of 1.0 x 10 -6 /℃。
Firstly, an overall coordinate system of the overhead ground wire is established as shown in fig. 2, wherein the in-plane direction is an X direction, the out-of-plane direction is a Y direction, and the vertical direction is a Z direction. Then the division of the overhead ground wire into cells is started, the overhead ground wire can be divided into 10 cells, and 31 nodes will be generated. Fig. 3 is a schematic diagram of a strand model of an overhead ground wire. Fig. 4 is a schematic diagram of the contact effect of each strand of the ground wire, and fig. 5 is an identification diagram of each strand of the overhead ground wire. A non-linear finite element method is used herein to create a local fine finite element model of each strand of the ground wire, which is 270mm long and comprises three complete helical segments of three layers of steel strands, as shown in figure 3. The structural model comprises 37000 nodes, 30412 three-dimensional solid units, and the ground wire model has 111000 degrees of freedom.
And (4) writing a computer program according to a formula (6) to determine a rigidity matrix K of the overall analysis of the overhead ground wire.
And (4) writing a computer program according to a formula (15) to establish a tension analysis method for the integral analysis of the overhead ground wire.
Writing a computer program to establish a fine stiffness matrix for a strand according to equations (20) and (21)
And the external load vector
And writing a computer program according to the formulas (22) to (27) to establish a nonlinear contact analysis method of the strands.
A computer program is written according to equations (31) and (32) to establish a strand contact force nonlinear iterative algorithm.
And writing a computer program according to the formulas (36) and (37) to analyze and calculate the contact force of each strand of the ground wire.
Since overhead ground wires of different spans usually have different dead weight loads and running tensions, it is necessary to study the influence of the ground wire span on the contact stresses.
Fig. 6 shows the results of a comparison of the contact stress of the strands of the second layer at a gauge of 300 m.
Fig. 7 shows the variation of the contact stress of the second layer of strands at different pitches.
It can be seen from the results shown in the figure that as the ground wire span increases, the tension in the ground wire increases, and the axial deformation of the outer strands and the steel core increases due to the increase in tension, so that the squeezing effect between the strands and the steel core increases, and the squeezing effect between the outer strands also increases.
It can be seen from fig. 7 that the contact stress gradually increases with increasing span. Further inspection of fig. 7 reveals that the contact stress remains substantially constant along the length despite the different pitches, and that the contact stresses are very close for different strands at different pitches. According to analysis results, the contact stress peak values of different positions of different ground wires have certain difference, the contact stress peak value of the inner layer steel core is 31.5MPa, and the peak contact stress of the second layer strand wire is 32.2MPa. Since the third layer of strands is wound in the opposite direction to the second layer of strands, the contact stress peak is also different from that of the second layer of strands. But in general the contact stress of the ground wire strands is typically several tens of MPa, much less than the axial stress of the ground wire strands.
It follows that, both for the inner steel core and for the outer strands, local point contact of the strands occurs at different points, due to the effect of the strand extrusion effect, resulting in a spatial distribution of the contact stresses between the strands and the inner steel core that is not continuous.
The analysis result shows that: the method provided by the invention can accurately and effectively analyze the contact stress of each strand of the overhead ground wire, and completely meets the fine requirement of practical engineering analysis. The equivalent analysis method provided by the invention has the advantages of wide application range, small calculation workload, high analysis precision and the like. The analysis method and the system have applicability, and are suitable for analyzing and calculating the contact effect of the overhead ground wires with different spans, verticality and physical parameters.
Claims (2)
1. A method for analyzing contact effect of an overhead power transmission ground wire strand comprises the steps of determining coordinate information of overall analysis of the overhead ground wire, and determining elastic modulus, dead weight, external load physical parameters and load parameters of the ground wire; characterized in that the method further comprises the steps of:
(1) Determining a total rigidity matrix K of the overall analysis of the overhead ground wire;
(2) Establishing a tension analysis method during the integral analysis of the overhead ground wire, and determining the stress condition under the action of self weight and external load;
(3) Establishing a fine stiffness matrix of strands
And the external load vector
(4) Establishing a nonlinear contact analysis method of the strands, and determining the contact force between the strands;
(5) Establishing a strand contact force nonlinear iterative algorithm, and determining a stress balance equation of the whole ground wire;
(6) Analyzing and calculating the contact force of each strand of the ground wire;
the total rigidity matrix K of the overhead ground wire is as follows:
K＝K e +K g +K f
in the formula, K e Elastic stiffness matrix, K, for an overhead ground wire unit g Is a dead weight stress stiffness matrix of the ground wire; k is f An external load stress stiffness matrix of the ground wire;
the elastic stiffness matrix of the ground wire unit under the local coordinate system is expressed as follows:
in the formula: e is the elastic modulus of the ground wire; a is the cross sectional area of the ground wire; l is the length of the ground wire unit;
the elastic rigidity matrix of the overhead ground wire unit under the overall coordinate system is expressed as follows:
in the formula: t is a coordinate transformation matrix of the local coordinate system and the whole coordinate system;
the overhead ground wire belongs to a flexible cable structure and can generate a stress rigidity matrix caused by self weight and external load; dead weight stress rigidity matrix K of overhead ground wire under action of dead weight load g Expressed as:
W＝AEε g ，
in the formula: w is the internal force in the ground wire caused by the dead weight load; epsilon g Is the overhead ground wire strain induced by W; k 0 Is a coefficient matrix; from this, the dead weight stress stiffness matrix K g Further expressed as:
stress stiffness matrix K of overhead ground wire under external load action f Expressed as:
f＝AEε f ，
in the formula: f is the internal force in the ground wire caused by the external load; epsilon f Is the overhead ground wire strain induced by F; stress stiffness matrix K under external load effect f Further expressed as:
the stress conditions under the action of the dead weight and the external load are as follows:
Kx＝G+F
wherein x is the displacement response of the overhead ground wire; g is the dead weight load of the ground wire; f is the equivalent node load of the ground wire caused by the external load; k is a total rigidity matrix of the overhead ground wire;
a fine stiffness matrix of the strands
And the external load vector
Comprises the following steps:
in the formula, D is a strand unit elastic coefficient matrix; b is a geometrical matrix of strand units; n is a folded yarn unit shape function matrix; b is a mixture of s Is the load volume force vector acting on the folded yarn unit; p is a radical of s The external load distribution force vector acting on the strand unit; omega is a strand unit integral area; a is the outer load action area subarea of the strand unit;
contact force f between the strands n ：
In the formula, K n Is the contact stiffness between the strands; d is the distance between the contact areas of the strands;
the stress balance equation of the whole ground wire is as follows:
in the formula, x i,j Is the displacement of the jth strand of the ith layer; g i,j The dead load of the ground wire is obtained; f i,j The equivalent node load of the ground wire caused by external load;
is a contact force vector acting on the strand;
the contact force of each strand of the air-ground wire is as follows:
in the formula, K t The rigidity of the contact surface during sliding is shown;
the contact force of the jth strand of the ith layer of ground wire in the x direction is obtained;
the contact force of the jth strand of the ith layer of ground wire in the y direction;
deformation of the ith layer of ground wire in the x direction of the contact point of the jth strand wire;
the contact point y direction deformation of the jth strand of the ith layer ground wire.
2. An overhead power transmission ground wire strand contact effect analysis system for implementing an overhead power transmission ground wire strand contact effect analysis method according to claim 1, the system comprising:
the overhead ground wire parameter analysis module is used for determining node information, line type information and physical parameters of the overhead ground wire; the node information comprises node coordinates, the ground wire linear information is the length of a ground wire unit, and the physical parameters of the ground wire comprise elastic modulus, self weight and external load;
the system comprises an overhead ground wire rigidity matrix analysis module, a ground wire dynamic stress matrix analysis module and a ground wire dynamic stress matrix analysis module, wherein the overhead ground wire rigidity matrix analysis module is used for firstly establishing a linear rigidity matrix, a self-weight stress rigidity matrix degree and an external load stress rigidity matrix of a ground wire in the ground wire overall analysis and then establishing a ground wire overall rigidity matrix under an overall coordinate system;
the overhead ground wire tension analysis module is used for establishing a stress balance equation of the overhead ground wire under the action of self weight and external load, and analyzing and determining the integral operation tension of the overhead ground wire;
the strand stiffness matrix and external load analysis module is used for establishing a strand fine analysis model to form a strand stiffness matrix and a load vector;
the stranded wire stress equation analysis module firstly establishes a deformation expression of each stranded wire of the ground wire and then establishes an overhead ground wire stranded wire stress balance equation set;
and the strand contact stress analysis module is used for establishing a strand contact force nonlinear iterative algorithm and analyzing and calculating the nonlinear contact force of the strand.
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