CN105302977A - Calculating method for mechanical waving force and frequency relation of overhead transmission line - Google Patents
Calculating method for mechanical waving force and frequency relation of overhead transmission line Download PDFInfo
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Abstract
The invention discloses a calculating method for a mechanical waving force and frequency relation of an overhead transmission line. According to the calculating method, the fact that when a transmission wire waves, the wire does elliptic motion is analyzed and calculated to obtain a relation of the force condition needed when the wire waves and the frequency, a curve graph of the change relation of the force and the frequency when the wire waves is drawn, and a theoretical basis is supplied to the fact that a mechanical method is utilized to enable the transmission wire to generate precise elliptic orbit waving.
Description
The technical field is as follows:
the invention relates to a method for calculating the relation between mechanical dancing stress and frequency of an overhead transmission line.
Background art:
the relation between the tension and the amplitude of the wire during galloping of the power transmission line is given in a literature report (dynamic tension analysis of the wire during galloping of the overhead power transmission line is Juanwujun, Liu-super group, Ninxin spring, China institute for electric power construction, Vol.38, No. 10, 1004-; the track of any point on the transmission line conductor is an ellipse when the transmission line conductor is waved (monitoring and analyzing the waving track of the transmission line conductor is Wangyuan, Nianhuan, Dulin, Chongqing university transmission and distribution equipment and system safety and new technology country key laboratory high-voltage electricity technology volume 36, No. 5, 1003-6520 (2010) 05-1113-06). If the transmission conductor is waved by a mechanical method, the analysis of the change relation between the stress condition of the conductor and the waving frequency when the conductor forms an elliptical track when the transmission conductor waves in the past literature does not exist, and at present, a calculation method of the relation between the mechanical waving stress and the frequency of the overhead transmission line is blank.
The invention content is as follows:
the invention aims to overcome the defects of the prior art and provides a method for calculating the relationship between the mechanical dancing force and the frequency of the overhead transmission line, which provides a theoretical basis for enabling a transmission conductor to generate accurate elliptical orbit dancing by utilizing an artificial mechanical method.
The object of the invention can be achieved by the following measures: a method for calculating the relation between mechanical dancing stress and frequency of an overhead transmission line is characterized by comprising the following steps:
analyzing the stress of the transmission conductor when the transmission conductor is waved by using mechanical equipment:
if the track of the transmission conductor during mechanical galloping is an ellipsoid, an oxyz rectangular coordinate system is established, and the ellipsoid equation is(1) The track of each point on the wire is an ellipse when the wire waves; the center point M of the transmission conductor is taken as a research object, and an M-point motion equation is set as(2) (ii) a Equation of parameters（3）Is the circular frequency of the conductor as it is waved,is the time of day or the like,when the conductor is wavedMaximum amplitude in the axial direction;
calculating the first derivative of equation (3)(4) Obtaining the velocity components of the M point in the x direction, the y direction and the z direction; first derivative of formula (4)(5) Obtaining acceleration components of the M point in the x direction, the y direction and the z direction; according to newton's second law:(6) obtaining the center point M of the transmission conductorResultant force in direction and railThe relationship between the two or more of the components,
（7）
wherein、、Is the center point M of the power transmission conductorThe resultant force exerted in the direction of the force,、、is the center point M of the power transmission conductorThe component of the velocity in the direction of the,is the center point M of the power transmission conductorThe component of the acceleration in the direction of the,the quality of the transmission conductor when the span is L meters;
setting the center point M of a transmission conductor to be acted by tension T, gravity G and force N applied by a mechanical rocker arm; sequentially analyzing the stress condition when the central point M of the power transmission conductor is located at A, C, B, D points;
assuming that the timing starts from point D, the center point M of the power line moves from point D to point a, ，is the period of the conductor waving,is the frequency of conductor waving;
1. analyzing the stress condition of the central point M of the power transmission conductor at the point A:
when the center point M of the transmission conductor is at the point A, the center point M of the transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionLying in the plane oxz, the force has no component in the y-direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionResultant force in the z-axis direction ofWherein(8) mechanical rocker arm forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（9）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point a is:
（10），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point A is along the z axis and is determined by the gravity, the tension and the acting force of the mechanical rocker arm;
wherein the supporting force given by the mechanical rocker arm is as follows,(9) oriented along the z-axis;
2. and (3) analyzing the stress condition of the central point M of the power transmission conductor at the point c:
when the center point M of the power transmission conductor is located at the point C, the center point M of the power transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point C,according to the formula (7),
(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofSimilar to the formula (8), at the point C,
mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
wherein（11）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to gravity G along the negative direction of the z axis, the tension T is positioned on the oxy plane, no component exists along the y direction, and the acting force of a mechanical rocker armIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point C is:
（12），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point C is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（11)，，
the supporting force given by the mechanical rocker arm at the point C is as follows:
(13)，lying in a plane parallel to the plane oyz, consisting ofAnddetermining;
3. analyzing the stress condition of the central point M of the power transmission conductor at the point B:
when the center point M of the transmission conductor is located at the point B, the center point M of the transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionIn the 0xz plane, the force has no component in the y direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, rootAccording to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionResultant force along the z-axisWherein(8) mechanical rocker arm forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（14）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at the point B is:
(15) the direction of resultant force applied when the center point M of the transmission conductor is positioned at the point B is determined by gravity, tension and acting force of a mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm is as follows,(14) oriented along the z-axis;
4. and (3) analyzing the stress condition of the central point M of the power transmission conductor at the point D:
when the center point M of the transmission conductor is located at the point D, the center point M of the transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point D,according to the formula (7),(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofAccording to the formula (8), at the point D,mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
，
wherein,（16）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionOn the oxy plane, with no component in the y-direction, mechanical rocker actionIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force applied when the center point M of the power transmission line is located at the point D is:
(17) the direction of resultant force applied when the central point M of the transmission conductor is positioned at the point D is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（16)，，
the supporting force given by the mechanical rocker arm at the point D is as follows:
(18)，lying in a plane parallel to the plane oyz, consisting ofAndand (6) determining.
Compared with the prior art, the invention can produce the following positive effects: the invention obtains the force condition and the relation with the frequency when the transmission conductor waves from the analysis and calculation of the elliptic motion of the transmission conductor when the transmission conductor waves, and draws the curve graph of the force and frequency change relation when the transmission conductor waves, thereby providing a theoretical basis for the transmission conductor to generate accurate elliptic orbit waves by using a mechanical method.
Description of the drawings:
figure 1 is a schematic diagram of transmission conductor galloping;
fig. 2 is an elliptical trajectory diagram (solid line ellipse) of the motion of the center point M of the power transmission conductor;
FIG. 3 is a force analysis diagram of a power transmission line when a center point M moves to a point A;
FIG. 4 shows the pitch, major axis and length of the ellipse when the center point M of the power transmission line is located at A, BAn angular relationship diagram;
FIG. 5 is a force analysis diagram of the power transmission line when the center point M moves to the point c;
FIG. 6 shows the pitch, major axis and length of the ellipse when the center point M of the power transmission line is located at D, CAn angular relationship diagram;
FIG. 7 is a force analysis diagram of a power transmission line when a center point M moves to a point B;
fig. 8 is a stress analysis diagram when the central point M of the power transmission conductor moves to a point D;
FIG. 9 shows a point A of a single conductorA graph of the relationship;
FIG. 10 shows a single conductor COf dotsA graph of the relationship;
FIG. 11 shows a single conductor at point BA graph of the relationship;
FIG. 12 shows a single conductor at point DA graph of the relationship;
the specific implementation mode is as follows: the following detailed description of embodiments of the invention refers to the accompanying drawings in which:
example (b): a method for calculating the relation between mechanical dancing stress and frequency of an overhead transmission line comprises the following steps:
firstly, analyzing the stress of the transmission conductor when the transmission conductor is waved by using mechanical equipment:
assuming that the track of the transmission conductor during mechanical galloping is an ellipsoid, an oxyz rectangular coordinate system is established, as shown in FIG. 1, and the ellipsoid equation is(1) The locus of each point on the wire as it waves is an ellipse, as shown in fig. 2. The center point M of the transmission conductor is taken as a research object, and an M-point motion equation is set as(2) (ii) a Equation of parameters（3）Is the circular frequency of the conductor as it is waved,is the time of day or the like,when the conductor is wavedMaximum amplitude in the axial direction;
calculating the first derivative of equation (3)(4) Obtaining the velocity components of the M point in the x direction, the y direction and the z direction; first derivative of formula (4)(5) Obtaining acceleration components of the M point in the x direction, the y direction and the z direction; according to newton's second law:(6) obtaining the center point M of the transmission conductorThe relationship between the resultant force experienced in the direction and the track,
（7）
wherein、、Is a power transmission conductorCenter point M of line is atThe resultant force exerted in the direction of the force,、、is the center point M of the power transmission conductorThe component of the velocity in the direction of the,is the center point M of the power transmission conductorThe component of the acceleration in the direction of the,the quality of the transmission conductor when the span is L meters;
setting the center point M of a transmission conductor to be acted by tension T, gravity G and force N applied by a mechanical rocker arm; sequentially analyzing the stress condition when the central point M of the power transmission conductor is located at A, C, B, D points;
assuming that the timing starts from point D, the center point M of the power line moves from point D to point a, ，is the period of the conductor waving,is the frequency of conductor waving;
1. analyzing the stress condition of the central point M of the power transmission conductor at the point A:
referring to fig. 3, when the center point M of the power transmission line is located at point a, it is assumed that the center point M of the power transmission line is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The centre point M of the power transmission conductor is subjected to gravity along the z-axisNegative direction, tensionLying in the plane oxz, the force has no component in the y-direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionResultant force in the z-axis direction ofWherein(8) see fig. 4.
Mechanical rocker arm acting forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（9）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point a is:
（10），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point A is along the z axis and is determined by the gravity, the tension and the acting force of the mechanical rocker arm;
wherein the supporting force given by the mechanical rocker arm is as follows,(9) oriented along the z-axis;
2. and (3) analyzing the stress condition of the central point M of the power transmission conductor at the point c:
referring to fig. 5 and 6, when the center point M of the power transmission line is located at point C, it is assumed that the center point M of the power transmission line is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point C,according to the formula (7),
(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofSimilar to the formula (8), at the point C,
mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
wherein（11）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to gravity G along the negative direction of the z axis, the tension T is positioned on the oxy plane, no component exists along the y direction, and the acting force of a mechanical rocker armIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point C is:
（12），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point C is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（11)，，
the supporting force given by the mechanical rocker arm at the point C is as follows:
(13)，lying in a plane parallel to the plane oyz, consisting ofAnddetermining;
3. analyzing the stress condition of the central point M of the power transmission conductor at the point B:
referring to fig. 7, when the center point M of the power transmission line is located at point B, it is assumed that the center point M of the power transmission line is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionIn the 0xz plane, the force has no component in the y direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionResultant force along the z-axisWherein(8) see fig. 4.
Mechanical rocker arm acting forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（14）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at the point B is:
(15) the direction of resultant force applied when the center point M of the transmission conductor is positioned at the point B is determined by gravity, tension and acting force of a mechanical rocker arm along the z axis; wherein the supporting force given by the mechanical rocker arm is as follows,(14) with the direction along the z-axis.
4. And (3) analyzing the stress condition of the central point M of the power transmission conductor at the point D:
referring to fig. 8, when the center point M of the power transmission line is located at point D, it is assumed that the center point M of the power transmission line is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; transmission conductorThe central point M is under negative tension along the z-axis by gravityOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point D,according to the formula (7),(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofAccording to the formula (8), at the point D,mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
wherein（16）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionOn the oxy plane, with no component in the y-direction, mechanical rocker actionIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force applied when the center point M of the power transmission line is located at the point D is:
(17) the direction of resultant force applied when the central point M of the transmission conductor is positioned at the point D is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（16)，，
the supporting force given by the mechanical rocker arm at the point D is as follows:
(18)，lying in a plane parallel to the plane oyz, consisting ofAndand (6) determining.
The above is a general analysis, and the specific calculation needs to consider the approximate conditions and specific reference data. The following analysis gives the approximate conditions and calculation parameters, which are applied to a single conductor model with a span of 80 meters and transmission conductor type number JL/LB 20A-400/35.
Two, approximate condition
1. The design deflection of the steel pipe rod is 5 per thousand, the deformation amount is 3cm, the influence caused by the bending of the steel pipe rod can be ignored, and the bending of the steel pipe rod is not considered in the following calculation.
2. The sag is approximately constant when the power transmission conductor waves.
3. The galloping amplitude is not large, and the deformation of the material is small when the transmission conductor gallops, so that the influence caused by the elastic deformation of the transmission conductor is ignored, and the length of the transmission conductor is considered to be unchanged when galloping.
4. Since the length of the power conductors varies less with temperature, the effect of the variation of the length of the power conductors with temperature is neglected.
5. The effect of sag on the length of the power transmission conductor is calculated as follows:
dead weight ratio load of power transmission conductor，QIs the quality of the transmission conductor per kilometreQ=1307.5kg/km, A being the cross-sectional area of the power conductor A =425.24Is calculated to
。
Stress，Is the maximum allowable stress at the lowest point of the power conductor,is the breaking force of the power transmission conductor, the unit is N,the magnitude of the tensile resistance is 95 percent of rated tensile resistance (or calculated breaking force), 5 is the minimum allowable safety factor of the power transmission conductor, and the calculated value isAnd calculating a formula according to the length of the overhead line between the suspension points with equal height at two sides:
because the experimental span is smaller, the first two items can be taken during calculation to reach the precision required by the experimentIs calculated toThat is, the influence of the sag on the length of the power transmission conductor during galloping is only 0.008m, and the influence of the sag on the length of the power transmission conductor during galloping can be considered to be small, so that the influence of the sag on the length of the power transmission conductor during galloping is neglected in the following calculation.
Based on the above approximate conditions, it is considered that the length of time during which the power transmission conductor is oscillated is constant.
Thirdly, calculating parameters
1. The span value L =80m, the length of the tension string is 2.445m, the length of 2.445m of the tension string is deducted, and the length of the actual transmission wire in the span is 75.14 m.
2. (1) the quality values of single conductor JL/LB20A-400/35 type transmission conductors are as follows:
and the mass of each strain insulator-string: 27.1kg of hardware string, 25kg of 2 composite insulators and 104.2kg of total mass at two ends, wherein the mass of the rocker arm acting on the central point M of the transmission conductor during galloping is approximately considered to be the sum of the mass of the transmission conductor and the mass of the strain insulator string。
(2) The mass of the double bundle conductor JL/LB20A-400/35 type power transmission conductor is 196.5kg twice that of a single conductor, the gravity load is G =1925.7N, and the mass of each tension string is as follows: 56.3kg of hardware string, 27.6kg of 2 composite insulators and 167.8kg of total mass at two ends, and the mass of the rocker arm acting on the central point M of the power transmission conductor when the double-split conductor waves is also approximately considered to be the sum of the mass of the power transmission conductor and the mass of the strain insulator string。
3. The safety factor is 5.
4. (1) gravity load when single conductor JL/LB20A-400/35 dancing
Rated tensile resistance of 105.7kN, maximum static design tension of single conductorThe maximum tension during galloping is 2 times of the maximum static design tension (the test data of a Hill real type galloping test base in Henan electric academy is 1.6-1.7 times, and the test safety factor is considered in calculation and is 2 times), namely 40.166kN, so that the maximum design tension variation range of the single conductor is wide。
(2) Gravity load of double bundle conductor 2 XJL/LB 20A-400/35 during galloping
The maximum static tension of the double bundle conductor is 2 times of the maximum static tension of the single conductor and is 40.166kN, and the maximum tension during galloping is 2 times of the maximum static design tension, namely 80.322kN, so the maximum design tension variation range of the double bundle conductor。
5. Considering the technical conditions of mechanical waving, the frequency value range is taken during calculation。
Fourthly, calculating results
Single conductor case:
1. the central point M of the power transmission conductor is positioned at the point A and is subjected to the force exerted by the mechanical rocker arm:
（9）；
g =1984.01N, m =202.54kg,、c=1m、b=0.5m、By bringing into (9) the formulaThe tension is respectively obtained from 20083N and 40166N，
；
At the point AHaving only z-component, i.e. supporting forceThe direction is along the z-axis direction.
FIG. 9 shows point AA relationship curve.
2. The central point M of the power transmission conductor is positioned at the point C and is subjected to the force exerted by the mechanical rocker arm:
（13）；
g =1984.01N, m =202.54kg,、c=1m、b=0.5m、The compound is obtained by the formula (13),
，
the tension is respectively obtained from 20083N and 40166N,
，
，
the direction lies in the oyz plane.
FIG. 10 shows point CA relationship curve.
3. The central point M of the power transmission conductor is positioned at the point B and is subjected to the force exerted by the mechanical rocker arm:
（14）；
g =1984.01N, m =202.54kg,、c=1m、b=0.5m、By bringing into (14) the formula，
The tension is respectively obtained from 20083N and 40166N,
，
，
at point BHaving only z-component, i.e. supporting forceThe direction is along the z-axis direction.
FIG. 11 shows point BA relationship curve.
4. The central point M of the power transmission conductor is positioned at the point D and is subjected to the force exerted by the mechanical rocker arm:
（18）；
g =1984.01N, m =202.54kg,、c=1m、b=0.5m、The product of the formula (18) is,
，
the tension is respectively obtained from 20083N and 40166N,
，
the direction lies in the oyz plane.
FIG. 12 showsA relationship curve.
The relation between the change of the acting force of the mechanical rocker arm along with the frequency and the tension of the wire in a waving period is obtained through calculation. Provides a theoretical basis for the wire galloping experiment under the mechanical action.
Double split conductor case
In the above single-split conductor calculation formula, if only the relationship that the tension of the double-split conductor is twice that of the single-split conductor is considered, the double-split conductor can be directly applied to the double-split conductor, and the calculation result is not repeated.
The above examples are only for describing the preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims (1)
1. A method for calculating the relation between mechanical dancing stress and frequency of an overhead transmission line is characterized by comprising the following steps:
analyzing the stress of the transmission conductor when the transmission conductor is waved by using mechanical equipment:
if the track of the transmission conductor during mechanical galloping is an ellipsoid, an oxyz rectangular coordinate system is established, and the ellipsoid equation is(1) The locus of each point on the conductor is an ellipse when the conductor is waved(ii) a The center point M of the transmission conductor is taken as a research object, and an M-point motion equation is set as(2) (ii) a Equation of parameters（3）Is the circular frequency of the conductor as it is waved,is the time of day or the like,when the conductor is wavedMaximum amplitude in the axial direction;
calculating the first derivative of equation (3)(4) Obtaining the velocity components of the M point in the x direction, the y direction and the z direction; first derivative of formula (4)(5) Obtaining acceleration components of the M point in the x direction, the y direction and the z direction; according to newton's second law:(6) obtaining the center point M of the transmission conductorThe relationship between the resultant force experienced in the direction and the track,
（7）
wherein、、Is the center point M of the power transmission conductorThe resultant force exerted in the direction of the force,、、is the center point M of the power transmission conductorThe component of the velocity in the direction of the,is the center point M of the power transmission conductorThe component of the acceleration in the direction of the,the quality of the transmission conductor when the span is L meters;
setting the center point M of a transmission conductor to be acted by tension T, gravity G and force N applied by a mechanical rocker arm; sequentially analyzing the stress condition when the central point M of the power transmission conductor is located at A, C, B, D points;
assuming that the timing starts from point D, the center point M of the power line moves from point D to point a, ，is the period of the conductor waving,is the frequency of conductor waving;
analyzing the stress condition of the central point M of the power transmission conductor at the point A:
when the center point M of the transmission conductor is at the point A, the center point M of the transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionLying in the plane oxz, the force has no component in the y-direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionResultant force in the z-axis direction ofWherein(8) mechanical rocker arm forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（9）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point a is:
（10），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point A is along the z axis and is determined by the gravity, the tension and the acting force of the mechanical rocker arm;
wherein the supporting force given by the mechanical rocker arm is as follows,(9) oriented along the z-axis;
and (3) analyzing the stress condition of the central point M of the power transmission conductor at the point c:
when the center point M of the power transmission conductor is located at the point C, the center point M of the power transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point C,according to the formula (7),
(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofSimilar to the formula (8), at the point C,
mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
wherein（11）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to gravity G along the negative direction of the z axis, the tension T is positioned on the oxy plane, no component exists along the y direction, and the acting force of a mechanical rocker armIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force received by the power transmission line center point M at point C is:
（12），
the direction of resultant force received by the power transmission conductor when the central point M of the power transmission conductor is positioned at the point C is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（11)，，
the supporting force given by the mechanical rocker arm at the point C is as follows:
(13)，lying in a plane parallel to the plane oyz, consisting ofAnddetermining;
analyzing the stress condition of the central point M of the power transmission conductor at the point B:
when the center point M of the transmission conductor is located at the point B, the center point M of the transmission conductor is under tensionGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesThe force in the x-direction must be 0,(ii) a The resultant force experienced in the x-direction is 0, i.e.(ii) a In the y direction, according to the formula (7),at this time, the process of the present invention,therefore, the temperature of the molten steel is controlled,(ii) a The central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionIn the 0xz plane, the force has no component in the y direction, and the mechanical rocker arm actsThe force in the y-direction must be 0,(ii) a The resultant force experienced in the y-direction is 0, i.e.(ii) a In the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to gravity G along the z-axisTo, tensionResultant force along the z-axisWherein(8) mechanical rocker arm forceA force in the z direction ofSo that, along the z-axis, the centre point M of the power conductor is subjected to a resultant force of
Therefore, the first and second electrodes are formed on the substrate,（14）；
in summary, the magnitude of the resultant force received by the power transmission line center point M at the point B is:
(15) the direction of resultant force applied when the center point M of the transmission conductor is positioned at the point B is determined by gravity, tension and acting force of a mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm is as follows,(14) oriented along the z-axis;
and (3) analyzing the stress condition of the central point M of the power transmission conductor at the point D:
when the center point M of the transmission conductor is located at the point D, the center point M of the transmission conductor is set to be stretchedForce ofGravity G and mechanical rocker arm forceThe function of (1); along the x-direction, according to the formula (7),the resultant force applied in the x direction should be 0; the central point M of the transmission conductor is subjected to gravity along the negative direction of the z axis and the tensionOffset each other along the x-direction, mechanical rocker arm forcesComponent in the x-directionMust be 0, so the resultant force received in the x direction is 0,(ii) a In the y-direction, when the centre point M of the power conductor moves to point D,according to the formula (7),(ii) a Gravity G is in the negative direction of the z-axis, tensionResultant force along the y-axis ofAccording to the formula (8), at the point D,mechanical rocker arm forceIn the y-direction component ofAlong the y-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
，
wherein,（16）
in the z direction, according to the formula (7),(ii) a The central point M of the transmission conductor is subjected to the gravity G along the negative direction of the z axis and the tensionOn the oxy plane, with no component in the y-direction, mechanical rocker actionIn the z-direction has a component ofAlong the z-axis, therefore, the centre point M of the power conductor is subjected to a resultant force,
(12) wherein；
in summary, the magnitude of the resultant force applied when the center point M of the power transmission line is located at the point D is:
(17) the direction of resultant force applied when the central point M of the transmission conductor is positioned at the point D is determined by the gravity, the tension and the acting force of the mechanical rocker arm along the z axis;
wherein the supporting force given by the mechanical rocker arm along the directions of x, y and z is respectively,，
（16)，，
the supporting force given by the mechanical rocker arm at the point D is as follows:
(18)，lying in a plane parallel to the plane oyz, consisting ofAndand (6) determining.
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