JP6291688B2 - Temperature analysis method and power supply device manufacturing method - Google Patents

Description

  The present invention relates to a temperature analysis method for a trolley wire and a sliding plate used in a railway vehicle, and a method for manufacturing a power supply device including the trolley wire and a sliding plate.

  Since the life of trolley wire files that make up current collecting materials (power supply devices) used in electric railways is determined by wear, many studies and material developments related to wear of current collecting materials have been reported so far. (See Non-Patent Documents 1 to 3). In general, the wear characteristics of the trolley wire and the sliding plate vary depending on the combination of materials. According to Non-Patent Document 4, a trolley wire wear map arranged from the viewpoint of a contact surface temperature rise is created from a wear test result obtained by changing a combination of a sliding plate with respect to a Cr—Zr-based copper alloy trolley wire. Further, according to Non-Patent Document 5, there is reported a comparison organized by the accumulated value of arc discharge energy based on the result of wear test in which the combination of the sliding plates with respect to oxygen-free copper is changed.

  Further, according to Non-Patent Document 6, a wear test on a combination of a hard copper trolley wire and an iron-based sintered alloy has been performed so far, and the wear mode under energization depends on the contact temperature governed by load and current. It can be classified into two types. Further, according to Non-Patent Document 7, a wear form transition mechanism under energization is proposed based on the temperature distribution analysis result in the vicinity of the contact point, and the film resistance such as an oxide film existing on the contact surface greatly affects the wear form. Has been revealed.

Kaoru Sugawara: "Development and application of new trolley lines", railway vehicles and technology, No.96 pp.46-50 (2004) Hiroo Miyahira, Hiroshi Tsuchiya: “Reduce pantograph wear”, RRR, Vol. 71, No.2 pp.8-11 (2014) M. Ikeda, H. Tsuchiya: Recent Trends on Pantograph for High-Speed Railways in Terms of Tribology, Journal of Japanese Society of Tribolosists, Vol. 58, No. 7, pp.447-454 (2013) Mitsuru Ikeda, Hiroshi Tsuchiya: “Recent Trends in Pantograph Tribology for High-Speed Railways”, Tribologist, Vol.58, No.7 pp.447-454 (2013) Hiroki Nagasawa: "Study on wear characteristics of Cr-Zr copper alloy trolley wire under current flow", Tohoku University Doctoral Dissertation, (1996) Shunichi Kubo: “Study on wear mechanism of carbon pantograph strip infiltrated with copper or copper-lead-tin alloy under arc discharge”, Tohoku University dissertation, (1996) C. Yamashita, K. Adachi: Influence of Current on Wear Modes and Transition Condition of Current Collecting Materials, Journal of Japanese Society of Tribolosists, Vol. 58, No. 7, pp.496-503 (2013) Yamashita Main Tax, Adachi Koji : "Effects of current flow on wear patterns and transition conditions of current collecting materials", Tribologist, Vol.58, No.7 pp.496-503 (2013) C. Yamashita, K. Adachi: Wear Mechanism of Current Collecting Materials due to Temperature Distribution Analysis Considering Degenerated Layer, Journal of Japanese Society of Tribolosists, Vol. 59, No. 5, pp. 302-309 (2014) Yamashita Main Tax, Adachi Yuki: "Elucidation of the current wear mechanism of current collecting materials by temperature distribution analysis considering inclusions", Tribologist, Vol.59, No.5 pp. 302-309 (2014)

  However, in the above non-patent literature, although a wear mechanism under energization is proposed and quantified, a clear wear reduction guideline, that is, a guideline for selecting a material used for a trolley wire and a sliding plate is given. Not reached. Therefore, the development of a new power supply apparatus requires exhaustive experiments and simulations on candidate materials, which takes time and effort.

  An object of the present invention has been made in view of the above-described problems, and is a temperature analysis method and power that can reduce labor and cost required for selecting materials for a trolley wire and a sliding plate constituting a power supply device used in an electric railway. It is providing the manufacturing method of a supply apparatus.

  One aspect of the present invention is a temperature analysis method for analyzing a temperature generated in a power supply device formed by contact between a trolley wire and a sliding plate, the trolley wire, the sliding plate, the trolley wire and the sliding plate Between the contact voltage applied from the trolley wire to the sliding plate via the contact point and the overall maximum temperature, which is the maximum temperature generated in the predetermined region, in a predetermined region including the contact point The relationship between the temperature distribution with respect to the potential distribution generated in the predetermined region is shown based on the step of specifying the overall maximum temperature based on the theoretical formula indicating the above, the contact voltage, and the specified overall maximum temperature. Identifying a curve, identifying a maximum temperature for each member, which is a maximum temperature of each of the trolley wire and the sliding plate, based on the potential at the contact point and the curve; It is the temperature analysis method with.

  Further, according to one aspect of the present invention, in the step of specifying the curve of the temperature analysis method described above, the curve is specified so as to be a parabola having the overall maximum temperature as a vertex at an intermediate value of the contact voltage, In the step of specifying the highest temperature for each member, the highest temperature for each member including the position that is an intermediate value of the contact voltage among the trolley wire and the sliding plate is specified as the overall highest temperature, and the contact The other maximum temperature for each member that does not include a position that is an intermediate voltage value is specified as the temperature at the contact point.

  Further, according to one aspect of the present invention, in the temperature analysis method described above, based on the theoretical formula, the melting point of the metal material constituting the trolley wire, and the melting point of the metal material constituting the sliding plate, The method further includes a step of mapping a contact voltage and a range in which at least one of the trolley wire and the sliding plate melts, of a contact boundary coefficient indicating a contact voltage and a ratio of a potential at the contact point to the contact voltage.

  Further, according to one aspect of the present invention, in the first step of specifying the maximum temperature for each member of the trolley wire and the sliding plate based on the above-described temperature analysis method, and in the specific contact voltage, the contact point The metal material constituting the trolley wire and the metal constituting the sliding plate so that at least the maximum temperature of each member of the trolley wire does not exceed the melting point of the metal material constituting the trolley wire And a second step of determining a combination of materials.

  Further, according to one aspect of the present invention, in the second step of the temperature analysis method described above, a trolley wire side resistivity that is an electrical resistivity of a metal material that constitutes the trolley wire, and a metal material that constitutes the sliding plate The combination of the metal material that constitutes the trolley wire and the metal material that constitutes the sliding plate is determined based on the combination of the resistivity and the sliding plate side resistivity.

  Further, according to one embodiment of the present invention, an area where neither the trolley wire nor the sliding plate is melted, an area where only one of the trolley wire or the sliding plate is melted, and the trolley wire or the sliding plate The trolley based on the division defined by the coefficient that defines the boundary of the region where both melt, and the magnitude relationship between the melting point of the metallic material constituting the trolley wire and the melting point of the metallic material constituting the sliding plate. A combination of a metal material constituting the line and a metal material constituting the sliding plate is determined.

  According to the temperature analysis method and the power supply device manufacturing method described above, it is possible to reduce labor and cost required for selecting a material for the power supply device used in the electric railway.

It is a figure which shows the temperature analysis model of the temperature analysis method which concerns on 1st Embodiment. It is a figure which shows the circuit structure in the temperature analysis model shown in FIG. It is a figure which shows the example of an analysis result of the temperature analysis method which concerns on 1st Embodiment. It is the 1st figure explaining the temperature analysis method concerning a 1st embodiment. It is a 2nd figure explaining the temperature analysis method concerning a 1st embodiment. It is a 3rd figure explaining the temperature analysis method which concerns on 1st Embodiment. It is a 4th figure explaining the temperature analysis method which concerns on 1st Embodiment. It is a 5th figure explaining the temperature analysis method concerning a 1st embodiment. It is a 6th figure explaining the temperature analysis method concerning a 1st embodiment. It is the 1st figure explaining the temperature analysis method concerning a 2nd embodiment. It is a 2nd figure explaining the temperature analysis method which concerns on 2nd Embodiment. It is a 3rd figure explaining the temperature analysis method which concerns on 2nd Embodiment. It is a 4th figure explaining the temperature analysis method which concerns on 2nd Embodiment. It is a 1st figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 2nd figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 3rd figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 4th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 5th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 6th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 7th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is an 8th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is a 9th figure explaining the manufacturing method of the electric power supply apparatus which concerns on 3rd Embodiment. It is the figure which put together the example of the physical-property value used for the example of an analysis result shown in FIG.

<First Embodiment>
Hereinafter, the temperature analysis method according to the first embodiment will be described with reference to the drawings.
The temperature analysis method according to the present embodiment is a temperature analysis method for analyzing a temperature generated in a power supply device mainly used in an electric railway and in which a trolley wire and a sliding plate are in contact with each other.

[Analysis method of potential distribution and temperature distribution]
(Mode of temperature analysis model)
FIG. 1 is a diagram illustrating a temperature analysis model of the temperature analysis method according to the first embodiment.
FIG. 2 is a diagram showing a configuration of an electric circuit in the temperature analysis model shown in FIG.
First, in describing the temperature analysis method according to the present embodiment, the trolley wire 100 constituting the electric railway power supply device, the sliding plate 110 constituting the electric railway power supply device, the trolley wire 100, and A model simulating a predetermined area including the contact point of the sliding plate 110 will be described.

Specifically, as shown in FIG. 1, a trolley wire 100 and a sliding plate 110 are used as cylindrical electrodes that are in contact with each other on a circular surface, and an oxide film existing on the contact surface of each of the trolley wire 100 and the sliding plate 110 is used. Build a model with film resistance. Here, the radius of the base material of the trolley wire 100 and the sliding plate 110 is D, and the radius of the contact surface (hereinafter also referred to as the contact point A) where the trolley wire 100 and the sliding plate 110 physically contact is a. The thickness of the trolley wire surface coating 101 which is an oxide film existing on the contact surface of the trolley wire 100 is d ₁ , and the thickness of the sliding plate surface coating 111 which is an oxide film existing on the contact surface of the sliding plate 110 is d ₂ . To do.
Note that the mode of the temperature analysis model shown in FIG. 1 is one of the simplest modes among models having sufficient analysis accuracy in the temperature analysis method according to the present embodiment, and the model is also used in other embodiments. It is not limited to.

Here, a model simulating a predetermined region of the cylindrical trolley wire 100 and the sliding plate 110 shown in the left of FIG. 1 is divided in the circumferential direction, and a model for one piece as shown in the right of FIG. 1 is considered. FIG. 2 shows a configuration of an electric circuit for each element when the one-piece model shown in the right of FIG. 1 is divided into a mesh shape in the r direction and the z direction. Of the electrical circuit shown in FIG. 2, the potential phi ₀ in the central portion connected to the electric resistance _R 1 to R ₄ is the potential phi ₁ to [phi] ₄ and the electrical resistance _R 1 to R ₄ in each element of the vertical and horizontal The following equation (1) can be used.

In FIG. 2, the temperature θ _{0 of the} central portion connected to the electric resistances R _{1 to} R ₄ can be obtained by the following expression (2) (see the reference (7) described later). In addition, since the actual contact point A between the trolley wire 100 and the sliding plate 110 is a sliding contact, unsteady heat conduction analysis should be performed in consideration of the movement of the contact point A. However, since the temperature rise near the contact point A between the trolley wire 100 and the sliding plate 110 occurs in a sufficiently short time with respect to the movement time of the contact point A, the contact point A between the trolley wire 100 and the sliding plate 110. Even if is regarded as a static contact, it is considered that no large error occurs in the temperature analysis result. Therefore, in the present embodiment, temperature analysis that can be placed in the vicinity of the contact point A is performed using simpler steady state heat conduction analysis. However, in other embodiments, the temperature analysis may be performed using an unsteady heat conduction analysis in consideration of the sliding contact.

Here, “L” is the Lorentz number (= 2.4 × 10 ⁻⁸ [K / V] ² ), and “Φ” is a potential difference [V] between each element divided in a mesh shape.

Electrical resistivity ρ _d1 , ρ _d2 and thermal conductivity λ _d1 , λ _{d2 of} trolley wire surface coating 101 and sliding plate surface coating 111 are Wiedemann-Franz's law (metal thermal conductivity K and electrical conductivity, respectively). This shows that the ratio of σ is proportional to the temperature (see reference (8) described later), and the electrical resistivity ρ ₁ , ρ ₂ and thermal conductivity λ ₁ of each of the trolley wire 100 and the sliding plate 110. , Λ ₂ can be expressed by equations (3) and (4).

Here, the alteration coefficients f ₁ and f ₂ are coefficients indicating an increase in electrical resistivity of the trolley wire surface coating 101 and the sliding plate surface coating 111 with respect to the trolley wire 100 and the sliding plate 110.

(Example of temperature analysis results)
FIG. 3 is a diagram illustrating an example of an analysis result of the temperature analysis method according to the first embodiment.
FIG. 23 is a table summarizing examples of physical property values used in the analysis result example shown in FIG.
As an example, the temperature analysis result shown in FIG. 3 assumes that the material of the trolley wire 100 to be analyzed is hard copper and the material of the sliding plate 110 is an iron-based sintered alloy, as shown in FIG. It is the result of having performed temperature analysis. Here, the physical properties of each metal material are as shown in FIG. In addition, the temperature analysis result shown in FIG. 3 is calculated using the following conditions, for example. Specifically, in the model shown in FIG. 1, the number of grid meshes is 30 × 30 and the mesh size is Δr = Δz = 10 μm (electrode radius D = 300 μm) for the size of the trolley wire 100 and the sliding plate 110. The number of elements in contact with is 10 (radius a of contact point A = 100 μm). Further, the convergence calculation is performed so that the expressions (1) and (2) are satisfied for all elements, and the calculation is terminated when the temperature change of each element becomes less than 1 × 10 ⁻⁶ K.

Further, the analysis result example shown in FIG. 3, in a clean contact the trolley wire surface coating 101 and sliding plate surface coating 111 is not present, the temperature analysis result in the case where a contact voltage V _c and 0.4V. Here, the contact voltage is a voltage (potential difference) generated in the vicinity of a contact point between the trolley wire and the sliding plate when predetermined electric power (current) is supplied to the electric vehicle through the trolley wire and the sliding plate. In the present embodiment, in the model of the trolley wire 100 and the sliding plate 110 shown in FIG. 1, the potential difference generated from the contact point A in the vertical direction (the + Z direction end surface of the trolley wire 100 to the −Z direction end surface of the sliding plate 110). It is. Note that a voltage value generated when a current flows from the trolley wire 100 toward the sliding plate 110 is a positive value.

[Analysis result]
(Influence of contact voltage)
FIG. 4 is a first diagram for explaining the temperature analysis method according to the first embodiment.
According to the simulation results for the models shown in FIGS. 1 and 2, the relationship between the potential distribution and the temperature distribution in the model is as shown in the graph of FIG. Here, FIG. 4 is a diagram in which the relationship between each parameter is plotted for each element on the z-axis of the model shown in FIG. 1, with temperature (K) on the vertical axis and potential (V) on the horizontal axis. As a boundary condition, the temperature at the ends of the trolley wire 100 and the sliding plate 110 in the z-axis direction is set to 300K.

As shown in FIG. 4, the temperature in the vicinity of the contact point A in the trolley wire 100 and the sliding plate 110 is distributed in a parabolic shape with respect to the electric potential generated in the trolley wire 100 and in the sliding plate 110. electrode in) total maximum temperature indicated (overall maximum temperature theta _max), the intermediate value and a position of the contact voltage _{V c,} for example, the contact voltage _{V c} is in the case of 0.4V is generated at the position where the 0.2V I understand that. Further, parabolic relationship, regardless of the size of the contact voltage V _c, also different metals (i.e., contact wire 100 Karasuri plate 110) continuously over, it can be read that occurs seamlessly. Therefore, the phenomenon in which the relationship between the potential distribution and the temperature distribution shown in FIG. 4 is a parabolic shape can be applied even when a voltage (contact voltage V _c ) is applied across different metals, and is inherent to the metal material. It can be said that it does not depend on the characteristic value.

  In FIG. 4, the potential and temperature (contact boundary) at the contact point A between the trolley wire 100 and the sliding plate 110 obtained from the results of the potential distribution and temperature distribution analysis are indicated by broken lines. As shown in the table in FIG. 23, the electrical resistivity of the sliding plate 110 is larger than that of the trolley wire 100, and therefore the ratio of the voltage drop in the sliding plate 110 to the entire voltage drop is large. Therefore, as shown in FIG. 4, the contact boundary between the trolley wire 100 and the sliding plate 110 is located on the right side of the parabola.

FIG. 5 is a second diagram illustrating the temperature analysis method according to the first embodiment.
FIG. 5 shows the relationship between the member-specific maximum temperature (θ _{max — t} , θ _{max — s} ) and the contact voltage V _c in each of the trolley wire 100 and the sliding plate 110. FIG. 5 also shows the φ-θ theoretical value calculated by the following equation (5) (see Document (8)).

As shown in FIG. 5, the maximum temperature (maximum member-specific maximum temperature θ _max — _t ) of the sliding plate 110 including the position at which the intermediate value (1/2 · V _c ) of the contact voltage V _c is approximately equal to the φ-θ theoretical value. It can be seen that even between different metals, the relationship between the overall maximum temperature θ _max and the contact voltage V _c follows the φ-θ theory. On the other hand, the maximum temperature of the trolley wire 100 (the member-specific maximum temperature θ _{max — s} ) is smaller than the φ-θ theoretical value. The difference between the maximum temperatures of the trolley wire 100 and the sliding plate 110 is caused by the contact boundary deviating from the apex of the parabola in the parabola shown in FIG. That is, the maximum temperature of the trolley wire 100 (the member-specific maximum temperature θ _{max — s} ) matches the temperature (contact boundary) at the contact point A between the trolley wire 100 and the sliding plate 110.

(Effect of film resistance)
FIG. 6 is a third diagram for explaining the temperature analysis method according to the first embodiment.
FIG. 6 assumes a trolley wire surface coating 101 having a thickness d ₁ = 10 μm on the surface of the trolley wire 100 as a temperature analysis condition in the temperature analysis method according to the present embodiment, and the contact voltage V _c is V _c = 0.4 V. The analysis results of the potential distribution and temperature distribution for each condition when the alteration coefficient f1 of the trolley wire surface coating 101 is varied between ₁ and 100 are shown. In the boundary condition, the end temperature in the z-axis direction of the trolley wire 100 and the sliding plate 110 is set to 300K as described above. Further, it is assumed that no coating (strip plate surface coating 111) exists on the surface of the sliding plate 110, and d ₂ = 0 is set.

As shown in FIG. 6, the parabola indicating the relationship between the potential distribution and the temperature distribution does not depend on the alteration coefficient f ₁ , that is, the magnitude of the film resistance, and all follows the same locus. That is, the parabola is found to be dependent only on the contact voltage V _c (see FIG. 4). However, with the increase of the deterioration factor f _1, it can be seen that the contact interface between the contact wire 100 and the sliding plate 110 is approaching the apex of the parabola. This is because the ratio of the voltage drop in the trolley wire 100 to the entire voltage drop increases with the increase in the resistance of the trolley wire surface coating 101.

FIG. 7 is a fourth diagram illustrating the temperature analysis method according to the first embodiment.
FIG. 7 shows a comparison between the maximum temperature of each of the trolley wire 100 and the sliding plate 110 obtained from the result of the temperature distribution analysis and the theoretical value of φ-θ. As shown in FIG. 7, since the contact voltage V _c is constant at 0.4 V, the φ-θ theoretical value shows a constant value regardless of the alteration coefficient f _1, and the maximum temperature in the entire electrode (total maximum temperature). theta _max) at which the maximum temperature of the sliding plate 110 (member by the maximum temperature _θ max_s) also has a substantially equal value. On the other hand, it can be seen that the maximum temperature of the trolley wire 100 (the member-specific maximum temperature θ _{max — t} ) increases as the alteration coefficient f ₁ increases. This is because the distribution of the voltage drop generated in the trolley wire 100 increases as the film resistance on the surface of the trolley wire 100 increases, and the contact boundary approaches the apex of the parabola as shown in FIG.

(Influence of bulk temperature)
FIG. 8 is a fifth diagram illustrating the temperature analysis method according to the first embodiment.
The above-mentioned temperature distribution analysis result and equation (5) are analyzed with the boundary condition that the end temperature of the trolley wire 100 and the sliding plate 110, that is, the bulk temperature is 300K. However, in an actual power supply apparatus, there is a difference between both bulk temperatures when the trolley wire 100 and the sliding plate 110 are in contact with each other. This is because the time intervals at which the trolley wire 100 and the sliding plate 110 are subjected to friction are different. According to the reference (9), which will be described later, the temperature of the running plate is actually measured, and is reported to be 160 ° C. at a distance of 2 mm from the contact surface of the sliding plate 110 and 80 ° C. at 5 mm. Therefore, the influence of the bulk temperature of the sliding plate 110 on the in-electrode potential distribution and the temperature distribution will be clarified using FIG.

As an analysis condition, the contact voltage V _c = 0.4 V, the terminal temperature of the sliding plate 110 was changed between 300 to 500 K, and the potential distribution and the temperature distribution analysis were performed. Note that neither the trolley wire surface coating 101 nor the sliding plate surface coating 111 exists. FIG. 8 shows the relationship between the potential distribution on the z-axis and the temperature distribution when the bulk temperature of the sliding plate 110 is changed in five steps. Although the temperature in the vicinity of the potential 0 V, which is the terminal (lower end) on the z-axis of the sliding plate 110, is affected by the bulk temperature of the sliding plate 110, the potential and temperature (contact boundary) at the contact point A and the overall maximum temperature θ. _It can be seen that _max does not change substantially.

FIG. 9 is a sixth diagram illustrating the temperature analysis method according to the first embodiment.
FIG. 9 _compares the maximum temperatures θ _max — _t and θ _max — s for each member of the trolley wire 100 and the sliding plate 110 obtained from the results of the temperature distribution analysis and the theoretical values of φ-θ. As shown in FIG. 9, it can be seen that the influence of the bulk temperature of the sliding plate 110 on the maximum temperatures θ _{max_t} and θ _{max_s} of each of the trolley wire 100 and the sliding plate 110 can be ignored.

The analysis results of the potential distribution and temperature distribution obtained from the above are organized.
(1) The maximum temperature in the electrode (see the model shown in FIG. 1) including the contact point A between the trolley wire 100 and the sliding plate 110 follows the φ-θ theory shown in equation (5).
(2) The temperature distribution with respect to the potential distribution generated in the electrode has a parabolic relationship, and the curve depends only on the contact voltage.
(3) (1) and (2) do not depend on the combination of the material of the trolley wire 100 and the sliding plate 110, the film resistance such as an oxide film, and the bulk temperature.
(4) The potential and temperature (contact boundary) at the contact point A between the trolley wire 100 and the sliding plate 110 vary depending on the film resistance of the surface.

In accordance with the above facts, the temperature analysis method according to the first embodiment firstly includes a predetermined region including the trolley wire 100, the sliding plate 110, and the contact point A of the trolley wire 100 and the sliding plate 110 (see FIG. 1). In the model shown), the correlation between the contact voltage V _c applied from the trolley wire 100 to the sliding plate 110 via the contact point A and the overall maximum temperature θ _max generated in the predetermined region (the model) is The overall maximum temperature θ _max is specified based on the theoretical formula shown (formula (5)).
Subsequently, based on the contact voltage V _c and the specified overall maximum temperature θ _max , a curve indicating the relationship of the temperature distribution to the potential distribution generated in the predetermined region is specified.
Then, based on the potential (contact boundary) at the contact point A and the above curve, the member-specific maximum temperatures θ _{max_t} and θ _{max_s} that are the maximum temperatures of the trolley wire 100 and the sliding plate 110 are specified.

According to such a temperature analysis method, the dissimilarity that occurs when a predetermined voltage (contact voltage V _c ) is applied between dissimilar metals (the trolley wire 100 and the sliding plate 110) having a contact point (contact point A). The temperature (overall maximum temperature θ _max ) generated at the metal contact point can be grasped very simply and with high accuracy. Accordingly, the metallic material constituting each of the contact wire 100 and the contact strip 110, melting point be selected so as not to exceed the maximum temperature theta _max whole, it is possible to obtain guidelines that, the trolley line 100 and contact strip 110 The burden required for material selection can be reduced.
In addition, by grasping the temperature distribution in a predetermined region near the contact point, it is possible to specify the highest temperature for each different metal having the contact point (the member-specific maximum temperature θ _{max — t ,} θ _max−s ), thereby The choice of metal materials can be expanded.

Further, according to the temperature analysis method according to the first embodiment, in the step of specifying the curve, the curve is defined by using the overall maximum temperature θ _max as the apex at the intermediate value (1/2 · V _c ) of the contact voltage. To be a parabola.
In the step of specifying the member-specific maximum temperatures θ _{max — t} , θ _{max — s} , one member-specific maximum including the position of the intermediate value (1/2 · V _c ) of the contact voltage among the trolley wire 100 and the sliding plate 110. temperature whole _(θ max_t, θ one _{Max_s)} was identified as the highest temperature theta _max, does not include the intermediate value becomes (1/2 · _{V c)} position of the contact voltage other member by the maximum temperature _(θ max_t, θ The other of _{max_s} ) is specified as the temperature at the contact point (contact point A).

  By doing in this way, based on the electric potential (contact boundary) in the contact point A of the trolley wire 100 and the sliding plate 110, it grasps | ascertains how each maximum temperature of the trolley wire 100 and the sliding plate 110 changes. be able to. Therefore, by controlling the distribution of the voltage drop depending on the characteristics of the resistance film of the trolley wire 100 and the sliding plate 110, the options for selecting the metal material used for the trolley wire 100 and the sliding plate 110 can be further expanded.

<Second Embodiment>
[Creation of wear form map]
Hereinafter, the temperature analysis method according to the second embodiment will be described with reference to the drawings.
In the second embodiment, based on the facts (1) to (4) described above, which are the basis of the temperature analysis method according to the first embodiment, the wear mode (energization under energization of the trolley wire 100 and the sliding plate 110 is performed. A wear form map that generalizes the wear form) is created. And based on the said wear form map, the manufacturing method of the electric power supply apparatus which has the trolley wire 100 and the sliding board 110 is provided.

  First, in order to create an equation for specifying a parabola indicating the relationship between the potential distribution on the z axis and the temperature distribution of the model (FIG. 1) simulating the trolley wire 100 and the sliding plate 110, a two-dimensional cylindrical coordinate system Expression (2) created by the model is converted into the following expression (6) of the one-dimensional orthogonal coordinate system.

The bulk temperature of the trolley wire 100 and the sliding plate 110 as the boundary condition is 300 K, and the overall maximum temperature θ _max is obtained at a position where the potential is ½ · V _c , so the following equation (7) is obtained.

  Next, the temperature θ at an arbitrary potential φ in the parabola can be expressed by the following equation (8).

  Substituting equation (7) into equation (8), the following equation (9) is derived.

FIG. 10 is a first diagram illustrating a temperature analysis method according to the second embodiment.
FIG. 10 shows a graph in which the horizontal axis of the graph shown in FIG. 4 is replaced with a dimensionless value φ / V _c (hereinafter referred to as dimensionless potential) from the potential (V). By taking φ / V _c in equation (9) again on the horizontal axis, as shown in FIG. 10, the temperature distribution for various contact voltages V _c can be organized into one graph. In FIG. 10, the melting point of the trolley wire 100 (hereinafter referred to as the trolley wire melting point) 1334K and the melting point of the sliding plate 110 (hereinafter referred to as the melting point of the sliding plate) 1646K are shown together, and the dimensionless potential φ / The point where V _c ≧ 0.5 and the parabola intersects with the trolley melting point is indicated by a circle symbol, and the point where the dimensionless potential φ / V _c ≦ 0.5 and the sliding plate melting point is indicated by a triangle symbol. When the contact boundary between the trolley wire 100 and the sliding plate 110 coincides with these points, the trolley wire 100 and the sliding plate 110 start to melt.

Here, since the potential at the end (lower end) in the z-axis direction of the sliding plate 110 is set to 0 V, the potential φ _{c at the} contact boundary is equal to the voltage drop generated in the sliding plate 110. The ratio between the potential φ _{c at the} contact boundary and the contact voltage V _c , that is, the dimensionless potential φ _c / V _c at the contact boundary between the trolley wire 100 and the sliding plate 110 is defined as α, and this is referred to as the “contact boundary coefficient”. It is called. The contact boundary coefficient α is expressed by equation (10) from the concentrated resistance equation and the film resistance equation.

As can be seen from equation (10), the increase in resistance created sliding plate 110 (i.e., an increase of alteration factor f ₂₎ contacting the boundary coefficient α with the increases. Then, since the contact boundary moves to the right side of the parabola shown in FIG. 10, the maximum temperature of the trolley wire 100 (the member-specific maximum temperature θ _{max — t} ) decreases. Further, the contact boundary coefficient α decreases with an increase in the contact resistance generated in the trolley line 100 (that is, the alteration coefficient f ₁ increases), and the contact boundary moves to the left of the parabola shown in FIG. The maximum temperature (the maximum temperature for each member θ _{max — t} ) increases.

FIG. 11 is a second diagram illustrating the temperature analysis method according to the second embodiment.
11, takes the contact voltage V _c on the vertical axis, a graph showing taking contact boundary coefficient α on the horizontal axis, the formula (9), on the basis of (10), contact wire 100, sliding plate 110 It is a wear form map which specifies the combination (area | region) of the conditions where each of these begins to melt | dissolve. Further, FIG. 10 shows the condition of the contact voltage V _{c at which} the overall maximum temperature θ _max reaches the melting point of the trolley wire 100 and the sliding plate 110 based on the equation (5), and is indicated by a horizontal broken line.

  The inventor has so far proposed a mechanism in which the wear form changes under the condition that each of the trolley wire 100 and the sliding plate 110 is melted (refer to the references (6) and (7)), and the trolley wire shown in FIG. The wear forms under energization are classified into the following four types based on the melting conditions of 100 and the sliding plate 110, and the characteristics of each wear form will be described with reference to the literature (6).

(A) A region where the contact voltage V _c is small and neither of them melts is called a mechanical wear mode. As shown in FIG. 11, under the condition that the contact voltage V _c is 0.4 V or less, the entire maximum temperature θ _max does not reach the melting point of the trolley wire 100, so that it does not melt regardless of the contact boundary coefficient α. However, under the condition where the contact boundary coefficient α is large, that is, the condition where the contact resistance of the sliding plate 110 is large, even if the contact voltage V _c exceeds the melting point equivalent of the trolley wire 100, In some cases, the maximum temperature θ _{max — t} is kept low, resulting in a mechanical wear form.
As a feature of the mechanical wear mode, wear characteristics such as wear rate and friction coefficient do not depend on the load and are almost constant values (see Document (6)).

(B) A region where the contact voltage V _c is 0.4 to 0.5 V and the contact boundary coefficient α is relatively small, that is, a region where the contact resistance of the trolley wire 100 is large due to the film resistance (trolley wire surface coating 101) or the like. Then, since there is a difference between the melting point of the trolley wire 100 made of hard copper and the melting point of the sliding plate 110 made of an iron-based sintered alloy, only the trolley wire 100 is melted. This region is referred to as electrical wear form I.
As a feature of the electrical wear form I, the wear rate and the friction coefficient of the trolley wire 100 are maximized (see Document (6)).

(C) In the region where the contact voltage V _c is 0.5 V or more and the contact boundary coefficient α is large, only the sliding plate 110 is melted. This region is referred to as electrical wear form II.
As a feature of the electrical wear form II, the specific wear amount of the sliding plate 110 significantly increases as the load decreases, but the wear rate and the friction coefficient of the trolley wire 100 decrease (see Document (6)).

(D) contacting voltage V _c is in a relatively small area and contact boundary coefficient α above 0.5V, both of which there is a region of melting. This region is referred to as a mixed melt wear mode.
Reference (6) does not mention this form of wear.

For the combination of the metal materials of the trolley wire 100 and the sliding plate 110 (hard copper and iron-based sintered alloy), the contact boundary coefficient α ₀ in clean contact without film resistance is expressed by the following equation (11) from Equation (10): Is derived by

Here, when the contact boundary coefficient α ₀ in a clean contact is 0.96, according to the wear form map shown in FIG. 11, the trolley wire 100 does not melt even if the contact voltage V _c increases, and the mechanical wear form. It can be seen that only the electrical wear form II appears. That is, by referring to the wear form map shown in FIG. 11, it is possible to grasp that the trolley wire 100 does not melt unless there is a film resistance such as an oxide film on the surface of the trolley wire 100.

FIGS. 12 and 13 are a third diagram and a fourth diagram, respectively, for explaining the temperature analysis method according to the second embodiment. Here, FIG. 12 shows the relationship between the trolley wire wear rate and the load, and FIG. 13 shows the state of the trolley wire wear surface in the vicinity of the load 10N.
In the literature (10), the inventor conducted a wear test in which the apparent contact area of the sliding plate 110 was changed in the combination of the trolley wire 100 made of hard copper and the sliding plate 110 made of an iron-based sintered alloy. The change of the trolley wire wear rate with respect to the load as shown in FIG. As shown in FIG. 12, as a result of the wear test, the influence of the apparent contact area was significant only in the vicinity of the load of 10N. When the apparent contact area is 70 mm ² or more, the surface of the trolley wire 100 melts as shown in FIG. 13A, and when the apparent contact area is 50 mm ² or less, the surface of the trolley wire 100 does not melt as shown in FIG. 13B. The mechanism of this phenomenon is that the wear depth increases with a decrease in the apparent contact area, and when the apparent contact area is 50 mm ² or less, the coating on the surface of the trolley wire 100 (the trolley wire surface coating 101) is removed. Is close to 0.96, and it is considered that the trolley wire 100 did not melt.
That is, by appropriately controlling the area at the contact point A between the trolley wire 100 and the sliding plate 110 so that the surface oxide film that can be generated on each of the trolley wire 100 and the sliding plate 110 is removed, the contact boundary coefficient α is set. A high value can be maintained and melting of the trolley wire 100 can be prevented.

11 and equations (9) and (10), the factors governing the wear mode under energization can be narrowed down to the melting point of metal material, the contact boundary coefficient α, and the contact voltage V _c . Among these, since the melting point and contact boundary coefficient α of the metal material are mainly material properties, various metal materials can be obtained by creating a wear form map (FIG. 11) in advance for any combination of metal materials. The wear form can be estimated for the combination of the above. Furthermore, depending on the setting of the contact boundary coefficient α and the melting point of the metal material, it is possible to propose a material combination that can reduce the melting of the trolley wire 100 as much as possible regardless of the contact voltage V _c .

As described above, as a result of conducting the analysis of the potential distribution and the temperature distribution in the vicinity of the contact point A of the trolley wire 100 and the sliding plate 110 and trying to organize the mapping factors (see FIG. 11) of the governing factors of the current wear form, It has been found that the controlling factors of the wear form are specified by the melting point, the contact boundary coefficient α and the contact voltage V _c of the metal material. Accordingly, it is possible to estimate the wear form according to the combination of the metal material of the trolley wire 100 and the sliding plate 110. Further, depending on the setting of the contact boundary coefficient α and the melting point of the metal material, it is possible to propose a combination of metal materials that can reduce the melting of the trolley wire 100 as much as possible regardless of the contact voltage V _c .

As described above, the temperature analysis method according to the second embodiment includes the above theoretical formula (formula (5)), the melting point of the metal material constituting the trolley wire 100, and the melting point of the metal material constituting the sliding plate 110. Based on the contact voltage V _c and at least one of the trolley wire 100 and the sliding plate 110 having the contact boundary coefficient α indicating the ratio of the potential (contact boundary) at the contact point A to the contact voltage V _c . The method further includes the step of mapping the melting range.

By referring to this manner creates a wear type map (FIG. 11), based on the contact voltage V _c and the contact boundary coefficient alpha, whether metallic material of interest is melted, easily grasp be able to. Therefore, the manufacturer of the power supply apparatus in the electric railway can quickly and accurately grasp whether or not the metal material can be used according to the contact voltage V _c and the contact boundary coefficient α based on the operation conditions. it can.

In addition, the manufacturer can also understand under what operating conditions (contact voltage V _c , contact boundary coefficient α) it is necessary to operate the target metal material so as not to melt. For example, if the manufacturer assumes that the contact voltage V _c is 0.4 V or higher based on the operating conditions of the power supply device, the manufacturer can use the operating conditions that can maintain the contact boundary coefficient α ≧ 0.96 (that is, By adopting a load condition such that the trolley wire surface coating 101 is removed, it is possible to obtain knowledge that melting can be prevented even if the material of the trolley wire 100 remains existing.

Further, when it is assumed that the respective surface coatings (the trolley wire surface coating 101 and the sliding plate surface coating 111) do not exist at the contact point A between the trolley wire 100 and the sliding plate 110, the contact boundary coefficient α is calculated as follows. The electric resistivity ρ ₁ and ρ ₂ of the plate 110 can be expressed as α = ρ ₁ / (ρ ₁ + ρ ₂ ). That is, since the contact boundary coefficient α indicates the ratio of the voltage drop generated in each of the trolley wire 100 and the sliding plate 110, the contact boundary coefficient α is a metal material constituting each of the trolley wire 100 and the sliding plate 110. It becomes a value depending on the ratio of the electrical resistivity ρ ₁ , ρ ₂ .
Therefore, the metal material that can reduce the melting of each of the trolley wire 100 and the sliding plate 110 as much as possible by focusing on the contact boundary coefficient α determined by the combination of the two metal materials, not focusing only on the eigenvalue of the metal material alone. The selection range can be further expanded.

Moreover, the manufacturing method of the power supply device according to each embodiment includes the first step of specifying the maximum temperatures θ _{max_t} and θ _{max_s} for each member of the trolley wire 100 and the sliding plate 110 based on the temperature analysis method described above. At a specific contact voltage V _c , the potential (contact boundary) at the contact point A is such that at least the maximum temperature θ _{max_t} for each member of the trolley wire 100 does not exceed the melting point of the metal material constituting the trolley wire 100. In addition, a second step of determining a combination of a metal material constituting the trolley wire 100 and a metal material constituting the sliding plate 110 is included.
By doing in this way, the member of the trolley wire 100 is controlled while controlling the potential at the contact point A as desired based on the combination of the metal material constituting the trolley wire 100 and the metal material constituting the sliding plate 110. Since the other maximum temperature θ _{max — t} can be adjusted, the range of selection of the metal material can be expanded.

Further, in the above-described method for manufacturing the power supply apparatus, in the second step, the trolley wire side resistivity ρ ₁ , which is the electrical resistivity of the metal material constituting the trolley wire 100, and the electric power of the metal material constituting the sliding plate 110. Based on the combination of the sliding plate side resistivity ρ _{2 that} is the resistivity, the combination of the metal material constituting the trolley wire 100 and the metal material constituting the sliding plate 110 is determined.

<Third Embodiment>
In the first and second embodiments described above, potential distribution and temperature distribution analysis in the vicinity of the contacts of “hard copper trolley wire” and “iron-based sintered alloy sliding plate” as examples of the material of trolley wire 100 and sliding plate 110. The wear mechanism was clarified by creating a wear form map (FIG. 11).
In the third embodiment, based on the created wear form map (FIG. 11), a more detailed analysis is performed, and then a combination of materials used for the power supply apparatus is selected.

FIG. 14 is a first diagram illustrating a method for manufacturing the power supply apparatus according to the third embodiment.
FIG. 14 shows the same thing as the example of the wear form map shown in FIG.
The trolley wire shown in FIG. 14 and the curve section of the melting boundary of the sliding plate can be calculated as follows.

  Moreover, the horizontal section of the trolley wire and the melting boundary of the sliding plate shown in FIG. 14 can be calculated as follows.

Here, “Tm” is the melting point [K] of the material, “Vc” is the contact voltage [V], and “L” is the Lorentz number (= 2.4 × 10 ⁻⁸ [V / K] ² ). .
Further, from the above equation (10), the contact boundary coefficient α increases as the film resistance (modification coefficient f ₂ ) of the sliding plate 110 increases, and as the film resistance (modification coefficient f ₁ ) of the trolley wire 100 increases. It can be seen that the contact boundary coefficient α decreases. In addition, the contact boundary coefficient α ₀ in the clean contact where there is no film resistance is as shown in the equation (11).

Although it is difficult to actively set the film resistance in the normal operation of the power supply apparatus used for the electric railway, the melting point Tm and the clean contact boundary coefficient α ₀ can be set by a combination of materials. The contact voltage V _c can be set by applying the contact force and current. Here, in order to select a combination of materials, a boundary where each wear form occurs is obtained, and a quantitative guideline for the melting point Tm and the clean contact boundary coefficient α ₀ is set.
Hereinafter, the melting point Tm of the trolley wire 100 is referred to as “trolley wire melting point Tmt”, and the melting point Tm of the sliding plate 110 is referred to as “slip plate melting point Tms”.

Here, the contact boundary coefficient α _{1 at} which the trolley wire melting boundary and the sliding plate melting boundary coincide with each other in the wear form map (FIG. 14) is expressed by the following expressions (14) and (15) from Expression (12) and Expression (13). ) Is calculated.

  Here, the equation (14) is applied when the trolley wire melting point Tmt is equal to or higher than the sliding plate melting point Tms. Equation (15) is applied when the trolley wire melting point Tmt is less than the sliding plate melting point Tms.

With this contact boundary coefficient α ₁ as a boundary, a trolley wire melt wear form (electric wear form I shown in FIG. 11) in which a large trolley wire wear occurs due to the coating resistance of the material surface, or a large wear on a sliding plate occurs. The sliding plate melts and wears form (electric wear form II shown in FIG. 11).

Next, the boundary where the mixed melt wear form occurs is determined. The condition under which a material having a relatively high electrical resistivity is sufficiently melted is regarded as the boundary of the mixed melt wear mode (FIG. 14). Here, a temperature higher than the melting point of a material having a relatively high electrical resistance by 800K (as a contact voltage difference). 0.25V) is set, and the contact boundary coefficients α ₂ and α ₃ at which the mixed melt wear form occurs are obtained using the equations (14) and (15).

  Here, Expression (16) is applied when the trolley wire melting point Tmt is equal to or higher than the sliding plate melting point Tms. Expression (17) is applied when the trolley wire melting point Tmt is less than the sliding plate melting point Tms.

15 to 18 are second to fifth diagrams for explaining a method of manufacturing the power supply apparatus according to the third embodiment.
From Expressions (14) to (17), the contact boundary coefficients α ₁ , α ₂ , and α ₃ are determined by the melting points of the trolley wire 100 and the sliding plate 110 (the trolley wire melting point Tmt and the sliding plate melting point Tms). I understand. Therefore, FIG. 15 shows the results of calculating the contact boundary coefficients α ₁ , α ₂ , and α ₃ with the horizontal axis being the difference between the trolley melting point Tmt and the sliding plate melting point Tms (Tmt−Tms). In addition, the vertical axis | shaft of FIG. 15 is made into the contact boundary coefficient (alpha) ₀ at the time of a clean.
As shown in FIG. 15, it can be seen that the generation condition of the wear form is divided into eight regions depending on the material combination. 16 and 17, the contact boundary coefficients α ₁ , α ₂ , and α ₃ are indicated by broken lines with respect to two types of wear form maps having different melting points of the trolley wire 100 and the sliding plate 110, and are shown in FIG. Eight areas are schematically represented, and the generation condition of the wear form is displayed for each area.
Hereinafter, the eight sections r1 to r8 shown in FIG. 15 (FIGS. 16 and 17) will be described with reference to the list shown in FIG.

Section r1 (Tmt> Tms and α ₀ > α ₃ ):
In this region, if there is no thick film resistance on the surface of the trolley wire 100, the trolley wire melt wear form and the mixed melt wear form do not occur. In addition, the melting of the trolley wire 100 becomes small because the coating resistance is generated on the surface of the sliding plate 110 due to the melting of the sliding plate 110 and the contact boundary coefficient α tends to increase. Thus, the trolley wire 100 is a material combination that is most difficult to melt.

Section r2 (Tmt <Tms and α ₀ > α ₃ ):
In this region, since the melting point of the trolley wire 100 (the trolley wire melting point Tmt) is lower than the melting point of the sliding plate 110 (the sliding plate melting point Tms), the presence of the film resistance on the surface of the trolley wire 100 causes Will occur. However, when the sliding plate 110 is melted, film resistance is generated on the surface of the sliding plate 110, and the contact boundary coefficient α is increased. Therefore, the mixed melt wear mode is hardly generated and the ground plate melt wear mode is obtained. Note that the combination of “hard copper trolley wire” and “iron-based sintered alloy sliding plate” falls under category r2, and the iron-based sintered alloy sliding developed in an era when there was no clear guide for combining the sliding plates. Although it is a board, it turns out that the trolley wire 100 is a combination that is relatively difficult to melt electrically.

Section r3 (Tmt> Tms and α ₁ <α ₀ <α ₃ ):
In this region, if there is no thick film resistance on the surface of the trolley wire 100, the trolley wire melt wear form does not occur, but the mixed melt wear form always occurs, so that the contact voltage V _c increases. Sometimes the trolley wire 100 melts. In addition, since the melting point of the sliding plate 110 (sliding plate melting point Tms) is lower than that of the trolley wire 100, a sliding plate melting and wearing form always occurs.

Section r4 (Tmt <Tms and α ₁ <α ₀ <α ₃ ):
In this region, since the melting point of the trolley wire 100 (the trolley wire melting point Tmt) is lower than the melting point of the sliding plate 110 (the sliding plate melting point Tms), the presence of the film resistance on the surface of the trolley wire 100 causes Will occur. In addition, the sliding plate melt wear mode and the mixed melt wear mode always occur.

Section r5 (Tmt> Tms and α ₂ <α ₀ <α ₁ ):
In this region, the melting point of the sliding plate 110 (the melting point of the sliding plate Tms) is lower than the melting point of the trolley wire 100 (the melting point of the trolley wire Tmt). Will occur. Note that the trolley wire melt wear mode and the mixed melt wear mode always occur.

Section r6 (Tmt <Tms and α ₂ <α ₀ <α ₁ ):
In this area, if there is a thick film resistor on the surface of the sliding plate 110, but never sliding plate melt wear type occurs, the mixed melt wear form always occurs, contact voltage V _c increases contact break Sometimes the sliding plate 110 melts. In addition, since the melting point of the trolley wire 100 (the trolley wire melting point Tmt) is lower than the melting point of the sliding plate 110 (the slab plate melting point Tms), the trolley wire melting and wearing form is inevitably generated.

Section r7 (Tmt> Tms and α ₀ <α ₂ ):
In this region, the melting point of the sliding plate 110 (the melting point of the sliding plate Tms) is lower than the melting point of the trolley wire 100 (the melting point of the trolley wire Tmt). Will occur. However, when the trolley wire 100 is melted, a film resistance is generated on the surface of the trolley wire 100, and the contact boundary coefficient α is reduced. Therefore, the mixed melt wear form hardly occurs and the trolley wire melt wear form is obtained.

Section r8 (Tmt <Tms and α ₀ <α ₂ ):
In this region, if there is no thick film resistance on the surface of the sliding plate 110, the sliding plate melting wear form and the mixed melting wear form do not occur. Moreover, since the film resistance is generated on the surface of the trolley wire 100 by melting the trolley wire 100 and the contact boundary coefficient α tends to decrease, the melting of the sliding plate 110 becomes small. From this, it becomes the material combination that the sliding plate 110 is most difficult to melt.

Next, a material combination to be used for the power supply apparatus is selected with reference to FIGS.
In general, the trolley wire 100 needs to have high conductivity, and the sliding plate 110 is required not to wear the trolley wire 100. From this, the electrical resistivity (trolley wire side resistivity ρ ₁ ) of the trolley wire 100 is smaller than the electrical resistivity (slide plate side resistivity ρ ₂ ) of the sliding plate 110, and α _{0 in} FIGS. 15 to 18. Used in areas where> 0.5. That is, the combinations are the sections r1, r2, r3, r4, and r6 of FIGS.

19 to 22 are sixth to ninth diagrams illustrating a method for manufacturing the power supply apparatus according to the third embodiment.
Necessary considerations are shown below as materials to be used for power supply equipment used in electric railways.
(1) The dissimilar metal should be used, and the component analysis of the transferred material and melt after the wear test should be easy.
(2) It can be easily obtained.
(3) It can be processed into a trolley wire or a strip shape.
(4) Easy handling.

As a result of considering the above items, the selected material combinations are shown in FIG.
The combination of the “hard copper trolley wire” and the “nickel ground plate” corresponds to the section r6 in FIGS. 15 to 18, and the combination in which the trolley wire 100 is most easily melted in the range where α ₀ > 0.5. Become. The wear form map for this material combination is shown in FIG.

  The combination of “hard copper trolley wire” and “aluminum slip plate” corresponds to the section r3 in FIGS. Note that “aluminum” is used as an auxiliary sliding plate for pantographs, and it has been reported that trolley wire wear becomes significant at locations where the “aluminum sliding plate” and the “hard copper trolley wire” contact. The wear form map for this material combination is shown in FIG.

  The combination of the “nickel trolley wire” and the “iron-based sintered alloy slip plate” corresponds to the section r1 in FIGS. 15 to 18 and is the combination in which the trolley wire 100 is most difficult to melt. The wear form map for this material combination is shown in FIG. The reason why hard copper was not selected as the trolley wire material was that it was classified as r1 with respect to the “hard copper trolley wire” and there was no appropriate material satisfying the items (1) to (4) described above. It is.

As described above, in the method for manufacturing the power supply apparatus according to the third embodiment, the contact boundary coefficients α ₁ and α ₂ that define the boundaries of the four regions shown in the wear form map (FIGS. 11 and 14). , Α ₃ , and the magnitude relationship between the trolley wire melting point Tmt and the sliding plate melting point Tms, which of the eight sections (sections r1 to r8) defined by the combination is specified, so that a more optimal combination of materials Is selected.
Here, specifically, the above four regions are a region where neither the trolley wire 100 nor the sliding plate 110 melts (mechanical wear region), and only one of the trolley wire 100 or the sliding plate 110 melts. It refers to a region (a trolley wire melting wear region, a sliding plate wear melting region) and a region where both the trolley wire 100 and the sliding plate 110 are melted (mixed melting wear region).

The documents referred to above are described below.
Reference (1) Sakaki Sugawara: “Development and application of new trolley wire”, Railway vehicles and technology, No.96 pp.46-50 (2004)
Reference (2) Hiroo Miyahira, Hiroshi Tsuchiya: “Reduce wear of pantograph sliding plates”, RRR, Vol. 71, No.2 pp.8-11 (2014)
Reference (3) M. Ikeda, H. Tsuchiya: Recent Trends on Pantograph for High-Speed Railways in Terms of Tribology, Journal of Japanese Society of Tribolosists, Vol. 58, No. 7, pp.447-454 (2013)
Mitsuru Ikeda, Hiroshi Tsuchiya: “Recent Trends on Tribology of Pantographs for High-Speed Railways”, Tribologist, Vol.58, No.7 pp.447-454 (2013)
Reference (4) Hiroki Nagasawa: “Study on wear characteristics of Cr-Zr copper alloy trolley wire under current flow”, Tohoku University dissertation, (1996)
Reference (5) Kubo Shunichi: “A study of wear mechanism of carbon pantograph strips infiltrated with copper or copper-lead-tin alloy under arc discharge”, Tohoku University dissertation, (1999)
Reference (6) C. Yamashita, K. Adachi: Influence of Current on Wear Modes and Transition Condition of Current Collecting Materials, Journal of Japanese Society of Tribolosists, Vol. 58, No. 7, pp.496-503 (2013)
Yamashita Main Tax, Koshi Adachi: "Effects of current flow on wear forms and transition conditions of current collecting materials", Tribologist, Vol.58, No.7 pp.496-503 (2013)
Reference (7) C. Yamashita, K. Adachi: Wear Mechanism of Current Collecting Materials due to Temperature Distribution Analysis Considering Degenerated Layer, Journal of Japanese Society of Tribolosists, Vol. 59, No. 5, pp. 302-309 (2014)
Yamashita Main Tax, Koshi Adachi: “Elucidation of Current Wear Mechanism of Current Collection Materials by Temperature Distribution Analysis Considering Inclusions”, Tribologist, Vol.59, No.5 pp. 302-309 (2014)
Reference (8) R, Holm: Electric Contacts Theory and Applications, 4th ed. (1967)
Literature (9) M. Iwase, K. Yokoi, K. Kokubu, K. Kumagai, T. Sato, M. Maeda: Pantograph Contact Strip (2) Development of new contact strip for the new tram line, Railway Technical Research Report, No. 574, pp.20-21 (1967)
Masaru Iwase, Kazuo Yokoi, Koji Kokubun, Masahiro Kumagai, Ikuo Saito, Masami Maeda: "Pantograph Sliding Plate (2)-Development and Improvement of Shinkansen Sliding Plate-, Railway Technology Research Report, No.574, pp.20-21 (1967)
Reference (10) C. Yamashita: Influence of Apparent Contact Area on Wear Mode of Current Collecting Materials, 2014 Annual Meeting Record IEEJ, 5-135, pp.232-233 (2014)
Yamashita Main Tax: “Effect of apparent contact area on the current wear pattern”, Proceedings of the 2014 Annual Conference of the Institute of Electrical Engineers of Japan, 5-135, pp.232-233 (2014)

[Potential distribution and temperature distribution analysis method]
As in the literature (7), a model in which the trolley wire 100 file plate 110 is a cylindrical electrode and an oxide film or the like existing on the contact surface is assumed to be a film resistance is assumed as shown in FIG. The base material radius was D, the contact radius was a, the thickness of the trolley wire surface coating 101 was d ₁ , and the thickness of the sliding plate surface coating 111 was d ₂ .

FIG. 2 shows an electric circuit in which the left cylinder in FIG. 1 is divided in the circumferential direction and one piece as in the right in FIG. 1 is divided in the r direction and the z direction. From the potentials φ _{1 to} φ ₄ and the electric resistances R _{1 to} R _{4 of the} upper, lower, left and right elements, the central potential φ ₀ is obtained from the equation (1).

The temperature θ _{0 in the} center of FIG. 2 is obtained from the equation (2). Since the actual trolley wire 100 and the sliding plate 110 are sliding contacts, unsteady heat conduction analysis should be performed in consideration of the movement of the contacts. However, since the temperature rise occurs in a sufficiently short time with respect to the contact moving time, it can be regarded as a static contact, and here, a steady heat conduction analysis was performed. Refer to Document (7) for the derivation of Equation (2).

Here, L is the Lorentz number (= 2.4 × 10 ⁻⁸ [K / V] ² ), and Φ is the potential difference [V] between the elements.

The electrical resistivity ρ _d1 , ρ _d2 and the thermal conductivity λ _d1 , λ _d2 of the film resistance of the trolley wire 100 and the sliding plate 110 are determined according to Wiedemann-Franz's law (reference (8)). The electrical resistivity ρ ₁ , ρ _{2 of} 110 and the thermal conductivity λ ₁ , λ ₂ are expressed by equations (3) and (4).

Here, f ₁ and f ₂ are coefficients indicating increments of the electrical resistivity of each film, and are referred to as “degeneration coefficients” in this specification.

Table 1 (FIG. 23) shows physical property values of the trolley wire and the sliding plate material to be analyzed. The size of the electrode model is the same as in the literature (7), the number of grid meshes is 30 × 30, the size of the mesh is Δr = Δz = 10 μm (electrode radius D = 300 μm), and the number of elements actually in contact is 10 (contact radius) a = 100 μm). Convergence calculation was performed so that Formula (1) and Formula (2) were materialized about all the elements, and the calculation was terminated when the temperature change of each element became less than 1 × 10 ⁻⁶ K.

  As an analysis example, FIG. 3 shows the potential distribution and temperature distribution analysis results when the contact voltage is 0.4 V in clean contact without a surface coating. From FIG. 3 (b), it can be seen that the maximum temperature in the electrode exists inside the slide plate. In the following, the influence of various factors on the potential distribution and temperature distribution in the electrode will be clarified.

[Analysis result]
(Influence of contact voltage)
This section clarifies the relationship between the potential distribution in the electrode and the temperature distribution when there is no surface coating and the contact voltage is different. The anode of the trolley wire 100 as the analysis condition, the contact strip 110 as a cathode, was carried potential distribution and temperature distribution analysis by changing the contact voltage _{V c} between the 0.1～0.7V. As a boundary condition, the end temperatures of the trolley wire 100 and the sliding plate 110 were set to 300K in accordance with Holm (Reference (8)).

FIG. 4 shows the relationship between the potential on the z-axis and the temperature in the analysis result when the contact voltage is changed in seven steps. From this figure, the temperature in the electrode is parabolic with respect to the potential, and the overall maximum temperature θ _max is a position where the contact voltage is an intermediate value, for example, a position where the contact voltage is 0.2 V when the contact voltage is 0.4 V. It can be seen that According to Holm (Reference (8)), the relationship between the potential and temperature of the same kind of metal contact is a parabola, and the overall maximum temperature is generated at an intermediate point of the contact voltage. From the above, it can be said that the relationship between the potential distribution and the temperature distribution as shown in FIG. 4 can be applied to different metals and does not depend on the combination of electrode materials.

  In FIG. 4, the contact boundary between the trolley wire 100 and the sliding plate 110 obtained from the results of the potential distribution and temperature distribution analysis is indicated by a broken line. As shown in Table 1 (FIG. 23), the electrical resistivity of the sliding plate 110 is larger than that of the trolley wire 100, and the ratio of the voltage drop in the sliding plate electrode to the entire voltage drop is large. On the right side of the parabola. FIG. 5 shows the relationship between the maximum temperature of each electrode and the contact voltage. The figure also shows the φ-θ theoretical value (reference (8)) calculated by equation (5).

  From this figure, it can be seen that the maximum temperature of the sliding plate 110 substantially coincides with the φ-θ theoretical value, and that the relationship between the overall maximum temperature and the contact voltage also follows the φ-θ theory even for dissimilar metal contacts. On the other hand, the maximum temperature of the trolley wire 100 is smaller than the φ-θ theoretical value. This difference in maximum temperature is caused by the contact boundary deviating from the apex of the parabola in the parabola of FIG.

(Effect of film resistance)
Next, the relationship between the potential distribution and the temperature distribution is clarified when a film such as an oxide film is present on the electrode surface. As an analysis condition, a coating film having a thickness d ₁ = 10 μm is assumed on the surface of the trolley wire 100, a contact voltage is set to V _c = 0.4 V, and the alteration coefficient f ₁ of the trolley wire surface coating 101 is changed between ₁ and 100. The potential distribution and temperature distribution analysis were performed. As for the boundary conditions, the end temperatures of the trolley wire 100 and the sliding plate 110 were set to 300K as described above. It is assumed that no coating is present on the surface of the sliding plate 110, and d ₂ = 0 was set.

FIG. 6 shows the relationship between the potential on the z-axis and the temperature, and the contact boundary when the alteration coefficient f ₁ is changed in three steps. From this figure, it can be seen that the parabola of potential and temperature does not depend on the alteration coefficient f ₁ , that is, the film resistance, but only on the contact voltage. However, the contact boundary of the contact wire 100 and the sliding plate 110 with the increase of the deterioration factor f ₁ it can be seen that the closer to the vertex of the parabola. This is because the ratio of the voltage drop in the trolley wire 100 to the total voltage drop increases with an increase in the trolley wire film resistance.

FIG. 7 shows a comparison between the maximum temperature of each of the trolley wire 100 and the sliding plate 110 and the theoretical value of φ-θ obtained from the result of the temperature distribution analysis. Since the contact voltage is constant at 0.4 V, the theoretical value of φ-θ shows a constant value regardless of the alteration coefficient f _1, and the maximum temperature of the sliding plate, which is the maximum temperature in the electrode, is almost the same value. On the other hand, it can be seen that the maximum temperature of the trolley wire 100 increases as the alteration coefficient f ₁ increases. This is because the voltage drop in the trolley wire 100 increases as the film resistance on the surface of the trolley wire 100 increases, and the contact boundary approaches the apex of the parabola as shown in FIG.

(Influence of bulk temperature)
The temperature distribution analysis results and equation (5) up to the previous section are based on the boundary condition that the end temperature of the trolley wire 100 and the sliding plate 110, that is, the bulk temperature is 300K. However, there is a difference between both bulk temperatures when the trolley wire 100 and the sliding plate 110 actually contact each other. This is because the time intervals at which the trolley wire 100 and the sliding plate 110 are subjected to friction are different. Iwase et al. (Reference (9)) measured the temperature of the sliding plate during traveling and reported that it was 160 ° C. at a distance of 2 mm from the contact surface of the sliding plate 110 and 80 ° C. at 5 mm. Therefore, in this section, the influence of the bulk temperature of the sliding plate 110 on the potential distribution in the electrode and the temperature distribution will be clarified.

The contact voltage V _c = 0.4 V was set as an analysis condition, and the terminal temperature of the sliding plate 110 was changed between 300 to 500 K, and the potential distribution and temperature distribution analysis was performed. It is assumed that there is no surface coating. FIG. 8 shows the relationship between the potential on the z-axis and the temperature when the bulk temperature of the sliding plate 110 is changed in five steps. It can be seen that the temperature in the vicinity of the potential 0 V, which is the end of the sliding plate 110, is affected by the bulk temperature of the sliding plate 110, but the temperature at the contact boundary and the maximum temperature in the electrode do not substantially change.

  FIG. 9 shows a comparison between the maximum temperature of the trolley wire 100 and the sliding plate 110 and the theoretical value of φ-θ obtained from the result of the temperature distribution analysis. Also from this figure, it can be seen that the influence of the bulk temperature of the sliding plate 110 on the maximum temperature of the trolley wire 100 and the sliding plate 110 is negligible.

The potential distribution and temperature distribution analysis results obtained above are organized.
(1) The maximum temperature in the electrode follows the φ-θ theory.
(2) The temperature distribution with respect to the potential in the electrode has a parabolic relationship, and the curve depends only on the contact voltage.
(3) (1) and (2) do not depend on the combination of contact materials, film resistance such as oxide film, and bulk temperature.
(4) The potential at the contact boundary between the trolley wire and the sliding plate changes depending on the film resistance of the surface.

[Creation of wear form map]
A wear form map that generalizes the above results is created. First, in order to create an equation representing the parabola of potential and temperature on the electrode model z-axis, the equation (2) created by the model of the two-dimensional cylindrical coordinate system is converted into the equation of the one-dimensional orthogonal coordinate system.

Since the bulk temperature of the trolley wire 100 and the sliding plate 110 which are boundary conditions is 300 K, and the potential becomes V _c / 2, the maximum temperature θ _max in the electrode is obtained, so that the equation (7) is obtained.

  Next, the temperature θ at an arbitrary potential φ in the parabola can be expressed by Expression (8).

  By substituting equation (7) into equation (8), equation (9) is derived.

By using φ / V _c in the equation, the temperature distribution in the electrode with respect to various contact voltages V _c can be arranged in one graph as shown in FIG. Here, φ / V _c is referred to as a dimensionless potential. In FIG. 10, the trolley wire melting point 1334K and the sliding plate melting point 1646K are written together, φ / V _c ≧ 0.5, and the point where the parabola intersects with the trolley wire melting point is indicated by a circle symbol, φ / V _c ≦ 0.5 and The point where the melting point of the slab is intersected is indicated by a symbol with a triangle mark. When the contact boundary between the trolley wire 100 and the sliding plate 110 coincides with these points, the trolley wire 100 and the sliding plate 110 start to melt.

Since the potential at the end of the sliding plate 110 is 0V, the potential φ _{c at the} contact boundary is equal to the voltage drop in the sliding plate 110. The ratio of φ _c to the contact voltage V _c , that is, the dimensionless potential φ / V _c at the contact boundary between the trolley wire 100 and the sliding plate 110 is defined as α, which is referred to as “contact boundary coefficient”. α is expressed by equation (10) from the concentrated resistance equation and the film resistance equation.

  From equation (10) and FIG. 10, α increases as the contact resistance of the sliding plate 110 increases, and the contact boundary moves to the right of the parabola, so the maximum temperature of the trolley wire 100 decreases. Further, as the contact resistance of the trolley wire 100 increases, α decreases and the contact boundary moves to the left of the parabola, so that the maximum temperature of the trolley wire 100 increases.

Equation (9), using (10), a condition in which the contact wire 100 and sliding plate 110 begins to melt, as expressed in the vertical axis _{V c} and the horizontal axis α is 11. In the same figure, the contact voltage condition at which the maximum temperature in the electrode reaches the melting point of the trolley wire 100 and the sliding plate 110 is calculated from the equation (5) and is shown by a horizontal broken line.

  The author has so far proposed a mechanism in which the wear form transitions under conditions where the electrode melts (references (6) and (7)), and the energized condition is determined from the melting conditions of the trolley wire 100 or the sliding plate 110 shown in FIG. The wear forms are classified into the following four types, and the characteristics of each wear form will be described with reference to the literature (6).

(A) A region where the contact voltage is small and neither melts is called a mechanical wear mode. The point to be noted in FIG. 11 is that under the condition that α is large, that is, the condition that the contact resistance of the sliding plate 110 is large, even if the contact voltage reaches the melting point of the trolley wire 100, the mechanical wear form is obtained.
As a feature of the mechanical wear mode, wear characteristics such as wear rate and friction coefficient do not depend on the load and are almost constant values (reference (6)).

(B) In a region where the contact voltage is 0.4 to 0.5 V and α is relatively small, that is, a region where the contact resistance of the trolley wire 100 is large due to film resistance or the like, the hard copper trolley wire and the iron-based sintered alloy sliding plate Since there is a difference in melting point, only the trolley wire 100 melts. This region is referred to as electrical wear form I.
As a feature of the electrical wear form I, the wear rate and the friction coefficient of the trolley wire 100 are maximized (Reference (6)).

(C) In the region where the contact voltage is 0.5 V or more and α is large, only the sliding plate 110 is melted. This region is referred to as electrical wear form II.
As a feature of the electrical wear form II, the specific wear amount of the sliding plate 110 significantly increases as the load decreases, but the wear rate and the friction coefficient of the trolley wire 100 decrease (Reference (6)).

(D) In the region where the contact voltage is 0.5 V or more and α is relatively small, there is a region where both melt. This region is referred to as a mixed melt wear mode.
Reference (6) does not mention this form of wear.

For the combination of the hard copper trolley wire and the iron-based sintered alloy sliding plate, the contact boundary coefficient α ₀ in the clean contact without film resistance is obtained from the equation (10):

It becomes. In the case of α ₀ = 0.96, the trolley wire 100 does not melt even when the contact voltage increases as shown in FIG. 11, and only the mechanical wear form and the electrical wear form II appear. That is, if there is no film resistance such as an oxide film on the surface of the trolley wire 100, the trolley wire 100 does not melt.

In the literature (10), the author conducted a wear test in which the apparent contact area of the sliding plate 110 was changed in the combination of the hard copper trolley wire and the iron-based sintered alloy sliding plate, and obtained the trolley wire wear rate of FIG. Yes. As a result of the abrasion test, the influence of the apparent contact area was significant only in the vicinity of a load of 10N. When the apparent contact area is 70 mm ² or more, the surface of the trolley wire 100 melts as shown in FIG. 13A, and when the apparent contact area is 50 mm ² or less, the surface of the trolley wire 100 does not melt as shown in FIG. 13B. The mechanism of this phenomenon is that the wear depth increases as the apparent contact area decreases, and when the apparent contact area is 50 mm ² or less, the coating on the surface of the trolley wire 100 is removed, so that α becomes close to 0.96 and the trolley wire 100 Is considered to have not melted.

  As described above, from FIG. 11 and formulas (9) and (10), the factors governing the wear mode under energization can be narrowed down to 1: melting point, 2: contact boundary coefficient α, 3: contact voltage. Among these, material characteristics are mainly for 1 and 2, and a wear form map can be created for any material combination, and it is considered that the wear form can be estimated in advance. Further, depending on the setting of α and melting point, it is considered that a material combination that can reduce the melting of the trolley wire 100 as much as possible can be proposed regardless of the contact voltage.

[in conclusion]
We analyzed the potential distribution and temperature distribution in the vicinity of the contact between the trolley wire and the sliding plate, and tried to organize the controlling factors of the current wear form by mapping. As a result, the following conclusions were obtained.
(1) The maximum temperature in the electrode follows the φ-θ theory.
(2) The potential and temperature in the electrode have a parabolic relationship.
(3) The contents described in (1) and (2) do not depend on the combination of contact materials, the presence or absence of film resistance such as an oxide film, and the bulk temperature.
(4) A wear form map was created from the boundary conditions at which the electrode melts, and the governing factors of the wear form were specified as the melting point, the contact boundary coefficient α, and the contact voltage.

  The present invention relates to a contact voltage applied from the trolley wire to the sliding plate in a predetermined region including a contact point between the trolley wire and the sliding plate, a potential at each position of the predetermined region, and a position at each position of the predetermined region. A step of referring to a theoretical formula showing a correlation with temperature, and a step of specifying a maximum temperature of each of the trolley wire and the sliding plate in the predetermined region according to the contact voltage and a potential at the contact point; Is a temperature analysis method.

  Further, the present invention is based on the theoretical formula, the melting point of the metal material constituting the trolley wire, and the melting point of the metal material constituting the sliding plate, and the contact voltage and the contact voltage with respect to the contact voltage. Mapping a range in which at least one of the trolley wire and the sliding plate melts, of a contact boundary coefficient indicating a potential ratio at a contact point.

  The invention of the present application is a method for manufacturing a power supply device having a trolley wire and a sliding plate, and a contact applied from the trolley wire to the sliding plate in a predetermined region including a contact point between the trolley wire and the sliding plate. Based on a theoretical formula showing a correlation between a voltage, a potential at each location in the predetermined region, and a temperature at each location in the predetermined region, the voltage in the predetermined region according to the contact voltage and the potential at the contact point A first step of specifying a maximum temperature of each of the trolley wire and the sliding plate; and at a specific contact voltage, the potential at the contact point is at least a maximum temperature of the trolley wire of the metal material constituting the trolley wire. A second step for determining a combination of the metal material constituting the trolley wire and the metal material constituting the sliding plate so that the potential does not exceed the melting point. When a method of manufacturing a power supply device having a.

  In the second step of the present invention, in the second step, a trolley wire side resistivity that is an electrical resistivity of a metal material that constitutes the trolley wire, and a slip plate side that is an electrical resistivity of a metal material that constitutes the slide plate It is a manufacturing method of the electric power supply apparatus which determines the combination of the metallic material which comprises the said trolley wire, and the metallic material which comprises the said sliding board based on the combination with resistivity.

100 Trolley wire 101 Trolley wire surface coating 110 Slip plate 111 Slip plate surface coating A Contact point

Claims (6)

A temperature analysis method for analyzing a temperature generated in a power supply device formed by contact between a trolley wire and a sliding plate,
In a predetermined region including the trolley wire, the sliding plate, and a contact point of the trolley wire and the sliding plate, a contact voltage applied from the trolley wire to the sliding plate via the contact point, and the predetermined Determining the overall maximum temperature based on a theoretical formula showing a correlation with the overall maximum temperature, which is the maximum temperature occurring in the region,
Identifying a curve indicating a relationship of a temperature distribution to a potential distribution generated in the predetermined region based on the contact voltage and the specified overall maximum temperature;
Identifying the highest temperature for each member, which is the highest temperature of each of the trolley wire and the sliding plate, based on the potential at the contact point and the curve;
A temperature analysis method comprising: In the step of specifying the curve, the curve is specified so as to be a parabola having the overall maximum temperature as a vertex at an intermediate value of the contact voltage,
In the step of specifying the highest temperature for each member, the highest temperature for each member including the position that is an intermediate value of the contact voltage among the trolley wire and the sliding plate is specified as the overall highest temperature, and the contact The temperature analysis method according to claim 1, wherein the other maximum temperature for each member that does not include a position that is an intermediate voltage value is specified as the temperature at the contact point. Based on the theoretical formula, the melting point of the metal material constituting the trolley wire, and the melting point of the metal material constituting the sliding plate, the contact voltage and the ratio of the potential at the contact point to the contact voltage The temperature analysis method according to claim 1, further comprising a step of mapping a contact boundary coefficient indicating a range in which at least one of the trolley wire and the sliding plate melts. Based on the temperature analysis method according to any one of claims 1 to 3, a first step of specifying a maximum temperature for each member of the trolley wire and the sliding plate;
The metal constituting the trolley wire so that, at the specific contact voltage, the potential at the contact point is such that at least the maximum temperature of each member of the trolley wire does not exceed the melting point of the metal material constituting the trolley wire. A second step of determining a combination of a material and a metal material constituting the sliding plate;
A method of manufacturing a power supply apparatus having In the second step, a combination of a trolley wire side resistivity, which is an electrical resistivity of a metal material constituting the trolley wire, and a slip plate side resistivity, which is an electrical resistivity of a metal material constituting the sliding plate The method of manufacturing a power supply device according to claim 4, wherein a combination of a metal material that constitutes the trolley wire and a metal material that constitutes the sliding plate is determined based on the above. Defines the boundary between the trolley wire and the region where neither the sliding plate melts, the region where only one of the trolley wire or the sliding plate melts, and the region where both the trolley wire and the sliding plate melt. And a metal material constituting the trolley wire based on a category defined by a coefficient defined by the relationship between the melting point of the metal material constituting the trolley wire and the melting point of the metal material constituting the sliding plate, and The method for manufacturing a power supply device according to claim 4 or 5, wherein a combination with a metal material that constitutes the sliding plate is determined.