A measuring device for minimum bending radius of a pipeline and a method for using the same

Abstract

The present invention provides a measuring device for the minimum bending radius of a pipeline and a method for using the same, and belongs to the technical field of minimum bending radius measurement. The measuring device includes a double-layer curling track assembly, a head drive assembly, and a hose fixing lock assembly. The hose fixing lock assembly is evenly placed on the slide, the hose is placed on the arc support plate of the lock assembly, and the hose is fixed to the evenly distributed arc support plate by a fixing device. The device is powered on, and the head arc support plate pulls the entire hose forward along the track. The values ​​output by the strain gauges at each position are observed, and when the material buckling strain is reached, the bending radius value where the strain gauge is located is recorded. The device of the present invention has a reliable structure and a clever design. The minimum bending radius values ​​at multiple positions can be measured through one test, and the averaged data is more accurate. In addition, the test operation is simple, and the data can be gradually obtained by binding the hose at the initial position and attaching the strain gauge.

Description

Technical Field

[0001] The invention belongs to the technical field of minimum bending radius measurement, and relates to a device for measuring the minimum bending radius of a flexible pipe and a method for using the device. Background Art

[0002] Marine pipelines are important equipment for the development of marine oil and gas resources. Marine pipelines include steel pipes and flexible pipes. Steel pipes are all made of metal materials, while flexible pipes are made of metal and composite materials. Flexible pipes have excellent flexibility and can withstand large bending deformations, which enables the pipeline to adapt to complex sea conditions and generate relatively small stresses. Therefore, bending performance is an important indicator of flexible pipes, and the bending performance of pipes is measured by the minimum bending radius. In addition, when the hose is stored and laid using the coiling method, the curved pipe may yield due to excessive deformation in some parts, resulting in failure of the minimum bending radius.

[0003] The existing process for checking the minimum bending radius of marine flexible pipelines is to conduct tests according to the values ​​required in the specifications. If the pipeline does not undergo plastic deformation and obvious damage after the test and can be restored to the state before the test, the flexible pipeline is considered to meet the requirements of the minimum bending radius specification. However, this method cannot directly measure the exact value of the minimum bending radius, so it cannot provide bending test data for subsequent design.

[0004] To this end, the present invention proposes a device for measuring the minimum bending radius of a pipeline, through which the accurate value of the minimum bending radius of a hose can be measured by only one measurement. Summary of the invention

[0005] In view of the requirements of the existing technology, the present invention provides a minimum bending radius measuring device to achieve the function of accurately measuring the minimum bending radius. The device has a reliable structure and a clever design and can complete the tasks in the actual test process.

[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0007] A device for measuring the minimum bending radius of a pipeline comprises a double-layer curling track assembly, a head drive assembly, and a hose fixing lock assembly.

[0008] The double-layer curling track assembly includes an upper plate 1, a lower plate 2, a roller track 3, and a gear track 4. The upper plate 1 and the lower plate 2 are the main structures of the double-layer curling track assembly, and the cross-sectional contour lines of the upper plate 1 and the lower plate 2 are concentric arcs. The two ends of the upper plate 1 and the lower plate 2 are connected by a connecting plate, that is, the upper plate 1, the lower plate 2 and the plates at both ends constitute a hollow strip structure with four closed sides and an arc. A gap is provided in the middle of the upper plate 1, and the roller track 3 and the gear track 4 are installed near the middle gap. The upper side adjacent to the central gap of the upper plate 1 is provided with a left-right symmetrical roller track 3, and the lower side adjacent to the gap is provided with a left-right symmetrical gear track 4 (the gear track 4 is close to the inner surface of the lower plate 2). The middle gap of the upper plate 1 is the track line of the roller track 3. The bending radius values ​​are engraved on the connecting plates at both ends of the upper plate 1 and the lower plate 2. The track line of the roller track 3 is a straight line for a long distance at the beginning, and a constant velocity spiral inside the center, and the equation is ρ=αθ. The radius of curvature of the curve increases from the center along the length direction of the track line. The end with the largest radius of curvature of the central curve segment and the end of the straight line are connected by a curve tangent to the ends of the two lines, so that the curve has a smooth transition.

[0009] Furthermore, the thickness of the upper plate 1 near the middle gap increases, and a plate is provided at the changed position for support, that is, the plate is located inside the double-layer curling track assembly, connecting the upper plate 1 and the lower plate 2.

[0010] The head drive assembly is used to drive the entire hose to move forward slowly, and includes a brush sheet 5, a head gear 6, a motor 7, a wire rack 8, a brush roller 9, an arc-shaped support plate 14, a head type transmission rod 15, a head roller 16, and a head bearing 17. The outer sides of the two gear tracks 4 are provided with brush sheets 5. Two rotating shafts extend from the central axis of the motor 7, and the two rotating shafts are respectively connected to the left and right head gears 6, and the two head gears 6 cooperate with the two gear tracks 4. The middle part of the motor 7 body: the wire rack 8 is installed on one side of the gear track 4, and the head type transmission rod 15 is installed on the back of the gear track 4. Specifically: the middle part of the motor 7 body adjacent to the gear track 4 is connected to the short axis of the "T-shaped" wire rack 8, and the long axis of the T-shaped wire rack 8 is placed horizontally above the two gear tracks 4. A brush roller 9 in contact with the brush sheet 5 is installed at each end, that is, one end of the short axis is fixedly connected to the middle part of the motor 7 body, and the other end is fixedly connected to the middle of the long axis. The wire rack 8 is used to supply power to the motor 7, and the motor 7 drives the two head gears 6 to rotate after being powered on. The middle part of the motor 7 is connected to the head bearing 17 and the arc-shaped support plate 14 through the head type transmission rod 15. Specifically: the two ends of the crossbeam of the head type transmission rod 15 are connected to the head roller 16 through the head bearing 17, and the two rollers move on the roller track 3.

[0011] The hose fixing lock assembly includes a gear 10, a bearing 11, an I-shaped transmission rod 12, and a roller 13. The gear 10 is engaged with the bottom gear track 4, and a bearing 11 is provided at the axis of each of the two gears 10. The lower crossbar of the I-shaped transmission rod 12 is installed between the two bearings 11. The upper crossbar end of the I-shaped transmission rod 12 is connected to two rollers 13, and the connection method between them also adopts the bearing 11. An arc-shaped support plate 14 is provided above the I-shaped transmission rod 12. The I-shaped transmission rod 12 and the arc-shaped support plate 14 are welded together by three short rods. The arc-shaped support plate 14 is provided with several groups of rope binding joints that are symmetrical on the left and right to bind the two ends of the rope.

[0012] Furthermore, the short axis of the wire rack 8 is a square tube inclined downward, and the long axis is a horizontal round tube, through which the wires pass and are connected to the brush roller, and the wire rack structure is welded.

[0013] The double-layer curled track assembly is the main structure of the structure and is placed in a curled shape on the horizontal ground. The head drive assembly is the power device for pulling the pipeline. It is clamped on the track of the double-layer curled track assembly through the gears and rollers connected by the I-type transmission rod. Before the experiment, it was located at the intersection of the straight section of the track and the constant velocity spiral. The hose fixing lock assembly makes the pipeline close to the outer surface of the double-layer curled track assembly, forcing the pipeline to slide along the track. It is also clamped on the track of the double-layer curled track assembly through its own gears and rollers. There are 7 in total, located after the head drive assembly on the track and evenly distributed on the straight section.

[0014] A method for using a device for measuring the minimum bending radius of a pipeline comprises the following steps:

[0015] The first step is to slide the head drive assembly to the intersection of the straight section of the double-layer curling track assembly and the constant velocity spiral, and slide the 7 hose fixing lock assemblies to evenly distribute them on the straight section of the double-layer curling track assembly, located behind the head drive assembly. Then, the hose head is fixed to the arc-shaped support plate 14 of the head drive assembly with a rope, and then the hose head is fixed to the arc-shaped support plate 14 of the evenly distributed hose fixing lock assembly. After the entire hose is fixed, the position of the fixed hose includes the eight positions where the head drive assembly and the hose fixing lock assembly are fixed to the hose, which can be referred to Figure 1 At eight fixed positions, two strain gauges are attached between every two positions, one is attached to the side of the pipeline circumferentially facing the double-layer curling track assembly track, and the other is attached to the side of the pipeline circumferentially and 180° from the first attachment position. A total of 14 strain gauges are attached to the entire pipeline.

[0016] In the second step, the head drive assembly is energized through the bottom brush plate 5, and the motor 7 of the head drive assembly works, driving the two head gears 6 to rotate on the gear track 4, driving the head type transmission rod 15 and the arc-shaped support plate 14 to move forward along the gear track 4, and the hose head fixed on the arc-shaped support plate 14 is pulled. The position of the hose head is fixed to the double-layer curling track assembly track by the hose fixing lock assembly, and will also be pulled forward. As the movement progresses, the bending radius of the double-layer curling track gradually decreases. Specifically:

[0017] The brush sheet 5 in the head drive assembly is energized, and the brush roller 9 contacts the brush sheet 5. The electricity is transmitted to the motor 7 through the wires in the wire rack 8. The motor 7 drives the head gear 6 to rotate, and the head gear 6 moves forward slowly along the gear track 4, pushing the head type transmission rod 15 to move forward. The head roller 16 connected to the other side of the head type transmission rod 15 through the head bearing 17 moves forward, so that it moves forward along the roller track 3. The arc-shaped support plate 14 connected to the head type transmission rod 15 moves forward, and the hose head fixed on the arc-shaped support plate 14 is pulled. The 7 hose fixing lock assemblies after the hose head are pulled because they are fixed to the hose. The arc-shaped support plate 14 on the hose fixing lock assembly is driven to move, and the type transmission rod 12 connected to the arc-shaped support plate 14 is driven. The roller 13 connected to the type transmission rod 12 rolls along the roller track 3, and the gear 10 connected to the type transmission rod 12 rolls along the gear track 4.

[0018] In the third step, the position of the head drive assembly is named ①, and the positions of the 7 hose fixing lock assemblies from near to far from the head drive assembly are named ②, ③, ④, ⑤, ⑥, ⑦, and ⑧. There are two strain gauges between every two serial number positions, namely, the strain gauge along the circumferential direction of the hose toward the track side of the double-layer curling track assembly, which is called the inner strain gauge; and the strain gauge along the circumferential direction of the hose and 180° from the first patch position is called the outer strain gauge. As the bending radius of the hose becomes smaller and smaller, each patch position will gradually yield. A total of 14 strain gauges are included. The data of the 14 strain gauges are transmitted to the computer display device to observe the strain of each strain gauge position as the bending radius of the hose decreases. When the strain value transmitted back by a certain strain gauge is greater than the yield strain of the pipeline material, it is considered that the pipeline has been damaged, and the bending radius value at the corresponding position of the strain gauge is recorded at this time. After the 14 strain gauges gradually yield, a total of 14 bending radius values ​​corresponding to them are recorded. The average value of the 7 bending radii at yield measured by all the internal strain gauges is taken, and the average value of the 7 bending radii at yield measured by all the external strain gauges is taken. The smaller value of the two average values ​​is the minimum bending radius of the hose.

[0019] The beneficial effects of the present invention are:

[0020] The minimum bending radius values ​​at multiple locations can be measured in one test, and the averaged data is more accurate. The test is easy to operate, and the data can be gradually obtained after the hose is bound at the initial position and the strain gauge is attached. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a three-dimensional oblique view of the minimum bending radius measuring device;

[0022] Figure 2 A top view of a double-layer curly track assembly with a constant velocity spiral track line

[0023] Figure 3 It is a cross-sectional view of a double-layer curled track assembly;

[0024] Figure 4 shows the head drive assembly, (a) inner view and (b) outer view;

[0025] Figure 5 is a hose fixing lock assembly, (a) inner view and (b) outer view;

[0026] Figure 6 Secures the lock superstructure for the head drive assembly and hoses;

[0027] Figure 7 Hose fixing lock assembly arc-shaped support plate structure;

[0028] In the figure: 1 upper plate; 2 lower plate; 3 roller track; 4 gear track; 5 brush plate; 6 gear; 7 motor; 8 wire rack; 9 brush roller; 10 gear; 11 bearing; 12 I-shaped transmission rod; 13 roller; 14 arc-shaped support plate; head I-shaped transmission rod 15, head roller 16, head bearing 17. DETAILED DESCRIPTION

[0029] In order to further explain the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings.

[0030] A device for measuring the minimum bending radius of a pipeline comprises a double-layer curling track assembly, a head drive assembly, and a hose fixing lock assembly.

[0031] The double-layer curling track assembly includes an upper plate 1, a lower plate 2, a roller track 3, and a gear track 4. The upper plate 1 and the lower plate 2 are the main structures of the double-layer curling track assembly, and the cross-sectional contour lines of the upper plate 1 and the lower plate 2 are concentric arcs. The two ends of the upper plate 1 and the lower plate 2 are connected by a connecting plate, that is, the upper plate 1, the lower plate 2 and the plates at both ends constitute a hollow strip structure with four closed sides and an arc. A gap is provided in the middle of the upper plate 1, and the roller track 3 and the gear track 4 are installed near the middle gap. The upper side adjacent to the central gap of the upper plate 1 is provided with a left-right symmetrical roller track 3, and the lower side adjacent to the gap is provided with a left-right symmetrical gear track 4. The middle gap of the upper plate 1 is the track line of the roller track 3. The bending radius values ​​are engraved on the connecting plates at both ends of the upper plate 1 and the lower plate 2. The track line of the roller track 3 is a straight line for a long distance at the beginning, and a constant velocity spiral in the center, with the equation ρ=αθ. The radius of curvature of the curve increases from the center along the length of the track line. The end with the largest radius of curvature of the central curve segment and the end of the straight line are connected by a curve tangent to the ends of the two lines, so that the curve transitions smoothly. The thickness of the upper plate 1 near the middle gap increases, and a plate is provided at the change position for support, that is, the plate is located inside the double-layer curling track assembly, connecting the upper plate 1 and the lower plate 2.

[0032] The head drive assembly is used to drive the entire hose to move forward slowly, and includes a brush sheet 5, a head gear 6, a motor 7, a wire rack 8, a brush roller 9, an arc-shaped support plate 14, a head type transmission rod 15, a head roller 16, and a head bearing 17. The outer sides of the two gear tracks 4 are provided with brush sheets 5. Two rotating shafts extend from the central axis of the motor 7, and the two rotating shafts are respectively connected to the left and right head gears 6, and the two head gears 6 cooperate with the two gear tracks 4. The middle part of the motor 7 body: the wire rack 8 is installed on one side of the gear track 4, and the head type transmission rod 15 is installed on the back of the gear track 4. Specifically: the middle part of the motor 7 body adjacent to the gear track 4 is connected to the short axis of the "T-shaped" wire rack 8, and the long axis of the T-shaped wire rack 8 is placed horizontally above the two gear tracks 4. A brush roller 9 in contact with the brush sheet 5 is installed at each end, that is, one end of the short axis is fixedly connected to the middle part of the motor 7 body, and the other end is fixedly connected to the middle of the long axis. The wire rack 8 is used to supply power to the motor 7, and the motor 7 drives the two head gears 6 to rotate after being powered on. The middle part of the motor 7 is connected to the head bearing 17 and the arc-shaped support plate 14 through the head type transmission rod 15. Specifically: the two ends of the crossbeam of the head type transmission rod 15 are connected to the head roller 16 through the head bearing 17, and the two rollers move on the roller track 3.

[0033] The hose fixing lock assembly includes a gear 10, a bearing 11, an I-shaped transmission rod 12, and a roller 13. The gear 10 is engaged with the bottom gear track 4. A bearing 11 is provided at the axis of each of the two gears 10. The lower crossbar of the I-shaped transmission rod 12 is installed between the two bearings 11. The upper crossbar end of the I-shaped transmission rod 12 is connected to two rollers 13, and the connection between them also adopts the bearing 11. An arc-shaped support plate 14 is provided above the I-shaped transmission rod 12. The I-shaped transmission rod 12 and the arc-shaped support plate 14 are welded into one by three short rods. The arc-shaped support plate 14 is provided with several groups of rope binding joints that are symmetrical on the left and right to bind the two ends of the rope. The short axis of the wire rack 8 is a square tube that is inclined downward, and the long axis is a horizontal circular tube. The wires pass through it and are connected to the brush roller. The wire rack structure is welded.

[0034] like Figure 1 As shown, the hose fixing lock assembly is evenly placed on the slideway, and the hose is placed on the lock assembly arc support plate 14, and the hose is fixed on the evenly distributed arc support plate by the fixing device. As shown in FIG5, a strain gauge is attached to the side of the round tube facing the support plate at the position between the two binding wires, and a strain gauge is attached to the opposite side of the support plate at the next position along the pipeline axis, and is attached to the entire round tube in sequence.

[0035] The device is powered on, and the current is connected to the motor 7 along the brush sheet 5 and the wires in the wire rack 8. The I-type transmission rod 12 connected to the motor 7 will drive the arc-shaped support plate 14 at the head position connected to it. The head arc-shaped support plate pulls the entire hose forward along the track. Observe the values ​​output by the strain gauges at various positions, and when the material buckling strain is reached, record the bending radius value where the strain gauge is located.

[0036] After all the strain gauge data are obtained, the average value of the bending radius measured by the strain gauge attached away from the support plate is taken, and the average value of the bending radius measured by the strain gauge attached close to the support plate is taken. The minimum value of the two is the minimum bending radius of the hose.

[0037] The above-mentioned embodiments only express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the present invention. It should be pointed out that for the convenience of measurement, the material strain value measurement method can be changed, such as changing to optical fiber to measure the strain value. However, it is undeniable that this method proposes a new concept of single quantitative measurement of bending radius, which greatly simplifies the test process.

Claims

1. A device for measuring the minimum bending radius of a pipeline, characterized in that: The measuring device comprises a double-layer curling track assembly, a head drive assembly, and a hose fixing lock assembly; The double-layer curling track assembly comprises an upper plate (1), a lower plate (2), a roller track (3), and a gear track (4); the upper and lower plates are the main structure of the double-layer curling track assembly, and the cross-sectional contour lines of the two are concentric arcs. The two ends of the upper and lower plates are connected by a connecting plate, and the connecting plate is engraved with a bending radius value; a gap is provided in the middle of the upper plate (1), and the roller track (3) and the gear track (4) are installed near the middle gap. The upper side adjacent to the central gap of the upper plate (1) is provided with left-right symmetrical roller tracks (3), and the lower side adjacent to the gap is provided with left-right symmetrical gear tracks (4). The central gap of the upper plate (1) is the track line of the roller track (3); the initial section of the track line of the roller track (3) is a straight line, and the center is a constant velocity spiral. The radius of curvature of the curve increases from the center along the length direction of the track line, and the curve end and the straight line end transition smoothly; The head drive assembly is used to drive the entire hose to move slowly forward, and comprises a brush sheet (5), a head gear (6), a motor (7), a wire rack (8), a brush roller (9), an arc-shaped support plate (14), a head type transmission rod (15), a head roller (16), and a head bearing (17); the outer sides of the two gear tracks (4) are provided with a brush sheet (5); the two ends of the central axis of the motor (7) are respectively connected to the head gear (6) through a rotating shaft, and the two head gears (6) cooperate with the two gear tracks (4); the motor (7) is adjacent to the gear track The middle part of the body of the motor (4) is connected to the short axis of a "T-shaped" wire rack (8), the long axis of the T-shaped wire rack (8) is placed horizontally above the two gear tracks (4), and a brush roller (9) in contact with the brush sheet (5) is installed at each end of the T-shaped wire rack (8). After the motor (7) is powered by the wire rack (8), it drives the two head gears (6) to rotate; the middle part of the body of the motor (7) is connected to the head bearing (17) and the arc-shaped support plate (14) through the head I-shaped transmission rod (15), the head bearing (17) is connected to the head roller (16), and the two rollers move on the roller track (3); The hose fixing lock assembly comprises a gear (10), a bearing (11), an I-shaped transmission rod (12), and a roller (13); the gear (10) is engaged with the bottom gear track (4), the two gears (10) are connected to the lower crossbar end of the I-shaped transmission rod (12) through the bearing (11), and the upper crossbar end of the I-shaped transmission rod (12) is connected to the two rollers (13) through the bearing (11); The double-layer curled track assembly serves as the main structure and is placed in a curled shape on the horizontal ground; the head drive assembly serves as the power device for pulling the pipeline, and is clamped on the track of the double-layer curled track assembly through gears and rollers connected by the I-shaped transmission rod. Before the experiment, it was located at the intersection of the straight section of the track and the constant velocity spiral; the hose fixing lock assembly makes the pipeline close to the outer surface of the double-layer curled track assembly, forcing the pipeline to slide along the track, and is also clamped on the track of the double-layer curled track assembly through its own gears and rollers. It is located behind the head drive assembly on the track and is evenly distributed on the straight section.

2. A device for measuring the minimum bending radius of a pipeline according to claim 1, characterized in that: The thickness of the upper plate (1) increases near the middle gap, and a plate is provided at the changed position for support, that is, the plate is located inside the double-layer curling track assembly and connects the upper plate (1) and the lower plate (2).

3. The device for measuring the minimum bending radius of a pipeline according to claim 1, characterized in that: An arc-shaped support plate (14) is arranged above the I-shaped transmission rod (12). The I-shaped transmission rod (12) and the arc-shaped support plate (14) are welded into one body by three short rods. The arc-shaped support plate (14) is provided with left-right symmetrical rope binding joints for binding two ends of the rope.

4. A method for using the device for measuring the minimum bending radius of a pipeline according to any one of claims 1 to 3, characterized in that: The following steps are involved: The first step is to slide the head drive assembly to the intersection of the straight section of the double-layer curling track assembly and the constant velocity spiral, and evenly distribute the hose fixing lock assembly on the straight section of the double-layer curling track assembly, which is located behind the head drive assembly; then, the hose head is fixed to the arc support plate (14) of the head drive assembly by a rope, and the other hose parts are fixed to the arc support plate (14) of the evenly distributed hose fixing lock assembly; two strain gauges are attached between every two fixed positions, one is attached to the side of the double-layer curling track assembly along the circumferential direction of the pipeline, which is called the inner strain gauge; the other is attached to the side of the double-layer curling track assembly along the circumferential direction of the pipeline and opposite to the first The patch position is 180° to the side, which is called the external strain gauge; in the second step, the head drive assembly is energized through the bottom brush plate (5), and the motor (7) of the head drive assembly works, driving the two head gears (6) to rotate on the gear track (4), driving the head type transmission rod (15) and the arc-shaped support plate (14) to move forward along the gear track (4), and the hose head fixed on the arc-shaped support plate (14) is pulled; the position after the hose head is fixed on the double-layer curling track assembly track by the hose fixing lock assembly, and will also be pulled forward; as the movement proceeds, the bending radius of the double-layer curling track gradually decreases; In the third step, as the bending radius of the hose becomes smaller and smaller, each position where the strain gauge is attached will gradually yield; the data of the strain gauge is transmitted to the computer display device, and the strain situation of each strain gauge position is observed as the bending radius of the hose becomes smaller. When the strain value sent back by a strain gauge is greater than the yield strain of the pipeline material, it is considered that the pipeline is damaged, and the bending radius value at the corresponding position of the strain gauge is recorded at this time; all strain gauges gradually yield; the average of the bending radii measured by all internal strain gauges when yielding is taken, and the average of the bending radii measured by all external strain gauges when yielding is taken, and the smaller value of the two average values ​​is the minimum bending radius of the hose.

5. The method for using the device for measuring the minimum bending radius of a pipeline according to claim 4, characterized in that: The second step is specifically as follows: the brush sheet (5) in the head driving assembly is energized, the brush roller (9) contacts the brush sheet (5), and the electricity is transmitted to the motor (7) through the wires in the wire rack (8), the motor (7) drives the head gear (6) to rotate, and the head gear (6) moves forward slowly along the gear track (4), pushing the head type transmission rod (15) to move forward; the head roller (16) connected to the other side of the head type transmission rod (15) through the head bearing (17) moves forward, so that it moves forward along the roller track (3); the head The arc-shaped support plate (14) connected to the I-shaped transmission rod (15) moves forward, and the hose head fixed on the arc-shaped support plate (14) is pulled; the seven hose fixing lock assemblies behind the hose head are pulled because they are fixed to the hose; the arc-shaped support plate (14) on the hose fixing lock assembly is driven to move, and the I-shaped transmission rod (12) connected to the arc-shaped support plate (14) is driven; the roller (13) connected to the I-shaped transmission rod (12) rolls along the roller track (3), and the gear (10) connected to the I-shaped transmission rod (12) rolls along the gear track (4).

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