Pad printing ink supply self-adaptive adjustment method, system and device based on ink viscosity prediction and storage medium

Abstract

The application discloses a pad printing ink supply self-adaptive adjustment method and system based on ink viscosity prediction, a device and a storage medium, relates to the technical field of pad printing ink supply self-adaptive control, and comprises the following steps: a contact model between a pad printing rubber head and a to-be-printed object is established based on curved surface contact finite element analysis, and a pressure distribution matrix of the contact area between the rubber head and the curved surface in the pad printing process is inverted; according to the shear thinning rheological property of the ink, the ink storage viscosity is corrected by using the shear rate distribution, and the effective viscosity of the transfer under the current curved surface contact condition is obtained; the effective viscosity of the transfer is taken as an initial state, the ink supply demand change amount of the next pad printing cycle is predicted by combining the effective viscosity drift state in the pad printing cycle; and the ink supply is controlled based on the ink supply demand change amount and the pressure distribution matrix, so that the problems of ink viscosity prediction deviation and inaccurate ink supply control caused by the change of the contact curvature in the curved surface pad printing process of the plastic bottle are solved.

Description

Technical Field

[0001] This invention relates to the field of adaptive control technology for pad printing ink supply, and more specifically, to a method, system, device, and storage medium for adaptive adjustment of pad printing ink supply based on ink viscosity prediction. Background Technology

[0002] Plastic packaging products are widely used in the daily chemical industry. Shampoo bottles, cosmetic bottles, and other plastic containers are typically printed with trademarks, text, or patterns using pad printing. The fluidity, transferability, and adhesion of ink are closely related to its viscosity. Existing pad printing equipment usually establishes viscosity variation patterns by detecting parameters such as ink temperature and solvent evaporation in the ink supply area, and adjusts the ink supply pump output flow rate or ink supply cycle based on the prediction results to achieve adaptive ink supply regulation. Current methods use the ink state in the ink tank or ink storage chamber as the viscosity prediction object, assuming that the ink storage state can represent the ink working state during the pad printing process.

[0003] However, the printing surface of plastic bottles typically has a non-planar structure, with curvature variations in the bottle shoulder, rounded transitions, and local uneven areas. During the process of the printing head pressing and adhering to the curved surface of the plastic bottle, different curvature areas lead to changes in the degree of printing head deformation, actual contact area, and local pressure state, causing ink with the same stored viscosity to exhibit different shear flow states at different curved surface locations. Since ink is a non-Newtonian fluid with shear-thinning properties, its apparent viscosity during the actual transfer process changes with the shear state. Therefore, the stored viscosity obtained by existing methods cannot adequately characterize the effective transfer viscosity under curved surface contact conditions, resulting in a discrepancy between the ink supply adjustment criteria and the actual ink transfer requirements.

[0004] To address the issue of changes in the actual material state caused by variations in the curvature of the contact object, the field of tire-road contact analysis has proposed an analytical technique based on the inversion of contact pressure distribution. This technique involves establishing a finite element model of the tire-road contact to obtain the pressure distribution at different spatial locations within the contact area, and then analyzing the local deformation and contact state changes of the rubber material. This type of technique provides a technical foundation for analyzing material state changes during curved surface contact. Inspired by this, it can be applied to the pad printing process on plastic bottles. Specifically, a contact model between the pad printing nozzle and the curved surface of the plastic bottle can be established to obtain the pressure distribution within the contact area. The pressure changes can then reflect the influence of the curved surface contact conditions on the ink transfer state, thus providing a reference for correcting the deviation between the stored ink viscosity and the actual transfer viscosity.

[0005] However, directly applying the aforementioned contact pressure distribution inversion technique to predict the viscosity of pad printing ink supply still faces technical obstacles. Existing contact pressure inversion techniques are mainly aimed at continuous elastic solid materials such as tire rubber and elastic gaskets, and the pressure distribution results are used to describe the degree of deformation or contact load state of the solid material. However, the ink in the pad printing process is a non-Newtonian fluid with viscoelastic characteristics, and its apparent viscosity is not directly determined by contact pressure, but is affected by pressure gradient, flow velocity, ink layer thickness, and shear rate. At the same time, in the pad printing process on the curved surface of plastic bottles, the direction of the printing head movement, the local curvature of the curved surface, and the ink flow path all affect the shear state of the ink, making it difficult to directly use the traditional contact pressure model for ink viscosity correction.

[0006] Therefore, accurately obtaining the actual effective viscosity of the ink when the pad printing head is in contact with the curved surface of the plastic bottle, and adaptively adjusting the ink supply based on the change in the actual effective viscosity, has become a technical problem that needs to be solved in the current control of ink supply in pad printing on curved plastic bottles.

[0007] To address the above problems, this invention proposes a solution. Summary of the Invention

[0008] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method, system, device, and storage medium for adaptive adjustment of pad printing ink supply based on ink viscosity prediction. By achieving accurate correction of the stored ink viscosity to the effective viscosity for curved surface transfer, the problem of ink viscosity prediction deviation and inaccurate ink supply control caused by changes in contact curvature during pad printing on curved surfaces of plastic bottles is solved.

[0009] To achieve the above objectives, the present invention provides the following technical solution: An adaptive adjustment method for pad printing ink supply based on ink viscosity prediction includes the following steps: establishing a contact model between the pad printing head and the object to be printed based on finite element analysis of curved surface contact, and inverting the pressure distribution matrix of the contact area between the head and the curved surface during the pad printing process; determining the pressure gradient distribution within the contact area based on the pressure distribution matrix, determining the ink flow velocity distribution based on the pressure gradient distribution, determining the ink shear rate distribution based on the flow velocity distribution, correcting the ink storage viscosity using the shear rate distribution based on the ink shear thinning rheological characteristics, and obtaining the effective transfer viscosity under the current curved surface contact conditions; using the effective transfer viscosity as the initial state, and combining the effective viscosity drift state during the pad printing cycle, predicting the change in ink supply demand for the next pad printing cycle; and controlling the ink supply execution based on the change in ink supply demand and the pressure distribution matrix.

[0010] An adaptive ink supply adjustment system for pad printing based on ink viscosity prediction includes a curved surface contact module, a viscosity state reconstruction module, an ink supply prediction module, and an ink supply adjustment module. The curved surface contact module is used to establish a contact model between the pad printing head and the object to be printed based on finite element analysis of the curved surface contact, and to invert the pressure distribution matrix of the contact area between the head and the curved surface during the pad printing process. The viscosity state reconstruction module is used to determine the pressure gradient distribution within the contact area based on the pressure distribution matrix, determine the ink flow velocity distribution based on the pressure gradient distribution, determine the ink shear rate distribution based on the flow velocity distribution, and correct the ink storage viscosity using the shear rate distribution based on the ink shear thinning rheological characteristics to obtain the effective transfer viscosity under the current curved surface contact conditions. The ink supply prediction module is used to predict the change in ink supply demand for the next pad printing cycle, using the effective transfer viscosity as the initial state and combining it with the effective viscosity drift state during the pad printing cycle. The ink supply adjustment module is used to control the ink supply execution based on the change in ink supply demand and the pressure distribution matrix.

[0011] An electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform an adaptive adjustment method for pad printing ink supply based on ink viscosity prediction.

[0012] A computer-readable storage medium storing a computer program that, when executed by a processor, implements an adaptive adjustment method for pad printing ink supply based on ink viscosity prediction.

[0013] The technical effects and advantages of the present invention regarding the adaptive adjustment method, system, equipment, and storage medium for pad printing ink supply based on ink viscosity prediction are as follows: 1. This invention transforms ink viscosity prediction from traditional single-point viscosity analysis based on the state of the ink storage area to spatial distribution analysis combined with the actual transfer contact area, thereby realizing the state correlation between ink storage viscosity and effective viscosity for curved surface transfer and reducing viscosity prediction deviation caused by differences in the curved surface structure of the bottle.

[0014] 2. By establishing an effective viscosity drift state sequence during the pad printing cycle, this invention enables advance prediction of ink supply demand changes in the next pad printing cycle, transforming ink supply adjustment from ex-post compensation to feedforward predictive adjustment, thereby improving the timeliness and accuracy of ink supply control.

[0015] 3. By spatially allocating ink supply variations in conjunction with local pressure differences in the curved surface contact area, priority ink supply compensation is achieved for areas with concentrated pressure, avoiding the mismatch between overall uniform ink supply and local consumption differences, and further improving the ink supply uniformity and printing quality consistency of curved surface pad printing. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to the present invention. Detailed Implementation

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

[0018] Example 1, Figure 1 The present invention provides an adaptive adjustment method for pad printing ink supply based on ink viscosity prediction, comprising the following steps: S1. Based on the finite element analysis of curved surface contact, a contact model between the pad printing head and the object to be printed is established, and the pressure distribution matrix of the contact area between the pad printing head and the curved surface is inverted during the pad printing process.

[0019] S1.1 In this embodiment, the establishment of the contact model between the pad printing head and the object to be printed based on the finite element analysis of curved surface contact specifically refers to: Obtain the three-dimensional scanned point cloud data of the object to be printed, and perform surface fitting on the point cloud data to obtain the three-dimensional surface equation of the area to be printed. The principal curvature at each surface position is calculated based on the three-dimensional surface equation. The surface mesh density is determined according to the curvature change between adjacent positions. Nodes are densified in regions where the curvature change is greater than the first threshold and sparsed in regions where the curvature change is less than the second threshold, thereby generating a bottle surface finite element model containing spatial coordinate information. Based on the geometric dimensions, elastic material parameters, and free surface profile of the pad printing head, solid elements are used to discretize the head, a finite element solid model of the head is established, and the material parameters are set according to the elastic modulus, Poisson's ratio, and stress-strain relationship of the head material. Based on the actual pressing and moving process of the pad printing head, a displacement loading sequence of the pad printing head reference node is established. The displacement loading sequence is used as the displacement boundary condition of the finite element solid model of the pad printing head to describe the motion change of the pad printing head from the initial position to the printing area. Based on the spatial positional relationship between the finite element solid model of the rubber head and the finite element model of the bottle body surface, the finite element surface of the outer surface of the rubber head and the finite element surface of the bottle body surface are matched accordingly to determine the potential contact area between the two, and the contact relationship between the outer surface of the rubber head and the bottle body surface is established by using a surface-to-surface contact algorithm. Based on the combination of the contact relationship, the displacement boundary conditions, the finite element solid model of the printing pad, and the finite element model of the bottle surface, a contact model is formed to describe the pressure deformation of the printing pad and its contact state with the surface to be printed.

[0020] In this embodiment, the 3D scanned point cloud data is a set of discrete coordinate data used to describe the real spatial shape of the object to be printed. The specific acquisition process involves scanning the outer surface of the plastic bottle using a structured light scanning device, laser scanning device, or industrial 3D vision device, collecting the spatial coordinate information corresponding to multiple sampling points on the bottle surface. Due to the influence of reflections, occlusions, and equipment noise during the actual scanning process, the acquired point cloud data undergoes outlier removal, noise filtering, and missing area compensation processing to obtain a point cloud set that continuously describes the spatial morphology of the area to be printed. This point cloud data is used to replace traditional 2D dimension measurement methods, enabling the subsequent finite element model to be built based on the real curved surface structure of the plastic bottle.

[0021] In this embodiment, the three-dimensional surface equation is a continuous spatial surface expression obtained by fitting discrete point cloud data, used to describe the geometric relationships between various spatial positions in the printing area of ​​the bottle. Specifically, the preprocessed point cloud is arranged according to its spatial position, and existing surface fitting methods, such as non-uniform rational B-spline surface fitting, least squares surface fitting, or radial basis function surface fitting, are used to convert the discrete points into a continuous surface. Through this surface expression, the spatial coordinates of different positions on the bottle and the surface change trend can be obtained, providing a basis for subsequent curvature analysis. The above-mentioned surface fitting method belongs to the existing technology in the field of three-dimensional geometric reconstruction; this embodiment applies it based on the surface characteristics of the pad printing object.

[0022] In this embodiment, principal curvature is a geometric parameter used to describe the degree of local bending of the bottle surface, and it is used to determine the degree of contact change that may occur when different areas are pressed by the glue head. Specifically, based on the established three-dimensional surface equation, surface direction analysis is performed on different spatial locations within the area to be printed to obtain the degree of bending change along two main directions at that location, and the representative surface change parameter is used as the principal curvature value for that location. For example, the bottle shoulder has a larger principal curvature due to the rapid transition of the surface; the middle of the bottle body has a smaller principal curvature due to the flatter surface. This embodiment uses principal curvature to distinguish surface change areas, allowing the finite element node distribution to adapt to the actual geometric changes of the bottle.

[0023] In this embodiment, the curvature change is an evaluation parameter used to determine the degree of geometric change in adjacent surface regions. Specifically, during the acquisition process, the principal curvatures corresponding to adjacent finite-position nodes are compared to analyze the changes in the curvature degree of adjacent regions. When the curvature change between adjacent positions is large, it indicates a significant surface transition in that region, such as the area near the shoulder or mouth of a bottle; when the curvature change is small, it indicates a gentle surface change in that region. This parameter is used to control the finite element mesh density, enabling regions with significant surface changes to have higher spatial description accuracy.

[0024] In this embodiment, the first threshold and the second threshold are preset judgment conditions used to distinguish the degree of curvature change. The specific acquisition process is as follows: they are set according to the allowable geometric fitting error of the object to be printed, the accuracy requirements of finite element contact analysis, and computational resource limitations. Specifically, finite element models of curved surfaces are established under multiple candidate mesh densities, and the geometric fitting error of each model relative to the original point cloud data is calculated. Simultaneously, a glue head pressing contact test is performed using this model. When the difference between the pressure distribution result at a certain mesh density and the result obtained after further refinement is less than a preset tolerance, the mesh density is determined to meet the accuracy requirements, and the curvature change critical value corresponding to that density is used as the first threshold. The curvature change critical value corresponding to the lowest mesh density that meets the basic geometric fitting accuracy is used as the second threshold. The first threshold is used to determine high-variable regions where node density needs to be increased, and the second threshold is used to determine gentler regions where node density can be reduced.

[0025] In this embodiment, the finite element model of the bottle surface is a finite element analysis model formed by discretizing the actual bottle surface structure. Specifically, the surface partitioning result after curvature adjustment is converted into multiple spatial nodes, and surface elements are generated according to the connection relationships between the nodes, thus converting the continuous bottle surface into a digital model composed of nodes and elements. This model is not simply used to describe the bottle's shape, but rather to provide surface spatial constraints during the glue head pressing process, enabling the finite element solution to analyze the influence of different curvature regions on the glue head contact state.

[0026] In this embodiment, solid elements are a type of discrete element used in finite element analysis to describe the deformation of three-dimensional solid structures. This is existing technology in the field of finite element modeling and will not be elaborated further here. Specifically, solid elements include, for example, tetrahedral elements and hexahedral elements. By dividing the continuous adhesive head solid into multiple small volume elements, different locations within the material can participate in the stress analysis. This embodiment uses solid elements to discretize the adhesive head because the pad printing adhesive head is a flexible material with thickness. When pressed against the curved surface of the bottle, not only does the surface undergo displacement changes, but the interior also experiences compression and diffusion deformation. Therefore, a three-dimensional solid model is needed to describe the overall deformation process of the adhesive head.

[0027] In this embodiment, the finite element solid model of the printing pad is a three-dimensional flexible deformation model established based on the actual structure of the printing pad. In the specific acquisition process, the actual size parameters of the printing pad are first acquired, including the height of the printing pad, the shape of the contact end face, the overall outline size, and the surface outline in the free state. Then, the solid finite element modeling method is used to mesh the printing pad structure, so that multiple solid units are formed inside the printing pad, thereby establishing a digital model that can reflect the compression deformation process of the printing pad.

[0028] In this embodiment, elastic modulus, Poisson's ratio, and stress-strain relationship are material parameters describing the mechanical properties of the rubber head material. Elastic modulus describes the rubber head material's ability to resist deformation under pressure, Poisson's ratio describes the degree of lateral expansion when the rubber head deforms along the compression direction, and stress-strain relationship describes the variation of the rubber head material's deformation response under different levels of pressure. These parameters are obtained through actual rubber head material experiments. For example, compression experiments are performed on samples identical to the actual rubber head material, the deformation under different pressure conditions is recorded, and the material's mechanical parameters are determined based on the experimental results. Elastic modulus, Poisson's ratio, and stress-strain relationship are existing technologies in the finite element method (FEM) material definition. This embodiment, by setting corresponding material parameters, enables the rubber head model to reflect the flexible deformation during the actual pad printing process.

[0029] In this embodiment, the displacement loading sequence is a data set describing the spatial motion changes of the printing head during a single printing operation. Specifically, the motion trajectory of the printing head during its descent from the initial position, contact with the bottle, continuous pressing, and return is acquired according to the printing equipment control program. The changes in the reference position of the printing head are recorded in chronological order to form a continuous motion sequence. This sequence is used to simulate how the printing head gradually approaches and presses against the curved surface of the bottle during actual production.

[0030] In this embodiment, the displacement boundary condition is a constraint condition used in the finite element model to limit the motion state of the model. It belongs to the prior art in finite element analysis and will not be elaborated here. Specifically, the displacement boundary condition is used to specify the distance that a designated node in the rubber head model can move along a set direction, so that the rubber head finite element model moves according to the actual equipment action. For example, if the actual equipment controls the rubber head to descend vertically, then a corresponding rubber head reference node is set in the finite element model to generate displacement changes in the same direction.

[0031] In this embodiment, the matching of the finite element surface of the rubber head's outer surface with the finite element surface of the bottle body is the process for determining the possible contact area between the two models. Specifically, the rubber head finite element model is moved to the vicinity of the bottle body according to a displacement loading sequence. Based on the spatial distance relationship between the nodes on the rubber head's outer surface and the nodes on the bottle body's curved surface, the spatial range of possible contact locations between the two is selected, and a positional correspondence between the two models is established. This location range serves as the potential contact area, used for initialization of subsequent contact solutions. The actual contact area is ultimately determined after the contact solution is completed based on contact judgment conditions. This process determines the spatial range of possible interaction between the rubber head and the bottle body, providing a foundation for subsequent contact calculations.

[0032] In this embodiment, the surface-to-surface contact algorithm is an existing technique in finite element contact analysis and will not be elaborated further. Commonly used surface-to-surface contact algorithms include penalty function contact algorithms, Lagrange multiplier contact algorithms, and enhanced Lagrange contact algorithms. In a preferred embodiment, since the stiffness of the pad printing adhesive material is significantly lower than that of the plastic bottle material, the adhesive head is the primary deformation agent during contact. Therefore, the enhanced Lagrange contact algorithm is preferred to ensure the accuracy of contact force calculation while achieving a more stable convergence effect. This embodiment uses a surface-to-surface contact algorithm to establish the contact relationship between the finite element solid model of the adhesive head and the finite element model of the bottle surface because the contact between the adhesive head and the plastic bottle during pad printing is a continuous region contact, rather than a single node collision. By using the outer surface of the adhesive head as the contact surface and the curved surface of the bottle as the target contact surface, the changes in the contact area with curvature during the adhesive head pressing process can be described, allowing subsequent pressure inversion to obtain the pressure state corresponding to different curved surface positions.

[0033] In this embodiment, the contact relationship refers to the data relationship describing the interaction state between the rubber nozzle and the curved surface of the bottle. Specifically, during the acquisition process, the area where the rubber nozzle actually contacts the curved surface of the bottle is determined based on the analysis results of the surface-to-surface contact algorithm, and the positional correspondence and contact constraint relationships of the contact areas are established. This contact relationship is used to limit unrealistic mutual penetration between the rubber nozzle and the bottle, while preserving the true contact state of the rubber nozzle after it is deformed under pressure.

[0034] In this embodiment, model combination is a process of uniformly associating different finite element objects according to the actual pad printing process. This is an existing technology in finite element multi-physics object modeling and will not be elaborated here. Specifically, model combination includes using the bottle surface finite element model as the contact object, the glue head finite element solid model as the moving and deforming object, loading the glue head displacement boundary conditions onto the glue head model, and loading the surface-to-surface contact relationship between the two models, so that multiple independent models form an overall contact analysis model that can jointly describe the glue head pressing process onto the bottle.

[0035] It should be noted that the contact model established in this embodiment is not simply to simulate the mechanical movement of the printing head, but rather to obtain the contact pressure state formed by the combined influence of the bottle curvature and the flexible deformation of the printing head during the curved surface printing process. Because different regions of the plastic bottle have different curvatures, the local compression degree of the printing head, the actual contact area, and the pressure concentration area will change, and this pressure change will further alter the shear state of the ink. Therefore, by establishing a contact model that includes the actual curved surface structure and the deformation characteristics of the printing head, a data foundation is provided for subsequently inverting the pressure distribution matrix of the contact area between the printing head and the curved surface, and for further reconstructing the ink shear state based on the pressure gradient.

[0036] In a specific embodiment, for example, when pad printing brand logos on the surface of a cosmetic plastic bottle, the curvature of the central area of ​​the bottle is relatively small, while the shoulder area has a significant arc transition. If a conventional planar contact model is used, it cannot reflect the pressure changes caused by the concentrated pressure on the adhesive head at the shoulder. This embodiment establishes a curved surface model by scanning the bottle surface, increases the number of finite element nodes in the shoulder area, and simultaneously establishes a solid model of the silicone adhesive head. A surface-to-surface contact algorithm is used to simulate the downward pressing process of the adhesive head, forming a finite element model that can reflect the differences in contact states at different curvature locations. This provides a foundation for subsequent analysis of the ink transfer state in different areas.

[0037] S1.2, in this embodiment, the pressure distribution matrix of the contact area between the printing head and the curved surface during the inversion pad printing process is specifically as follows: Based on the contact model between the pad printing head and the object to be printed, the finite element contact solution is performed on the pad printing head pressing process according to the material parameters and displacement boundary conditions corresponding to the finite element solid model of the pad printing head, and the set of contact nodes between the outer surface of the pad printing head and the surface to be printed is obtained. Based on the set of contact nodes, extract the normal contact load corresponding to each contact node and the area of ​​the curved region represented by each contact node; The local contact pressure corresponding to each contact node is calculated based on the ratio between the normal contact load corresponding to each contact node and the area of ​​the curved region represented by each contact node. Based on the spatial coordinates of each contact node in the finite element model of the bottle surface, the local contact pressure corresponding to each contact node is mapped to the spatial position on the bottle surface. Based on the topological relationship of the finite element nodes on the curved surface of the bottle, a spatial sorting is performed to form a two-dimensional pressure distribution matrix corresponding to the contact area between the rubber head and the curved surface.

[0038] In this embodiment, the finite element contact solution is a process of numerically solving the deformation and contact state of the printing pad during the pressing process, based on the established contact model of the printing pad and the object to be printed. Specifically, the finite element solid model of the printing pad, the finite element model of the bottle surface, the material parameters of the printing pad, and the displacement boundary conditions established in the previous stage are input into the finite element analysis program. Based on the movement of the printing pad gradually approaching the bottle surface, the displacement changes of the nodes inside the printing pad and the contact state between the outer surface of the printing pad and the bottle surface are calculated step by step. When the distance between the nodes on the outer surface of the printing pad and the nodes on the bottle surface meets the contact condition, the corresponding node is marked as a contact node, and the contact state during the pressing process is continuously updated. The finite element contact solution in this step belongs to the existing technology in the field of finite element analysis. Commonly used methods include nonlinear finite element solution methods based on Newton iteration, incremental loading solution methods, and contact constraint solution methods. This embodiment does not limit the internal iterative process of the finite element solver, but rather uses the output node contact states and force results to provide a data foundation for subsequent pressure inversion.

[0039] In this embodiment, the material parameters corresponding to the finite element solid model of the printing pad are a set of material properties used to describe the flexible deformation characteristics of the printing pad, specifically including parameters such as elastic modulus, Poisson's ratio, and stress-strain relationship. These parameters are not set manually, but are obtained through material testing based on the actual printing pad material used. For example, a compression test is performed on a silicone sample with the same material as the actual printing pad, and the pressure changes and deformations of the material under different degrees of compression are collected. The deformation law of the material under stress is determined based on the experimental results, and this law is input into the finite element model so that the deformation state of the printing pad during the finite element solution process is consistent with the actual printing pad.

[0040] In this embodiment, the displacement boundary conditions are constraint parameters that limit the motion mode and range of the finite element model of the printing head. Specifically, during the acquisition process, the descent height, pressing distance, and return path of the printing head are collected based on the actual operating trajectory of the pad printing equipment. The positional changes of the printing head reference nodes at each time stage are then converted into node displacement constraints in the finite element model. For example, in actual production, if the printing head descends from its initial height to the bottle surface and continues to compress a certain distance, the corresponding nodes in the finite element model are set to generate the same displacement along the pressing direction, enabling the finite element model to simulate the process of the printing head gradually pressing against the curved surface during actual pad printing.

[0041] In this embodiment, the contact node set is the set of nodes obtained by matching the nodes on the outer surface of the adhesive head and the curved surface of the bottle body during the finite element contact solution process. It represents the actual position where the adhesive head and the bottle body experience force transfer. Specifically, during the finite element solution process, the spatial distance between the nodes on the outer surface of the adhesive head and the curved surface of the bottle body is continuously monitored. When the contact judgment condition is met between two nodes, the corresponding adhesive head node and the corresponding bottle body node are recorded as contact nodes. For example, in the flat area in the middle of the bottle body, the adhesive head may have a continuous and large range of contact nodes; while in areas with significant changes in the curvature of the bottle shoulder, only some adhesive head nodes participate in contact. Therefore, the contact node set can reflect the changes in the actual positions involved in the transfer in different curved surface areas.

[0042] In this embodiment, the contact judgment condition is used to determine whether actual contact has occurred between the adhesive head node and the curved surface node of the bottle. Specifically, during the acquisition process, a minimum allowable distance between nodes is set according to the finite element contact algorithm. When the adhesive head node moves near the curved surface of the bottle and the distance between them reaches the contact range, the node is marked as being in contact; when the node distance exceeds the set range, it is considered that no contact has occurred. This contact judgment condition is usually automatically set by the finite element contact algorithm. For example, the penalty function contact algorithm determines the contact state by setting an allowable contact distance, which is an existing finite element contact analysis technique. This embodiment applies this technique based on the contact characteristics between the pad printing adhesive head and the curved surface of the plastic bottle.

[0043] In this embodiment, the normal contact load is a parameter representing the force applied by the adhesive head along the normal direction of the bottle's curved surface, used to describe the magnitude of the pressure exerted on different positions during the adhesive head pressing process. Specifically, after the finite element contact solution is completed, the contact force component along the normal direction of the bottle's curved surface is extracted for each contact node; this component is the normal contact load of that node. It should be noted that the normal direction differs at different positions on the bottle's curved surface; therefore, the force decomposition direction must be determined based on the normal direction at each contact node's location on the curved surface. For example, in the bottle shoulder region, due to curvature changes leading to increased local compression of the adhesive head, the normal contact load on the corresponding node will be higher than in the flatter areas of the bottle body.

[0044] In this embodiment, the surface area represented by each contact node is the effective range of action represented by each contact node on the bottle surface, used to convert the force on discrete nodes into pressure over a continuous region. Specifically, the area is first calculated based on the surface elements adjacent to each contact node in the finite element model of the bottle surface, according to the positional weight of each contact node within its respective element. For example, for a quadrilateral surface element, the area is divided equally among the four nodes and assigned to each contact node; for a triangular element, it is divided equally among the three nodes. A contact node may belong to multiple surface elements simultaneously; the areas allocated to the node in each element are summed to obtain the theoretical surface area represented by the node. Then, based on the contact determination result, only the area corresponding to the surface portion that actually participates in contact within the node is retained, while the areas of surface elements that did not engage in contact are discarded, ultimately yielding the surface area represented by the contact node. For example, at the edge of the bottle or at abrupt changes in curvature, because the glue head cannot fully fit the curved surface, some theoretical mesh areas exist in the model but do not actually make contact, and therefore are not included in the area of ​​the curved surface region of that node.

[0045] In this embodiment, local contact pressure is a parameter describing the pressure magnitude at different spatial locations within the contact area between the rubber nozzle and the curved surface of the bottle. Specifically, during the acquisition process, the force acting on each contact node is normalized based on the normal contact load corresponding to that node and the area of ​​the curved surface represented by that node, converting the discrete node load into a pressure value per unit area. For example, under the same large normal load, if the area represented by a node is small, it indicates a higher degree of pressure concentration in that area; if the area represented by the node is large, it indicates a more dispersed pressure effect. This method effectively demonstrates the local pressure concentration phenomenon caused by the curvature of the bottle.

[0046] In this embodiment, the bottle surface coordinate system serves as a reference coordinate system for uniformly describing the spatial location of pressure. Specifically, during the acquisition process, the spatial node coordinates from the establishment of the finite element model of the bottle surface are used as the basis. The contact node positions obtained from the finite element solution are mapped to the spatial coordinate positions of the bottle surface, ensuring that each pressure value has a clearly defined spatial location. For example, if the same pressure value is located in the bottle shoulder area and the bottle body area, the corresponding ink shear effects will differ; therefore, it is necessary to distinguish the location where the pressure occurs using the bottle surface coordinate system.

[0047] In this embodiment, pressure corresponds to the process of allocating discrete contact pressure data obtained from finite element analysis to spatial locations on the bottle surface. Specifically, based on the spatial coordinates of the contact node in the finite element model of the bottle surface, the local contact pressure corresponding to that node is recorded at the corresponding spatial location on the bottle surface. If the contact node and the bottle surface node completely coincide, the pressure value is directly allocated to that node location. If there is a deviation between the two locations due to the tolerance settings in the contact search algorithm, the pressure value is allocated to the nearest bottle surface node according to the principle of closest spatial distance. When multiple contact nodes correspond to the same bottle surface node, a weighted average is calculated based on the proportion of the surface area represented by each contact node to the total corresponding area. The weighted pressure value is then used as the local contact pressure of that bottle surface node. Through the above processing, a continuous surface pressure expression result is formed.

[0048] In this embodiment, the finite element node topology of the bottle surface describes the data relationships between the connection structures of the bottle surface nodes, specifically generated during the previous stage of establishing the finite element model of the bottle surface. This topology includes the connection order, adjacency relationships, and surface element arrangement relationships between nodes. For example, a surface node connects to multiple adjacent nodes; these connections determine the arrangement order of pressure data on the bottle surface. Finite element node topology relationships are existing technology in finite element mesh modeling; this embodiment utilizes existing node connection information to spatially sort the pressure data.

[0049] In this embodiment, the two-dimensional pressure distribution matrix is ​​a data matrix formed by arranging the local contact pressures corresponding to different spatial locations within the curved surface contact area according to the unfolding direction of the bottle surface. It is used to represent the spatial distribution of pressure throughout the entire rubber head-bottle contact area. Specifically, during the acquisition process, based on the finite element node topology of the bottle surface, two extension directions along the bottle surface are selected as the row and column directions of the matrix. The pressure values ​​at different spatial locations are organized according to the node arrangement order in these two directions, so that pressure values ​​corresponding to adjacent spatial locations are stored in adjacent positions of the matrix. For example, if the circumference of the plastic bottle is used as the row direction of the matrix and the axial direction of the plastic bottle is used as the column direction, then adjacent rows in the matrix represent adjacent areas in the circumference direction of the bottle, and adjacent columns represent adjacent areas in the axial direction of the bottle. This pressure distribution matrix serves as the data basis for subsequent pressure gradient calculations and ink shear state reconstruction.

[0050] It should be noted that the pressure inversion in this step does not involve directly measuring the pressure between the printing head and the bottle. Instead, it utilizes the previously established finite element model of curved surface contact to obtain the pressure state of the contact area based on the deformation response of the printing head material and contact constraints. Since it is impossible to directly place pressure sensors between the printing head and the plastic bottle during actual pad printing, the finite element contact inversion method can obtain the pressure distribution of the curved surface area without changing the pad printing process. This provides a data foundation for subsequent analysis of ink shear state changes based on pressure gradients and addresses the problem that traditional ink viscosity prediction methods cannot reflect the actual transfer viscosity of curved surfaces.

[0051] In a specific embodiment, for example, when pad printing a trademark on the surface of a shampoo bottle, the front area of ​​the bottle is nearly flat, resulting in a large contact area after the adhesive pad is pressed together. Finite element analysis reveals that this area contains a large number of continuous contact nodes, corresponding to relatively uniform local pressure. However, the curvature increases at the bottle's side shoulder, causing local compression of the adhesive pad. This reduces the number of contact nodes in some areas but increases the normal load. After correction using the area of ​​the curved surface represented by the nodes, a higher local pressure value is obtained. Finally, all contact node pressures are rearranged according to the bottle's curved surface position to form a pressure distribution matrix that reflects the pressure differences in different areas of the bottle.

[0052] S2, determine the pressure gradient distribution within the contact area based on the pressure distribution matrix, determine the ink flow velocity distribution based on the pressure gradient distribution, determine the ink shear rate distribution based on the flow velocity distribution, and correct the ink storage viscosity using the shear rate distribution based on the ink shear thinning rheological characteristics to obtain the effective transfer viscosity under the current curved surface contact conditions.

[0053] S2.1 In this embodiment, the pressure gradient distribution within the contact area is determined according to the pressure distribution matrix, the ink flow velocity distribution is determined based on the pressure gradient distribution, and the ink shear rate distribution is determined based on the flow velocity distribution, specifically as follows: Based on the pressure distribution matrix, differential calculation is performed on the pressure values ​​corresponding to the finite element nodes of adjacent curved surfaces to obtain the pressure change at different spatial positions within the contact area between the glue head and the curved surface to be printed. The pressure gradient at each location is calculated based on the ratio between the pressure change at each location and the corresponding spatial spacing between nodes, thus obtaining the pressure gradient distribution within the contact area. Based on the pressure gradient distribution, the flow direction of ink in the contact area under pressure is determined, and based on the moving speed of the printing head and the relative motion relationship between the printing head and the surface to be printed, the ink flow velocity distribution at each position in the contact area is determined. Based on the ink flow velocity distribution and ink layer thickness parameters, the ink velocity gradient at different curved surface positions is calculated, and the local shear rate distribution of the ink is determined based on the velocity gradient. Based on the spatial correspondence between the local shear rate distribution of the ink and the pressure distribution matrix, the shear rates corresponding to each surface position are organized according to the spatial arrangement of the pressure distribution matrix to form an ink shear rate distribution matrix that is consistent with the spatial coordinates of the pressure distribution matrix.

[0054] In this embodiment, the pressure distribution matrix is ​​a set of contact area pressure data obtained in the previous step through the finite element method of the pad printing pad-surface contact. It represents the pressure difference between different spatial locations of the pad printing pad and the curved surface of the plastic bottle. Each data unit in this matrix corresponds to a spatial node position in the finite element model of the bottle surface, recording the local contact pressure applied by the pad printing pad to the bottle surface at that position. In this step, the pressure distribution matrix is ​​not used as the final control variable, but rather as input data to analyze how pressure affects the ink flow state. By analyzing the pressure changes at adjacent positions, the solid contact pressure state is converted into an ink flow state change.

[0055] In this embodiment, adjacent surface finite element nodes are nodes that are spatially adjacent and connected in the finite element model of the bottle surface. Specifically, based on the node topology established in the previous step, adjacent nodes corresponding to each pressure matrix element are found, such as two adjacent nodes along the circumferential direction of the bottle or two adjacent nodes along the axial direction of the bottle. Since these nodes represent adjacent regions on the bottle surface, their pressure differences can reflect the pressure change trend within that region.

[0056] In this embodiment, pressure difference calculation is a data processing procedure used to analyze the degree of pressure change between adjacent spatial locations. Specifically, the pressure values ​​corresponding to adjacent nodes in the pressure distribution matrix are compared to obtain the amount of pressure change between two spatial locations. For example, if the pressure in a certain area of ​​the bottle shoulder is significantly higher than that in adjacent areas, a larger pressure change occurs between the corresponding nodes; if the pressure change is smaller in the flat areas of the bottle body, the pressure change between the corresponding nodes is lower. This process is used to extract local variation features in the pressure distribution, rather than simply analyzing the absolute pressure magnitude.

[0057] In this embodiment, the node spatial spacing is the distance between adjacent curved surface finite element nodes along the actual curved surface direction of the bottle. Specifically, the actual spatial distance between two adjacent nodes is determined based on the node spatial coordinates and node connection relationships in the bottle's curved surface finite element model. Since the plastic bottle has a curved surface structure, the distance between nodes cannot be simply calculated using a two-dimensional unfolded distance; instead, it needs to be determined based on the spatial coordinate relationships in the curved surface finite element model to ensure that the subsequent pressure gradient reflects changes along the actual curved surface direction.

[0058] In this embodiment, the pressure gradient distribution describes the spatial distribution of pressure variation within a unit space. Specifically, during the acquisition process, the pressure variation in different directions is analyzed based on the pressure variation between adjacent nodes and the spatial distance between corresponding nodes to obtain the pressure variation trend corresponding to each curved surface position. For example, in areas with a large curvature on the bottle shoulder, the pressure changes rapidly due to the curvature restricting the ink nozzle, resulting in a larger pressure gradient in this area; conversely, pressure changes are slower in areas with gentler curves on the bottle body, resulting in a smaller pressure gradient. This pressure gradient distribution is used to describe how pressure drives ink flow changes.

[0059] In this embodiment, the change in displacement during the pressing process of the adhesive head describes the change in the spatial position of the adhesive head from contact with the bottle to the completion of pressing. Specifically, based on the adhesive head displacement boundary conditions established in the previous stage, the position changes of the adhesive head reference node at different pressing time stages are read to obtain the direction of motion and distance of movement of the adhesive head relative to the curved surface of the bottle. For example, if the adhesive head gradually approaches the bottle surface during its descent and continues to generate compressive displacement after contact, this change in compressive displacement is used to analyze the extrusion flow trend of the ink under pressure.

[0060] In this embodiment, the correspondence between the ink flow direction under pressure and the pressure gradient direction is a mapping relationship describing how pressure changes affect the ink flow direction. Specifically, during the acquisition process, the direction of pressure increase is determined based on the pressure gradient distribution, and this direction is taken as the main driving force direction for the ink under pressure. Simultaneously, the pressure gradient direction is corrected by considering the movement direction of the printing head during the pressing process, ensuring it conforms to the actual ink flow direction after being squeezed by the printing head during the actual pad printing process. For example, when the pressure in the bottle shoulder area changes rapidly from low to high, the ink tends to flow towards the area with lower pressure. Therefore, this correspondence is used to determine the main flow direction of the ink within the curved contact area.

[0061] In this embodiment, the pad printing head movement speed is the change in position per unit time during the movement of the pad printing head driven by the pad printing equipment. Specifically, it is obtained by reading the speed setting value in the control parameters of the pad printing equipment or the motion control program. For example, if the equipment controls the pad printing head to descend at a fixed speed, then this speed is used as the pad printing head pressing speed input; if there is a variable speed stage during the descent of the pad printing head, then the speed changes in different stages are obtained to describe the ink flow state in different pressing stages.

[0062] In this embodiment, the relative displacement change between the printing head and the surface to be printed is data describing the mutual motion relationship between the printing head surface and the bottle surface. Specifically, during the acquisition process, the distance the printing head moves relative to the bottle surface at different time stages is determined based on the change in position difference between the printing head's trajectory and the fixed position of the bottle surface. Since the bottle is usually kept fixed during the pad printing process, this relative displacement is mainly generated by the printing head's movement; however, for rotational positioning or fixture fine-tuning processes, it can also include changes in the bottle's position. It should be noted that this relative displacement change is used to assist in determining the relative velocity direction between the printing head and the surface, rather than being directly used as a velocity quantity in the calculation of the ink flow velocity.

[0063] In this embodiment, the ink flow velocity distribution is a data set representing the magnitude and direction of ink flow velocity at different spatial locations within the contact area. Specifically, the pressure gradient is used as the primary driving force for ink flow. Based on the pressure gradient distribution, the direction and magnitude of the flow velocity generated by pressure at each location are determined. Simultaneously, the nozzle movement speed is used as an auxiliary driving force for ink flow. The flow velocity driven by the pressure gradient and the flow velocity driven by the nozzle movement are combined using a vector superposition method to obtain the composite ink flow velocity at each location. For example, in areas of concentrated pressure, the ink experiences stronger extrusion force, resulting in a higher flow velocity than in areas of uniform pressure; in areas with smaller curvature changes, the ink flow velocity is relatively stable. The above method forms an ink flow velocity distribution covering the entire contact area. In one embodiment, the vector superposition is primarily driven by pressure gradient and secondarily by the movement of the printing head. The weights of both are pre-calibrated based on the printing head pressing speed and the ink rheological properties. Specifically, the superposition weight of the pressure gradient driving speed and the printing head movement speed is pre-calibrated based on the printing head pressing speed and the ink rheological properties. The calibration method is as follows: finite element fluid simulation or actual testing is performed at multiple printing head pressing speeds. By comparing the simulation / test results with the preset ink transfer target value, the weight coefficient that makes the ink transfer amount closest to the target value is determined and used as the superposition weight under that working condition. For different printing head speeds or different ink formulations, the weight coefficient can be adaptively adjusted according to the actual working conditions.

[0064] In this embodiment, the ink layer thickness parameter refers to the actual thickness of the ink layer subjected to shearing during the transfer process, rather than the total ink thickness within the ink storage area. Specifically, the initial ink thickness on the pad printing head surface is obtained based on the ink adhesion state after the pad printing head is dipped in ink, through microscopic morphology detection of the head surface, ink coating experiments, or production process settings. Simultaneously, the actual ink thickness participating in the flow within the contact area is corrected by considering the degree of head deformation and ink spreading changes during the pressing process. For example, the ink layer in the central area of ​​the head may be compressed and thinned due to higher pressure, while the ink layer thickness in the edge areas is relatively larger. Therefore, an ink layer thickness parameter corresponding to the actual contact state needs to be used.

[0065] In this embodiment, the ink velocity gradient is a parameter describing the degree of change in ink flow velocity at different locations. Specifically, during its acquisition, the spatial velocity variation of the ink is analyzed based on the velocity differences between adjacent locations in the ink flow velocity distribution and their corresponding spatial distances. When the difference in ink flow velocity between two adjacent regions is large, it indicates a strong velocity change in that region; when the velocities of adjacent regions are similar, it indicates relatively stable ink flow.

[0066] In this embodiment, the local shear rate of the ink is determined based on the ink velocity gradient. Specifically, for each spatial location within the contact area, the corresponding shear rate value is determined based on the magnitude of the ink velocity gradient at that location, combined with the rheological properties of the pad printing ink. The ink rheological properties are obtained through rotational rheometer testing, and a correspondence between the velocity gradient and the shear rate is established based on the test results. For example, the bottle shoulder area has a larger pressure gradient, resulting in a significant change in ink flow velocity, thus corresponding to a higher shear rate; the bottle body area has a smaller pressure change, resulting in a slower change in ink velocity, thus corresponding to a lower shear rate. This distribution reflects how the contact pressure on the curved surface alters the internal flow state of the ink.

[0067] The quantitative relationship between velocity gradient and shear rate is as follows: For each spatial location within the contact area, the velocity gradient tensor is calculated from the ink flow velocity field, and its components are: velocity gradient component = partial derivative of velocity component along the spatial coordinate direction; the velocity gradient tensor is decomposed into a symmetric tensor and an antisymmetric tensor, and the components of the symmetric tensor are taken; the equivalent shear rate is calculated and determined based on each component of the symmetric tensor, that is: equivalent shear rate = sqrt(2 × sum of squares of each component of the symmetric tensor); the equivalent shear rate is the local shear rate value of the ink corresponding to that spatial location.

[0068] The following are feasible calculation formulas: For three-dimensional flow, the velocity gradient tensor is: ; The strain rate tensor (symmetric part) is: ; The equivalent shear rate is: ; In the above formula, , These represent the flow velocity components of the ink in different directions within the spatial coordinate system; , These represent the coordinate positions in different directions within the spatial coordinate system; The components representing the strain rate tensor are used to describe the deformation rate in different directions within the ink. This represents the equivalent shear rate, which is the local shear rate value of the ink at that spatial location.

[0069] In this embodiment, the spatial correspondence is a positional mapping relationship used to ensure that the ink shear rate data and the spatial position in the pressure distribution matrix remain consistent. Specifically, during the acquisition process, based on the coordinates of the bottle surface nodes used in the ink flow velocity analysis, each shear rate calculation position is matched with the corresponding node in the pressure distribution matrix. For example, if the first region in the pressure matrix corresponds to the left side of the bottle shoulder, the shear rate calculated at that position must also be stored in the corresponding region of the pressure matrix, and cannot be randomly arranged according to the calculation order.

[0070] In this embodiment, matrix mapping is the process of reorganizing the shear rate data at discrete spatial locations according to the arrangement of the pressure distribution matrix. Specifically, during the acquisition process, based on the bottle surface node number corresponding to each element in the pressure distribution matrix, the local shear rate value corresponding to that node is found and filled into the new matrix structure according to the same node number order, so that the ink shear rate distribution matrix and the pressure distribution matrix have the same size, the same spatial coordinates, and the same regional correspondence. For example, if the 5th row and 8th column in the pressure distribution matrix represents a node in the bottle shoulder region, then the 5th row and 8th column in the shear rate distribution matrix also represents the ink shear state corresponding to that location.

[0071] In this embodiment, the ink shear rate distribution matrix is ​​a two-dimensional data matrix describing the degree of ink shearing within the curved contact area during pad printing. Each position corresponds to a spatial region on the curved surface of the bottle, and the local shear rate experienced by the ink within that region is recorded. This matrix is ​​used to subsequently analyze the ink viscosity changes at different locations based on the ink shear thinning rheological properties, thereby converting the ink storage state into an effective viscosity that more closely approximates the actual transfer state.

[0072] It should be noted that this step does not directly equate the pressure value with the ink rheological state. Instead, it converts the solid contact pressure field into a fluid shear state by exploring the correlation between pressure gradient, nozzle movement, and ink flow velocity. Since techniques such as tire contact pressure analysis primarily target the deformation of elastic solids, while pad printing inks are non-Newtonian fluids with shear-thinning properties, this step adds a conversion process from pressure gradient to shear rate. This allows the pressure distribution to be used in subsequent viscosity correction based on ink flow mechanism, addressing the problem that traditional viscosity prediction methods, relying solely on ink storage conditions, cannot reflect the actual shear conditions experienced during curved surface pad printing.

[0073] In a specific embodiment, for example, when pad printing a logo on the surface of a shampoo bottle, the central area of ​​the bottle has a smaller curvature, resulting in a more uniform pressure distribution after the printing head is pressed, lower ink velocity variation, and a correspondingly lower shear rate. However, at the bottle shoulder, due to the significant curvature change, the local compression of the printing head increases, the pressure gradient rises, and the ink flows more noticeably along the curved surface, leading to a stronger velocity variation in this area. By using the above method, the pressure change in the bottle shoulder area is converted into a corresponding ink shear rate change, providing a basis for subsequent calculation of the actual transfer viscosity in this area.

[0074] S2.2 In this embodiment, the step of correcting the ink storage viscosity based on the shear rate distribution according to the ink shear thinning rheological characteristics to obtain the effective transfer viscosity under the current curved surface contact conditions specifically involves: Based on the shear-thinning rheological properties of the ink material, the apparent viscosity of the ink corresponding to each local shear rate value is determined by pre-established rheological property data, thus forming a correspondence between shear rate and apparent viscosity. Based on the correspondence, the local apparent viscosity of the ink at each curved surface position under the corresponding shear rate is determined, and a local viscosity distribution matrix consistent with the spatial coordinates of the ink shear rate distribution matrix is ​​formed according to the spatial arrangement of the ink shear rate distribution matrix. The ink viscosity of the ink in the pad printing ink supply area under static state is obtained, and the ink viscosity is used as the initial viscosity reference. Based on the degree of deviation of the local apparent viscosity at each spatial position in the local viscosity distribution matrix relative to the ink storage viscosity, the ink storage viscosity is corrected, and the corrected viscosity value at each position is taken as the effective transfer viscosity at that position under the current curved surface contact condition.

[0075] In this embodiment, the ink shear rate distribution matrix is ​​a spatialized data set obtained in step S2.1 based on the pressure gradient, the state of the printing head, and the change in ink flow velocity. It represents the degree of ink shear at different locations within the contact area between the printing head and the curved surface of the plastic bottle. Each data unit in this matrix corresponds to a spatial location in the finite element model of the bottle's curved surface, recording the degree of shear change of the ink at that location due to the compression and flow of the printing head. For example, areas with greater curvature on the bottle shoulder exhibit more significant changes in ink flow velocity due to varying degrees of printing head compression, resulting in a higher shear rate value at those locations; conversely, areas with gentler ink flow variations have lower shear rate values ​​at those locations.

[0076] In this embodiment, the local shear rate value is the amount of ink shear change corresponding to a single spatial location in the ink shear rate distribution matrix. Specifically, during the acquisition process, the shear rate data corresponding to each surface location is extracted based on the correspondence between the finite element node numbers of the bottle surface and the elements of the shear rate distribution matrix. For example, if a node in the pressure distribution matrix represents the bottle shoulder region, the ink shear rate value corresponding to that node is simultaneously read and used as the input parameter for the ink rheological state analysis at that location.

[0077] In this embodiment, the shear-thinning rheological property of the ink material describes the material property that the viscosity of the ink decreases with increasing shear rate after being subjected to shear. Since pad printing ink is usually composed of pigments, resins, solvents, and additives, it has a polymer chain structure and a particulate dispersion structure. In a static state, the internal structure remains stable, exhibiting a high viscosity. When the ink is subjected to shear due to the pressing of the printing head, the internal structure undergoes orientation, reducing the ink flow resistance and resulting in a decrease in apparent viscosity.

[0078] This rheological property needs to be obtained based on the actual ink being used. Specifically, a rotational rheometer can be used to test the ink under different shear rates, collecting corresponding viscosity change data. For example, low shear, medium shear, and high shear conditions can be set respectively, and the viscosity values ​​of the ink under different shear conditions can be recorded to form the shear rate-apparent viscosity change data corresponding to this ink model.

[0079] In this embodiment, the mapping relationship between shear rate and apparent viscosity of ink is a data relationship describing the viscosity change of ink under different shear conditions. This relationship is not a fixed ratio set by humans, but is established based on the material characteristics of the pad printing ink. Specifically, in the acquisition process, the pad printing ink is subjected to shear rheology testing using a rotational rheometer to obtain apparent viscosity data under different shear rate conditions, forming the rheological characteristic curve of the ink. In subsequent applications, based on this rheological characteristic curve, the apparent viscosity of the ink corresponding to each local shear rate value is determined, forming a correspondence between shear rate and apparent viscosity. For example, if the test shows that the ink has a higher viscosity under low shear conditions and a lower viscosity under high shear conditions, then a correspondence between the ink's static viscosity and dynamic viscosity is established.

[0080] Establishing the relationship between shear rate and apparent viscosity based on ink rheological experiments is an existing technique in the field of rheology. Existing techniques typically employ non-Newtonian fluid models such as power-law models, Herschel-Bulkley models, and Carreau models to describe the relationship between shear rate and viscosity. This embodiment does not limit the specific mathematical model but selects the corresponding rheological model based on the actual type of pad printing ink and applies it to the curved surface pad printing process.

[0081] In this embodiment, the local apparent viscosity is the dynamic viscosity value exhibited by the ink at the actual curved surface contact location and under actual shear conditions. Specifically, during the acquisition process, based on each shear rate value in the ink shear rate distribution matrix, the actual viscosity state of the ink at the corresponding location after being squeezed by the printing head is obtained by querying or calculating using the pre-established shear rate-apparent viscosity correspondence. The query method is as follows: for shear rate values ​​already included in the rheological characteristic curve, the corresponding apparent viscosity is directly read; the calculation method is as follows: the test data is fitted using a power-law model or a Carreau model, and the apparent viscosity corresponding to the shear rate values ​​not covered by the rheological characteristic curve is calculated based on the fitting parameters. The model type and fitting parameters are determined through rheological testing according to the type of pad printing ink. Both the power-law model and the Carreau model are existing rheological models describing the shear-thinning behavior of non-Newtonian fluids.

[0082] Taking the Carreau model as an example, the relationship between shear rate and apparent viscosity can be expressed as the following function: Apparent viscosity = zero shear viscosity + (zero shear viscosity - infinite shear viscosity) / (1 + (shear rate × material time constant)). The power law exponent is calculated as (-1) / 2), where zero shear viscosity, infinite shear viscosity, material time constant, and power law exponent are model parameters determined by fitting test data from a rotational rheometer.

[0083] The following is a feasible formulaic expression for apparent viscosity: ; In the formula, Apparent viscosity (Pa·s) represents the apparent viscosity of the ink at a specific shear rate. Shear rate (s) -1 ), Zero shear viscosity indicates the limiting viscosity of the ink when the shear rate approaches zero; Infinite shear viscosity represents the limiting viscosity of the ink as the shear rate approaches infinity. Let the material time constant (s) represent the relaxation time constant of the ink material. The power-law exponent is used to describe the degree of nonlinearity in shear-thinning behavior.

[0084] For example, the shear rate is lower in the central region of the bottle, resulting in a higher apparent viscosity according to the corresponding relationship; while the shear rate is higher at the shoulder of the bottle due to the larger pressure gradient, resulting in a lower apparent viscosity. The viscosity value obtained through this process can reflect the actual flowability of the ink during printing at different curved surface locations.

[0085] In this embodiment, the local viscosity distribution matrix is ​​a data set formed by arranging the local apparent viscosity corresponding to different curved surface positions according to the same spatial structure as the ink shear rate distribution matrix. Specifically, during the acquisition process, based on the bottle surface node number corresponding to each shear rate matrix element, the apparent viscosity value obtained through the correspondence is written to the same node position, ensuring that the local viscosity distribution matrix maintains spatial consistency with the pressure distribution matrix and the shear rate distribution matrix.

[0086] For example, if the 3rd row and 5th column of the pressure distribution matrix represents the right side of the bottle shoulder, then the 3rd row and 5th column of the shear rate distribution matrix and the local viscosity distribution matrix also represent the same region, thus ensuring that the specific curved surface region can be located during subsequent viscosity correction.

[0087] In this embodiment, the ink storage viscosity refers to the initial viscosity of the ink in the pad printing ink supply area before it is subjected to pressure and shearing action from the printing head. Specifically, during the production process, ink samples to be used are collected from the ink supply tank or ink storage chamber. Under specified temperature, humidity, and settling time conditions, the viscosity of the ink in its natural state is measured using a viscosity testing device and used as the ink storage viscosity.

[0088] For example, after the ink in the ink supply tank of a pad printing equipment has been left to stand for a long time, the internal structure of the ink has returned to stability. The viscosity measured at this time is used as the ink storage viscosity to indicate the state of the ink used in the traditional ink supply control process.

[0089] In this embodiment, the initial viscosity benchmark is a reference value used to describe the original state of the ink before curved surface transfer. Specifically, the ink storage viscosity detected in the ink supply area is used as the base state before the start of the entire pad printing cycle, and this state is used as the comparison benchmark for subsequent analysis of viscosity changes caused by pad pressing.

[0090] For example, the basic viscosity of the same ink may vary in different batches of production. Therefore, it is necessary to obtain the storage viscosity of the current ink batch at the beginning of each production run to avoid prediction deviations caused by using fixed empirical values.

[0091] In this embodiment, the degree of deviation of the local apparent viscosity relative to the ink storage viscosity is the degree of difference between the dynamic viscosity and the ink storage viscosity at each spatial location in the local viscosity distribution matrix. Specifically, during the acquisition process, the local apparent viscosity at each curved surface location is compared with the initial ink storage viscosity to determine the degree of viscosity decrease caused by the pressing of the adhesive head.

[0092] For example, if a certain area has a high ink viscosity, but the apparent viscosity of that area is significantly reduced due to strong shearing at the bottle shoulder, then the corresponding offset in that area is larger; while the shearing effect is weaker in planar areas, so the offset is smaller.

[0093] In this embodiment, viscosity offset correction under curved surface contact conditions is a process of spatially adjusting the traditional ink storage viscosity based on the actual shearing degree at different curved surface positions. Specifically, the ink storage viscosity is used as a baseline value, and the ink storage viscosity is corrected according to the degree of offset of the local apparent viscosity relative to the ink storage viscosity at each position in the local viscosity distribution matrix: for areas with a large offset, the ink storage viscosity is reduced to a level close to the local apparent viscosity at that position; for areas with a small offset, the ink storage viscosity remains basically unchanged. Finally, the corrected viscosity value at each position is the effective transfer viscosity corresponding to that position.

[0094] For example, in the central area of ​​a cylindrical bottle, the contact pressure and shearing action are relatively small, resulting in a small difference between the local apparent viscosity and the ink storage viscosity, thus requiring a smaller correction. In the curved area of ​​the bottle shoulder, the curvature change leads to local pressure concentration, causing the ink to be subjected to stronger shearing action. The local apparent viscosity is significantly lower than the ink storage viscosity, so the ink storage viscosity in this area needs to be reduced accordingly to reflect the enhanced ink flow capacity during the actual transfer process.

[0095] In this embodiment, the effective transfer viscosity is the ink viscosity state after correction for the curved surface contact state. It is used to represent the rheological state of the ink when the pad printing head actually contacts the curved surface of the bottle and ink transfer occurs. This parameter differs from the traditional ink storage viscosity, as it includes not only the properties of the ink material itself, but also the dynamic effects caused by the bottle curvature, pad pressure, and ink shearing action.

[0096] It should be noted that this step does not directly change the ink viscosity using pressure values. Instead, it converts mechanical contact pressure into ink rheological changes using the ink shear rate distribution matrix obtained in step S2.1, and then uses the ink's own shear thinning properties to complete the viscosity correction. This process avoids the physical state mismatch problem caused by directly applying the elastic contact pressure model to a non-Newtonian fluid, ensuring that the obtained effective transfer viscosity reflects the ink flow capacity in the actual pad printing process. This transforms ink supply control from static viscosity compensation to adaptive adjustment based on the actual transfer state.

[0097] In a specific embodiment, for example, when pad printing labels on shampoo plastic bottles, the traditional method usually determines the ink supply amount based on the ink viscosity in the ink supply tank. However, due to the significant curvature change in the bottle shoulder area, the ink in this area is subjected to strong shearing after the printing head is pressed, resulting in an actual viscosity lower than that of the stored ink. Through this step, the shear rate of the ink in the bottle shoulder area is first obtained based on the pressure gradient, and then the local apparent viscosity is obtained based on the rheological properties of the ink. The stored ink viscosity is then corrected, allowing the ink supply control to be adjusted according to the actual transfer state.

[0098] S3, using the effective viscosity of the transfer as the initial state, and combining the effective viscosity drift state during the pad printing cycle, predict the change in ink supply demand for the next pad printing cycle.

[0099] In this embodiment, the step of using the effective transfer viscosity as the initial state and combining it with the effective viscosity drift state during the pad printing cycle to predict the change in ink supply demand for the next pad printing cycle specifically involves: Using the effective viscosity of the transfer as the initial state, establish an effective viscosity state sequence corresponding to the initial cycle of the pad printing cycle; Collect data on ink replenishment amount, printing interval time and ambient temperature change for each ink supply cycle during continuous pad printing. Based on the effective viscosity state sequence, the viscosity change between adjacent pad printing cycles is analyzed, and the effects of the ink replenishment amount, the printing interval time, and the ambient temperature change data on the viscosity change are combined to determine the effective viscosity drift within a unit cycle, thus forming the effective viscosity drift state sequence corresponding to the pad printing cycle process. Based on the effective viscosity drift state sequence, a recursive relationship is established between the effective viscosity of the current cycle and the viscosity drift of the historical cycles according to the order of the pad printing cycle. Based on the transfer effective viscosity corresponding to the current cycle and the recursive relationship, the predicted effective viscosity corresponding to the next pad printing cycle is calculated. Based on the viscosity difference between the predicted effective viscosity and the current transfer effective viscosity, and combined with the viscosity recovery ratio corresponding to the pre-calibrated unit ink supply, the viscosity compensation requirement for the next transfer printing cycle is determined. The viscosity compensation requirement is converted into the ink supply requirement change corresponding to the ink supply actuator.

[0100] In this embodiment, the effective transfer viscosity is the viscosity state value obtained in step S2.2 after correcting the ink storage viscosity based on the ink shear state change caused by the curved surface contact pressure. This viscosity value differs from the static ink storage viscosity obtained during traditional ink supply detection. It represents the actual flow state of the ink after the pad printing head has contacted the surface to be printed and the ink has been subjected to the current curvature pressure and shearing action. For example, the same ink may maintain a high viscosity in the ink supply tank, but after being squeezed by the pad printing head, the viscosity actually participating in the transfer decreases in the bottle shoulder area due to the higher shear rate. Therefore, the effective transfer viscosity is used as the initial viscosity state for the pad printing cycle prediction process.

[0101] In this embodiment, the initial cycle of pad printing is the first complete pad printing cycle established based on the current transfer state after the start of a pad printing task, tracking the viscosity change. Specifically, during the acquisition process, one pad printing cycle is defined as the completion of one ink application, pressing and transfer, and return process of the pad. At the beginning of this cycle, the effective viscosity obtained in S2.2 is used as the initial viscosity state of the current cycle. For example, if the pad printing equipment continuously prints labels on the surfaces of multiple plastic bottles, then each time the pad is ink applied, transferred, and returned, the effective viscosity change of the corresponding cycle is recorded.

[0102] In this embodiment, the effective viscosity state sequence is a set of multiple periodic effective viscosity states arranged in chronological order of the pad printing cycle, used to describe the viscosity change trajectory of the ink during continuous printing. Specifically, in the first pad printing cycle, the transfer effective viscosity obtained in S2.2 is used as the initial value. In subsequent cycles, the corresponding cycle viscosity values ​​are continuously updated based on the detected or estimated ink state changes. For example, the first printing corresponds to the initial effective viscosity, and the second and third printings correspond to the continuously changing effective viscosity states, forming the effective viscosity state sequence through chronological arrangement.

[0103] In this embodiment, the ink replenishment amount corresponding to each ink supply cycle during continuous pad printing is the amount of ink replenished to the ink supply area after each pad printing cycle to maintain normal printing effect. Specifically, the amount of ink actually replenished into the ink storage area of ​​the printing head for each pad printing cycle is obtained by reading the ink supply pump control signal, the ink supply valve opening time, or the displacement of the ink supply mechanism. For example, if the ink supply pump is open for 0.5 seconds, corresponding to a certain volume of ink replenishment, then this replenishment volume is taken as the ink replenishment amount for that cycle.

[0104] In this embodiment, the printing interval is the length of time the ink remains in a non-transfer state between two adjacent pad printing cycles. Specifically, during the acquisition process, the time interval between the completion of one printing cycle and the start of the next is recorded based on the cycle timestamp in the pad printing equipment control program. For example, if the transfer between two plastic bottles takes 2 seconds, then this 2 seconds is used as the printing interval for the corresponding cycle. This parameter describes the viscosity change caused by the structural recovery of the ink during the resting process.

[0105] In this embodiment, the ambient temperature change data refers to the record of temperature changes around the ink supply area during continuous pad printing. Specifically, temperature data is continuously collected during production using temperature sensors located near the ink supply tank or inside the pad printing equipment, and time-matched according to the pad printing cycle. For example, if the ambient temperature is 25°C at the start of production and rises to 28°C after continuous operation due to heat accumulation in the equipment, this temperature change serves as an auxiliary parameter affecting ink viscosity drift. Temperature changes affect viscosity drift in two ways: firstly, increased temperature accelerates solvent evaporation, increasing the ink solids content and leading to increased viscosity; secondly, increased temperature reduces the viscosity of the ink itself. The combined effect of these two factors on viscosity is determined based on the actual temperature change amplitude and ink formulation characteristics.

[0106] In this embodiment, the viscosity change between adjacent printing cycles refers to the degree of change between the effective viscosity states of two adjacent printing cycles. Specifically, the effective viscosity state of the current cycle is compared with that of the previous cycle to determine the viscosity change of the ink during one printing cycle due to shearing, ink replenishment, resting, and environmental changes. For example, if the ink is repeatedly sheared during continuous printing, causing the viscosity of the next cycle to be lower than that of the previous cycle, a corresponding negative viscosity change will occur.

[0107] In this embodiment, the effective viscosity drift per unit cycle is a parameter describing the viscosity change trend of ink within a complete pad printing cycle. Specifically, the viscosity change is based on the viscosity changes of adjacent cycles, and the effects of ink replenishment, printing interval, and ambient temperature changes on viscosity are comprehensively considered to correct the baseline change. Specifically, ink replenishment reflects the dilution or restoration effect of new ink on the existing ink state; printing interval reflects the degree of structural recovery after ink shearing stops; and ambient temperature changes reflect the combined effect of temperature on solvent evaporation rate and ink viscosity. For example, if continuous high-speed operation of the printing head in a certain cycle leads to a decrease in ink viscosity, but a large amount of new ink is replenished and the downtime is long, while the increased ambient temperature accelerates solvent evaporation, then the actual viscosity drift needs to be determined by considering all the above factors. By correcting the baseline viscosity change using these parameters, a viscosity drift per unit cycle that better reflects continuous production conditions is obtained.

[0108] In this embodiment, the effective viscosity drift state sequence is a set of multiple unit-cycle viscosity drift values ​​arranged in the order of the pad printing cycle, used to describe the trend of the effective viscosity of the ink gradually changing with the continuous production process. Specifically, in the acquisition process, the unit-cycle drift values ​​calculated from the first pad printing cycle to the current cycle are arranged in chronological order, such as the viscosity decrease in the first cycle, the viscosity recovery in the second cycle, and the decrease again in the third cycle, forming a continuous viscosity drift state record.

[0109] In this embodiment, the effective viscosity recursive relationship describes the temporal correlation between the effective viscosity state of the current pad printing cycle and the viscosity state of the next cycle, based on the historical cycle variation trend. Specifically, during the acquisition process, based on the effective viscosity drift state sequence, the direction and magnitude of viscosity changes in multiple consecutive historical cycles, as well as the correlation between cycles, are analyzed, and a correspondence between the effective viscosity of the current cycle and the predicted effective viscosity of the next cycle is established.

[0110] For example, if the viscosity gradually decreases over several consecutive cycles, and the rate of decrease stabilizes with the number of consecutive prints, the recursive relationship can predict that the viscosity will continue to decrease in the next cycle based on the current viscosity state; if the viscosity recovers rapidly after ink replenishment, the recursive relationship can reflect the recovery trend.

[0111] In this embodiment, the predicted effective viscosity for the next printing cycle is calculated based on the effective viscosity of the current cycle and the viscosity drift of historical cycles. Specifically, the effective viscosity state, viscosity drift, ink replenishment amount, interval time, and ambient temperature change data in historical printing cycles are used as historical data. The viscosity change results for the next cycle under different historical conditions are analyzed, and the change parameters in the prediction relationship are established so that the prediction results gradually approach the effective viscosity state in the actual production process.

[0112] In this embodiment, the prediction method can be a time series prediction method, such as an autoregressive model (AR), a moving average model (MA), an ARIMA model, or a Kalman filter prediction method. This type of method, which predicts the future state based on historical sequences, is existing technology. In this embodiment, the corresponding prediction method is selected according to the viscosity drift characteristics of pad printing ink. The specific algorithm implementation is a conventional choice for those skilled in the art and will not be described in detail.

[0113] In this embodiment, the predicted effective viscosity is the ink's effective viscosity state for the next printing cycle, calculated based on the current printing cycle status and historical viscosity drift patterns. Specifically, the current cycle's effective transfer viscosity is used as the baseline state, and the viscosity changes that may occur in the next cycle are predicted based on the ink's drift trends caused by continuous shearing, ink replenishment, and environmental changes throughout historical cycles.

[0114] For example, if the effective viscosity for the current cycle is at a certain state, and historical records show that the viscosity decreases to a certain extent in each cycle during continuous high-speed printing, then the predicted effective viscosity for the next cycle will decrease accordingly; if the previous cycle was completed with ink replenishment, then the predicted value will be increased based on the recovery trend caused by ink replenishment.

[0115] In this embodiment, the viscosity difference between the predicted effective viscosity and the current transfer effective viscosity represents the expected degree of viscosity change in the next cycle. Specifically, the predicted effective viscosity is compared with the current actual transfer effective viscosity to determine whether the ink state in the next cycle tends to decrease or recover compared to the current cycle. For example, if the predicted effective viscosity is lower than the current transfer effective viscosity, it indicates that the ink fluidity is enhanced in the next cycle, requiring increased ink supply compensation; if the predicted value is higher than the current state, it indicates that the ink is recovering, requiring reduced compensation.

[0116] In this embodiment, the viscosity recovery ratio corresponding to a unit ink supply volume is a parameter describing the degree to which the effective viscosity can be restored after adding a certain amount of ink. This parameter is obtained through actual production testing. For example, under the same ink conditions, a fixed volume of ink is added to the ink supply area, and the change in effective viscosity before and after ink replenishment is detected, thus obtaining the corresponding relationship of how much viscosity can be restored for each additional ink supply volume. This parameter needs to be calibrated according to the specific ink type, ink supply structure, and mixing state; different ink systems and equipment structures correspond to different recovery ratios.

[0117] In this embodiment, the viscosity compensation requirement is determined based on the predicted change in effective viscosity, specifying the amount of ink that needs to be replenished or adjusted in the next cycle. Specifically, the difference between the predicted effective viscosity and the current effective transfer viscosity is used, combined with the viscosity recovery ratio corresponding to the unit ink supply, to deduce how much ink needs to be replenished to restore the effective viscosity to the target transfer state in the next cycle. For example, if the predicted ink viscosity for the next cycle decreases due to continuous shearing, and experiments show that replenishing a certain amount of ink can restore the corresponding viscosity, then the amount of ink to be added in that cycle is determined based on the relationship between the two.

[0118] In this embodiment, the change in ink supply demand is the result of converting the viscosity compensation demand into the actual control parameters of the ink supply equipment. Specifically, based on the unit ink supply capacity of the ink supply mechanism, the viscosity state to be restored is converted into the ink supply pump running time, the number of times the ink supply valve opens, or the change in ink supply flow rate. For example, if it is calculated that a certain volume of ink needs to be added in the next cycle, then the increase in running time is converted based on the unit time output of the ink supply pump.

[0119] It should be noted that this step does not simply increase the ink supply based on the decrease in ink viscosity. Instead, it uses the effective viscosity for curved surface transfer obtained in S2.2 as the starting point for continuous cycle prediction, further considering the viscosity drift caused by repeated shearing, ink mixing, and environmental changes during continuous pad printing. By establishing an effective viscosity drift state sequence, the ink supply adjustment is transformed from current state compensation to predictive adjustment for the next pad printing cycle. This solves the problem that traditional pad printing ink supply methods, which adjust the ink supply based solely on a fixed viscosity threshold or current detection results, cannot adapt to the continuous drift of ink state during continuous production.

[0120] In a specific embodiment, for example, during continuous label pad printing production of plastic shampoo bottles, the ink viscosity is relatively stable at the beginning of the equipment's operation. However, after printing hundreds of bottles continuously, the repeated ink dipping and pressing of the printing head causes the internal structure of the ink to be continuously sheared, resulting in a gradual decrease in the actual transfer viscosity. The system records the effective viscosity change, ink replenishment amount, and pause time for each cycle. It was found that the ink viscosity showed a downward trend after each cycle in the continuous high-speed production phase. Based on this historical trend, the viscosity state for the next bottle printing is predicted, and the ink supply is adjusted in advance, rather than compensating after the printing quality deteriorates.

[0121] S4, the ink supply operation is controlled based on the change in ink supply demand and the pressure distribution matrix.

[0122] In this embodiment, controlling the ink supply based on the change in ink demand and the pressure distribution matrix specifically involves: Based on the pressure distribution matrix, the region identification method in finite element post-processing is used to extract continuous node regions in the pressure distribution matrix where the pressure value is greater than a preset threshold, which are taken as pressure concentration regions. The priority compensation region in the ink supply process is determined according to the spatial distribution of the pressure concentration regions in the contact area. The change in ink supply demand is obtained, and the total ink compensation amount required by the ink supply actuator is determined based on the change in ink supply demand. Combined with the spatial distribution of the priority compensation area, the total ink compensation amount is allocated to the ink supply execution channel corresponding to the priority compensation area, and the ink supply output flow rate and ink supply duration corresponding to each ink supply execution channel are determined. The ink supply actuator is controlled to adjust the ink supply based on the ink output flow rate and ink supply duration corresponding to each ink supply execution channel.

[0123] In this embodiment, the pressure distribution matrix is ​​the spatial distribution data of contact pressure obtained from the inversion of the finite element model of the pad printing head-curved surface contact in step S1. It is used to represent the magnitude of local pressure at different locations within the contact area between the pad printing pad and the curved surface of the plastic bottle. Each data unit in the pressure distribution matrix corresponds to a spatial node position in the finite element model of the bottle body's curved surface, thus reflecting the pressure differences in different areas caused by variations in the bottle's curvature. For example, due to the larger curvature variation at the bottle shoulder, local pressure concentration may occur after the pad printing head is pressed, while the pressure is relatively uniform in the flat area in the middle of the bottle body. This difference is described by the pressure distribution matrix.

[0124] In this embodiment, the contact area between the printing head and the surface to be printed is the actual contact range determined in step S1 by spatial matching between the finite element solid model of the printing head and the finite element model of the bottle surface. Specifically, during the acquisition process, the nodes on the printing head surface where contact occurs and the corresponding nodes on the bottle surface are read according to the finite element contact solution results. All node areas with contact relationships are taken as the areas that actually participate in ink transfer in the current pad printing cycle.

[0125] For example, when pad printing on the side wall of a cylindrical plastic bottle, the central area of ​​the pad forms the main contact area with the bottle surface, while the edge of the pad may not be fully aligned due to changes in curvature, and therefore is not considered the main ink transfer area.

[0126] In this embodiment, pressure distribution features are data features used to describe the magnitude, degree of pressure variation, and pressure concentration trend within the contact area. Specifically, during the acquisition process, the pressure magnitudes at different locations within the contact area are sorted according to the pressure values ​​corresponding to each spatial location in the pressure distribution matrix, and the pressure variations between adjacent areas are analyzed. For example, when the pressure values ​​corresponding to multiple consecutive nodes in a certain area are greater than a preset threshold, it indicates that there is a significant pressure concentration trend in that area; when the pressures at all nodes are similar, it indicates that the pressure distribution in that area is relatively uniform.

[0127] This pressure distribution characteristic is used to determine the local transfer intensity of ink during the contact process on curved surfaces, rather than relying solely on the overall contact pressure for ink supply control.

[0128] In this embodiment, the pressure concentration region is a continuous curved surface region in the pressure distribution matrix where the pressure value is greater than a preset threshold and the nodes are interconnected through the finite element mesh. The preset threshold is determined based on the difference between the maximum and average pressure values ​​in the pressure distribution matrix, or according to a conventional threshold setting method for stress concentration region identification in finite element post-processing. Specifically, during the acquisition process, the pressure variation range is determined based on historical pad printing pressure data before production or the calculation results of the current batch's pad-bottle contact model. Node regions where the pressure value reaches the preset threshold and is continuously distributed are marked as pressure concentration regions.

[0129] For example, at the shoulder of a shampoo bottle, due to the rapid change in the curvature of the bottle, the compression deformation of the rubber head increases, causing multiple adjacent nodes in this area to experience high pressure simultaneously. This area is then identified as a pressure concentration area.

[0130] It should be noted that the identification of pressure concentration areas is a post-processing technique for finite element analysis results. Existing techniques typically employ methods such as contour analysis, threshold segmentation, and cluster analysis to extract local high-value regions from finite element field data, for example, the high-value region identification method in stress cloud maps within finite element software. In this embodiment, the preset threshold can be determined based on a combination of the average and standard deviation of the pressure at all nodes in the pressure distribution matrix (e.g., the average plus one standard deviation), or it can be determined using conventional threshold setting methods for identifying high-value regions in finite element post-processing. This embodiment applies this type of region identification method to the pad printing pressure distribution matrix to determine key ink supply compensation locations within the curved contact area.

[0131] In this embodiment, the priority compensation region is the curved surface area that prioritizes ink replenishment during ink supply adjustment. Specifically, during the acquisition process, the spatial coordinates corresponding to the pressure concentration area are associated with the subsequent ink supply adjustment area, so that the ink supply adjustment not only considers the overall ink consumption but also prioritizes the ink supply to the location corresponding to the pressure concentration area.

[0132] For example, the bottle shoulder area has higher pressure and stronger ink shearing, resulting in a higher ink consumption rate than the bottle body flat area during the actual transfer process. Therefore, this area is designated as a priority compensation area, and the corresponding ink supply will be increased first when the ink supply demand changes.

[0133] In this embodiment, the change in ink supply demand is the ink supply adjustment demand calculated based on the predicted effective viscosity change state for the next pad printing cycle. It represents the change in ink supply that needs to be increased or decreased in order to maintain the target transfer state of the ink in the next cycle.

[0134] This parameter does not simply indicate how much ink is currently lacking, but rather the compensation requirement predicted based on the drift trend of the effective transfer viscosity. For example, if ink shearing during continuous printing causes a decrease in effective viscosity, the ink supply needs to be increased to restore a stable transfer state; if the ink state recovers, the compensation amount should be reduced.

[0135] In this embodiment, the spatial relationship corresponding to the pressure concentration area is a data relationship describing the correspondence between the change in ink supply demand and the local area of ​​the curved surface. Specifically, during the acquisition process, based on the proportion of the pressure value corresponding to each node in the priority compensation area to the total pressure value, the overall change in ink supply demand is allocated to each priority compensation area, so that areas with higher pressure values ​​receive a greater ink supply compensation weight. For example, if a certain amount of ink needs to be increased in the next cycle, instead of directly controlling the ink supply mechanism to increase by a fixed amount, the allocation ratio of each area is determined based on the pressure distribution of the priority compensation areas, allocating more compensation to areas with higher pressure concentration.

[0136] In this embodiment, the ink supply actuator has multiple independent ink supply channels, each corresponding to a different spatial location within the contact area. The spatial distribution of the priority compensation area is used to determine the ink supply allocation ratio of each channel, ensuring that the spatial distribution of ink supply compensation matches the spatial distribution of the priority compensation area. Specifically, during the acquisition process, based on the ink supply compensation amount allocated to each priority compensation area and combined with the calibration parameters of the corresponding ink supply channel, the ink supply output flow rate and ink supply duration of each channel are determined.

[0137] In this embodiment, the mapping relationship between the change in ink supply demand and the ink supply execution parameters is a data conversion relationship that transforms the theoretical ink supply demand into the actual action parameters of the equipment. Specifically, during the acquisition process, a correspondence between ink output capacity and execution actions is established based on the structural parameters of the ink supply mechanism, such as the output volume of the ink supply pump per unit time, the valve opening time, and the delivery delay time of the ink supply pipeline.

[0138] Based on the changes in ink supply demand and the current output characteristics of the ink supply mechanism, determine the ink supply pump flow rate and continuous operating time that need to be adjusted.

[0139] Converting demand into actuator control parameters is a common technique in the field of automatic control. For example, flow-valve opening mapping in industrial flow control systems and flow-speed mapping in pump control systems are existing technologies. In this embodiment, the corresponding relationship is established based on the actual structure of the pad printing ink supply mechanism.

[0140] In this embodiment, the output flow rate of the ink supply pump is the volume of ink delivered by the ink supply mechanism to the pad printing ink supply area per unit time. Specifically, this flow rate is determined based on the ink supply pump model, drive speed, and actual calibration data. For example, increasing the ink supply pump speed increases the amount of ink output per unit time; decreasing the speed decreases the amount of ink output per unit time.

[0141] This parameter controls the ink supply speed, rather than directly representing the final total ink supply.

[0142] In this embodiment, the ink supply duration is the length of time the ink supply actuator maintains its current output state. Specifically, it is determined based on the required amount of compensated ink and the current output flow rate of the ink supply pump. For example, when the output capacity of the ink supply pump per unit time is fixed, if the ink supply amount needs to be increased, the ink supply pump operating time is extended; if the ink supply amount needs to be reduced, the operating time is shortened.

[0143] In this embodiment, the ink supply actuator is a mechanical component that actually performs the ink replenishment action. It has multiple independent ink supply channels, and the ink outlets of each channel are respectively located in different spatial positions within the contact area to achieve differentiated ink supply to the priority compensation area. The ink supply actuator includes, but is not limited to, an ink supply pump, an ink supply valve, an ink supply pipeline, and a drive control unit. Specifically, the multiple independent ink supply channels can be implemented as follows: each channel is equipped with an independent ink supply pump or an independent flow control valve group, and the end of the ink supply pipeline of each channel is provided with an ink outlet, which corresponds spatially to different areas of the pad printing head. By controlling the speed of the ink supply pump or the opening degree of the control valve of each channel, the ink supply amount of each channel can be independently adjusted. After the system determines the required ink supply compensation amount for each area based on the spatial distribution of the priority compensation area, the ink supply compensation amount is converted into a control signal for the speed of the ink supply pump or the opening degree of the control valve of the corresponding channel, so that the amount of ink output by each channel matches the compensation requirement of its corresponding area. In another implementation, a single ink supply pump combined with a multi-channel time-switching valve assembly can be used to achieve spatially differentiated ink supply. This involves controlling the switching sequence and duration of each switch between channels using the time-switching valves, ensuring that each channel receives the appropriate amount of ink to match the compensation demand within the total ink supply time. Specifically, based on the structure of the pad printing equipment, spatially differentiated adjustments to the ink supply volume are achieved by controlling the operating speed of the ink supply pumps in each channel, the valve opening status, or the movement distance of the ink supply mechanism.

[0144] In this embodiment, ink supply adjustment is a process of dynamically adjusting the ink supply status of the current pad printing equipment based on changes in ink supply demand. Specifically, the predicted changes in ink supply demand for the next cycle are allocated according to the spatial distribution of the priority compensation area and converted into ink supply execution parameters for each ink supply execution channel. The ink supply execution mechanism is then controlled to adjust in advance so that the ink state entering the next pad printing cycle meets the target transfer conditions.

[0145] For example, if it is predicted that the ink viscosity will decrease in the next cycle of continuous production and that more ink needs to be replenished, the ink supply will be increased in advance before the next ink-dip is dipped, so that the amount of ink carried by the ink-dip is restored to a stable level.

[0146] It's important to note that this step doesn't simply control the ink supply mechanism based on changes in ink demand. Instead, it further analyzes the differences in ink transfer intensity within the curved surface contact area, building upon the pressure distribution matrix. Since plastic bottles are non-planar printing objects, different curvature areas correspond to different pressure states. Therefore, the same change in ink supply cannot be uniformly applied to all printing areas. This step identifies areas of concentrated pressure, correlates the overall change in ink demand with local curved surface areas, and achieves spatialized ink supply adjustment for curved structures through multiple independent ink supply channels.

[0147] In a specific embodiment, for example, when pad printing a brand logo on the sidewall of a shampoo bottle, the central area of ​​the bottle has a smaller curvature, allowing for sufficient adhesive adhesion and uniform pressure distribution. However, the curvature of the shoulder area changes significantly, and finite element analysis reveals pressure concentration in this area. During continuous production, the ink in the shoulder area experiences stronger shear forces, predicting an increase in ink supply for the next cycle. The system identifies the shoulder area as a priority compensation region based on the pressure distribution matrix and adjusts the ink pump output flow through multiple ink supply channels, ensuring more ink compensation is applied to the corresponding transfer area, thereby maintaining consistent overall printing quality.

[0148] Example 2: This invention also includes a system for an adaptive adjustment method of pad printing ink supply based on ink viscosity prediction, comprising a curved surface contact module, a viscosity state reconstruction module, an ink supply prediction module, and an ink supply adjustment module. The curved surface contact module is used to establish a contact model between the pad printing head and the object to be printed based on finite element analysis of the curved surface contact, and to invert the pressure distribution matrix of the contact area between the head and the curved surface during the pad printing process. The viscosity state reconstruction module is used to determine the pressure gradient distribution within the contact area according to the pressure distribution matrix, determine the ink flow velocity distribution based on the pressure gradient distribution, determine the ink shear rate distribution based on the flow velocity distribution, and correct the ink storage viscosity using the shear rate distribution based on the ink shear thinning rheological characteristics to obtain the effective transfer viscosity under the current curved surface contact conditions. The ink supply prediction module is used to predict the change in ink supply demand for the next pad printing cycle, using the effective transfer viscosity as the initial state and combining it with the effective viscosity drift state during the pad printing cycle. The ink supply adjustment module is used to control the ink supply based on the change in ink supply demand and the pressure distribution matrix.

[0149] The present invention also includes an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform an adaptive adjustment method for pad printing ink supply based on ink viscosity prediction.

[0150] The present invention also includes a computer-readable storage medium storing a computer program that, when executed by a processor, implements an adaptive adjustment method for pad printing ink supply based on ink viscosity prediction.

Claims

1. A method for adaptive adjustment of pad printing ink supply based on ink viscosity prediction, characterized in that, Includes the following steps: A contact model between the pad printing nozzle and the object to be printed is established based on finite element analysis of curved surface contact, and the pressure distribution matrix of the contact area between the nozzle and the curved surface during the pad printing process is inverted. The pressure gradient distribution within the contact area is determined based on the pressure distribution matrix. The ink flow velocity distribution is determined based on the pressure gradient distribution. The ink shear rate distribution is determined based on the flow velocity distribution. Based on the ink shear thinning rheological characteristics, the ink storage viscosity is corrected using the shear rate distribution to obtain the effective transfer viscosity under the current curved surface contact conditions. Using the effective viscosity of the transfer as the initial state, and combining the effective viscosity drift state during the pad printing cycle, the change in ink supply demand for the next pad printing cycle is predicted. The ink supply operation is controlled based on the changes in ink demand and the pressure distribution matrix.

2. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 1, characterized in that, The contact model between the pad printing nozzle and the object to be printed is established based on finite element analysis of curved surface contact, specifically as follows: Obtain the three-dimensional scanned point cloud data of the object to be printed, and perform surface fitting on the point cloud data to obtain the three-dimensional surface equation of the area to be printed. The principal curvature at each surface position is calculated based on the three-dimensional surface equation. The surface mesh density is determined according to the curvature change between adjacent positions. Nodes are densified in regions where the curvature change is greater than the first threshold and sparsed in regions where the curvature change is less than the second threshold, thereby generating a bottle surface finite element model containing spatial coordinate information. Based on the geometric dimensions, elastic material parameters, and free surface profile of the pad printing head, solid elements are used to discretize the head, a finite element solid model of the head is established, and the material parameters are set according to the elastic modulus, Poisson's ratio, and stress-strain relationship of the head material. Based on the actual pressing and moving process of the pad printing head, a displacement loading sequence of the pad printing head reference node is established. The displacement loading sequence is used as the displacement boundary condition of the finite element solid model of the pad printing head to describe the motion change of the pad printing head from the initial position to the printing area. Based on the spatial positional relationship between the finite element solid model of the rubber head and the finite element model of the bottle body surface, the finite element surface of the outer surface of the rubber head and the finite element surface of the bottle body surface are matched accordingly to determine the potential contact area between the two, and the contact relationship between the outer surface of the rubber head and the bottle body surface is established by using a surface-to-surface contact algorithm. Based on the combination of the contact relationship, the displacement boundary conditions, the finite element solid model of the printing pad, and the finite element model of the bottle surface, a contact model is formed to describe the pressure deformation of the printing pad and its contact state with the surface to be printed.

3. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 2, characterized in that, The pressure distribution matrix of the contact area between the printing head and the curved surface during the inversion printing process is specifically as follows: Based on the contact model between the pad printing head and the object to be printed, the finite element contact solution is performed on the pad printing head pressing process according to the material parameters and displacement boundary conditions corresponding to the finite element solid model of the pad printing head, and the set of contact nodes between the outer surface of the pad printing head and the surface to be printed is obtained. Based on the set of contact nodes, extract the normal contact load corresponding to each contact node and the area of ​​the curved region represented by each contact node; The local contact pressure corresponding to each contact node is calculated based on the ratio between the normal contact load corresponding to each contact node and the area of ​​the curved region represented by each contact node. Based on the spatial coordinates of each contact node in the finite element model of the bottle surface, the local contact pressure corresponding to each contact node is mapped to the spatial position on the bottle surface. Based on the topological relationship of the finite element nodes on the curved surface of the bottle, a spatial sorting is performed to form a two-dimensional pressure distribution matrix corresponding to the contact area between the rubber head and the curved surface.

4. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 3, characterized in that, The pressure gradient distribution within the contact area is determined based on the pressure distribution matrix. The ink flow velocity distribution is then determined based on the pressure gradient distribution, and the ink shear rate distribution is determined based on the flow velocity distribution. Specifically: Based on the pressure distribution matrix, differential calculation is performed on the pressure values ​​corresponding to the finite element nodes of adjacent curved surfaces to obtain the pressure change at different spatial positions within the contact area between the glue head and the curved surface to be printed. The pressure gradient at each location is calculated based on the ratio between the pressure change at each location and the corresponding spatial spacing between nodes, thus obtaining the pressure gradient distribution within the contact area. Based on the pressure gradient distribution, the flow direction of ink in the contact area under pressure is determined, and based on the moving speed of the printing head and the relative motion relationship between the printing head and the surface to be printed, the ink flow velocity distribution at each position in the contact area is determined. Based on the ink flow velocity distribution and ink layer thickness parameters, the ink velocity gradient at different curved surface positions is calculated, and the local shear rate distribution of the ink is determined based on the velocity gradient. Based on the spatial correspondence between the local shear rate distribution of the ink and the pressure distribution matrix, the shear rates corresponding to each surface position are organized according to the spatial arrangement of the pressure distribution matrix to form an ink shear rate distribution matrix that is consistent with the spatial coordinates of the pressure distribution matrix.

5. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 4, characterized in that, The method of correcting the ink storage viscosity based on the shear-thinning rheological properties of ink and using the shear rate distribution to obtain the effective transfer viscosity under the current curved surface contact conditions is as follows: Based on the shear-thinning rheological properties of the ink material, the apparent viscosity of the ink corresponding to each local shear rate value is determined by pre-established rheological property data, thus forming a correspondence between shear rate and apparent viscosity. Based on the correspondence, the local apparent viscosity of the ink at each curved surface position under the corresponding shear rate is determined, and a local viscosity distribution matrix consistent with the spatial coordinates of the ink shear rate distribution matrix is ​​formed according to the spatial arrangement of the ink shear rate distribution matrix. The ink viscosity of the ink in the pad printing ink supply area under static state is obtained, and the ink viscosity is used as the initial viscosity reference. Based on the degree of deviation of the local apparent viscosity at each spatial position in the local viscosity distribution matrix relative to the ink storage viscosity, the ink storage viscosity is corrected, and the corrected viscosity value at each position is taken as the effective transfer viscosity at that position under the current curved surface contact condition.

6. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 5, characterized in that, The method of using the effective viscosity of the transfer as the initial state and combining it with the effective viscosity drift state during the pad printing cycle to predict the change in ink supply demand for the next pad printing cycle is as follows: Using the effective viscosity of the transfer as the initial state, establish an effective viscosity state sequence corresponding to the initial cycle of the pad printing cycle; Collect data on ink replenishment amount, printing interval time, and ambient temperature changes for each ink supply cycle during continuous pad printing. Based on the effective viscosity state sequence, the viscosity change between adjacent pad printing cycles is analyzed, and the effects of the ink replenishment amount, the printing interval time, and the ambient temperature change data on the viscosity change are combined to determine the effective viscosity drift within a unit cycle, thus forming the effective viscosity drift state sequence corresponding to the pad printing cycle process. Based on the effective viscosity drift state sequence, a recursive relationship is established between the effective viscosity of the current cycle and the viscosity drift of the historical cycles according to the order of the pad printing cycle. Based on the transfer effective viscosity corresponding to the current cycle and the recursive relationship, the predicted effective viscosity corresponding to the next pad printing cycle is calculated. Based on the viscosity difference between the predicted effective viscosity and the current transfer effective viscosity, and combined with the viscosity recovery ratio corresponding to the pre-calibrated unit ink supply, the viscosity compensation requirement for the next transfer printing cycle is determined. The viscosity compensation requirement is converted into the ink supply requirement change corresponding to the ink supply actuator.

7. The adaptive adjustment method for pad printing ink supply based on ink viscosity prediction according to claim 6, characterized in that, The control of ink supply based on the change in ink demand and the pressure distribution matrix specifically involves: The control of ink supply based on the change in ink demand and the pressure distribution matrix specifically involves: Based on the pressure distribution matrix, the region identification method in finite element post-processing is used to extract continuous node regions in the pressure distribution matrix where the pressure value is greater than a preset threshold, which are taken as pressure concentration regions. The priority compensation region in the ink supply process is determined according to the spatial distribution of the pressure concentration regions in the contact area. The change in ink supply demand is obtained, and the total ink compensation amount required by the ink supply actuator is determined based on the change in ink supply demand. Combined with the spatial distribution of the priority compensation area, the total ink compensation amount is allocated to the ink supply execution channel corresponding to the priority compensation area, and the ink supply output flow rate and ink supply duration corresponding to each ink supply execution channel are determined. The ink supply actuator is controlled to adjust the ink supply based on the ink output flow rate and ink supply duration corresponding to each ink supply execution channel.

8. A system using the adaptive adjustment method for pad printing ink supply based on ink viscosity prediction as described in any one of claims 1-7, characterized in that, It includes a curved surface contact module, a viscous state reconstruction module, an ink supply prediction module, and an ink supply adjustment module; The curved surface contact module is used to establish a contact model between the pad printing pad and the object to be printed based on the finite element analysis of curved surface contact, and to invert the pressure distribution matrix of the pad printing pad and the curved surface contact area during the pad printing process; The viscosity reconstruction module is used to determine the pressure gradient distribution within the contact area based on the pressure distribution matrix, determine the ink flow velocity distribution based on the pressure gradient distribution, determine the ink shear rate distribution based on the flow velocity distribution, and correct the ink storage viscosity using the shear rate distribution based on the ink shear thinning rheological characteristics to obtain the effective transfer viscosity under the current curved surface contact conditions. The ink supply prediction module is used to predict the change in ink supply demand for the next pad printing cycle by taking the effective viscosity of the transfer as the initial state and combining it with the effective viscosity drift state during the pad printing cycle. The ink supply adjustment module is used to control the ink supply operation based on the change in ink supply demand and the pressure distribution matrix.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; And, a memory communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the pad printing ink supply adaptive adjustment method based on ink viscosity prediction as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the adaptive adjustment method for pad printing ink supply based on ink viscosity prediction as described in any one of claims 1 to 7.

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