JP7302283B2 - Image forming apparatus and image forming method - Google Patents

Description

The present invention relates to an image forming apparatus and an image forming method.

The liquid ejection apparatus disclosed in Japanese Patent Application Laid-Open No. 2002-200001 replaces the amount of paper curl that varies depending on the humidity and the amount of ink ejected, with the relationship between the determination duty and the throughput. As a result, the amount of curling (degree of curling) occurring in the paper is predicted from the ambient humidity (moisture content) of the paper and the amount of ink ejected onto the paper.

JP 2017-144623 A

The amount of curl that occurs on a sheet when ink is applied to the sheet is greatly affected by the ink permeability distribution in the thickness direction of the sheet. However, the liquid ejection apparatus described in Patent Document 1 does not consider the ink penetration rate distribution in the thickness direction of the sheet.

SUMMARY OF THE INVENTION It is an object of the present invention to provide an image forming apparatus and an image forming method capable of suitably calculating the amount of curl generated in a sheet based on the permeation state of ink into the sheet. With the goal.

According to one aspect of the present invention, an image forming apparatus includes a detection section, a derivation section, and a prediction section. The detection unit detects a sheet state of a sheet before image formation and outputs sheet information, and detects an environmental state around the sheet and outputs environmental information. The derivation unit derives a penetration rate model representing a state of ink penetration into the sheet based on the sheet information and the environment information, and a curl representing a curl state of the sheet based on the penetration rate model. Derive the model. The prediction unit predicts the curl state based on the curl model.

According to still another aspect of the present invention, an image forming method detects a sheet state of a sheet before an image is formed, outputs sheet information, detects an environmental state around the sheet, and detects an environmental state. a step of outputting information; a step of deriving a curl model representing a curl state of ink on the sheet based on the sheet information and the environmental information; and a step of predicting the curl state based on the curl model. and a step.

According to the present invention, it is possible to suitably calculate the curling amount of the sheet based on the state of ink permeation into the sheet.

1 is a diagram showing a typical example of an image forming apparatus according to an embodiment of the present invention; FIG. 1 is a diagram showing a specific example of an image forming apparatus according to an embodiment; FIG. 2 is a diagram showing an image forming section of the image forming apparatus according to the embodiment; FIG. (a) to (c) are diagrams showing nozzles in the image forming section of the image forming apparatus according to the present embodiment. (a) to (c) are diagrams for explaining a one-dimensional diffusion equation used in the image forming apparatus according to the present embodiment. (a) to (d) are diagrams for explaining a one-dimensional diffusion equation used in the image forming apparatus according to the present embodiment. FIG. 10 is a diagram showing a first modified example of the image forming apparatus according to the present embodiment; FIG. 10 is a diagram showing a first modified example of the image forming apparatus according to the present embodiment; FIG. 10 is a diagram showing a second modified example of the image forming apparatus according to the present embodiment; 4 is a flow chart showing an example of the operation of the image forming apparatus according to the embodiment; 4 is a flow chart showing an example of the operation of the image forming apparatus according to the embodiment; 4 is a flow chart showing an example of the operation of the image forming apparatus according to the embodiment;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings, the same or corresponding parts are denoted by the same reference numerals, and description thereof will not be repeated.
(Typical example)

A typical example of an image forming apparatus 100 according to this embodiment will be described with reference to FIG. FIG. 1 is a diagram showing a typical example of an image forming apparatus 100 according to this embodiment.

As shown in FIG. 1, the image forming apparatus 100 includes a feeding section 2, a detecting section 4, a conveying section 6, an image forming section 8, a correcting section 10, a detecting section 12, a discharging section 14, and a control unit 16 .

The image forming apparatus 100 forms an image on the sheet Se based on the image data using ink 11, which will be described later with reference to FIGS. 4(a) to 4(c). A specific example of the image forming apparatus 100 is an inkjet printer.

The feeding section 2 can store a plurality of sheets Se. The feeding unit 2 may include a tray that can be pulled out or stored in the image forming apparatus 100, and the sheet Se is placed and stored in the tray. The user can replenish the tray with sheets Se by pulling the tray out of the feeding unit 2 . The feeding section 2 picks up the sheet Se and feeds the sheet Se to the conveying section 6 . The sheet Se is made of paper or synthetic resin, for example.

The detection unit 4 detects the sheet state of the sheet Se before an image is formed, outputs sheet information, detects the environmental state around the sheet Se, and outputs the environmental information. The “sheet state” refers to, for example, the length of the sheet Se in the conveying direction before the ink 11 is applied, the material of the sheet Se, the treatment applied to the front surface of the sheet Se, or the orientation of the sheet Se (cellulose orientation), roughness of cellulose, degree of deterioration of sheet Se, and moisture content S(x) of sheet Se. The “environmental conditions” are, for example, the temperature and humidity around the feeding section 2 . The moisture content S(x) will be described later.

The detector 4 includes a first detector 4A and a second detector 4B. The first detection unit 4A irradiates the sheet Se with sound waves or light, receives the sound waves or light reflected by the sheet Se, or captures an image of the sheet Se. The first detection unit 4A detects the sheet state such as the moisture content S(x) of the sheet Se and the length of the sheet Se in the conveying direction, and outputs it as sheet information. The second detection unit 4B detects environmental conditions such as temperature and humidity around the feeding unit 2 and outputs them as environmental information.

Note that the detection unit 4 detects sheet information or environment information as appropriate even after the sheet Se is started to be conveyed from the feeding unit 2 .

The transport unit 6 transports the sheet Se. That is, the conveying section 6 conveys the sheet Se picked up by the feeding section 2 to the image forming section 8 or the like. The transport unit 6 includes, for example, a pickup roller, a retard roller, a transport roller, a transport belt, and a discharge roller.

The image forming section 8 forms an image on the sheet Se with the ink 11 . The operation of the image forming section 8 will be further described later with reference to FIG. A specific configuration of the image forming section 8 will be described in detail with reference to FIG.

The correction unit 10 corrects the curl of the sheet Se (decurler). In the correction unit 10, for example, a soft roller and a hard roller (not shown) face each other while forming a nip, and the curl is corrected by passing the curled sheet Se through the nip. The operation of the correction unit 10 will be further described later with reference to FIG.

The detection unit 12 detects, for example, the density of the ink 11 applied to the sheet Se, the moisture content S(x), or the print rate. The moisture content S(x) and the print rate will be described later. Further, the detection unit 12 detects the length of the sheet Se in the conveying direction after the ink 11 has been applied.

The detection unit 12 includes a first detection unit 12A, a second detection unit 12B, a third detection unit 12C, a fourth detection unit 12D, and a fifth detection unit 12E. Any one of the first detection unit 12A to the fourth detection unit 12D detects the length of the sheet Se in the conveying direction after the ink 11 has been applied. Hereinafter, unless there is a special reason, the first detection unit 12A will be described as detecting the length of the sheet Se in the conveying direction after the ink 11 has been applied.

Each of the first detection section 12A to the fourth detection section 12D has a light emitting element and a light receiving element. The fifth detector 12E includes a light emitter 12F and a light receiver 12G. The second detection unit 12B is arranged downstream of the first detection unit 12A in the conveying direction of the sheet Se.

The first detection section 12A and the second detection section 12B detect the state of the ink 11 on the back surface of the conveyed sheet Se. That is, the light-emitting element of the first detection unit 12A emits light toward the back side surface of the sheet Se, and the light-receiving element receives the light reflected by the back side surface of the sheet Se. The same applies to the light-emitting element and the light-receiving element of the second detection section 12B. In other words, the outputs of the first detection section 12A and the second detection section 12B are used to measure the amount of change in the density of the ink 11 or the amount of change in the area of the ink 11 on the back surface of the sheet Se.

The third detection unit 12C and the fourth detection unit 12D respectively detect the density of the ink 11 on the front surface of the sheet Se on which the ink 11 is applied or the area of the ink 11 on the front surface. That is, the light-emitting element of the third detection unit 12C emits light toward the front surface of the sheet Se, and the light-receiving element receives light reflected by the front surface of the sheet Se. The same applies to the light-emitting element and the light-receiving element of the fourth detector 12D. In other words, the outputs of the third detection section 12C and the fourth detection section 12D are used to measure the amount of change in the density of the ink 11 or the amount of change in the area of the ink 11 on the front surface of the sheet Se.

Furthermore, the third detection unit 12C detects the amount of ink 11 applied to the sheet Se, and measures the coverage rate for each sheet Se. The print rate is not limited to being measured for each sheet Se.

Here, the front surface of the sheet Se is the surface facing the image forming section 8 and is the surface on which an image is formed with the ink 11 in the image forming section 8 . The back side of the sheet Se is the back side of the front side of the sheet Se.

Examples of the light emitting elements of the first detection unit 12A to the fourth detection unit 12D are light emitting diodes (LEDs) and organic electroluminescence (EL). Examples of light receiving elements are CCDs (charged-coupled devices) and CMOSs (complementary metal-oxide-semiconductors).

The discharge section 14 discharges the sheet Se on which the image is formed by the image forming section 8 to the outside of the image forming apparatus 100 .

The control section 16 controls the operation of each section of the image forming apparatus 100 . The control unit 16 specifically includes a processor such as a CPU (Central Processing Unit). The processor of the control unit 16 controls the operation of each unit of the image forming apparatus 100 by executing a computer program stored in a storage device (not shown).

Furthermore, when the user instructs image formation from a terminal or the like, the control section 16 acquires image data from the terminal or the like. The control unit 16 estimates, for example, the amount of ink applied to one sheet Se based on the image data, and estimates the coverage rate for each sheet Se based on the amount of ink.
(Concrete example)

Next, following FIG. 1, a specific example of the image forming apparatus 100 will be described with reference to FIG. FIG. 2 is a diagram showing a specific example of the image forming apparatus 100 according to the present embodiment, and shows the configuration of the control unit 16 of the image forming apparatus 100 and each unit controlled by the control unit 16. As shown in FIG.

In a specific example, as will be described later, the difference between the curl state of the sheet Se predicted from the curl model derived before applying the ink 11 and the curl state of the sheet Se actually measured after applying the ink 11 Based on this, a new curl model is derived. The “curling state” indicates, for example, the curling direction of the sheet Se and the amount of curling C of the sheet Se.

In order to derive a new curl model, the transport direction length of the sheet Se before the ink 11 is applied and the transport direction length of the sheet Se after the ink 11 is applied are used. Therefore, the first detection section 4A of the detection section 4 shown in FIG. 1 detects the length in the conveying direction of the sheet Se placed on the tray of the feeding section 2 and before the ink 11 is applied.

Next, regarding the detection unit 4, the image forming unit 8, and the detection unit 12 shown in FIG. 2, additional items to those described with reference to FIG. 1 will be described.

The control unit 16 shown in FIG. 2 includes a derivation unit 30, a prediction unit 32, a correction unit 34, and a change unit .

Based on the sheet information and the environment information, the derivation unit 30 derives a penetration rate model representing the penetration state of the ink 11 into the sheet Se, and based on the penetration rate model, creates a curl model representing the curling state of the sheet Se. derive

That is, the deriving unit 30 acquires the sheet information and the environmental information from the detecting unit 4, derives the permeability model based on the sheet information and the environmental information, and calculates the moisture content S(x) of the sheet Se from the permeability model. to derive

Furthermore, the derivation unit 30 acquires the printing rate from the control unit 16 .

The derivation unit 30 derives a curl model based on the moisture content S(x) and the print rate. The penetration rate model, the print rate, and the curl model at this stage are the model of the distribution of the moisture content S(x) in the sheet Se before image formation, the print rate, and the curl model. Model and show.

The prediction unit 32 predicts the curled state of the sheet Se based on the curl model. That is, based on the curl model derived by the derivation unit 30, the prediction unit 32 predicts the curl that will occur when the sheet Se placed on the tray of the feeding unit 2 is image-formed by the image forming unit 8. direction and curl generation amount C are predicted.

The control unit 16 sets the pick-up timing of the pickup roller of the transport unit 6, the rotation speed of the transport roller, and the like, based on the curl occurrence amount C of the sheet Se predicted by the prediction unit 32 .

According to the present embodiment, the derivation unit 30 calculates the diffusion coefficient D, which will be described later, based on the sheet state such as the material of the sheet Se and the environmental state in which the sheet Se is placed such as the temperature and humidity around the tray. and based on the diffusion coefficient D, a permeability model is derived. Then, the derivation unit 30 derives the curl model based on the water content S(x) derived from the permeability model and the print rate.

Based on the curl model, the prediction unit 32 can suitably predict the amount of curl C of the ink 11 on the sheet Se after image formation. Therefore, the image forming apparatus 100 can suitably suppress obstacles such as offset caused by the ink 11 that has not permeated the sheet Se. The diffusion coefficient D, permeability model, moisture content S(x), curl model, and curl generation amount C will be described later.

The image forming unit 8 forms an image on the sheet Se with the ink 11 based on the predicted curl state derived from the curl model. That is, the control unit 16 sets the ejection amount of the ink 11 by the image forming unit 8 and the like based on the curl generation amount C of the sheet Se predicted by the prediction unit 32 . The image forming section 8 forms an image on the sheet Se based on the set ejection amount of the ink 11 and the like.

The straightening section 10 straightens the curl of the sheet Se based on the prediction of the curled state of the sheet Se by the prediction section 32 . That is, the control unit 16 sets the nip force between the soft roller and the hard roller of the correction unit 10 based on the curl occurrence amount C of the sheet Se predicted by the prediction unit 32 .

Next, the detection unit 12 detects the sheet state of the sheet Se after the curl is corrected. Specifically, the first detection unit 12A and/or the second detection unit 12B detect the density of the ink 11 permeating the back surface of the sheet Se and output density data.

The detector 12 detects the amount of density change from the density data output by the first detector 12A and/or the second detector 12B. Henceforth, when it is not necessary to distinguish between the first detection section 12A and the second detection section 12B, they will be referred to as the first detection section 12A.

Also, the first detection unit 12A and/or the second detection unit 12B detect the area of the ink 11 permeating the back surface of the sheet Se, and output area data. The detector 12 detects the area change amount based on the area data output by the first detector 12A and/or the second detector 12B.

The first detection unit 12A detects the length in the transport direction of the sheet Se after the ink 11 has been applied.

Next, the third detection section 12C and/or the fourth detection section 12D detect the image density of the front surface of the sheet Se. The third detection unit 12C detects the sheet state of the sheet Se after the curl is corrected. Specifically, the third detection unit 12C and/or the fourth detection unit 12D detect the density of the ink 11 permeating from the front surface of the sheet Se and output density data.

The detector 12 detects the density change amount from the density data output by the third detector 12C and/or the fourth detector 12D. Henceforth, when it is not necessary to distinguish between the third detection unit 12C and the fourth detection unit 12D, they will be referred to as the third detection unit 12C.

Further, the third detection unit 12C and/or the fourth detection unit 12D detects the area of the ink 11 permeating the front surface of the sheet Se and outputs area data. The detection unit 12 detects the area change amount based on the area data output by the third detection unit 12C and/or the fourth detection unit 12D.

The fifth detection unit 12E detects the permeation amount (permeation state) of the ink 11 permeated in the thickness x direction of the sheet Se. The “permeation state” refers to, for example, the reflection density of the ink 11 on the front surface of the sheet Se and the amount of change in the reflection density, the permeation density of the ink 11 inside the sheet Se and the amount of change in the permeation density, and It shows the permeation speed of the ink 11, the amount of change in the permeation speed, or the amount of change in the moisture content S(x) of the sheet Se.

The correcting unit 34 corrects the diffusion coefficient based on the difference in length in the conveying direction of the sheets Se before and after the ink 11 is applied and the printing rate. Specifically, the correction unit 34 detects the permeation state of the sheet Se after image formation predicted based on the permeation state of the sheet Se detected by the detection unit 4, and the actual measurement value detected by the detection unit 12. The permeation state of the sheet Se after image formation is compared, and the diffusion coefficient D of the permeation rate model is corrected.

As described above, the derivation unit 30 outputs the curl generation amount C derived from the curl model to the prediction unit 32 and also outputs the curl generation amount C derived from the curl model to the correction unit 34 . This is because the detection unit 12 detects the curl state of the sheet Se after image formation and curl correction, and derives a new curl model based on actual measurement values from the predicted curl model.

The derivation unit 30 acquires the corrected new diffusion coefficient D (hereinafter referred to as “corrected diffusion coefficient Dc” described later in Equation (3)) from the correction unit 34 and reflects it in the permeability model. The derivation unit 30 calculates a new moisture content S(x) from the permeability model. In addition, the deriving unit 30 calculates a new elongation coefficient K (hereinafter referred to as a "post-correction elongation rate coefficient Kc”) is calculated and reflected in the curl model. The derivation unit 30 derives a new curl generation amount C from the new curl model. The derivation unit 30 outputs the new curl generation amount C to the change unit 36 .

The changing unit 36 changes the setting of the conveying unit 6, the image forming unit 8, or the correcting unit 10 based on the curl model after the ink 11 is applied to the sheet Se. Specifically, the changing unit 36 calculates a new curling amount C from the curl model after the ink 11 is applied to the sheet Se, and based on the new curling amount C, the conveying unit 6 performs image forming. Change the setting of the section 8 or the correction section 10.

The correction unit 10 corrects the curl of the sheet Se based on the changed setting.

More specific operations of the conveying unit 6, the image forming unit 8, the correcting unit 10, the deriving unit 30 included in the control unit 16, the predicting unit 32, the correcting unit 34, and the changing unit 36 are as follows ( First modified example) or (second modified example) will be described later.
(description of the head)

Here, the image forming section 8 of the image forming apparatus 100 will be described with reference to FIG. FIG. 3 is a diagram showing the configuration of the head section 9 of the image forming section 8 in the image forming apparatus 100. As shown in FIG.

As shown in FIG. 3 , the image forming section 8 has a housing 41 and a head section 9 . A housing 41 supports the head portion 9 . The head section 9 includes, for example, a first head section 42 , a second head section 43 , a third head section 44 and a fourth head section 45 . Each of the first head portion 42 to the fourth head portion 45 is arranged to face the conveying portion 6 (FIG. 1). The number of the first head portion 42 to the fourth head portion 45 is an example, and the number is not limited to this.

The first head section 42 to the fourth head section 45 each include a recording head 9A. The recording head 9A is a single or multiple inkjet heads. When the image forming apparatus 100 is of color specification, the recording head 9A has, for example, cyan (C), magenta (M), yellow (Y), and black (Bk) inkjet heads.

The recording head 9A ejects the ink 11 onto the sheet Se. The first head portion 42 to the fourth head portion 45 are arranged in a zigzag pattern so that when the ink 11 is ejected onto the sheet Se, no blank space is generated between adjacent dots. The first head portion 42 to the fourth head portion 45 are arranged along the conveying direction X of the sheet Se. Ink 11 is supplied to each of the first head portion 42 to the fourth head portion 45 . An example of the ink 11 is water-based ink. The color of the ink 11 may be different for each of the first head section 42 to the fourth head section 45 .

For example, black ink 11 is supplied to the first head unit 42 . For example, cyan ink 11 is supplied to the second head unit 43 . For example, magenta ink 11 is supplied to the third head unit 44 . For example, yellow ink 11 is supplied to the fourth head unit 45 . As a result, a color image is generated on the sheet Se in which four colors of ink 11 of cyan, magenta, yellow, and black are superimposed.

Each of the first head portion 42 to the fourth head portion 45 has the same structure. Therefore, the structure of the first head portion 42 will be described, and the description of the structure of the other head portions will be omitted.

Each of the recording heads 9A of the first head section 42 has a plurality of nozzles 9B. The first head section 42 includes, for example, a first head 42a, a second head 42b, and a third head 42c.

The first head 42a to the third head 42c are arranged in a zigzag pattern along the arrangement direction Y. As shown in FIG. The arranging direction Y is a direction orthogonal to the conveying direction X of the sheet Se.

The first head 42a has a plurality of first nozzles 46a. The second head 42b has a plurality of second nozzles 46b. The third head 42c has a plurality of third nozzles 46c. Each of the plurality of nozzles 9B is arranged to face the transport section 6 (FIG. 1).

The method of ejecting the ink 11 from the plurality of nozzles 9B includes, for example, a piezo method in which the ink 11 is pushed out using a piezo element, a thermal inkjet method in which air bubbles are generated by a heating element and pressure is applied to eject the ink 11, and the like. Various methods can be applied.

For example, in the case of the piezo method, the pressure due to the deformation of the piezoelectric element is transmitted to the ink 11 in each nozzle 9B to oscillate the meniscus and eject the ink 11. FIG.
(Ink dripping)

Next, nozzles 9B in image forming section 8 of image forming apparatus 100 will be described with reference to FIGS. FIGS. 4A to 4C are schematic diagrams of the image forming section 8 viewed from the side, showing how the ink 11 dropped onto the sheet Se from the nozzle 9B permeates the sheet Se.

First, as shown in FIG. 4A, the nozzle 9B drops the ink 11 toward the sheet Se. As shown in FIG. 4B, the ink 11 stays on the front surface of the sheet Se immediately after being dropped onto the sheet Se. As shown in FIG. 4C, the ink 11 penetrates into the sheet Se over time.

The permeation speed of the ink 11 shown in FIGS. 4B and 4C depends on the composition of the ink 11, sheet conditions such as the material of the sheet Se, and the environment in which the sheet Se is placed. It varies based on environmental conditions such as inclusions.

For example, since the dye ink easily permeates in the thickness direction of the sheet Se, the permeation speed in the dropping direction is relatively high, and the speed in which the dye ink spreads in the front side surface direction of the sheet Se is relatively low. On the other hand, since the pigment ink contains particles and does not easily permeate the sheet Se in the thickness direction, the permeation speed in the thickness direction of the sheet Se is relatively low, and the speed at which it spreads in the front side surface direction of the sheet Se is relatively high.

Even when dye ink is used, if the sheet Se has a low density of cellulose (coarse mesh), the permeation speed in the thickness direction of the sheet Se is relatively high, and the density of cellulose is high (fine mesh). In the case of the sheet Se, the permeation speed in the thickness direction of the sheet Se is relatively small.

In order for the image forming apparatus 100 to form a high-quality image, in addition to the selection of the ink 11, the density of cellulose forming the sheet Se, the percentage of moisture contained in the sheet Se (moisture content S(x)) ), environmental conditions such as the temperature environment, humidity environment, and placement time of the feeding unit 2 on which the sheet Se is placed, and the printing rate indicating the amount of the ink 11 per sheet Se. of which any necessary number can be considered.

In this embodiment, the image forming apparatus 100 performs image formation under image forming conditions set based on a penetration rate model in which at least one of a sheet state, an environmental state, and a printing rate is used as a parameter. The sheet state, the environmental state, and the print rate may not all be used, and any one of them may be selectively used.

(permeability model and diffusion coefficient)
Next, the permeability model will be explained.

The derivation unit 30 of the control unit 16 derives a permeability model based on the sheet state of the sheet Se detected by the first detection unit 4A of the detection unit 4 and the environmental state detected by the second detection unit 4B of the detection unit 4. to derive

The penetration model describes how the ink 11 penetrates into the sheet Se. That is, the permeability model represents the speed change (acceleration) of the water content S(x) at the position x at the time t after the ink 11 is dropped onto the sheet Se. A good example of a permeability model is the one-dimensional diffusion equation. However, the one-dimensional diffusion equation is an example of the permeability model, and the permeability model is not limited to the one-dimensional diffusion equation.

A one-dimensional diffusion equation is specifically represented by a differential equation as shown in Equation (1).

In Expression (1), x indicates the coordinate in the thickness direction of the sheet Se. D indicates the diffusion coefficient. S(S(x)) indicates the moisture content at the predetermined coordinates of the thickness x. t indicates the elapsed time after the ink 11 is dropped onto the sheet Se.

The diffusion coefficient D is represented by Equation (2) as an example.

In Equation (2), D ₀ represents a standard diffusion coefficient determined for each type of ink 11 . T indicates temperature. T ₀ indicates the reference temperature. W indicates humidity. W ₀ indicates the reference humidity. P indicates a correction value corresponding to the type of sheet Se.

Next, the penetration of the ink 11 into the sheet Se described by the one-dimensional diffusion equation of formula (1) will be briefly described with reference to FIGS. 5(a) to 6(c). 5A to 6C are diagrams for explaining the one-dimensional diffusion equation used in the image forming apparatus according to this embodiment. FIGS. 5(a) to 6(c) show the penetration of the ink 11 into the sheet Se described by the one-dimensional diffusion equation.

In FIG. 5A, the x-axis is taken in the thickness direction from the front surface of the sheet Se, and a fixed point x1 is taken at an arbitrary position on the sheet Se. The formula (∂S/∂t) on the left side of formula (1) is obtained by fixing the position x in the thickness direction to a fixed point x1 and performing the first-order partial differentiation of the moisture content S(x) with respect to time t. As shown in FIG. 5(b), the formula (∂S/∂t) is the water content S(x) at a fixed point x1 after the ink 11 has been dropped onto the sheet Se when the time Δt has passed. A variation ΔS(x) is shown.

That is, as shown in FIG. 5B, immediately after the ink 11 is dropped (time t≈0), the ink 11 stays near the front surface of the sheet Se. Therefore, as shown in FIG. 5C, the moisture content S(x) at the fixed point x1 near the front surface of the sheet Se is maximum at time t≈0. However, the ink 11 subsequently penetrates in the thickness direction (x direction) of the sheet Se. Therefore, as shown in FIG. 5(c), the water content S(x) at the fixed point x1 rapidly decreases and converges to zero as the time t progresses.

Next, FIGS. 6A to 6C are diagrams showing the relationship between the thickness x of the sheet Se and the moisture content S(x) over time t. The formula (∂ ² S/∂x ² ) on the right side of the formula (1) is a formula obtained by second-order partial differentiation of the water content S(x) at the position x with the time t fixed.

That is, as shown in FIG. 6A, immediately after the ink 11 is dropped (t≈0), the ink 11 gathers at the dropping position (thickness x≈0) of the sheet Se, so that the front surface of the sheet Se The water content S(x) of the fixed point x1 in the vicinity of is the maximum. The water content S(x) rapidly decreases as the sheet Se advances slightly in the thickness x direction from the front surface of the sheet Se.

However, after that, the ink 11 permeates the sheet Se in the thickness x direction. Therefore, as shown in FIG. 6B, when time t=T, the moisture content S(x) at the dropping position (thickness x≈0) of the sheet Se is higher than the moisture content S(x) at t≈0. also decreases, and the moisture content S(x) gradually decreases in the thickness x direction from the front surface of the sheet Se.

Furthermore, when a sufficient amount of time has passed (t=∞), the moisture content S(x) gradually decreases in the thickness x direction from the front surface of the sheet Se. Then, the moisture content S(x) at an arbitrary thickness x converges to zero.

Next, the diffusion coefficient D shown in Equation (2) is a coefficient determined by the sheet state of the sheet Se and the environmental state in which the sheet Se is placed, as described above. Specifically, the higher the environmental temperature T is relative to the reference temperature T ₀ , the easier it is for the ink 11 to permeate the sheet Se, so the diffusion coefficient D increases. Also, the lower the environmental humidity W is relative to the reference humidity _W0 , the easier it is for the ink 11 to permeate the sheet Se, so the diffusion coefficient D increases.

Similarly, the lower the ambient temperature T relative to the reference temperature T ₀ , the less likely the ink 11 permeates the sheet Se, so the diffusion coefficient D becomes smaller. Further, as the environmental humidity W is higher than the reference humidity _W0 , the ink 11 is less likely to permeate the sheet Se, so the diffusion coefficient D increases.

_D0 is a value determined according to the type of ink 11, and P is a value determined according to the type of sheet Se. That is, the diffusion coefficient D becomes small when the cellulose forming the sheet Se is a dense sheet Se, when the ink 11 is a pigment ink with large particles, or when the viscosity of the ink 11 is high.

Conversely, if the sheet Se is made of coarse cellulose, if the ink 11 is dye ink, or if the viscosity of the ink 11 is low, the diffusion coefficient D increases.
(Curl model using paper elongation)

Next, the curl model will be described. The curl model is a formula for predicting in which direction and how much the sheet Se will curl when the ink 11 is applied to the sheet Se, depending on the position of the sheet Se and the passage of time.

The curl model is not limited as long as it is a formula that can express the amount of curl generated, but in the present embodiment, Formula (3) is used as an example.

Here, ε(x) is the elongation rate of the length of the sheet Se in the conveying direction at a predetermined coordinate of the thickness x. K is the elongation coefficient. The elongation coefficient K is a coefficient given in advance for each type of sheet Se.

That is, the elongation rate ε(x) shown in formula (3) is a value determined by the elongation rate coefficient K and the water content S(x), and the water content derived from the one-dimensional diffusion equation shown in formula (1) It is obtained using the rate S(x).

The curling amount C of the sheet Se is derived from Equation (4).

In formula (4), C is the amount of curl generated. H is the curling factor. R is the print rate. L is the sheet thickness.

Equation (4) derives the elongation rate ε(x) at four points in the thickness direction of the sheet Se from Equation (3), and the elongation rate ε(x) at the four points, the curl occurrence coefficient H, and the printing rate R is substituted into the equation (4) to calculate the curling amount C.

The image forming apparatus 100 according to the present embodiment derives the curl model of formula (3) from the penetration rate model of formula (1), and predicts the curl generation amount C when an image is formed on the sheet Se with the ink 11 . For example, the image forming apparatus 100 suitably corrects the curl of the sheet Se by controlling the conveying speed of the conveying section 6 (FIG. 1), the ejection control of the ink 11 in the image forming section 8, and the nip pressure of the correcting section 10. .
(First modification)

Next, a first modified example of the image forming apparatus 100 according to the present embodiment will be described with reference to FIGS. 7 and 8 in addition to FIGS. 7 and 8 are diagrams showing a first modification of the image forming apparatus 100. FIG.

In the first modification, the diffusion coefficient D of the penetration rate model derived from the sheet information and environmental information before image formation on the sheet Se is combined with the density change amount of the ink 11 on the back side surface of the sheet Se after image formation, and the area The post-correction diffusion coefficient Dc after image formation is calculated in consideration of the measured values such as the amount of change. A new permeability model is derived based on the corrected diffusion coefficient Dc, and a new curl model is derived based on the new permeability model. Then, a new curl generation amount C is calculated based on the new curl model.

As shown in FIGS. 1 and 2, in the first modified example, the control unit 16 first outputs the print rate of the sheet Se based on the print data acquired from the terminal. Furthermore, the control unit 16 activates the detection unit 4 . The first detection portion 4A of the detection portion 4 detects the length of the sheet Se in the conveying direction before being printed by the image forming portion 8 .

The first detection unit 4A outputs the sheet state and the length in the conveying direction as sheet information. The second detection portion 4B of the detection portion 4 detects the environmental condition around the feeding portion 2 on which the sheet Se is placed, and outputs environmental information.

A derivation unit 30 included in the control unit 16 calculates the diffusion coefficient D of the equation (2) based on the seat information and the environment information, and derives the permeability model of the equation (1). Alternatively, the derivation unit 30 may calculate the diffusion coefficient D based on only one of the sheet information and the environment information. This matter can be applied throughout the specification of the present application.

Next, the deriving unit 30 calculates the curl shown in the equation (3) based on the distribution of the water content S(x) calculated from the permeability model shown in the equation (1) and the printing rate acquired from the detection unit 4. Derive the model. Then, the derivation unit 30 calculates the curl generation amount C shown in Equation (4) based on the distribution of the elongation rate ε(x) calculated from the curl model.

A prediction unit 32 included in the control unit 16 predicts the curled state of the sheet Se based on the calculated curl occurrence amount C, and also determines a suitable operation timing of the transport rollers included in the transport unit 6 and a suitable transport timing. Predict speed. The control unit 16 suitably sets the transport speed of the transport roller of the transport unit 6 based on the prediction of the prediction unit 32 .

Similarly, the prediction unit 32 predicts a suitable ejection amount of the ink 11 in the image forming unit 8 based on the derived curl generation amount C. FIG. The control unit 16 suitably sets the ejection amount of the ink 11 in the image forming unit 8 based on the prediction of the prediction unit 32 .

Furthermore, the prediction unit 32 predicts a suitable nip pressure in the correction unit 10 based on the derived curl amount C. FIG. The control unit 16 suitably sets the nip pressure of the correction unit 10 based on the prediction of the prediction unit 32 .

Specifically, when the derivation unit 30 calculates a relatively small diffusion coefficient D, the ink 11 dropped onto the sheet Se is not dried and is likely to remain on the front surface of the sheet Se. The unit 32 predicts that the curling amount C of the sheet Se is relatively small. However, the drying of the ink 11 is not sufficient and there is a high possibility that offset will occur.

Further, when the derivation unit 30 calculates a relatively large diffusion coefficient D, the prediction unit 32 predicts that the ink 11 dropped onto the sheet Se will permeate the inside of the sheet Se relatively rapidly, and are likely to dry relatively quickly. In this case, since the possibility of causing an offset is low, the control unit 16 sets the rotation speed of the transport roller of the transport unit 6 to be high according to the prediction of the prediction unit 32 .

Further, when the derivation unit 30 calculates a relatively small diffusion coefficient D, it is highly possible that the ink 11 dropped onto the sheet Se does not dry and stays on the front surface of the sheet Se. Therefore, the control section 16 sets the image forming section 8 to reduce the amount of the ink 11 according to the prediction of the prediction section 32 .

Further, when the derivation unit 30 calculates a relatively large diffusion coefficient D, there is a high possibility that the ink 11 permeates the inside of the sheet Se, thereby lowering the reflection density. Therefore, the control section 16 sets the image forming section 8 so that the amount of the ink 11 is relatively large according to the prediction of the prediction section 32 .

Further, as shown in FIG. 7, the image forming section 8 can form patch images 50 of four colors of cyan, magenta, yellow, and black in a test mode or the like. The patch image 50 is normally outside the conveying area of the sheet Se on a conveying belt (not shown), and is formed by arranging small images for each color of cyan, magenta, yellow, and black in the conveying direction of the sheet Se. be.

Also, the control unit 16 controls the nip pressure of the correction unit 10 based on the prediction of the prediction unit 32 . Specifically, when the derivation unit 30 calculates a relatively small diffusion coefficient D, the prediction unit 32 predicts that the curling amount C of the sheet Se is relatively small. Based on the permeation state predicted by the prediction unit 32, the control unit 16 sets the nip pressure between the soft roller and the hard roller of the correction unit 10 to be weak.

Further, when the derivation unit 30 calculates a relatively large diffusion coefficient D, the prediction unit 32 predicts that the curling amount C of the sheet Se is relatively large. Based on the permeation state predicted by the prediction unit 32, the control unit 16 sets the nip pressure between the soft roller and the hard roller of the correction unit 10 to be increased.
(Correction of permeability model)

Next, the controller 16 activates the detector 12 . As an example, the detection unit 12 detects the image density of the patch image 50 of each color. When the patch images 50 are formed on both sides of the sheet Se in the conveying direction, the first detection unit 12A to the fifth detection unit 12E of the detection unit 12 may also be provided in two rows according to the positions of the patch images 50. FIG.

FIG. 7 is a diagram for explaining how the sheet Se on which the patch image 50 is formed is detected by the first detection section 12A and the second detection section 12B.

As shown in FIG. 7, the first detection unit 12A of the detection unit 12 irradiates light onto the back side surface (the surface on which an image is not formed) of the conveyed sheet Se, detects the reflected light, and detects the reflected light. Output concentration data. In other words, the first detection unit 12A captures an image of the ink 11 that has permeated the inside of the sheet Se and seeped out to the back surface of the sheet Se, and determines the amount of the ink 11 or the amount of the sheet. Image data such as the area of the ink 11 on the back surface of Se is output.

After that, following the first detection section 12A, the second detection section 12B irradiates the back surface of the sheet Se with light and detects the reflected light. The second detection unit 12B captures an image of the ink 11 oozing out on the back side of the sheet Se, and outputs image data such as the amount of the ink 11 or the area of the ink 11 on the back side of the sheet Se.

Further, the first detection unit 12A detects the length of the conveyed sheet Se in the conveying direction.

The third detection unit 12C is arranged to face the surface (front surface) of the conveyed sheet Se on which the ink 11 is applied. The third detection unit 12C outputs the reflection density data of the front surface of the sheet Se, detects the printing rate of the sheet Se, outputs the printing rate data, or detects the length of the sheet Se in the conveying direction, Output length data.

After that, following the third detection unit 12C, the fourth detection unit 12D irradiates the front surface of the sheet Se with light and detects the reflected light. The fourth detection unit 12D captures an image of the ink 11 oozing out on the front surface of the sheet Se, and outputs image data such as the amount of the ink 11 or the area of the ink 11 on the back surface of the sheet Se.

The fifth detector 12E includes a light emitter 12F and a light receiver 12G. The fifth detection unit 12E causes the light emitting unit 12F to irradiate the ink image on the sheet Se with light, and causes the light receiving unit 12G to receive the light transmitted through the ink image. The fifth detector 12E outputs transmission density data.

The correction unit 34 shown in FIG. 2 acquires reflection density data, transmission density data, printing ratio data, area change rate data, and length data from the first detection unit 12A to the fifth detection unit 12E.

The correction unit 34 considers any one of the reflection density data, the transmission density data, the coverage data, the area change rate data, and the length change rate data acquired from the detection unit 12, and calculates the post-correction diffusion coefficient. Calculate Dc.

For correction of the diffusion coefficient D, the reflection density data, the transmission density data, the coverage data, and the area change rate data can be used instead of the length data. The length data can be used in deriving a new curl model as described below.

The derivation unit 30 reflects the corrected diffusion coefficient Dc in the permeability model to derive a new permeability model.

The third detection unit 12C detects the reflection density of the patch image 50 formed on the sheet Se, as shown in FIG. After that, the fourth detector 12D measures the transmission density of the patch image 50. FIG. The mode of penetration of the ink 11 into the sheet Se can be obtained from the relationship between the reflection density and transmission density of the patch image 50 .

The reflection density of the patch image 50 depends on the amount of the ink 11 applied to the front surface of the sheet Se detected by the third detection unit 12C. On the other hand, the fourth detection unit 12D can detect the reflection density of the ink 11 applied to the front surface of the sheet Se and the density of the ink 11 permeated inside the sheet Se. The derivation unit 30 can roughly calculate the permeability model of the ink 11 from the relationship between the reflection density and the transmission density.

Specifically, the correction unit 34 shown in FIG. 2 corrects the diffusion coefficient D of Equation (2) used in the first-order diffusion equation of Equation (1) to the corrected diffusion coefficient Dc as shown in Equation (5). .

In Equation (5), Dc indicates the corrected diffusion coefficient. Mr indicates the measured reflection density. Mr ₀ indicates the reference reflection density. Mt indicates the measured transmission density. Mt ₀ indicates the reference transmission density.

Based on the reflection density or transmission density obtained by measuring the density of the patch image 50 by the detection unit 12, the correction unit 34 corrects the diffusion coefficient D in Equation (1), and the derivation unit 30 corrects the diffusion coefficient Dc A new permeability model is derived by substituting into the permeability model of equation (1).

Equation (3) indicates that the larger the measured reflection density Mr with respect to the reference reflection density Mr ₀ is, the more difficult it is for the ink 11 to permeate the sheet Se. In that case, the diffusion coefficient D is corrected to a smaller post-correction diffusion coefficient Dc. Further, the larger the measured transmission density Mt with respect to the reference transmission density _Mt0 , the more the ink 11 permeates the sheet Se. Therefore, the diffusion coefficient D is corrected to a larger post-correction diffusion coefficient Dc. be.

Note that the reference reflection density Mr0 is calculated by Equation (6) as an example.

The reference reflection density Mr ₀ in equation (6) is the initial value. That is, M is the reflection density when the water content is 100% immediately after the ink 11 is dropped onto the sheet Se. S(0) is the water content on the front surface of the sheet Se (the predetermined coordinate of the thickness x is 0).

When the diffusion coefficient D of the permeability model is corrected for the first time, the equation (6) is used, and the correction of the diffusion coefficient D of the permeability model after the second time is performed by measuring the previously acquired equation (5) Correction of the diffusion coefficient D is repeated with the reflection density Mr as the reference reflection density Mr ₀ .

The second and subsequent corrections of the diffusion coefficient D of the permeability model are performed when environmental conditions such as the time the image forming apparatus 100 is not operating, the execution time of image formation, and the amount of change in temperature and humidity exceed a predetermined threshold. may be performed. This matter can be applied throughout the specification of the present application.

The permeability model may be derived for each color (CMYBk) of the image forming apparatus 100 , and the diffusion coefficient D of the permeability model may be corrected for each color (CMYBk) of the image forming apparatus 100 . This matter can be applied throughout the specification of the present application.

Further, the permeability model may be derived for each combination of colors (CMYBk) of the image forming apparatus 100, and correction of the diffusion coefficient D of the permeability model is performed for each combination of colors (CMYBk) of the image forming apparatus 100. may be done. This matter can be applied throughout the specification of the present application.
(Correction of curl model)

Next, the derivation unit 30 corrects the curl model of Equation (3). To correct the curl model, the derivation unit 30 corrects the elongation coefficient K. An example of the post-correction elongation coefficient Kc is Formula (7).

In Equation (7), Kc is the post-correction elongation coefficient. Cr is the measured elongation rate. Cp is the elongation rate prediction value.

The derivation unit 30 calculates the elongation rate predicted value Cp based on the length data of the sheet Se before the ink 11 is applied, which is acquired from the first detection unit 4A. The derivation unit 30 calculates the measured elongation rate Cr based on the length data of the sheet Se after the ink 11 is applied, which is detected by the first detection unit 12A.

The elongation coefficient K is a coefficient given in advance according to the type of the sheet Se, as described above. The derivation unit 30 acquires the elongation coefficient K of the sheet Se. The derivation unit 30 substitutes the elongation coefficient K of the sheet Se, the elongation rate predicted value Cp, and the elongation rate actual measurement value Cr into the equation (7) to calculate the corrected elongation rate coefficient Kc. The derivation unit 30 derives the corrected moisture content S(x) based on the already acquired corrected permeability model.

The derivation unit 30 derives a new curl model from Equation (5) based on the post-correction elongation coefficient Kc and the corrected moisture content S(x).

The deriving unit 30 calculates a new curl generation amount C based on the new curl model.

The changing unit 36 changes the settings of the conveying unit 6 (FIG. 1), the image forming unit 8, and the correcting unit 10 based on the new curl occurrence amount C. FIG. That is, the changing unit 36 changes the rotation speed of the transport roller of the transport unit 6 based on the new curl generation amount C, changes the ejection amount of the ink 11 of the image forming unit 8, and changes the nip pressure of the correction unit 10. to change

The image forming apparatus 100 repeats the above operation and repeats the correction of the permeability model and the curl model, thereby suitably improving the print quality.

(Second modification)
Next, with reference to FIG. 9, a second modified example according to this embodiment will be described. The second modified example illustrates the operation performed by the image forming apparatus 100 when a sheet Se whose sheet state is unknown is placed on the feeding unit 2 by the user. FIG. 9 is a diagram showing a second modification of the image forming apparatus 100. As shown in FIG.

For example, image forming apparatus 100 has a test mode. When the user selects the test mode, the first detection section 4A of the detection section 4 detects the length of the sheet Se in the conveying direction. The feeding section 2 feeds the sheet Se from a tray, and the conveying section 6 conveys the sheet Se to the image forming section 8 . The image forming section 8 forms a so-called solid image 52 as shown in FIG. 9 on the sheet Se. The correction unit 10 corrects the curl of the sheet Se on which an image is formed.

At this time, the control unit 16 controls the rotation speed of the transport roller of the transport unit 6, controls the amount of ink in the image forming unit 8, and controls the amount of ink in the correction unit 10 based on the latest penetration rate model and/or curl model. Control nip force. The detection unit 12 detects the reflection density and transmission density of the sheet Se, and the length of the sheet Se in the conveying direction.

The correction unit 34 corrects the diffusion coefficient D, and the derivation unit 30 derives a new permeability model based on the post-correction diffusion coefficient Dc. The derivation unit 30 has Equation (8) as an example to correct the curl model.

In Equation (8), K ₀ is the post-correction elongation rate generation coefficient. ε ₀ is the measured elongation in test mode.

Specifically, the correction unit 34 detects the length of the sheet Se in the conveying direction before the ink 11 is applied, which is detected by the first detection unit 4A, and the length of the sheet Se when the ink 11 is applied, which is detected by the first detection unit 12A. The length of the subsequent sheet Se in the conveying direction is obtained, and the measured elongation rate ε ₀ in the test mode is calculated.

The derivation unit 30 derives the curl model of Equation (8) by using the elongation rate actual measurement value ε ₀ in the test mode as the post-correction elongation rate generation coefficient K ₀ . The correction unit 34 calculates a new curl generation amount C of Equation (4) from the curl model of Equation (8).

Based on the new curl occurrence amount C, the changing unit 36 controls the rotation speed of the transport roller of the transport unit 6 , controls the amount of ink in the image forming unit 8 , and controls the nip force in the correction unit 10 .

Thus, the image forming apparatus 100 ends the test mode.

Next, an example of an image forming method of the image forming apparatus 100 will be described with reference to FIGS. 10 to 12. FIG. 10 to 12 are flowcharts showing an example of the operation of the image forming apparatus 100. FIG. As shown in FIGS. 10-12, the process includes steps S10 through S50. The control unit 16 executes the processing from step S10 to step S50. Specifically, it is as follows.

As shown in FIG. 10, first, in step S10, the control unit 16 activates the detection unit 4 to acquire sheet information of the sheet Se. The process proceeds to step S12.

In step S12, the detection unit 4 detects the print rate of the sheet Se. The process proceeds to step S14.

In step S14, the detection unit 4 acquires environment information. The process proceeds to step S16.

In step S16, the derivation unit 30 calculates the diffusion coefficient D. FIG. The process proceeds to step S18.

In step S18, the derivation unit 30 derives a permeability model. The process proceeds to step S20.

In step S20, the derivation unit 30 calculates the moisture content S(x) of the sheet Se. The process proceeds to step S22.

In step S22, the derivation unit 30 derives a curl model. The process proceeds to step S24.

In step S<b>24 , the prediction unit 32 calculates the curl amount C. As shown in FIG. The process proceeds to step S26.

In step S26, the controller 16 sets the rotation speed of the transport roller. The process proceeds to step S28.

In step S<b>28 , the control section 16 sets the ejection amount of the ink 11 from the image forming section 8 . The process proceeds to step S30.

In step S<b>30 , the control section 16 sets the nip pressure of the correction section 10 . The process proceeds to step S32.

In step S32, the image forming section 8 forms an image on the sheet Se.

In step S34, the straightening section 10 straightens the curl of the sheet Se. The process proceeds to step S36.

In step S36, the detection unit 12 detects the penetration state of the sheet Se. The process proceeds to step S38.

In step S38, the detection unit 12 acquires the amount of change in image density. The process proceeds to step S40.

In step S40, the correction unit 34 determines whether or not the amount of change in image density is equal to or greater than a threshold. If it is equal to or greater than the threshold (Yes in step S40), the process proceeds to step S42.

If it is less than the threshold (No in step S40), the process ends.

In step S42, the correction unit 34 calculates the post-correction diffusion coefficient Dc. The process proceeds to step S44.

In step S44, the derivation unit 30 derives a new permeability model using the corrected diffusion coefficient Dc. The process proceeds to step S46.

In step S46, the derivation unit 30 calculates a new moisture content S(x) from the new permeability model. The process proceeds to step S48.

In step S48, the derivation unit 30 derives a new curl model based on the moisture content S(x) and the print rate. The process proceeds to step S50.

In step S<b>50 , the derivation unit 30 calculates a new curl generation amount C. FIG. The process proceeds to step S52.

In step S<b>52 , the changing section 36 changes settings of the conveying section 6 , the image forming section 8 , and the correcting section 10 . Then, the process repeats steps S16 to S52.

The embodiments of the present invention have been described above with reference to the drawings. However, the present invention is not limited to the above-described embodiments, and can be implemented in various aspects without departing from the gist of the present invention. Various inventions can be formed by appropriately combining the plurality of constituent elements disclosed in the above embodiments. For example, some components may be deleted from all components shown in this embodiment. Furthermore, the constituent elements of different embodiments may be combined as appropriate. In order to facilitate understanding, the drawings mainly show each component schematically, and the number of each component shown in the drawing differs from the actual number for the convenience of drawing. Further, the shape and the like of each component shown in the above embodiment is an example and is not particularly limited, and various modifications are possible within the scope of the configuration of the present invention.

INDUSTRIAL APPLICABILITY The present invention can be used in the field of image forming apparatuses.

100 Image forming apparatus 2 Feeding unit 4 Detecting unit 6 Conveying unit 8 Image forming unit 10 Correcting unit 12 Detecting unit 14 Discharge unit 16 Control unit 30 Derivation unit 32 Prediction unit 34 Correction unit 36 Change unit

Claims (10)

a detection unit that detects a sheet state of a sheet before an image is formed and outputs sheet information, detects an environmental state around the sheet and outputs the environmental information;
deriving a penetration rate model representing a state of ink penetration into the sheet based on the sheet information and the environment information, and deriving a curl model representing a curl state of the sheet based on the penetration rate model; Department and
a prediction unit that predicts the curl state based on the curl model ;
a detection unit that detects the permeation state after the ink is applied;
a correction unit that corrects the diffusion coefficient based on the permeation states before and after the ink is applied;
with
The derivation unit derives the permeability model after the ink is applied based on the diffusion coefficient, and the ink is applied based on the permeability model after the ink is applied. An image forming apparatus for deriving said curl model afterward . a conveying unit that conveys the sheet;
an image forming unit that forms an image on the sheet;
a straightening section for straightening the curl of the sheet;
a control unit that sets the conveying unit, the image forming unit, or the correction unit based on the prediction;
The image forming apparatus according to claim 1. 3. The image forming apparatus according to claim 2 , further comprising a changing section that changes the setting of the conveying section, the image forming section, or the correcting section based on the curl model after the ink is applied. . The detection unit includes a first detection unit and a second detection unit,
The first detection unit and the second detection unit respectively detect the concentration of the ink on the back side of the surface of the sheet to which the ink is applied, or the area of the ink on the back side,
The correction unit is based on the amount of change between the density of the ink detected by the first detection unit and the density of the ink detected by the second detection unit, or is detected by the first detection unit. correcting the curl model based on the amount of change between the area of the ink and the area of the ink detected by the second detection unit;
The image forming apparatus according to claim 1 . The detection unit includes a third detection unit and a fourth detection unit,
The third detection unit and the fourth detection unit respectively detect the concentration of the ink on the front surface of the sheet to which the ink is applied or the area of the ink on the front surface,
The correction unit is based on the amount of change between the density of the ink detected by the third detection unit and the density of the ink detected by the fourth detection unit, or the amount detected by the third detection unit correcting the curl model based on the amount of change between the area of the ink and the area of the ink detected by the fourth detection unit;
The image forming apparatus according to claim 1 . a step of detecting a sheet state of a sheet before image formation and outputting sheet information, and detecting an environmental state around the sheet and outputting the environmental information;
deriving a curl model representing a curl state of ink on the sheet based on the sheet information and the environment information;
predicting the curl state based on the curl model ;
detecting the state of penetration after the ink has been applied;
correcting the curl model based on the respective penetration states before and after the ink is applied;
An image forming method comprising : conveying the sheet;
forming an image on the sheet;
straightening the curl of the sheet;
7. The image forming method according to claim 6 , further comprising: setting a conveying section, an image forming section, or a correcting section based on the prediction. 7. The image forming method according to claim 6 , further comprising changing settings of a conveying section, an image forming section, or a correcting section based on the corrected curl model. a step of detecting the density of the ink on the back side of the sheet to which the ink is applied, or the area of the ink on the back side;
9. The image forming method according to claim 6 , further comprising : correcting the curl model based on the amount of change in the density of the ink or based on the amount of change in the area of the ink. . a step of detecting the density of the ink on the surface of the sheet to which the ink is applied, or the area of the ink on the surface;
9. The image forming method according to claim 6 , further comprising : correcting the curl model based on the amount of change in the density of the ink or based on the amount of change in the area of the ink. .

Images