A high-reliability axial electric connection structure for a thermal power generating unit

Abstract

The application provides a high-reliability axial electric connection structure for a thermal power generator unit and relates to the technical field of generators. The problem that the radial soft connection structure in the prior art gradually cannot meet the development requirements of high parameters and large-capacity steam turbine generators in terms of reliability, service life, maintenance convenience and current bearing uniformity is solved. The high-reliability axial electric connection structure comprises a conductive rod and a plurality of strip-shaped multi-contact flexible conductive contact pieces. The conductive rod is a split cylindrical conductive body, a plurality of positioning grooves are arranged on the outer surface of the cylinder in the axial direction, and the strip-shaped multi-contact flexible conductive contact pieces are one-to-one correspondingly arranged in the positioning grooves. The high-reliability axial electric connection structure is mainly used for constructing a novel electric connection scheme with high contact reliability, a long service life and quick maintenance characteristics.

Description

Technical Field

[0001] This invention relates to the field of generator technology, and in particular to a highly reliable axial electrical connection structure for thermal power generator sets. Background Technology

[0002] Traditional thermal power generator sets commonly employ a radial flexible connection composite structure for rotor lead wire electrical connections. The core technology of this structure lies in dividing the conductive copper busbar at the rotor winding end into upper and lower semi-cylindrical conductive rods. These are mechanically coupled and electrically connected via a flexible connection assembly formed by stacked layers of thin copper sheets. Current is ultimately led out to the external slip ring system via radially inserted lead screws. While this classic design is widely used, it suffers from a series of inherent problems stemming from its structural principles. First, its structural complexity and assembly precision requirements are extremely high. The alignment of the split conductive rods, the flat installation of the flexible connection plates, and the balanced stress control of numerous fastening bolts all increase assembly difficulty and maintenance time, contradicting the modern operational philosophy of rapid maintenance for power equipment. Second, the flexible connection assembly, as a weak link in mechanical and electrical performance, must withstand strong centrifugal forces, electromagnetic vibrations, and intense thermal cycling during generator start-up and shutdown processes during long-term operation. This can easily lead to stress relaxation, fatigue cracks, and creep deformation in the copper sheet material, causing a decrease in contact pressure, a gradual increase in contact resistance, and a vicious cycle, resulting in localized hot spots. In severe cases, it may burn out the insulation and threaten the generator's safety. In addition, the current is mainly transmitted through a single or a few flexible connection paths, and the uneven current distribution limits its current-carrying capacity. Moreover, the lifespan of the flexible connection often determines the maintenance cycle of the entire connection system, resulting in high maintenance costs.

[0003] Specifically, the traditional structure adopts a design mode of split conductive rods combined with multi-layer copper sheet flexible connections. In practical applications, it has exposed three prominent defects: Structural level - the assembly process is complicated, requiring the alignment of multiple connection interfaces and the even tightening of a large number of bolts, resulting in low efficiency of maintenance and disassembly; Performance level - the flexible connection components are prone to stress relaxation and fatigue deterioration under long-term electromagnetic vibration and thermal cycling conditions, resulting in increased time-varying contact resistance and the risk of local overheating; Maintenance level - as a component with a limited lifespan, the flexible connection needs to be replaced as a whole, resulting in high maintenance costs and a lack of modular maintenance conditions. Summary of the Invention

[0004] In view of this, the existing radial flexible connection structure is gradually failing to meet the development requirements of high-parameter, large-capacity thermal power generating units in terms of reliability, lifespan, ease of maintenance, and current carrying uniformity. The fundamental contradiction lies in the fact that relying on the mechanical compensation capability of flexible conductors sacrifices long-term contact stability; the pursuit of structural disassembly introduces too many connection interfaces and potential failure points. This invention aims to construct a novel electrical connection scheme that combines high contact reliability, long lifespan, and rapid maintenance characteristics through a redesign of the structural principle. This invention provides a highly reliable axial electrical connection structure for thermal power generating units. It utilizes strip-shaped multi-contact flexible conductive contact sheets, arranged in an arc or cylindrical shape, to achieve electrical connections between components on the inner and outer radial sides using elliptical conductive sheets and isosceles trapezoidal conductive sheets, respectively. This eliminates weak flexible connections, achieves multi-point uniform pressure contact, eliminates stress distribution, and possesses axial direct connection for rapid assembly and disassembly, improving the fatigue resistance and thermal expansion and contraction adaptability of the rotor conductive connection components.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a highly reliable axial electrical connection structure for thermal power generator sets, comprising a conductive rod and multiple strip-shaped multi-contact flexible conductive contact pieces, wherein the conductive rod is a segmented cylindrical conductor, and multiple positioning grooves are spaced apart along the axial direction on its outer cylindrical surface, and the strip-shaped multi-contact flexible conductive contact pieces are installed in the positioning grooves one by one. The strip-shaped multi-contact flexible conductive contact sheet includes a pair of strip-shaped conductive sheets, multiple elliptical conductive sheets, and multiple pairs of isosceles trapezoidal conductive sheets. The pair of conductive strips are coplanar and parallel to each other; The two ends of the elliptical conductive sheet are perpendicularly connected to a pair of strip conductive sheets, and the middle part intersects with the plane containing the top surface of the strip conductive sheet at an angle of θ. α ; The isosceles trapezoidal conductive sheets are symmetrically arranged on both sides of a pair of strip conductive sheets, with their bottoms connected to the strip conductive sheets. The plane containing the top surface of the isosceles trapezoidal conductive sheet intersects the plane containing the top surface of the strip conductive sheet, with an included angle of θ. β ; Both the elliptical conductive sheet and the isosceles trapezoidal conductive sheet are arranged in a linear array along the length of the strip conductive sheet; The minor axis length of the elliptical conductive sheet is m The height of the isosceles trapezoidal conductive sheet is h The α , β , m , h satisfy: ; The elliptical conductive sheet is electrically connected to the positioning groove, and the isosceles trapezoidal conductive sheet is used for electrical connection with external parts. The depth of the positioning groove isl The l satisfy: .

[0006] Furthermore, the conductive rod is composed of two semi-circular copper rods.

[0007] Furthermore, the positioning groove is an annular groove or an arc-shaped groove opened along the circumference of the conductive rod.

[0008] Furthermore, the number of the strip-shaped multi-contact flexible conductive contact piece is 3-5.

[0009] Furthermore, the aforementioned α The angle is 30°-40°. m It is 2-4mm.

[0010] Furthermore, the aforementioned β The length of the lower base of the isosceles trapezoidal conductive sheet with an angle of 165°-175° is b The h It is 2-3mm. b It is 2-2.5mm.

[0011] Furthermore, the spacing L1 of the elliptical conductive sheet linear array is 5-8 mm, and the spacing L2 of the isosceles trapezoidal conductive sheet linear array is 3-5 mm.

[0012] Furthermore, the strip-shaped multi-contact flexible conductive contact sheet has a silver-plated surface with a plating thickness of 15μm.

[0013] Furthermore, the strip-shaped multi-contact flexible conductive contact sheet is made of a flexible metal alloy and can be arranged in an arc or cylindrical shape with the top surface of the strip conductive sheet as the outer wall.

[0014] Furthermore, the strip-shaped multi-contact flexible conductive contact sheet is made of beryllium copper alloy with a tensile strength ≥1200MPa and a yield strength ≥960MPa.

[0015] Compared with the prior art, the advantages of the high-reliability axial electrical connection structure for thermal power generating units described in this invention are: 1. The multiple strip-shaped multi-contact flexible conductive contact sheets of this invention independently and elastically contact the positioning groove, working in parallel. This eliminates the need for traditional weak soft connections, achieving multi-point uniform pressure contact, eliminating the risk of single-point failure, and significantly improving structural contact stability. The modular design simplifies the disassembly and assembly process, eliminating the need to handle complex soft connection components and improving maintenance efficiency. The elastic contact design effectively compensates for thermal deformation, enhancing resistance to vibration fatigue. Current is uniformly discharged from multiple contact points, reducing current density and improving heat dissipation. By using standardized strip-shaped multi-contact flexible conductive contact sheets to replace complex soft connection systems, maintenance costs are reduced.

[0016] 2. The strip-shaped multi-contact flexible conductive contact sheet of this invention is used in an arc or cylindrical shape. Elliptical conductive sheets and isosceles trapezoidal conductive sheets are used on the inner and outer radial sides to achieve electrical connections between components, thus realizing flexible connections between components. This flexible structure avoids the rigid electrical connection method of traditional rotor conductive connection components, eliminates stress distribution, effectively disperses the micro-vibration alternating stress generated by the high-speed rotation of the rotor, improves the fatigue resistance and thermal expansion and contraction adaptability of the rotor conductive connection components, eliminates the stress concentration problem of traditional rigid connections, improves fatigue resistance, and significantly extends the service life of the equipment.

[0017] 3. The strip-shaped multi-contact flexible conductive contact sheet of the present invention adopts a flexible structure, which can better adapt to thermal expansion and contraction deformation under high temperature, and avoid contact problems or breakage caused by thermal stress. Combined with the material selection, the thermal compensation capability of the present invention is further enhanced. The present invention adopts a linear array gap structure layout, which provides gaps for thermal expansion and contraction. It is particularly suitable for rotor systems with frequent generator start-stop, frequent thermal expansion and contraction of excitation circuit conductive components, high speed, and near 100-degree high temperature operating conditions. It effectively solves the reliability problem of generator conductive contact sheet operation under frequent start-stop, high temperature, and high speed conditions, and has important engineering application value.

[0018] 4. This invention employs a flexible structure, reducing contact resistance and improving the contact quality of conductive components. The isosceles trapezoidal conductive sheet generates a wedge-like self-locking effect, resulting in more concentrated and stable contact pressure, effectively resisting vibration and impact, and preventing loosening. The isosceles trapezoidal conductive sheet provides a smooth guide slope, reducing resistance during insertion and minimizing contact surface scratching. Furthermore, the isosceles trapezoidal conductive sheet effectively disperses the mechanical stress generated during insertion and removal, reducing stress concentration and improving the lifespan of the conductive contact sheet. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of a highly reliable axial electrical connection structure for a thermal power generator set according to the present invention. Figure 2 This is a cross-sectional view of the conductive rod described in this invention; Figure 3 This is an exploded view of the conductive rod described in this invention; Figure 4 This is a schematic diagram of the structure of the strip-shaped multi-contact flexible conductive contact sheet of the present invention; Figure 5This is a front view of the strip-shaped multi-contact flexible conductive contact sheet described in this invention. Figure 6 This is a left view of the strip-shaped multi-contact flexible conductive contact sheet described in this invention. Figure 7 For the present invention Figure 5 A sectional view along line A in the middle; Figure 8 For the present invention Figure 7 A magnified view of a section at point B in the middle; Figure 9 This is a schematic diagram of the structure when the elliptical conductive sheet and the strip conductive sheet are on the same plane according to the present invention; Figure 10 This is a schematic diagram of the structure of the strip-shaped multi-contact flexible conductive contact sheet of the present invention when it is arranged in a cylindrical shape; Figure 11 This is a schematic diagram of the structure of the strip-shaped multi-contact flexible conductive contact sheet of the present invention when it is arranged in an arc shape; In the diagram: 1-Strip conductive sheet; 2-Elliptical conductive sheet; 3-Isosceles trapezoidal conductive sheet; 4-Conductive rod; 41-Positioning groove; l The depth of the positioning groove; α The angle between the minor axis of the elliptical conductive sheet and the top surface of the strip conductive sheet; β The angle between the top surfaces of the isosceles trapezoidal conductive sheet and the strip conductive sheet; m is the length of the minor axis of the elliptical conductive sheet; h The height of the isosceles trapezoidal conductive sheet; b L1 is the length of the lower base of the isosceles trapezoidal conductive sheet; L2 is the spacing of the linear array of elliptical conductive sheets; L3 is the spacing of the linear array of isosceles trapezoidal conductive sheets. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0021] I. Detailed Implementation Method 1, see [link / reference] Figure 1-11This embodiment describes a highly reliable axial electrical connection structure for thermal power generator sets, comprising a conductive rod 4 and multiple strip-shaped multi-contact flexible conductive contact pieces. The conductive rod 4 is a segmented cylindrical conductor with multiple positioning grooves 41 spaced axially on its outer cylindrical surface. The strip-shaped multi-contact flexible conductive contact pieces are detachably pressed into the positioning grooves 41, corresponding one-to-one, to achieve multiple parallel electrical connections distributed along the axial direction of the conductive rod 4. The strip-shaped multi-contact flexible conductive contact pieces can be fixed to the positioning grooves 41 using a snap-fit ​​quick-locking structure.

[0022] The strip-shaped multi-contact flexible conductive contact sheet includes a pair of strip-shaped conductive sheets 1, multiple elliptical conductive sheets 2, and multiple pairs of isosceles trapezoidal conductive sheets 3; The pair of strip conductive sheets 1 are coplanar and parallel to each other; The two ends of the elliptical conductive sheet 2 are perpendicularly connected to a pair of strip conductive sheets 1, and the middle part intersects with the plane containing the top surface of the strip conductive sheet 1 at an angle of θ. α ; The isosceles trapezoidal conductive sheet 3 is symmetrically arranged on both sides of a pair of strip conductive sheets 1, and its bottom is connected to the strip conductive sheet 1. The plane containing the top surface of the isosceles trapezoidal conductive sheet 3 intersects with the plane containing the top surface of the strip conductive sheet 1, with an included angle of θ. β ; The elliptical conductive sheet 2 and the isosceles trapezoidal conductive sheet 3 are both arranged in a linear array along the length direction of the strip conductive sheet 1; The minor axis length of the elliptical conductive sheet 2 is m The height of the isosceles trapezoidal conductive sheet 3 is h The α , β , m , h satisfy: To ensure that after the elliptical conductive sheet 2 is folded over, the radial length of the elliptical conductive sheet 2 on the same side as the isosceles trapezoidal conductive sheet 3 is less than the radial length of the isosceles trapezoidal conductive sheet 3, so as to avoid the failure of the isosceles trapezoidal conductive sheet 3. The elliptical conductive sheet 2 is used for electrical connection with the positioning groove 41 and for generating elastic contact pressure, and the isosceles trapezoidal conductive sheet 3 is used for electrical connection with external parts and for assembly positioning. The depth of the positioning groove 41 is l The l satisfy: .

[0023] The conductive rod 4 is composed of an upper conductive rod and a lower conductive rod assembled together by high-strength insulating bolts to form a complete cylindrical conductive body. Both the upper and lower conductive rods are made of high-conductivity forged copper and have a semi-circular cross-section.

[0024] Preferably, there are three positioning grooves 41, and the upper and lower semi-conductive rods together form six axial contact points.

[0025] The positioning groove 41 is an annular groove, arc groove, V-shaped groove or multi-segment arc surface composite groove opened along the circumference of the conductive rod 4, and the positioning groove 41 is adapted to the elliptical conductive sheet 2.

[0026] Preferably, the positioning groove 41 has a cross-sectional shape of an arc-shaped groove with a radius of 8mm, an arc angle of 120°, an axial length of 15mm, a groove depth of 3mm, and a silver-plated surface with a thickness of not less than 10μm. The groove spacing of the positioning groove 41 is 200mm along the axial direction of the conductive rod 4.

[0027] The number of the strip-shaped multi-contact flexible conductive contact pieces can be adjusted according to the current level. For example, four contact pieces can be used for the 4000A level, and eight contact pieces can be used for the 8000A level.

[0028] The α The angle is 30°-40°; m The spacing L1 of the linear array of the elliptical conductive sheets 2 is 2-4 mm; the spacing L1 of the linear array of the elliptical conductive sheets 2 is 5-8 mm.

[0029] The β The angle is 165°-175°; the length of the lower base of the isosceles trapezoidal conductive sheet 3 is... b The h It is 2-3mm. b The spacing L2 of the linear array of isosceles trapezoidal conductive sheets 3 is 3-5 mm.

[0030] Preferably, the minor axis length of the strip-shaped multi-contact flexible conductive contact sheet 2 is... m The spacing L1 of the linear array of elliptical conductive sheets 2 is 5mm; the upper base length of the isosceles trapezoidal conductive sheet 3 is 1.6mm, and the lower base length is 3mm. b 2.25mm; height h The spacing L2 of the linear array of isosceles trapezoidal conductive sheets 3 is 3mm.

[0031] The strip-shaped multi-contact flexible conductive contact sheet has a thickness of 2mm and is silver-plated with a coating thickness of 15μm.

[0032] See attached document Figure 10 and attached Figure 11 The strip-shaped multi-contact flexible conductive contact sheet is made of a flexible metal alloy, with the top surface of the strip conductive sheet 1 as the outer wall, forming a cylindrical shape. Alternatively, it can be arranged in a half-circular arc or a quarter-circular arc, and can be used alone or in combination.

[0033] Preferably, the strip-shaped multi-contact flexible conductive contact sheet is made of beryllium copper alloy, whose composition includes 1.8-2.2% beryllium, 0.6-1% manganese, 26-40% nickel, and other alloying materials and unavoidable impurities. The material undergoes solution treatment followed by age hardening to achieve a tensile strength ≥1200MPa and a yield strength ≥960MPa.

[0034] The elliptical conductive sheet 2 can be replaced with a wave spring sheet structure or an array of micro bumps structure.

[0035] The working principle of this invention is as follows: (Refer to the attached document) Figure 1 The upper and lower semi-conductive rods are respectively mounted on the copper busbars at the ends of the rotor windings and initially fixed with insulating fasteners to form a complete cylindrical conductive path. Three strip-shaped multi-contact flexible conductive contact pieces are installed sequentially along the axial direction. During installation, the operator holds the strip-shaped multi-contact flexible conductive contact piece, aligning its isosceles trapezoidal conductive piece 3 with the entrance of the positioning groove 41 on the conductive rod 4, and gently pushes it along the axial direction to the assembly position. After the strip-shaped multi-contact flexible conductive contact piece is in place, the elliptical conductive piece 2 and the arc surface of the positioning groove 2 form an interference fit. The isosceles trapezoidal conductive piece 3 is used for electrical connection with external parts. The electrical connection between external parts and the conductive rod is realized through the strip-shaped multi-contact flexible conductive contact piece.

[0036] This invention discloses a highly reliable axial electrical connection structure for thermal power generating units, particularly suitable for large thermal power generating units with a rated capacity of 300 MVA and above. These units typically have the following characteristics: hydrogen cooling or water-hydrogen cooling, rotor winding rated current exceeding 5000 A, and average annual operating time exceeding 7500 hours. Throughout the entire lifecycle of such high-parameter generators, the electrical connection structure must simultaneously meet the dual requirements of "long maintenance-free period" and "short planned maintenance time."

[0037] Specifically, the technical advantages of this invention are particularly prominent in the following three typical application scenarios: First, in generator sets operating on a two-shift system for peak shaving, its structure can adapt to the intense thermal cycling caused by daily start-ups and shutdowns, avoiding contact pressure attenuation due to thermal stress; second, for power plants built in near-shore or industrial areas, the sealed contact interface of this design can effectively resist salt spray corrosion and industrial pollutant erosion, maintaining long-term stable contact resistance; finally, in the application of nuclear power units paired with conventional island thermal power generator sets, its modular design supports preventative replacement of the entire electrical contact system within a limited planned shutdown window, significantly reducing power generation losses caused by extended maintenance periods. A manufacturing process for the aforementioned strip-shaped multi-contact flexible conductive contact sheet involves stamping using a precision progressive die, and sequentially completing the following steps: 1. Stamping the outer contour; 2. Press and mold a strip-shaped substrate; 3. Punch holes to form a linear array of elliptical conductive sheets 2; 4. Form a linear array of isosceles trapezoidal conductive sheets 3, and fold them towards the top surface of the strip conductive sheet 1 until they form an angle with the top surface of the strip conductive sheet 1. β，β The preferred value is 173.5°; 5. Finally, refer to the appendix. Figure 9 and attached Figure 5 Fold the middle part of the elliptical conductive sheet 2 around its major axis until it forms an angle with the top surface of the strip conductive sheet 1. α , α The preferred value is 36.9°.

[0038] After forming, it undergoes heat treatment, followed by polishing, cleaning, and silver plating with a plating thickness of 15μm. Finally, it undergoes anti-oxidation treatment.

[0039] The embodiments of the present invention disclosed above are merely illustrative of the invention. These embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A highly reliable axial electrical connection structure for thermal power generating units, characterized in that, It includes a conductive rod (4) and multiple strip-shaped multi-contact flexible conductive contact pieces. The conductive rod (4) is a segmented cylindrical conductive body. Multiple positioning grooves (41) are spaced along the axial direction on the outer surface of the cylinder. The strip-shaped multi-contact flexible conductive contact pieces are installed in the positioning grooves (41) one by one. The strip-shaped multi-contact flexible conductive contact sheet includes a pair of strip-shaped conductive sheets (1), multiple elliptical conductive sheets (2) and multiple pairs of isosceles trapezoidal conductive sheets (3); The pair of strip conductive sheets (1) are coplanar and parallel to each other; The two ends of the elliptical conductive sheet (2) are perpendicularly connected to a pair of strip conductive sheets (1), and the middle part intersects with the plane containing the top surface of the strip conductive sheet (1), with an included angle of θ. α ; The isosceles trapezoidal conductive sheet (3) is symmetrically arranged on both sides of a pair of strip conductive sheets (1), and its bottom is connected to the strip conductive sheet (1). The plane containing the top surface of the isosceles trapezoidal conductive sheet (3) intersects the plane containing the top surface of the strip conductive sheet (1), with an included angle of θ. β ; The elliptical conductive sheet (2) and the isosceles trapezoidal conductive sheet (3) are arranged in a linear array along the length direction of the strip conductive sheet (1); The minor axis length of the elliptical conductive sheet (2) is m The height of the isosceles trapezoidal conductive sheet (3) is h The α、β , m, h satisfy: ; The elliptical conductive sheet (2) is electrically connected to the positioning groove (41), and the isosceles trapezoidal conductive sheet (3) is used for electrical connection with external parts; The depth of the positioning groove (41) is l The l satisfy: .

2. The highly reliable axial electrical connection structure for thermal power generating units according to claim 1, characterized in that, The conductive rod (4) is composed of two semi-circular copper rods.

3. The highly reliable axial electrical connection structure for thermal power generating units according to claim 1, characterized in that, The positioning groove (41) is an annular groove or arc-shaped groove opened along the circumference of the conductive rod (4).

4. A highly reliable axial electrical connection structure for thermal power generating units according to claim 1, characterized in that, The number of the strip-shaped multi-contact flexible conductive contact pieces is 3-5.

5. A highly reliable axial electrical connection structure for a thermal power generator set according to claim 1, characterized in that, The α The angle is 30°-40°. m It is 2-4mm.

6. A highly reliable axial electrical connection structure for a thermal power generator set according to claim 1, characterized in that, The β The angle is 165°-175°, and the length of the lower base of the isosceles trapezoidal conductive sheet (3) is... b The h It is 2-3mm. b It is 2-2.5mm.

7. A highly reliable axial electrical connection structure for a thermal power generator set according to claim 1, characterized in that, The spacing L1 of the linear array of elliptical conductive sheets (2) is 5-8 mm; the spacing L2 of the linear array of isosceles trapezoidal conductive sheets (3) is 3-5 mm.

8. A highly reliable axial electrical connection structure for thermal power generating units according to claim 1, characterized in that, The strip-shaped multi-contact flexible conductive contact sheet has a silver-plated surface with a plating thickness of 15μm.

9. A highly reliable axial electrical connection structure for a thermal power generator set according to claim 1, characterized in that, The strip-shaped multi-contact flexible conductive contact sheet is made of a flexible metal alloy and can be surrounded by an arc or cylindrical shape with the top surface of the strip conductive sheet (1) as the outer wall.

10. A highly reliable axial electrical connection structure for a thermal power generator set according to claim 1, characterized in that, The strip-shaped multi-contact flexible conductive contact sheet is made of beryllium copper alloy with a tensile strength ≥1200MPa and a yield strength ≥960MPa.

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