Robot cooperation online XRF analysis system for glass fiber raw materials

Abstract

The invention discloses a glass fiber raw material-oriented robot cooperation online XRF analysis system, which comprises two multi-channel quantitative sampling and sample preparation units, a multifunctional measurement unit and a central control system, and two cooperation robot units are arranged in an open operation area between the two multi-channel quantitative sampling and sample preparation units; the central control system is electrically connected with the two multi-channel quantitative sampling and sample preparation units, the multifunctional measuring unit and the two collaborative robot units, the material quantity is accurately controlled through a quantitative feeding mechanism of a double-stage gate plate matched material level sensor, powder is pressed into a sample cake with uniform density through a constant-pressure compaction assembly, and the sample cake is pressed into a sample. Meanwhile, the measuring station enables the sample cup to be tightly attached to the window of the detection equipment through an exclusive jacking mechanism, so that the X fluorescence analyzer is accurately matched with the moisture measuring instrument, and the measuring precision is comprehensively improved from sampling quantification, sample preparation form to the detection process.

Description

Technical Field

[0001] This invention relates to the field of analytical systems, and in particular to a robotic collaborative online XRF analysis system for glass fiber raw materials. Background Technology

[0002] The production process of glass fiber is complex, and the quality of its products requires extremely high stability of the chemical composition of raw materials. The production formula usually involves a variety of powder raw materials such as dolomite, quicklime, kaolin, high-mixed materials, and pyrophyllite. However, the traditional sampling method of existing online X-ray fluorescence (XRF) analysis devices cannot guarantee the consistency of sample thickness and density, which leads to a significant matrix effect in X-ray fluorescence analysis and greatly reduces the accuracy of measurement.

[0003] To address the aforementioned issues, this invention proposes a robotic collaborative online XRF analysis system for glass fiber raw materials that enables precise control of sample volume. Summary of the Invention

[0004] The main objective of this invention is to propose a robotic collaborative online XRF analysis system for glass fiber raw materials, aiming to solve the problem that the traditional sampling method of existing online X-ray fluorescence (XRF) analysis devices cannot guarantee the consistency of sample thickness and density, thereby significantly reducing the measurement accuracy of the equipment.

[0005] To address the aforementioned issues, this invention proposes a robotic collaborative online XRF analysis system for glass fiber raw materials, comprising: two multi-channel quantitative sampling and preparation units, a multi-functional measurement unit, and a central control system. Two collaborative robot units are located in the open operating area between the two multi-channel quantitative sampling and preparation units. The central control system is electrically connected to the two multi-channel quantitative sampling and preparation units, the multi-functional measurement unit, and the two collaborative robot units, respectively.

[0006] In one embodiment, the multi-channel quantitative sampling preparation unit includes a sampling cabinet, inside which are installed multiple sets of sampling modules arranged in parallel. Each sampling module includes a spiral sampling component and a quantitative feeding mechanism. The quantitative feeding mechanism is connected to the lower end of the discharge port of the spiral sampling component, and a compaction component is provided at the front end of the quantitative feeding mechanism.

[0007] In one embodiment, the spiral sampling assembly includes a raw material tube with a spiral cutter rotating inside the raw material tube. The connecting end of the spiral cutter passes through the raw material tube, and a drive motor is installed at one end of the raw material tube. The output end of the drive motor is connected to the connecting end of the spiral cutter.

[0008] In one embodiment, the quantitative feeding mechanism includes a receiving valve. The receiving valve is installed at the lower end of the material inlet of the raw material pipe. The bottom end of the receiving valve is connected to an upper constant volume pipe, an upper telescopic gate, a lower constant volume pipe, and a lower telescopic gate in sequence from top to bottom. A material level sensor is provided on the outer wall of one end of the upper constant volume pipe and the lower constant volume pipe.

[0009] In one embodiment, the lower end of the compaction component is provided with a lead screw module linear slide, on which multiple sample cups are placed, and the multiple sample cups are respectively opposite to the discharge ports of multiple quantitative feeding mechanisms. The bottom end of the lead screw module linear slide is equipped with multiple electric push rods, and the multiple electric push rods are vertically opposite to the compaction component.

[0010] In one embodiment, the multifunctional measurement unit includes a measurement cabinet, and an open window is provided at the end of the measurement cabinet near the collaborative robot unit. A support platform is installed inside the measurement cabinet, and a worktable is provided at the upper end of the support platform. The worktable has sample interaction stations, X-ray fluorescence measurement stations, moisture measurement stations and sample sorting and cleaning stations distributed along the circumference. A rotary indexing turntable is installed between the support platform and the worktable. Multiple placement slots are provided on the rotary indexing turntable, and the multiple placement slots are respectively opposite to each station. Sample cups are placed in each of the multiple placement slots.

[0011] In one embodiment, an X-ray fluorescence analyzer and an SDD detector are provided at the upper end of the worktable, and the X-ray fluorescence analyzer and the SDD detector are opposite to the X-ray fluorescence measurement station. A first measurement lifting cylinder is installed at the lower end of the support table, and the first measurement lifting cylinder is opposite to the X-ray fluorescence measurement station.

[0012] In one embodiment, a moisture meter is provided at the upper end of the workbench and is opposite to the moisture measurement station, and a second lifting cylinder is installed at the lower end of the support platform and is opposite to the moisture measurement station.

[0013] In one embodiment, the upper end of the workbench is provided with a composite self-cleaning component, which includes a cleaning lifting cylinder and a mechanical crushing head. The bottom end of the support platform is equipped with a cleaning lifting cylinder, and the upper end of the workbench is provided with a mechanical crushing head, which is opposite to the sorting and cleaning station. The top of the mechanical crushing head is connected to a Venturi negative pressure dust collection device.

[0014] In one embodiment, the collaborative robot unit includes an industrial robotic arm. Both collaborative robot units are equipped with industrial robotic arms, and the ends of both industrial robotic arms are equipped with pneumatic grippers. The shapes of the two pneumatic grippers are adapted to the outer wall of the sample cup.

[0015] Beneficial effects: 1. The quantitative feeding mechanism, which uses a dual-stage gate and a material level sensor, precisely controls the amount of material. The constant pressure compaction component compresses the powder into a uniformly dense sample cake. At the same time, the measurement station uses a dedicated lifting mechanism to press the sample cup tightly against the window of the detection equipment, thus ensuring precise compatibility with the X-ray fluorescence analyzer and moisture analyzer. This comprehensively improves measurement accuracy from sampling and quantitative analysis to sample preparation and detection.

[0016] 2. By replacing traditional rigid transmission with flexible transfer using collaborative robots, the sampling unit and measurement unit are separated. The open window design of the multi-functional measurement unit facilitates the operation of the industrial robotic arm and the maintenance of internal components. At the same time, the parallel configuration of dual sampling units and dual robot units can further adapt to more raw material testing needs, greatly improving the system's scalability and maintenance convenience.

[0017] 3. The spiral sampling component can discharge the residual material in the gap of the screw thread by reversing the drive motor, avoiding cross-contamination of different raw materials. At the same time, the composite self-cleaning component that combines mechanical crushing and negative pressure dust collection can thoroughly clean the residual material in the sample cup and prevent contamination caused by residual material.

[0018] 4. By rotating the indexing turntable, the sample cup is driven to complete X-ray fluorescence elemental analysis and moisture detection in sequence. Two key data can be obtained in a single sampling, without the need for separate detection of moisture index, thus providing complete data support for glass fiber batching control. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the overall system layout structure of the present invention; Figure 2 This is a three-dimensional structural diagram of the sampling module of the present invention; Figure 3 This is a schematic diagram of the internal structure of the sampling cabinet of the present invention; Figure 4 This is a schematic diagram of the internal structure of the measuring cabinet of the present invention.

[0021] The annotations in the attached figures are explained as follows: 1. Multi-channel quantitative sampling and sample preparation unit; 2. Multifunctional measurement unit; 3. Collaborative robot unit; 4. Sample cup; 11. Spiral sampling assembly; 12. Quantitative feeding mechanism; 13. Compaction assembly; 31. Industrial robotic arm; 32. Pneumatic gripper; 111. Raw material pipe; 112. Spiral auger; 113. Drive motor; 121. Receiving valve; 122. Upper constant volume pipe; 123. Upper telescopic gate; 124. Lower constant volume pipe; 125. Lower telescopic gate; 126. Material level sensor Sensor; 131, Lead screw module linear slide; 132, Electric push rod; 201, Support platform; 202, Worktable; 203, Rotary indexing turntable; 204, Placement slot; 205, X-ray fluorescence analyzer; 206, SDD detector; 207, First measuring lifting cylinder; 208, Moisture meter; 209, Second lifting cylinder; 210, Composite self-cleaning component; 211, Cleaning lifting cylinder; 212, Mechanical crushing head; 213, Venturi negative pressure dust collection device. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0023] To achieve the above-mentioned objectives of the invention, such as Figure 1-4 As shown, this invention provides a robotic collaborative online XRF analysis system for fiberglass raw materials, comprising: two multi-channel quantitative sampling and preparation units 1, used to connect multiple raw material conveying pipelines of the fiberglass production line, for independent sampling, quantitative measurement, and compaction of powder raw materials with different components; a multi-functional measurement unit 2 for receiving the prepared samples, performing elemental composition analysis and moisture content detection, and performing multiple cleaning of the sample cups 4 after testing; and a central control system. Two collaborative robot units 3 are located in the open operating area between the two multi-channel quantitative sampling and preparation units 1, used for grasping, transferring, and recycling the sample cups 4 between the units. The central control system is electrically connected to the two multi-channel quantitative sampling and preparation units 1, the multi-functional measurement unit 2, and the two collaborative robot units 3 to achieve centralized control, thereby coordinating the timing actions of each actuator. Furthermore, by replacing traditional rigid track transmission with two collaborative robots, the physical space of the sampling and preparation process is decoupled from that of the measurement process, which not only reserves sufficient maintenance space but also facilitates subsequent expansion of the number of sampling channels.

[0024] Preferred, such as Figure 2 and Figure 3As shown, the multi-channel quantitative sampling and sample preparation unit 1 includes a modularly designed open sampling cabinet that can connect to 12 or more independent pipelines. The sampling cabinet contains multiple sets of parallel sampling modules, each corresponding to a raw material delivery pipeline. Each sampling module includes a spiral sampling component 11 for collecting samples from the raw material production line pipeline in small, multiple batches, and a quantitative feeding mechanism 12 for quantifying the collected samples and transferring them to the sample cup 4. The quantitative feeding mechanism 12 is connected to the lower end of the spiral sampling component 11's outlet. The front end is equipped with a compaction component 13 for pressing the powder in the sample cup 4 to eliminate the particle effect. The spiral sampling component 11 includes a raw material tube 111. Inside the raw material tube 111, there is a rotating spiral auger 112 for picking up the material. The connecting end of the spiral auger 112 passes through the raw material tube 111. One end of the raw material tube 111 is equipped with a drive motor 113 that provides power to the spiral auger 112. The drive motor 113 is electrically connected to a power source through a power line, and the output end of the drive motor 113 is connected to the connecting end of the spiral auger 112. The drive motor 113 can rotate forward... To prevent cross-contamination of samples, the sampling mechanism 12 includes a receiving valve 121. The receiving valve 121 is installed at the lower end of the material inlet of the raw material pipe 111. From top to bottom, the bottom of the receiving valve 121 is connected to an upper volumetric pipe 122, an upper telescopic gate 123, a lower volumetric pipe 124, and a lower telescopic gate 125. Level sensors 126 are installed on the outer walls of one end of both the upper and lower volumetric pipes 122 and 124. Thus, the upper and lower telescopic gates 123 and 125, in conjunction with the two level sensors 126, precisely measure the sample cup 4. The lower end of the feeding and compaction assembly 13 is provided with a lead screw module linear slide 131. The lower end of the discharge port of the multiple quantitative feeding mechanisms 12 is provided with a lead screw module linear slide 131. Multiple sample cups 4 are placed on the lead screw module linear slide 131, and the multiple sample cups 4 are respectively opposite to the discharge ports of the multiple quantitative feeding mechanisms 12. The bottom end of the lead screw module linear slide 131 is equipped with multiple electric push rods 132, which are used to push the sample cups 4 upward toward the compaction assembly 13. The multiple electric push rods 132 are electrically connected to the power supply through power lines, and the multiple electric push rods 132 are vertically opposite to the compaction assembly 13.

[0025] Preferred, such as Figure 4As shown, the multi-functional measurement unit 2 includes a measurement cabinet, and the measurement cabinet has an open window at one end near the collaborative robot unit 3 to allow the industrial robotic arm 31 to enter and operate. A support platform 201 is installed inside the measurement cabinet, and a worktable 202 is located on the upper end of the support platform 201. The worktable 202 has sample interaction stations, X-ray fluorescence measurement stations, moisture measurement stations, and sample sorting and cleaning stations distributed circumferentially. A rotating indexing turntable 203 is installed between the support platform 201 and the worktable 202. The rotating indexing turntable 203... Multiple placement slots 204 are provided for placing the sample cups 4 for measurement, and each placement slot 204 is opposite to a different workstation. Each placement slot 204 contains a sample cup 4. An X-ray fluorescence analyzer 205 and an SDD detector 206 are installed at the upper end of the worktable 202, and the X-ray fluorescence analyzer 205 and SDD detector 206 are opposite to the X-ray fluorescence measurement workstation. A first measurement lifting cylinder 207 is installed at the bottom end of the support platform 201, and the first measurement lifting cylinder 207 is opposite to the X-ray fluorescence measurement workstation, so that when the sample cup 4 rotates to… During X-ray fluorescence measurement, the sample cup 4 is lifted to the predetermined measurement height by the first measuring lifting cylinder 207. A moisture meter 208 is installed at the upper end of the worktable 202, and the moisture meter 208 is opposite to the moisture measurement station. A second lifting cylinder 209 is installed at the bottom end of the support platform 201, and the second lifting cylinder 209 is opposite to the moisture measurement station. Thus, when the sample cup 4 rotates to the moisture measurement station, the second measuring lifting cylinder lifts the sample cup 4 to the predetermined measurement height. The upper end of the worktable 202 is equipped with a composite self-cleaning device. Component 210, the composite self-cleaning component 210 includes a cleaning lifting cylinder 211 and a mechanical crushing head 212. The bottom end of the support platform 201 is equipped with a cleaning lifting cylinder 211, which is used to lift the sample cup 4 to the position of the mechanical crushing head 212. The upper end of the worktable 202 is equipped with a mechanical crushing head 212, which is used to stir and break up the compacted sample cake in the sample cup 4. The mechanical crushing head 212 is opposite to the sample discharge and cleaning station. The top end of the mechanical crushing head 212 is connected to a Venturi negative pressure dust suction device 213, which is used to suck away the crushed powder.

[0026] Preferred, such as Figure 1 As shown, the collaborative robot unit 3 includes an industrial robotic arm 31. Both collaborative robot units 3 are equipped with industrial robotic arms 31, which can reciprocate between the compaction station of the sampling cabinet and the interactive station of the measurement cabinet according to preset coordinates. The ends of the two industrial robotic arms 31 are equipped with pneumatic grippers 32, and the shapes of the two pneumatic grippers 32 are adapted to the outer wall of the sample cup 4 to facilitate stable clamping of the sample cup 4.

[0027] In use, instructions are first sent through multiple units of the central control system, and then... Figure 2As shown, after receiving an instruction, the drive motor 113 of the spiral sampling assembly 11 drives the spiral cutter 112 inside the raw material pipe 111 to rotate forward, so as to collect powder raw materials from the production line pipeline into the inside of the raw material pipe 111. Then, the powder raw materials enter the receiving valve 121 through the outlet of the raw material pipe 111, and fall into the upper volumetric pipe 122 of the quantitative feeding mechanism through the receiving valve 121. When the material level sensor 126 on the outer wall of the upper volumetric pipe 122 detects the full material signal, the upper telescopic gate 123 closes. At this time, the drive motor 113 reverses to discharge the remaining material in the thread gap of the spiral cutter 112 to prevent cross-contamination of the powder raw materials. Then, the lower telescopic gate 125 opens, and the quantitative material falls into the corresponding sample cup 4 on the linear slide table 131 of the screw module through the lower volumetric pipe 124. Figure 3 As shown, the linear slide 131 of the lead screw module moves the sample cup 4 to below the compaction component 13. The electric push rod 132 moves upward to apply constant pressure, thereby pressing the powder in the sample cup 4 into a sample cake with a smooth surface and uniform density to ensure the consistency of the matrix in subsequent testing. Then, the pneumatic grippers 32 at the ends of the industrial robotic arms 31 of the two collaborative robot units 3 pick up the sample cup 4 carrying the sample cake from the compaction station of the sampling cabinet according to a preset trajectory. Through the open window opened by the multi-functional measurement unit 2, the sample cup 4 is accurately placed in the placement slot 204 of the rotating indexing turntable 203 between the support table 201 and the worktable 202. Then, as... Figure 4 As shown, the rotary indexing turntable 203 drives the sample cup 4 through each station in sequence. The sample cup 4 is first picked up and placed at the sample interaction station. Then the turntable rotates to the X-ray fluorescence measurement station. At this time, the first measurement lifting cylinder 207 at the bottom of the support stage 201 is activated, lifting the sample cup 4 to a preset height so that it is close to the detection window of the X-ray fluorescence analyzer 205 and the SDD detector 206 at the top of the worktable 202 to complete the elemental composition analysis. After the analysis is completed and the cylinder is reset, the turntable continues to drive the sample cup 4 to the moisture measurement station. The second lifting cylinder 209 drives the sample cup 4 to move upward to the preset position. The height is adjusted to cooperate with the moisture meter 208 to complete the non-contact moisture content detection. After the detection is completed and the cylinder is reset, the sample cup 4 is moved to the sample cleaning station. At this time, the cleaning lifting cylinder 211 lifts the sample cup 4 to the preset height, so that the mechanical crushing head 212 at the top of the workbench 202 extends into the cup and breaks up the clump of sample cake. At the same time, the Venturi negative pressure dust suction device 213 is activated to suck away the residual material to clean the sample cup 4. Finally, the two collaborative robot units 3 use the pneumatic gripper 32 at the end of the industrial robotic arm 31 to retrieve the cleaned empty cup and put it back to the corresponding station of the sampling unit.

[0028] Throughout the entire operation, two industrial robotic arms 31 completely replace the traditional rigid transmission, achieving physical spatial decoupling between the sampling and measurement ends. The central control system is electrically connected to two multi-channel quantitative sampling and preparation units 1, a multi-functional measurement unit 2, and two collaborative robot units 3, respectively. Based on PLC control, it coordinates the timing actions of each actuator, thereby accurately scheduling the entire process of sampling, quantification, compaction, transfer, measurement, and cleaning. At the same time, the elemental composition and moisture detection data are uploaded to the system in real time via Ethernet, providing complete data support for the control of glass fiber batching. The whole system achieves fully automated, high-precision, and low-pollution operation of multi-channel glass fiber raw material detection.

[0029] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A robotic collaborative online XRF analysis system for glass fiber raw materials, characterized in that, include: Two multi-channel quantitative sampling and preparation units (1), a multi-functional measurement unit (2), and a central control system are provided. Two collaborative robot units (3) are provided in the open operating area between the two multi-channel quantitative sampling and preparation units (1). The central control system is electrically connected to the two multi-channel quantitative sampling and preparation units (1), the multi-functional measurement unit (2), and the two collaborative robot units (3).

2. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 1, characterized in that, The multi-channel quantitative sampling preparation unit (1) includes a sampling cabinet. The sampling cabinet is equipped with multiple sampling modules arranged in parallel. Each sampling module includes a spiral sampling component (11) and a quantitative feeding mechanism (12). The quantitative feeding mechanism (12) is connected to the lower end of the discharge port of the spiral sampling component (11). The front end of the quantitative feeding mechanism (12) is provided with a compaction component (13).

3. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 2, characterized in that, The spiral sampling assembly (11) includes a raw material tube (111), inside which a spiral cutter (112) rotates, and the connecting end of the spiral cutter (112) passes through the raw material tube (111). One end of the raw material tube (111) is equipped with a drive motor (113), and the output end of the drive motor (113) is connected to the connecting end of the spiral cutter (112).

4. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 2, characterized in that, The quantitative feeding mechanism (12) includes a receiving valve (121). The receiving valve (121) is installed at the lower end of the material inlet of the raw material pipe (111). The bottom end of the receiving valve (121) is connected to the upper volumetric pipe (122), the upper telescopic gate (123), the lower volumetric pipe (124), and the lower telescopic gate (125) in sequence from top to bottom. A material level sensor (126) is installed on the outer wall of one end of the upper volumetric pipe (122) and the lower volumetric pipe (124).

5. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 2, characterized in that, The lower end of the compaction component (13) is provided with a screw module linear slide (131), on which multiple sample cups (4) are placed, and the multiple sample cups (4) are respectively opposite to the discharge ports of multiple quantitative feeding mechanisms (12). The bottom end of the screw module linear slide (131) is equipped with multiple electric push rods (132), and the multiple electric push rods (132) are vertically opposite to the compaction component (13).

6. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 1, characterized in that, The multi-functional measurement unit (2) includes a measurement cabinet, and the measurement cabinet is close to the collaborative robot unit (3) with an open window at one end. The measurement cabinet is equipped with a support platform (201), and the upper end of the support platform (201) is equipped with a worktable (202). The worktable (202) is equipped with sample interaction stations, X-ray fluorescence measurement stations, moisture measurement stations and sample cleaning stations distributed along the circumference. A rotating indexing turntable (203) is installed between the support platform (201) and the worktable (202). The rotating indexing turntable (203) is equipped with multiple placement slots (204), and the multiple placement slots (204) are respectively opposite to each station. Sample cups (4) are placed in the multiple placement slots (204).

7. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 6, characterized in that, The upper end of the worktable (202) is equipped with an X-ray fluorescence analyzer (205) and an SDD detector (206), and the X-ray fluorescence analyzer (205) and the SDD detector (206) are opposite to the X-ray fluorescence measurement station. The bottom end of the support table (201) is equipped with a first measurement lifting cylinder (207), and the first measurement lifting cylinder (207) is opposite to the X-ray fluorescence measurement station.

8. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 6, characterized in that, A moisture meter (208) is provided at the upper end of the workbench (202), and the moisture meter (208) is opposite to the moisture measurement station. A second lifting cylinder (209) is installed at the bottom end of the support platform (201), and the second lifting cylinder (209) is opposite to the moisture measurement station.

9. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 6, characterized in that, The upper end of the workbench (202) is provided with a composite self-cleaning component (210), which includes a cleaning lifting cylinder (211) and a mechanical crushing head (212). The bottom end of the support platform (201) is provided with a cleaning lifting cylinder (211), and the upper end of the workbench (202) is provided with a mechanical crushing head (212). The mechanical crushing head (212) is opposite to the sorting and cleaning station, and the top of the mechanical crushing head (212) is connected to a Venturi negative pressure dust collection device (213).

10. The robotic collaborative online XRF analysis system for glass fiber raw materials as described in claim 1, characterized in that, The collaborative robot unit (3) includes an industrial robotic arm (31). Both collaborative robot units (3) are equipped with industrial robotic arms (31). The ends of both industrial robotic arms (31) are equipped with pneumatic grippers (32), and the shapes of the two pneumatic grippers (32) are adapted to the outer wall of the sample cup (4).

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