Ring rolling cooling control method and system for large ring forgings

Abstract

The present invention relates to the field of data processing technology, and specifically provides a method and system for controlling the cooling of large ring forgings during rolling, comprising: utilizing infrared temperature measurement technology to scan the surface temperature of the large ring forging, and assigning the surface temperature to a pre-built three-dimensional model of the large ring forging; pre-setting a spray head travel path and a basic travel speed; dividing the surface of the three-dimensional model into multiple temperature zones based on the surface temperature of the three-dimensional model; and generating a travel speed for the travel path within the temperature zone based on the temperature value of the temperature zone and the basic travel speed, wherein the travel speed is inversely proportional to the temperature value. The present invention cleverly combines the dual requirements of high efficiency and uniform cooling, ensuring the excellent and stable quality of the ring forging products.

Description

Technical Field

[0001] The invention belongs to the technical field of data processing, and in particular relates to a ring rolling temperature reduction control method and system for large ring forgings. Background Art

[0002] Large alloy steel ring forgings are widely used in energy, automobile, aerospace, shipbuilding, marine engineering, metallurgy, chemical industry and other fields, playing an important role as key components. Therefore, their quality and performance have a significant impact on equipment operation and maintenance.

[0003] Currently, the main method for cooling rings is to hoist them to a fixed location after forging. However, the timeliness and uniformity of cooling are limited by the cooling location. This affects the uniformity of the ring's microstructure and performance, ultimately affecting the product's operational stability. While spraying coolant onto ring forgings can achieve efficient cooling, the spraying process is relatively crude, typically spraying at a fixed rate. Since the ends of ring forgings are typically cooler than the center, using uniform spray parameters can result in uneven cooling.

[0004] Although some spray systems take temperature gradients into account, they typically increase the spray intensity in higher temperature areas and reduce it in lower temperature areas. This approach achieves uniform cooling at the expense of spray efficiency, extending the cooling time of the ring forgings. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method and system for controlling the temperature drop during the rolling of large ring forgings to solve the above-mentioned technical problems.

[0006] In a first aspect, the present invention provides a method for controlling the temperature drop during the rolling of a large ring forging, comprising:

[0007] Scanning the surface temperature of the large ring forging using infrared temperature measurement technology and assigning the surface temperature to a pre-built three-dimensional model of the large ring forging;

[0008] Pre-set the sprinkler head travel path and basic travel speed;

[0009] Dividing the surface of the three-dimensional model into a plurality of temperature regions based on the surface temperature of the three-dimensional model;

[0010] Based on the temperature value of the temperature zone and the basic walking speed, a walking speed is generated for the walking path within the temperature zone, and the walking speed is inversely proportional to the temperature value.

[0011] In an optional embodiment, the surface temperature of the large ring forging is scanned using infrared temperature measurement technology, and the surface temperature is assigned to a pre-built three-dimensional model of the large ring forging, including:

[0012] Use 3D modeling tools to build 3D models based on the actual size and shape of large ring forgings;

[0013] Aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data of each area on the ring forging surface;

[0014] The temperature distribution data of each area on the surface of the ring forging is imported into the software used to process the three-dimensional model. The temperature data is mapped and matched with each part in the three-dimensional model using the data processing function in the software.

[0015] In an optional embodiment, the sprinkler head travel path and basic travel speed are pre-set, including:

[0016] The circumference of the ring forging is equally divided into N nodes, each node represents a potential stop point of the sprinkler head on the ring forging;

[0017] Create an N×N distance matrix, where each element represents the distance between two nodes;

[0018] If there are multiple sprinkler heads, the sprinkler area is planned for each sprinkler head and a sub-distance matrix is ​​created for the nodes in the sprinkler area;

[0019] The part of the path from the starting point to the last node is selected as the travel path of the sprinkler head;

[0020] Fine-tune the path based on cooling needs and sprinkler head performance;

[0021] Set the base walking speed based on the need for even cooling.

[0022] In an optional embodiment, setting a basic walking speed based on a uniform heat dissipation requirement includes:

[0023] Acquire spray parameters of the spray head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency;

[0024] Evaluate cooling requirements based on the material, size, initial temperature, and desired final temperature of the ring forging, including the maximum local cooling rate and average cooling rate;

[0025] Setting an average cooling time based on the material, size, initial temperature, desired final temperature, and average cooling rate of the ring forging;

[0026] Calculating the length of the walking path and calculating the quotient of the length and the average cooling time to obtain an average walking speed;

[0027] The actual cooling rate of the ring forging is simulated based on the average walking speed and the spray parameters of the spray head;

[0028] If the actual cooling rate does not exceed the average cooling rate, setting the average walking speed as the basic walking speed;

[0029] If the actual cooling rate exceeds the average cooling rate, the ratio of the average cooling rate to the actual cooling rate is calculated, and the product of the average walking speed and the ratio is set as the basic walking speed, and the new basic walking speed is verified and iterated until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

[0030] In an optional embodiment, based on the temperature value of the temperature zone and the basic walking speed, a walking speed is generated for the walking path within the temperature zone, wherein the walking speed is inversely proportional to the temperature value, including:

[0031] Calculate the average temperature value of each temperature zone;

[0032] Normalize the average temperature value of each temperature zone to obtain the temperature coefficient;

[0033] The product of the temperature coefficient and the basic walking speed is used as the walking speed in the corresponding temperature range.

[0034] In a second aspect, the present invention provides a large ring forging ring rolling cooling control system, comprising:

[0035] A temperature scanning module, configured to scan the surface temperature of the large ring forging using infrared temperature measurement technology and assign the surface temperature to a pre-built three-dimensional model of the large ring forging;

[0036] Parameter setting module, used to pre-set the sprinkler head travel path and basic travel speed;

[0037] a temperature partitioning module, configured to divide the surface of the three-dimensional model into a plurality of temperature zones based on the surface temperature of the three-dimensional model;

[0038] The walking control module is used to generate a walking speed for a walking path within the temperature zone based on a temperature value of the temperature zone and the basic walking speed, wherein the walking speed is inversely proportional to the temperature value.

[0039] In an optional embodiment, the temperature scanning module includes:

[0040] a model building unit for building a three-dimensional model according to the actual size and shape of the large ring forging using a three-dimensional modeling tool;

[0041] The temperature scanning unit is used to aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data of each area on the ring forging surface;

[0042] The temperature assignment unit is used to import the temperature distribution data of various areas on the surface of the ring forging into the software used to process the three-dimensional model, and use the data processing function in the software to map and match the temperature data with various parts in the three-dimensional model.

[0043] In an optional embodiment, the parameter setting module includes:

[0044] A node division unit is used to divide the circumference of the ring forging into N equal nodes, each node representing a potential stop point of the sprinkler head on the ring forging;

[0045] A matrix creation unit is used to create an N×N distance matrix, where each element represents the distance between two nodes;

[0046] The area division unit is used to plan the spraying area for each sprinkler head if there are multiple sprinkler heads, and to create a sub-distance matrix for the nodes in the spraying area;

[0047] A path generation unit is used to select the portion of the path from the starting point to the last node as the travel path of the sprinkler head;

[0048] Path fine-tuning unit, used to fine-tune the path according to cooling requirements and sprinkler head performance;

[0049] The speed setting unit is used to set the basic walking speed based on the uniform heat dissipation requirement.

[0050] In an optional embodiment, the speed setting unit includes:

[0051] A parameter acquisition subunit is used to obtain the spray parameters of the sprinkler head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency;

[0052] A demand acquisition subunit is used to evaluate the cooling demand based on the material, size, initial temperature and final temperature to be achieved of the ring forging, wherein the cooling demand includes the maximum local cooling rate and the average cooling rate;

[0053] a time calculation subunit, configured to set an average cooling time based on the material, size, initial temperature, desired final temperature, and average cooling rate of the ring forging;

[0054] a speed calculation subunit, configured to calculate the length of the walking path, and calculate the quotient of the length and the average cooling time to obtain an average walking speed;

[0055] The cooling simulation subunit is used to simulate the actual cooling rate of the ring forging based on the average walking speed and the spray parameters of the spray head;

[0056] a basic setting subunit, configured to set the average walking speed as a basic walking speed if the actual cooling rate does not exceed the average cooling rate;

[0057] The iterative update subunit is used to calculate the ratio of the average cooling rate to the actual cooling rate if the actual cooling rate exceeds the average cooling rate, set the product of the average walking speed and the ratio as the basic walking speed, and verify the new basic walking speed iteratively until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

[0058] In an optional embodiment, the walking control module includes:

[0059] Temperature averaging unit, used to calculate the average temperature value of each temperature zone;

[0060] A coefficient calculation unit is used to normalize the average temperature value of each temperature zone to obtain a temperature coefficient;

[0061] The speed generating unit is configured to use the product of the temperature coefficient and the basic walking speed as the walking speed in the corresponding temperature range.

[0062] According to a third aspect, a device is provided, comprising:

[0063] A memory for storing a ring rolling and cooling control program for large ring forgings;

[0064] The processor is used to implement the steps of the large ring forging ring rolling cooling control method provided in the first aspect when executing the large ring forging ring rolling cooling control program.

[0065] In a fourth aspect, a computer-readable storage medium is provided, on which a large ring forging ring rolling cooling control program is stored. When the large ring forging ring rolling cooling control program is executed by a processor, the steps of the large ring forging ring rolling cooling control method provided in the first aspect are implemented.

[0066] The beneficial effects of the present invention lie in the fact that the provided method and system for controlling the cooling of large ring forgings during rolling ring rolling employ precise control of the spray head's movement speed, which is dynamically adjusted based on the ring forging's surface temperature. This aims to maximize the travel rate without causing excessive cooling, while also carefully balancing the uniform reduction of the temperature gradient without reducing the spray head's spraying efficiency. This strategy cleverly combines the dual requirements of efficient and uniform cooling, ensuring excellent and stable ring forging product quality. Furthermore, the present invention boasts a reliable design principle and simple structure, promising a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0068] Figure 1 is a schematic flow chart of a method according to an embodiment of the present invention.

[0069] Figure 2 FIG. 4 is a schematic block diagram of a system according to an embodiment of the present invention.

[0070] Figure 3 A schematic structural diagram of a device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0073] The key terms appearing in the present invention are explained below.

[0074] Infrared thermometers play a vital role in product quality control and monitoring, online equipment fault diagnosis and safety protection, and energy conservation during the production process. Over the past 20 years, non-contact infrared body thermometers have experienced rapid technological advancements, with continuous improvements in performance, enhanced functionality, a growing variety, and a broadening range of applications. Compared to contact temperature measurement methods, infrared temperature measurement offers advantages such as fast response time, non-contact operation, safety, and a long service life. Non-contact infrared thermometers include three series: portable, online, and scanning, with a variety of options and software available. Within each series, there are a variety of models and specifications.

[0075] The temperature measuring instrument should have high accuracy and response speed to capture the temperature changes of the ring forgings in real time.

[0076] The ring cooling control method for large ring forgings provided in an embodiment of the present invention is executed by a computer device. Accordingly, the ring cooling control system for large ring forgings is run in the computer device.

[0077] Figure 1 is a schematic flow chart of a method according to an embodiment of the present invention. Figure 1 The execution subject can be a large ring forging ring rolling cooling control system. According to different requirements, the order of the steps in the flow chart can be changed, and some can be omitted.

[0078] like Figure 1 As shown, the method includes:

[0079] S1. Scan the surface temperature of the large ring forging using infrared temperature measurement technology, and assign the surface temperature to a pre-built three-dimensional model of the large ring forging.

[0080] High-precision infrared temperature measurement technology is used to scan the entire surface of a large ring forging. This step ensures that every subtle temperature difference on the ring forging surface is captured. The collected surface temperature data is then accurately assigned to a 3D model pre-built based on the actual size and shape of the ring forging. This process provides an accurate data foundation for subsequent temperature zone division and travel speed adjustment.

[0081] S2. Pre-set the sprinkler head travel path and basic travel speed.

[0082] Before officially commencing cooling operations, the spray head's path needs to be planned. This typically involves a thorough analysis of the ring forging's shape, dimensions, and cooling requirements to ensure comprehensive and even coverage of the entire surface. Furthermore, a baseline travel speed is established based on empirical data and preliminary testing. This speed is intended to provide a reasonable starting point for subsequent adjustments based on real-time temperature data.

[0083] S3. Based on the surface temperature of the three-dimensional model, divide the surface of the three-dimensional model into multiple temperature regions.

[0084] Based on the assigned 3D model surface temperature data, an advanced algorithm divides the model surface into multiple temperature zones. These zones are divided according to their temperature values, helping to more accurately identify areas that require faster cooling and those that can be cooled more slowly. This division enables more refined cooling control, thereby improving overall cooling efficiency and uniformity.

[0085] S4. Based on the temperature value of the temperature zone and the basic walking speed, generate a walking speed for the walking path within the temperature zone, wherein the walking speed is inversely proportional to the temperature value.

[0086] Based on the temperature zone divisions, the system dynamically generates corresponding travel speeds for each zone's temperature value and a pre-set baseline travel speed. An inverse relationship is established between travel speed and temperature: higher temperature zones require slower travel speeds to accelerate cooling. Conversely, lower temperature zones can be appropriately accelerated to maintain overall cooling uniformity and efficiency. This dynamic adjustment mechanism ensures that the sprinkler head can flexibly adjust its movement speed based on real-time temperature data, achieving efficient and uniform cooling while ensuring product quality.

[0087] To facilitate understanding of the present invention, the following is a further description of the large ring forging rolling ring cooling control method provided by the present invention based on the principle of the large ring forging rolling ring cooling control method of the present invention and the process of cooling control of the large ring forging rolling ring in the embodiment.

[0088] In an embodiment of the present invention, based on step S1, a possible embodiment will be given below to illustrate its specific implementation scheme in a non-limiting manner.

[0089] S101. Use 3D modeling tools to construct a 3D model based on the actual size and shape of the large ring forging.

[0090] Using professional 3D modeling tools such as SolidWorks, AutoCAD, or CATIA, a precise 3D model of the large ring forging is constructed based on its actual size, shape, and structural features. This step requires a high degree of accuracy and detail capture to ensure that subsequent temperature distribution data can be accurately mapped to the model, providing a solid foundation for the subsequent cooling strategy development.

[0091] S102. Aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data for each area on the surface of the ring forging.

[0092] In a specific example, this step can be implemented by using a robot or manipulator equipped with a temperature measuring instrument to move around the ring forging, measuring the temperature of each part one by one. Using the principle of infrared thermal radiation, the temperature distribution data of various areas on the ring forging surface is captured. This data directly reflects the thermal state of the ring forging during the cooling process, providing key information for subsequent temperature control and cooling strategy development.

[0093] S103. Import the temperature distribution data of each area on the surface of the ring forging into the software for processing the three-dimensional model, and use the data processing function in the software to map and match the temperature data with each part in the three-dimensional model.

[0094] The temperature distribution data for each area of ​​the ring forging surface, obtained in the previous step, is imported into software used to process 3D models, such as Ansys, SolidWorks Simulation, or ABAQUS, via a specific data interface or file format. Within the software, data processing and analysis capabilities are utilized to accurately map and match the temperature data to each component of the 3D model. This process typically involves complex algorithms and data processing techniques to ensure that the temperature data is accurately and correctly mapped to every point, surface, or volume element in the model. Once the mapping is complete, the 3D model becomes a "thermal model" containing detailed temperature information, providing intuitive and visual support for subsequent temperature control and cooling optimization.

[0095] In an embodiment of the present invention, based on step S2, a possible embodiment will be given below to illustrate its specific implementation scheme in a non-limiting manner.

[0096] S201. Divide the circumference of the ring forging into N equal nodes, each node representing a potential stop point of the sprinkler head on the ring forging.

[0097] The circumference of a large ring forging is divided into N equal parts. These nodes not only represent evenly distributed points on the ring forging's circumference but also serve as potential locations for the sprinkler head to rest on the ring forging. Each node is selected based on the ring forging's size, shape, and cooling requirements to ensure that the sprinkler head can fully cover and effectively cool all parts of the ring forging.

[0098] S202. Create an N×N distance matrix, where each element represents the distance between two nodes.

[0099] Create an N×N distance matrix to record the distance between every two nodes. This matrix is ​​crucial for subsequent path planning and optimization because it helps the algorithm quickly calculate the total length or total time of different paths, thereby finding the optimal spray travel path.

[0100] S203. If there are multiple sprinkler heads, plan a sprinkler area for each sprinkler head, and create a sub-distance matrix for the nodes in the sprinkler area.

[0101] If multiple sprinkler heads are operating simultaneously, the spray zones must be appropriately divided based on the size and shape of the ring forging, as well as the number, performance, and coverage of the sprinkler heads. Each spray zone will contain a certain number of nodes, and a sub-distance matrix will be created for these nodes. This helps each sprinkler head independently plan the optimal path within its area of ​​responsibility, reducing path overlap and conflicts and improving overall cooling efficiency.

[0102] S204: Select the portion of the path from the starting point to the last node as the travel path of the sprinkler head.

[0103] Based on the distance matrix and sub-distance matrix, a path is selected that starts from the starting point, passes through all nodes in sequence, and finally returns to the starting point, or a partial path is selected from the starting point to the last node (if returning to the starting point is not required). The goal of this step is to find a path that fully covers all nodes while minimizing the path length and reducing the travel time of the sprinkler head.

[0104] In a specific example, the circumference of a large ring forging is divided into six equal nodes (N=6), marked as A, B, C, D, E, and F. At the same time, a sprinkler head needs to start from the starting point (assuming it is point A), pass through all the nodes in sequence, and finally return to the starting point (or choose not to return to the starting point as needed).

[0105] In the example scenario, the nodes are divided into:

[0106] The circumference of the ring forging is equally divided into 6 nodes: A, B, C, D, E, and F.

[0107] Distance Matrix Construction: Construct a 6×6 distance matrix that records the distance between every two nodes. Since this is a simplified example, we can assume that the elements in the distance matrix are randomly generated, but in reality these distances should be calculated based on the actual size and shape of the ring forging.

[0108] Distance matrix example (unit: meters):

[0109] | A | B | C | D | D | E |

[0110] | 0 | 2.5 | 5.0 | 7.5 | 10.0 | 2.5 |

[0111] | 2.5 | 0 | 2.5 | 5.0 | 7.5 | 10.0 |

[0112] | 5.0 | 2.5 | 0 | 2.5 | 5.0 | 7.5 |

[0113] | 7.5 | 5.0 | 2.5 | 0 | 2.5 | 5.0 |

[0114] |10.0 | 7.5 | 5.0 | 2.5 | 0 | 2.5 |

[0115] | 2.5 | 10.0 | 7.5 | 5.0 | 2.5 | 0 |

[0116] Based on the distance matrix, we can choose a path starting from the starting point A, passing through B, C, D, E, F, and finally returning to A.

[0117] The total length of this path can be calculated by adding the distances between adjacent nodes on the path: 2.5 (A to B) + 2.5 (B to C) + 2.5 (C to D) + 2.5 (D to E) + 2.5 (E to F) + 2.5 (F back to A) = 15 meters.

[0118] If you don't need to return to the starting point, you can choose a partial path starting from A to F, with a total length of: 2.5 (A to B) + 2.5 (B to C) + 2.5 (C to D) + 2.5 (D to E) + 2.5 (E to F) = 12.5 meters.

[0119] S205. Fine-tune the path based on cooling requirements and sprinkler head performance.

[0120] Fine-tune the initially selected path based on actual cooling requirements and the performance characteristics of the sprinkler head. This may include adjusting the order of nodes, adding or removing certain nodes, or adjusting the shape of the path. The goal of fine-tuning is to ensure that the sprinkler head can cover the entire ring forging in the most efficient manner while meeting the specific cooling requirements.

[0121] In a specific example, assume that the circumference of the ring forging is equally divided into 8 nodes, marked as A, B, C, D, E, F, G, and H respectively.

[0122] The initially selected path is: A → B → C → D → E → F → G → H → A.

[0123] If a certain area (such as the area between E and G) is not adequately covered in the preliminary path, one or more nodes (such as E1, E2, etc.) can be added between E and G and the path adjusted accordingly.

[0124] If the sprinkler head sprays more effectively at certain angles (such as vertical or oblique angles), we can adjust the shape of the path to allow the sprinkler head to spray more at these angles during its movement. For example, the path can be adjusted to a curved shape to provide more uniform coverage of the ring forging during its movement.

[0125] The path after fine-tuning may be: A → B → C → D→ E → E1 (new node) → F→ G→ H → A (or adjusted as needed).

[0126] Alternatively, if the optimal spray angle of the sprinkler head is taken into consideration, the path after fine-tuning may be a curved shape, such as: A → B (slightly inclined) → C (more inclined) → D (maximum inclination, stay) → E (gradually return to vertical) → F (maximum inclination again, stay) → G (gradually return to horizontal) → H → A.

[0127] S206. Set a basic walking speed based on the uniform heat dissipation requirement.

[0128] To ensure uniform heat dissipation, set a base travel speed for the sprinkler head. This speed should ensure uniform and effective cooling of the ring forgings while avoiding uneven cooling or inefficiency caused by excessively fast or slow movement. Setting this base travel speed requires comprehensive consideration of factors such as sprinkler head performance, ring forging material and size, and cooling time requirements.

[0129] On the basis of the above embodiments, in order to further improve the rationality of the basic walking speed provided by the above embodiments, as an implementable method, in one embodiment, a method for setting the basic walking speed is provided, and the optimal basic walking speed is sought through iterative updating.

[0130] S206-1. Obtain the spray parameters of the spray head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency.

[0131] Before starting the cooling process, it is necessary to first collect the parameters of the sprinkler head in detail. These parameters are crucial for the subsequent steps and include:

[0132] Flow rate: The volume of coolant released by the sprinkler head per minute.

[0133] Spray Range: The maximum area or diameter that the coolant can cover.

[0134] Spray intensity: the pressure or impact force of coolant per unit area.

[0135] Cooling Efficiency: The ability of a coolant to reduce temperature under standard test conditions.

[0136] S206-2. Evaluate cooling requirements based on the material, size, initial temperature, and desired final temperature of the ring forging, including the maximum local cooling rate and the average cooling rate.

[0137] A detailed cooling requirements analysis is performed based on the ring forging characteristics (such as material, size, initial temperature) and the required final temperature. Key outputs of this step include:

[0138] Maximum Local Cooling Rate: The maximum cooling rate required for the hottest part of a ring forging to prevent thermal stress or deformation.

[0139] Average cooling rate: The average cooling rate that all parts of the ring forging should achieve to ensure uniform cooling throughout.

[0140] S206-3. Set an average cooling time based on the material, size, initial temperature and desired final temperature of the ring forging, as well as the average cooling rate.

[0141] Based on the material, size, initial temperature and final temperature required for the ring forging, as well as the average cooling rate, the average cooling time required is calculated. This time will be used to guide the movement speed of the sprinkler head to ensure that the ring forging can be cooled evenly and effectively.

[0142] The average cooling time is calculated as:

[0143] ;

[0144] Among them, T cool is the average cooling time required, ΔT is the difference between the initial and final temperatures, and AverageCoolingRate is the set average cooling rate.

[0145] S206-4. Calculate the length of the walking path, and calculate the quotient of the length and the average cooling time to obtain an average walking speed.

[0146] Once the total length of the travel path is determined, the average travel speed the sprinkler should maintain can be calculated by dividing that length by the average desired cooling time.

[0147] S206-5. Simulate the actual cooling rate of the ring forging based on the average walking speed and the spray parameters of the spray head.

[0148] In an example, the specific simulation method is as follows:

[0149] (1) Collect necessary data:

[0150] Spray parameters of the sprinkler head: including flow rate, spray range, spray intensity and cooling efficiency.

[0151] The material, size, initial temperature and final temperature required for ring forgings.

[0152] The total length of the walking path and the initially set average walking speed.

[0153] (2) Establishing a mathematical model:

[0154] A mathematical model of ring forging cooling is established based on heat transfer mechanisms such as heat conduction, convection and radiation.

[0155] Consider the influence of the movement speed of the sprinkler head and the spraying parameters on the cooling process.

[0156] When simulating the cooling of ring forgings, the heat conduction equation can be used as the basic mathematical model. The heat conduction equation describes the heat transfer process caused by the temperature gradient inside the object.

[0157] For objects such as ring forgings with complex geometric shapes and material properties, the heat conduction equation can be expressed as:

[0158] \rho c \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q\] where: - \(\rho\) is the density of the ring forging; - \(c\) is the specific heat capacity of the ring forging; - \(T\) is the temperature; - \(t\) is the time; - \(k\) is the thermal conductivity of the ring forging; and - \(Q\) is the heat source term, which represents the cooling effect of the sprinkler on the ring forging. To more accurately describe the cooling effect of the sprinkler, the sprinkler's spray parameters (such as flow rate, spray range, and spray intensity) can be incorporated into the heat source term \(Q\). Furthermore, the influence of the sprinkler's movement speed and travel path on the cooling process must be considered. These factors can be addressed by adjusting the spatial distribution and temporal variation of the heat source term.

[0159] (3) Select simulation software:

[0160] Choose simulation software that can handle complex heat transfer problems, such as CFD (computational fluid dynamics) software. Make sure the software can accurately simulate the movement and spraying of the sprinkler head, as well as the temperature changes in the ring forging.

[0161] (4) Set simulation parameters:

[0162] In the simulation software, the spray parameters of the sprinkler head, the material and size of the ring forging, etc. are set according to the collected data. The walking path and the average walking speed are set preliminarily.

[0163] (5) Establishing geometric model:

[0164] Retrieve the 3D model of the ring forging. Consider the movement trajectory and spray range of the sprinkler head to ensure geometric accuracy during the simulation.

[0165] (6) Set boundary conditions:

[0166] The simulation boundary conditions are set based on the initial temperature of the ring forging and the desired final temperature. The heat transfer process between the sprinkler head and the ring forging, as well as the influence of the environment on the cooling process, are considered.

[0167] Boundary conditions are external conditions that must be set during the simulation process, and they have a significant impact on the accuracy of the simulation results. When simulating the cooling of a ring forging, the following boundary conditions must be considered: 1. **Initial Temperature Condition**: - This sets the initial temperature distribution of the ring forging, typically a uniform temperature field. 2. **Sprinkler Cooling Condition**: - This sets the sprinkler head's spray parameters, such as flow rate, spray range, and spray intensity, as well as the sprinkler head's movement speed and path. - These parameters directly affect the sprinkler head's cooling effect on the ring forging and therefore must be accurately set during the simulation. 3. **Environmental Heat Exchange Condition**: - This considers heat exchange processes between the ring forging and the environment, such as convection and radiation. - This describes the heat exchange process between the ring forging and the environment by setting parameters such as the ambient temperature and heat exchange coefficient. 4. **Adiabatic Condition**: - If cooling of certain parts of the ring forging is not required, these parts can be designated as adiabatic boundaries. - Heat transfer across adiabatic boundaries is zero, meaning the temperature gradient is zero across these boundaries. When setting boundary conditions, it is necessary to ensure that these conditions are consistent with the actual situation in order to obtain accurate simulation results. At the same time, it is also necessary to adjust and optimize the boundary conditions according to the actual situation during the simulation process to improve the accuracy and reliability of the simulation.

[0168] (7) Run the simulation:

[0169] Run the simulation in the simulation software to observe the temperature evolution of the ring forging. Record key data during the simulation, such as cooling rate and temperature distribution.

[0170] (8) Analysis of cooling rate:

[0171] The actual cooling rate of the ring forging is analyzed under the optimal spray parameters and walking speed.

[0172] Ensure that the actual cooling rate is within the range of the average cooling rate to avoid problems such as thermal stress, deformation or cracks caused by too fast or too slow cooling.

[0173] However, the amount of calculation required for data simulation is relatively large. To avoid such a large amount of calculation, in other embodiments of the present invention, the actual cooling rate can be directly obtained by testing. Specifically, the following method is performed:

[0174] At the initially set average walking speed, the ring forgings are cooled using a sprinkler head, and the actual temperature is continuously measured using infrared temperature measurement technology, and the actual cooling rate is calculated based on the change in actual temperature.

[0175] S206-6. If the actual cooling rate does not exceed the average cooling rate, setting the average walking speed as the base walking speed;

[0176] If the actual cooling rate does not exceed the average cooling rate, it means that the current walking speed and spray parameters are effective, and the average walking speed can be used as the basic walking speed.

[0177] S206-7. If the actual cooling rate exceeds the average cooling rate, the ratio of the average cooling rate to the actual cooling rate is calculated, and the product of the average walking speed and the ratio is set as the basic walking speed, and the new basic walking speed is verified and iterated until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

[0178] If the actual cooling rate exceeds the average cooling rate, this may cause excessive thermal stress or deformation within the ring forging. In this case, it is necessary to calculate the ratio of the average cooling rate to the actual cooling rate and multiply the average travel speed by this ratio to obtain a new base travel speed. This new speed will reduce the movement speed of the sprinkler head, thereby reducing the cooling rate.

[0179] Repeat the actual cooling rate test for the new base walking speed. If the actual cooling rate still exceeds the average cooling rate at the new speed, continue adjusting the walking speed and iterating until you find a base walking speed that meets the cooling requirements without causing excessive cooling.

[0180] In an embodiment of the present invention, based on step S3, a possible embodiment will be given below to illustrate its specific implementation scheme in a non-limiting manner.

[0181] Extract surface temperature data from a 3D model. This data is usually in the form of points, each with a corresponding temperature value.

[0182] Determine the temperature zones based on actual needs. For example, you can define them as low, medium, and high temperature zones. Set corresponding temperature thresholds for each zone. For example, the low temperature zone might be set below a specific temperature, the high temperature zone above another specific temperature, and the medium temperature zone somewhere in between.

[0183] An algorithm is used to traverse the surface of the 3D model and determine the temperature of each point. The temperature value of each point is compared with the set temperature threshold to determine the temperature zone to which it belongs. Each point is classified into the corresponding temperature zone.

[0184] Based on the classification results, color coding or marking is performed on the 3D model surface to visually demonstrate the division of temperature zones. Different colors or textures can be used to represent different temperature zones.

[0185] In an embodiment of the present invention, based on step S4, a possible embodiment will be given below to illustrate its specific implementation scheme in a non-limiting manner.

[0186] S401. Calculate the average temperature value of each temperature zone.

[0187] For each temperature zone that has been divided, calculate the average temperature of all points in the zone. This can be achieved by adding up the temperature values ​​of all points in the zone and then dividing by the number of points.

[0188] The average temperature value obtained will represent the overall temperature level of the temperature area.

[0189] S402. Normalize the average temperature value of each temperature zone to obtain a temperature coefficient.

[0190] In order to convert the average temperature value of each temperature zone into a comparable temperature coefficient, normalization is required.

[0191] The purpose of normalization is to convert the average temperature value of all temperature areas into a value between 0 and 1 for subsequent calculation and comparison.

[0192] The normalization formula can be expressed as: Temperature coefficient = (average temperature of the area - average temperature of the lowest temperature area) / (average temperature of the highest temperature area - average temperature of the lowest temperature area).

[0193] Apply the above normalization formula to calculate the temperature coefficient for each temperature region.

[0194] The temperature coefficient will reflect the relative position of each temperature region with respect to the overall temperature range.

[0195] S403. The product of the temperature coefficient and the basic walking speed is used as the walking speed in the corresponding temperature range.

[0196] Multiply the temperature coefficient of each temperature zone by the basic walking speed to obtain the walking speed in that temperature zone.

[0197] The formula can be expressed as: walking speed in this temperature range = basic walking speed * temperature coefficient.

[0198] In this way, the walking speed can be dynamically adjusted according to different temperature zones to adapt to temperature changes during the cooling process.

[0199] In some embodiments, the large ring forging ring rolling cooling control system may include multiple functional modules composed of computer program segments. The computer program of each program segment in the large ring forging ring rolling cooling control system may be stored in the memory of a computer device and executed by at least one processor to perform (see Figure 1 Description) The function of cooling control during the rolling of large ring forgings.

[0200] In this embodiment, the large ring forging ring rolling cooling control system can be divided into multiple functional modules according to the functions it performs, such as Figure 2 As shown. The functional modules of system 200 may include: a temperature scanning module 210, a parameter setting module 220, a temperature zoning module 230, and a travel control module 240. As used herein, a module refers to a series of computer program segments that can be executed by at least one processor and perform fixed functions, and is stored in a memory. In this embodiment, the functions of each module will be described in detail in subsequent embodiments.

[0201] A temperature scanning module, configured to scan the surface temperature of the large ring forging using infrared temperature measurement technology and assign the surface temperature to a pre-built three-dimensional model of the large ring forging;

[0202] Parameter setting module, used to pre-set the sprinkler head travel path and basic travel speed;

[0203] a temperature partitioning module, configured to divide the surface of the three-dimensional model into a plurality of temperature zones based on the surface temperature of the three-dimensional model;

[0204] The walking control module is used to generate a walking speed for a walking path within the temperature zone based on a temperature value of the temperature zone and the basic walking speed, wherein the walking speed is inversely proportional to the temperature value.

[0205] Optionally, as an embodiment of the present invention, the temperature scanning module includes:

[0206] a model building unit for building a three-dimensional model according to the actual size and shape of the large ring forging using a three-dimensional modeling tool;

[0207] The temperature scanning unit is used to aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data of each area on the ring forging surface;

[0208] The temperature assignment unit is used to import the temperature distribution data of various areas on the surface of the ring forging into the software used to process the three-dimensional model, and use the data processing function in the software to map and match the temperature data with various parts in the three-dimensional model.

[0209] Optionally, as an embodiment of the present invention, the parameter setting module includes:

[0210] A node division unit is used to divide the circumference of the ring forging into N equal nodes, each node representing a potential stop point of the sprinkler head on the ring forging;

[0211] A matrix creation unit is used to create an N×N distance matrix, where each element represents the distance between two nodes;

[0212] The area division unit is used to plan the spraying area for each sprinkler head if there are multiple sprinkler heads, and to create a sub-distance matrix for the nodes in the spraying area;

[0213] A path generation unit is used to select the portion of the path from the starting point to the last node as the travel path of the sprinkler head;

[0214] Path fine-tuning unit, used to fine-tune the path according to cooling requirements and sprinkler head performance;

[0215] The speed setting unit is used to set the basic walking speed based on the uniform heat dissipation requirement.

[0216] Optionally, as an embodiment of the present invention, the speed setting unit includes:

[0217] The parameter acquisition subunit is used to obtain the spray parameters of the sprinkler head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency;

[0218] A demand acquisition subunit is used to evaluate the cooling demand based on the material, size, initial temperature and final temperature to be achieved of the ring forging, wherein the cooling demand includes the maximum local cooling rate and the average cooling rate;

[0219] a time calculation subunit, configured to set an average cooling time based on the material, size, initial temperature, desired final temperature, and average cooling rate of the ring forging;

[0220] a speed calculation subunit, configured to calculate the length of the walking path, and calculate the quotient of the length and the average cooling time to obtain an average walking speed;

[0221] The cooling simulation subunit is used to simulate the actual cooling rate of the ring forging based on the average walking speed and the spray parameters of the spray head;

[0222] a basic setting subunit, configured to set the average walking speed as a basic walking speed if the actual cooling rate does not exceed the average cooling rate;

[0223] The iterative update subunit is used to calculate the ratio of the average cooling rate to the actual cooling rate if the actual cooling rate exceeds the average cooling rate, set the product of the average walking speed and the ratio as the basic walking speed, and verify the new basic walking speed iteratively until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

[0224] Optionally, as an embodiment of the present invention, the walking control module includes:

[0225] Temperature averaging unit, used to calculate the average temperature value of each temperature zone;

[0226] A coefficient calculation unit is used to normalize the average temperature value of each temperature zone to obtain a temperature coefficient;

[0227] The speed generating unit is configured to use the product of the temperature coefficient and the basic walking speed as the walking speed in the corresponding temperature range.

[0228] Figure 3 The large ring forging ring rolling cooling control method provided for the embodiment of the present application can be applied to equipment. Those skilled in the art will understand that the equipment structure involved in the embodiment of the present invention does not constitute a limitation on the equipment, and the equipment may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently. In the embodiment of the present invention, the equipment includes but is not limited to laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The equipment can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments of the present application described and / or required herein.

[0229] The device 300 may include a processor 310, a memory 320, and a communication unit 330. These components communicate via one or more buses. Those skilled in the art will appreciate that the server structure shown in the figure does not limit the present invention. The server structure may be a bus structure or a star structure, and may include more or fewer components than shown, or combine certain components, or arrange the components differently.

[0230] The memory 320 can be used to store execution instructions of the processor 310. The memory 320 can be implemented by any type of volatile or non-volatile memory device, or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk. When the execution instructions in the memory 320 are executed by the processor 310, the device 300 can perform some or all of the steps in the above-described method embodiments.

[0231] The processor 310 is the control center of the storage device, which uses various interfaces and lines to connect various parts of the entire electronic device. It executes various functions of the electronic device and / or processes data by running or executing software programs and / or modules stored in the memory 320, and calling data stored in the memory. The processor can be composed of an integrated circuit (IC), for example, it can be composed of a single packaged IC, or it can be composed of multiple packaged ICs with the same or different functions. For example, the processor 310 can only include a central processing unit (CPU). In an embodiment of the present invention, the CPU can be a single computing core or multiple computing cores.

[0232] The communication unit 330 is configured to establish a communication channel so that the storage device can communicate with other devices, receive user data sent by other devices, or send user data to other devices.

[0233] The present invention also provides a computer storage medium, wherein the computer storage medium may store a program that, when executed, may include some or all of the steps of each embodiment provided herein. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0234] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software and a necessary general-purpose hardware platform. Based on this understanding, the technical solutions in the embodiments of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, among other media capable of storing program code, and includes instructions for causing a computer device (which can be a personal computer, a server, or a second device, a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention.

[0235] In this specification, the same or similar parts between the various embodiments can be referred to each other. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method embodiment.

[0236] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For example, the division of the modules is merely a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of systems or modules, and can be electrical, mechanical or other forms.

[0237] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules may be selected to achieve the purpose of the present embodiment according to actual needs.

[0238] In addition, each functional module in each embodiment of the present invention may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0239] Although the present invention has been described in detail with reference to the accompanying drawings and in conjunction with preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, persons of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and such modifications or substitutions shall be within the scope of the present invention. Any changes or substitutions that can be easily conceived by persons skilled in the art within the technical scope disclosed in the present invention shall be within the scope of protection of the present invention.

Claims

1. A method for controlling the temperature drop during the rolling of large ring forgings, characterized in that: include: Scanning the surface temperature of the large ring forging using infrared temperature measurement technology and assigning the surface temperature to a pre-built three-dimensional model of the large ring forging; Pre-set the sprinkler head travel path and basic travel speed; Dividing the surface of the three-dimensional model into a plurality of temperature regions based on the surface temperature of the three-dimensional model; Based on the temperature value of the temperature zone and the basic walking speed, a walking speed is generated for the walking path within the temperature zone, and the walking speed is inversely proportional to the temperature value.

2. The method according to claim 1, characterized in that Scan the surface temperature of a large ring forging using infrared temperature measurement technology and assign the surface temperature to a pre-built 3D model of the large ring forging, including: Use 3D modeling tools to build 3D models based on the actual size and shape of large ring forgings; Aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data of each area on the ring forging surface; The temperature distribution data of each area on the surface of the ring forging is imported into the software used to process the three-dimensional model. The temperature data is mapped and matched with each part in the three-dimensional model using the data processing function in the software.

3. The method according to claim 1, characterized in that Pre-set sprinkler head travel path and basic travel speed, including: The circumference of the ring forging is equally divided into N nodes, each node represents a potential stop point of the sprinkler head on the ring forging; Create an N×N distance matrix, where each element represents the distance between two nodes; If there are multiple sprinkler heads, the sprinkler area is planned for each sprinkler head and a sub-distance matrix is ​​created for the nodes in the sprinkler area; The part of the path from the starting point to the last node is selected as the travel path of the sprinkler head; Fine-tune the path based on cooling needs and sprinkler head performance; Set the base walking speed based on the need for even cooling.

4. The method according to claim 3, characterized in that Set the basic walking speed based on the uniform heat dissipation requirements, including: Acquire spray parameters of the spray head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency; Evaluate cooling requirements based on the material, size, initial temperature, and desired final temperature of the ring forging, including the maximum local cooling rate and average cooling rate; Setting an average cooling time based on the material, size, initial temperature and desired final temperature of the ring forging, and the average cooling rate; Calculating the length of the walking path and calculating the quotient of the length and the average cooling time to obtain an average walking speed; The actual cooling rate of the ring forging is simulated based on the average walking speed and the spray parameters of the spray head; If the actual cooling rate does not exceed the average cooling rate, setting the average walking speed as the basic walking speed; If the actual cooling rate exceeds the average cooling rate, the ratio of the average cooling rate to the actual cooling rate is calculated, and the product of the average walking speed and the ratio is set as the basic walking speed, and the new basic walking speed is verified and iterated until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

5. The method according to claim 4, characterized in that Generating a walking speed for a walking path within the temperature zone based on a temperature value of the temperature zone and the basic walking speed, wherein the walking speed is inversely proportional to the temperature value, including: Calculate the average temperature value of each temperature zone; Normalize the average temperature value of each temperature zone to obtain the temperature coefficient; The product of the temperature coefficient and the basic walking speed is used as the walking speed in the corresponding temperature range.

6. A large ring forging ring rolling cooling control system, characterized in that: include: A temperature scanning module, configured to scan the surface temperature of the large ring forging using infrared temperature measurement technology and assign the surface temperature to a pre-built three-dimensional model of the large ring forging; Parameter setting module, used to pre-set the sprinkler head travel path and basic travel speed; a temperature partitioning module, configured to divide the surface of the three-dimensional model into a plurality of temperature zones based on the surface temperature of the three-dimensional model; The walking control module is used to generate a walking speed for a walking path within the temperature zone based on a temperature value of the temperature zone and the basic walking speed, wherein the walking speed is inversely proportional to the temperature value.

7. The system according to claim 6, characterized in that The temperature scanning module includes: a model building unit for building a three-dimensional model according to the actual size and shape of the large ring forging using a three-dimensional modeling tool; The temperature scanning unit is used to aim the infrared temperature measuring instrument at the large ring forging and scan the entire surface according to a predetermined scanning path or grid layout to obtain temperature distribution data of each area on the ring forging surface; The temperature assignment unit is used to import the temperature distribution data of various areas on the surface of the ring forging into the software used to process the three-dimensional model, and use the data processing function in the software to map and match the temperature data with various parts in the three-dimensional model.

8. The system according to claim 6, wherein: The parameter setting module includes: A node division unit is used to divide the circumference of the ring forging into N equal nodes, each node representing a potential stop point of the sprinkler head on the ring forging; A matrix creation unit is used to create an N×N distance matrix, where each element represents the distance between two nodes; The area division unit is used to plan the spraying area for each sprinkler head if there are multiple sprinkler heads, and to create a sub-distance matrix for the nodes in the spraying area; A path generation unit is used to select the portion of the path from the starting point to the last node as the travel path of the sprinkler head; Path fine-tuning unit, used to fine-tune the path according to cooling requirements and sprinkler head performance; The speed setting unit is used to set the basic walking speed based on the uniform heat dissipation requirement.

9. The system according to claim 8, characterized in that The speed setting unit includes: The parameter acquisition subunit is used to obtain the spray parameters of the sprinkler head, wherein the spray parameters include flow rate, spray range, spray intensity, and cooling efficiency; A demand acquisition subunit is used to evaluate the cooling demand based on the material, size, initial temperature and final temperature to be achieved of the ring forging, wherein the cooling demand includes the maximum local cooling rate and the average cooling rate; a time calculation subunit, configured to set an average cooling time based on the material, size, initial temperature, desired final temperature, and average cooling rate of the ring forging; a speed calculation subunit, configured to calculate the length of the walking path, and calculate the quotient of the length and the average cooling time to obtain an average walking speed; The cooling simulation subunit is used to simulate the actual cooling rate of the ring forging based on the average walking speed and the spray parameters of the spray head; a basic setting subunit, configured to set the average walking speed as a basic walking speed if the actual cooling rate does not exceed the average cooling rate; The iterative update subunit is used to calculate the ratio of the average cooling rate to the actual cooling rate if the actual cooling rate exceeds the average cooling rate, set the product of the average walking speed and the ratio as the basic walking speed, and verify the new basic walking speed iteratively until the actual cooling rate corresponding to the latest basic walking speed does not exceed the average cooling rate.

10. The system according to claim 9, characterized in that The walking control module includes: Temperature averaging unit, used to calculate the average temperature value of each temperature zone; A coefficient calculation unit is used to normalize the average temperature value of each temperature zone to obtain a temperature coefficient; The speed generating unit is configured to use the product of the temperature coefficient and the basic walking speed as the walking speed in the corresponding temperature range.

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