A method for preparing and optimizing a composite roll for strip steel based on multi-parameter coordinated regulation

Abstract

The application provides a strip steel composite roller preparation optimization method based on multi-parameter cooperative regulation, relates to the roller manufacturing technical field, and the method comprises the following steps: obtaining initial process parameters based on equipment structure drawings, online sensors and a thermophysical property database, and forming an initial process parameter vector; establishing a set of kinetic differential equations based on the initial process parameter vector, and obtaining kinetic state parameters; constructing a transient sliding accumulation model according to the metal liquid impact state parameter set, and obtaining a transient accumulation thickness distribution; constructing a liquid film evolution model based on the transient accumulation thickness distribution, and obtaining a wall thickness fluctuation value; establishing a dynamic angular velocity function, and inversely solving an optimal dynamic rotation speed curve in combination with the wall thickness fluctuation value; discretizing the optimal dynamic rotation speed curve into a time rotation speed control sequence, and performing real-time dynamic speed control of a centrifugal driving system based on the time rotation speed control sequence. The technical problems that the existing technology has a single centrifugal rotation speed control mode, insufficient process parameter optimization capability and poor composite layer forming stability are solved.

Description

Technical Field

[0001] This application relates to the field of roll manufacturing technology, and in particular to an optimized method for preparing plate and strip composite rolls based on multi-parameter coordinated adjustment. Background Technology

[0002] Composite rolls are widely used in metallurgical manufacturing fields such as hot rolling, cold rolling, and medium-thick plate rolling. The quality of their working layer directly affects the wear resistance, thermal fatigue performance, and surface quality of the strip during the rolling process. Centrifugal composite casting has become the mainstream process in composite roll manufacturing because it can achieve stable composite bonding between different metal layers under the action of a high-speed rotating centrifugal field, effectively improving the density and interfacial bonding strength of the composite layer. In actual production, the uniformity of molten metal spreading within the centrifugal mold, the stability of the liquid film formation, and the consistency of the composite layer thickness have a significant impact on the final service performance of the composite roll. Therefore, how to accurately control the dynamic spreading behavior of molten metal during centrifugal composite casting and improve the uniformity of the composite layer wall thickness has become an important research direction and engineering requirement in the field of composite roll manufacturing.

[0003] In existing centrifugal composite casting processes, centrifugal molds are typically controlled by a fixed rotation speed. Process parameters are primarily preset based on empirical databases or manual experimental results, lacking dynamic modeling and real-time analysis capabilities for the flight, impact, slippage, and film evolution of the molten metal. Because the molten metal is subjected to multiple factors in the initial casting stage, including centrifugal inertia, interfacial friction, and impact dissipation, its slippage distance and local accumulation state on the mold inner wall exhibit significant dynamic nonlinear characteristics. Existing technologies often struggle to effectively predict the instantaneous slippage behavior after molten metal impact and the evolution of film thickness, easily leading to problems such as axial wall thickness fluctuations, localized excessive accumulation, uneven interfacial bonding, and localized shrinkage in the composite roll working layer. Furthermore, most existing processes lack a dynamic speed reverse optimization mechanism based on wall thickness prediction results, failing to adjust the centrifugal speed in real-time according to the film spreading state. This results in insufficient process control capabilities, making it difficult to adapt to the high-stability manufacturing requirements of different alloy systems, roll sizes, and casting conditions.

[0004] In summary, existing technologies lack dynamic coupling analysis capabilities for the impact behavior, slip accumulation behavior, and liquid film evolution behavior of molten metal, making it difficult to achieve online prediction and dynamic control of composite roll wall thickness uniformity. Furthermore, they suffer from limitations such as a single centrifugal speed control method, insufficient process parameter optimization capabilities, and poor stability in composite layer formation. Therefore, a method to address these issues is urgently needed. Summary of the Invention

[0005] This disclosure provides an optimized method for the preparation of composite rolls for sheet and strip steel based on multi-parameter coordinated adjustment. This method addresses the technical problems in the prior art, such as the lack of dynamic coupling analysis capabilities for the impact behavior, slip accumulation behavior, and liquid film evolution behavior of molten metal, the difficulty in achieving online prediction and dynamic control of the uniformity of composite roll wall thickness, the single centrifugal speed control method, insufficient process parameter optimization capabilities, and poor stability of composite layer forming.

[0006] According to a first aspect of this disclosure, an optimized method for preparing composite rolls for sheet and strip steel based on multi-parameter synergistic adjustment is provided, comprising: Initial process parameters are obtained based on equipment structural drawings, online sensors, and thermal property databases to form an initial process parameter vector. The initial process parameters include centrifugal casting mold structural parameters, gating system operating parameters, and molten metal rheological parameters. A set of dynamic differential equations is established based on the initial process parameter vector to obtain dynamic state parameters, and then a set of metal liquid impact state parameters is constructed, including velocity state parameters and metal liquid impact angle. An instantaneous slip-stacking accumulation model is constructed based on the set of metal liquid impact state parameters to obtain the instantaneous accumulation thickness distribution; A liquid film evolution model was constructed based on the instantaneous accumulation thickness distribution to obtain the wall thickness fluctuation value; Establish a dynamic angular velocity function and inversely solve the optimal dynamic rotational speed curve by combining the wall thickness fluctuation value; The optimal dynamic speed curve is discretized into a time-speed control sequence, and the centrifugal drive system is dynamically controlled in real time based on the time-speed control sequence.

[0007] One or more technical solutions provided in this disclosure have at least the following technical effects or advantages: Initial process parameters are obtained based on equipment structural drawings, online sensors, and a thermophysical property database to form an initial process parameter vector, wherein the initial process parameters include centrifugal casting mold structural parameters, gating system operating parameters, and molten metal rheological parameters; a set of dynamic differential equations is established based on the initial process parameter vector to obtain dynamic state parameters, and then a set of molten metal impact state parameters is constructed, wherein the dynamic state parameters include velocity state parameters and molten metal impact angle; an instantaneous slip-stacking accumulation model is constructed based on the molten metal impact state parameter set to obtain the instantaneous accumulation thickness distribution; a liquid film evolution model is constructed based on the instantaneous accumulation thickness distribution to obtain the wall thickness fluctuation value; a dynamic angular velocity function is established, and the optimal dynamic speed curve is solved in reverse by combining the wall thickness fluctuation value; the optimal dynamic speed curve is discretized into a time-speed control sequence, and the centrifugal drive system is dynamically speed-regulated in real time based on the time-speed control sequence. This invention addresses the shortcomings of existing technologies, such as the lack of dynamic coupling analysis capabilities for the impact behavior, slip accumulation behavior, and liquid film evolution behavior of molten metal, which hinders online prediction and dynamic control of composite roll wall thickness uniformity. It also solves the technical problems of limited centrifugal speed control methods, insufficient process parameter optimization capabilities, and poor composite layer forming stability. The resulting technology achieves the technical effects of reducing working layer wall thickness fluctuations in composite rolls, improving composite layer thickness uniformity, enhancing interface forming stability, and improving the control precision of the centrifugal composite casting process.

[0008] The above description is merely an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in this disclosure 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 merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0010] Figure 1 This is a schematic flowchart illustrating an optimized method for preparing composite rolls for sheet and strip steel based on multi-parameter coordinated adjustment, provided in an embodiment of this application. Detailed Implementation

[0011] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0012] Example 1: This disclosure provides an optimized method for the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment, which is referred to below. Figure 1 The methods include: S1: Based on the equipment structure drawings, online sensors and thermal property database, the initial process parameters are obtained to form an initial process parameter vector. The initial process parameters include centrifugal casting mold structure parameters, gating system operating parameters and molten metal rheological parameters. Furthermore, step S1 also includes: By consulting the equipment structure drawings and combining them with on-site geometric measurement methods, the structural parameters of the centrifugal casting mold are obtained. The structural parameters of the centrifugal casting mold include the inner radius of the mold, the inner diameter of the gate, the vertical distance between the lower end face of the gate and the inner wall of the mold, and the angle between the gate axis and the radial plane of the mold. The operating parameters of the casting system are obtained from online sensors, including the initial target angular velocity, the volumetric flow rate of the molten metal, and the outflow velocity of the molten metal. Based on online sensors and a thermal property database, the rheological parameters of the molten metal are obtained, including the density of the molten metal, the dynamic viscosity of the molten metal, and the coefficient of sliding friction. The initial process parameters are summarized into three categories: centrifugal mold structural parameters, gating system operating parameters, and molten metal rheological parameters, forming an initial process parameter vector.

[0013] Specifically, before implementing the centrifugal composite preparation process of plate and strip steel composite rolls, it is necessary to collect, calibrate and initialize the initial process parameters that affect the centrifugal spreading behavior of molten metal, interfacial bonding behavior and subsequent solidification microstructure evolution behavior, so as to construct the initial process state space of the subsequent multi-parameter collaborative adjustment model.

[0014] This step categorizes all initial process parameters into three types based on their physical properties and acquisition methods: centrifugal mold structural parameters, gating system operating parameters, and molten metal rheological parameters. Centrifugal mold structural parameters are primarily derived from the structural dimensions of the centrifugal casting equipment and are mainly used to describe the spatial geometric relationship between the centrifugal mold and the gating structure. Gating system operating parameters are mainly derived from drive system setpoints and online sensor detection results and are mainly used to describe the molten metal movement and centrifugal drive state during casting. Molten metal rheological parameters are mainly calculated based on the real-time temperature of the molten metal, alloy composition, and a thermophysical property database, and are mainly used to describe the flow characteristics and interfacial friction characteristics of the molten metal at high temperatures. By uniformly acquiring these three types of parameters, a standardized description of the initial working conditions for the centrifugal composite preparation of composite rolls can be achieved, thus providing basic input data for subsequent analysis of molten metal flow stability, prediction of centrifugal spreading state, evaluation of interfacial bonding quality, and dynamic process optimization.

[0015] First, obtain the structural parameters of the centrifugal casting mold. These parameters mainly include the inner radius of the mold, the inner diameter of the gating gate, the vertical distance from the lower end face of the gating gate to the inner wall of the mold, and the angle between the gating axis and the radial plane of the mold. These parameters are all fixed structural geometric parameters of the centrifugal casting equipment, primarily obtained through a combination of equipment structural drawings and on-site geometric measurements.

[0016] The inner radius R of the mold is used to characterize the radial distance between the inner wall of the centrifugal mold and the axis of rotation. This parameter is usually determined directly by the design dimensions of the centrifugal mold. In actual implementation, it is preferable to use a laser rangefinder, inside micrometer, or coordinate measuring machine to measure the inner wall dimensions of the mold. Alternatively, the nominal dimension data in the centrifugal mold design drawings can be read directly.

[0017] The gate inner diameter *d* characterizes the effective flow diameter of the molten metal outlet channel. This parameter is primarily determined by the design dimensions of the gating mechanism, preferably obtained using vernier calipers, an inner diameter gauge, or gate machining drawings. Typical values ​​for the gate inner diameter range from 10 mm to 30 mm. Furthermore, the gate inner diameter can be used to calculate the gate cross-sectional area; the specific calculation formula is as follows: ; in, d represents the cross-sectional area of ​​the gate, and d represents the inner diameter of the gate. Representing pi, the gate cross-sectional area is used for subsequent pouring flow rate calculation and molten metal flow rate analysis.

[0018] The vertical distance *h* between the lower end face of the gating gate and the inner wall of the mold is used to characterize the length of the free jet section of the molten metal. This parameter is mainly obtained through on-site installation dimension measurement, preferably using a laser rangefinder, steel ruler, or installation positioning reference. The typical range of parameter *h* is 50 mm to 200 mm.

[0019] The angle α between the gating axis and the radial plane of the mold is used to characterize the spatial relationship between the pouring direction and the radial direction of the mold. This parameter is mainly determined by the gating installation angle, and is preferably measured using a digital angle meter, tilt sensor, or installation fixture positioning angle. The typical range of parameter α is 30° to 90°, where 90° corresponds to the vertical pouring condition.

[0020] After obtaining the structural parameters of the centrifugal casting mold, the operating parameters of the gating system are further obtained. These parameters mainly include the initial target angular velocity, the molten metal volumetric flow rate, and the molten metal outflow velocity. Unlike the aforementioned fixed structural parameters, the gating system operating parameters are dynamically changing parameters, and their values ​​change in real time during the casting process. Therefore, it is preferable to use online sensors for real-time detection.

[0021] Initial target angular velocity This parameter is used to characterize the target angular velocity when the centrifugal casting mold rotates around its central axis. This parameter is primarily determined by the preset rotational speed. Specifically, the target rotational speed *n* of the centrifugal motor is preset based on the target outer diameter of the composite roll, the target centrifugal clamping strength, the alloy density, and the historical process database. Subsequently, the PLC control system or frequency converter drive system outputs the corresponding rotational speed command, and the initial target angular velocity is further calculated. The specific conversion relationship is as follows: ; in, Represents the initial target angular velocity, and n represents the centrifugal casting rotation speed. This represents pi. The typical range of the initial target angular velocity is 50 rad / s to 150 rad / s, corresponding to a centrifugal speed of approximately 500 rpm to 1500 rpm.

[0022] molten metal outflow rate This is used to characterize the average flow velocity of molten metal as it leaves the gate outlet section. In this embodiment, it is preferable to install an electromagnetic flowmeter or a high-temperature mass flow sensor inside the gating channel to obtain the real-time volumetric flow rate Q of molten metal passing through the gate per unit time. Simultaneously, this is combined with the previously calculated gate cross-sectional area. Further calculations were performed to obtain the outflow velocity of the molten metal. The specific calculation formula is as follows: ; in, Q represents the outflow velocity of the molten metal, and Q represents the volumetric flow rate of the molten metal per unit time. This represents the cross-sectional area of ​​the gating gate.

[0023] Further, the rheological parameters of the molten metal are obtained. These parameters mainly include the density, dynamic viscosity, and coefficient of sliding friction of the molten metal. These parameters are not fixed structural parameters, but rather physical properties that vary with the temperature of the molten metal, alloy composition, and the surface condition of the mold. Therefore, it is preferable to obtain them using real-time temperature monitoring and correction based on a thermophysical property database.

[0024] Metal liquid density This is used to characterize the mass of a unit volume of molten metal. In this embodiment, it is preferable to place high-temperature thermocouples or infrared temperature sensors near the tundish, ladle, or gate to acquire the molten metal temperature T in real time. Subsequently, a pre-established database of molten metal thermophysical properties is retrieved according to the current alloy grade, and the molten metal density at the current moment is dynamically corrected based on the temperature-density correspondence. Metal liquid density The typical value range is 6500 kg / m³. 3 ~7800kg / m 3 .

[0025] The dynamic viscosity μ of molten metal is used to characterize the internal flow resistance of molten metal. In this embodiment, the current dynamic viscosity μ(T) of the molten metal is calculated by calling a thermophysical property database or a viscosity-temperature empirical model, based on real-time temperature T and alloy composition data. A temperature-viscosity mapping table corresponding to different alloy grades can be pre-established, and the calculation can be performed in real-time using a PLC or host computer system. The typical range of the dynamic viscosity μ of molten metal is 0.003 Pa·s to 0.01 Pa·s.

[0026] The sliding friction coefficient *f* is used to characterize the interfacial frictional resistance during the spreading of molten metal along the inner wall of the mold. Since this parameter is difficult to measure directly online, this embodiment preferably uses a method combining offline experimental calibration and correction based on a historical process database. Specifically, the sliding distance of molten metal under different coating materials and pouring temperatures can be measured through small-sample centrifugal spreading experiments, and the corresponding sliding friction coefficient *f* can be obtained by combining this with inverse dynamics fitting. Furthermore, the parameter *f* can be empirically corrected by incorporating actual wall thickness uniformity results from a historical production database. The typical range of the sliding friction coefficient *f* is 0.2 to 0.5.

[0027] After completing the above parameter acquisition, all initial process parameters are uniformly input into the composite roll manufacturing process status database to construct the initial process parameter vector. .

[0028] S2: Based on the initial process parameter vector, establish a set of dynamic differential equations to obtain dynamic state parameters, and then construct a set of metal liquid impact state parameters, including velocity state parameters and metal liquid impact angle; Furthermore, step S2 also includes: The continuous molten metal flow is discretized into multiple molten metal micro-elements. The volume of the molten metal is determined by the molten metal density, the molten metal volumetric flow rate, and the discrete time step. The mass of the molten metal micro-elements is then calculated based on the molten metal volume. A centrifugal casting rotating coordinate system is established with the axis of rotation of the centrifugal mold center as the axial coordinate z direction, the direction perpendicular to the central rotation axis and pointing towards the inner wall of the mold as the radial coordinate r direction, the direction of rotation around the central rotation axis as the circumferential angular coordinate θ direction, and the center position of the gate outlet as the origin of the coordinate system. Based on Newton's second law in a rotating reference frame, a set of dynamic differential equations for the molten metal element is established. This set includes equations for radial motion, circumferential motion, and axial motion. The specific expressions for these three equations are as follows: Radial motion equations: ; in, Represents radial acceleration, where r represents the current radial position of the liquid metal element. Represents circumferential angular velocity. The angular velocity of the centrifugal casting is represented by m, and the mass of the molten metal element is represented by m. Represents the correction force for fluid flow disturbance at the end of flight; Equation of circumferential motion: ; Where r represents the current radial position of the liquid metal element. Represents circumferential angular acceleration. Represents radial velocity. Represents circumferential angular velocity. Represents the angular velocity of the centrifugal casting mold. Represents the angular acceleration of the centrifugal casting mold. The inertial term represents the motion at the circumferential angle. Represents the Coriolis coupling term. This represents the tangential inertial term caused by angular acceleration. Axial motion equation: ; in, λ represents axial acceleration, and g represents gravitational acceleration. The dynamic differential equations are solved by numerical integration using the fourth-order Runge-Kutta numerical integration method to obtain the velocity state parameters at the moment of impact. The velocity state parameters include radial impact velocity, circumferential relative velocity and axial impact velocity. The impact angle of the molten metal is calculated based on the velocity state parameters. The specific calculation formula is as follows: ; in, Represents the impact angle of molten metal. Represents radial impact velocity. Represents the axial impact velocity. Represents the circumferential relative velocity; The impact time, velocity state parameters, and impact angle of all molten metal elements are uniformly summarized to construct a set of molten metal impact state parameters.

[0029] Specifically, after completing the initial process parameter acquisition in step S1, this step is used to establish a set of dynamic differential equations for the molten metal in the centrifugal rotating mold. By solving the motion trajectory, velocity evolution behavior, and impact state of the molten metal from the gate outlet to the inner wall of the mold, the dynamic state parameters of the molten metal when it impacts the inner wall of the mold are obtained, thus providing dynamic input for subsequent analysis of liquid film spreading behavior, slip accumulation behavior, and adjustment of composite layer uniformity.

[0030] First, the continuous molten metal flow is discretized into multiple molten metal elements. These elements are not actual independent particles, but rather discrete fluid units used for numerical calculations. Each molten metal element is considered an independent moving particle, and its mass is determined by the molten metal density obtained in step S1. The flow rate Q of the molten metal and the discrete time step are jointly determined. Specifically, the volume of molten metal flowing out within a single time step is set as: ; in, The value represents the volume of molten metal flowing out within a single time step, and Q represents the molten metal flow rate obtained in step S1. This represents the time step of numerical integration.

[0031] Furthermore, the mass of a single molten metal element can be obtained from the volume of the molten metal. The specific calculation formula is as follows: ; Where m represents the mass of a single liquid metal element, in kg. This represents the density of the molten metal obtained in step S1. This represents the volume of molten metal flowing out within a single time step. Therefore, the mass of the molten metal element is not an arbitrarily set constant, but is calculated jointly from the initial process parameters in step S1.

[0032] It should be noted that although the continuous molten metal flow is discretized into multiple molten metal elements for motion analysis, it is not a case of solving for each and every actual molten metal particle. Instead, a representative element modeling approach under time-discrete conditions is used. Specifically, at each time step... Within this time period, the local molten metal flowing through the gate is regarded as an equivalent representative molten metal micro-element, and its motion trajectory model is established based on the process parameters corresponding to the current moment.

[0033] Subsequently, a rotating coordinate system for the centrifugal casting mold is established. This embodiment employs a cylindrical rotating coordinate system, rather than a traditional rectangular coordinate system. This coordinate system is established with the central rotation axis of the centrifugal casting mold as the reference center. Specifically, the axial direction of the central rotation axis is used as the axial coordinate z-direction, the direction perpendicular to the central rotation axis and pointing towards the inner wall of the mold is used as the radial coordinate r-direction, and the direction of rotation around the central rotation axis is used as the circumferential angular coordinate θ-direction, thus forming a three-dimensional rotating cylindrical coordinate system of "radial-circumferential-axial".

[0034] The origin of the entire coordinate system is set at the center of the gate outlet, which is the position when the molten metal leaves the gate, as the starting point of the motion. Since the origin is located at the center of the gate outlet, the initial position coordinates satisfy r(0)=0, θ(0)=0, z(0)=0, where r(0) represents the initial radial position of the molten metal element, θ(0) represents the initial circumferential angular position, and z(0) represents the initial axial position.

[0035] Furthermore, the initial flight distance of the molten metal element from the inner wall of the mold is determined based on the inner radius of the mold and the inner diameter of the gating. Since the gating outlet is located inside the mold, the initial radial distance between the center of the gating outlet and the inner wall of the mold can be expressed as: ; in, The initial radial flight distance represents the distance the molten metal element travels from the gate outlet to the inner wall of the mold, where R represents the inner radius of the mold and d represents the inner diameter of the gate. The purpose of this initial radial flight distance is to determine the termination condition of the molten metal element's radial motion, which is the condition that, during subsequent numerical integration, the molten metal element reaches a certain radial displacement. At that time, it is assumed that the molten metal impacts and reaches the inner wall of the mold. This is because it usually satisfies... Therefore, in engineering calculations, further approximations are taken. This approximate value can simplify the subsequent flight trajectory calculation process.

[0036] Furthermore, the position variable of the liquid metal element in the rotating coordinate system is defined as: ; Where r(t) represents the radial position of the liquid metal element at time t. This represents the circumferential angular position of the liquid metal element at time t. The three position variables represent the axial position of the liquid metal element at time t. These three position variables are all variables to be solved, not directly obtained data, but need to be solved through subsequent dynamic differential equations.

[0037] Based on the first derivative of the position variable with respect to time, the velocity variable of the molten metal element in the rotating coordinate system can be defined, and the specific expressions are as follows: Radial: Zhou Xiang: Axial direction: in, Represents radial velocity. Represents circumferential linear velocity. Representing axial velocity, the above three types of velocity variables are all obtained by differentiating the position variables with respect to time, and belong to the state variables that need to be updated in real time during the solution of dynamic differential equations.

[0038] Subsequently, based on the angle α between the gate axis and the radial plane of the mold obtained in step S1, and the molten metal outflow velocity... The initial velocity conditions of the molten metal element are established. The outflow velocity of the molten metal is decomposed along the radial and axial directions to obtain the initial radial and axial velocities. The specific calculation formulas are as follows: ; ; in, The initial radial velocity represents the micro-element of the liquid metal. Represents the initial axial velocity. The flow velocity of the molten metal obtained in step S1 is represented by α, and the angle between the gate axis and the radial plane of the mold obtained in step S1 is represented by α. Therefore, the process parameters in step S1, after velocity decomposition, are further transformed into the initial conditions of the kinetic equations for this step.

[0039] Since the molten metal is not fully coupled with the circumferential rotation of the mold when it just leaves the gate, the initial circumferential relative velocity is: This indicates that the molten metal does not initially possess circumferential motion relative to the rotating coordinate system.

[0040] Subsequently, a set of dynamic differential equations for the molten metal element is established. Since the centrifugal casting mold is constantly rotating at high speed, the molten metal element is subjected to the combined effects of centrifugal inertial force, Coriolis inertial force, and gravity during its motion. Based on Newton's second law in a rotating reference frame, a set of dynamic differential equations for the molten metal element can be established. The unknowns in the equations mainly include the radial position r(t), the circumferential angular position θ(t), the axial position z(t), and the corresponding velocity variables.

[0041] First, the radial motion equation is established, with the following expression: ; in, Represents radial acceleration, where r represents the current radial position of the liquid metal element. Represents circumferential angular velocity. The angular velocity of the centrifugal casting is represented by m, and the mass of the molten metal element is represented by m. This represents the correction force for fluid flow disturbance at the end of flight.

[0042] It should be noted that the end-of-flight flow disturbance correction force is used to characterize the additional radial disturbance effect generated by the molten metal element near the inner wall of the mold due to flow turbulence, local airflow disturbance, free liquid column breakage, and unstable jet behavior. Under ideal stable pouring conditions, since the free jet process of the molten metal is relatively short and the flow continuity is good, it is preferable to take [the appropriate value]. This means ignoring the additional disturbance at the end of the flight path. When the pouring speed is high, the gate inner diameter is large, or there is obvious unsteady jet phenomenon in the liquid flow, this correction term can be further estimated through experimental calibration or fluid dynamics numerical simulation methods. Preferably, the liquid flow disturbance correction force at the end of the flight path can be expressed as: ; in, This represents the fluid flow disturbance correction factor, with a typical value range of 0 to 0.05; in this case, it is set to 0.03. Represents the density of liquid metal. Represents the outflow velocity of molten metal. This represents the cross-sectional area of ​​the gating gate.

[0043] The equations for circumferential motion are then established, with the following specific expression: ; Where r represents the current radial position of the liquid metal element. Represents circumferential angular acceleration. Represents radial velocity. Represents circumferential angular velocity. Represents the angular velocity of the centrifugal casting mold. Represents the angular acceleration of the centrifugal casting mold. The inertial term represents the motion at the circumferential angle. Represents the Coriolis coupling term. This represents the tangential inertia term caused by the rotational angular acceleration.

[0044] The further equation of axial motion is expressed as follows: ; in, λ represents axial acceleration, and g represents gravitational acceleration, with a typical value of 9.81 m / s². 2 This equation describes the axial motion behavior of a liquid metal element under gravity.

[0045] Furthermore, since the centrifugal casting mold undergoes a rotational speed establishment process in the initial stage of casting, the angular velocity of the centrifugal casting mold is theoretically a time-dependent variable. However, since the flight time of a single molten metal element from the gate outlet to the inner wall of the mold is typically less than 0.1 s, much smaller than the acceleration establishment time of the entire centrifugal system, the angular velocity of the centrifugal casting mold can be approximated as constant during the solution process of a single molten metal element's flight, that is, the angular velocity of the centrifugal casting mold remains constant at any given time. ,in The initial target angular velocity is obtained in step S1. It should be emphasized that the above setting only applies to the initial dynamic modeling stage in step S2. To reduce the computational complexity of single trajectory prediction, a constant centrifugal casting angular velocity approximation can be preferred. In the subsequent dynamic rotational speed optimization process in step S5, the centrifugal casting angular velocity will be expressed as a time-dependent function. Therefore, the representative molten metal element released at different time steps will correspond to different centrifugal casting angular velocities. Different centrifugal casting angular velocities will cause differences in the motion trajectory, impact velocity, impact angle, and subsequent sliding distance of the representative molten metal element, thus forming a continuously changing liquid film accumulation distribution along the axial direction of the roll.

[0046] Subsequently, the aforementioned dynamic differential equations are solved by numerical integration. In this embodiment, the fourth-order Runge-Kutta numerical integration method is preferably used to perform discrete integration calculations on the motion trajectory of the molten metal element, and the numerical integration time step is set to [value missing]. The time step is used to control the increment of position and velocity in each iteration of the numerical integration process; that is, the velocity and position variables at the current moment are recalculated after each time step. A smaller time step can improve the accuracy of trajectory integration under high-speed rotation conditions and reduce numerical oscillation errors.

[0047] During the integration process, the system continuously updates the position variables [r(t), θ(t), z(t)] and velocity variables of the molten metal element. , , When the radial position is full. When the molten metal element impacts and reaches the inner wall of the mold, the corresponding moment is defined as the impact moment. .

[0048] Further extraction of velocity state parameters at the moment of impact, including radial impact velocity, circumferential relative velocity, and axial impact velocity.

[0049] Specifically, the radial impact velocity is defined as: ; in, Represents the radial impact velocity at the moment of impact. This represents the radial velocity of the molten metal element at the moment of impact, obtained by numerical integration of the dynamic differential equations.

[0050] Circumferential relative velocity is defined as Since the inner wall of the centrifugal casting mold rotates synchronously around the central axis at an angular velocity, the actual circumferential sliding velocity of the molten metal element relative to the inner wall of the mold is only related to the additional circumferential motion component of the molten metal itself. The overall synchronous rotational velocity terms in the rotating coordinate system can cancel each other out. Therefore, further simplification yields: ; in, R represents the circumferential relative velocity of the molten metal with respect to the inner wall of the rotating mold, and R represents the inner radius of the mold. This represents the circumferential angular velocity of the molten metal element at the moment of impact, obtained by numerical integration of the dynamic differential equations.

[0051] The axial impact velocity is defined as: ; in, This represents the axial impact velocity at the moment of impact. This represents the axial velocity of the molten metal element at the moment of impact, obtained by numerical integration of the dynamic differential equations.

[0052] After obtaining the above three velocity state parameters, the metal molten impact angle β is further calculated to characterize the angular relationship between the metal molten impact direction and the tangential direction of the casting mold. The specific calculation formula is as follows: ; in, Represents the impact angle of molten metal. Represents radial impact velocity. Represents the axial impact velocity. Represents the circumferential relative velocity. Impact angle. This is used to evaluate the coupling relationship between the tangential spreading ability and the normal impact ability when molten metal impacts the inner wall of the mold. When the impact angle is small, it indicates that the molten metal spreads mainly in the tangential direction, which is conducive to the formation of a stable liquid film. When the impact angle is large, it indicates that the normal impact component is large, which can easily cause liquid splashing, gas entrainment and interface disturbance.

[0053] Finally, the impact times corresponding to all the liquid metal elements are determined. Radial impact velocity Circumferential relative velocity Axial impact velocity and impact angle A unified set of metal liquid impact state parameters is constructed by summarizing and combining these parameters.

[0054] S3: Construct an instantaneous slip-stacking accumulation model based on the metal liquid impact state parameter set to obtain the instantaneous accumulation thickness distribution; Furthermore, step S3 also includes: Define the normal restoration coefficient Tangential velocity retention coefficient It is 0.7; Based on the tangential velocity retention coefficient and combined with the velocity state parameters, the tangential sliding velocity of the molten metal element relative to the inner wall of the mold is calculated. The specific calculation formula is as follows: ; in, This represents the tangential sliding velocity of the molten metal element along the inner wall of the mold after impact. Represents the tangential velocity retention coefficient. Represents the circumferential relative velocity. Represents the axial impact velocity; A tangential deceleration model is established for the sliding process of a molten metal element along the inner wall of the mold, and the tangential deceleration is obtained. The specific calculation formula is as follows: ; in, The tangential deceleration represents the sliding velocity of the molten metal element as it slides along the inner wall of the mold, and f represents the coefficient of sliding friction. R represents the centrifugal casting angular velocity, and R represents the inner radius of the casting mold. Based on the uniformly decelerated motion relationship, the sliding duration of the molten metal element is obtained, and the specific calculation formula is as follows: ; in, This represents the duration of the sliding motion of the molten metal element along the inner wall of the mold. Represents tangential slip velocity. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. Based on the uniformly decelerated motion relationship, the total sliding distance of the molten metal element along the inner wall of the mold is calculated using the following formula: ; Where S represents the total sliding distance along the inner wall of the mold after the impact of the molten metal element. Represents tangential slip velocity. Represents the duration of the slip. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. The effective sliding distance in the axial direction is extracted using the following formula: ; in, S represents the effective sliding distance of the molten metal element along the axial direction of the roll, and S represents the total sliding distance. Represents the axial impact velocity. Represents tangential slip velocity; Setting the casting process time interval to 0.01s, the mass of molten metal impacting the inner wall of the mold within each time interval can be expressed as: ; in, This represents the mass of molten metal deposited onto the inner wall of the mold per unit time step. Q represents the density of the molten metal, and Q represents the volumetric flow rate of the molten metal. This indicates that the casting process takes a long time compared to the walking process; The Gaussian distribution function is used to describe the local accumulation morphology of molten metal along the axial direction. By convolving and superimposing the local accumulation contributions formed within each time interval, the instantaneous accumulation thickness distribution function along the axial direction of the roll at any given time is obtained. The specific expression is as follows: ; in, This represents the instantaneous build-up thickness at the axial position z. This represents the scaling factor for the stacking thickness. Q represents the density of the molten metal, and Q represents the volumetric flow rate of the molten metal. Represents tangential slip velocity. Represents the stacking center offset coefficient. The z-axis represents the Gaussian diffusion width coefficient, and z represents the axial position. This represents the effective sliding distance of the molten metal element along the axial direction of the roll.

[0055] Specifically, after completing the dynamic analysis of the molten metal micro-element in step S2, this step further establishes an instantaneous slip accumulation model after the molten metal impacts, which is used to describe the tangential slip behavior along the mold surface after the molten metal impacts the inner wall of the mold and the instantaneous accumulation thickness distribution formed by continuous molten metal deposition.

[0056] Since a stable and uniform liquid film has not yet formed in the centrifugal composite roll during the initial stage of casting, the molten metal does not immediately solidify after impacting the inner wall of the mold. Instead, it slides a certain distance along the inner wall of the mold under the combined influence of centrifugal inertia and interfacial friction. This sliding behavior directly affects the initial thickness distribution of the liquid film, local segregation behavior, and the uniformity of the subsequent solidification structure. Therefore, this step analyzes the velocity dissipation behavior after impact, the sliding deceleration behavior, and the local accumulation behavior near the sliding endpoint, and finally establishes an instantaneous sliding accumulation model of the molten metal.

[0057] First, the momentum change process after the impact of the molten metal element is analyzed. When the molten metal element impacts the inner wall of the mold, its normal velocity component will be rapidly dissipated due to plastic collision, while the tangential velocity component will be partially retained and drive the molten metal to continue sliding along the inner wall of the mold.

[0058] In this embodiment, the radial direction is regarded as the normal collision direction, and a normal restitution coefficient is defined. Used to characterize the velocity retention capability after a normal collision. Since high-temperature molten metal impacting the inner wall of the mold typically exhibits significant plastic dissipation characteristics, it is preferable to select... This indicates that the radial velocity of the molten metal element is completely dissipated after impact, meaning it no longer bounces radially after impact.

[0059] Further define the tangential velocity retention coefficient This parameter is used to characterize the ratio of circumferential velocity to axial velocity retained after impact. The tangential velocity retention coefficient is mainly affected by the dynamic viscosity of the molten metal, the state of the casting coating, and the impact temperature. Its typical value range is 0.6 to 0.9, and it is preferably set to 0.7 here. A larger tangential velocity retention coefficient indicates that the molten metal can retain more tangential motion capability after impact, thus forming a longer spreading and sliding distance; a smaller tangential velocity retention coefficient indicates stronger impact dissipation and a greater likelihood of forming local accumulation.

[0060] After obtaining the velocity retention relationship after the impact, the tangential sliding velocity of the molten metal element relative to the inner wall of the mold is further calculated. The specific calculation formula is as follows: ; in, This represents the tangential sliding velocity of the molten metal element along the inner wall of the mold after impact. Represents the tangential velocity retention coefficient. This represents the circumferential relative velocity obtained in step S2. This represents the axial impact velocity obtained in step S2. The physical meaning of this formula is that the circumferential relative velocity and the axial impact velocity obtained in step S2 are both proportional after the impact. The velocity is retained, and then the actual tangential slip velocity after impact is obtained through vector synthesis. Therefore, These are the core input parameters for calculating the subsequent slip distance in this step.

[0061] Since the molten metal element will gradually decelerate under the action of interfacial sliding friction after adhering to the inner wall of the mold, a tangential deceleration model can be further established during the sliding process of the molten metal element along the inner wall of the mold. Combining the centrifugal pressing state and the characteristics of interfacial sliding friction, the tangential deceleration experienced by the molten metal element can be obtained. The specific calculation formula is as follows: ; in, The tangential deceleration represents the sliding velocity of the molten metal element as it slides along the inner wall of the mold, and f represents the coefficient of sliding friction. R represents the angular velocity of the centrifugal casting mold, and R represents the inner radius of the casting mold.

[0062] Furthermore, under the action of sliding friction, the molten metal element gradually decelerates along the inner wall of the mold until it stops. Based on the relationship of uniformly decelerated motion, the sliding duration of the molten metal element can be obtained, and the specific calculation formula is as follows: ; in, This represents the duration of the sliding motion of the molten metal element along the inner wall of the mold. Represents tangential slip velocity. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. The formula indicates that the greater the tangential sliding velocity, the longer the molten metal slides; conversely, the greater the centrifugal angular velocity ω or the greater the coefficient of sliding friction f, the faster the molten metal decelerates.

[0063] Based on the uniformly decelerated motion relationship, the total sliding distance of the molten metal element along the inner wall of the mold is calculated. The specific calculation formula is as follows: ; Where S represents the total sliding distance along the inner wall of the mold after the impact of the molten metal element. Represents tangential slip velocity. Represents the duration of the slip. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. The first term in the formula represents the displacement caused by the initial sliding velocity, and the second term represents the displacement correction caused by frictional deceleration. The total sliding distance characterizes the overall spreading ability of the molten metal along the inner wall of the mold after impact; the larger the value, the greater the migration range of the molten metal on the inner wall of the mold. The liquid film uniformity analysis in subsequent steps will be calculated directly based on this sliding distance.

[0064] Since the tangential slip velocity includes both circumferential and axial velocity components, the actual slip path of the molten metal is a spatial vector path. To analyze the material diffusion behavior of the liquid film along the axial direction of the roll, it is necessary to further extract the effective slip distance in the axial direction. The specific calculation formula is as follows: ; in, S represents the effective sliding distance of the molten metal element along the axial direction of the roll, and S represents the total sliding distance. Represents the axial impact velocity. This represents the tangential slip velocity. Since subsequent liquid film thickness fluctuations are mainly analyzed along the axial direction of the roll, the effective slip distance in the axial direction must be extracted.

[0065] Furthermore, in the initial stage of casting, a large number of continuous molten metal elements continuously impact the inner wall of the mold and slide and deposit along the mold surface, thereby forming a transient liquid film accumulation layer. To describe this dynamic accumulation process, this embodiment discretizes the entire casting process according to a fixed time step. Preferably, the time step of the casting process can be taken as... The step size at this point is different from the step size in step S2. It is reset and its function is to divide the continuous casting process into multiple discrete time periods and calculate the contribution of local accumulation formed in each time period.

[0066] The mass of molten metal impacting the inner wall of the mold at each time interval can be expressed as: ; in, This represents the mass of molten metal deposited onto the inner wall of the mold per unit time step. Q represents the density of the molten metal obtained in step S1, and Q represents the volumetric flow rate of the molten metal. This represents the time elapsed between the casting process and the settling time. The mass of the molten metal describes the total amount of material participating in the deposition process per unit time.

[0067] Since the molten metal gradually decelerates and undergoes localized deposition near the slip endpoint, this embodiment uses a Gaussian distribution function to describe the local accumulation morphology of the molten metal along the axial direction. The center of the Gaussian distribution corresponds to the main deposition location of the molten metal, while the width of the Gaussian distribution describes the diffusion range of the molten metal deposition. Based on numerous centrifugal casting experiments, it has been found that the actual deposition width of the molten metal is typically about one-third of the slip distance; therefore, in this embodiment, one-third of the slip distance is preferably used as the Gaussian distribution width.

[0068] Furthermore, by convolving and superimposing the local accumulation contributions formed within each time interval, the instantaneous accumulation thickness distribution function along the axial direction of the roll at any given time can be obtained, specifically expressed as: ; in, This represents the instantaneous build-up thickness at the axial position z. This represents the scaling factor for the stacking thickness. Q represents the density of the molten metal, and Q represents the volumetric flow rate of the molten metal. Represents tangential slip velocity. Represents the stacking center offset coefficient. represents the Gaussian diffusion width coefficient, and z represents the axial position, used to characterize the local position along the length of the roll. This represents the effective sliding distance of the molten metal element along the axial direction of the roll. Among these, the three empirical coefficients are preferably selected as follows: The aforementioned empirical coefficients were all obtained through a combination of extensive centrifugal composite casting experiments and numerical simulation results. Among them, Used to correct the deviation between the theoretical deposition thickness and the actual liquid film thickness; Used to correct the offset position of the main liquid film accumulation center relative to the theoretical slip endpoint; This parameter is used to correct the actual diffusion width of the liquid film. The above parameters can be dynamically corrected and updated based on different roll sizes, alloy systems, casting coating materials, and casting process conditions.

[0069] Finally, through the above instantaneous slip stacking model, the instantaneous stacking thickness distribution of molten metal along the axial direction of the roll can be obtained in real time, thus providing basic state input for subsequent liquid film uniformity analysis, composite layer thickness adjustment and multi-parameter collaborative optimization control.

[0070] S4: Construct a liquid film evolution model based on the instantaneous stacking thickness distribution to obtain wall thickness fluctuation values; Furthermore, step S4 also includes: The molten metal film is considered as a thin viscous film flowing along the axial direction of the roll. The evolution behavior of the film is described by the quasi-one-dimensional form of the shallow water wave equation. The local thickness of the film is defined as h(z,t), and the average axial velocity of the film is defined as u(z,t), where z represents the axial spatial coordinate of the roll and t represents the evolution time of the film. The equation for the conservation of liquid film mass is established, and its specific expression is as follows: ; Among them, symbols Represents the partial differential operator. Represents the rate of change of liquid film thickness. This represents the mass flow rate gradient of the liquid film along the axial direction. Further, the equation for the conservation of axial momentum of the liquid film is established, and its specific expression is as follows: ; in, This represents the rate of change of the average axial velocity of the liquid film with respect to time. Represents the inertial convection term during liquid film flow. Represents the equivalent centrifugal acceleration. The equivalent pressure driving force formed by the liquid film thickness gradient is represented by f, which represents the coefficient of sliding friction. This represents the frictional dissipation term between the liquid film and the mold interface; Set the initial conditions for the liquid film, and set the initial thickness condition of the liquid film to... ,in, Let be the instantaneous deposition thickness distribution function, and the initial axial velocity of the liquid film be set to be... ; The finite difference method is used to discretize and solve the above set of liquid film evolution control equations to obtain the final stable liquid film thickness distribution; The deviation of the final stable liquid film thickness distribution from the theoretical average thickness is defined as the final wall thickness fluctuation function, and its specific expression is as follows: ; in, This represents the final wall thickness fluctuation value at the axial position z. The final stable liquid film thickness at the end of the liquid film evolution at axial position z represents the thickness of the liquid film. This represents the average thickness of the liquid film.

[0071] Specifically, after completing the instantaneous accumulation thickness distribution analysis in step S3, this step further establishes a liquid film evolution model from the instantaneous accumulation state to the final composite roll wall thickness fluctuation state. This model is used to describe the secondary spreading behavior of the molten metal under the continuous action of the centrifugal field, the liquid film redistribution behavior, and the wall thickness fluctuation formation process after final solidification, thereby realizing the dynamic prediction of the axial wall thickness uniformity of the composite roll.

[0072] Since the instantaneous accumulation thickness distribution function obtained in step S3 can only characterize the local accumulation state at the initial stage of molten metal impact, in actual centrifugal composite casting, the molten metal will continue to slowly spread and flow axially under the action of centrifugal inertial driving force after impact and accumulation. Therefore, the initial accumulation morphology will not be completely retained, but will gradually become smoother in the subsequent liquid film flow process. However, due to the existence of viscous resistance of molten metal, interfacial frictional resistance, and solidification viscosity effect, local thickness disturbances cannot be completely eliminated, and will eventually remain in the composite roll working layer in the form of residual wall thickness fluctuations. Therefore, this step establishes a liquid film evolution model to dynamically solve the propagation and attenuation behavior of liquid film thickness disturbances.

[0073] In this embodiment, the molten metal film is considered as a thin, viscous liquid film flowing along the axial direction of the roll, and its evolution behavior is described using a quasi-one-dimensional form of the shallow water wave equation. The local thickness of the liquid film is defined as h(z,t), and the average axial velocity of the liquid film is defined as u(z,t). Specifically, h(z,t) represents the local thickness of the liquid film at axial position z and time t, characterizing the dynamic change of the film thickness over time; u(z,t) represents the average axial velocity of the liquid film at the corresponding position, characterizing the dynamic flow capability of the liquid film in the axial direction; z represents the axial spatial coordinate of the roll; and t represents the liquid film evolution time. These two state variables are the core variables to be solved in this step.

[0074] Further, the liquid film mass conservation equation is established, and its specific expression is as follows: ; In this context, the symbol ∂ represents the partial differential operator, used to indicate the local rate of change of a variable with respect to an independent variable. Represents the rate of change of liquid film thickness, which physically means the speed at which the local thickness of the liquid film changes per unit time. The mass flow gradient of the liquid film along the axial direction represents the local mass migration capacity caused by the liquid film flow. When the liquid film thickness is high in a local area, due to the thickness gradient within the liquid film, the liquid film will flow to adjacent areas with lower thickness under the influence of centrifugal driving force, thus forming a liquid film redistribution behavior. This equation essentially describes the coupling relationship between the time-varying liquid film thickness and axial mass transport, and ensures the conservation of the total mass of the liquid film during its evolution.

[0075] Further, the equation for the conservation of axial momentum of the liquid film is established, and its specific expression is as follows: ; in, This represents the rate of change of the axial average velocity of the liquid film with respect to time; its physical meaning is the transient change behavior of the liquid film velocity. This represents the inertial convection term in the liquid film flow process, used to characterize the velocity self-coupling effect under high-speed liquid film flow conditions. Represents the equivalent centrifugal acceleration. The equivalent pressure driving force formed by the liquid film thickness gradient is represented by f, which represents the coefficient of sliding friction. The term representing frictional dissipation between the liquid film and the mold interface describes the velocity decay behavior caused by interfacial friction during liquid film flow. Essentially, this equation describes the flow equilibrium of the liquid film under the combined influence of centrifugal driving force and frictional resistance.

[0076] It should be noted that the equivalent centrifugal acceleration The calculation formula is: ; in, Represents the equivalent centrifugal acceleration under centrifugal rotation conditions. R represents the angular velocity of the centrifugal casting mold, and R represents the inner radius of the casting mold. The equivalent centrifugal acceleration is used to characterize the indirect driving force of the radial centrifugal pressure field on the axial liquid film spreading behavior. When the centrifugal speed increases, the radial compaction inside the liquid film increases, thereby enhancing the spreading stability and flow driving force of the liquid film in the axial direction.

[0077] After establishing the aforementioned set of governing equations for liquid film evolution, the initial conditions for the liquid film are further defined. Since step S3 has already obtained the instantaneous accumulation thickness distribution formed during the initial stage of casting, the initial thickness condition of the liquid film is set to... ,in, This is the instantaneous accumulation thickness distribution function output in step S3. The purpose of this step is to directly use the instantaneous accumulation state obtained in step S3 as the initial input state for the liquid film evolution model, thereby achieving continuous data transfer between steps S3 and S4. Simultaneously, since the molten metal has not yet formed a stable axial flow at the initial moment, the initial axial flow velocity of the liquid film is set to... It is believed that there is no obvious overall axial flow in the initial state of the liquid film, and only local thickness disturbance exists.

[0078] Furthermore, to achieve a numerical solution for the liquid film evolution behavior, this embodiment preferably employs the finite difference method to discretize and solve the aforementioned liquid film evolution control equations. Specifically, the solution logic of this step is as follows: First, the axial spatial region of the roll is discretized, dividing the continuous space into multiple discrete spatial grid nodes; then, the liquid film evolution time is discretized, dividing the continuous time into multiple time steps; subsequently, within each time step, the local thickness h of the liquid film is updated based on the liquid film mass conservation equation, and the axial average velocity u of the liquid film is updated based on the liquid film axial momentum conservation equation, and this process is continuously iterated to finally obtain the complete evolution process of the local thickness and the axial average velocity of the liquid film over time.

[0079] Specifically, the axial length of the roll is discretized into multiple spatial grid nodes, as expressed in the following expression: ; in, This represents the axial position coordinates corresponding to the i-th spatial grid node. represents the axial spatial discrete step size, and i represents the spatial grid number. The purpose of this step is to divide the continuous liquid film spatial region into a finite number of discrete computational nodes, thereby facilitating subsequent numerical solutions using the finite difference method.

[0080] At the same time, time is discretized into multiple time steps, as specifically expressed by: ; in, This represents the calculation time corresponding to the nth time step. The time integration step size is represented by , and n represents the time step number. The purpose of time discretization is to divide the continuous liquid film evolution process into multiple finite time periods and gradually update the liquid film state within each time step.

[0081] Within each time step, the local thickness of the liquid film is iteratively updated using a finite difference scheme. Average flow velocity along the liquid film axis ,in, The local thickness of the liquid film at the nth time step and the i-th spatial grid node; This represents the average axial velocity of the liquid film at the corresponding location. Specifically, within each time step, the liquid film thickness distribution and velocity distribution from the previous time step are first retrieved, and the change in liquid film thickness is calculated using the liquid film mass conservation equation. Then, based on the updated liquid film thickness gradient, the change in liquid film velocity is calculated using the liquid film axial momentum conservation equation. After that, the iteration continues into the next time step. Through continuous time-step iterations, the propagation, spread, and decay process of liquid film disturbances over time can be obtained.

[0082] Furthermore, since the molten metal typically stabilizes within 1-2 seconds after centrifugal spreading, the liquid film evolution termination time is set in this embodiment. The time range is derived from the statistical results of a large number of centrifugal composite casting experiments. The experiments found that under high-speed centrifugation conditions, the liquid film usually enters a slow change phase after about 1 second, and basically completes the axial spreading and liquid film redistribution process within about 2 seconds.

[0083] The liquid film spreading process can be considered basically completed when any of the following conditions are met: First, the rate of change of liquid film thickness within multiple consecutive time steps satisfies ,in, In this embodiment, the threshold for determining liquid film stability is... Preferred selection This threshold is derived from the numerical stability analysis of the centrifuged liquid film. When the rate of change of the liquid film thickness is lower than this threshold, it can be considered that the liquid film thickness has essentially stopped changing significantly.

[0084] Second, the axial average flow velocity of the liquid film satisfies ,in, In this embodiment, the liquid film flow termination threshold is used. Preferred selection This threshold is derived from the calibration results of the liquid film flow termination experiment. When the axial flow velocity of the liquid film is lower than this threshold, it can be considered that the liquid film as a whole has basically stopped axial flow.

[0085] After the liquid film spreading process is completed, the final stable liquid film thickness distribution obtained is considered as the stable liquid film morphology before solidification. Furthermore, its deviation from the theoretical average thickness is defined as the final wall thickness fluctuation function, specifically expressed as: ; in, This represents the final wall thickness fluctuation value at the axial position z. The final stable liquid film thickness at the end of the liquid film evolution at axial position z represents the thickness of the liquid film. The average thickness of the liquid film can be obtained by spatially averaging the final stable liquid film thickness over the entire axial region. Its physical meaning is the theoretical average wall thickness under ideal homogeneous conditions.

[0086] S5: Establish a dynamic angular velocity function and combine it with the wall thickness fluctuation value to solve for the optimal dynamic rotational speed curve in reverse; Furthermore, step S5 also includes: The dynamic angular velocity function is constructed using a piecewise linear function, and its specific expression is as follows: ; in, The angular velocity represents the dynamic velocity of the centrifugal mold throughout the entire casting process, and t represents time. The initial target angular velocity is represented by 'a', and 'a' represents the rate of change of angular velocity in the first stage. This represents the end time of the first phase. 'b' represents the inflection point angular velocity at the end of the first stage, and 'b' represents the rate of change of angular velocity in the second stage. This represents the end time of the second phase. This represents the target stable angular velocity for the subsequent stable rotation phase; Taking the final wall thickness fluctuation uniformity as the core optimization objective, and comprehensively considering the mechanical impact constraints of the equipment and the final centrifugal stability constraints, a dynamic rotational speed optimization objective function is established, the specific expression of which is: ; Where J represents the dynamic speed optimization objective function. Represents the dynamic angular velocity function The final wall thickness fluctuation function obtained under the action, where L represents the axial length of the composite roll. The penalty weighting coefficient for changes in angular velocity. This represents the penalty weighting coefficient for deviation from the final stable rotational speed; An intelligent optimization algorithm is used to iteratively search for the parameters to be optimized, thereby obtaining the optimal dynamic control variables. .

[0087] Generate the optimal dynamic speed curve based on the optimal dynamic control variables. .

[0088] Specifically, after completing the liquid film evolution analysis and wall thickness fluctuation prediction in step S4, this step further establishes a dynamic angular velocity function to solve the optimal centrifugal speed adjustment strategy that minimizes the wall thickness fluctuation of the composite roll, thereby realizing active dynamic control of the centrifugal composite casting process.

[0089] Since the fundamental source of wall thickness fluctuation in composite rolls lies in the non-uniform slippage and accumulation behavior of molten metal after impact during the initial stage of casting, and the calculation formulas for total slippage distance and effective slippage distance established in step S3 show a significant negative correlation between the effective slippage distance and the square of the centrifugal casting angular velocity, the dynamic change of centrifugal speed directly affects the molten metal spreading range, liquid film redistribution capability, and the uniformity of the final wall thickness. Especially in the short timeframe after casting begins, before a stable liquid film structure has formed, the speed change during this stage has the most significant impact on subsequent wall thickness fluctuations. Therefore, this step aims to minimize wall thickness fluctuation by establishing a dynamic angular velocity function and inversely solving for the optimal dynamic speed curve.

[0090] First, based on the relationship between the effective sliding distance and the square of the centrifugal casting angular velocity in step S3, it can be seen that the centrifugal casting angular velocity is mainly determined by... The rotational speed changes during the initial 0–0.5 s stage of casting are most sensitive to the uniformity of the liquid film. Therefore, this embodiment preferably uses a piecewise linear function to construct the dynamic angular velocity function, the specific expression of which is: ; in, The angular velocity represents the dynamic velocity of the centrifugal mold throughout the entire casting process, and t represents time. This represents the initial target angular velocity set in step S1, where 'a' represents the rate of change of angular velocity in the first stage. This represents the end time of the first phase. 'b' represents the inflection point angular velocity at the end of the first stage, and 'b' represents the rate of change of angular velocity in the second stage. This represents the end time of the second phase. This represents the target stable angular velocity for the subsequent stable rotation phase.

[0091] Wherein, parameter a, Both parameter a and parameter b are control variables to be optimized in this step. Their initial search range is determined by the allowable speed range of the equipment, the response capability of the drive motor, and the historical process database, and is not the initial process parameter directly obtained in step S1. Specifically, the typical search range of parameter a can be set to... ,parameter A typical search range can be set to 0.7. ~1.1 The typical search range for parameter b can be set to When a < 0, it indicates that active deceleration control is performed in the initial stage of casting; when a > 0, it indicates that acceleration control is performed.

[0092] Furthermore, to ensure that the dynamic angular velocity function remains continuous at the segmented connection points, this embodiment preferably satisfies the following conditions: as well as Two constraints, and the time parameter in the first stage must satisfy... The time parameters for the second stage must meet the following requirements. The aforementioned time range mainly corresponds to the liquid film formation and initial spreading stages. Implementing dynamic speed regulation within this time window can effectively alter the slippage behavior of the molten metal.

[0093] Subsequently, a dynamic rotational speed optimization objective function is established. In this embodiment, the final wall thickness fluctuation uniformity is taken as the core optimization objective, while comprehensively considering the mechanical impact constraints of the equipment and the final centrifugal stability constraints, thereby establishing the dynamic rotational speed optimization objective function, the specific expression of which is: ; Where J represents the dynamic speed optimization objective function. Represents the dynamic angular velocity function The final wall thickness fluctuation function obtained under the action, where L represents the axial length of the composite roll. The penalty weighting coefficient for changes in angular velocity. The penalty weighting coefficient representing the deviation from the final stable speed is preferably... A value of 0.05 to 0.2 is acceptable; here, a value of 0.1 is used to limit mechanical shock caused by rapid changes in rotational speed. The value can be between 0.1 and 0.5, and is set to 0.2 here to ensure that the centrifugal compaction capability meets the requirements for composite layer forming in the later stage. The above weighting coefficients are preferably obtained through a combination of statistical analysis of historical process data and equipment stability experiments.

[0094] The physical meaning of each component term in the objective function described above will be further explained in detail. The value used to evaluate wall thickness fluctuation is that the smaller the value, the higher the axial wall thickness uniformity of the roll. Ideally, it should meet the following conditions. That is, the axial wall thickness of the rolls remains basically uniform. This is used to limit the mechanical shock caused by excessive changes in angular velocity. When the centrifugal speed changes too quickly, it can easily lead to vibration of the drive system, bearing impact, and unstable fluid flow. Therefore, an angular velocity change penalty term is introduced to improve the smoothness of the control curve. This is used to constrain the deviation between the final stable speed and the target process speed, thereby ensuring that sufficient centrifugal clamping capacity can still be maintained in the later stages of centrifugal composite casting.

[0095] Furthermore, to obtain the optimal dynamic speed curve, this embodiment employs an intelligent optimization algorithm to iteratively search the parameters to be optimized. Preferably, a Bayesian optimization algorithm or a particle swarm optimization algorithm is used. The Bayesian optimization algorithm is primarily suitable for operating conditions with high computational costs and strong nonlinearity of the objective function. It predicts the potential optimal region in the parameter space using a Gaussian process surrogate model, thereby reducing the number of invalid searches. The particle swarm optimization algorithm is suitable for industrial control scenarios with high real-time requirements, achieving rapid convergence through multi-particle collaborative search. The appropriate optimization strategy can be selected based on the controller's computing power in the industrial setting.

[0096] Specifically, the optimization process includes the following steps: First, initialize multiple candidate sets of control variables to be optimized. ,in, Represents the vector of the i-th control variable to be optimized. Represents the rate of change of angular velocity in the first stage of the i-th group. This represents the angular velocity at the corresponding inflection point. This represents the rate of change of the angular velocity in the second stage.

[0097] Subsequently, for each group of candidate control variables, a corresponding dynamic angular velocity function is constructed, and the dynamic differential equations in step S2, the instantaneous slip-stacking model in step S3, and the liquid film evolution model in step S4 are called sequentially to obtain the corresponding final wall thickness fluctuation function. .

[0098] The corresponding dynamic speed optimization objective function is further calculated, and then the candidate control variables for the next round are updated according to the optimization algorithm, continuing the iterative search. The optimization algorithm automatically compares the objective function values ​​J corresponding to all control variables. i When the objective function value corresponding to a certain set of control variables is minimized, it indicates that the final wall thickness fluctuation corresponding to that set of control variables is minimal and the liquid film uniformity is optimal. Therefore, this set of control variables is determined as the current optimal dynamic control variables. As the iteration continues, the objective function value will gradually converge, eventually obtaining the global optimum or near-global optimum solution.

[0099] Because this invention employs a simplified engineering model, the calculation time for a single complete wall thickness prediction is typically less than 0.1 seconds. In industrial control computing platforms, convergence can usually be achieved after approximately 20 iterations. Ultimately, the optimal dynamic control variables are obtained. .

[0100] Furthermore, the corresponding optimal dynamic speed curve is generated based on the obtained optimal dynamic control variables. The optimal dynamic speed curve will serve as the real-time control input for the subsequent centrifugal drive system.

[0101] Furthermore, considering that some optimization results may exceed the actual operating capabilities of the equipment, this embodiment further establishes an anomaly constraint correction mechanism. When the optimization results satisfy... or If the current optimization result is not executable, then it is determined that the current optimization result is not executable. This represents the maximum permissible safe centrifugal mold angular velocity for centrifugal casting equipment. Its value is primarily determined by the mold's mechanical strength, the main bearing's load-bearing capacity, the drive motor power, and the equipment's dynamic balance limits. Preferably, The speed can be selected from 150 rad / s to 250 rad / s, and can be set to 200 rad / s here. In this case, the embodiment employs a heuristic suboptimal correction strategy. Preferably, the centrifugal casting angular velocity is kept constant, i.e. At the same time, by adjusting the gate angle By altering the impact direction of the molten metal, the slip distance and accumulation behavior can be indirectly adjusted. Alternatively, instantaneous pulse deceleration control can be applied during the initial stage of casting. For example, an instantaneous deceleration control of approximately 10% can be performed within a 0.1s time window, followed by a return to the target rotational speed, thereby reducing the initial impact slip intensity of the molten metal.

[0102] S6: Discretize the optimal dynamic speed curve into a time-speed control sequence, and perform real-time dynamic speed regulation control on the centrifugal drive system based on the time-speed control sequence.

[0103] Furthermore, step S6 also includes: The optimal dynamic speed curve is discretely sampled according to a fixed sampling period to generate a time-speed control sequence: ; in, Represents the time-speed control sequence. Represents the i-th sampling time. This represents the target angular velocity at the corresponding moment; The generated time-speed control sequence is uploaded to the programmable logic controller of the centrifugal casting equipment and used as the real-time control input of the frequency conversion drive system.

[0104] Specifically, this step further implements the obtained optimal dynamic speed curve in engineering and combines it with real-time process control to realize the dynamic execution and real-time monitoring of the centrifugal casting process of composite rolls, thereby achieving stable operation of the dynamic speed regulation strategy in actual centrifugal composite casting equipment.

[0105] The core objective of this step is to obtain the optimal dynamic speed curve from step S5. The control commands are converted into real-time control instructions that can be executed by the centrifugal casting equipment, and the stable control of the uniformity of the composite roll wall thickness is achieved through the coordinated operation between the centrifugal drive system and the casting system.

[0106] First, the dynamic speed command generation process is executed. This is based on the optimal dynamic speed curve obtained in step S5. Since the values ​​are continuous time values, while industrial centrifugal casting control systems typically use discrete sampling for speed control, it is necessary to discretize the optimal dynamic speed curve over time.

[0107] In this embodiment, the optimal dynamic speed curve is discretely sampled according to a fixed sampling period to generate a time-speed control sequence: ; in, Represents the time-speed control sequence. Represents the i-th sampling time. This represents the target angular velocity at the corresponding moment.

[0108] It should be noted that the fixed sampling period is set to The control system updates the target angular velocity of the centrifugal casting mold every 0.02 seconds. This sampling period is mainly determined based on the industrial PLC control refresh cycle, the frequency regulation response capability of the inverter, and the mechanical inertia of the centrifugal drive system. If the sampling period is too large, it may lead to an increase in the discrete error of the dynamic speed curve; if the sampling period is too small, it will increase the PLC's computational load and cause frequent speed regulation oscillations. Therefore, this embodiment preferably uses 0.02 seconds as the dynamic speed regulation control period. Furthermore, each sampling time satisfies... The corresponding target angular velocity satisfies .

[0109] Subsequently, the generated time-speed control sequence is uploaded to the programmable logic controller (PLC) of the centrifugal casting equipment and used as the real-time control input for the variable frequency drive system. Based on the discretized time-speed control sequence, the PLC automatically calls the corresponding target angular velocity data at the corresponding sampling time, thereby realizing the real-time execution of the dynamic speed regulation curve.

[0110] Furthermore, before the formal casting begins, the centrifugal mold is first controlled to maintain the initial target angular velocity set in step S1. Initiate rotation. When the real-time detected angular velocity meets... At that point, the centrifuge system was determined to have entered a stable operating state. Represents the actual angular velocity detected in real time. This represents the speed stability judgment threshold. Preferably, the speed stability judgment threshold can be set to 1~3 rad / s. This threshold is mainly determined based on the steady-state speed fluctuation range of the drive system and the actual centrifugal casting stability requirements. When the deviation between the actual speed and the target speed is less than this threshold, the centrifugal system can be considered to have entered a stable rotation state, which can meet the subsequent dynamic speed regulation control requirements.

[0111] Furthermore, when the casting system receives the casting start signal, the PLC begins to perform real-time speed control on the variable frequency drive motor according to the preset time and speed control sequence.

[0112] In this embodiment, the centrifugal drive system preferably employs a variable frequency speed control motor combined with a high-speed encoder feedback control structure. The PLC determines the target angular velocity based on the current moment. The inverter output frequency is adjusted in real time, thereby changing the rotation speed of the centrifugal casting mold.

[0113] While the centrifugal speed is dynamically adjusted, the casting system operates at a preset constant flow rate. Molten metal is continuously poured into the centrifugal mold. Maintaining a constant flow rate reduces the impact of additional flow fluctuations on the liquid film accumulation state, thereby ensuring the stability of dynamic speed control.

[0114] Furthermore, after casting is completed, the injection of molten metal is stopped, but the centrifugal mold continues to maintain the final stable angular velocity obtained in step S5. Continuous rotation. The duration of continuous rotation satisfies... ,in, This represents the duration of rotation during subsequent pressure holding. This represents the time required for the outer working layer of the composite roll to completely solidify. Continuous centrifugal rotation can maintain a stable centrifugal clamping force during the solidification stage, thereby reducing the risk of liquid film collapse, local shrinkage, and interfacial delamination. Among these parameters... It can be estimated based on the thickness of the composite layer, the thermal properties of the alloy, and the actual cooling conditions, and is preferably determined by a thermal equilibrium solidification model or a historical process database.

[0115] Finally, through the above-mentioned dynamic speed control execution process, the optimal dynamic speed regulation strategy obtained in step S5 can be stably applied to the actual centrifugal composite casting process, thereby realizing active dynamic control over the liquid film spreading behavior, wall thickness uniformity, and interface forming stability of the composite roll working layer.

[0116] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0117] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An optimized method for preparing composite rolls for sheet and strip steel based on multi-parameter coordinated adjustment, characterized in that, The method includes: Initial process parameters are obtained based on equipment structural drawings, online sensors, and thermal property databases to form an initial process parameter vector. The initial process parameters include centrifugal casting mold structural parameters, gating system operating parameters, and molten metal rheological parameters. A set of dynamic differential equations is established based on the initial process parameter vector to obtain dynamic state parameters, and then a set of metal liquid impact state parameters is constructed, including velocity state parameters and metal liquid impact angle. An instantaneous slip-stacking accumulation model is constructed based on the set of metal liquid impact state parameters to obtain the instantaneous accumulation thickness distribution; A liquid film evolution model was constructed based on the instantaneous accumulation thickness distribution to obtain the wall thickness fluctuation value; Establish a dynamic angular velocity function and inversely solve the optimal dynamic rotational speed curve by combining the wall thickness fluctuation value; The optimal dynamic speed curve is discretized into a time-speed control sequence, and the centrifugal drive system is dynamically controlled in real time based on the time-speed control sequence.

2. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, Form the initial process parameter vector, including: By consulting the equipment structure drawings and combining them with on-site geometric measurement methods, the structural parameters of the centrifugal casting mold are obtained. The structural parameters of the centrifugal casting mold include the inner radius of the mold, the inner diameter of the gate, the vertical distance between the lower end face of the gate and the inner wall of the mold, and the angle between the gate axis and the radial plane of the mold. The operating parameters of the casting system are obtained from online sensors, including the initial target angular velocity, the volumetric flow rate of the molten metal, and the outflow velocity of the molten metal. Based on online sensors and a thermal property database, the rheological parameters of the molten metal are obtained, including the density of the molten metal, the dynamic viscosity of the molten metal, and the coefficient of sliding friction. The initial process parameters are summarized into three categories: centrifugal mold structural parameters, gating system operating parameters, and molten metal rheological parameters, forming an initial process parameter vector.

3. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, A set of dynamic differential equations is established based on the initial process parameter vector to obtain dynamic state parameters, and then a set of metal liquid impact state parameters is constructed, including: The continuous molten metal flow is discretized into multiple molten metal micro-elements. The volume of the molten metal is determined by the molten metal density, the molten metal volumetric flow rate, and the discrete time step. The mass of the molten metal micro-elements is then calculated based on the molten metal volume. A centrifugal casting rotating coordinate system is established with the axis of rotation of the centrifugal mold center as the axial coordinate z direction, the direction perpendicular to the central rotation axis and pointing towards the inner wall of the mold as the radial coordinate r direction, the direction of rotation around the central rotation axis as the circumferential angular coordinate θ direction, and the center position of the gate outlet as the origin of the coordinate system. Based on Newton's second law in a rotating reference frame, a set of dynamic differential equations for the molten metal element is established. This set includes equations for radial motion, circumferential motion, and axial motion. The specific expressions for these three equations are as follows: Radial motion equations: ; in, Represents radial acceleration, where r represents the current radial position of the liquid metal element. Represents circumferential angular velocity. The angular velocity of the centrifugal casting is represented by m, and the mass of the molten metal element is represented by m. Represents the correction force for fluid flow disturbance at the end of flight; Equation of circumferential motion: ; Where r represents the current radial position of the liquid metal element. Represents circumferential angular acceleration. Represents radial velocity. Represents circumferential angular velocity. Represents the angular velocity of the centrifugal casting mold. Represents the angular acceleration of the centrifugal casting mold. The inertial term represents the motion at the circumferential angle. Represents the Coriolis coupling term. This represents the tangential inertial term caused by angular acceleration. Axial motion equation: ; in, λ represents axial acceleration, and g represents gravitational acceleration. The dynamic differential equations are solved by numerical integration using the fourth-order Runge-Kutta numerical integration method to obtain the velocity state parameters at the moment of impact. The velocity state parameters include radial impact velocity, circumferential relative velocity and axial impact velocity. The impact angle of the molten metal is calculated based on the velocity state parameters. The specific calculation formula is as follows: ; in, Represents the impact angle of molten metal. Represents radial impact velocity. Represents the axial impact velocity. Represents the circumferential relative velocity; The impact time, velocity state parameters, and impact angle of all molten metal elements are uniformly summarized to construct a set of molten metal impact state parameters.

4. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, Obtain the instantaneous stacking thickness distribution, including: Define the normal restoration coefficient Tangential velocity retention coefficient It is 0.7; Based on the tangential velocity retention coefficient and combined with the velocity state parameters, the tangential sliding velocity of the molten metal element relative to the inner wall of the mold is calculated. The specific calculation formula is as follows: ； in, This represents the tangential sliding velocity of the molten metal element along the inner wall of the mold after impact. Represents the tangential velocity retention coefficient. Represents the circumferential relative velocity. Represents the axial impact velocity; A tangential deceleration model is established for the sliding process of a molten metal element along the inner wall of the mold, and the tangential deceleration is obtained. The specific calculation formula is as follows: ； in, The tangential deceleration represents the sliding velocity of the molten metal element as it slides along the inner wall of the mold, and f represents the coefficient of sliding friction. R represents the centrifugal casting angular velocity, and R represents the inner radius of the casting mold. Based on the uniformly decelerated motion relationship, the sliding duration of the molten metal element is obtained, and the specific calculation formula is as follows: ； in, This represents the duration of the sliding motion of the molten metal element along the inner wall of the mold. Represents tangential slip velocity. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. Based on the uniformly decelerated motion relationship, the total sliding distance of the molten metal element along the inner wall of the mold is calculated using the following formula: ； Where S represents the total sliding distance along the inner wall of the mold after the impact of the molten metal element. Represents tangential slip velocity. Represents the duration of the slip. This represents the tangential deceleration of a molten metal element as it slides along the inner wall of the mold. The effective sliding distance in the axial direction is extracted using the following formula: ； in, S represents the effective sliding distance of the molten metal element along the axial direction of the roll, and S represents the total sliding distance. Represents the axial impact velocity. Represents tangential slip velocity; Setting the casting process time interval to 0.01s, the mass of molten metal impacting the inner wall of the mold within each time interval can be expressed as: ； in, This represents the mass of molten metal deposited onto the inner wall of the mold per unit time step. Q represents the density of the molten metal, and Q represents the volumetric flow rate of the molten metal. This indicates that the casting process takes a long time compared to the walking process; The Gaussian distribution function is used to describe the local accumulation morphology of molten metal along the axial direction. By convolving and superimposing the local accumulation contributions formed within each time interval, the instantaneous accumulation thickness distribution function along the axial direction of the roll at any given time is obtained. The specific expression is as follows: ； in, This represents the instantaneous build-up thickness at the axial position z. This represents the scaling factor for the stacking thickness. Q represents the density of the molten metal, and Q represents the volumetric flow rate of the molten metal. Represents tangential slip velocity. Represents the stacking center offset coefficient. The z-axis represents the Gaussian diffusion width coefficient, and z represents the axial position. This represents the effective sliding distance of the molten metal element along the axial direction of the roll.

5. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, Obtaining wall thickness fluctuation values ​​includes: The molten metal film is considered as a thin viscous film flowing along the axial direction of the roll. The evolution behavior of the film is described by the quasi-one-dimensional form of the shallow water wave equation. The local thickness of the film is defined as h(z,t), and the average axial velocity of the film is defined as u(z,t), where z represents the axial spatial coordinate of the roll and t represents the evolution time of the film. The equation for the conservation of liquid film mass is established, and its specific expression is as follows: ； Here, the symbol ∂ represents the partial differential operator. Represents the rate of change of liquid film thickness. This represents the mass flow rate gradient of the liquid film along the axial direction. Further, the equation for the conservation of axial momentum of the liquid film is established, and its specific expression is as follows: ； in, This represents the rate of change of the average axial velocity of the liquid film with respect to time. Represents the inertial convection term during liquid film flow. Represents the equivalent centrifugal acceleration. The equivalent pressure driving force formed by the liquid film thickness gradient is represented by f, which represents the coefficient of sliding friction. This represents the frictional dissipation term between the liquid film and the mold interface; Set the initial conditions for the liquid film, and set the initial thickness condition of the liquid film to... ,in, Let be the instantaneous deposition thickness distribution function, and the initial axial velocity of the liquid film be set to be... ; The finite difference method is used to discretize and solve the above set of liquid film evolution control equations to obtain the final stable liquid film thickness distribution; The deviation of the final stable liquid film thickness distribution from the theoretical average thickness is defined as the final wall thickness fluctuation function, and its specific expression is as follows: ； in, This represents the final wall thickness fluctuation value at the axial position z. The final stable liquid film thickness at the end of the liquid film evolution at axial position z represents the thickness of the liquid film. This represents the average thickness of the liquid film.

6. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, Establish a dynamic angular velocity function and, in conjunction with wall thickness fluctuation values, inversely solve for the optimal dynamic rotational speed curve, including: The dynamic angular velocity function is constructed using a piecewise linear function, and its specific expression is as follows: ； in, The angular velocity represents the dynamic velocity of the centrifugal mold throughout the entire casting process, and t represents time. The initial target angular velocity is represented by 'a', and 'a' represents the rate of change of angular velocity in the first stage. This represents the end time of the first phase. 'b' represents the inflection point angular velocity at the end of the first stage, and 'b' represents the rate of change of angular velocity in the second stage. This represents the end time of the second phase. This represents the target stable angular velocity for the subsequent stable rotation phase; Taking the final wall thickness fluctuation uniformity as the core optimization objective, and comprehensively considering the mechanical impact constraints of the equipment and the final centrifugal stability constraints, a dynamic rotational speed optimization objective function is established, the specific expression of which is: ； Where J represents the dynamic speed optimization objective function. Represents the dynamic angular velocity function The final wall thickness fluctuation function obtained under the action, where L represents the axial length of the composite roll. The penalty weighting coefficient for changes in angular velocity. This represents the penalty weighting coefficient for deviation from the final stable rotational speed; An intelligent optimization algorithm is used to iteratively search for the parameters to be optimized, thereby obtaining the optimal dynamic control variables. . Generate the optimal dynamic speed curve based on the optimal dynamic control variables. .

7. The method for optimizing the preparation of composite rolls for strip steel based on multi-parameter coordinated adjustment as described in claim 1, characterized in that, The optimal dynamic speed curve is discretized into a time-speed control sequence, including: The optimal dynamic speed curve is discretely sampled according to a fixed sampling period to generate a time-speed control sequence: ； in, Represents the time-speed control sequence. Represents the i-th sampling time. This represents the target angular velocity at the corresponding moment; The generated time-speed control sequence is uploaded to the programmable logic controller of the centrifugal casting equipment and used as the real-time control input of the frequency conversion drive system.

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