A coating design method for an irregular region and a coating

Abstract

The application relates to a heating film design method for an irregular area of a heating film design technology and a heating film. The method comprises the following steps: acquiring geometric parameters of the irregular area and determining a geometric domain, and constructing a polar coordinate system and a polar coordinate origin; constructing a boundary function of the irregular area, defining basic physical parameters of a heating film and solving to obtain core physical parameters; acquiring a calculation equation of film thickness and / or material resistivity and / or local area duty ratio of the heating film at different polar coordinate points in the polar coordinate system varying with a polar radius and a polar angle; and based on the geometric parameters, the boundary function, the basic physical parameters, the core physical parameters and the calculation equation, calculating target film thickness and / or material resistivity and / or local area duty ratio of the heating film at different polar coordinate points in the irregular area. The method can realize second-level deterministic forward inverse design of the heating film, has clear physical meaning and extremely strong parameter generalization capability, and can realize perfect heat field without sacrificing heating area.

Description

Technical Field

[0001] This application relates to the field of heat-coating design technology, and in particular to a coating design method and coating for irregular areas. Background Technology

[0002] Aircraft and automobiles rely heavily on windshield de-icing and defogging capabilities to ensure visibility and driving safety in adverse weather conditions and under aerodynamic loads. Similarly, related fields such as the irregularly shaped curved anti-fog lenses of AR / VR smart helmets, the de-icing films for irregular optical windows in polar research equipment, and the irregularly shaped dome heating layers of high-end security cameras also require excellent de-icing and defogging capabilities. Currently, the industry typically achieves this by applying voltage to the windshield for heating. To ensure windshield safety and consistent visibility, the heating temperature must be uniform. This macroscopically requires a uniform current density distribution within the heated surface, meaning the power density per unit area must remain equal. If the current is too concentrated in certain locations, extreme high temperature points will appear.

[0003] In an ideal, regular rectangular region, the current flows uniformly from one end to the other due to the consistent width. In this case, as long as the thickness of the heating film is uniform throughout, uniform heating can be achieved. However, in practical engineering applications, the heating area is often irregular. In an irregular conductive film, the current preferentially converges along the shortest path of least resistance, a phenomenon known in physics as current crowding. Current crowding causes a surge in heating power in areas of high current density, forming extremely dangerous localized hotspots that can lead to material burnout or glass shattering; while in the sparsely current edge areas, insufficient heating results in cold zones, causing de-icing and defogging failures. Therefore, how to overcome this physical limitation in irregular regions and achieve uniform heating is a common technical challenge that urgently needs to be solved in the industry.

[0004] To achieve uniform heating in irregular regions (such as irregularly shaped, curved, or porous substrates), industry and academia currently employ various approximation methods for coating design, including finite element analysis (FEA)-based trial-and-error iterative methods, numerical solutions based on topology optimization and heuristic algorithms, and irregular electrode compensation methods. However, FEA-based trial-and-error iterative methods involve blind trial and error, resulting in extremely long design cycles, huge computational resource consumption, and heavy reliance on expensive commercial multiphysics simulation software, significantly increasing the R&D threshold and costs for enterprises. Numerical solutions based on topology optimization and heuristic algorithms are based on complex objective functions. The numerical approximation makes the calculation prone to getting stuck in local optima, and the calculated thickness distribution often presents fragmented patches without physical regularity. This not only leads to a lack of clear physical guidance in the design results, but also makes it extremely difficult to process and manufacture in actual coating processes. It also lacks parameter scalability (the algorithm needs to be iterated again once the size changes). The irregular electrode compensation method is a compromise for uniform film thickness. It forcibly changes the current distribution by designing complex wavy or comb-shaped edge electrodes. Therefore, it not only seriously sacrifices the valuable effective heating area and increases the difficulty and cost of electrode processing, but also still cannot completely eliminate local hot spots or cold areas when facing extremely irregular boundaries.

[0005] Therefore, this invention is proposed. Summary of the Invention

[0006] In view of the problems existing in the background technology, this application provides a coating design method and coating for irregular areas. The coating design method can realize deterministic forward and reverse design of heating film at the second level, has clear physical meaning and strong parameter generalization ability, and can achieve perfect thermal field without sacrificing heating area.

[0007] According to one aspect of the present invention, a method for designing a coating for irregular regions is provided, comprising the following steps: S1. Obtain the geometric parameters of the irregular region to be heated, determine the geometric domain of the irregular region based on the geometric parameters, and construct a polar coordinate system to describe the geometric domain. The polar coordinate system takes the equivalent curvature center of the inner and outer boundaries of the irregular region or the intersection of their extensions as the origin of the polar coordinate system. S2. Construct the boundary function of the irregular region, define the basic physical parameters of the heating film, and solve for the core physical parameters of the heating film; S3. Obtain the calculation equations for the film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the polar coordinate system as a function of the polar diameter and polar angle; S4. Based on the geometric parameters, boundary functions, basic physical parameters, core physical parameters, and the calculation equations, calculate the target film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the irregular region.

[0008] In some embodiments of the present invention, in step S1, the irregular region includes standard sector and sector-like region (or irregular region with irregular shape). Both standard sector and sector-like region can be directly solved by forward and reverse design using the core polar coordinate calculation equation of the present invention.

[0009] In some embodiments of the present invention, in step S2, the geometric parameters include the radius r and angle θ of the current polar coordinate point, the boundary functions include the inner boundary function r1(θ) and the outer boundary function r2(θ) of the standard sector or sector-like applied voltage, the basic physical parameters include the voltage U of the standard sector or sector-like applied voltage, and the core physical parameters include the target uniform power density w of the heating film.

[0010] In some embodiments of the present invention, the calculation equations for the film thickness at different polar coordinate points of the heating film as a function of the polar diameter and polar angle are as follows: ; Where: h(r, θ) is the film thickness at the polar coordinate point (r, θ) of the heating film; ρ is the material resistivity of the heating film; w is the designed target uniform power density; r is the radius of the current polar coordinate point (r, θ); U is the voltage applied to the electrode; r1(θ) and r2(θ) are the inner and outer boundary functions of the sector, θ is the independent variable, and when the sector is a standard sector, r1 and r2 do not change with the polar angle θ and are constants; In the radial direction of the sector, the film thickness decreases inversely with the square of the radius r; in the angular direction, the film thickness is dynamically adjusted using a proportionality coefficient based on the change in total resistance caused by the absolute position of the inner and outer boundaries.

[0011] In some embodiments of the present invention, when the thickness of the heating film is fixed, by changing the composition ratio or doping concentration of the conductive material at different polar coordinate points, the local material resistivity of the heating film undergoes a gradient change, thereby making the distribution law of its macroscopic equivalent sheet resistance consistent with the sheet resistance distribution calculated by the calculation equation.

[0012] In some embodiments of the present invention, when the heating film is a grid-like or patterned structure with holes of equal thickness and resistivity, the distribution law of its macroscopic equivalent sheet resistance is made consistent with the sheet resistance distribution calculated by the calculation equation by changing the local area duty cycle (or line width / line spacing) of the conductive material at different polar coordinate points.

[0013] In some embodiments of the present invention, after completing step S4, local morphology correction is performed on the corner areas of the heating film.

[0014] In some embodiments of the present invention, after completing step S4, the printing trajectory of the applied voltage electrode is actively changed according to the theoretically derived isobaric line, so that its local trajectory is tangent to the theoretically derived isobaric line, thereby weakening the high temperature points at the corners.

[0015] According to another aspect of the present invention, a coating is provided, which is designed and prepared using the above-described coating design method for irregular regions.

[0016] Compared with the prior art, the present invention achieves the following technical effects: 1. This invention enables deterministic "forward and reverse design" within seconds (overcoming the shortcomings of trial and error): Through rigorous physical and mathematical derivation, this invention obtains an analytical solution formula for film thickness distribution. It eliminates the need for time-consuming numerical iterative simulations; by simply inputting the geometric parameters of the irregular region, the target heating power, and the material conductivity, a precise thickness distribution model can be calculated instantly (within seconds) (the same applies to material resistivity and local area duty cycle). This completely eliminates dependence on expensive commercial simulation software, significantly reducing R&D costs and shortening the design cycle.

[0017] 2. This invention possesses clear physical meaning and strong parameter generalization ability (overcoming the shortcomings of topology optimization): Compared to the random numerical solutions, the thickness distribution output by the formula of this invention (material resistivity, and similarly, local area duty cycle) is continuous and has a clear physical mechanism. It not only theoretically guarantees 100% heating uniformity but also possesses strong scalability—when the size of the heating film is scaled up or down proportionally, or when materials with different basic conductivity are replaced, rapid scaling design can be achieved simply by adjusting the corresponding variables in the formula, without the need for remodeling and calculation.

[0018] 3. This invention achieves a perfect thermal field without sacrificing the heating area (overcoming the shortcomings of the electrode compensation method): This invention fully regulates the local surface resistance through the precise spatial gradient change of the film thickness (and similarly the material resistivity and local area duty cycle), without relying on complex irregularly shaped electrodes to forcibly guide the current. This not only maximizes the effective heating area and simplifies the electrode fabrication process, but also fundamentally eliminates the problems of current congestion and local overheating caused by irregular geometric boundaries. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. In the drawings: Figure 1This is a schematic diagram of the non-uniform film thickness design principle of the present invention; Figure 2 This is a schematic diagram of the parameterization of irregular regions in this invention; Figure 3 This is a temperature simulation result diagram of the standard sector-shaped uniform film thickness design in Comparative Example 1 of this invention; Figure 4 This is a temperature simulation result diagram of the standard sector film thickness design according to its calculation equation in Embodiment 1 of the present invention; Figure 5 This is a temperature result diagram of the comparative example 2 of the present invention with uniform film thickness in a fan-shaped shape; Figure 6 This is a temperature simulation result diagram of the film thickness design of three types of fan-shaped structures according to the standard fan-shaped calculation equation of this invention; Figure 7 This is a temperature simulation result diagram of the film thickness design of type 2 sector according to its calculation equation in Embodiment 2 of the present invention; Figure 8 This is the temperature simulation result after correcting the intersection point of the boundary in Embodiment 3 of the present invention. Detailed Implementation

[0020] It should be understood that the described embodiments are merely some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0021] In the following description, when referring to the accompanying drawings, the same numbers in different drawings denote the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0022] In the description of this application, it should be understood that the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances. Furthermore, in the description of this application, unless otherwise stated, "multiple" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship.

[0023] The main principles and technical limitations of existing design methods for achieving uniform heating of thin films in irregular regions (such as irregular shapes, curved surfaces, or porous substrates) are as follows: These methods rely on finite element analysis (FEA) for trial-and-error iteration, numerical solutions based on topology optimization and heuristic algorithms, and irregular electrode compensation methods. The trial-and-error iterative method based on finite element method (FEA) is currently the most commonly used engineering design method in enterprises. This method does not change the uniformity of the thin film, but finds a "barely usable" thickness or shape distribution through continuous trial and error. Engineers use multiphysics simulation software such as COMSOL or ANSYS to build geometric models of irregular regions, manually set the initial film thickness based on experience, and continuously approach the uniform temperature through a cycle of "simulating the thermal field distribution -> manually modifying the film thickness of the overheated / undercooled regions -> resimulating". This method is essentially a blind trial and error process of "first assuming the thickness, then simulating the thermal field, and finally modifying it based on experience", which leads to an extremely long design cycle (usually requiring dozens of iterations and several days), huge consumption of computational resources, and heavy reliance on expensive commercial multiphysics simulation software, which greatly increases the R&D threshold and cost for enterprises. Moreover, the solution obtained is often an approximate one. Once the product size changes, it is necessary to start from scratch and try again, with no parameter generalization ability.

[0024] Numerical solutions based on topology optimization and heuristic algorithms discretize the heating region into thousands of tiny grids, setting "minimum temperature variance" as the objective function. Relying on computer algorithms (such as the SIMP method), after a long numerical calculation, the method automatically determines whether to "retain" or "remove" the conductive material on each grid. Such algorithms (such as genetic algorithms) are based on numerical approximation of complex objective functions, so the calculation is prone to getting stuck in local optima. Moreover, the calculated thickness distribution often presents an extremely fragmented "sponge-like" or irregular porous structure with no physical laws. Such fragmented microstructures cannot guarantee the processing yield in actual photolithography or screen printing processes. Furthermore, this method is still an extremely computationally intensive black-box numerical solution. This not only leads to the lack of clear physical guidance for the design results, but also makes it extremely difficult to process and manufacture in actual coating processes, and lacks parameter scalability (the algorithm must be rerun if the size changes).

[0025] The irregular electrode compensation method, due to the difficulty of accurately calculating and controlling the spatial distribution of film thickness with existing technology, often has to compromise on uniform film thickness. Instead, it forcibly changes the current distribution by designing complex wavy or comb-shaped edge electrodes. This method targets the manufacturing process limitation that "the thickness of the heating film must be kept absolutely uniform". Instead, it forcibly distributes the current by changing the shape of the metal electrodes at both ends. The uniform heating film covers the entire irregular substrate with equal thickness everywhere. Irregular electrode groups are printed on both sides of the heating film. Unlike conventional straight electrodes, these electrodes are designed in comb-shaped, wavy, or locally widened / narrowed shapes. By lengthening the distance between electrodes in areas prone to hot spots or shortening the distance between electrodes in cold areas, the local potential difference is artificially changed. However, this method has an extremely complex structure, which increases the difficulty and cost of electrode processing and sacrifices a large amount of effective area that could originally be used for heating. Moreover, when facing extremely irregular boundaries, edge heating dead corners still cannot be completely eliminated.

[0026] In view of the above-mentioned shortcomings of the prior art, the purpose of this invention is to provide a coating design method and coating for irregular areas to improve the uniformity of heating in irregular areas. It derives the theoretical calculation equation for heating film design based on the shape characteristics of irregular areas such as windshields and the current field distribution characteristics, and can achieve deterministic "forward and reverse design" at the second level. It has clear physical meaning and strong parameter generalization ability, and can achieve a perfect thermal field without sacrificing the heating area.

[0027] This application discloses a coating design method for irregular regions. The coating design method for irregular regions includes the following steps: S1. Obtain the geometric parameters of the irregular region to be heated, determine the geometric domain of the irregular region based on the geometric parameters, and construct a polar coordinate system to describe the geometric domain. The polar coordinate system takes the equivalent curvature center of the inner and outer boundaries of the irregular region or the intersection of their extensions as the origin of the polar coordinate system.

[0028] S2. Construct the boundary function of the irregular region, define the basic physical parameters of the heating film, and solve for the core physical parameters of the heating film.

[0029] S3. Obtain the calculation equations for the film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the polar coordinate system as a function of the polar diameter and polar angle.

[0030] S4. Based on geometric parameters, boundary functions, basic physical parameters, core physical parameters, and calculation equations, calculate the target film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the irregular region.

[0031] In this invention, to achieve uniform temperature within the heating area, it is necessary to ensure that the heating power density per unit area is equal, i.e., the current density is uniformly distributed within the surface. To achieve the above function, this invention abandons the traditional trial-and-error method and establishes a polar coordinate system to transform the complex condition of zero current field divergence into an accurate analytical function model of film thickness, material resistivity, and local area duty cycle as a function of spatial coordinates. This enables second-level deterministic "forward and reverse design" of the heating film, possesses clear physical meaning and strong parameter generalization ability, and achieves a perfect thermal field without sacrificing the heating area.

[0032] In some embodiments of the present invention, based on calculation equations, the present invention can achieve uniform in-plane current density distribution by adjusting only the film thickness, material resistivity, or local area duty cycle, or simultaneously control and adjust two parameters, such as film thickness and material resistivity, film thickness and local area duty cycle, or material resistivity and local area duty cycle, or simultaneously control and adjust three parameters, film thickness, material resistivity, and local area duty cycle, to achieve uniform in-plane current density distribution. Preferably, uniform in-plane current density distribution is achieved by adjusting only the film thickness, material resistivity, or local area duty cycle.

[0033] In some embodiments of the present invention, in step S1, the irregular region is a fan-shaped or irregularly shaped region. The fan-shaped region includes a standard fan-shaped region and a fan-like region. It should be understood that in the present invention, the quasi-fan-shaped region, the fan-like region, and the irregularly shaped region can all be solved by forward and reverse design using the core polar coordinate calculation equation of the present invention, which can directly achieve perfect uniform heating in the irregularly shaped region.

[0034] In some embodiments of the present invention, it is assumed that the irregular area to be heated can be approximated as a sector, and a coordinate system is established with the equivalent center of the inner and outer arcs of the sector as the origin of the polar coordinates; in this coordinate system, the radius of the current calculation point is determined to be r, and the polar angle parameter is θ, such as... Figure 1 As shown. In reality, irregular regions often cannot be approximated as standard sectors, such as... Figure 2 As shown, AB and CD are the boundaries of the applied voltage, AC and BD are the boundaries of the coating partitions, and the extensions of CA and DB intersect at point O, which is the origin of the polar coordinates.

[0035] In some embodiments of the present invention, in step S2, the geometric parameters include the radius r and angle θ of the current polar coordinate point, the boundary functions include the inner boundary function r1(θ) and the outer boundary function r2(θ) of the standard sector or sector-like applied voltage, the basic physical parameters include the voltage U of the standard sector or sector-like applied voltage, and the core physical parameters include the target uniform power density w of the heating film.

[0036] Wherein, voltage U is a constant voltage difference applied between the upper and lower electrodes. Preferably, voltage U is applied at the boundary of the upper electrode (inner arc), and voltage 0 is applied at the boundary of the lower electrode (outer arc). The target uniform power density w required by the design is in W / m³. 2 Subsequently, the contour features of the inner and outer boundaries of the irregular region are extracted. The inner boundary (such as the upper base) is fitted with a function r1(θ) of angle θ, and the outer boundary is fitted with r2(θ). (Reference) Figure 2 The radius of any point on curve AB (with O as the center) is denoted as r1(θ), and similarly, the radius of any point on curve CD (with O as the center) is denoted as r2(θ).

[0037] In some embodiments of the present invention, the calculation equations for the film thickness at different polar coordinate points of the heating film as a function of the polar diameter and polar angle are as follows: (1) Where: h(r, θ) is the film thickness at the polar coordinate point (r, θ) of the heating film; ρ is the material resistivity of the heating film; w is the designed target uniform power density (W / m³). 2 ); r is the radius of the current polar coordinate point (r, θ); U is the voltage applied to the electrode; r1(θ) and r2(θ) are the inner and outer boundary functions of the sector (θ is the independent variable), and when the sector is a standard sector, r1 and r2 are constants as the sector angle changes.

[0038] In this invention, it is assumed that the current mainly flows radially along the heating film and the power density is constant throughout the region. The target sector area is divided into countless tiny sector slices along the angle θ. For each coordinate point (r, θ), the required polar coordinate point target film thickness or material resistivity can be directly calculated by calling the mathematical formula derived above.

[0039] In this invention, the formula achieves dual adjustment of radial distribution and angular correction. For example, in the radial direction, the film thickness decreases inversely with the square of the radius r; in the angular direction, the film thickness is dynamically adjusted using a proportional coefficient based on the change in total resistance caused by the absolute position of the inner and outer boundaries, thereby ensuring that the power density in the micro-slice reaches the target value w.

[0040] In some embodiments of the present invention, when the thickness of the heating film is fixed (constant), by changing the composition ratio or doping concentration of the conductive material at different polar coordinate points, the local resistivity of the heating film is changed in a gradient, so that the distribution law of its macroscopic equivalent sheet resistance is completely consistent with the sheet resistance distribution calculated by calculation equation (1).

[0041] In this embodiment, the thickness (h) of the heating film is kept uniform and constant by replacing the gradient change in the material resistivity (ρ) gradient. Instead, the same sheet resistance distribution is achieved by changing the composition ratio of the material. For example, when using conductive inks (such as a mixture of carbon nanotubes, graphene, and silver nanowires) for inkjet printing or screen printing, the concentration or doping ratio of the conductive ink in different regions is dynamically changed according to the spatial distribution law of the calculation equation derived in this invention, so that the in-plane resistivity of the heating film exhibits a gradient change. This equivalent alternative also falls within the protection scope of the physical distribution principle derived from this analytical formula in this invention.

[0042] In some embodiments of the present invention, when the heating film is a grid-like or patterned structure with holes of equal thickness and resistivity, by changing the local area duty cycle (or line width / line spacing) of the conductive material at different polar coordinate points, the distribution law of its macroscopic equivalent sheet resistance is made to be completely consistent with the sheet resistance distribution calculated by calculation equation (1).

[0043] In this embodiment, a continuous solid film is replaced by microstructure patterning (mesh / perforation). A uniform heating film with equal thickness and resistivity is used. The heating film is processed into a mesh, serpentine line, or patterned structure with dense micropores by laser etching or photolithography. By controlling the "duty factor" or "line width / spacing" of the conductive lines in different polar coordinate regions, the macroscopic equivalent sheet resistance completely conforms to the sheet resistance distribution law derived by the formula of this invention. This implementation method of "replacing thickness with structural density" is also within the protection scope of this invention.

[0044] In some embodiments of the present invention, after step S4 is completed, the corner areas of the heating film are locally morphologically corrected.

[0045] In this invention, since the actual pressure boundary may not be able to form a standard arc in any differential region, it is easy to generate high and low temperature points in the four corner areas. In order to further improve uniformity, before generating the final processing pattern, the edge position of the boundary (i.e. the intersection of the inner and outer boundaries and the insulation side, such as points A, B, C, and D) is locally morphologically corrected so that the boundary shape of perpendicular intersection is formed in a small local area of ​​the intersection, thereby effectively reducing the high temperature points at the corners (intersection of the electrode and the partition line).

[0046] In other embodiments of the present invention, in addition to locally modifying the morphology of the corner area of ​​the heating film, after completing step S4, the printing trajectory of the voltage-applied electrode can be actively changed according to the theoretically derived isobaric line so that its local trajectory is tangent to the theoretically derived isobaric line, thereby weakening the high temperature point at the corner.

[0047] In this invention, by changing the printed trajectory of the voltage-applied electrode (Busbar) instead of changing the physical cutting shape of the insulation boundary, that is, by making the direction of the metal electrode actively bend in the area near the edge intersection, so that it is forced to be tangent to the theoretically derived isobaric line, the secondary optimization effect of reducing the corner temperature high point and making the temperature more uniform can be achieved.

[0048] This invention introduces a partitioning design concept using polar coordinates and sector division. Based on the shape of irregular heating areas such as windshields, and the distribution characteristic where the current vector field divergence within the cross-section of a single heating area is 0, i.e., divF= By using F=0 and introducing a polar coordinate system, the irregular region is divided into countless tiny sector slices along angle θ for independent analysis and design, effectively breaking away from the traditional experience-based trial-and-error approach of mesh generation. The core analytical formula for achieving uniform power density is based on the principle of equal target uniform power density per unit area. Macroscopically, this manifests as an absolutely uniform distribution of current density within the plane, eliminating high-temperature points caused by current concentration. The derived formula for accurately calculating the spatial distribution of film thickness uses the target power density w, conductivity ρ, voltage U, and coordinate variables as inputs to directly output the complete set of computational logic for the continuous thickness matrix h(r,θ).

[0049] This invention can precisely eliminate the current congestion effect and achieve a breakthrough improvement in temperature uniformity. This invention strictly follows the distribution principles of "thickness is inversely proportional to the square of the polar coordinate radius" and "angular direction is dynamically adjusted according to the boundary span". When necessary, it is combined with the correction method of local verticalization of edge intersection points. This method guides the current distribution from the physical source and effectively overcomes the technical problem of local hot spots easily generated in irregular areas (such as approximately fan-shaped or trapezoidal areas). The maximum temperature difference of the entire area designed using the formula of this invention can be reduced to 5.5℃. With the help of edge intersection point correction, the temperature difference can be further reduced to 4.4℃. The temperature uniformity effect is at the leading level in the industry.

[0050] The physical laws of this invention are clear, and it has excellent engineering manufacturability. The film thickness distribution of this invention is derived from a continuous mathematical analytical function, rather than relying on numerical algorithms to blindly seek optimization. Compared with the extremely fragmented, irregular and unprocessable "sponge-like" pore structure that is easily generated by existing topology optimization algorithms, the film thickness gradient output by this invention has continuous and smooth characteristics, which can perfectly adapt to existing dynamic mask sputtering, inkjet printing and other processes, greatly ensuring the actual processing yield and mass production feasibility of irregular gradient heating films.

[0051] This embodiment also proposes a coating, which is designed and prepared using the above-described coating design method for irregular regions.

[0052] To more clearly illustrate the implementation process of the present invention and its superior technical effects, the coating design method for irregular areas described above will be further explained below with reference to specific embodiments.

[0053] Example 1 The film thickness design structure and parameter settings for the standard sector-shaped heating area: The heating area is a standard sector, and the upper and lower voltage application boundaries are standard circular arcs (r1 and r2 are constants); at this time, the analytical model (calculation) in step S3 above naturally degenerates into a standard form, the resistivity of the heating film material is fixed (constant), and when the heating film is a complete film, the calculation equation for the film thickness at different polar coordinate points as a function of the polar diameter and polar angle is as follows: (2) Comparative Example 1 The heating area is a standard fan shape, and the heating film adopts a uniform film thickness design. Other conditions are the same as in Example 1.

[0054] Comparison Results: Simulations were conducted under the assumption that the partition boundaries were adiabatic, with the same voltage and heat transfer coefficient. If the existing "uniform film thickness design" is used, the temperature difference within the fan-shaped region reaches 10℃. Figure 3 As shown; and by using the gradient film thickness calculated using the formula in this embodiment for design, a completely uniform heating effect (0 temperature difference) can be achieved within the fan-shaped region, as... Figure 4 As shown, this verifies the absolute validity of the theoretically derived formula.

[0055] Example 2 Film thickness design and boundary correction for irregular geometric regions Structure and parameter settings: Design an irregular heating region (similar to a fan shape). Apply a voltage U to the upper electrode boundary. The boundary feature is fitted as a polar coordinate function: r1=0.2+0.06sinθ. Apply a voltage 0 to the lower electrode boundary. Fit the polar coordinate function: r2=0.5-0.06sinθ.

[0056] Technical implementation: Substitute the expressions for r1 and r2 above into formula (2) to calculate the spatial thickness distribution matrix.

[0057] Example 3 Further edge correction was performed on the heating film of Example 2.

[0058] Comparative Example 2 The heating area is fan-shaped, and the heating film adopts a uniform film thickness design. Other conditions are the same as in Example 2.

[0059] Comparative Example 3 The heating area is fan-shaped, and the thickness of the heating film is designed using the standard fan-shaped formula. Other conditions are the same as in Example 2.

[0060] Effect Comparison: As shown in Comparative Example 2, if the existing "uniform film thickness design" is adopted, due to severe current congestion, the temperature difference across the entire area reaches as high as 30°C, and extremely high temperature points are formed at the corners. The result is as follows. Figure 5 As shown in Example 3, if the standard sector formula is forcibly applied to the design, the temperature difference will still be 12.5℃. Figure 6 As shown in Example 2, using the model calculated by the above steps of this invention, the heating uniformity of the main field of view is significantly improved, and the maximum temperature difference across the entire region is greatly reduced to 5.5℃. Figure 7 As shown in Example 3, further edge correction is applied: after locally verticalizing the intersection points (A, B, C, D), the high temperature peaks at the corners are effectively weakened, and the heat at the high points is evenly distributed, further reducing the extreme temperature difference in the entire area to 4.4℃. Figure 8 As shown. The above embodiments and comparative examples fully demonstrate that, based on engineering feasibility, the present invention can still achieve highly practical uniform heating in extremely irregular areas.

[0061] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A coating design method for irregular regions, characterized in that, Includes the following steps: S1. Obtain the geometric parameters of the irregular region to be heated, determine the geometric domain of the irregular region based on the geometric parameters, and construct a polar coordinate system to describe the geometric domain. The polar coordinate system takes the equivalent curvature center of the inner and outer boundaries of the irregular region or the intersection of their extensions as the origin of the polar coordinate system. S2. Construct the boundary function of the irregular region, define the basic physical parameters of the heating film, and solve for the core physical parameters of the heating film; S3. Obtain the calculation equations for the film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the polar coordinate system as a function of the polar diameter and polar angle; S4. Based on the geometric parameters, boundary functions, basic physical parameters, core physical parameters, and the calculation equations, calculate the target film thickness and / or material resistivity and / or local area duty cycle of the heating film at different polar coordinate points in the irregular region.

2. The coating design method for irregular areas according to claim 1, characterized in that, In step S1, the irregular region includes standard sector and sector-like region.

3. The coating design method for irregular areas according to claim 2, characterized in that, In step S2, the geometric parameters include the radius r and angle θ of the current polar coordinate point, the boundary functions include the inner boundary function r1(θ) and outer boundary function r2(θ) of the standard sector or sector-like applied voltage, the basic physical parameters include the voltage U applied by the standard sector or sector-like, and the core physical parameters include the target uniform power density w of the heating film.

4. The coating design method for irregular areas according to claim 3, characterized in that, The equations for calculating the film thickness at different polar coordinate points as a function of polar diameter and polar angle are as follows: ； Where: h(r, θ) is the film thickness at the polar coordinate point (r, θ) of the heating film; ρ is the material resistivity of the heating film; w is the designed target uniform power density; r is the radius of the current polar coordinate point (r, θ); U is the voltage applied to the electrode; r1(θ) and r2(θ) are the inner and outer boundary functions of the sector, θ is the independent variable, and when the sector is a standard sector, r1 and r2 do not change with the polar angle θ and are constants; In the radial direction of the sector, the film thickness decreases inversely with the square of the radius r; in the angular direction, the film thickness is dynamically adjusted using a proportionality coefficient based on the change in total resistance caused by the absolute position of the inner and outer boundaries.

5. The coating design method for irregular areas according to claim 4, characterized in that, When the thickness of the heating film is fixed, by changing the composition ratio or doping concentration of the conductive material at different polar coordinate points, the local resistivity of the heating film changes in a gradient, so that the distribution law of its macroscopic equivalent sheet resistance is consistent with the sheet resistance distribution calculated by the calculation equation.

6. The coating design method for irregular areas according to claim 4, characterized in that, When the heating film is a grid-like or patterned structure with holes of equal thickness and resistivity, by changing the local area duty cycle of the conductive material at different polar coordinate points, the distribution law of its macroscopic equivalent sheet resistance is made consistent with the sheet resistance distribution calculated by the calculation equation.

7. The coating design method for irregular regions according to any one of claims 1 to 6, characterized in that, After completing step S4, the corner areas of the heating film are locally morphologically corrected.

8. The coating design method for irregular regions according to any one of claims 1 to 6, characterized in that, After completing step S4, based on the theoretically derived isobaric line, the printing trajectory of the applied voltage electrode is actively changed so that its local trajectory is tangent to the theoretically derived isobaric line, thereby reducing the high temperature points at the corners.

9. A coating, characterized in that, The coating is designed and prepared using the coating design method for irregular regions as described in any one of claims 1 to 8.

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