Programmed temperature control system for diaphragm printing process

Abstract

The invention belongs to the technical field of automatic control, and discloses a programmed temperature control system for a diaphragm printing process. The method comprises the following steps: acquiring ink layer surface temperature, substrate contact temperature and environment gas phase temperature data through a multi-source temperature acquisition module, and identifying solvent evaporation refrigeration characteristics; the volatilization dynamics modeling module constructs a dynamic phase change model according to the refrigeration characteristics and the steam partial pressure gradient; the temperature difference compensation module determines a real-time compensation amount based on latent heat absorption space-time distribution characteristics; the crust state recognition module judges a surface crust forming moment; the segmented control module divides the heating process into a pre-volatilization section, a transition section and a curing section and configures a differential control strategy; the residual solvent prediction module predicts internal solvent distribution; the dynamic regulation and control module adjusts the heating rate in real time to avoid the solvent breaking-through defect. The temperature control precision is improved, surface defects such as pinholes and bubbles are effectively eliminated, and the stability and consistency of product quality are ensured.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and more specifically, to a programmed temperature control system for film printing processes. Background Technology

[0002] The varistor diaphragm is the core sensing element of an automotive pressure sensor. It is typically manufactured by printing varistor paste onto a flexible diaphragm on a ceramic or silicon substrate, followed by a precise high-temperature sintering process to form a Wheatstone bridge structure. Precise control of the sintering temperature profile is crucial in this manufacturing process, especially in the sintering process where the peak temperature reaches 850°C. Temperature control accuracy directly determines key performance indicators such as the sensor's zero-point stability, pressure sensitivity, and temperature drift characteristics.

[0003] However, existing temperature control technologies for film printing have a problem: they cannot effectively handle the cooling effect during solvent evaporation and the series of chain reactions it causes. In a typical film printing curing process, during the critical stage of temperature rise from 100°C to 250°C, a large amount of organic solvents in the ink (such as methyl ethyl ketone, toluene, and isopropanol) undergoes a dramatic phase change and volatilization. This process instantaneously absorbs a large amount of latent heat (typically 300-500 J of heat per gram of solvent), resulting in the actual temperature of the ink surface being 5-10°C or even lower than the temperature monitored by the thermocouples in the heating system. However, traditional temperature control systems rely solely on single-point thermocouple monitoring of the heating plate or oven air temperature, completely ignoring this significant temperature difference. This leads to serious misjudgments in the control program—the system incorrectly assumes the ink has reached the preset solvent evaporation temperature and begins the next stage of rapid heating, while in reality, a large amount of incompletely volatilized residual solvent remains inside the ink, especially in thicker areas. As the control system continues to rapidly heat up according to the predetermined program, a relatively dense "skin" forms on the ink surface due to the decrease in solvent content. However, this skin is actually an unstable and weak structure. At this time, the residual solvent inside will undergo secondary evaporation and rapid expansion driven by the rapid heating. The huge internal pressure will break through the already formed surface skin, forming a large number of pinholes, bubbles, or microcracks on the membrane surface, which are fatal defects. These defects will not only cause open circuits or short circuits in the circuit pattern, but also seriously affect the electrical performance and mechanical strength of the membrane. Ultimately, this will cause a series of quality problems such as resistance value deviation, decreased insulation performance, and shortened bending life. This will significantly reduce the pass rate of the entire batch of products, seriously affect production efficiency and economic benefits, and increase rework costs and waste of raw materials.

[0004] In view of this, the present invention proposes a programmed temperature control system for film printing process to solve the above problems. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art and to achieve the above objectives, the present invention provides the following technical solution: a programmed temperature control system for film printing process, comprising: The multi-source temperature acquisition module is used to acquire ink layer surface temperature data, substrate contact temperature data and ambient gas phase temperature data, and to identify solvent evaporation cooling characteristics based on the instantaneous change rate of ink layer surface temperature data. The evaporation kinetics modeling module is used to construct a dynamic phase transition model of solvent evaporation based on the solvent evaporation cooling characteristics and the vapor partial pressure gradient in the ambient gas phase temperature data. The temperature difference compensation module is used to determine the real-time temperature difference compensation amount based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase change model and the heat transfer path of the substrate contact temperature data. The skin formation status recognition module is used to determine the time of skin formation on the ink surface based on the temperature difference compensation amount and the thickness distribution data of the ink layer; The segmented control module is used to divide the heating process into a pre-volatile section, a transition section, and a curing section according to the skin formation time, and to configure a different temperature control strategy for each section. The residual solvent prediction module is used to predict the distribution of residual solvent inside the ink based on the coupling relationship between the segmented temperature control strategy and the dynamic phase change model. The dynamic control module is used to adjust the heating rate in real time based on the residual solvent distribution to prevent internal solvent from breaking through the surface and forming defects.

[0006] Furthermore, methods for identifying the cooling characteristics of solvent evaporation include: Calculate the rate of temperature change between adjacent sampling points based on the time series of ink layer surface temperature data; Identify the temperature drop range based on the negative peak value of the temperature change rate; The presence of a cooling effect can be determined by the degree of deviation of the positive correlation between the temperature drop range and the heating power. The cooling characteristics of solvent evaporation are quantified based on the duration of the cooling effect and the magnitude of the temperature drop.

[0007] Furthermore, the methods for constructing dynamic phase transition models include: Based on the time-varying characteristics of the temperature drop rate in the cooling characteristics of solvent evaporation, the instantaneous rate function of solvent evaporation is determined. The diffusion driving force of solvent molecules is calculated based on the vapor partial pressure gradient in the ambient gas phase temperature data. Based on the coupling relationship between the instantaneous rate function and the diffusion driving force, a dynamic equation for the volatile flux is established; Based on the spatial distribution of the latent heat absorption term in the dynamic equation, a three-dimensional temperature field evolution model is constructed as a dynamic phase transition model.

[0008] Furthermore, the method for determining the real-time temperature difference compensation amount includes: Based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase transition model, the instantaneous heat absorption power at different depths of the ink layer is calculated. The total latent heat absorption rate per unit area is determined by integrating the instantaneous heat absorption power along the thickness direction. The actual heat transfer rate is calculated based on the difference between the substrate contact temperature data and the ink layer surface temperature data, combined with the thermal conductivity of the ink layer. The instantaneous heat gap is determined based on the difference between the total latent heat absorption rate and the actual heat transfer rate. Based on the instantaneous heat gap and the heat capacity parameters of the heating system, the additional temperature increase required to maintain the target heating rate is calculated as the real-time temperature difference compensation.

[0009] Furthermore, methods for determining the timing of crust formation include: Based on the time evolution curve of the temperature difference compensation amount, identify the inflection point where the compensation amount changes from increasing to decreasing; Calculate the radial gradient of the surface solvent concentration based on the ink layer thickness distribution data; The degree of homogenization of the radial gradient determines whether a continuous solid film has formed on the surface. The timing of crust formation is determined by the consistency between the inflection point and the time of continuous solid film formation.

[0010] Furthermore, the configuration method for the differentiated temperature control strategy includes: For the pre-evaporation section, a slow heating rate is set based on the initial solvent content, and feedforward control with temperature difference compensation is added. For the transition section, a stepped heating curve is adopted according to the degree of surface solidification at the time of crust formation, and a constant temperature residence time is maintained for each step; For the curing section, a variable rate of heating is implemented based on the depth gradient of the residual solvent distribution, with a reduced heating rate in areas with more solvent in the deeper layers. Based on the temperature continuity requirements at the connection points between segments, the temperature ramp function for the transition between segments is optimized.

[0011] Furthermore, methods for predicting the distribution of residual solvents include: The time-varying temperature curve defined by the segmented temperature control strategy is used as the driving input for time evolution, and the initial solvent concentration distribution of the ink is set as the simulation starting point. The time evolution process is discretized into multiple consecutive time steps. In each time step, the temperature value at that moment is used to drive the dynamic phase change model to calculate the change in solvent concentration inside the ink caused by solvent evaporation. Based on the change in solvent concentration, the solvent concentration distribution inside the ink is updated, and the updated distribution is used as the initial condition for the calculation in the next time step. The process iterates through all time steps until the segmented temperature control strategy ends, and the resulting spatial distribution of solvent concentration inside the ink is the residual solvent distribution.

[0012] Furthermore, the method for constructing a three-dimensional temperature field evolution model includes: A three-dimensional spatial mesh is established based on the geometric dimensions of the ink layer; Based on the spatial distribution of the latent heat absorption term, a heat source term is assigned to each grid point in the three-dimensional spatial grid. Based on the heat conduction equations between adjacent grid points, a set of partial differential equations for the temperature field is constructed. Based on the dynamic update of the boundary conditions, the partial differential equations are solved using the finite difference method to obtain the spatiotemporal evolution trajectory of the three-dimensional temperature field, which is the three-dimensional temperature field evolution model.

[0013] Furthermore, the methods for determining the formation of a continuous solid film include: Calculate the concentration difference between adjacent sampling points based on the radial gradient of the surface solvent concentration; The degree of surface homogenization is determined based on the proportion of sampling points with concentration differences less than a preset uniformity threshold. Predict the surface rheological properties based on the relationship between surface viscosity and temperature and solvent content; A continuous solid phase film is determined to be formed when the rheological properties reach the solid-state threshold and the homogenization degree exceeds a preset ratio.

[0014] Furthermore, the method for real-time adjustment of the heating rate includes: Based on the distribution of residual solvent, identify areas of high solvent concentration; The solvent breach risk level is assessed based on the distance between the high-concentration area and the already formed skin layer. Determine the adjustment factor for the heating rate based on the solvent breakthrough risk level; The corrected heating rate is calculated based on the difference between the current temperature and the target temperature, combined with the adjustment coefficient. Based on the corrected mapping relationship between heating rate and heating power, the output power of the heating element is adjusted in real time to ensure that the internal solvent gradually evaporates without causing an explosive burst.

[0015] The technical effects and advantages of the programmed temperature control system for film printing process of the present invention are as follows: This invention solves the temperature control inaccuracy problem in film printing by accurately identifying and compensating for the cooling effect during solvent evaporation, achieving precise and controllable sintering of varistor paste. It improves the formation quality of the Wheatstone bridge structure, effectively eliminating surface defects such as pinholes, bubbles, and microcracks, ensuring the continuity and uniformity of the resistance strip, and improving the zero-point stability, pressure sensitivity consistency, and temperature drift characteristics of the pressure sensor. Through intelligent process state identification and dynamic control strategies, it can adapt to the compositional differences and environmental changes of different batches of paste, improving the reproducibility and stability of the production process, and ensuring high consistency in product quality between batches and between equipment. This precise temperature control capability not only significantly improves the product yield and reduces scrap and rework caused by process defects, but also shortens the process development cycle and reduces the technical risks of introducing new products. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a programmed temperature control system for film printing process according to the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] This application provides a programmed temperature control system for film printing processes. The executing entities of the programmed temperature control system for film printing processes include, but are not limited to, the following: film printing equipment, temperature control system, printing process control platform, ink curing equipment, process parameter monitoring system, etc., which can be considered as general control nodes in this application. The data processing platform includes, but is not limited to, at least one of the following: temperature monitoring system, phase change analysis system, and process optimization system.

[0019] Please see Figure 1 The present invention provides a programmed temperature control system for film printing process, including a multi-source temperature acquisition module, a volatilization kinetics modeling module, a temperature difference compensation module, a skinning state identification module, a segmented control module, a residual solvent prediction module, and a dynamic adjustment module. The modules are connected via wired and / or wireless means to enable data transmission between them.

[0020] The multi-source temperature acquisition module is used to acquire ink layer surface temperature data, substrate contact temperature data and ambient gas phase temperature data, and to identify solvent evaporation cooling characteristics based on the instantaneous change rate of ink layer surface temperature data. The evaporation kinetics modeling module is used to construct a dynamic phase transition model of solvent evaporation based on the solvent evaporation cooling characteristics and the vapor partial pressure gradient in the ambient gas phase temperature data. The temperature difference compensation module is used to determine the real-time temperature difference compensation amount based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase change model and the heat transfer path of the substrate contact temperature data. The skin formation status recognition module is used to determine the time of skin formation on the ink surface based on the temperature difference compensation amount and the thickness distribution data of the ink layer; The segmented control module is used to divide the heating process into a pre-volatile section, a transition section, and a curing section according to the skin formation time, and to configure a different temperature control strategy for each section. The residual solvent prediction module is used to predict the distribution of residual solvent inside the ink based on the coupling relationship between the segmented temperature control strategy and the dynamic phase change model. The dynamic control module is used to adjust the heating rate in real time based on the residual solvent distribution to prevent internal solvent from breaking through the surface and forming defects.

[0021] This invention achieves precise capture of the printing process temperature state by acquiring ink layer surface temperature data, substrate contact temperature data, and ambient gas phase temperature data. A dynamic phase change model is constructed based on solvent evaporation cooling characteristics and vapor pressure gradient, enabling the system to characterize phase change processes. The real-time temperature difference compensation amount is determined based on the spatiotemporal distribution characteristics of latent heat absorption and heat transfer paths, improving the accuracy of temperature control. The timing of skin formation is determined based on temperature difference compensation amount and thickness distribution data, making process control more targeted. Segmented control and differentiated strategies based on skin formation timing enhance the system's adaptability and process controllability. Precise control of the ink curing process is achieved by predicting residual solvent distribution and dynamically adjusting the heating rate, improving printing quality and process stability.

[0022] During the film printing process, temperature acquisition devices such as infrared thermal imagers, contact temperature sensors, and vapor phase temperature monitors are used to collect various temperature information in real time. Ink layer surface temperature data reflects the real-time temperature changes of the ink surface during printing; substrate contact temperature data reflects the temperature conditions at the interface between the substrate and the ink layer; ambient vapor phase temperature data includes parameters such as ambient temperature, humidity, and vapor partial pressure, as well as their changing trends.

[0023] It should be noted that the temperature acquisition device adopts a distributed deployment method to ensure comprehensive coverage of key locations in the printing area. The temperature acquisition device continuously collects data at each sampling moment to ensure the continuity and integrity of the data.

[0024] In one implementation of this invention, the sampling frequency is set to once every 0.5 seconds.

[0025] In one implementation of this invention, the collected data undergoes preprocessing steps such as filtering, temperature compensation, and standardization to ensure data quality. Kalman filtering is used for data filtering, temperature compensation is performed using sensor characteristic curves, and min-max standardization is used for data standardization. The specific methods of these preprocessing steps are not described here, as they are all techniques well-known to those skilled in the art. Other data preprocessing algorithms may also be used, and are not limited thereto.

[0026] The following steps all use the surface temperature data of the pre-treated ink layer, the substrate contact temperature data, and the ambient gas phase temperature data for analysis.

[0027] In this embodiment of the invention, the method for identifying the cooling characteristics of solvent evaporation includes: Calculate the rate of temperature change between adjacent sampling points based on the time series of ink layer surface temperature data; Identify the temperature drop range based on the negative peak value of the temperature change rate; The presence of a cooling effect can be determined by the degree of deviation of the positive correlation between the temperature drop range and the heating power. The cooling characteristics of solvent evaporation are quantified based on the duration of the cooling effect and the magnitude of the temperature drop.

[0028] In this embodiment, time series analysis is performed on the surface temperature data of the ink layer to calculate the temperature difference between adjacent sampling points. The temperature change rate is obtained by dividing the difference by the time interval. A time series of the temperature change rate is constructed, and the instantaneous temperature change rate at each sampling moment is recorded. Digital filtering technology is applied to eliminate the influence of measurement noise on the change rate calculation. The change rate series is smoothed using the moving average method or the exponential smoothing method to ensure the reliability of the change rate data.

[0029] Analyze the negative change characteristics in the temperature change rate sequence to identify time periods with negative temperature change rates, indicating a decreasing temperature trend. Use peak detection algorithms (such as local extrema method, threshold detection method, etc.) to identify peak points in the negative change rate. These peak points represent the moments when the temperature drops most drastically. Based on the size and duration of the peaks, determine the boundaries of the temperature drop intervals. Record the start time, end time, and maximum rate of decrease for each drop interval to form a set of temperature drop intervals.

[0030] The correlation between the temperature drop range and the heating power was analyzed. Under normal circumstances, an increase in heating power should lead to a temperature increase, and the two are positively correlated. However, when there is a cooling effect due to solvent evaporation, the temperature may still drop even if the heating power is increased, which shows a deviation from the positive correlation. The correlation coefficient between heating power and the rate of temperature change was calculated, and an expected threshold for the positive correlation was set. The deviation between the actual correlation coefficient and the expected threshold was compared. When the deviation exceeds the preset range, it is determined that there is a cooling effect. This deviation indicates that there is an additional endothermic process affecting the temperature change.

[0031] The identified cooling effect is quantitatively analyzed by measuring the duration of the cooling effect, i.e., the time from the start of the deviation to the return to normal, calculating the temperature drop amplitude, i.e., the maximum and average temperature drop, and analyzing the intensity variation law of the cooling effect, such as gradually increasing, stable or gradually decreasing type. A quantitative descriptive model of the cooling characteristics is established, including parameters such as characteristic intensity, characteristic period, and characteristic frequency. These quantitative solvent evaporation cooling characteristics provide important input parameters for the subsequent construction of dynamic phase transition models.

[0032] In this embodiment of the invention, the method for constructing a dynamic phase transition model includes: Based on the time-varying characteristics of the temperature drop rate in the cooling characteristics of solvent evaporation, the instantaneous rate function of solvent evaporation is determined. The diffusion driving force of solvent molecules is calculated based on the vapor partial pressure gradient in the ambient gas phase temperature data. Based on the coupling relationship between the instantaneous rate function and the diffusion driving force, a dynamic equation for the volatile flux is established; Based on the spatial distribution of the latent heat absorption term in the dynamic equation, a three-dimensional temperature field evolution model is constructed as a dynamic phase transition model.

[0033] In this embodiment, the time variation law of temperature drop rate in the cooling characteristics of solvent evaporation is analyzed, and the time-varying characteristic parameters of temperature drop rate, such as the trend, periodicity, and abrupt change point, are extracted. Based on mass transfer theory and Fick's law, a correlation model between solvent evaporation rate and temperature drop rate is established. Considering the influence of temperature on solvent vapor pressure, the Clausius-Clapeyron equation is used to describe the relationship between temperature and vapor pressure. Combining the time-varying characteristics of temperature drop rate, the instantaneous rate function of solvent evaporation is constructed. Instantaneous rate function of solvent evaporation:

[0034] in, This represents the instantaneous evaporation rate of the solvent per unit area of ​​the ink layer surface at time t and temperature T. This is the frequency factor, representing a combination of molecular collision frequency and geometric factor. It reflects the maximum possible evaporation rate of solvent molecules in the absence of energy barriers. It is an inherent parameter related to the type of solvent and ink formulation, and different solvent systems have different values. For activation energy, is a temperature change sensitive factor, and n is the reaction order (usually taken as 0.5-2.0). This represents the local concentration of the solvent in the ink.

[0035] This function describes the dynamic change of solvent evaporation rate with time and temperature. The function can be exponentially decaying, polynomial, or piecewise. The appropriate function form should be selected according to the actual process characteristics.

[0036] By analyzing the vapor partial pressure information in the ambient gas phase temperature data, the partial pressure distribution of solvent vapor in the environment is calculated. Based on the ideal gas law and the partial pressure law of mixed gases, the vapor partial pressure values ​​at different locations are determined. The vapor partial pressure gradient between the ink surface and the environment is calculated. This gradient is the main driving force for the diffusion of solvent molecules. The diffusion coefficient of solvent molecules in the gas phase is calculated using diffusion theory, taking into account the influence of temperature and pressure on the diffusion coefficient. Based on the partial pressure gradient and the diffusion coefficient, the diffusion driving force of solvent molecules is determined. This driving force determines the mass transfer rate of solvent from the ink surface to the environment.

[0037] diffusion driving force Calculation formula: ; in, For the effective diffusion coefficient, It is the saturated vapor pressure. The reference diffusion coefficient (typically in the range of 10 for small molecule solvents) is used. -9 ~10 -6 (range in m² / s) For reference temperature, room temperature (298K) or process reference temperature is usually taken as the reference point; For concentration gradient, the rate of change of solvent concentration per unit distance; Effective mass transfer area (the surface area of ​​the ink that participates in solvent diffusion and mass transfer). This refers to the ambient vapor partial pressure, which is the actual partial pressure of solvent vapor in the ambient air. The coupling relationship between the instantaneous rate function and the diffusion driving force is established, and the mutual influence mechanism between the two is analyzed. The volatilization rate affects the vapor concentration at the interface, which in turn affects the partial pressure gradient. The partial pressure gradient, in turn, affects the volatilization rate, forming a nonlinear coupling relationship. Using the law of conservation of mass and the mass transfer equation, a dynamic equation describing the volatilization flux is established. This equation comprehensively considers the coupling effect of internal volatilization and external diffusion. The equation is in the form of a system of partial differential equations, including time derivative terms and spatial derivative terms. Finally, the latent heat absorption term in the dynamic equation of volatilization flux is analyzed.

[0038] Solvent phase transition processes absorb latent heat, leading to local temperature drops. Based on phase transition thermodynamics, the latent heat required for the evaporation of a unit mass of solvent is calculated, and the spatial distribution characteristics of latent heat absorption are analyzed. Different evaporation rates at different locations result in uneven spatial distribution of latent heat absorption. A three-dimensional spatial grid is established, and the latent heat absorption term is allocated to each grid point. The evolution of the three-dimensional temperature field is described using the heat conduction equation. Considering the influence of latent heat absorption on the temperature field, a three-dimensional temperature field evolution model is constructed. This model can predict the temperature change over time at any location within the ink layer. This three-dimensional temperature field evolution model is the dynamic phase transition model, which fully describes the mass and heat transfer coupling phenomenon during solvent evaporation.

[0039] In this embodiment of the invention, the method for determining the real-time temperature difference compensation amount includes: Based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase transition model, the instantaneous heat absorption power at different depths of the ink layer is calculated. The total latent heat absorption rate per unit area is determined by integrating the instantaneous heat absorption power along the thickness direction. The actual heat transfer rate is calculated based on the difference between the substrate contact temperature data and the ink layer surface temperature data, combined with the thermal conductivity of the ink layer. The instantaneous heat gap is determined based on the difference between the total latent heat absorption rate and the actual heat transfer rate. Based on the instantaneous heat gap and the heat capacity parameters of the heating system, the additional temperature increase required to maintain the target heating rate is calculated as the real-time temperature difference compensation.

[0040] In this embodiment, based on the calculation results of the dynamic phase change model, the distribution information of latent heat absorption in time and space is extracted, the solvent evaporation rate at different depths of the ink layer is analyzed, and the latent heat absorption per unit time at each depth is calculated according to the latent heat coefficient of phase change. The latent heat absorption is divided by the time interval to obtain the instantaneous heat absorption power. Considering the non-uniformity of the ink layer thickness, the heat absorption power is calculated for different thickness regions, and a depth-heat absorption power distribution function is established. This function describes the variation law of heat absorption power with depth, and the instantaneous heat absorption power value at each depth at each sampling time is recorded.

[0041] The instantaneous heat absorption power is integrated along the thickness direction using numerical integration methods (such as the trapezoidal rule, Simpson's rule, etc.). The integration interval is the entire thickness range of the ink layer, from the bottom substrate contact surface to the top free surface. The integration result represents the total latent heat absorption rate per unit area, which is the sum of the heat absorption power at all depths within the entire ink layer thickness range. This total latent heat absorption rate reflects the degree of influence of the phase change process on the overall heat transfer.

[0042] The temperature difference between the substrate contact temperature and the ink layer surface temperature is calculated. This temperature difference drives the conduction of heat from the substrate to the ink layer surface. Based on Fourier's law of heat transfer, and combined with the thermal conductivity and geometric dimensions of the ink layer, the actual heat transfer rate q is calculated.

[0043] The formula for calculating the heat transfer rate is: Where k is thermal conductivity and A is heat transfer area. Let L be the temperature difference and L be the heat transfer path length. Considering the change in thermal conductivity of the ink layer with temperature and solvent content, the thermal conductivity value is corrected using the functional relationship between temperature and composition to obtain a more accurate actual heat transfer rate. Then, the difference between the total latent heat absorption rate and the actual heat transfer rate is calculated. This difference represents the instantaneous heat gap, which is the heat demand required to maintain the phase change process but which cannot be met by the current heat transfer. A positive value indicates that additional heat input is required, and a negative value indicates that the current heat transfer exceeds the phase change demand. The time variation trend of the heat gap is analyzed to identify the peak time and duration of the gap. This information is crucial for formulating a compensation strategy.

[0044] Based on the instantaneous heat gap and the heat capacity parameters of the heating system, the additional heat required to maintain the target heating rate is calculated. The heat capacity parameters of the heating system include heater power, thermal response time, and thermal efficiency. According to the principle of energy balance, the required increase in heating power is determined, and the increased heating power is converted into an equivalent temperature rise. Considering the thermal inertia and control delay of the system, the temperature rise is dynamically corrected to obtain the real-time temperature difference compensation. This compensation is used to guide the heating system to make real-time adjustments to ensure that the ink layer can be heated according to the preset heating curve.

[0045] In this embodiment of the invention, the method for determining the time of crust formation includes: Based on the time evolution curve of the temperature difference compensation amount, identify the inflection point where the compensation amount changes from increasing to decreasing; Calculate the radial gradient of the surface solvent concentration based on the ink layer thickness distribution data; The degree of homogenization of the radial gradient determines whether a continuous solid film has formed on the surface. The timing of crust formation is determined by the consistency between the inflection point and the time of continuous solid film formation.

[0046] In this embodiment, the time series data of temperature difference compensation amount are analyzed, and the evolution curve of temperature difference compensation amount over time is plotted to analyze the trend and characteristic points of the curve. In the early stage of the skin formation process, due to the rapid evaporation of solvent and the large latent heat absorption, the temperature difference compensation amount usually shows an increasing trend. When a solid film begins to form on the surface, solvent evaporation is hindered, latent heat absorption decreases, and the temperature difference compensation amount begins to decrease. The derivative analysis method is used to identify the extreme points and inflection points of the curve, focusing on the turning point where the compensation amount changes from an increasing trend to a decreasing trend. Variable point detection algorithms (such as cumulative sum test, Bayesian variable point detection, etc.) are applied to accurately locate the turning point and record the time position and numerical characteristics of the inflection point. These inflection points are important indicators of the skin formation process.

[0047] To analyze the spatial characteristics of ink layer thickness distribution data, the ink layer surface is divided into multiple sampling areas. The thickness value of each area is measured to establish a thickness distribution map. Based on the thickness distribution and solvent evaporation model, the solvent concentration on the surface of each area is calculated. The difference in solvent concentration between adjacent areas is analyzed, and the radial gradient (i.e., the concentration gradient along the surface direction) is calculated. A large radial gradient indicates uneven concentration distribution, while a small radial gradient indicates that the concentration tends to be uniform. The gradient value at each point is calculated using the numerical differentiation method to construct a spatial distribution map of the radial gradient.

[0048] The degree of homogenization of the radial gradient is evaluated by calculating the standard deviation or coefficient of variation of the radial gradient as a quantitative indicator of homogenization. A threshold for judging homogenization is set. When the standard deviation is less than the threshold, the solvent concentration on the surface is considered to have reached a relatively uniform state. The time evolution of the homogenization process is analyzed, and the change of the standard deviation over time is tracked to identify the moment when the standard deviation begins to stabilize at a low value. Combined with the critical value of the solvent concentration, it is determined whether the surface has reached the conditions for solid-phase transformation. When the solvent concentration is lower than the critical value and the radial gradient is small, it is determined that a continuous solid phase film has been formed.

[0049] By comparing the consistency between the inflection point and the continuous solid film formation time, the time difference between the two times is analyzed, the degree of consistency is evaluated, and a tolerance range for time consistency is set, usually several sampling periods. When the difference between the two times is within the tolerance range, the time consistency is confirmed, and the earlier or average of the two times is selected as the skin formation time. Alternatively, a more conservative time can be selected based on process experience and safety considerations. The determined skin formation time is used as an important node for segmented control. This time marks the transition of the printing process from the solvent evaporation-dominated stage to the curing-dominated stage.

[0050] In this embodiment of the invention, the method for configuring a differentiated temperature control strategy includes: For the pre-evaporation section, a slow heating rate is set based on the initial solvent content, and feedforward control with temperature difference compensation is added. For the transition section, a stepped heating curve is adopted according to the degree of surface solidification at the time of crust formation, and a constant temperature residence time is maintained for each step; For the curing section, a variable rate of heating is implemented based on the depth gradient of the residual solvent distribution, with a reduced heating rate in areas with more solvent in the deeper layers. Based on the temperature continuity requirements at the connection points between segments, the temperature ramp function for the transition between segments is optimized.

[0051] In this embodiment, the control strategy design for the pre-evaporation stage involves analyzing the initial solvent content of the ink. Different solvent contents require different evaporation times and heating strategies. Based on the solvent type and content, a corresponding slow heating rate is set, typically 0.5-2℃ / min, to avoid rapid heating that could lead to solvent boiling or premature surface skinning. The previously calculated temperature difference compensation is used as a feedforward control signal and superimposed on the basic heating curve. Feedforward control can pre-compensate for the effects of phase change endothermic heat, improving the accuracy and response speed of temperature control. The parameters of the feedforward controller, including gain coefficient and time constant, are designed to ensure the stability and effectiveness of the compensation signal. The solvent evaporation rate in the pre-evaporation stage is monitored, and the heating strategy is adjusted according to the actual evaporation situation.

[0052] For the control strategy design of the transition section, based on the assessment of the surface curing degree at the time of skin formation, the surface curing degree affects the subsequent heat and mass transfer process. A stepped heating curve is designed, dividing the transition section into multiple temperature steps. Each step is set with a specific target temperature and dwell time. The number of steps is usually 3-5, the temperature increment is 5-15℃, and the dwell time is determined according to the ink thickness and curing requirements, usually 2-10 minutes. During each isothermal step, the system maintains a stable temperature, allowing internal temperature homogenization and further curing. The curing progress of each step is monitored, and the dwell time is adjusted as necessary.

[0053] For the control strategy design of the curing section, based on the depth gradient information of the residual solvent distribution, different depths have different solvent contents, requiring differentiated heating strategies. Variable rate heating control is implemented, with a slower heating rate for deeper areas with high solvent content to avoid internal solvent vaporization and defects, and a faster heating rate for surface areas with low solvent content to accelerate the curing process. A depth-heating rate mapping relationship is established, and the heating rate of each area is adjusted in real time according to the solvent distribution. A regional control strategy is designed to implement independent temperature control for different areas.

[0054] Optimize the transition between segments to ensure temperature continuity and avoid thermal stress and deformation caused by sudden temperature changes. Design smooth temperature transition functions, such as cubic spline functions and Bézier curves, and calculate the temperature ramp parameters between segments, including ramp time and ramp rate. Verify the continuity and differentiability of the transition function to ensure smooth transition of temperature and heating rate. Set up monitoring and verification mechanisms at each transition point between segments to ensure that the actual temperature curve meets the design requirements. This differentiated temperature control strategy can adapt to the process requirements of different stages and improve printing quality and process stability.

[0055] In this embodiment of the invention, the method for predicting the distribution of residual solvent includes: The time-varying temperature curve defined by the segmented temperature control strategy is used as the driving input for time evolution, and the initial solvent concentration distribution of the ink is set as the simulation starting point. The time evolution process is discretized into multiple consecutive time steps. In each time step, the temperature value at that moment is used to drive the dynamic phase change model to calculate the change in solvent concentration inside the ink caused by solvent evaporation. Based on the change in solvent concentration, the solvent concentration distribution inside the ink is updated, and the updated distribution is used as the initial condition for the calculation in the next time step. The process iterates through all time steps until the segmented temperature control strategy ends, and the resulting spatial distribution of solvent concentration inside the ink is the residual solvent distribution.

[0056] In this embodiment, the complete time-varying temperature curve defined in the segmented temperature control strategy is extracted. This curve contains all temperature change information of the pre-volatile section, the transition section and the curing section. The temperature curve is digitized into a time-temperature data point sequence to ensure that the time interval between data points is small enough to guarantee calculation accuracy. It is usually set to 0.1-1 seconds. This time-varying temperature curve is used as the external input to drive the entire prediction process. At the same time, based on the ink's composition and initial state, the initial solvent concentration distribution inside the ink is set. The initial concentration may be different at different depths and locations. A three-dimensional spatial grid is established to describe the geometry of the ink layer, and an initial solvent concentration value is assigned to each grid point. This initial distribution serves as the starting point for the entire prediction calculation.

[0057] The entire time evolution process is discretized into multiple consecutive time steps. The choice of time step size needs to balance computational accuracy and efficiency, and is usually set to 0.1-1 seconds to ensure that the time step size is less than the characteristic time constant of the system. Within each time step, the system state can be approximated as a quasi-steady state. The temperature value corresponding to the current time step is extracted and used as the driving parameter of the dynamic phase change model to start the calculation process of the phase change model. The model calculates parameters such as solvent evaporation rate, diffusion coefficient, and phase change flux based on the current temperature. Based on the mass transfer equation, it calculates the amount of solvent concentration change inside the ink, considering the comprehensive effect of multiple mass transfer mechanisms such as evaporation, diffusion, and convection. Then, based on the calculated amount of solvent concentration change, the solvent concentration value of each grid point inside the ink is updated. The formula for updating the solvent concentration value is: ; in, Let be the solvent concentration value at grid point (i,j,k) and time step n+1; Let be the solvent concentration value at grid point (i,j,k) and time step n; This refers to the time interval between two adjacent time steps in numerical computation. Let be the total diffusion flux divergence at grid point (i,j,k), which follows the law of conservation of mass; Let be the spatial rate of change of the diffusion flux of the solvent in the x, y, and z directions; , , For diffusion flux in all directions; Temperature-related volatiles source terms;

[0058] in, is the evaporation rate constant (related to solvent type and ink formulation, determining the basic evaporation rate), a kinetic constant describing the evaporation reaction rate; C is the solvent concentration at the current grid point. To release activation energy, The dynamic heating enhancement factor describes the additional promoting effect of the heating rate on volatilization.

[0059] The updated concentration distribution is checked to ensure it meets physical constraints, such as concentration non-negativity and mass conservation. Unreasonable values ​​are corrected, and the updated concentration distribution is used as the initial condition for the next time step calculation, forming an iterative recursive relationship between time steps. Finally, all time step calculations are executed sequentially until the time cycle of the segmented temperature control strategy ends. Each time step calculation is based on the result of the previous step, forming a complete time evolution chain. The solvent concentration distribution at key moments is recorded to analyze the dynamic characteristics of the evaporation process. At the end of the calculation process, the final spatial distribution of solvent concentration inside the ink is obtained. This distribution describes the content of residual solvent at different locations, including three-dimensional spatial coordinates and corresponding solvent concentration values. The characteristics of the residual solvent distribution, such as high concentration areas, concentration gradients, and distribution uniformity, are analyzed. This information provides an important basis for subsequent dynamic control.

[0060] In this embodiment of the invention, the method for constructing a three-dimensional temperature field evolution model includes: A three-dimensional spatial mesh is established based on the geometric dimensions of the ink layer; Based on the spatial distribution of the latent heat absorption term, a heat source term is assigned to each grid point in the three-dimensional spatial grid. Based on the heat conduction equations between adjacent grid points, a set of partial differential equations for the temperature field is constructed. Based on the dynamic update of the boundary conditions, the partial differential equations are solved using the finite difference method to obtain the spatiotemporal evolution trajectory of the three-dimensional temperature field, which is the three-dimensional temperature field evolution model.

[0061] In this embodiment, a suitable three-dimensional spatial coordinate system is established based on the actual geometric dimensions and shape characteristics of the ink layer. Typically, a Cartesian coordinate system (x, y, z) is used to determine the boundary range and geometric parameters of the ink layer, such as length, width, and thickness. The three-dimensional space is then divided into regular grid cells. The grid can be a cube, cuboid, or other regular shape. The choice of grid density needs to balance computational accuracy and efficiency. A denser grid is used in key areas (such as near the boundary or where the thickness changes). A unique identifier and coordinate value are assigned to each grid point, and a mapping relationship between the grid points and the physical space is established. Considering the non-uniformity of the ink layer thickness, different grid division strategies are adopted for regions with different thicknesses.

[0062] Based on the previously calculated spatial distribution information of latent heat absorption terms, the distribution characteristics of latent heat absorption in three-dimensional space are analyzed. The different solvent evaporation rates at different locations lead to non-uniform spatial distribution of latent heat absorption. Interpolation methods are used to map the latent heat absorption data onto three-dimensional grid points. Commonly used interpolation methods include linear interpolation, cubic spline interpolation, and Kriging interpolation. A corresponding heat source term value is assigned to each grid point. A negative value of the heat source term indicates heat absorption (latent heat absorption), and a positive value indicates heat generation. A time-varying function of the heat source term is established because latent heat absorption changes with temperature and time, ensuring the conservation of mass and energy in the allocation of the heat source term.

[0063] Based on the fundamental physical laws of heat conduction, a heat conduction equation between adjacent grid points is established. According to Fourier's law of heat conduction, the heat conduction flux is proportional to the temperature gradient. For the three-dimensional case, the general form of the heat conduction equation is: ,in Let c be the density, c be the specific heat capacity, k be the thermal conductivity, and S be the heat source term. The partial differential equation is discretized using a finite difference scheme. The continuous temperature field is represented by discrete temperature values ​​at grid points. An algebraic relationship is established between the temperature of each grid point and the temperatures of adjacent grid points, forming a large sparse linear equation system. The temperature dependence of ink material properties, such as the change of thermal conductivity and specific heat capacity with temperature, is considered.

[0064] Appropriate boundary conditions are set to describe the heat exchange between the ink layer and the external environment. Common boundary conditions include: specified temperature boundary conditions (first type of boundary conditions), specified heat flux boundary conditions (second type of boundary conditions), and convection boundary conditions (third type of boundary conditions). The boundary conditions are updated in real time according to the dynamic changes in the process, such as changes in heater temperature and ambient temperature. The partial differential equation system is solved using the finite difference method. An appropriate difference scheme is selected, such as central difference, forward difference, or backward difference. Numerical solution algorithms, such as Gauss-Seidel iteration and conjugate gradient method, are used to solve for the temperature distribution at each time step. The evolution trajectory of the temperature field is obtained by time progression. The temperature changes at key moments and locations are recorded. The spatial distribution characteristics and temporal evolution law of the temperature field are analyzed to verify the rationality and convergence of the calculation results. Finally, a complete three-dimensional temperature field evolution model is obtained, which can predict the temperature value at any location and time inside the ink layer.

[0065] In this embodiment of the invention, the method for determining the formation of a continuous solid film includes: Calculate the concentration difference between adjacent sampling points based on the radial gradient of the surface solvent concentration; The degree of surface homogenization is determined based on the proportion of sampling points with concentration differences less than a preset uniformity threshold. Predict the surface rheological properties based on the relationship between surface viscosity and temperature and solvent content; A continuous solid phase film is determined to be formed when the rheological properties reach the solid-state threshold and the homogenization degree exceeds a preset ratio.

[0066] In this embodiment, based on the radial gradient data of the surface solvent concentration, the concentration change between adjacent sampling points in the surface region is analyzed. An appropriate sampling point spacing is selected, typically a few millimeters to a few centimeters, to ensure that the spatial variation characteristics of the concentration distribution can be captured. The concentration difference between each pair of adjacent sampling points is calculated, and Euclidean distance or absolute difference is used as the difference measure to construct a spatial distribution map of the concentration difference. The statistical characteristics of the difference distribution, such as the mean, standard deviation, and maximum value, are analyzed to identify areas with drastic concentration changes and relatively stable areas. Then, a preset uniformity threshold is set. This threshold is determined according to process requirements and material characteristics, and is typically 10%-30% of the initial concentration difference. The number of sampling points with concentration differences less than the uniformity threshold is counted, and the proportion of these sampling points to the total sampling points is calculated. This proportion reflects the degree of uniformity of the surface concentration distribution. The trend of the uniformity degree over time is analyzed to track the dynamic evolution of the uniformity process. A judgment standard for the degree of uniformity is set, such as "the proportion of uniform sampling points exceeds 80%". When this standard is reached, the surface concentration is considered to be uniform.

[0067] Based on rheological theory, a model is established to describe the relationship between surface viscosity and temperature and solvent content. Commonly used models include the Arrhenius model and the WLF model. The general form of the viscosity model is as follows: ,in Viscosity, Using the reference viscosity, T as temperature, C as solvent concentration, and f as a function describing the effects of temperature and concentration, the viscosity of the surface layer is calculated in real time based on the current temperature and solvent concentration. The time trend of viscosity change is analyzed to identify the stage of rapid viscosity growth and predict the rheological properties of the surface layer, including the transition process from liquid to gel and then to solid. Finally, a judgment threshold for solid rheological properties is set, which corresponds to the critical point at which the material transforms from a viscous fluid to an elastic solid. Viscosity or elastic modulus is usually used as the judgment standard. The surface rheological properties are monitored to see if they reach the solid threshold, while the homogenization degree is checked to see if it exceeds the preset ratio. When both conditions are met, i.e., "rheological properties reach the solid threshold" and "homogeneity degree exceeds the preset ratio", a continuous solid film is determined to have formed. The time and area of ​​continuous solid film formation are recorded, and the quality characteristics of the solid film, such as thickness, uniformity, and integrity, are analyzed to provide key information for subsequent skinning state identification. The formation of a continuous solid film marks the entry of the ink surface layer into the curing stage, which is an important node in process control.

[0068] In this embodiment of the invention, the method for real-time adjustment of the heating rate includes: Based on the distribution of residual solvent, identify areas of high solvent concentration; The solvent breach risk level is assessed based on the distance between the high-concentration area and the already formed skin layer. Determine the adjustment factor for the heating rate based on the solvent breakthrough risk level; The corrected heating rate is calculated based on the difference between the current temperature and the target temperature, combined with the adjustment coefficient. Based on the corrected mapping relationship between heating rate and heating power, the output power of the heating element is adjusted in real time to ensure that the internal solvent gradually evaporates without causing an explosive burst.

[0069] In this embodiment, the three-dimensional spatial data of residual solvent distribution is analyzed to identify areas with relatively high solvent concentrations. A threshold for judging high concentration is set, typically 1.5-3 times the average concentration. Clustering algorithms (such as K-means, DBSCAN, etc.) are used to group high-concentration points into regions. The geometric characteristics of each high-concentration region are analyzed, such as location, volume, shape, and concentration peak. The total amount and average concentration of solvent in the region are calculated, the relative importance and risk level of each region are assessed, and a dynamic monitoring mechanism for high-concentration regions is established to track the changes of these regions over time.

[0070] The spatial distance between each high-concentration area and the formed skin surface is calculated. The shortest distance, centroid distance, or average distance is used as the metric to analyze the relationship between distance and solvent breakthrough risk. The smaller the distance, the higher the breakthrough risk. The thickness and strength of the formed skin surface are considered to affect the barrier ability. A distance-risk assessment model is established, and the risk level is divided into multiple levels, such as low risk, medium risk, high risk, and extremely high risk. Judgment criteria for each risk level are set, such as "distance <2mm is extremely high risk" and "2-5mm is high risk". A corresponding risk level is assigned to each high-concentration area.

[0071] Based on the solvent breakthrough risk level, determine the adjustment coefficient for the heating rate. The higher the risk level, the smaller the adjustment coefficient, meaning the heating rate should be slower. Establish a mapping table between risk level and adjustment coefficient, such as "extremely high risk: coefficient 0.3", "high risk: coefficient 0.5", "medium risk: coefficient 0.7", and "low risk: coefficient 0.9". Considering the combined effects of multiple high-concentration regions, use the weighted average or minimum value principle to determine the overall adjustment coefficient. Design a smooth change mechanism for the adjustment coefficient to avoid sudden rate changes.

[0072] Calculate the difference between the current temperature and the target temperature. This temperature difference determines the basic temperature rise requirement. Combined with an adjustment factor, calculate the corrected heating rate. The correction formula is as follows:

[0073] in, This is the corrected heating rate. The base heating rate (the ideal heating rate set according to the standard process curve). Risk sensitivity coefficient (value range: 0.2-0.8); To prevent solvents from exceeding risk levels, Temperature difference feedback coefficient (value range: 0.1-0.5); The target temperature difference (the difference between the temperature that should be reached according to the ideal process curve and the starting temperature). This represents the actual temperature difference.

[0074] Considering the dynamic characteristics of temperature control, such as system inertia and response delay, the heating rate is further optimized, and a safe range for the heating rate is set to prevent heating from being too fast or too slow.

[0075] A mapping relationship between the corrected heating rate and the heating power is established, taking into account the characteristics and heat transfer efficiency of the heating system. A mathematical model of power-heating rate is established using heat transfer theory or experimental data. Based on the corrected heating rate, the required heating power is calculated, and the output power of the heating elements, including electric heaters, infrared lamps, and hot air, is adjusted in real time.

[0076] By monitoring the actual heating effect and comparing it with the target heating rate, a closed-loop control system is formed. Through a PID controller or other advanced control algorithms, precise power regulation is achieved to ensure that the internal solvent can gradually evaporate, avoiding explosive evaporation and surface breakage caused by excessively rapid heating. This real-time adjustment mechanism can adaptively optimize the heating process according to the dynamic changes in solvent distribution, thereby improving printing quality and process stability.

[0077] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0078] It should be noted that all formulas in this manual are calculated by removing dimensions and taking their numerical values. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0079] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A programmed temperature control system for film printing process, characterized in that, include: A multi-source temperature acquisition module is used to acquire ink layer surface temperature data, substrate contact temperature data, and ambient gas phase temperature data, and to identify solvent evaporation cooling characteristics based on the instantaneous change rate of the ink layer surface temperature data. The evaporation kinetics modeling module is used to construct a dynamic phase transition model of solvent evaporation based on the solvent evaporation cooling characteristics and the vapor partial pressure gradient in the ambient gas phase temperature data. The temperature difference compensation module is used to determine the real-time temperature difference compensation amount based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase change model and the heat transfer path of the substrate contact temperature data. The skin formation state identification module is used to determine the time of skin formation on the ink surface based on the temperature difference compensation amount and the ink layer thickness distribution data; The segmented control module is used to divide the heating process into a pre-volatile section, a transition section and a curing section according to the skin formation time, and to configure a different temperature control strategy for each section. The residual solvent prediction module is used to predict the distribution of residual solvent inside the ink based on the coupling relationship between the segmented temperature control strategy and the dynamic phase change model. The dynamic control module is used to adjust the heating rate in real time based on the residual solvent distribution to prevent the internal solvent from breaking through the surface and forming defects.

2. The system according to claim 1, characterized in that, The method for identifying the cooling characteristics of solvent evaporation includes: Calculate the temperature change rate of adjacent sampling points based on the time series of the ink layer surface temperature data; Identify the temperature decrease range based on the negative peak value of the temperature change rate; The presence of a cooling effect is determined based on the degree of deviation of the positive correlation between the temperature drop range and the heating power. The solvent evaporation cooling characteristics are quantified based on the duration of the cooling effect and the magnitude of the temperature drop.

3. The system according to claim 1, characterized in that, The method for constructing the dynamic phase transition model includes: Based on the time-varying characteristics of the temperature drop rate in the solvent evaporation cooling characteristics, the instantaneous rate function of solvent evaporation is determined; The diffusion driving force of solvent molecules is calculated based on the vapor partial pressure gradient in the ambient gas phase temperature data. Based on the coupling relationship between the instantaneous rate function and the diffusion driving force, a dynamic equation for the volatile flux is established; Based on the spatial distribution of the latent heat absorption term in the dynamic equation, a three-dimensional temperature field evolution model is constructed as the dynamic phase transition model.

4. The system according to claim 1, characterized in that, The method for determining the real-time temperature difference compensation amount includes: Based on the spatiotemporal distribution characteristics of latent heat absorption in the dynamic phase transition model, the instantaneous heat absorption power at different depths of the ink layer is calculated. The total latent heat absorption rate per unit area is determined by integrating the instantaneous heat absorption power along the thickness direction. The actual heat transfer rate is calculated based on the difference between the substrate contact temperature data and the ink layer surface temperature data, combined with the thermal conductivity of the ink layer. The instantaneous heat gap is determined based on the difference between the total latent heat absorption rate and the actual heat transfer rate. Based on the instantaneous heat gap and the heat capacity parameters of the heating system, the additional temperature increase required to maintain the target heating rate is calculated as the real-time temperature difference compensation.

5. The system according to claim 1, characterized in that, The method for determining the timing of crust formation includes: Based on the time evolution curve of the temperature difference compensation amount, identify the inflection point where the compensation amount changes from increasing to decreasing; Based on the thickness distribution data of the ink layer, calculate the radial gradient of the surface solvent concentration; Based on the degree of homogenization of the radial gradient, it is determined whether a continuous solid film has formed on the surface. The skin formation time is determined based on the consistency between the inflection point time and the formation time of the continuous solid phase film.

6. The system according to claim 1, characterized in that, The configuration method for the differentiated temperature control strategy includes: For the pre-evaporation section, a slow heating rate is set according to the initial solvent content, and feedforward control of the temperature difference compensation is superimposed. For the transition section, a stepped heating curve is adopted according to the degree of surface solidification at the time of crust formation, and a constant temperature residence time is maintained for each step; For the curing section, a variable rate of heating is implemented based on the depth gradient of the residual solvent distribution, with a reduced heating rate in areas with more solvent in the deeper layers. Based on the temperature continuity requirements at the connection points between segments, the temperature ramp function for the transition between segments is optimized.

7. The system according to claim 1, characterized in that, The method for predicting the distribution of residual solvent includes: The time-varying temperature curve defined by the segmented temperature control strategy is used as the driving input for time evolution, and the initial solvent concentration distribution of the ink is set as the simulation starting point. The time evolution process is discretized into multiple consecutive time steps. In each time step, the temperature value at that moment is used to drive the dynamic phase transition model to calculate the change in solvent concentration inside the ink caused by solvent evaporation. Based on the change in solvent concentration, the solvent concentration distribution inside the ink is updated, and the updated distribution is used as the initial condition for the calculation in the next time step. The process iterates through all time steps until the segmented temperature control strategy ends, and the resulting spatial distribution of solvent concentration inside the ink is the residual solvent distribution.

8. The system according to claim 3, characterized in that, The method for constructing the three-dimensional temperature field evolution model includes: A three-dimensional spatial mesh is established based on the geometric dimensions of the ink layer; Based on the spatial distribution of the latent heat absorption term, a heat source term is assigned to each grid point in the three-dimensional spatial grid. Based on the heat conduction equations between adjacent grid points, a set of partial differential equations for the temperature field is constructed. Based on the dynamic update of the boundary conditions, the partial differential equations are solved using the finite difference method to obtain the spatiotemporal evolution trajectory of the three-dimensional temperature field, which is the three-dimensional temperature field evolution model.

9. The system according to claim 5, characterized in that, The method for determining the formation of the continuous solid film includes: The concentration difference between adjacent sampling points is calculated based on the radial gradient of the surface solvent concentration. The degree of surface homogenization is determined based on the proportion of sampling points where the concentration difference is less than a preset uniformity threshold. Predict the surface rheological properties based on the relationship between surface viscosity and temperature and solvent content; When the rheological properties reach the solid-state threshold and the homogenization degree exceeds a preset ratio, it is determined that the continuous solid phase film has been formed.

10. The system according to claim 1, characterized in that, The real-time adjustment method for the heating rate includes: Based on the distribution of residual solvent, identify areas of high solvent concentration; The solvent breach risk level is assessed based on the distance between the high-concentration area and the already crusted surface. Based on the solvent breach risk level, determine the adjustment factor for the heating rate; The corrected heating rate is calculated based on the difference between the current temperature and the target temperature, combined with the adjustment coefficient. Based on the modified mapping relationship between heating rate and heating power, the output power of the heating element is adjusted in real time.

Images