Method for manufacturing rubber rollers in printing systems and printing systems

Abstract

This disclosure provides a method for manufacturing a rubber roller in a printing system and a printing system thereof. The method for manufacturing the rubber roller in the printing system includes: establishing a finite element analysis model of the rubber roller; determining the natural frequencies and mode shapes of the rubber roller based on the finite element analysis model; performing frequency response analysis based on the natural frequencies to obtain frequency response results under harmonic excitation; using the frequency response results to at least determine weak regions of the rubber roller that do not meet performance conditions; constructing dynamic equations based on the frequency response results and mode shapes, and obtaining the dynamic characteristics of the rubber roller based on the dynamic equations; constructing a topology optimization model and constraints based on the dynamic characteristics; optimizing the parameters of the rubber roller through iterative calculation of the topology optimization model based on the constraints to obtain optimized parameters; and manufacturing the rubber roller according to the optimized parameters.

Description

Technical Field

[0001] This invention relates to the field of printing equipment technology, and in particular to a method for manufacturing a rubber roller in a printing system and a printing system thereof. Background Technology

[0002] In the printing production process, the performance of the printing press directly determines production efficiency and product quality. The rubber roller, as a core component of the printing system, is responsible for transferring the printed image onto the paper with high precision, ensuring the accuracy and consistency of the printed product. Under high-speed operation, the dynamic characteristics of the rubber roller directly affect the printing quality. When the rotational speed exceeds a critical value, the system will experience significant vibration, resulting in defects such as ghosting and ink streaks (e.g., ...). Figure 1A As shown), alternating stress can cause fatigue cracks or even fracture failure at the roller shaft head (e.g. Figure 1B (As shown). Currently, the main design and optimization methods for rubber rollers include traditional empirical design and numerical simulation-based optimization methods. Traditional empirical design is usually based on engineers' experience and intuition, which has problems such as long design cycles, low efficiency, and difficulty in meeting complex production requirements. Although numerical simulation-based optimization methods can solve some problems well, they often require a lot of computational resources and time, and are sensitive to the selection of model parameters, making them prone to getting trapped in local optima. Summary of the Invention

[0003] One objective of this invention is to provide a method for manufacturing a rubber roller in a printing system and a printing system in order to improve the rigidity of the rubber roller, reduce the amount of deformation under the same load, reduce the impact of resonance on printing quality during the printing process, and improve the printing effect.

[0004] The first aspect of this invention provides a method for manufacturing a rubber roller in a printing system. The rubber roller comprises, from the inside out, a metal mandrel, a buffer layer, and a rubber layer. The metal mandrel has a support ring inside and multiple support ribs distributed along the axial direction of the support ring. The method includes: establishing a finite element analysis model of the rubber roller; determining the natural frequencies and mode shapes of the rubber roller based on the finite element analysis model; performing frequency response analysis based on the natural frequencies to obtain frequency response results under harmonic excitation; the frequency response results are used at least to determine the weak areas of the rubber roller that do not meet performance requirements; and constructing dynamic equations based on the frequency response results and the mode shapes, and obtaining the dynamic characteristics of the rubber roller based on the dynamic equations. Features; Based on the dynamic features, a topology optimization model and constraints are constructed; Based on the constraints, the parameters of the rubber roller are optimized through iterative calculation of the topology optimization model to obtain optimized parameters; The parameters of the rubber roller include at least one of the following: the topology parameters of the metal mandrel, the parameters of the buffer layer, and the parameters of the rubber layer: wherein, the topology parameters of the metal mandrel include at least one of the following: the material density, distribution position, thickness, number of support ribs, and spacing between the support ribs of the support ring; The parameters of the buffer layer include: the material type of the buffer layer and / or the thickness of the buffer layer; The parameters of the rubber layer include: the material type of the rubber layer and / or the thickness of the rubber layer; The rubber roller is manufactured according to the optimized parameters.

[0005] A second aspect of the present invention provides a printing system comprising the aforementioned rubber roller.

[0006] The beneficial effects of this invention are as follows: by establishing a finite element analysis model and carrying out modal analysis, frequency response analysis and dynamic characteristic analysis, and combining constraint conditions for structural optimization, the resonance risk modes and weak areas of the rubber roller can be accurately identified, and the topological parameters of the metal mandrel (support ring thickness, number of support ribs, etc.) and the material parameters of the buffer layer and rubber layer can be optimized. Through the synergistic optimization of the metal mandrel, buffer layer and rubber layer, the rubber roller produced is strong enough, has small deformation during printing, and is less affected by vibration, thereby improving printing quality and reducing printing tilt or deformation problems. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below. The accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the content of the embodiments of the present invention and these drawings.

[0008] Figure 1A This is a schematic diagram of a printing effect;

[0009] Figure 1B This is a schematic diagram of a broken roller shaft head;

[0010] Figure 2A This is a schematic flowchart of a method for manufacturing a rubber roller in a printing system according to an embodiment of the present disclosure;

[0011] Figure 2B This is a schematic flowchart of another method for manufacturing a rubber roller in a printing system provided in this embodiment of the present disclosure;

[0012] Figure 3 This is a schematic diagram of a printing system provided in an embodiment of this disclosure;

[0013] Figure 4 This is a schematic diagram of a three-dimensional model of a rubber roller provided in an embodiment of this disclosure;

[0014] Figure 5 This is a schematic diagram of the deformation corresponding to the three modal modes before optimization provided in the embodiments of this disclosure;

[0015] Figure 6 This is a schematic diagram of the topology optimization design domain provided in the embodiments of this disclosure;

[0016] Figure 7 These are schematic diagrams and enlarged views of the optimized model provided in the embodiments of this disclosure;

[0017] Figure 8 This is a schematic diagram illustrating the effect of the smoothing process provided in the embodiments of this disclosure;

[0018] Figure 9 This is a schematic diagram of the geometric reconstruction model provided in the embodiments of this disclosure;

[0019] Figure 10 This is a 3D color mapping surface diagram of Mises stress provided in an embodiment of this disclosure;

[0020] Figure 11 This is a schematic diagram of the deformation corresponding to the three optimized mode shapes provided in the embodiments of this disclosure;

[0021] Figure 12 This is a schematic diagram of the frequency changes before and after the first ten optimizations provided in this embodiment of the disclosure;

[0022] Figure 13 This is a schematic flowchart of another method for manufacturing a rubber roller in a printing system provided in this embodiment. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only portions of the structure relevant to the present invention, not the complete structure.

[0024] In the description of this invention, unless otherwise explicitly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the connection of the internal structures of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0026] In the description of this embodiment, the terms "upper," "lower," "left," and "right," etc., refer to the orientation or positional relationship shown in the accompanying drawings. They are used only for ease of description and simplification of operation, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first" and "second" are used only for distinction in description and have no special meaning.

[0027] This disclosure provides a method for manufacturing a rubber roller in a printing system. The rubber roller includes, from the inside out, a metal mandrel, a buffer layer, and a rubber layer. The metal mandrel has a support ring inside and multiple support ribs distributed axially along the support ring. Figure 2A As shown, the method includes:

[0028] S110: Establish the finite element analysis model of the rubber roller;

[0029] S120: Based on the finite element analysis model, determine the natural frequency and mode shape of the rubber roller;

[0030] S130: Perform frequency response analysis based on the natural frequency to obtain the frequency response results under harmonic excitation; the frequency response results are used at least to determine the weak areas of the rubber roller that do not meet the performance requirements;

[0031] S140: Based on the frequency response results and the mode shapes, construct the dynamic equations and obtain the dynamic characteristics of the rubber roller based on the dynamic equations;

[0032] S150: Based on the aforementioned dynamic characteristics, construct a topology optimization model and constraints;

[0033] S160: Based on the constraints, the parameters of the rubber roller are optimized through iterative calculation of the topology optimization model to obtain optimized parameters; the parameters of the rubber roller include at least one of the following: the topology parameters of the metal mandrel, the parameters of the buffer layer, and the parameters of the rubber layer: wherein, the topology parameters of the metal mandrel include at least one of the following: the material density, distribution position, thickness, number of support ribs, and spacing between the support ribs of the support ring; the parameters of the buffer layer include: the material type of the buffer layer and / or the thickness of the buffer layer; the parameters of the rubber layer include the material type of the rubber layer and / or the thickness of the rubber layer;

[0034] S170: Fabricate the rubber roller according to the optimized parameters.

[0035] In some embodiments, the optimal topological configuration of the material is solved through finite element analysis models and iterative calculations to improve key performance indicators such as stiffness and frequency of the structure. During the optimization process, finite element analysis models and mathematical optimization algorithms are typically combined to find the optimal material layout.

[0036] In some embodiments, S110 may include, but is not limited to, the following steps: meshing the metal mandrel using hexahedral elements; meshing the buffer layer and rubber layer using tetrahedral elements respectively; setting a binding contact between the metal mandrel and the buffer layer; and setting the coefficient of friction between the buffer layer and the rubber layer.

[0037] In some embodiments, the finite element analysis model discretizes the continuous rubber roller structure into a set of finite elements, connects them through nodes, and assigns material properties and boundary conditions.

[0038] Material nonlinearity: The hyperelastic properties of the rubber layer are described by the Mooney-Rivlin model, for example, using the third-order Mooney-Rivlin equation. Where W is the strain energy density, , For the invariants of the right Cauchy-Green deformation tensor, It is a volume ratio. and These are material parameters.

[0039] Geometric modeling was performed. The rubber roller consists of a metal core, a buffer layer, and a rubber layer. For example, a two-dimensional axisymmetric model of the three-layer structure was established.

[0040] Mesh generation, for example, uses hexahedral elements for the metal mandrel and tetrahedral elements for the buffer layer and rubber layer, with the element size adjusted according to the stress gradient.

[0041] Set boundary conditions: constrain displacement at both ends of the mandrel to simulate bearing support; set binding contact (Tie constraint) between each layer to ensure displacement coordination.

[0042] In some embodiments, natural frequency: the characteristic frequency of a structure during free vibration, corresponding to the vibration speed of a mode shape. Mode shape: the vibration pattern of a structure at a specific frequency (such as bending, torsion, etc.).

[0043] Eigenvalue solving:

[0044] Establish the characteristic equation based on the finite element analysis model: , Here is the stiffness matrix. For the quality matrix, For the natural frequency, This is the modal shape vector.

[0045] Algorithms such as the Block Lanczos method are used to solve for the first 20, 10, or 4-6 eigenvalues. These eigenvalues ​​can include natural frequencies and mode shapes. For example, the 4th natural frequency and the bending mode shape corresponding to the 4th natural frequency in the middle of the roller. Studies have found that the 4th, 5th, and 6th eigenvalues ​​typically best reflect the characteristics of the rubber roller under the current parameters; therefore, the 4th, 5th, and 6th eigenvalues ​​can be the focus for rapid parameter optimization.

[0046] In some embodiments, frequency response analysis studies the steady-state response of a structure under harmonic excitation. Harmonic excitation is a specific form of external excitation, whose advantages lie mainly in the controllability of excitation characteristics, the convenience of mathematical modeling, and the relevance to engineering applications. Compared to other highly random excitations such as random vibration and transient impact, harmonic excitation can include, but is not limited to, excitations that change periodically according to a sine or cosine function. Harmonic excitation has periodicity and regularity: the vibration waveform strictly follows a sine curve, and the frequency and amplitude are fixed, facilitating theoretical analysis and experimental reproduction.

[0047] In a simple harmonic excitation, the frequency is singular. For example, a simple harmonic excitation has a single frequency component: it contains only one dominant frequency, avoiding the complexity caused by multi-frequency coupling.

[0048] Since the stress amplitude under harmonic excitation can be directly used as a deterministic constraint, the ambiguity of probabilistic constraints in stochastic excitation is avoided, making the optimization process more efficient. If the harmonic excitation frequency is close to the structure's natural frequency, resonance is easily induced, thus the natural frequency of the rubber roller can be easily obtained. By adjusting the structural stiffness through topology optimization (such as the distribution of support rings in a metal mandrel), the excitation frequency can be precisely avoided, suppressing resonance response. At the same time, single-frequency excitation does not require processing wideband data, significantly reducing the computational load of finite element methods, making it particularly suitable for iterative solutions of large-scale topology optimization. For example, in the topology optimization modeling process, the solid isotropic material penalty method can be used to achieve rapid convergence of iterations. In summary, the core advantage of choosing harmonic excitation as the external excitation form is to achieve accurate optimization of the structure's dynamic performance with the lowest computational cost. By simplifying complex dynamic problems into amplitude constraints at a single frequency, combined with the weighted frequency maximization objective, topological configurations that balance lightweighting and vibration resistance (such as the support ring design of a rubber roller) can be quickly obtained, providing an efficient optimization path for periodic load scenarios in engineering practice.

[0049] In this embodiment, the weak area—the area of ​​stress concentration or excessive deformation—is determined by the response amplitude.

[0050] In some embodiments, S130 may include:

[0051] Load and Damping Settings: Load: Simulates the periodic pressure during the printing process by applying a sinusoidal load to the rubber layer surface, with the frequency range covering the printing press's operating speed. Damping: A Rayleigh damping model is used. Response Calculation: The frequency response function is obtained by solving the equations of motion.

[0052] Weak area identification: Plotting displacement / stress amplitude-frequency curves revealed that when the excitation frequency is close to the 4th natural frequency (e.g., but not limited to 349Hz), the displacement amplitude in the middle of the roller reaches 0.2mm (far exceeding the printing accuracy requirements), thus identifying it as a weak area.

[0053] In summary, determining the natural frequencies and mode shapes of the rubber roller based on the finite element analysis model includes: applying constraints to fix the two end faces of the metal mandrel, solving for the specified natural frequencies and mode shapes of the rubber roller; outputting the modal participation factor matrix to determine the contribution of each mode to the vibration response; the modal participation factor matrix includes the participation factor values ​​of the mode shapes corresponding to each natural frequency in different directions.

[0054] In some embodiments, the dynamic equation is a mathematical model describing the relationship between the structural vibration response and the load.

[0055] Dynamic characteristics include vibration energy distribution and modal participation. In some embodiments, dynamic characteristics may also include stress amplitude and vibration displacement.

[0056] The modal superposition method is adopted: the response is decomposed into a linear superposition of various modes.

[0057] Energy distribution analysis is performed to disperse vibrational energy across more modes, reducing the risk of resonance.

[0058] Before performing parameter optimization, S150 may include:

[0059] Based on the dynamic characteristics, the optimization objective is constructed by maximizing the natural frequency of the rubber roller, resulting in a topology optimization model;

[0060] The constraints are constructed; the constraints include at least one of the following:

[0061] The stress amplitude under harmonic excitation shall not exceed the material's yield strength.

[0062] The optimized structure volume does not exceed a preset proportion of the initial volume;

[0063] The cell density is not lower than the minimum manufacturing threshold.

[0064] In some embodiments, by introducing a penalty factor p, the material density is... ρ The relationship between the elastic modulus E and the material is nonlinear, and the mathematical expression is: .in, Let ρ be the elastic modulus of the material at a relative density ρ. The elastic modulus of a fully dense material (ρ=1); ρ is the minimum elastic modulus (ρ=0), used to avoid singularities in numerical calculations; ρ is the relative density of the material, with a value range of [0,1]; p is a penalty factor, used to suppress intermediate density values.

[0065] A topology optimization mathematical model is constructed with the goal of maximizing the natural frequency. The mathematical description of its optimization problem can be expressed as:

[0066]

[0067] in, Let i be the i-th natural frequency. The initial frequency, Frequency weighting factor; The frequency is the simple harmonic excitation frequency; The optimized structural volume; The initial material volume; Minimum material density; This represents the yield strength of the material.

[0068] In some embodiments, the method further includes:

[0069] The design domain and non-design domain of the rubber roller are defined, wherein the design domain includes the optimizable area inside the metal mandrel, and the non-design domain includes the shaft end and assembly interface; the topology optimization model is used to adjust the parameters of the design domain. In this embodiment, the non-design domain can also be referred to as the reserved area. The reserved area can typically be the installation area of ​​the rubber roller, etc. The design domain can also be referred to as the optimization area.

[0070] In topology optimization or structural design, the pre-setting of the design domain and non-design domain is a fundamental step in the optimization process, contributing to optimization performance in four aspects: goal orientation, functional preservation, computational efficiency improvement, and process feasibility. For example, goal orientation precisely focuses on the optimization objective, thus limiting the optimization scope. The design domain is the area where material removal or redistribution is permitted, while the non-design domain consists of critical structures that must be preserved (such as assembly interfaces and bearing housings). By dividing the design domain, the computational resources of the optimization algorithm are concentrated on non-critical areas (such as the interior of the metal mandrel of a rubber roller), avoiding erroneous modifications to functional areas and ensuring that objective functions such as maximizing the weighted frequency only take effect within an adjustable range.

[0071] The design domain and non-design domain can help quantify the objective function. For example, in the design domain, the material density distribution can be used as a variable to maximize the weighted natural frequency, while in the non-design domain, the material density can be kept at 1 (full material), ensuring that constraints (such as stress amplitude and volume) only act on the optimizable region.

[0072] By defining non-design domains, critical structures and performance can be protected, preventing functional failures. Non-design domains typically include functional components of the structure (such as shaft ends and bolt holes) or sensitive areas (such as stress concentration points). Pre-setting these domains prevents optimization algorithms from mistakenly deleting critical materials. For example, in this case, the shaft end of the rubber roller is set as a non-design domain to ensure that it can still be properly assembled with other components (such as gearboxes) after optimization, avoiding the risk of functional loss due to optimization.

[0073] By distinguishing between the design domain and the non-design domain, computational efficiency can be improved: redundant calculations are reduced, and the solution space is shrunk. Regions outside the design domain do not require density iteration calculations and can directly participate in finite element analysis with a fixed density, significantly reducing the number of meshes and iterations. For example, when the non-design domain (shaft head) of a rubber roller is set as a rigid body, the degrees of freedom of the finite element analysis model are reduced by approximately 30%, computation time is shortened by more than 40%, and local optima traps are avoided. A clearly defined design domain boundary guides the algorithm to prioritize exploring high-potential regions, avoiding wasting computational resources in non-optimizable areas and improving global optimization efficiency.

[0074] Non-design domains can be pre-defined as non-machinable areas or reserved areas to avoid unmanufacturable features (such as ultra-thin walls or sharp internal corners) in the optimization results. If a 10mm non-optimization margin is retained when expanding the design domain, it can ensure that the optimized topology meets the minimum feature size requirements for machining or 3D printing.

[0075] The pre-defined design and non-design domains serve as a bridge connecting theoretical optimization goals with engineering practice. Essentially, they achieve a multi-objective balance between performance, cost, and manufacturing processes through spatial constraints. In optimizing complex structures such as rubber rollers, this setup allows the algorithm to focus on core requirements (e.g., vibration resistance) while preserving functional boundaries, ultimately achieving the dual goals of efficient optimization and reliable manufacturing. In some cases, the optimization parameters obtained include structural and / or topological parameters, as well as the manufacturing process parameters for the rubber roller. Material distribution within the design domain (e.g., support rings, ribs) can be predefined based on process parameters (e.g., draft angle of injection molds), allowing the optimization results to directly connect with the production process.

[0076] In some embodiments, the optimization of the rubber roller parameters based on constraints and iterative calculations using a topology optimization model to obtain optimized parameters includes:

[0077] The mechanical transmission relationship between the metal mandrel and the buffer layer, and between the buffer layer and the rubber layer, is simulated by binding constraints;

[0078] With the goal of maximizing the dispersion of vibration energy, the material parameters and structural parameters of the buffer layer and the rubber layer are determined based on the vibration response of the rubber roller; the material parameters include at least the elastic modulus of the material; the structural parameters include at least the thickness.

[0079] In some embodiments, topology optimization is a method for finding the optimal distribution of materials within a given design space.

[0080] In some embodiments, the variable density method (e.g., the penalty method for solid isotropic materials) uses the material density as a design variable and drives discretization toward 0 (removal) or 1 (retention) through a penalty factor.

[0081] To establish a topology optimization model, the first step is to design the variable: the density distribution of the material inside the metal mandrel. Support ring thickness ,spacing Buffer layer thickness wait.

[0082] Objective function: The first item The second term represents the flexibility (the reciprocal of stiffness). Due to volume constraints, For weighting coefficients. Constraints: Volume fraction: , The value ranges from 0 to 1, preferably from 0.7 to 0.8, and represents the weight reduction ratio. Stress constraint: , σ max The maximum equivalent stress; Pressure threshold. Frequency constraint: , f i Let be the i-th natural frequency. For example, frequency constraints require the 4th, 5th, and 6th natural frequencies to rise above a specified value.

[0083] The Moving Asymptote Method (MMA) is used for iterative solution. The solution converges after a specified number of iterations (e.g., 200), yielding the position, thickness, number, distribution, and spacing of the support rings. The metal mandrel, originally a solid cylinder, can be modified by removing the portions of the solid cylinder without support rings and ribs after determining the optimization parameters, based on the relevant parameters of the support rings and ribs.

[0084] In some embodiments, manufacturing the rubber roller according to the optimized parameters includes:

[0085] The metal mandrel is manufactured using a forging process based on the optimized parameters of the metal mandrel.

[0086] The surface of the metal mandrel is hardened to a specified hardness.

[0087] The buffer layer is formed by centrifugal casting process according to the optimized parameters of the buffer layer.

[0088] The rubber layer is manufactured according to the optimized parameters of the rubber layer;

[0089] Laser engraving technology is used to process ink transfer dots on the surface of the rubber layer.

[0090] This disclosure addresses the dynamic optimization problem of the rubber roller, a core component of printing equipment, and proposes a topology optimization design method that integrates multi-physics characteristics. Dynamic performance constraints are introduced in the early stages of structural design, and an optimization model is established with the weighted natural frequency as the objective function, while also considering stress constraints under extreme conditions. This achieves comprehensive optimization of the structural dynamic performance.

[0091] This disclosure focuses on the rubber roller of a web offset printing press. As a core printing component, the rubber roller is prone to centrifugal force disturbance due to uneven mass distribution during high-speed rotation, and is also subjected to periodic impacts such as gear meshing and ink roller contact. When these excitation frequencies approach the natural frequency of the roller, resonance can occur, leading to printing registration errors and abnormal equipment vibration. The optimization flowchart is shown in Figure 2B.

[0092] Figure 3 The diagram shows a printing system including rubber rollers. The core function of the rubber rollers is achieved through contact pairs. Based on the principle of selective adsorption of dampening solution and ink, the dampening solution transport system precisely applies the solution to the non-image area (hydrophilic surface) of the printing plate cylinder via a water roller, forming an anti-ink wetting interface; the synchronously operating ink delivery system constructs a stable ink layer on the image area (hydrophobic surface) of the printing plate. The mirror transfer of the ink pattern is achieved through the dynamic contact pair between the printing plate and the rubber rollers, ultimately completing the pattern transfer on the substrate within the dynamic contact pair formed by the two rubber rollers. The periodic contact force generated by the coordinated movement of multiple rollers during this process constitutes the main vibration excitation source of the system.

[0093] The mechanical behavior of the rubber roller is essentially a three-dimensional nonlinear contact problem. A three-dimensional model is established to accurately characterize its dynamic response. In this example, the basic parameters are assumed as follows: total roller length is 1000mm, metal mandrel diameter is 250mm, surface is covered with an 8mm thick buffer layer and a 6mm thick rubber layer, and the final assembly diameter is 278mm. The shape of the rubber roller is as follows... Figure 4 As shown.

[0094] The rubber roller mainly consists of three parts: a metal core shaft provides primary support and rigidity; the rubber layer directly participates in image transfer, exhibiting excellent elasticity and wear resistance; and the buffer layer serves to absorb vibration and distribute pressure evenly. The specific material properties of each component are shown in Table 1.

[0095] Table 1 Material Properties Table

[0096]

[0097] Establishing a dynamic model is crucial for studying the dynamic response characteristics of rubber rollers in their design. This is essential for optimizing the structure, improving performance and durability, and reducing the risk of failure. Modal analysis allows us to determine the natural frequencies and mode shapes of the rubber roller, leading to a deeper understanding of its dynamic response characteristics. The structural dynamic equations can be expressed as follows:

[0098] formula:

[0099] In the formula, This is the overall stiffness matrix of the structure; The mass matrix of the structure; For eigenvalues; This is the corresponding structural mode vector.

[0100] For the periodic printing pressure exerted on the roller (typical amplitude 500-800N, frequency range 50-150Hz), the linearized equation of motion can be expressed as the formula:

[0101] In the formula, Represents the damping matrix of the system; Let be a time-varying harmonic excitation function. Under these conditions, the displacement response of the structure can be expressed as a harmonic function, as shown by the formula:

[0102] In the above formula, The vector represents the amplitude in complex form; ω is the angular frequency of the simple harmonic excitation. For ease of calculation, ... Substitute into the equation The formula can be obtained as follows:

[0103] because By introducing an equivalent dynamic stiffness matrix To replace the mathematical expression within the parentheses on the left side of the equation, the formula can be... Simplified to the following form:

[0104] Modal characteristic simulation: In the finite element modeling process, the interlayer interface was simplified based on the actual contact state of the rubber roller. The mechanical transmission relationship between the metal mandrel and the buffer layer, and between the buffer layer and the rubber layer, was simulated through binding constraints. The metal mandrel was set as a rigid body to reduce the computational complexity of the model. In the constrained modal analysis of the internal mechanism of the printing press, fixed support constraints were applied to both ends of the rubber roller according to the actual working conditions. To characterize the dynamic response of the roller under high-speed conditions, the system rotation speed was set to 50000 r / h, and a simple harmonic pressure load with a frequency of 30 Hz was applied to the surface of the rubber layer. The load application time domain was [0, 0.5] s, and an explicit dynamic algorithm was used for transient solution with a time step of 0.001 s. The distribution characteristics of the first ten natural frequencies obtained by numerical calculation are shown in Table 2.

[0105] Table 2. Frequency of the first ten modes

[0106]

[0107] Because the high-speed rotation of the rubber roller corresponds to frequencies close to the intermediate modal frequencies, resonance can lead to excessive vibration and fatigue damage in components. Therefore, in modal analysis, modes 4-6 within the first ten modal frequencies deserve special attention. Modes 4-6 differ from lower-order modes, which simply represent the overall motion trend, and unlike higher-order modes, which are excessively localized. Their moderate shape complexity reflects the interaction between different parts of the system, making them representative for analyzing the dynamic behavior of the system under complex operating conditions. Extracting the first 4-6 vibration modes of the structure, such as... Figure 5 As shown, the fourth natural frequency of the rubber roller is 349.04 Hz, with a mode shape of torsion in the y-axis direction and stress concentrated at both ends; the fifth natural frequency is 357.09 Hz, with a mode shape that can be summarized as torsion in the y-axis direction and stress concentrated at both ends; the sixth natural frequency is 792.3 Hz, close to a high-frequency excitation source, with no significant change in mode shape and deformation evenly distributed on the circumferential roller surface.

[0108] In some embodiments, the optimization of the rubber roller structure may specifically include:

[0109] Topology optimization model establishment: In the optimization research of continuum structures, a variety of mature algorithm systems have been formed, mainly including homogenization methods based on microstructure assumptions, variable density methods with relative density as design variables, incremental structural optimization (ESO) methods through iterative material reduction, and level set methods (MMV) based on interface evolution. These methods have their own characteristics in terms of mathematical modeling, optimization mechanisms, and applicable scope, providing diversified solutions for structural optimization in different engineering scenarios. This disclosure selects the variable density method as the research tool. The solid isotropic material penalty method model penalizes intermediate density values ​​(0 < 0). ρ<1), driving the optimization results to tend towards a clear 0-1 distribution (i.e., completely with material or completely without material), thereby achieving a clear definition of structural topology and lightweight design. By introducing a penalty factor p, the relationship between material density ρ and material elastic modulus E is made nonlinear, and the mathematical expression is formula (6): In the formula, For materials at relative density The elastic modulus below; The elastic modulus of a fully dense material (ρ=1); It is the minimum elastic modulus (ρ=0) to avoid singularities in numerical calculations; ρ is the relative density of the material, with a value range of [0,1]; p is a penalty factor that suppresses intermediate density values.

[0110] This disclosure focuses on optimizing the metal mandrel structure of a rubber roller. To ensure sufficient design space and freedom in the topology optimization process, the original model is first expanded in terms of design domain. Considering practical engineering requirements, the external contour of the structure cannot be significantly modified; therefore, a 10mm design margin is reserved as a non-optimization area. The original roller model is filled with solids, and the internal components are retained as non-design areas. A three-dimensional solid mesh is used to discretize the model, such as... Figure 6 As shown, the blue area represents the optimizable design domain, while the red area represents the fixed non-design domain.

[0111] Topology optimization design: Using the maximization of the weighted frequency as the objective function and the stress amplitude of the structure under harmonic excitation as the constraint, topology optimization is performed. The preliminary optimization is as follows: Figure 7 As shown.

[0112] Analysis results show that under circumferential symmetrical load conditions, significant stress concentration occurs in the contact area of ​​the roller surface, while the average Von Mises stress in the inner region of the mandrel is less than 15% of the material's yield strength, confirming structural redundancy in this area. Based on this, the topology optimization process uses a material removal threshold to achieve gradient elimination of materials in the non-load-bearing area, bringing the mass distribution towards a dynamic equilibrium. To meet the roller's functional constraints, the optimization scheme reconstructs the material spatial distribution: a high-density support ring is constructed inside the mandrel, forming a truss-like force transmission path, ensuring torque transmission efficiency while improving bending stiffness through a closed section design. Driven by the optimization criterion method and sequential convex programming, the iteratively converged topology configuration reduces the roller mass by 7.398%, effectively reducing rotational inertia while maintaining the first-order torsional frequency above the safety threshold.

[0113] In topology optimization results, jagged and irregular edges in the generated geometry can create local weak points, affecting the overall performance and reliability of the structure. To address this issue, the optimized geometric model underwent a smoothing process. Through smooth transitions and edge trimming, irregular regions were eliminated, enhancing the continuity and mechanical properties of the structure. Figure 8 As shown.

[0114] Since smoothed geometric models are typically based on mesh-discrete representations, they cannot be directly used for CAD modeling, limiting their application in subsequent simulations. To address this issue, the optimized geometry is reconstructed in SOLIDWORKS, converting it into a parametric CAD model, such as... Figure 9 As shown.

[0115] In Mechanical, all nodal coordinates and their strain values ​​are read and written to a file. The data is then imported into Origin to obtain a 3D color-mapped surface plot comparing the Mises stress before and after optimization, such as... Figure 10 As shown in Table 3, the optimized stress distribution is more uniform, the transition is smoother, and the maximum Mises stress has decreased. Compared with the strength analysis before optimization, the optimized roller's equivalent stress decreased by 28.59%, and both the maximum equivalent strain and the maximum total deformation decreased, indicating improved robustness, which meets expectations.

[0116] Table 3 Comparison of mechanical properties before and after optimization

[0117]

[0118] Modal analysis was performed on the optimized rubber roller, such as... Figure 11 As shown in the figure. Based on the modal analysis results, the optimization of the mode shapes of the intermediate modes from 4th to 6th order was identified as the core objective. The optimized mode shape characteristics are as follows: the stress concentration areas of the fourth and fifth order y-axis torsional modes are significantly reduced (peak stress reduced by ≥30%), and the stress gradient exhibits a smooth transition distribution along the axial direction, indicating the synergistic optimization of structural stiffness distribution and dynamic load transfer path; the sixth order high-frequency mode shape is reconstructed from uniform circular deformation to axially symmetrical wave-like segmented deformation (amplitude standard deviation reduced by 50%), and energy dissipation is achieved through internal wall support reinforcement. At the same time, the natural frequencies and working excitation frequency bands of each order are decoupled (frequency interval >20%), and the off-diagonal term value of the modal confidence matrix (MAC) is reduced to below 0.2, verifying the improvement of the system's dynamic independence. This mode shape reconstruction strategy was verified by ODS experiments and the Dang Van multiaxial fatigue criterion, reducing the risk of drum resonance by 42%.

[0119] Compare the first ten frequencies before and after optimization, such as Figure 12As shown, the natural frequencies of the rubber roller after topology optimization exhibit differentiated regulation characteristics: due to the global enhancement of structural stiffness, the first eight frequencies show a systematic increase (increase of 9.9%-15.8%); the ninth frequency decreases (decrease of 13.5%), which is attributed to the local reconstruction of mass distribution accompanied by stiffness weakening effect; the tenth frequency decreases slightly (decrease of 3.8%), which is due to the regional adjustment of stiffness gradient and the synergistic optimization of mass distribution.

[0120] This phenomenon indicates that topology optimization achieves directional modulation of structural dynamics through multiphysics coupling effects (stiffness-mass-geometry coupling), where the stiffness-dominant mechanism of low-order modes and the local parameter sensitivity of high-order modes together constitute the basis for hierarchical control of dynamic response.

[0121] Topology optimization, as an advanced structural optimization technique, can find the optimal layout of a structure within a given material and design space, under specific loads and constraints, to maximize or minimize performance objectives such as stiffness, weight, and resonant frequency. Applying this method to the design of rubber rollers has yielded the following significant results:

[0122] 1) Topology optimization improves the rigidity of the roller, reduces deformation under the same load, lowers the risk of vibration, and enhances the stability of the printing process.

[0123] 2) The natural frequency of the roller was adjusted to avoid resonance problems that may occur at a fixed speed, thus improving the safety of the equipment.

[0124] 3) The optimized drum structure has a more uniform mass distribution, which reduces the centrifugal force caused by mass imbalance, thereby reducing vibration during rotation.

[0125] 4) The reasonable design of high stress concentration areas reduces the risk of excessive local stress and material fatigue damage, and significantly extends the service life of the roller.

[0126] This disclosure provides a rubber roller, manufactured using the methods described in any of the above embodiments. For example... Figure 3 As shown. This disclosure provides a printing system including a rubber roller manufactured according to any of the foregoing embodiments. In some embodiments, the printing system includes two rubber rollers through which paper for printing passes; the printing system further includes an ink roller, a wet roller, and a plate cylinder; the ink roller and the wet roller are located on different sides above the plate cylinder; the plate cylinder is abutted against one of the rubber rollers.

[0127] like Figure 13 As shown in the embodiments of this disclosure, another method for manufacturing a rubber roller may include:

[0128] Clearly define the optimization goals and constraints;

[0129] Construct the initial finite element analysis model;

[0130] Design domain expansion and non-design domain partitioning;

[0131] Define a mathematical model for topology optimization;

[0132] Select an optimization algorithm;

[0133] Iterative optimization solution;

[0134] Determine whether the convergence condition is met;

[0135] If the convergence condition is met, an optimized topology configuration is generated;

[0136] Structural restructuring and smoothing;

[0137] Performance verification;

[0138] Determine whether the design requirements are met;

[0139] If the design requirements are met, output the final design;

[0140] If the design requirements are not met, return to the design domain or adjust the model parameters;

[0141] If the convergence condition is not met, adjust the parameters and iterate again.

[0142] Note that the foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method of making a blanket in a printing system, characterized by, The rubber roller comprises, from the inside out, a metal mandrel, a buffer layer, and a rubber layer; the metal mandrel has a support ring inside and multiple support ribs distributed along the axial direction of the support ring; the method includes: Establish a finite element analysis model of the rubber roller; Based on the finite element analysis model, the natural frequencies and mode shapes of the rubber roller are determined, including: applying constraints to fix the two end faces of the metal mandrel, solving for the specified natural frequencies and mode shapes of the rubber roller; and determining the contribution of each mode to the vibration response based on the modal participation factor matrix. The modal participation factor matrix includes the participation factor values ​​of the mode shapes corresponding to each natural frequency in different directions. Frequency response analysis is performed based on the natural frequency to obtain the frequency response results under harmonic excitation; the frequency response results are used at least to determine the weak areas of the rubber roller that do not meet the performance requirements. Based on the frequency response results and the mode shapes, a dynamic equation is constructed, and the dynamic characteristics of the rubber roller are obtained based on the dynamic equation. Based on the aforementioned dynamic characteristics, a topology optimization model and constraints are constructed. Based on the constraints, the parameters of the rubber roller are optimized through iterative calculations using the topology optimization model to obtain optimized parameters, including: simulating the mechanical transmission relationship between the metal mandrel and the buffer layer, and between the buffer layer and the rubber layer, using binding constraints; determining the material and structural parameters of the buffer layer and the rubber layer based on the vibration response of the rubber roller, with the goal of maximizing the dispersion of vibration energy; the material parameters include at least the elastic modulus of the material; the structural parameters include at least the thickness; the parameters of the rubber roller include at least one of the following: the topology parameters of the metal mandrel, the parameters of the buffer layer, and the parameters of the rubber layer: wherein, the topology parameters of the metal mandrel include at least one of the following: the material density, distribution position, thickness, number of support ribs, and spacing between the support ribs of the support ring; the parameters of the buffer layer include: the material type of the buffer layer and / or the thickness of the buffer layer; the parameters of the rubber layer include the material type of the rubber layer and / or the thickness of the rubber layer; The rubber roller is manufactured according to the optimized parameters.

2. The method according to claim 1, characterized in that, Establishing the finite element analysis model of the rubber roller includes: The metal mandrel is meshed using hexahedral elements; The buffer layer and the rubber layer are respectively meshed using tetrahedral elements; Set the bonding contact between the metal mandrel and the buffer layer, and set the coefficient of friction between the buffer layer and the rubber layer.

3. The method according to claim 1 or 2, characterized in that, The step of manufacturing the rubber roller according to the optimized parameters includes: The metal mandrel is manufactured using a forging process based on the optimized parameters of the metal mandrel. The surface of the metal mandrel is hardened to a specified hardness. The buffer layer is formed by centrifugal casting process according to the optimized parameters of the buffer layer. The rubber layer is manufactured according to the optimized parameters of the rubber layer; Laser engraving technology is used to process ink transfer dots on the surface of the rubber layer.

4. The method according to claim 1 or 2, characterized in that, The construction of the topology optimization model and constraints based on the dynamic characteristics includes: Based on the dynamic characteristics, the optimization objective is constructed by maximizing the natural frequency of the rubber roller, thus obtaining the topology optimization model; The constraints are constructed; the constraints include at least one of the following: The stress amplitude under harmonic excitation shall not exceed the material's yield strength. The optimized structure volume does not exceed a preset proportion of the initial volume; The cell density is not lower than the minimum manufacturing threshold.

5. The method according to claim 1 or 2, characterized in that, The method further includes: Define the design domain and non-design domain of the rubber roller, wherein the design domain includes the optimizable area inside the metal mandrel, and the non-design domain includes the shaft head and assembly interface; the topology optimization model is used to adjust the parameters of the design domain.

6. A printing system, characterized in that, The printing system includes a rubber roller as described in any one of claims 1 to 5.

7. The system according to claim 6, characterized in that, The printing system includes two rubber rollers through which the paper to be printed passes; the printing system also includes an ink roller, a wet roller, and a plate cylinder; the ink roller and the wet roller are located on different sides above the plate cylinder; the plate cylinder is connected to one of the rubber rollers.

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