Derivation Method of Color Registration Control Error Model in Steady-Speed ​​Printing Process of Mechanical Shaft Gravure Printing Machine

Abstract

This invention discloses a method for deriving a color registration control error model during steady-speed printing in a mechanical shaft gravure printing machine. Based on the mathematical model, the color registration control method of this invention employs a recursive iterative analysis method for control design. The control method of this invention not only theoretically ensures zero registration error, but also features fast response speed, effectively eliminates color differences throughout the system, and improves registration accuracy, making it highly suitable for widespread use in steady-speed printing processes on mechanical shaft gravure printing machines.

Description

Technical Field

[0001] This invention relates to the field of printing control, and in particular to a method for deriving a color registration control error model during steady-speed printing in a mechanical shaft gravure printing machine. Background Technology

[0002] In the printing process of a mechanical shaft gravure printing machine, the complex pattern to be printed is broken down into several simple patterns, each engraved on a printing roller. During printing, the substrate passes sequentially through each printing unit via the feeding section. Each printing unit prints its corresponding simple pattern onto the substrate, ultimately resulting in the complex printed pattern. A problem arises during the printing process: the accurate positioning of the corresponding printed patterns between each unit, also known as registration error. Registration accuracy is crucial to product quality. Therefore, when deviations occur in the relative positions of the printed patterns during printing, control methods must be employed to reduce or eliminate these positional deviations, i.e., registration errors. Given the impact of registration accuracy on product quality, control methods to quickly reduce or eliminate registration errors become particularly important.

[0003] Color registration control is a highly complex technical issue, and the methods vary depending on the printing method. Industrially commonly used methods maintain a control accuracy of approximately ±0.15mm. Summary of the Invention

[0004] The purpose of this invention is to provide a method for deriving a color registration control error model during steady-speed printing in a mechanical shaft gravure printing machine.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0006] The present invention provides a derivation method for the color registration control error model during steady-speed printing in a mechanical shaft gravure printing machine: Through Laplace transforms of the mathematical model and iterative recursion, its model expression is obtained as follows:

[0007]

[0008] The control system for the i-unit compensation roller consists of PD control and compensation control:

[0009]

[0010] V i (s) represents the total control quantity of unit i, controlled by the proportional-derivative control V of unit i. iPD (s) and compensation amount for all preceding compensation roller control quantities Composition; Substituting the control equation into the aforementioned model, the compensation control calculation formula is obtained through recursive iteration:

[0011]

[0012] V iPD (s)=-KP*E i+1 (s)-KD*sE i+1 (s)

[0013]

[0014] KP and KD are the proportional control coefficient and derivative control coefficient of the controller, respectively; V ij (s) represents the proportional-derivative control V of the preceding j-th unit in the compensation amount of unit i. jPD The compensation amount of (s); the above formula is the compensation formula in the control formula proposed in this invention.

[0015] Application of the derivation method of the color registration control error model in the steady-speed printing process of the mechanical shaft gravure printing machine: The mechanical shaft gravure printing machine includes two or more (i) printing units, and each printing unit is equipped with a color registration control system. The derivation method of the color registration control error model in the steady-speed printing process of the mechanical shaft gravure printing machine is used to calculate the longitudinal linear speed change of the compensation roller between color group i-1 and color group i in the color registration control system.

[0016] The color-matching control method of the color-matching control system includes the following:

[0017] The printing material sequentially passes through each printing control unit of the mechanical shaft gravure printing machine for color group printing. The error detection system of color group i determines whether there is a registration error between color group i and color group i-1. If so, the control system of color group i calculates the registration error value between color group i and color group i-1. Under a determined registration accuracy, based on the control calculation formula designed according to the model of the registration control error model derivation method in the steady-speed printing process of the mechanical shaft gravure printing machine, the longitudinal linear speed change of the compensation roller between color group i-1 and color group i is calculated according to the registration error value and the control amount of the preceding compensation roller. This is then sent to the servo motor of the mechanical shaft gravure printing machine as a control command. The servo motor receives the control command and adjusts the longitudinal linear speed of the compensation roller between color group i-1 and color group i until the registration error between color group i and color group i-1 is eliminated. The error detection system of each subsequent color group determines whether there is a registration error between the color group and color group i-1. If so, the above method is used to eliminate the error between the color group and the preceding color group.

[0018] The color matching control system includes a sensing device and a controller. The sensing device is used to detect color matching errors and send the color matching errors to the controller. The controller is based on a model and calculates a control quantity according to the received color matching error and the control quantity of the previous color group, based on the control calculation formula obtained by recursive iteration of the model. The control quantity is then sent to the servo motor of the mechanical shaft gravure printing machine as a control command to adjust the longitudinal linear speed of the compensation roller. The control quantity is the change in the longitudinal linear speed of the compensation roller between color groups.

[0019] The mathematical model for the color matching error and the change in longitudinal linear velocity of the compensation roller between color groups is as follows:

[0020]

[0021] In the above model, E i (t) represents the color registration error between the printing cursor of the i-th color group and the printing cursor of the (i-1)-th color group, V i (t) represents the longitudinal linear velocity of the compensation roller between color group i and color group i+1, i.e., the compensation roller of unit i, ΔT i (t) represents the change in material tension between color group i and color group i+1, T * Let be the material tension under equilibrium tensile conditions, w be the angular velocity of the printing roller, and K be the tensile coefficient of the printing material, which is related to the elastic modulus and cross-sectional area of ​​the material. i * t is the material threading length when the material tension between color group i and color group (i+1) is in a balanced tensile state; r is the radius of each printing roller; t i-1 The material processing time between element i-1 and element i, i.e.

[0022] The beneficial effects of this invention are:

[0023] This invention relates to a method for deriving a color registration control error model during steady-speed printing on a mechanical shaft gravure printing machine. Compared with existing technologies, the color registration control method of this invention, based on the mathematical model, employs a recursive iterative analysis method for control design. The control method of this invention not only theoretically ensures zero registration error but also features fast response speed, effectively eliminates color differences throughout the system, and improves registration accuracy, making it highly suitable for widespread use in steady-speed printing on mechanical shaft gravure printing machines. Attached Figure Description

[0024] Figure 1 This is a simplified structural diagram of the (i-1) unit and the i unit described in this invention;

[0025] Figure 2 The flowchart corresponding to the modeling process described in this invention.

[0026] Figure 3 This is a flowchart of a color registration control method for a mechanical shaft gravure printing machine during steady-speed operation, according to the present invention.

[0027] Figure 4 This is the error response curve of the control method of the present invention under the presence of initial disturbance in two colors.

[0028] Figure 5The error response curves for colors 3 and 4 in the control method of this invention are shown.

[0029] Figure 6 The error comparison curves of the control method of the present invention and existing industrial control methods are shown in two colors.

[0030] Figure 7 The error comparison curves of the control method of the present invention and existing industrial control methods are shown in three colors.

[0031] Figure 8 This is a four-color error comparison curve between the control method of this invention and existing industrial control methods. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0033] The control system of a gravure printing press consists of two main parts: a tension control system and a color registration control system. Tension control aims to maintain tension balance in the unwinding and take-up sections of the printing equipment to prevent wrinkles and breakage of the printing material, and to lay the foundation for color registration control in the printing units. Color registration control, on the other hand, aims to eliminate color registration errors caused by various disturbances, improving registration accuracy and product quality. While these two control systems differ in their control objectives, they essentially address the core issue of tension control. In the unwinding and take-up sections, pressure sensors detect tension. Tension control uses the tension values ​​detected by these sensors to adjust the speed of the unwinding and take-up motors, thereby maintaining tension balance. Between the printing color groups, color difference detection devices are installed. Color registration control uses color difference feedback to adjust the longitudinal linear speed of the compensation rollers, thereby adjusting the tension between color groups and ultimately eliminating color registration errors.

[0034] The mechanical shaft gravure printing machine of this invention mainly consists of three parts: an unwinding and feeding section, a printing unit, and an unwinding and rewinding section. The unwinding and feeding section feeds the printing material from a circular roller wound with the material into the printing unit at a constant linear speed. This section has a dedicated tension control system to ensure stable printing tension. The printing unit sequentially prints monochrome patterns onto the printing material. A dryer is installed between each color group; the material must be dried before entering the next printing unit after the current color is printed to prevent the newly printed pattern from smudging. To improve registration accuracy, each color group is equipped with a registration control system. The unwinding and rewinding section continuously and smoothly collects the printed material onto the rewinding shaft. Before printing, a complete color pattern is broken down into several monochrome films, which are then engraved on a circular roller to form a printing plate roller. During printing, the unwinding and feeding section pulls the printing material to the printing unit. The material sequentially passes through each color group for monochrome printing and hot air drying. After the last color is printed, the material enters the unwinding and rewinding section, where a rewinding motor winds the material onto the rewinding shaft, thus completing the printing of a color pattern.

[0035] like Figure 1 The diagram shows a flowchart of a color registration control method for a mechanical shaft gravure printing machine during steady-speed operation, comprising the following contents:

[0036] Based on the mathematical model of the mechanical shaft, a control calculation formula for eliminating overprinting errors is derived using the recursive iterative processing analysis method based on the model.

[0037] In this embodiment, the printing material sequentially passes through each control unit of the mechanical shaft gravure printing machine for color group printing. The error detection system of color group i determines whether there is a color registration error between color group i (i>1) and color group (i-1). If so, the control system of color group i calculates the color registration error value between color group i and color group (i-1). Under a determined color registration accuracy, based on the control method proposed in this invention, the longitudinal linear speed of the compensation roller between color group i-1 and color group i is calculated according to the color registration error value, and sent to the servo motor of the mechanical shaft gravure printing machine in the form of a control command. The servo motor receives the control command and adjusts the longitudinal linear speed of the compensation roller between color group i-1 and color group i until the color registration error of color group i is eliminated. The error detection system of each color group determines whether there is a color registration error between the color group and color group 1. If so, the above method is used to eliminate the error between the color group and color group (i-1).

[0038] The color matching control system includes a sensor and a controller. The sensor, which is a photoelectric sensor, is used to detect color matching errors and send the errors to the controller. The controller stores the calculation formulas for color matching errors and control quantities, and calculates the control quantity for this unit based on the received color matching errors and the control quantity of the preceding unit. The controller then sends the control quantity to the servo motor of the mechanical shaft gravure printing machine as a control command to adjust the longitudinal linear speed of the compensation roller. The control quantity is the longitudinal linear speed of the compensation roller between color groups.

[0039] When the printing material passes through the first color group, it not only prints the pattern but also imprints a mark of a specific shape on the edge of the pattern. If the color registration is accurate, the actual position of this mark in color group i should be the same as its theoretically correct position. If they are different, the error is calculated based on the encoder deviation when the mark is captured each time. Thus, the error of color group i is obtained. Therefore, the goal of color registration control is to adjust the longitudinal linear speed and direction of the compensation roller to ensure that the encoder calculation error when the mark is captured is zero.

[0040] Meanwhile, based on the characteristics of printing color registration systems such as strong coupling, large pure hysteresis, uncertainty, and multiple inputs and outputs, the control formula derived in this invention theoretically eliminates registration errors and the coupling between color groups. The derivation process of the control formula is detailed below:

[0041] Combination Figure 1 According to the law of conservation of mass, we can obtain:

[0042]

[0043] Density (ρ) multiplied by cross-sectional area Multiplying by the velocity (radius multiplied by the rotational angular velocity rw) represents the mass of material entering the Ti tension zone per unit time. The second term on the left side of the equation represents the mass of material exiting the Ti tension zone per unit time. The right side of the equation represents the change in the mass of material in the Ti tension zone per unit time.

[0044] ρ is the density of the printing material. The printing material tension is T i-1 The cross-sectional area of ​​the material at time (t), where r and ω are the radius and angular velocity of the printing roller, respectively. i (t) is the material length between unit i and unit (i+1). Note: The cross-sectional area of ​​the printed material between unit i and unit (i+1) is the corresponding cross-sectional area (A0) under natural conditions, and the material tension (T) between unit i and unit (i+1) is... i The relationship between (t) and its expression is as follows:

[0045] Write Hooke's theorem here. According to Hooke's theorem, we can obtain...

[0046] Equation (2) applies Hooke's theorem to the cross-sectional area of ​​a mesh, stating that the cross-sectional area of ​​the mesh is directly proportional to its cross-sectional area in its natural state, where the proportionality coefficient is related to the mesh tension. Here, K is the tensile elongation of the material. Figure 1 As shown, when the compensating roller between unit i and unit (i+1) moves upward, the mesh fabric stretches, increasing the length of the mesh fabric between the two units. Conversely, the length of the mesh fabric between the two units decreases when the roller moves downward. In other words, the upward or downward movement of the compensating roller between unit i and unit (i+1) changes the material length between them. This relationship can be expressed as follows:

[0047]

[0048] V i (t) represents the linear velocity of the compensating roller, with the upward vertical direction being the positive direction. The printing material tension and the material length between unit i and unit (i+1) can be considered as components of the equilibrium and variation values, respectively. That is:

[0049] T i (t)=T * +ΔT i (t) (4)

[0050] l i (t)=l i * +Δl i (t) (5)

[0051] Among them (l) i * T i * ,) and (Δl i (t), ΔT i (t) represents the equilibrium value and change value of material tension and length between the i-th element and the (i+1)-th element, respectively.

[0052] The change is very small compared to the equilibrium value. Otherwise, the printing material will be damaged. Substituting (2)-(5) into (1), we get:

[0053]

[0054] Because Δl i (t), ΔT i (t) and l i * T i * It is much smaller than and K is very small, approaching 0. Therefore, in K(l i* +Δl i Δl is discarded in (t)) i (t ) And apply the Taylor approximation to (6), that is... This can be addressed as follows: When using Taylor's approximation theorem here, we cannot substitute X, which is unrelated to the formula. X must be replaced with a variable that has the same effect as X. If it is these two Δl... i (t), ΔT i If (t), then use it to replace X; otherwise, it's unclear which variables are omitted in the formula.

[0055]

[0056] (6)-(7) Detailed Derivation

[0057]

[0058] Further development

[0059]

[0060] Applying Taylor's approximation theorem Furthermore, Vi is very small due to the control limitations under steady-speed printing, thus negating Δl. i (t), ΔT i (t) and 2V i (t) Higher-order product of subterms:

[0061]

[0062] To analyze the relationship between material tension, registration error, and compensation roller linear speed Figure 2 A set of charts is provided to illustrate the relationships between them. Note: In this chart, the overprinting error is defined as the mark (pattern) printed in unit 1 and unit i respectively.

[0063] At the initial time t0, unit (i-1) prints a pattern and corresponding mark on the printing material, such as... Figure 2 As shown in (a). After a time interval Δt, the mark and its corresponding pattern have traveled a distance as the printing roller rotates, as shown in (a). Figure 2 As shown in (b). In this case, the distance between cell (i-1) and the marker is represented by λ. 1-1 (t0+Δt) represents this. According to the law of conservation of mass, the relationship regarding the mass of the mesh material over this distance can be given as follows:

[0064]

[0065] Equation (8) represents λ 1-1The mass of material in the distance (t0+Δt) is equal to the mass of material fed into the tension zone from time t0 to time t0+Δt (i-2). Substituting (2) into (8), (8) can be simplified to:

[0066]

[0067] In time At time t0, element i prints a new mark on the material. If all goes well, this mark will coincide with the mark printed by element (i-1) at time t0, as shown below. Figure 2 As shown in (c). In this case, the overprinting error of cell i, i.e., E i The distance between the two marks is 0. However, many factors are unavoidable during the printing process, such as tension oscillations. Therefore, E i It is usually not 0, such as Figure 2 As shown in (d). Figure 2 In section (d), the distance relationship between the marks printed in cell (i-1) and cell i is described. Figure 2 In section (d), the mass of the mesh fabric within the same vertical distance is equal. Therefore, the mass relationship of the mesh fabric at corresponding vertical distances can be obtained according to the law of conservation of mass:

[0068]

[0069] According to equation (9), substituting (2) into (10) yields:

[0070]

[0071] Due to ΔT i With 1+KT * In comparison, it is extremely small. Therefore, The left side of equation (11) is passed through Ignoring KΔT i Subsequently, t0+t in (11) i-1 Replacing it with t yields:

[0072]

[0073] Differentiating both sides of (12) and substituting into (1), we get:

[0074]

[0075] Substituting (4) into (12) and applying Taylor approximation, (13) can be transformed into:

[0076]

[0077] Combined equations (7) and (14):

[0078]

[0079] definition Corresponding to the printing press parameters in the experiment:

[0080] a i =0.12820513 / s,b i =1368.56187 N / m, c =0.00018736 m / (Ns). The unit of measurement for overprinting error is m.

[0081] Model (15) can be adjusted as follows:

[0082]

[0083] Equation (16) shows the relationship between the derivative of the overprinting error of unit i and the change in mesh tension between the first two units. The derivative of the change in mesh tension is related to the corresponding change in mesh tension and the linear speed of the compensation roller.

[0084] Applying the Laplace transform to equation (16) yields:

[0085]

[0086] Because the unwinding unit has a tension controller, the tension of the material entering unit 1 is maintained at a stable state. Therefore, ΔT0 = 0. Secondly, the mark printed in unit 1 serves as the reference mark for the first unit, so E1 does not exist. Based on the above reasons and equation (17), the printing error of unit 2 can be obtained as:

[0087]

[0088] Similarly, based on equation (17), the printing error of unit 3 can be obtained as follows:

[0089]

[0090] Substituting (18) into (19) yields:

[0091]

[0092] By repeatedly using equation (17), we can obtain:

[0093]

[0094] Equation (21) gives the relationship between the system printing error and the linear speed of the compensation roller. The control method proposed in this invention consists of closed-loop feedback proportional-derivative control and compensation control:

[0095]

[0096] Where V ij (s) represents the compensation from the feedback control of the i-th compensation roller to the j-th compensation roller. KP and KD are parameters corrected by the field engineer based on the actual system conditions and experience. Starting from the third unit, the derivation of V... ij (s).

[0097]

[0098] Based on (22), (23) can be adjusted as follows:

[0099]

[0100] (24) In the compensation roller 1, there is no preceding compensation roller action, so there is no compensation for the action of the preceding compensation roller. Since the function of compensation control is to eliminate the influence of the preceding compensation roller action, V 21 (s) should make the second term on the right side of (24) equal to 0, that is:

[0101]

[0102] Solving (25) yields:

[0103]

[0104] Therefore, the control formula for the second compensation roller can be obtained as follows:

[0105]

[0106] Similarly, for Unit 4:

[0107]

[0108] According to (22), (28) can be written as:

[0109]

[0110] The function of the compensation control of the compensation roller 3 in (29) is to eliminate the influence of the preceding compensation roller. Therefore, the second and third items in (29) should be 0 respectively, that is:

[0111]

[0112] Substituting (26) into (30), we can obtain:

[0113]

[0114] Therefore, the control formula for the third compensation roller is:

[0115]

[0116] Similarly, by repeating the above steps, the control formula for unit i can be obtained:

[0117]

[0118] (33) is the control formula described in this invention.

[0119] V i (s) represents the total control quantity of unit i, controlled by the proportional-derivative control V of unit i. iPD (s) and compensation amount for all preceding compensation roller control quantities Composition. KP and KD are the proportional control coefficient and derivative control coefficient of the controller, respectively. V ij (s) represents the proportional-derivative control V of the preceding j-th unit in the compensation amount of unit i. jPD The compensation amount of (s). The above formula is the compensation formula in the control formula proposed in this invention.

[0120] The color registration control method of the mechanical shaft gravure printing machine in the steady-speed printing process of the present invention is based on the mathematical model of the mechanical shaft and uses a recursive iterative analysis method. It not only theoretically proves the effectiveness of the control method, but also proves by comparison with existing industrial methods that the control method proposed in this invention has a fast response speed, can effectively and quickly eliminate color difference in the entire system, and improve color registration accuracy. It is very suitable for widespread use in the steady-speed printing process of the mechanical shaft gravure printing machine.

[0121] Table 1 System parameters of the simulation experiment corresponding to this invention

[0122] Printing speed (m / s)(rw) 5 / 6 <![CDATA[The material length (m) between two adjacent units (l j * , 1 ≤ j ≤ i)]]> 6.50 The circumference of the printing roller (m) means that the radius of the printing roller is known. 0.52 <![CDATA[Equilibrium state material tension (N) T * > 100 Material tensile coefficient (1 / N) K 0.00023

[0123] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical modifications made in accordance with the technical solutions of the present invention fall within the protection scope of the present invention.

Claims

1. A method for deriving a color registration control error model during steady-speed printing on a mechanical shaft gravure printing machine, characterized in that: Through Laplace transformations and recursive iterations, the mathematical model is expressed as follows: ； Let r be the registration error of unit i, and rw be the printing speed. The tensile strength of the material. For equilibrium material tension, The length of material between two adjacent units; The control system for the i-unit compensation roller consists of PD control and compensation control: ； The total control quantity of unit i is determined by the proportional-derivative control of unit i. And the compensation amount for all preceding compensation roller control quantities Composition; Substituting the control formula into the aforementioned model, the compensation control calculation formula is obtained through recursive iteration, starting with the third unit of derivation. : ； KP and KD are the proportional control coefficient and derivative control coefficient of the controller, respectively. For the compensation amount of unit i, the proportional-derivative control of the preceding unit j The amount of compensation.

2. An application of the derivation method for the color registration control error model during steady-speed printing of a mechanical shaft gravure printing machine as described in claim 1, characterized in that: The mechanical shaft gravure printing machine includes two or more (i) printing units, each of which is equipped with a color registration control system. The derivation method of the color registration control error model during the steady-speed printing process of the mechanical shaft gravure printing machine is used to calculate the longitudinal linear velocity change of the compensation roller between color group i-1 and color group i in the color registration control system.

3. The application of the derivation method for the color registration control error model during steady-speed printing of a mechanical shaft gravure printing machine according to claim 2, characterized in that: The color-matching control method of the color-matching control system includes the following: The printing material sequentially passes through each printing control unit of the mechanical shaft gravure printing machine for color group printing. The error detection system of color group i determines whether there is a registration error between color group i and color group i-1. If so, the control system of color group i calculates the registration error value between color group i and color group i-1. Under a determined registration accuracy, based on the control calculation formula designed according to the model of the registration control error model derivation method in the steady-speed printing process of the mechanical shaft gravure printing machine, the longitudinal linear speed change of the compensation roller between color group i-1 and color group i is calculated according to the registration error value and the control amount of the preceding compensation roller. This is then sent to the servo motor of the mechanical shaft gravure printing machine as a control command. The servo motor receives the control command and adjusts the longitudinal linear speed of the compensation roller between color group i-1 and color group i until the registration error between color group i and color group i-1 is eliminated. The error detection system of each subsequent color group determines whether there is a registration error between the color group and color group i-1. If so, the error between the color group and the preceding color group is eliminated according to the above method. The color matching control system includes a sensing device and a controller. The sensing device is used to detect color matching errors and send the color matching errors to the controller. The controller is based on a model and calculates a control quantity according to the received color matching error and the control quantity of the previous color group, based on the control calculation formula obtained by recursive iteration of the model. The control quantity is then sent to the servo motor of the mechanical shaft gravure printing machine as a control command to adjust the longitudinal linear speed of the compensation roller. The control quantity is the change in the longitudinal linear speed of the compensation roller between color groups.

4. The application of the derivation method for the color registration control error model during steady-speed printing of a mechanical shaft gravure printing machine according to claim 3, characterized in that: The mathematical model for the color matching error and the change in longitudinal linear velocity of the compensation roller between color groups is as follows: ； In the above model, Let represent the color registration error between the printed cursor of the i-th color group and the printed cursor of the (i-1)-th color group. The longitudinal linear velocity of the compensation roller between color group i and color group i+1, i.e., the i-unit compensation roller. This represents the change in material tension between color group i and color group i+1. The material tension when the material is in equilibrium under tensile conditions. ω represents the rotational angular velocity of the printing roller; K represents the tensile coefficient of the printing material, which is related to the elastic modulus and cross-sectional area of ​​the material. is the material threading length when the material tension between color group i and color group (i+1) is in a balanced tensile state; r is the radius of each printing roller; The material processing time between element i-1 and element i, i.e. .

Images