A temperature gradient analysis method and device for a copper foil plating apparatus

Abstract

The application provides a copper foil electroplating equipment temperature gradient analysis method and device, comprising: obtaining real-time temperature data of each sector of the roller surface, combining the temperature difference of the cooling liquid inlet area and the outlet area to form an initial data record; identifying a local surface temperature difference expansion value according to the initial data record and the current speed of the roller body; determining the deviation coefficient of the actual temperature gradient and the surface temperature difference of the deposition area according to the surface temperature difference expansion value; correcting the real-time temperature data using the deviation coefficient to obtain the real temperature distribution state of the deposition area and divide it into three temperature gradient categories: uniform area, transition area and abnormal area; determining the temperature imbalance area that needs to be controlled according to the distribution range of the three temperature gradient categories of the uniform area, the transition area and the abnormal area; predicting the future change trend of the circumferential temperature difference of the roller surface for the temperature imbalance area, determining and executing the temperature uniformity control scheme to make the temperature gradient of the deposition area tend to be stable.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method and apparatus for analyzing temperature gradients in copper foil electroplating equipment. Background Technology

[0002] In the industrial manufacturing sector, copper foil production, as a crucial step in electronic material manufacturing, directly impacts the performance and stability of electronic products, making its quality control paramount. Particularly in electroplating equipment, the uniformity of temperature distribution plays a decisive role in controlling copper foil thickness; even slight deviations can lead to substandard product quality, affecting the reliability of downstream supply chains. Therefore, accurately monitoring and controlling temperature changes during equipment operation has become a focal point in the industry. However, existing methods for addressing temperature distribution often overlook the dynamic interactions of various factors during equipment operation. Many solutions focus solely on measuring and adjusting surface temperature, failing to deeply analyze the impact of changes in the internal heat transfer path on the overall temperature field. This limitation significantly reduces the effectiveness of temperature control under complex operating conditions, especially when equipment operating parameters change, making it difficult to accurately determine the true trend of temperature distribution. A deeper technical challenge lies in the highly complex impact of changes in roller rotation speed on temperature distribution. Roller speed not only affects the heat transfer path but also alters the internal coolant circulation distribution, thus producing unpredictable effects on the temperature gradient in the copper foil deposition area. This imbalance in heat distribution caused by changes in roller speed directly leads to difficulties in standardizing the criteria for judging temperature gradients. For example, during production, when the roller speed increases, the temperature difference in a certain area of ​​the surface may appear to increase, but due to the redistribution of the internal coolant, the actual temperature change in the deposition area may tend to level off. This contradiction between appearance and reality renders traditional temperature control methods ineffective. Therefore, accurately identifying the true temperature distribution trend of the copper foil deposition area under dynamically changing roller speeds and establishing appropriate judgment criteria has become a key issue in improving the uniformity control of copper foil thickness. Summary of the Invention

[0003] This invention provides a method for analyzing the temperature gradient in copper foil electroplating equipment, mainly including: Acquire real-time temperature data for each sector of the roller surface, and combine the temperature difference between the coolant inlet and outlet zones to form initial data records; Based on the real-time temperature data of each sector of the roller surface recorded in the initial data, the temperature difference between adjacent sectors is analyzed, and the temperature difference between adjacent sectors is fitted with the roller rotation speed change to identify the local surface temperature difference expansion value. The deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference is determined based on the surface temperature difference expansion value and the actual temperature gradient from the inner wall to the outer wall of the deposition area. The temperature data of each sector were corrected using the deviation coefficient to obtain the true temperature distribution of the deposition area, and the area was divided into three temperature gradient categories: uniform zone, transition zone, and abnormal zone. Based on the distribution range of the three temperature gradient categories—uniform region, transition region, and abnormal region—the temperature imbalance areas that require key regulation are identified. For areas with temperature imbalance, predict the future trend of the circumferential temperature difference on the roller surface, determine and implement a temperature uniformity control scheme to stabilize the temperature gradient in the deposition area.

[0004] Furthermore, the acquisition of real-time temperature data for each sector of the roller surface, combined with the temperature difference between the coolant inlet and outlet zones to form initial data records, includes: Multiple sector roller surface temperature values ​​are acquired, real-time flow rate data is obtained from the coolant main pipeline, and the current rotation speed signal is obtained from the encoder of the roller drive motor. The temperature gradient change pattern is identified based on the spatial distribution of sector temperature values, and temperature field data containing the temperature values ​​and gradient distribution of each sector is obtained. The inlet and outlet temperatures of coolant are collected based on the gradient distribution in the temperature field data, and the heat exchange is calculated. The heat load distribution of each sector is determined based on the ratio of the heat exchange to the roller rotation speed, and initial data records are formed.

[0005] Furthermore, based on the real-time temperature data of each sector of the roller surface recorded in the initial data analysis, the temperature difference between adjacent sectors is analyzed, and the temperature difference between adjacent sectors is fitted with the roller rotation speed change to identify the local surface temperature difference expansion value, including: Based on the real-time temperature data of each sector of the roller surface recorded in the initial data analysis, the temperature difference between adjacent sectors is analyzed, the area where the temperature difference exceeds the preset threshold is identified, and the temperature difference between adjacent sectors and the change of roller speed are linearly fitted to determine the local surface temperature difference expansion value.

[0006] Furthermore, based on the surface temperature difference amplification value and the actual temperature gradient from the inner wall to the outer wall of the deposition area, the deviation coefficient between the actual temperature gradient and the surface temperature difference in the deposition area is determined, including: The radial temperature distribution on the roller wall is obtained, the actual temperature gradient value of the deposition area is identified, the degree of radial temperature transmission attenuation is identified by comparing the ratio of the actual temperature gradient value to the expansion value of the surface temperature difference, and the deviation coefficient between the actual temperature gradient and the surface temperature difference in the deposition area is determined by combining the degree of radial temperature transmission attenuation.

[0007] Furthermore, the temperature data of each sector is corrected using a deviation coefficient to obtain the true temperature distribution of the deposition area, and is divided into three temperature gradient categories: uniform zone, transition zone, and anomalous zone, including: The temperature data of each sector collected in real time is corrected using a deviation coefficient. The difference between the surface temperature and the actual internal temperature is eliminated by multiplying the original temperature value by the deviation coefficient. The temperature field distribution of the deposition area is reconstructed based on the corrected temperature value to obtain corrected temperature data. The temperature sequence is extracted along the copper foil growth direction based on the corrected temperature data. The temperature difference between adjacent sampling points is calculated and divided by the sampling interval to obtain the local temperature gradient value. If the gradient value is less than a preset uniformity threshold, it is marked as a uniform region. If the gradient value is between the uniformity threshold and the abnormal threshold, it is marked as a transition region. If the gradient value is greater than the abnormal threshold, it is marked as an abnormal region. Three categories of temperature gradient distribution are determined. The distribution state of the three temperature gradient categories divided according to the copper foil growth direction is determined based on the temperature gradient distribution.

[0008] Furthermore, based on the distribution range of the three temperature gradient categories—uniform region, transition region, and abnormal region—the temperature imbalance areas requiring key regulation are identified, including: Based on the distribution range of the three temperature gradient categories, the spatial coordinates and area proportions of the uniform zone, transition zone, and abnormal zone are extracted. Combined with the time series data of the roller speed from start-up to stable operation, Fourier transform is used to identify the main frequency component and phase information of speed fluctuations. The time change of temperature category distribution is mapped to the speed cycle to obtain the response characteristics of each category area with speed change. Using the response characteristics of each category area with speed change, a monitoring time window is set according to the speed cycle length in each temperature gradient category area. The standard deviation and mean of temperature values ​​within the window are statistically analyzed. The coefficient of variation is calculated by the ratio of the standard deviation to the mean. If the coefficient of variation is less than a preset value, it is determined to be a stable state. The temperature fluctuation stability index of each area is determined according to the proportion of the stable state duration to the total monitoring time. The stability index is used to identify the temperature imbalance area.

[0009] Furthermore, for areas of temperature imbalance, the future trend of circumferential temperature difference on the roller surface is predicted, and a temperature uniformity control scheme is determined and implemented to stabilize the temperature gradient in the deposition area, including: For areas with temperature imbalance, an autoregressive moving average model is used to predict future temperature values ​​based on historical temperature data sequences, determine the future trend of the circumferential temperature difference of the roller surface, allocate sector flow based on the future trend of the circumferential temperature difference of the roller surface, and determine and implement a temperature uniformity control scheme.

[0010] Furthermore, the flow rate of each sector is allocated based on the future trend of the circumferential temperature difference of the roller surface, and a temperature uniformity control scheme is determined and implemented. This includes: identifying the heat transfer delay time when the roller speed changes; adjusting the coolant flow rate in advance according to the delay time to compensate for the time difference before the speed change; determining the flow rate compensation value at different speeds; correcting the actual liquid supply of each sector using the flow rate compensation value at different speeds; monitoring the real-time change of the temperature gradient in the deposition area; and determining that the temperature uniformity control is effective if the temperature gradient value in the deposition area continues to decrease and the rate of change of the temperature gradient in the deposition area approaches zero.

[0011] Furthermore, the flow compensation value at different speeds is determined, including: determining the flow compensation value at different speeds based on the principle of increasing the flow rate in advance when the speed increases and decreasing the flow rate in a delayed manner when the speed decreases.

[0012] This invention provides a temperature gradient analysis device for copper foil electroplating equipment, mainly comprising: The data acquisition module is used to acquire real-time temperature data of each sector of the roller surface and combine it with the temperature difference between the coolant inlet and outlet zones to form initial data records. The temperature difference identification module is used to analyze the temperature difference between adjacent sectors based on the real-time temperature data of each sector of the roller surface recorded in the initial data, and to fit the temperature difference between adjacent sectors with the change of roller rotation speed to identify the local surface temperature difference expansion value. The deviation coefficient determination module is used to determine the deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference based on the surface temperature difference expansion value and the actual temperature gradient of the deposition area from the inner wall to the outer wall. The temperature correction module is used to correct the temperature data of each sector using the deviation coefficient to obtain the true temperature distribution of the deposition area and divide it into three temperature gradient categories: uniform zone, transition zone and abnormal zone. The region determination module is used to identify the temperature imbalance regions that require key control based on the distribution range of the three temperature gradient categories: uniform region, transition region, and abnormal region. The control and execution module is used to predict the future trend of the circumferential temperature difference of the roller surface in areas of temperature imbalance, determine and execute the temperature uniformity control scheme, so that the temperature gradient in the deposition area tends to be stable.

[0013] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: This invention discloses a method and apparatus for temperature gradient analysis in copper foil electroplating equipment, aiming to solve the temperature imbalance problem caused by uneven temperature distribution on the roller surface and uncoordinated coolant circulation. By real-time acquisition of temperature data from each sector of the roller surface and coolant flow and rotation speed information, this invention constructs an initial temperature distribution record and identifies the impact of changes in heat transfer paths on temperature. It then analyzes the effect of surface temperature difference expansion and coolant flow trajectory on heat transfer efficiency, determines a temperature deviation coefficient to correct real-time data, classifies temperature gradient categories, calculates the temperature fluctuation stability index within the region, and accurately locates the imbalance area. Finally, by predicting the temperature difference change trend, this invention dynamically adjusts the coolant flow distribution ratio and compensates for the heat transfer time difference caused by rotation speed changes, achieving coordinated control of coolant circulation and rotation speed, thus stabilizing the temperature gradient in the deposition area. Its core technical effect is to significantly improve the uniformity of roller surface temperature, optimize the stability of the deposition process, and provide an efficient and reliable temperature control solution for related industrial production. Attached Figure Description

[0014] Fig. 1 This is a flowchart of a temperature gradient analysis method for copper foil electroplating equipment according to the present invention.

[0015] Fig. 2 This is a schematic diagram of the temperature gradient analysis device for copper foil electroplating equipment according to the present invention. Detailed Implementation

[0016] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0017] like Figs. 1-2 This embodiment of a method and apparatus for analyzing temperature gradients in copper foil electroplating equipment may specifically include: S101. Obtain real-time temperature data for each sector of the roller surface, and combine it with the temperature difference between the coolant inlet and outlet zones to form an initial data record.

[0018] Temperature sensors arranged at preset angular intervals along the circumference of the roller body acquire roller surface temperature values ​​for multiple sectors. Simultaneously, real-time flow rate data is read from the electromagnetic flowmeter in the coolant main pipeline, and the current rotational speed signal is obtained from the encoder of the roller drive motor. The temperature gradient variation pattern is identified based on the spatial distribution of sector temperature values, resulting in temperature field data containing the temperature values ​​and gradient distribution of each sector. Based on the gradient distribution in the temperature field data, coolant temperature is collected from temperature sensors in the inlet and outlet pipelines, and the inlet-outlet temperature difference is calculated. If the temperature difference exceeds a preset threshold, the heat exchange rate per unit time is calculated by multiplying the flow rate data by the coolant's specific heat capacity and density. Based on the ratio of the heat exchange rate to the roller rotational speed, the heat load distribution of each sector is determined, forming an initial data record containing sector temperature, coolant parameters, and roller rotational speed.

[0019] In one embodiment, the temperature sensor along the circumference of the roller is a platinum resistance temperature sensor with a response time of less than 0.5 seconds, enabling real-time capture of dynamic changes in roller surface temperature. The preset angle interval is determined based on the roller diameter and production accuracy requirements, typically set to 10 to 15 degrees to ensure that the spatial resolution of temperature acquisition meets the needs of subsequent gradient analysis. The identification of temperature gradient change patterns is achieved through differential calculation of temperature values ​​between adjacent sectors. First, the temperature difference between adjacent sectors is calculated, then a temperature distribution curve is constructed along the circumference. Second-order differential analysis identifies acceleration and deceleration regions of temperature change, thereby determining the spatial distribution characteristics of the temperature gradient.

[0020] For example, the calculation of heat exchange is performed using the basic formula of heat transfer. Where c is the specific heat capacity of the coolant, m is the mass flow rate of the coolant per unit time, obtained by multiplying the flow velocity data by the cross-sectional area of ​​the pipe and the density of the coolant, and ΔT is the temperature difference between the inlet and outlet liquids. Determining the heat load distribution requires comprehensive consideration of the roller rotation speed. When the roller rotates at high speed, the path of heat transfer from the surface to the interior changes periodically. By dividing the heat exchange amount by the product of the roller circumference and the rotation speed, the heat load density per unit arc length is obtained, thus forming the heat load distribution map of each sector.

[0021] S102. Analyze the temperature difference between adjacent sectors based on the real-time temperature data of each sector of the roller surface recorded in the initial data, and fit the temperature difference between adjacent sectors with the change of roller rotation speed to identify the local surface temperature difference expansion value.

[0022] Based on the temperature values ​​of each sector in the initial data record, the ratio of the roller's rotation angle per unit time to the temperature acquisition cycle is calculated to identify the temperature data's variation characteristics over time. By comparing the temperature differences of the same sector at adjacent moments, the amplitude of temperature fluctuations caused by roller rotation is obtained, and the path distribution of heat transfer from the high-temperature zone to the low-temperature zone is determined. Using the path distribution data, the temperature values ​​of each sector of the roller at different rotation speeds are extracted, and the temperature difference of the same sector before and after the rotation speed change is calculated. Simultaneously, the inlet and outlet pressure difference is obtained from the pressure sensor of the coolant circulation pipeline. If the pressure difference exceeds a preset threshold, the intensity of the effect of the heat transfer path change on the roller surface temperature is determined based on the product of the pressure difference and the temperature difference. By comparing the intensity of the effect with the temperature acquisition values ​​of each sector at the current rotation speed, the temperature difference between adjacent sectors is calculated, areas where the temperature difference exceeds the preset threshold are identified, and the local surface temperature difference expansion value is determined based on the ratio of the rotation speed change amplitude to the temperature difference.

[0023] In one implementation, the path distribution data is obtained based on the thermal conduction characteristics during the roller rotation process. When the roller rotates at a specific speed, heat from the high-temperature region is transferred to the low-temperature region along the thermal conductivity direction of the roller material, while simultaneously being affected by the coolant circulation, forming a dynamic temperature field distribution. By continuously collecting the temperature values ​​of each sector at different times, the direction with the largest temperature gradient is identified as the main heat transfer path.

[0024] Specifically, the intensity of the effect of changes in heat transfer path on roller surface temperature reflects the degree of influence of rotational speed changes on temperature field stability. During copper foil electroplating, when the roller speed increases from 30 rpm to 50 rpm, the contact time between the roller surface and the electrolyte shortens, and the heat exchange per unit area changes. Simultaneously, the flow state of the coolant inside the roller also changes, transitioning from laminar to turbulent flow, leading to a significant increase in the heat transfer coefficient. This effect is quantified by the product of the pressure difference and the temperature difference, its physical meaning being to reflect the degree of influence of the change in coolant flow state on temperature control. When the pressure difference increases, it indicates that the coolant flow rate is faster, carrying away more heat, and the corresponding temperature change amplitude will also increase. Determining the magnitude of the increase in local surface temperature difference involves the periodic characteristics of roller rotation. Under a stable rotational speed, the temperature of each sector exhibits periodic fluctuations, with a relatively stable temperature difference between adjacent sectors. However, when the rotational speed changes, this balance is disrupted, and the temperature difference in some areas increases sharply.

[0025] In one possible implementation, by establishing a ratio between the speed change and the temperature difference, the trend of temperature difference widening can be accurately predicted. When the speed increases by 20%, if the temperature difference exceeds a preset threshold, it indicates that the thermal balance in that region is out of balance, and the coolant flow distribution needs to be adjusted to compensate.

[0026] Preferably, the ratio relationship is determined by a linear fitting method. By collecting historical data at different speeds, a correspondence between the speed change rate and the temperature difference change rate is established. This method can adapt to the temperature control requirements of rollers of different specifications and achieve a rapid response to local temperature anomalies.

[0027] S103. Determine the deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference based on the surface temperature difference expansion value and the actual temperature gradient from the inner wall to the outer wall of the deposition area.

[0028] A flow velocity sensor array arranged axially and radially inside the roller body acquires the flow velocity values ​​of the coolant at different locations, recording the path of the coolant from the inlet through each internal channel to the outlet. The volumetric flow rate of each region is calculated based on the flow velocity values ​​and the channel cross-sectional area, resulting in a spatiotemporal distribution map of the coolant flow trajectory. Based on this spatiotemporal distribution map, the average flow velocity of the coolant in the corresponding internal channel of the deposition area is extracted. The residence time is calculated using the ratio of flow velocity to channel length. The convective heat transfer coefficient is calculated using the Nusselt number correlation based on the coolant's physical properties and flow state. If the residence time is less than a preset threshold, insufficient heat transfer is determined. The heat transfer efficiency of each deposition area is determined by multiplying the convective heat transfer coefficient by the coolant temperature difference. Using the heat transfer efficiency data, the radial thermal resistance is calculated based on the roller body material's thermal conductivity and wall thickness. The radial temperature distribution is acquired using temperature sensors embedded at different depths in the roller body wall. The temperature gradient change characteristics are identified based on the slope of the temperature distribution curve, yielding the actual temperature gradient value from the inner wall to the outer wall of the deposition area. By comparing the ratio of the actual temperature gradient value to the surface temperature difference amplification value, the degree of temperature attenuation during radial transmission is identified. Combined with the thickness of the thermal boundary layer formed on the inner wall after the coolant redistribution, the deviation coefficient between the actual temperature gradient and the surface temperature difference in the deposition area is determined based on the difference between the temperature gradient in the thermal boundary layer and the temperature gradient in the mainstream area.

[0029] In one embodiment, the flow rate sensor array is arranged in a three-dimensional mesh configuration. A monitoring section is set every 100 mm along the roller axis, with four sensor nodes radially distributed on each section, located at distances of 5 mm, 15 mm, 25 mm, and 35 mm from the inner wall surface, respectively. This arrangement can capture the flow rate changes of the coolant at different radial depths, particularly the flow rate gradient near the wall. The sensors are thermal mass flow sensors, calculating the flow rate by measuring the heat carried away by the fluid, with a response time of less than 0.1 seconds, enabling real-time reflection of the dynamic changes in the coolant flow state.

[0030] Specifically, the construction of the spatiotemporal distribution map involves three-dimensional reconstruction of the data. First, the instantaneous flow velocity data of each sensor node are arranged according to spatial coordinates to form a flow velocity matrix. Then, an interpolation algorithm is used to spatially interpolate the discrete measurement point data to obtain a continuous flow velocity field distribution. In the time dimension, flow velocity changes are recorded at a sampling interval of 0.5 seconds, and the periodic characteristics and transient fluctuations of the flow are identified through time series analysis. The spatiotemporal distribution map not only reflects the mainstream direction of the coolant but also reveals the influence of local flow phenomena such as eddies and backflow on the heat transfer process. The choice of the Nusselt number correlation depends on the flow state and geometric characteristics. For the annular channel flow inside the roller body, when the Reynolds number Re is between 2300 and 10000, the flow is in the transition zone, and the Gnielinski correlation is used to calculate the Nusselt number Nu. This correlation considers the influence of the fluid Prandtl number Pr, Reynolds number Re, and pipe length-to-diameter ratio, and the expression is: Where f is the friction factor, calculated using the Filonenko formula. Once the Nusselt number is determined, the convective heat transfer coefficient h is obtained through... The calculation is performed, where k is the thermal conductivity of the coolant and D is the characteristic length. This calculation method fully considers the influence of the flow state on the heat transfer intensity and can accurately predict the heat transfer efficiency under different operating conditions.

[0031] For example, the calculation of residence time needs to take into account the actual path of the streamline. After entering from the inlet, the coolant does not flow in a straight line to the outlet, but rather along a spiral path. By tracking the movement of tracer particles, it was found that the actual flow path of the coolant in the internal channels corresponding to the deposition area is 1.3 to 1.5 times the straight-line distance. The residence time is equal to the actual flow path divided by the average flow velocity, typically between 2 and 5 seconds.

[0032] In one possible implementation, the radial thermal resistance is calculated based on a cylindrical wall thermal conductivity model. The roller wall can be considered as a multi-layered cylindrical wall, with each layer having a thermal resistance... Where r1 and r2 are the inner and outer radii, respectively, L is the axial length, and k is the thermal conductivity of the material. For a copper roller, the thermal conductivity is approximately 380 W / (m·K), and the radial thermal resistance with a wall thickness of 20 mm is approximately 0.0001 K / W.

[0033] Preferably, the temperature sensor uses an armored thermocouple with a diameter of 2 mm, pre-embedded at different depths on the roller wall through radial drilling. Five temperature measurement points are set at each monitoring point, located on the inner wall, at 1 / 4 of the wall thickness, 1 / 2 of the wall thickness, 3 / 4 of the wall thickness, and the outer wall. The temperature data from these measurement points are used to fit a radial temperature distribution curve using the least squares method; the first derivative of the curve is the temperature gradient. The formation of a thermal boundary layer is an inevitable result of heat exchange between the fluid and the solid wall. When the coolant flows through the inner wall of the roller, the fluid layer close to the wall has a near-zero velocity due to viscosity, forming a velocity boundary layer. Simultaneously, the temperature difference between the wall and the fluid leads to a large temperature gradient in the near-wall region, forming a thermal boundary layer. The thermal boundary layer thickness δt is related to the flow Reynolds number and Prandtl number, and is typically determined by... The thickness of the velocity boundary layer is estimated, where δ represents the thickness of the thermal boundary layer. Under typical operating conditions, the thermal boundary layer thickness is approximately 2 to 5 millimeters, within which the temperature gradient can reach more than 10 times that of the mainstream region. Furthermore, determining the deviation coefficient requires comprehensive consideration of multiple factors. The actual temperature gradient value reflects the true heat transfer within the roller wall, while the expansion of the surface temperature difference is an externally observed phenomenon. The ratio between the two is influenced by factors such as the coolant flow state, wall material properties, and the degree of thermal boundary layer development. Statistical analysis of a large amount of experimental data reveals that the deviation coefficient is typically between 0.6 and 0.85. When the coolant flow rate increases, the thermal boundary layer thins, and the deviation coefficient tends towards 1; conversely, when the flow rate decreases, the thermal boundary layer thickens, and the deviation coefficient decreases.

[0034] S104. The temperature data of each sector is corrected using the deviation coefficient to obtain the true temperature distribution of the deposition area and divided into three temperature gradient categories: uniform zone, transition zone, and abnormal zone.

[0035] The temperature data of each sector acquired in real time is corrected using a deviation coefficient. By multiplying the original temperature value by the deviation coefficient, the difference between the surface temperature and the actual internal temperature is eliminated. The temperature field distribution of the deposition area is reconstructed based on the corrected temperature values ​​to obtain corrected temperature data reflecting the true thermal state. Based on the corrected temperature data, a temperature sequence is extracted along the growth direction of the copper foil from the cathode outwards. The temperature difference between adjacent sampling points is calculated and divided by the sampling interval to obtain the local temperature gradient value. If the gradient value is less than a preset uniformity threshold, it is marked as a uniform region; if the gradient value is between the uniformity threshold and the abnormal threshold, it is marked as a transition region; if the gradient value is greater than the abnormal threshold, it is marked as an abnormal region, thus determining the temperature gradient distribution of three categories. Using the temperature gradient distribution data, the spatial proportion of uniform regions, transition regions, and abnormal regions along the growth direction is statistically analyzed. By identifying the boundary positions and sizes of each category of region, the overall uniformity of the temperature distribution is judged, resulting in the distribution status of the three temperature gradient categories divided according to the copper foil growth direction.

[0036] In one implementation, the deviation coefficient is applied based on the nonlinear transmission characteristics of the temperature field. After the raw temperature data is acquired by the sensor, due to the hysteresis of heat conduction and the heat capacity effect of the roller material, the surface temperature value measured deviates systematically from the actual internal temperature. By multiplying the raw temperature value of each sector by the corresponding deviation coefficient, the true temperature state of the deposition area can be restored. The deviation coefficient is dynamically adjusted according to the actual operating conditions within the range of 0.6 to 0.85; a coefficient close to 1 is used when the roller speed is high, and a smaller coefficient value is used when the speed is low.

[0037] Specifically, the copper foil growth direction refers to the radial direction outward from the cathode surface. Under the influence of an electric field, copper ions are reduced on the cathode surface and deposited layer by layer. The temperature distribution along this direction directly affects the crystal quality and thickness uniformity of the copper foil. The temperature gradient is calculated using a differential method. A sampling point is set every 0.5 mm along the growth direction, and the temperature difference between adjacent sampling points divided by 0.5 mm yields the local temperature gradient value at that location. The classification of the three temperature gradient categories is based on the thermodynamic characteristics of the copper foil deposition process. The temperature gradient in the uniform region is typically less than 2℃ / mm. In this region, the reduction rate of copper ions is stable, resulting in fine and uniform copper foil grains. The temperature gradient in the transition region is between 2℃ / mm and 5℃ / mm. The copper foil thickness in this region may fluctuate slightly but remains within an acceptable range. The temperature gradient in the abnormal region exceeds 5℃ / mm. At this point, the local temperature changes are drastic, easily leading to defects such as pinholes and wrinkles in the copper foil.

[0038] Preferably, the overall temperature control quality is evaluated by statistically analyzing the spatial proportion of each category of area. When the proportion of the uniform area exceeds 70%, it indicates good temperature control; when the proportion of the abnormal area exceeds 15%, the coolant flow rate or roller speed needs to be adjusted immediately. The boundary position is identified using a gradient abrupt change detection method. When the gradient value change between adjacent positions exceeds 1℃ / mm, it is determined to be a category boundary.

[0039] In one possible implementation, the temperature gradient distribution is presented in the form of a visual map, using different colors to identify three categories of areas, so that operators can intuitively understand the temperature distribution and promptly identify potential quality risk areas.

[0040] S105. Based on the distribution range of the three temperature gradient categories—uniform region, transition region, and abnormal region—determine the temperature imbalance areas that require key control.

[0041] Based on the distribution range of the three temperature gradient categories, the spatial coordinates and area proportions of the uniform zone, transition zone, and abnormal zone are extracted. Combined with the time series data of the roller speed from startup to stable operation, Fourier transform is used to identify the dominant frequency component and phase information of speed fluctuations, mapping the temporal changes of temperature category distribution onto the speed cycle to obtain the response characteristics of each category region with speed changes. Using the aforementioned response characteristics, a monitoring time window is set according to the speed cycle length within each temperature gradient category region. The standard deviation and mean of temperature values ​​within the window are statistically analyzed. The coefficient of variation is calculated by the ratio of the standard deviation to the mean. If the coefficient of variation is less than 0.1, it is determined to be a stable state. The temperature fluctuation stability index of each region is determined based on the proportion of the stable state duration to the total monitoring time. By comparing the stability index, regions with an index below 0.6 are marked as imbalance candidate regions. According to the rule of assigning a weight of 1.0 to the abnormal zone, a weight of 0.6 to the transition zone, and a weight of 0.3 to the uniform zone, the product of the weight value of each candidate region and the reciprocal of the stability index is calculated as the imbalance score. The top three regions in the score ranking are determined as temperature imbalance regions.

[0042] In one implementation, the response characteristics are obtained based on the dynamic influence mechanism of rotational speed changes on temperature distribution. Periodic changes in roller rotational speed cause periodic disturbances in the coolant flow field, leading to periodic fluctuations in the temperature field. By performing a Fourier transform on the rotational speed time series, the dominant frequency components of the rotational speed changes can be extracted, typically within the range of 0.1 Hz to 1 Hz. Simultaneously, the area percentage of each temperature category region is recorded over time, and cross-correlation analysis is performed between these curves and the rotational speed spectrum to identify the response delay and amplitude of the temperature distribution to rotational speed changes.

[0043] Specifically, the monitoring time window length is set to an integer multiple of the rotation speed cycle, typically 3 to 5 cycles. Within each window, temperature data is continuously collected and its statistical characteristics are calculated. The coefficient of variation, as a measure of relative dispersion, can eliminate the influence of absolute fluctuations at different temperature levels. When the coefficient of variation is less than 0.1, it indicates that the temperature fluctuation amplitude is small relative to the average temperature level, and the system is in a stable operating state. The stability index is quantified by the proportion of time in a statistically stable state, reflecting the reliability of temperature control in that area. The weighting rules are set based on the degree of influence of different categories of areas on product quality. The abnormal area, due to its excessive temperature gradient, is prone to uneven copper foil thickness or even defects, and therefore is given the highest weight of 1.0. Although the temperature gradient in the transition area is within an acceptable range, there is a risk of transformation into an abnormal area, so it is given a medium weight of 0.6. The uniform area has an ideal temperature distribution and the least impact on product quality, so it is given a low weight of 0.3. The imbalance score is calculated by multiplying the weight value by the reciprocal of the stability index; the worse the stability of the area, the larger its reciprocal, and the higher the score obtained after multiplying by the weight.

[0044] Preferably, after identifying the temperature imbalance region, differentiated control strategies are formulated based on the imbalance score. The region with the highest score prioritizes adjusting the coolant flow rate, the region with the second highest score adjusts the local rotational speed of the rollers, and the region with the third highest score increases the frequency of temperature monitoring.

[0045] For example, when the stability index of an abnormal region is 0.4, its imbalance score is 1.0 × (1 / 0.4) = 2.5; when the stability index of a transition region is 0.5, its imbalance score is 0.6 × (1 / 0.5) = 1.2. Through this quantitative scoring mechanism, the temperature imbalance regions that most need to be focused on for regulation can be objectively identified.

[0046] S106. For areas with temperature imbalance, predict the future trend of the circumferential temperature difference on the roller surface, determine and implement a temperature uniformity control scheme to stabilize the temperature gradient in the deposition area.

[0047] For areas of temperature imbalance, an autoregressive moving average model is used to predict future temperature values ​​based on historical temperature data sequences. The temperature change trend is identified by calculating the difference between the predicted and current temperatures. Combined with the temperature differences between adjacent sectors along the roller surface, sectors requiring urgent control are marked if the rate of increase in temperature difference exceeds a preset threshold, thus obtaining temperature change prediction data. Based on the location and temperature deviation of the sectors requiring urgent control in the prediction data, the current coolant flow rate of the corresponding sector is obtained. The required heat change is obtained by dividing the temperature deviation by the heat transfer coefficient, and then by the coolant's specific heat capacity and density to obtain the flow rate adjustment. Proportional-integral control is used to calculate the valve opening adjustment value based on the deviation and the rate of change of deviation, forming an optimized flow distribution scheme. Using this flow distribution scheme, the delay time of heat transfer when the roller speed changes is identified. The time difference is compensated by adjusting the coolant flow rate in advance according to the delay time before the speed change. Based on the principle of increasing the flow rate in advance when the speed increases and decreasing the flow rate after the speed decreases, the flow compensation value at different speeds is determined. The actual liquid supply of each sector is corrected by the compensation value, and the real-time change of the temperature gradient in the deposition area is monitored. If the gradient value continues to decrease and the rate of change approaches zero, the control is determined to be effective, and the coordinated control of the coolant circulation distribution and the roller speed is executed to keep the temperature gradient in the deposition area stable.

[0048] In one implementation, the autoregressive moving average model is constructed based on the historical data characteristics of temperature time series. The model decomposes the temperature series into an autoregressive component and a moving average component. The autoregressive component reflects the inertial characteristics of temperature, while the moving average component captures the effects of random disturbances. The model's order parameter is determined by analyzing temperature data collected every 5 minutes over the past 48 hours. An autoregressive order of 3 to 5 and a moving average order of 1 to 2 typically strike a good balance between prediction accuracy and computational efficiency. The model estimates parameters using the least squares method to predict the temperature change trend over the next 30 minutes.

[0049] Specifically, identifying temperature change trends requires comprehensive consideration of both time and space dimensions. In the time dimension, the difference between the predicted temperature and the current measured temperature is compared to determine whether the temperature is trending upwards or downwards. In the spatial dimension, the temperature difference between adjacent circumferential sectors is calculated; when the rate of increase in this difference exceeds 0.5℃ per minute, it indicates that the unevenness of temperature distribution is intensifying. Combining the analysis of time trends and spatial differences identifies key areas for temperature control. The calculation of flow rate adjustment is based on Newton's law of cooling and the principle of energy conservation. The change in heat is equal to the product of the heat transfer coefficient, the heat exchange area, and the temperature difference. For cylindrical rollers, the heat exchange area is the inner surface area of ​​the roller corresponding to the sector. The heat transfer coefficient depends on the flow state of the coolant; it is approximately 500 W / (m²·K) for laminar flow and can reach 2000 W / (m²·K) for turbulent flow. When the temperature of a certain sector deviates from the target value by 3℃, the required change in heat is calculated using Q=hAΔT. Based on the coolant's specific heat capacity of 4.2 kJ / (kg·K) and density of 1000 kg / m³, the change in heat is converted into a volumetric flow rate adjustment. This flow rate adjustment is achieved by changing the opening of the electric regulating valve on the corresponding sector's supply pipeline; the valve opening and flow rate have an approximately linear relationship.

[0050] For example, the implementation process of proportional-integral (PI) control includes two parts: a proportional term and an integral term. The proportional term immediately generates a control action based on the current temperature deviation, and its gain coefficient Kp is typically set to 0.3 to 0.5. The integral term accumulates historical deviations to eliminate steady-state errors, and its integral time constant Ti is set to 100 to 200 seconds. The control output is... Where e(t) is the temperature deviation. This control method can ensure response speed while avoiding overshoot oscillation.

[0051] Preferably, the heat transfer delay time is determined through an impulse response experiment. Under stable roller operation, the coolant flow rate in a certain sector is suddenly changed, and the moment the temperature in that sector begins to change is recorded; the time difference between these two changes is the delay time. The delay time is related to the roller wall thickness, the material's thermal diffusivity, and the current rotational speed. For a 20mm thick copper roller, the delay time is approximately 8 to 12 seconds at 30 rpm, decreasing to 5 to 8 seconds when the speed is increased to 60 rpm.

[0052] In one possible implementation, the compensation mechanism employs a feedforward control approach. When a change in roller speed is detected, the coolant flow rate is adjusted in advance. If the speed is about to increase, the relative velocity between the roller surface and the electrolyte increases, enhancing convective heat transfer, requiring an increase in coolant flow rate to absorb the additional heat. The advance amount equals the delay time, ensuring that the effect of the flow rate adjustment is synchronized with the speed change.

[0053] Understandably, the core of coordinated control lies in synchronizing the coolant circulation cycle with the roller rotation cycle. The time it takes for the coolant to flow out of the roller constitutes one circulation cycle, and the time it takes for the roller to rotate once is the rotation cycle. By adjusting the total coolant flow rate, the two cycles are kept in an integer multiple relationship, avoiding beat frequency phenomena in temperature control. Furthermore, the stability of the temperature gradient is determined using a sliding window statistical method. Within a 10-minute observation window, the temperature gradient value is calculated every 30 seconds. If the standard deviation of 20 consecutive gradient values ​​is less than 0.1℃ / mm, and the rate of change of the gradient mean is less than 0.01℃ / (mm·min), then the temperature gradient is considered to have reached a stable state.

[0054] For example, in actual production, as the roller gradually accelerates from a low speed to the rated speed, the control system adjusts the coolant supply to each sector in stages according to a preset speed-flow mapping table. The flow rate is lower during the start-up phase, gradually increases during acceleration, and remains constant after stable operation. Through this coordinated control, the uniformity of copper foil thickness is significantly improved, with thickness deviation reduced from ±5% to within ±2%.

[0055] This invention provides a temperature gradient analysis device for copper foil electroplating equipment, mainly comprising: The data acquisition module is used to acquire real-time temperature data of each sector of the roller surface and combine it with the temperature difference between the coolant inlet and outlet zones to form initial data records. The temperature difference recognition module is used to identify the expansion value of the local surface temperature difference based on the initial data record and the current rotation speed of the roller. The deviation coefficient determination module is used to determine the deviation coefficient between the actual temperature gradient and the surface temperature difference in the deposition area based on the surface temperature difference expansion value. The temperature correction module is used to correct real-time temperature data using a deviation coefficient to obtain the true temperature distribution of the deposition area and divide it into three temperature gradient categories: uniform zone, transition zone, and abnormal zone. The region determination module is used to identify the temperature imbalance regions that require key control based on the distribution range of the three temperature gradient categories: uniform region, transition region, and abnormal region. The control and execution module is used to predict the future trend of the circumferential temperature difference of the roller surface in areas of temperature imbalance, determine and execute the temperature uniformity control scheme, so that the temperature gradient in the deposition area tends to be stable.

[0056] Obviously, those skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. Therefore, if these modifications and variations to the embodiments of this application fall within the scope of the claims of this application and their equivalents, this application also intends to include these modifications and variations.

Claims

1. A method for analyzing the temperature gradient in copper foil electroplating equipment, characterized in that, The method includes: Acquire real-time temperature data for each sector of the roller surface, and combine the temperature difference between the coolant inlet and outlet zones to form initial data records; Based on the real-time temperature data of each sector of the roller surface recorded in the initial data, the temperature difference between adjacent sectors is analyzed, and the temperature difference between adjacent sectors is fitted with the roller rotation speed change to identify the local surface temperature difference expansion value. The deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference is determined based on the surface temperature difference expansion value and the actual temperature gradient from the inner wall to the outer wall of the deposition area. The temperature data of each sector were corrected using the deviation coefficient to obtain the true temperature distribution of the deposition area, and the area was divided into three temperature gradient categories: uniform zone, transition zone, and abnormal zone. Based on the distribution range of the three temperature gradient categories—uniform region, transition region, and abnormal region—the temperature imbalance areas that require key regulation are identified. For areas with temperature imbalance, predict the future trend of the circumferential temperature difference on the roller surface, determine and implement a temperature uniformity control scheme to stabilize the temperature gradient in the deposition area.

2. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The process of acquiring real-time temperature data for each sector of the roller surface and combining this data with the temperature difference between the coolant inlet and outlet zones to form initial data records includes: Multiple sector roller surface temperature values ​​are acquired, real-time flow rate data is obtained from the coolant main pipeline, and the current rotation speed signal is obtained from the encoder of the roller drive motor. The temperature gradient change pattern is identified based on the spatial distribution of sector temperature values, and temperature field data containing the temperature values ​​and gradient distribution of each sector is obtained. The inlet and outlet temperatures of coolant are collected based on the gradient distribution in the temperature field data, and the heat exchange is calculated. The heat load distribution of each sector is determined based on the ratio of the heat exchange to the roller rotation speed, and initial data records are formed.

3. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The step of analyzing the temperature difference between adjacent sectors based on the real-time temperature data of each sector of the roller surface recorded in the initial data, and fitting the temperature difference between adjacent sectors with the roller rotation speed change to identify the local surface temperature difference expansion value includes: Based on the real-time temperature data of each sector of the roller surface recorded in the initial data, the temperature difference between adjacent sectors is analyzed, areas where the temperature difference exceeds a preset threshold are identified, and the temperature difference between adjacent sectors is linearly fitted with the roller rotation speed change to determine the local surface temperature difference expansion value.

4. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The step of determining the deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference based on the surface temperature difference amplification value and the actual temperature gradient of the deposition area from the inner wall to the outer wall includes: The radial temperature distribution on the roller wall is obtained, the actual temperature gradient value of the deposition area is identified, the degree of radial temperature transmission attenuation is identified by comparing the ratio of the actual temperature gradient value to the expansion value of the surface temperature difference, and the deviation coefficient between the actual temperature gradient and the surface temperature difference in the deposition area is determined by combining the degree of radial temperature transmission attenuation.

5. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The temperature data of each sector is corrected using a deviation coefficient to obtain the true temperature distribution of the deposition area, and is divided into three temperature gradient categories: uniform zone, transition zone, and anomalous zone. The temperature data of each sector collected in real time is corrected using a deviation coefficient. The difference between the surface temperature and the actual internal temperature is eliminated by multiplying the original temperature value by the deviation coefficient. The temperature field distribution of the deposition area is reconstructed based on the corrected temperature value to obtain corrected temperature data. The temperature sequence is extracted along the copper foil growth direction based on the corrected temperature data. The temperature difference between adjacent sampling points is calculated and divided by the sampling interval to obtain the local temperature gradient value. If the gradient value is less than a preset uniformity threshold, it is marked as a uniform region. If the gradient value is between the uniformity threshold and the abnormal threshold, it is marked as a transition region. If the gradient value is greater than the abnormal threshold, it is marked as an abnormal region. Three categories of temperature gradient distribution are determined. The distribution state of the three temperature gradient categories divided according to the copper foil growth direction is determined based on the temperature gradient distribution.

6. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The determination of temperature imbalance regions requiring key control, based on the distribution range of the three temperature gradient categories—uniform region, transition region, and abnormal region—includes: Based on the distribution range of the three temperature gradient categories, the spatial coordinates and area proportions of the uniform zone, transition zone, and abnormal zone are extracted. Combined with the time series data of the roller speed from start-up to stable operation, Fourier transform is used to identify the main frequency component and phase information of speed fluctuations. The time change of temperature category distribution is mapped to the speed cycle to obtain the response characteristics of each category area with speed change. Using the response characteristics of each category area with speed change, a monitoring time window is set according to the speed cycle length in each temperature gradient category area. The standard deviation and mean of temperature values ​​within the window are statistically analyzed. The coefficient of variation is calculated by the ratio of the standard deviation to the mean. If the coefficient of variation is less than a preset value, it is determined to be a stable state. The temperature fluctuation stability index of each area is determined according to the proportion of the stable state duration to the total monitoring time. The stability index is used to identify the temperature imbalance area.

7. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 1, characterized in that, The method for predicting the future trend of the circumferential temperature difference on the roller surface in areas of temperature imbalance, determining and implementing a temperature uniformity control scheme to stabilize the temperature gradient in the deposition area includes: For areas with temperature imbalance, an autoregressive moving average model is used to predict future temperature values ​​based on historical temperature data sequences, determine the future trend of the circumferential temperature difference of the roller surface, allocate sector flow based on the future trend of the circumferential temperature difference of the roller surface, and determine and implement a temperature uniformity control scheme.

8. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 7, characterized in that, The method of allocating sector flow based on the future trend of the circumferential temperature difference of the roller surface, and determining and implementing the temperature uniformity control scheme, includes: identifying the heat transfer delay time when the roller speed changes, adjusting the coolant flow rate in advance according to the delay time to compensate for the time difference before the speed change, determining the flow compensation value at different speeds, correcting the actual liquid supply of each sector through the flow compensation value at different speeds, monitoring the real-time change of the temperature gradient in the deposition area, and determining that the temperature uniformity control is effective if the temperature gradient value in the deposition area continues to decrease and the rate of change of the temperature gradient in the deposition area approaches zero.

9. The method for analyzing the temperature gradient of copper foil electroplating equipment according to claim 8, characterized in that, The determination of flow compensation values ​​at different speeds includes: determining flow compensation values ​​at different speeds based on the principle of increasing flow in advance when the speed increases and decreasing flow in delay when the speed decreases.

10. A temperature gradient analysis device for copper foil electroplating equipment, characterized in that, The device includes: The data acquisition module is used to acquire real-time temperature data of each sector of the roller surface and combine it with the temperature difference between the coolant inlet and outlet zones to form initial data records. The temperature difference identification module is used to analyze the temperature difference between adjacent sectors based on the real-time temperature data of each sector of the roller surface recorded in the initial data, and to fit the temperature difference between adjacent sectors with the change of roller rotation speed to identify the local surface temperature difference expansion value. The deviation coefficient determination module is used to determine the deviation coefficient between the actual temperature gradient of the deposition area and the surface temperature difference based on the surface temperature difference expansion value and the actual temperature gradient of the deposition area from the inner wall to the outer wall. The temperature correction module is used to correct the temperature data of each sector using the deviation coefficient to obtain the true temperature distribution of the deposition area and divide it into three temperature gradient categories: uniform zone, transition zone and abnormal zone. The region determination module is used to identify the temperature imbalance regions that require key control based on the distribution range of the three temperature gradient categories: uniform region, transition region, and abnormal region. The control and execution module is used to predict the future trend of the circumferential temperature difference of the roller surface in areas of temperature imbalance, determine and execute the temperature uniformity control scheme, so that the temperature gradient in the deposition area tends to be stable.

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