JP2009113530A - Method for estimating strain of trolley wire from contact force of pantograph - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for estimating the strain of trolley wire from the contact force of a pantograph capable of accurately and continuously estimating the stress (strain) exerted on the trolley wire during passing of the pantograph, by using the actually measured contact force between a wire and the pantograph. <P>SOLUTION: The method relates to estimating of the stress (strain) of the trolley wire at a pantograph point. That is, from a characteristic equation (a) obtained from the wave equation of the trolley wire, λ<SP>4</SP>-(T-ρν<SP>2</SP>/EI)λ<SP>2</SP>-i(2ρνω/EI)λ-(ρω<SP>2</SP>/EI)=0 ... (A), where in these four characteristic roots of the formula (A), λ<SB>1</SB>is a complex number whose real part is positive, λ<SB>3</SB>is a complex number whose real part is negative, λ<SB>2</SB>is a positive pure imaginary number, and λ<SB>4</SB>is a negative pure imaginary number, the stress (strain) of the trolley wire at the pantograph point is estimated by multiplying a measured contact force by a conversion factor (b) into the strain of the trolley wire, (γ/EI)×[(λ<SB>1</SB>+λ<SB>2</SB>)/(λ<SB>1</SB>-λ<SB>3</SB>)(λ<SB>1</SB>-λ<SB>4</SB>)] ...(B). <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a method for estimating the distortion of a trolley wire from the contact force of a pantograph.

  The bending force (strain) is generated in the trolley wire due to the contact force between the pantograph and the trolley wire. If this bending stress is repeatedly applied, the trolley wire may be subject to fatigue fracture (disconnection). Is set. In particular, in the Shinkansen operating at high speed, the bending stress generated on the trolley line tends to be significant, and this is one of the important indicators for judging whether the speed is high.

  Previously, a strain gauge was directly attached to the trolley wire to actually measure the value when passing through the pantograph. However, the measurement location was practically limited, and the measurement location necessarily generated the maximum value of stress (strain). Therefore, spatially continuous measurement has been desired. Therefore, a method for continuously calculating the maximum stress (strain) of the trolley wire by measuring the contact force acting on the pantograph has been desired.

In recent years, a method for calculating a trolley line strain of a pantograph point using an elastic floor beam model has been proposed.
Shunichi Kusumi, Takahiro Fukuya, Atsushi Iwainaka, “Examination of Trolley Line Strain Estimation by Contact Force”, 2004 Annual Meeting of the Institute of Electrical Engineers of Japan, August 2004, 3-27, pp. III -239-242

  However, the above-described method uses a formula derived from the relationship between the contact force and the trolley line stress in the steady state, and has a drawback that the calculation error is large for the varying contact force.

  In view of the above situation, the present invention has recently made it possible to accurately measure the contact force acting on a pantograph, and to take advantage of the characteristic that the trolley line stress at the pantograph point is maximized. To provide a method for estimating the strain of a trolley wire from the contact force of a pantograph, which can accurately and continuously estimate the stress (strain) acting on the pantograph using the measured contact force between the overhead line and the pantograph Objective.

In order to achieve the above object, the present invention provides
[1] A method for estimating a trolley line stress (strain) at a pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ ⁴ − (T−ρν ² / EI) λ ² −i (2ρνω / EI) λ− (ρω ² / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ ₁ is a real complex number, λ ₃ is a real complex negative number, λ ₂ is a positive pure imaginary number, and λ ₄ is a negative pure imaginary number. Conversion coefficient (b) (γ / EI) · [(λ ₁ + λ ₂ ) / (λ ₁ −λ ₃ ) (λ ₁ −λ ₄ )] for the measured contact force
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
The trolley line stress (strain) at the pantograph point is estimated by multiplying by.

  [2] In the trolley wire strain estimation method from the contact force of the pantograph described in [1] above, since the equation (B) indicates a frequency characteristic, an impulse response function is prepared in advance, and the measured time axis The trolley line stress (strain) at the pantograph point on the time axis is estimated by superimposing and integrating the impulse response function on the contact force waveform.

  According to the present invention, the following effects can be achieved.

  (1) The maximum stress (strain) of the trolley wire when passing through the pantograph can be estimated spatially continuously, and it is possible to easily and accurately check traveling safety and extract a point requiring attention.

  (2) The measurement efficiency in the current vehicle running test is greatly improved.

  (3) The risk of accidents such as trolley wire breakage is reduced and safety is improved.

The strain estimation method of the trolley line from the contact force of the pantograph of the present invention is a method of estimating the trolley line stress (strain) at the pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ ⁴ − (T−ρν ² / EI) λ ² −i (2ρνω / EI) λ− (ρω ² / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ ₁ is a real complex number, λ ₃ is a real complex negative number, λ ₂ is a positive pure imaginary number, and λ ₄ is a negative pure imaginary number. Conversion coefficient (b) (γ / EI) · [(λ ₁ + λ ₂ ) / (λ ₁ −λ ₃ ) (λ ₁ −λ ₄ )] for the measured contact force
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
The trolley line stress (strain) at the pantograph point is estimated by multiplying by.

  Hereinafter, embodiments of the present invention will be described in detail.

  FIG. 1 is a block diagram of an apparatus for estimating distortion of a trolley wire from the contact force of a pantograph according to the present invention.

In FIG. 1, 1 is a data input device, 2 is an estimation device, 3 is a CPU (central processing unit), 4 is a storage device for information relating to the trolley wire, and here, the line density ρ of the trolley wire, the tension of the trolley wire T, bending rigidity EI of the trolley wire, train traveling speed ν, λ ₁ , λ ₃ , λ ₂ , λ ₄ (described later) are stored. Reference numeral 5 denotes an input interface, 6 denotes an output interface, and 7 denotes an output device.

When the exciting force F is moving at a speed ν using an infinitely long beam model to which tension is applied, the wave equation of the trolley wire is expressed by the following equation (1). Here, the attenuation of the trolley wire is ignored.
^{[Ρ (∂ 2 y / ∂t 2} ) ] - ^{[T (∂ 2 y / ∂x 2} ) ] + ^{[EI (∂ 4 y / ∂x 4} ) ] = F · δ (x-νt ) ... (1 )
When this is converted into the moving coordinate system ξ = x−νt, [ρ (∂ ² y / ∂t ² )] − [2ρνT (∂ ² y / ∂t∂ξ)] − (T−ρν ² ) (∂ ² y / ∂ξ ² ) + [EI (∂ ⁴ y / ∂ξ ⁴ )] = F · δ (ξ)
... (2)
It becomes.

Here, the excitation force F is expressed as F = f · exp (iωt) (3)
Here, i is an imaginary unit, and the form of the solution is y = A · exp (λξ) · exp (iωt) (4)
Assuming that the above equation (2) is substituted, the following characteristic equation can be obtained.
λ ⁴ − (T−ρν ² / EI) λ ² −i (2ρνω / EI) λ− (ρω ² / EI) = 0 (5)
Of the four characteristic roots of Equation (5), λ ₁ is a real complex number with a real part, λ ₃ is a complex number with a negative real part, λ ₂ is a positive pure imaginary number, and λ ₄ is a negative pure imaginary number. .

  The expression of the ratio between the contact force and the trolley line stress (strain) at the pantograph point is strictly different when the moving excitation force acts on the trolley line and when the wave enters the pantograph. However, if it is limited to about 50 Hz or less using the characteristics of the actual overhead line / pantograph, the characteristics are almost the same.

Therefore, when the strain / contact force ratio is expressed by the following equation (6),
(Ε / F) = (γ / EI) · [(λ ₁ + λ ₂ ) / (λ ₁ −λ ₃ ) (λ ₁ −λ ₄ )] (6)
It becomes.

  Here, γ is the distance from the neutral axis of the trolley line to the surface.

  If applied to the actually measured contact force, the calculation error can be kept within 10%.

  Since the above equation (6) is a frequency characteristic, if an impulse response function is prepared in advance and this impulse response function is superimposed and integrated with the actually measured contact force waveform on the time axis, the pantograph points on the time axis are obtained. The trolley line stress (strain) in can be estimated.

  Since the pantograph point has the maximum trolley wire stress (strain), the maximum stress (strain) of the trolley wire can be spatially estimated using this method.

  According to the present invention, the maximum stress (strain) of the trolley wire when passing through the pantograph can be continuously estimated, and it is possible to easily and accurately check traveling safety and extract a point requiring attention. it can.

  In addition, the efficiency of measurement in the current vehicle running test is greatly improved.

  Furthermore, the risk of accidents such as trolley wire disconnection is reduced, and safety is improved.

  Thus, based on the above formula (6), the contact force and the trolley wire strain are estimated.

  FIG. 2 shows an example in which the contact force of the pantograph and the trolley line distortion at that point are calculated using the computer simulation method according to the present invention. Assuming that this is a true value, the value shown in the figure is 497 μ. On the other hand, the conventional method using an elastic floor beam model has a large error of 685 μm, but it can be understood that the method of the present invention can be estimated almost accurately as 517 μm.

  In addition, this invention is not limited to the said Example, Based on the meaning of this invention, a various deformation | transformation is possible and these are not excluded from the scope of the present invention.

  The strain estimation method of the trolley wire from the contact force of the pantograph according to the present invention can continuously estimate the maximum stress (strain) of the trolley wire when passing through the pantograph, confirming driving safety and The present invention can be used as a trolley wire distortion estimation method that can be easily and accurately extracted.

It is a block diagram of the distortion estimation apparatus of the trolley line from the contact force of the pantograph which concerns on this invention. It is a figure which shows the example which calculated the contact force of the pantograph and the trolley line distortion of the point using the computer simulation method which concerns on this invention.

Explanation of symbols

1 data input device 2 estimation device 3 CPU (central processing unit)
4 Storage device for trolley wire information 5 Input interface 6 Output interface 7 Output device

Claims (2)

A method of estimating trolley line stress (strain) at a pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ ⁴ − (T−ρν ² / EI) λ ² −i (2ρνω / EI) λ− (ρω ² / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ ₁ is a real complex number, λ ₃ is a real complex negative number, λ ₂ is a positive pure imaginary number, and λ ₄ is a negative pure imaginary number. Conversion coefficient to trolley wire strain for measured contact force (b) (γ / EI) · [(λ ₁ + λ ₂ ) / (λ ₁ −λ ₃ ) (λ ₁ −λ ₄ )]
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
Is used to estimate the trolley line stress (strain) at the pantograph point, and the trolley line strain estimation method from the contact force of the pantograph.   2. A method for estimating distortion of a trolley wire from a contact force of a pantograph according to claim 1, wherein the equation (B) indicates a frequency characteristic, so that an impulse response function is prepared in advance, and an actually measured contact force waveform on a time axis. A trolley wire strain estimation method based on a contact force of a pantograph, wherein the trolley wire stress (strain) at the pantograph point on the time axis is estimated by superimposing and integrating the impulse response function with respect to.

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