Method for predicting temperature of conductive contact

Abstract

To provide a temperature prediction method in the vicinity of a current-carrying contact based on heat generation through Joule heat generated when carrying a current while sliding and moving a sliding surface of a contact strip along a trolley wire.SOLUTION: The temperature prediction step includes a step of calculating a reaching temperature at a distance X from the sliding surface based on a potential distribution in the slider during energization, and a position temperature calculation step of calculating a normalized temperature normalized by an initial temperature of the sliding surface and the reaching temperature at the distance X with respect to a thermal diffusion time which is a function of the distance X at the position temperature of the distance X.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a method for predicting the temperature of a current-carrying contact based on heat generation via Joule heat, and more particularly to a method for predicting the temperature of a current-carrying contact based on heat generation via Joule heat that occurs when current is passed through a contact strip while the contact surface of the contact strip is slidingly moved along a trolley wire. [Background technology]

[0002] The φ-θ theory, which states that the contact voltage of a current-carrying contact is determined by the maximum temperature of the contact, is also used to analyze the temperature that occurs in power supply devices that are in contact with each other, such as the combination of a contact wire and a slider used in railway vehicles.

[0003] For example, Patent Document 1 discloses a method for determining the component-specific temperatures, which are the maximum temperatures of the contact wire and the contact strip, using the φ-θ theory. In a predetermined area including the contact wire, the contact strip, and their contact points, the φ-θ theory is applied to the correlation between the contact voltage applied from the contact wire to the contact strip via the contact point and the overall maximum temperature, which is the maximum temperature generated in the predetermined area, to calculate the overall maximum temperature. Then, a curve showing the relationship between the temperature distribution and the potential distribution generated in the predetermined area is obtained from the contact voltage and the overall maximum temperature, and the component-specific maximum temperatures of the contact wire and the contact strip are calculated from this curve. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2016-37280 DISCLOSURE OF THE INVENTION [Problem to be solved by the invention]

[0005] However, when calculating the temperature rise due to Joule heating from the contact voltage, the above-mentioned φ-θ theory cannot be applied near the contact point, considering the high-speed relative movement of the contact wire and the contact strip, and it is necessary to use unsteady heat conduction analysis such as the finite element method. On the other hand, when considering the micrometer-order transferred material as the wear surface condition of the contact surface, analysis using the finite element method is also difficult. Therefore, other methods, especially a method that can calculate the temperature rise while taking into account the wear surface condition, have been sought.

[0006] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a method for predicting the temperature in the vicinity of an electric contact based on the heat generated through Joule heating when an electric current is passed through a contact strip while the contact strip is slidingly moved along the contact wire. [Means for solving the problem]

[0007] A method according to the present invention is a method for predicting a temperature in the vicinity of a current-carrying contact based on heat generation via Joule heating that occurs when an electric current is applied while the sliding surface of a contact strip is slidingly moved along a trolley wire, and includes a temperature prediction step of calculating a position temperature, which is a time change of temperature at a position a distance X away from the current-carrying contact perpendicular to the sliding surface, wherein the temperature prediction step includes: a step of determining an ultimate temperature at the distance X from the sliding surface based on a potential distribution in the contact strip when an electric current is applied; and a position temperature calculation step of calculating a normalized temperature at the position temperature at the distance X, normalized by an initial temperature of the sliding surface and the ultimate temperature at the distance X, for a thermal diffusion time that is a function of the distance X.

[0008] According to this feature, it is possible to easily predict the temperature in the vicinity of the current-carrying contact based on the heat generated through Joule heat that is generated when current is passed through the contact strip while the sliding surface of the contact strip is slidingly moved along the trolley wire.

[0009] In the above-described invention, the position temperature calculation step may be characterized in that it is a step of calculating a function of the normalized temperature on an equipotential surface including the position at the distance X relative to the thermal diffusion time. Furthermore, the thermal diffusion time and the normalized temperature may include parameters corresponding to the material combination, contact radius, contact voltage, and surface condition of the current-carrying contact. According to this feature, even if the material combination, contact radius, contact voltage, surface condition, etc. of the current-carrying contact are arbitrarily changed, the change in temperature over time at any position near the current-carrying contact can be represented by a function, i.e., a single curve, and the temperature near the current-carrying contact can be easily predicted.

[0010] In the above-described invention, the function may be calculated by regression calculation using data measured by actual measurements or experiments. According to this feature, by defining several parameters, it becomes possible to easily calculate the unsteady temperature rise due to Joule heat. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 10 is a diagram showing an example of an analytical model for obtaining a potential distribution used in the temperature prediction method according to the present invention. [Figure 2] (a) Electric potential distribution and (b) temperature distribution obtained by unsteady heat conduction analysis. [Figure 3] (a) A graph showing the difference in temperature rise depending on the position on the z-axis, and (b) a graph in which they are normalized and unified. [Figure 4] (a) A graph showing the difference in temperature rise depending on the contact radius, and (b) a graph in which the two are normalized and unified. [Figure 5] (a) is a graph showing the difference in temperature rise due to contact voltage, and (b) is a graph that unifies the difference by normalizing the temperature rise and the contact voltage. [Figure 6] (a) A graph showing the difference in temperature rise depending on the combination of materials, and (b) a graph that unifies the difference by normalization. [Figure 7]1 is a graph showing the correspondence between a logistic regression curve and analytical values. [Figure 8] 10 is a graph showing a range of predicted values ​​of fused bridge voltage based on a temperature prediction method in accordance with the present invention. [Figure 9] FIG. 1 is a side view of a high-speed pantograph testing machine used to verify the validity of the temperature prediction method. [Figure 10] 1 is a histogram of the measured contact voltage. [Figure 11] FIG. 10 is a plot of measured molten bridge voltage on a graph showing a range of estimated values ​​of the molten bridge voltage. [Figure 12] FIG. 10 is a diagram showing the results of a component analysis of copper on the surface of the contact strip after an electrical current test using a high-speed pantograph tester. DETAILED DESCRIPTION OF THE INVENTION

[0012] When an electric current is applied to the sliding surface of a contact strip while the sliding surface is moving along the contact wire, the temperature rise at a position inside the contact strip at a distance X perpendicular to the sliding surface, i.e., the temperature change over time from the initial temperature to the final temperature, can be expressed by the initial temperature at the position X (which usually coincides with the initial temperature of the sliding surface), the normalized temperature normalized by the final temperature, and the thermal diffusion time (position temperature). Note that the temperature distribution inside the contact strip due to Joule heat becomes similar to the electric potential distribution after a sufficient time has passed and the temperature reaches a saturated (stable) state, and the final temperature can be obtained corresponding to the electric potential at that position. Since the thermal diffusion time is a function of the distance X, and distance is replaced with time, the position temperature can be expressed as a time change of temperature that is independent of the distance X.

[0013] Furthermore, if the temperature distribution is similar to the electric potential distribution even before the temperature is saturated, the temperature change over time on the equipotential surface will be the same. In other words, the positional temperature mentioned above will be equal to the positional temperature at another position on the equipotential surface.

[0014] Here, we consider formulating the time change of temperature, which is expressed in a form independent of the distance X, as a function of the thermal diffusion time. Such a function can be calculated, for example, as a regression curve of several data measured by actual measurements or experiments. In particular, if a function including parameters corresponding to the combination of materials of the contact wire and the contact strip, the contact radius, the contact voltage, and the surface condition is defined, the position temperature can be calculated in response to the changes of these parameters.

[0015] The method for predicting the temperature of a current-carrying contact according to the present invention will be described below with reference to FIGS.

[0016] For example, an analytical model 10 as shown in Fig. 1 is used to obtain the potential distribution and the distribution of the temperature reached when the temperature is stable and saturated (hereinafter referred to as the saturated state). The analytical model 10 is a model using the finite element method (FEM) consisting of a cylindrical electrode with a radius D and a center axis on the z-axis. In this cylindrical electrode, the upper side of the plane at z=0 is assumed to be a contact wire 1, and the lower side is assumed to be a contact strip 2. On the plane at z=0, which is the sliding surface, a circular area of ​​radius a from the z-axis is assumed to be the current-carrying contact 3 where the contact wire 1 and the contact strip 2 come into contact with each other. The mesh of the analytical model 10 is divided into the z-axis direction, the r-direction perpendicular to the z-axis, and the circumferential direction around the z-axis.

[0017] The method for determining the potential and the ultimate temperature is the same as in Patent Document 1, and so details are omitted here. While Patent Document 1 states that the temperature rise occurs in a sufficiently short time, this embodiment deals with a state during the temperature rise (hereinafter referred to as a non-saturated state). Meanwhile, the potential distribution stabilizes to a constant value in a sufficiently short time compared to the transition of the temperature distribution to a saturated state.

[0018] Incidentally, Figure 2 shows an example of unsteady heat conduction analysis performed on the above-mentioned analysis model. -2This shows a non-saturated state after 20 seconds, before the temperature has stabilized. As a result of this non-steady state heat conduction analysis, it was found that the potential distribution and temperature distribution are similar even in a non-saturated state where the temperature is changing. In other words, the temperature on an equipotential surface is the same even in a non-saturated state. Therefore, if we can find the positional temperature, which is the temperature change over time at any point on the z-axis, we can also find the positional temperature on the equipotential surface that includes that point. In other words, the temperature at any position within the cylindrical electrode mentioned above can be found from the temperature at the intersection of the equipotential surface that includes that position and the z-axis. Therefore, below we will find the temperature at any position (0,X), where X is the distance from the sliding surface on the z-axis.

[0019] As mentioned above, the temperature at any position (0,X) on the z-axis is found and expanded to other positions on the equipotential surface. For this reason, the position on the z-axis is expressed using μ as follows. Equation (1) is the equation for the equipotential surface, and a is the radius [m] of the current-carrying contact 3 as mentioned above. From this equation, the intersection point with the z-axis of this equipotential surface is determined by substituting r=0, and it is expressed as z=μ 0.5 In other words, the square root of μ is X. Furthermore, μ is obtained by solving equation (1) as equation (2). Therefore, the equipotential surface including any position (r, z) is located at the position (0, μ 0.5 ) passes through.

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[0020] Next, the position on the z-axis (0,μ 0.5 ), the normalized potential β obtained by dividing the potential at the same position by the contact voltage Vc can be expressed by the following equation (3). Here, α is the potential on the sliding surface (z=0) divided by the contact voltage Vc. c is used as the contact boundary coefficient of the current-carrying contact 3 according to the condition of the sliding surface (contact surface) as shown in equation (4). ρ1 and ρ2 are the electrical resistivities [Ωm] of the contact wire and the contact strip, respectively. d1 and ρ d2are the electrical resistivities [Ωm] of the films formed on the surfaces of the contact wire and the contact strip, respectively, and d1 and d2 are the thicknesses [m] of the films formed on the surfaces of the contact wire and the contact strip, respectively. In other words, the contact boundary coefficient α includes parameters corresponding to the material combination and surface condition of the contact wire and the contact strip.

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[0021] On the other hand, the temperature reached at the saturated state at the position where the normalized potential is β is the temperature θ βmax [K] can be expressed by the formula (5). This formula is similar to the formula (9) in Patent Document 1, and is expressed as φ / V c is replaced with β. Here, V c is the contact voltage, L is the Lorentz number [V 2 / K 2 ], and the bulk temperature of the contact wire and contact strip was set to 300[K].

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[0022] This reached temperature θ βmax Using the initial temperature θ min When the temperature rise from [K] is normalized, the normalized temperature θ * [-] is expressed as equation (6). Here, θ t is the temperature [K] at the same location at any time.

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[0023] In addition, Joule heat is generated at the outer periphery (a, 0) of the current-carrying contact 3, and at the position (0, μ 0.5 ), the thermal diffusion time t * is expressed by the following equation (7): where λ is the thermal conductivity [W / mK], c is the specific heat [J / kgK], and ρ is the density [kg / m 3 ]. In other words, the thermal diffusion time t * is "X" ("μ0.5 ") is a function of

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[0024] Referring to FIG. 3, the temperature at multiple positions on the z-axis changes over time as shown in FIG. 3(a) by the unsteady heat conduction analysis. The vertical axis represents the normalized temperature θ * The horizontal axis is the thermal diffusion time t * That is, at any position on the z-axis of the above-mentioned analytical model 10, the thermal diffusion time t * Initial temperature θ min and the reached temperature θ max Normalized temperature θ * Then, as shown in Figure 1(b), the time variations of multiple temperatures at multiple positions on the z-axis can be normalized to one point on the graph and superimposed onto a single curve. This allows the distance X (μ 0.5 ) can be used to determine the temperature at a distance of

[0025] Furthermore, as mentioned above, the temperature on an equipotential surface is the same even in a non-saturated state. In other words, the temperature rise at any point on the z-axis is the same on the equipotential surface passing through that point. Therefore, the temperature rise due to Joule heat at any position near the current-carrying contact 3 can be calculated.

[0026] Furthermore, as shown in Figures 4 and 5, if a graph of temperature rise is plotted using normalized temperature versus thermal diffusion time in the same way as above, it becomes possible to consolidate the changes in positional temperature over time into a single curve, even if some of the conditions change. For example, the difference in temperature rise due to contact radius in Figure 4(a) and the difference in temperature rise due to contact voltage in Figure 5(a) can be consolidated by normalization as shown in each figure (b).

[0027] By the way, the thermal diffusion time t *Regarding the thermal conductivity λ, the assumption was made that both the contact wire and the contact strip were made of Cu (hard copper) as shown in Fig. 4 and Fig. 5. The materials of the contact wire and the contact strip are often different materials, for example, an iron-based sintered alloy and hard copper, respectively. Therefore, the thermal diffusion time t * For the thermal conductivity λ, we use the following equation (8): * 1 or λ * 2 to accommodate the combination of different materials. * is the composite thermal conductivity [W / mK] taking into account the contact points of the dissimilar metals of the contact wire and the contact strip, and the subscripts "1" and "2" indicate the thermal diffusion time when heat is diffused into the contact wire and the contact strip, respectively. Also, λ1 and λ2 are the thermal conductivities [W / mK] of the materials of the contact wire and the contact strip, respectively. λ * 1 and λ * 2 is the thermal conductivity of the contact wire and the contact strip combined on the path from the outer periphery of the contact to the z-axis on the sliding surface, and the thermal conductivity of the contact wire or the contact strip at the position (0,μ 0.5 This means that one thermal conductivity is used in the path up to the

[0028]

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[0029] As shown in Fig. 6, by using the composite thermal conductivity calculated by Eq. (8), it is possible to unify multiple normalized temperature curves even when the combination of materials for the contact wire and the contact strip is different. That is, as shown in Fig. 6(a), for the time change of temperature in the case of different material combinations obtained by the unsteady heat conduction analysis, the vertical axis is the normalized temperature θ calculated by Eq. (6). * The horizontal axis is the thermal diffusion time t taking into account the combined thermal conductivity according to Eqs. (7) and (8). * Then, the temperature changes over time for different combinations of materials can be normalized and superimposed onto a single curve, as shown in Figure 1(b).

[0030] The curve of the normalized temperature of the temperature rise unified as described above can be formulated using logistic regression as shown in the following equations (9) to (11), and calculated as a regression curve. * Thermal diffusion time t * In this case, this function is determined to fit a unified curve that overlaps with a single curve even if some of the conditions change as described above. In other words, this function includes parameters corresponding to the combination of materials of the contact wire and the contact strip, the contact radius, the contact voltage, and the surface condition. Here, t * 50% is the thermal diffusion time when the normalized temperature reaches 50%, that is, when the normalized temperature reaches 0.5, assuming that the initial temperature is 0 and the final temperature is 1. Also, y1 and y2 are coefficients for logistic regression, and for example, t * 50% = 0.303, y1 = 0.949, y2 = 0.594. Note that the coefficients of such a regression curve may be calculated by regression calculation using data measured by actual measurements or experiments. Also, this function may be formulated by a method other than logistic regression.

[0031]

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[0032] As shown in FIG. 7, the formulation of the normalized temperature using the logistic regression equation described above closely matches the normalized temperature obtained by unsteady heat conduction analysis.

[0033] By doing so, the normalized temperature at any position in the electrode near the current-carrying contact can be obtained, and temperature prediction can be easily performed.

[0034] Next, the results of verifying the validity of the above-described method for predicting the temperature of the current-carrying contacts will be described.

[0035] First, as shown in Fig. 8, the position temperature is calculated by the above-mentioned temperature prediction method, and the contact voltage V c In other words, the range of the estimated value of the molten bridge voltage was obtained by using equations (9) to (11) that show the normalized temperature. In detail, the contact wire material was hard copper and the contact strip material was iron-based sintered alloy, and the temperature θ was calculated when the contact boundary coefficient α was changed from 0.5 to 1.0 at a certain speed. t is the maximum contact voltage at which the contact wire and the contact strip reach their boiling points, and the temperature θ t The minimum value of the contact voltage at which the contact melts was determined using the temperature prediction method described above, and plotted as the upper and lower limits of the melting bridge voltage. Similar plots were then made for multiple speeds ranging from 0 to 300 km / h. The upper and lower limits of the melting bridge voltage were also determined for two cases: with and without copper transfer to the contact strip. When copper transfer occurs, the contact strip surface is treated as copper, which increases the thermal conductivity and makes it easier for the contact temperature to rise. In other words, the contact voltage that melts the contacts decreases, and in the figure, the case with copper transfer is plotted on the lower side, where the voltage is lower, compared to the case without copper transfer.

[0036] Separately, a sliding test was conducted using a high-speed pantograph testing machine 20 shown in Fig. 9, in which a contact wire test piece 12 and a contact strip test piece 13 were slid against each other while an electric current was applied, to measure the contact voltage. The high-speed pantograph testing machine 20 is an apparatus in which the contact wire test piece 12 is attached in an annular shape to the circumference of the underside of a disk 11 that rotates in a horizontal plane, and the disk 11 is rotated while the contact strip test piece 13 attached to a pantograph 14 is brought into contact with the underside of the contact wire test piece 12, thereby obtaining the sliding speed. The high-speed pantograph testing machine 20 can also measure the contact voltage using a contact voltage measuring device 16 while applying a voltage between the contact wire test piece 12 and the contact strip test piece 13 via a slip ring 17 using a current-carrying device 15.

[0037] As shown in Fig. 10, a histogram of contact voltages measured in a sliding test using a high-speed pantograph tester 20 was created. Here, since the voltage that generally leads to arc discharge is 10 V, contact voltages below 10 V were recorded as experimental values ​​of the molten bridge voltage along with the sliding speed.

[0038] As shown in Fig. 11, the recorded experimental values ​​of the molten bridge voltage were plotted for each sliding speed on Fig. 8, which shows the range of the estimated values ​​of the molten bridge voltage. As a result, the experimental value of the molten bridge voltage at a sliding speed of 300 km / h was roughly in agreement with the range of the estimated value of the molten bridge voltage when there is no copper transfer to the contact strip by the temperature prediction method. In addition, in the experiment at a sliding speed of 200 km / h, the estimated value was within the range of both the cases with and without copper transfer to the contact strip. Furthermore, the experimental value at a sliding speed of 100 km / h or less was roughly in agreement with the range of the estimated value when there is copper transfer to the contact strip.

[0039] Figure 12 shows the results of the copper content analysis on the surface of the contact strip specimen after the sliding test, summarized by sliding speed. As shown in the figure, it was found that the copper content on the surface of the contact strip tends to increase when the sliding speed is reduced from 60 km / h. In other words, it is considered that copper was transferred to the contact strip at sliding speeds below 60 km / h.

[0040] From these results, it was found that the estimated values ​​of the molten bridge voltage for each sliding speed generally agreed with the experimental values ​​of the molten bridge voltage and the experimental results of whether or not copper was transferred to the contact strip, although there was a difference in the estimated value of the speed at which copper began to transfer. In other words, it is considered that the temperature prediction for obtaining the estimated value of the molten bridge voltage by the above-mentioned method is also generally consistent with the experimental results by the high-speed pantograph testing machine 20.

[0041] While the exemplary embodiments of the present invention and the accompanying modifications have been described above, the present invention is not necessarily limited thereto and can be modified as appropriate by those skilled in the art. In other words, those skilled in the art will be able to find various alternative embodiments and modifications without departing from the scope of the appended claims. [Explanation of symbols]

[0042] 1 Contact wire 2 sliders 3 Current-carrying contacts 10 Analysis Model

Claims

1. A method for predicting a temperature in the vicinity of an electric contact based on heat generated through Joule heat when an electric current is applied while the sliding surface of a contact strip is slidingly moved along a trolley wire, comprising the steps of: a temperature prediction step of calculating a position temperature, which is a change over time in temperature at a position a distance X away from the current-carrying contact perpendicular to the sliding surface, The temperature prediction step includes: determining an attained temperature at the distance X from the sliding surface based on a potential distribution in the contact strip when a current is applied; and a position temperature calculation step of calculating a normalized temperature normalized by the initial temperature of the sliding surface and the reached temperature at the distance X for a thermal diffusion time that is a function of the distance X, at the position temperature at the distance X.

2. 2. The method for predicting the temperature of a current-carrying contact according to claim 1, wherein the position temperature calculation step is a step of calculating a function of the normalized temperature on an equipotential surface including the position at the distance X with respect to the thermal diffusion time.

3. 3. The method for predicting the temperature of a current-carrying contact according to claim 2, wherein the function includes parameters corresponding to a material combination, a contact radius, a contact voltage, and a surface condition of the current-carrying contact.

4. 4. The method for predicting the temperature of a current-carrying contact according to claim 3, wherein the function is calculated by a regression calculation using data measured by actual measurement or experiment.

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