CN101655588A - Method for simulating mechanical properties of OPGW optical cable ice coating - Google Patents

Abstract

The invention provides a method for simulating mechanical properties of OPGW (optical fiber composite overhead ground wire) optical cable ice coating, comprising the steps of figuring out the maximumtension, the extension, the sag and the stress strain borne by the OPGW optical cable during ice coating, calculating and analyzing the influences of wind and temperature on the mechanical propertiesof OPGW ice coating.

Description

A kind of method for simulating mechanical properties of OPGW optical cable ice coating

Technical field

The present invention relates to power communication special optical cable icing field, be specifically related to Optical Fiber composite overhead Ground Wire (OPGW) icing method for simulating mechanical properties.Be used to calculate under the comprehensive meteorological condition such as OPGW optical cable ice coating and temperature, wind, the suffered tension force of optical cable, elongation and the isoparametric variation of sag, thus draw the influence of icing to the optical cable transmission performance.

Background technology

Seldom, and be based on the experience and the achievement of powerline ice-covering more in the past, lack the icing performance of labor OPGW optical cable targetedly the research of OPGW optical cable ice coating.

At the beginning of in January, 2008 to 2 month, China's south freezing disaster makes the lightguide cable link ice covering thickness considerably beyond design load, existing cable ice coating achievement in research is not enough to say something, therefore, need analyse in depth to changes of properties under OPGW optical icing, the especially heavy icing, potential hidden danger and to the influence of lightguide cable link operation.

Summary of the invention

The objective of the invention is to propose a kind of analogy method of variation of the mechanical property when being used to analyze the OPGW cable ice coating, the variation of properties of optical fiber cable and the hidden danger of existence before and after the especially heavy icing are for the otherness of special area provides design, construction foundation.

Technical scheme of the present invention is: a kind of Optical Fiber composite overhead Ground Wire (OPGW) cable ice coating method for simulating mechanical properties is characterized in that with catenary equation:

$y=a(\mathrm{ch}\frac{x}{a}-1),$ Wherein, a in the equation is the ratio of the deadweight W of optical cable Horizontal Tension H and unit for introducing parameter, and ch (x) is a hyperbolic cosine function;

For the basis calculate optical cable hang naturally and ice coating state under relational expression between each parameter, and find the solution this when concerning with Newton method, the physical relationship formula is as follows:

When a) optical cable hangs naturally

Make t=1/a, must be about the relational expression of t by catenary equation:

$\mathrm{tl}=\ln (({\mathrm{ty}}_A+1)+\sqrt{{({\mathrm{ty}}_A+1)}^2-1})+\ln (({\mathrm{ty}}_B+1)+\sqrt{{({\mathrm{ty}}_B+1)}^2-1})$

In the formula, l is the horizontal range of adjacent two shaft towers, and unit is m; y _ABe the vertical range of optical cable left side hanging point A from minimum point, unit is m; y _BBe the vertical range of optical cable the right hanging point B from minimum point, unit is m;

B) during cable ice coating

By cable length equation L ₁-e ₁=Lo, (wherein, L and L ₁Suspension cable when being optical cable deadweight and icing respectively is long, e and e ₁Be respectively the elongation that produces when optical cable is conducted oneself with dignity with the icing load, Lo is the former length of optical cable), obtain relational expression:

$\mathrm{Lo}=\sqrt{{(2a^{\′}\·\mathrm{sh}\frac{l}{2a^{\′}})}^2+h^2}-\frac{a^{\′}{\mathrm{\γ}}_3}{E}(\frac{l}{2}+\frac{h^2}{2a^{\′}}\·\coth \frac{l}{2a^{\′}}+\frac{a^{\′}}{2}\·\mathrm{sh}\frac{l}{a^{\′}})$

In the formula, the parameter a that a ' has changed for icing is caused, sh (x) is a hyperbolic sine function, and h is the difference in height of two hitch points about optical cable, and unit is m, γ ₃For the suffered icing load of optical cable, comprise that from heavy load unit is N/mmm ², E is the optical cable elastic modulus, unit is kN/mm ², coth (x) is the coth function.

Wherein, to OPGW cable ice coating mechanical property calculation process, may further comprise the steps:

The first step: input known parameters y _A, h, γ ₁, l, E, S, (γ wherein ₁For optical cable from heavy load, S is the optical cable sectional area, other are the same), calculate the initial value that Newton method is found the solution $t_0=\frac{4(y_A+y_B)}{l^2},$ This initial value during as above-mentioned deadweight the first of relational expression separate;

Second step: will just separate the recursion formula that the substitution Newton method draws $t_{i+1}=t_i-\frac{f\left(t_i\right)}{f^{\′}\left(t_i\right)},$ Obtain the modified value of separating;

The 3rd step: judge the precision of the modified value separate, as do not reach the degree of accuracy of requirement, then with modified value for dragover apply-official formula, the value that solves judges that more so iteration until obtaining desired degree of accuracy, draws the t that separates of relational expression _iThereby, release the parameter a that introduces;

The 4th step:, must the optical cable elongation be by parameter a substitution relational expression:

$e=\frac{{\mathrm{\σ}}_0}{E}(\frac{l}{2}+\frac{a}{4}\mathrm{sh}\frac{2l_B}{a}+\frac{a}{4}\mathrm{sh}\frac{2l_A}{a})$

The final lengths that hangs optical cable is:

$L=a(\mathrm{sh}\frac{l_B}{a}+\mathrm{sh}\frac{l_A}{a})$

The former length that gets optical cable is:

Lo＝L-e

The known conditions that Lo calculates as cable ice coating;

The 5th step: input parameter E, S, l, h, y _A, Lo etc., the initial value of the introduction parameter a ' when determining icing; The pole line minimum point with respect to the horizontal offset distance of span mid point is herein $l^{\′}=a\·\sinh \left(\frac{h}{2a\·\sinh (l/2a)}\right),$ When contour setting up, difference in height h is zero do not have horizontal offset distance, i.e. y _AEqual maximum sag;

The 6th step: utilize recursion formula $\mathrm{xip}=\mathrm{xi}-\frac{f\left(\mathrm{xi}\right)}{f^{\′}\left(\mathrm{xi}\right)},$ Initial value is $x_0=\frac{l^2}{4(y_A+y_B)},$ Repeatedly iteration draws accurately and separates, i.e. the parameter a ' that is asked;

The 7th step: parameter a ' substitution relational expression, the suffered maximum tension of optical cable when getting icing:

$\left\{\begin{array}{c}{T}_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_B/a^{\′})\·{10}^{-3}\\ T_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_A/a^{\′})\·{10}^{-3}\end{array}\right.$

The optical cable elongation is:

$e=\frac{a^{\′}\·{\mathrm{\γ}}_3}{E}(\frac{l}{2}+\frac{a^{\′}}{4}\mathrm{sh}\frac{2l_B}{a^{\′}}+\frac{a^{\′}}{4}\mathrm{sh}\frac{2l_A}{a^{\′}})$

Maximum sag is:

$f_m=a^{\′}[\left(\mathrm{ch}\frac{l}{2a^{\′}}\right)\sqrt{1+{\left(\frac{h}{2a^{\′}\mathrm{sh}\frac{l}{2a^{\′}}}\right)}^2}-\sqrt{1+{\left(\frac{h}{l}\right)}^2}+\frac{h}{l}({\mathrm{sh}}^{-1}\frac{h}{l}-{\mathrm{sh}}^{-1}\frac{h}{2a^{\′}\mathrm{sh}\frac{l}{2a^{\′}}})$

Icing optical cable total length is:

$L=a^{\′}(\mathrm{sh}\frac{l_B}{a^{\′}}+\mathrm{sh}\frac{l_A}{a^{\′}})$

Then the optical cable strain is:

$\frac{L-\mathrm{Lo}}{\mathrm{Lo}}\×100\%$

Wherein, the influence of temperature and wind is by under the DIFFERENT METEOROLOGICAL CONDITIONS, and the load in the above-mentioned analogy method is revised in the variation of comprehensive load, thereby calculated ice wind is arranged, stressed, the elongation of OPGW optical cable and sag situation of change are arranged under the comprehensive meteorological condition such as ice and temperature variation etc.:

Comprehensive load γ when having ice that wind is arranged ₅:

${\mathrm{\γ}}_5=\sqrt{{({\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}^2+{{\mathrm{\γ}}_4}^2}$

In the formula, γ ₁For from heavy load, γ ₂Be icing load, γ ₄Be the blast load of icing optical cable, when ice was arranged, aerodynamic coefficient c was taken as 1.2, and then the blast load is:

${\mathrm{\γ}}_4=\frac{0.735a(2b+D)v^2{\sin }^2\mathrm{\θ}}{S}\×{10}^{-3}$

In the formula, the inhomogeneous value of a-wind speed, its concrete value sees the following form 1;

B-cable ice coating thickness, m;

D-wind-engaging cable diameter, mm;

The angle that θ-wind direction and circuit are axial;

The v-wind speed, m/s;

S-optical cable sectional area, mm ²

Table 1 uneven factor of wind speed

Wind speed v (m/s)	??v＜20	??20≤v＜30	?30≤v＜35	??v≥35
					The inhomogeneous a of wind speed	??1.0	??0.85	?0.75	??0.70

When ice was arranged, the cable length that temperature variation causes changed, and cable length becomes:

Lo′＝Lo(1+β·ΔT)

In the formula, the variation of Δ T-environment temperature;

β-linear expansion coefficient (1/ ℃);

Revise the length of optical cable in the aforementioned calculation formula, just can obtain the value of the optical cable temperature influence produces under the icing maximum tension, elongation, sag and ess-strain.

The invention has the beneficial effects as follows:

1) adopted the variation of stretched wire collimation method computational analysis OPGW in the mechanical property (being tension force on the cable, parameters such as the maximum sag of cable length and optical cable) of icing, especially heavy icing front and back;

2) adopted Newton method in calculating,, drawn precise calculation result through iterative equation root repeatedly;

3) computational analysis under the icing, comprehensive meteorological condition such as temperature, wind is to OPGW cable machinery Effect on Performance;

Description of drawings

In order to make content of the present invention by clearer understanding, and be convenient to the description of embodiment, it is as follows to provide description of drawings related to the present invention below:

Fig. 1 is the synoptic diagram according to the suspension optical cable state of analogy method of the present invention;

Fig. 2 is the calculation flow chart according to optical cable deadweight method for simulating mechanical properties of the present invention;

Fig. 3 is the calculation flow chart according to cable ice coating method for simulating mechanical properties of the present invention.

Among the figure, parameter, the unit of each symbolic representation are as follows:

L---set up the horizontal range of shaft tower, unit is m;

H---the vertical drop of two hitch points, unit is m;

l _A---left side hanging point A is from the horizontal range of minimum point, and unit is m;

l _B---the right hanging point B is from the horizontal range of minimum point, and unit is m;

y _A---left side hanging point A is from the vertical range of minimum point, and unit is m;

y _B---the right hanging point B is from the vertical range of minimum point, and unit is m;

σ---horizontal stress, N/mm ²(or MPa);

E---optical cable elastic modulus, unit are kN/mm ²

S---optical cable sectional area, unit are mm ²

Lo---the former length of optical cable, unit is m;

γ---the load that optical cable is suffered, unit are N/mmm ²

Embodiment

Method for simulating mechanical properties of OPGW optical cable ice coating adopts the stretched wire collimation method, and the stretched wire collimation method is to study, set up it according to the pole line unit load along the equally distributed condition of its line length to calculate principle and computing method.Static suspension optical cable model is a hitch point with A and 2 of B as shown in Figure 1.Catenary equation is among the figure:

$y=a(\mathrm{ch}\frac{x}{a}-1)$

In the formula, a is the ratio of the deadweight W of optical cable Horizontal Tension H and unit for introducing parameter.Ch (x) is a hyperbolic cosine function.

Under the optical cable nature suspension status, make t=1/a, catenary equation must be about the relational expression of t

$\mathrm{tl}=\ln (({\mathrm{ty}}_A+1)+\sqrt{{({\mathrm{ty}}_A+1)}^2-1})+\ln (({\mathrm{ty}}_B+1)+\sqrt{{({\mathrm{ty}}_B+1)}^2-1})$

In the formula, l is the horizontal range of adjacent two shaft towers, and unit is m; y _ABe the vertical range of optical cable left side hanging point A from minimum point, unit is m; y _BBe the vertical range of optical cable the right hanging point B from minimum point, unit is m.Separate the above-mentioned relation formula with Newton method, draw parametric t, release parameter a, draw the former long Lo of optical cable again by the relational expression of parameter a and cable length and elongation, the starting condition that this former long Lo calculates as icing.

Calculation process as shown in Figure 2 under the icing.Icing simulation method flow down is:

Behind the icing, the tension force of cable, elongation and suspension cable length overall all can change, and reach another balance again, suc as formula Lo=L ₂-e ₂, Lo is dangle the down former length of the suspension optical cable that obtains of nature, is known conditions, L ₂And e ₂(parameter expression formula a) of a ' changed for icing is caused is represented, draws relational expression all to use containing parameter a '

$\mathrm{Lo}=\sqrt{{({2a}^{\′}\·\mathrm{sh}\frac{l}{2a^{\′}})}^2+h^2}-\frac{a^{\′}{\mathrm{\γ}}_3}{E}(\frac{l}{2}+\frac{h^2}{2a^{\′}}\·\coth \frac{l}{2a^{\′}}+\frac{a^{\′}}{2}\·\mathrm{sh}\frac{l}{a^{\′}})\·{10}^{-3}$

In the formula, γ ₃Be the icing load of optical cable, unit is N/mmm ²Following formula is solved parameter a ' with Newton method, thereby release other parameters such as tension force, elongation and sag.

The first step: input parameter E, S, l, h, y _A, Lo etc., determine to introduce the initial value of parameter a '; It should be noted that pole line minimum point herein with respect to the horizontal offset distance of span mid point is $l^{\′}=a\·\sinh \left(\frac{h}{2a\·\sinh (l/2a)}\right),$ When contour setting up, difference in height h is zero do not have horizontal offset distance, i.e. y _AEqual maximum sag;

Second step: utilize recursion formula, repeatedly iteration draws accurately and separates, i.e. the parameter a ' that is asked;

The 3rd step: utilize a ' and corresponding relation formula, draw other parameters such as tension force, elongation and sag.

The influence of temperature and wind is by under the DIFFERENT METEOROLOGICAL CONDITIONS, and the load in the above-mentioned analogy method is revised in the variation of comprehensive load, thereby calculated ice wind is arranged, and stressed, the elongation of OPGW optical cable and sag situation of change are arranged under the comprehensive meteorological condition such as ice and temperature variation etc.

Be a preferred embodiment of the present invention below, the technical scheme that the present invention realizes be described further below in conjunction with this accompanying drawing.

Known conditions y when the input nature hangs earlier _A, h, γ ₁, l, E, S calculates the former long Lo of optical cable, and this former long Lo is as known conditions and E, S, l, h, y _ASubstitution icing calculation procedure together.Calculation process is during icing

The input known conditions, calculation process as shown in Figure 2.The basis of calculating is a catenary equation

$y=a(\mathrm{ch}\frac{x}{a}-1)$

In the formula, a is the ratio of the deadweight W of optical cable Horizontal Tension H and unit for introducing parameter.Ch (x) is a hyperbolic cosine function.Get the relation of each parameter, substitution equation by catenary equation

L ₁-e ₁＝Lo

In the formula, L ₁Suspension cable during for cable ice coating is long, e ₁The elongation that produces during for cable ice coating, Lo is that the former length of optical cable is known conditions; The all available introduction parameter a ' of each parameter expression.Find the solution above-mentioned equation with Newton method, draw recursion formula, repeatedly iteration is tried to achieve and is separated a ' accurately.A ' substitution relational expression

$\left\{\begin{array}{c}{T}_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_B/a^{\′})\·{10}^{-3}\\ T_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_A/a^{\′})\·{10}^{-3}\end{array}\right.$

Get the suffered maximum tension value of optical cable, other parametric solutions in like manner.

With the influence of this analogy method computational analysis icing to OPGW optical cable maximum tension, result of calculation sees Table 2.

The experiment of table 2 simulation icing is compared with computational data

The simulated experiment span is 25m, and the initial tension value is 13.662kN under the state of nature, the about 12mm of ice covering thickness for the first time, the about 33mm of icing gross thickness for the second time, the tension value of correspondence as shown in Table, computational data and experimental data difference are very little.So, satisfy the requirement of engineering calculation fully.

Above by special embodiment content description the present invention, but those skilled in the art also can recognize the multiple possibility of modification and optional embodiment, for example, by combination and/or change the feature of single embodiment.Therefore, be understandable that these modification and optional embodiment will be considered as included among the present invention, only enclosed patent claims of scope of the present invention and coordinator restriction thereof.

Claims (3)

1, a kind of Optical Fiber composite overhead Ground Wire (OPGW) cable ice coating method for simulating mechanical properties is characterized in that with catenary equation:

Wherein, a in the equation is the ratio of the deadweight W of optical cable Horizontal Tension H and unit for introducing parameter, and ch (x) is a hyperbolic cosine function;

For the basis calculate optical cable hang naturally and ice coating state under relational expression between each parameter, and find the solution this when concerning with Newton method, the physical relationship formula is as follows:

When a) optical cable hangs naturally

Make t=1/a, must be about the relational expression of t by catenary equation:

$\mathrm{tl}=\ln (({\mathrm{ty}}_A+1)+\sqrt{{({\mathrm{ty}}_A+1)}^2-1})+\ln (({\mathrm{ty}}_B+1)+\sqrt{{({\mathrm{ty}}_B+1)}^2-1})$

In the formula, l is the horizontal range of adjacent two shaft towers, and unit is m; y _ABe the vertical range of optical cable left side hanging point A from minimum point, unit is m; y _BBe the vertical range of optical cable the right hanging point B from minimum point, unit is m;

B) during cable ice coating

By cable length equation L ₁-e ₁=Lo, (wherein, L and L ₁Suspension cable when being optical cable deadweight and icing respectively is long, e and e ₁Be respectively the elongation that produces when optical cable is conducted oneself with dignity with the icing load, Lo is the former length of optical cable), obtain relational expression:

$\mathrm{Lo}=\sqrt{{(2a^{\′}\·\mathrm{sh}\frac{l}{2a^{\′}})}^2+h^2}-\frac{a^{\′}{\mathrm{\γ}}_3}{E}(\frac{l}{2}+\frac{h^2}{2a^{\′}}\·\coth \frac{l}{2a^{\′}}+\frac{a^{\′}}{2}\·\mathrm{sh}\frac{l}{a^{\′}})$

In the formula, the parameter a that a ' has changed for icing is caused, sh (x) is a hyperbolic sine function, and h is the difference in height of two hitch points about optical cable, and unit is m, γ ₃For the suffered icing load of optical cable, comprise that from heavy load unit is N/mmm ², E is the optical cable elastic modulus, unit is kN/mm ², coth (x) is the coth function.

2, analogy method as claimed in claim 1 is characterized in that OPGW cable ice coating mechanical property calculation process be may further comprise the steps:

The first step: input known parameters y _A, h, γ ₁, l, E, S, (γ wherein ₁For optical cable from heavy load, S is the optical cable sectional area, other are the same), calculate the initial value that Newton method is found the solution

This initial value during as above-mentioned deadweight the first of relational expression separate;

Second step: will just separate the recursion formula that the substitution Newton method draws

Obtain the modified value of separating;

The 3rd step: judge the precision of the modified value separate, as do not reach the degree of accuracy of requirement, then with modified value for dragover apply-official formula, the value that solves judges that more so iteration until obtaining desired degree of accuracy, draws the t that separates of relational expression _iThereby, release the parameter a that introduces;

The 4th step:, must the optical cable elongation be by parameter a substitution relational expression:

$e=\frac{{\mathrm{\σ}}_0}{E}(\frac{l}{2}+\frac{a}{4}\mathrm{sh}\frac{{2l}_B}{a}+\frac{a}{4}\mathrm{sh}\frac{{2l}_A}{a})$

The final lengths that hangs optical cable is:

$L=a(\mathrm{sh}\frac{l_B}{a}+\mathrm{sh}\frac{l_A}{a})$

The former length that gets optical cable is:

Lo＝L-e

The known conditions that Lo calculates as cable ice coating;

The 5th step: input parameter E, S, l, h, y _A, Lo etc., the initial value of the introduction parameter a ' when determining icing; The pole line minimum point with respect to the horizontal offset distance of span mid point is herein

When contour setting up, difference in height h is zero do not have horizontal offset distance, i.e. y _AEqual maximum sag;

The 6th step: utilize recursion formula

Initial value is Repeatedly iteration draws accurately and separates,

The parameter a ＇ that is promptly asked;

The 7th step: parameter a ＇ substitution relational expression, the suffered maximum tension of optical cable when getting icing:

$\left\{\begin{array}{c}{T}_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_B/a^{\′})\·{10}^{-3}\\ T_{\max }=a^{\′}\·{\mathrm{\γ}}_3\·S\·\cosh (l_A/a^{\′})\·{10}^{-3}\end{array}\right.$

The optical cable elongation is:

$e=\frac{a^{\′}\·{\mathrm{\γ}}_3}{E}(\frac{l}{2}+\frac{a^{\′}}{4}\mathrm{sh}\frac{{2l}_B}{a^{\′}}+\frac{a^{\′}}{4}\mathrm{sh}\frac{{2l}_A}{a^{\′}})$

Maximum sag is:

$f_m=a^{\′}[\left(\mathrm{ch}\frac{l}{2a^{\′}}\right)\sqrt{1+{\left(\frac{h}{2a^{\′}\mathrm{sh}\frac{l}{2a^{\′}}}\right)}^2}-\sqrt{1+{\left(\frac{h}{l}\right)}^2}+\frac{h}{l}({\mathrm{sh}}^{-1}\frac{h}{l}-{\mathrm{sh}}^{-1}\frac{h}{2a^{\′}\mathrm{sh}\frac{l}{2a^{\′}}})$

Icing optical cable total length is:

$L=a^{\′}(\mathrm{sh}\frac{l_B}{a^{\′}}+\mathrm{sh}\frac{l_A}{a^{\′}})$

Then the optical cable strain is:

$\frac{L-\mathrm{Lo}}{\mathrm{Lo}}\×100\%$

3, analogy method as claimed in claim 2, the influence that it is characterized in that temperature and wind is by under the DIFFERENT METEOROLOGICAL CONDITIONS, the load in the above-mentioned analogy method is revised in the variation of comprehensive load, thereby calculated ice wind has been arranged, stressed, the elongation of OPGW optical cable and sag situation of change are arranged under the comprehensive meteorological condition such as ice and temperature variation etc.:

Comprehensive load γ when having ice that wind is arranged ₅:

${\mathrm{\γ}}_5=\sqrt{{({\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}^2+{{\mathrm{\γ}}_4}^2}$

In the formula, γ ₁For from heavy load, γ ₂Be icing load, γ ₄Be the blast load of icing optical cable, when ice was arranged, aerodynamic coefficient c was taken as 1.2, and then the blast load is:

${\mathrm{\γ}}_4=\frac{0.735a(2b+D)v^2{\sin }^2\mathrm{\θ}}{S}\×{10}^{-3}$

In the formula, the inhomogeneous value of a-wind speed, its concrete value sees the following form 1;

B-cable ice coating thickness, m;

D-wind-engaging cable diameter, mm;

The angle that θ-wind direction and circuit are axial;

The v-wind speed, m/s;

S-optical cable sectional area, mm ²

Table 1 uneven factor of wind speed

Wind speed v (m/s) ??v＜20 ??20≤v＜30 ??30≤v＜35 ??v≥35 The inhomogeneous a of wind speed ??1.0 ??0.85 ??0.75 ??0.70

When ice was arranged, the cable length that temperature variation causes changed, and cable length becomes:

Lo′＝Lo(1+β·ΔT)

In the formula, the variation of Δ T-environment temperature;

β-linear expansion coefficient (1/ ℃);

Revise the length of optical cable in the aforementioned calculation formula, just can obtain the value of the optical cable temperature influence produces under the icing maximum tension, elongation, sag and ess-strain.

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