JP2006185173A - Simulation method for heater, program, recording medium and image formation apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately simulate a change in various physical quantity (temperature, currents, resistance value) of the filament of a heater which is valid for estimating a flicker. <P>SOLUTION: In a block 111, I×I×R(=V×I) is calculated. A value acquired by calculating a temperature T of a filament to the power four in a block 112, and multiplying the result by β in a block 113 and a value acquired by subtracting an atmosphere temperature T<SB>0</SB>of the filament inputted from the block 114 from the temperature T of the filament in a block 115, and multiplying the result by h are subtracted from the above mentioned value in a block 117. The value is divided by a thermal capacity C<SB>f</SB>of the filament in a block 118, and integrated by a time t in a block 119 so that the temperature T can be acquired. Also, the T to the power 1.2 is calculated in a block 121, and multiplied by α in a block 122 so that a resistance value R of the filament can be acquired. Also, the resistance value R is used for the estimation of a flicker. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a heater simulation method for numerically analyzing changes in various physical quantities of the filament, and a program, recording medium, and image to which the simulation method is applied. The present invention relates to a forming apparatus.

  Conventionally, a heater including a filament that generates heat in response to energization has been applied to various fields such as a heat source for fixing for an image forming apparatus such as a laser printer. Further, when this type of heater is used as the heat source for fixing, flicker generated when the image forming apparatus is turned on may be a problem.

For example, an image forming apparatus sold in Europe must satisfy the flicker value condition defined in EN61000-3-3. Thus, it has been proposed to reduce flicker by various methods such as providing a plurality of filaments and shifting the energization timing (see, for example, Patent Documents 1, 2, and 3).
JP-A-10-111623 JP 2003-173107 A JP 2002-182520 A

  However, conventionally, flicker evaluation is performed by measuring with an actual machine after product trial production, and it has been difficult to simulate in advance how much flicker occurs. For this reason, when a prototype is actually manufactured and the specified conditions cannot be satisfied, it is necessary to review from the basic design, which may cause a great time loss in development. Therefore, the present invention has been made for the purpose of accurately simulating changes in various physical quantities (temperature, current, resistance value) of the filament of the heater effective for estimating flicker.

  The present invention made to achieve the above object is a heater simulation method for numerically analyzing a change in temperature of a filament of a heater having a filament that generates heat in response to energization. A heat amount calculation process for calculating stored energy; a heat release amount calculation process for calculating energy dissipated from the filament; a heat conduction calculation process for calculating energy taken away from the filament by heat conduction; and a temperature of the filament. And a resistance value calculation process for calculating the corresponding resistance value of the filament.

  In the method of the present invention configured as described above, the sum of each energy calculated by the heat amount calculation process, the heat release amount calculation process, and the heat conduction calculation process is equal to the energy given to the filament, that is, the power. Further, since the resistance value of the filament is obtained as a function of temperature by the resistance value calculation process, the electric power is obtained as a function of the current flowing through the filament and the temperature.

Therefore,
Electric power = V · I = I ² · R (T) = total of the above-mentioned energies (1)
Where V is the voltage applied to the filament,
I is the current through the filament,
R is the resistance value of the filament,
T is the temperature of the filament,
To obtain an equation with the temperature and current of the filament as variables. If the temperature change of the filament is numerically analyzed based on this equation, the simulation of the temperature change of the filament can be accurately executed in consideration of the resistance value change according to the temperature of the filament.

  The present invention is also a heater simulation method for numerically analyzing a change in current flowing through a filament of a heater having a filament that generates heat in response to energization, and calculating energy stored in the filament as heat. Heat amount calculation processing, heat dissipation amount calculation processing for calculating energy radiated from the filament, heat conduction calculation processing for calculating energy deprived from the filament by heat conduction, and the filament according to the temperature of the filament And a resistance value calculating process for calculating a resistance value.

  Also in this case, an equation having the temperature and current of the filament as variables is obtained as in the above-described equation (1). If the change in the current flowing through the filament is numerically analyzed based on this equation, the simulation of the change in the current flowing through the filament can be accurately executed in consideration of the resistance value change according to the temperature of the filament. .

  Still further, the present invention is a heater simulation method for numerically analyzing a change in the resistance value of a filament of a heater having a filament that generates heat in response to energization, the energy stored in the filament as heat. A heat amount calculation process to calculate, a heat release amount calculation process to calculate the energy radiated from the filament, a heat conduction calculation process to calculate energy taken away from the filament by heat conduction, and the filament according to the temperature of the filament And a resistance value calculation process for calculating the resistance value.

  Also in this case, an equation having the temperature and current of the filament as variables is obtained as in the above-described equation (1). Based on this equation, the simulation of the temperature change of the filament can be accurately executed in consideration of the change in the resistance value as described above, and the simulation of the change in the resistance value of the filament can be accurately performed from the temperature. Can be executed.

The present invention does not limit the form of processing in the heat amount calculation process, the heat radiation amount calculation process, the heat conduction calculation process, and the resistance value calculation process. However, in the heat amount calculation process, C _f · dT The energy is calculated by the equation (t) / dt (where T (t) is the filament temperature (K) and C _f is the heat capacity of the filament). In the heat dissipation amount calculation process, β · T ⁴ (t ) (Where β is a coefficient determined according to the heater), and the energy is calculated by the equation of h (T (t) −T ₀ ) (where T ₀ is the _value of the filament). The energy is calculated by the ambient temperature (K), h is a coefficient determined according to the heater, and in the resistance value calculation process, an equation of α · T ^1.2 (t) (where α is determined according to the filament) Coefficient) Thus, the resistance value may be calculated.

  In this case, the right side of the above equation (1) can be replaced by a simple function with the temperature T of the filament as a variable, the processing according to the present invention is simplified, the processing speed is improved, and the processing device cost is reduced. Can be achieved.

  Further, the relationship between the applied voltage V (t) to the filament, the current I (t) flowing through the filament, and the temperature T (t) of the filament may be calculated by the following equation. By eliminating V (t) from this equation using Ohm's law (V = I · R), an equation equivalent to the above equation (1) can be obtained. Also in this case, the processing according to the present invention can be simplified to improve the processing speed and reduce the cost of the processing apparatus.

また、これらの場合において、前記Ｃ_f ，β，ｈ，及びαを、実測値に基づいて設定すしてもよい。このように、各種係数を実測値に基づいて設定することにより、ヒータの実際の動作に即した一層正確なシミュレーションが可能となる。

In these cases, C _f , β, h, and α may be set based on actually measured values. As described above, by setting various coefficients based on the actual measurement values, it is possible to perform a more accurate simulation according to the actual operation of the heater.

Furthermore, in this case, the C _f , β, h, and α may be set on the basis of actually measured values from the start of energization of the filament, and this produces the following further effect. . That is, when energization is started, changes in I (t), T (t), etc. are large, and a lot of data can be obtained. For this reason, the coefficient can be set more accurately, and further accurate simulation is possible.

  Further, in each of the above inventions, a process for numerically analyzing the flicker value based on the analyzed temperature, resistance value, or current change may be provided. In this case, the following further effect occurs. . In other words, the flicker value can be accurately simulated, and by extension, it can be accurately predicted whether or not the flicker value of the heater satisfies the specified condition.

  In each of the above inventions, various heaters can be applied as long as they have a filament that generates heat in response to energization. For example, the heater may be a halogen lamp heater.

  Further, in each of the above inventions, the use of the heater is not particularly limited, but the heater may be a heat source for fixing for image formation by electrophotography. In this case, as requested from regulations in Europe and the like, there is a strong demand for suppressing flicker, so that the effects of the above-described inventions appear more remarkably.

  A program according to the present invention is a program for causing a computer to execute each of the processes according to any one of the above inventions. For this reason, if the program of the present invention is executed by a computer, the simulation method of any one of the above inventions can be easily implemented.

  The recording medium of the present invention is characterized in that the program of the present invention is recorded so as to be readable by a computer. For this reason, if the computer executes the program recorded on the recording medium of the present invention, the simulation method of any one of the above inventions can be easily implemented.

  Furthermore, an image forming apparatus of the present invention includes an image forming unit that forms an image on a recording medium by electrophotography, and a fixing unit that fixes the image formed by the image forming unit using the heater as a heat source. An image forming apparatus provided with the program according to the invention or the recording medium according to the invention.

  In the present invention configured as described above, the image forming unit forms an image on a recording medium by electrophotography, and the fixing unit fixes the image formed by the image forming unit using the heater as a heat source. In addition, since the image forming apparatus of the present invention incorporates the program of the above invention or the recording medium of the above invention, the simulation according to any of the above inventions can be executed and the result reflected in the control. .

  The image forming apparatus of the present invention includes an image forming unit that forms an image on a recording medium by electrophotography, and a fixing unit that fixes the image formed by the image forming unit using the heater as a heat source. An image forming apparatus provided may be designed based on an analysis result using the simulation method according to any one of the inventions.

  Also in this case, the image forming unit forms an image on the recording medium by electrophotography, and the fixing unit fixes the image formed by the image forming unit using the heater as a heat source. In addition, since the image forming apparatus of the present invention is designed based on an analysis result using any one of the simulation methods, the temperature, current, or resistance value of the filament can be changed as desired.

Next, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a cross-sectional view illustrating a configuration of an electrophotographic printer P (corresponding to an image forming apparatus) to which the present invention is applied. The printer P is a laser printer that performs exposure with a laser. First, the configuration of the printer P will be briefly described with reference to FIG.
<Configuration of printer and fixing device>
The printer P includes a paper feed cassette unit A in which sheets as recording media are stacked and stored, a manual paper feed unit B capable of sucking sheets one by one, and a paper feed cassette unit A or a manual paper feed unit B. Equipped with a paper transporting section C that transports the sucked paper and a drum-type electrophotographic photosensitive member, a charger, a developing device, a static eliminator, etc. An electrophotographic process section D (corresponding to an image forming means) for forming the photosensitive member and the charged photosensitive member are scanned with a laser beam modulated in accordance with image data and exposed to form an electrostatic latent image on the photosensitive member. A laser beam scanner S (exposure device), a fixing heat roller, a pressure roller, and the like, a heat fixing portion E (corresponding to a fixing means) for fixing the toner adhering to the paper by heat, and the paper on which the toner is fixed The body And a sheet discharge unit F for transporting the receiving tray parts, comprising housed in the main body casing G.

  FIG. 2 is a cross-sectional view illustrating a configuration of the fixing device 51 disposed in the heat fixing unit E. The fixing device 51 includes a heat roller 1 that heats toner adhered to the paper, and a heat-resistant silicone rubber or the like around the metal shaft 53a, and pressure that presses the paper against the outer peripheral surface of the heat roller 1. A roller 53, discharge rollers 55 and 57 for discharging the paper to the outside of the apparatus, paper guides 59 and 61 for guiding the paper to a predetermined position, and a cover 63 that covers the heat roller 1 and the pressure roller 53 are provided.

  The heat roller 1 includes a drum-shaped roller body 11 made of a metal tube having a release layer formed on its surface, a halogen lamp heater 12 disposed along the rotation axis of the roller body 11, a roller And a thermistor 13 for detecting the temperature of the main body 11. The heat roller 1 uses the halogen lamp heater 12 as a heat source to provide heat for fixing the toner onto the paper, and conveys the paper in the direction of the discharge rollers 55 and 57 with the paper between the pressure roller 53 and the heat roller 1. Is also responsible.

As is well known, the halogen lamp heater 12 generates heat in response to energization of the filament 14 (see FIG. 3). Next, a simulation method for numerically analyzing changes in temperature T, resistance value R, and current I flowing through the filament 14 will be described. In the following description, a method for describing a model on a display such as a personal computer using a general model description method (for example, MATLAB / Simulink (both are registered trademarks: MathWorks)) will be described. Needless to say, the simulation model may be constructed by the above method.
<Basic principle of simulation model>
First, prior to describing the specific configuration of the simulation model, the basic concept of the simulation model will be described. As shown in FIG. 3, power V · I (V is a voltage across the filament 14) is supplied to the filament 14. This electric power is converted into thermal energy and stored as heat in the filament 14 itself to raise its temperature T, or radiated (radiated) as radiant heat, or the surrounding halogen gas (Gas) or terminals at both ends of the filament 14 ( It is consumed by being taken away by heat conduction.

Therefore, when the temperature T of the filament 14 is considered as a function T (t) of the time t, the energy stored as the heat is an expression of C _f · dT (t) / dt (where C _f is the heat capacity of the filament 14). Can be calculated by: Further, the heat dissipated energy can be calculated by an equation β · T ⁴ (t) (where β is a coefficient determined according to the halogen lamp heater 12). Further, the energy taken away by the heat conduction is an expression h (T (t) −T ₀ ) (where T ₀ is the ambient temperature (K) of the filament 14 and h is a coefficient determined according to the halogen lamp heater 12). Can be calculated by:

  Therefore, assuming that the sum of these thermal energies is equal to the power V (t) · I (t) as a function of time t, the following differential equation can be established.

また、フィラメント１４の抵抗値Ｒ（ｔ）は、温度Ｔ（ｔ）によって変化し、次式によって表される。

Further, the resistance value R (t) of the filament 14 varies depending on the temperature T (t) and is expressed by the following equation.

但し、αはフィラメント１４に応じて定まる係数。
そこで、これら２つの等式から、オームの法則（Ｖ＝Ｉ・Ｒ）を利用してＶ（ｔ）を消去すれば、Ｔ（ｔ）とＩ（ｔ）とを変数とする微分方程式が得られる。本シミュレーションモデルでは、この微分方程式に基づいてＶ（ｔ），Ｉ（ｔ），Ｒ（ｔ）の変化を求めるのである。なお、以下の説明では、便宜上各変数の（ｔ）を省略する場合がある。

However, α is a coefficient determined according to the filament 14.
Therefore, from these two equations, if V (t) is eliminated using Ohm's law (V = I · R), a differential equation having T (t) and I (t) as variables is obtained. It is done. In this simulation model, changes in V (t), I (t), and R (t) are obtained based on this differential equation. In the following description, (t) of each variable may be omitted for convenience.

Further, in this simulation model, a power supply impedance as shown in FIG. 4 is assumed in order to simulate the flicker at the time of power-on. That is, it is assumed that the resistor R _s , the reactance L, and the switch SW are connected in series between the AC power source V _s and the halogen lamp heater 12. In this case, flicker can be simulated based on the power supply voltage fluctuation V (t) obtained as the fluctuation of the voltage applied to both ends of the halogen lamp heater 12 and the switch SW.

In this case, the power supply voltage fluctuation V (t) when the switch SW is ON can be obtained by the following simultaneous differential equations. However, in the following expression, the resistance value R (t) of the filament 14 is expressed as R _h in order to distinguish it from the resistance R _s .

＜シミュレーションモデルの構成＞
続いて、本シミュレーションモデルの具体的な構成を説明する。なお、以下に示す各処理を実行するためのプログラムは、図５に示すパーソナルコンピュータ７０のＲＯＭ７１ｂ（ハードディスク等であってもよい）に格納されている。パーソナルコンピュータ７０は、ＣＰＵ７１ａ，ＲＯＭ７１ｂ，ＲＡＭ７１ｃを備えた本体７１に、ディスプレイ７２、キーボード７３、マウス７４等が接続された一般的な構成を有している。

<Configuration of simulation model>
Next, a specific configuration of the simulation model will be described. A program for executing each process shown below is stored in the ROM 71b (which may be a hard disk or the like) of the personal computer 70 shown in FIG. The personal computer 70 has a general configuration in which a display 72, a keyboard 73, a mouse 74, and the like are connected to a main body 71 including a CPU 71a, a ROM 71b, and a RAM 71c.

  FIG. 6 is a block diagram showing the whole image of the simulation model. As shown in FIG. 6, this simulation model includes a block 90 for inputting a pulse signal corresponding to ON / OFF of a switch SW, a halogen lamp heater 12 and a halogen lamp heater model 100 corresponding to the power source, and a flicker meter. Flicker meter model 200 corresponding to the above. The flicker meter model 200 is configured in accordance with flicker meter specifications defined in “IEC60868 Flickermeter Functional and design specifications”.

  In addition, the halogen lamp heater model 100 includes a halogen block 110 and a power supply block 130 as shown in FIG. Details of the halogen block 110 are shown in FIG. The halogen block 110 corresponds to the above-described two equations (Equations 3 and 4) as follows.

That is, at block 111, I × I × R (= V · I) is calculated. From this value, T is raised to the fourth power in block 112 and further multiplied by β in block 113, and T ₀ input from block 114 is subtracted from T in block 115 and further multiplied by h in block 116. The obtained value is subtracted in block 117.

That is, in block 117, C _f · dT (t) / dt is calculated. By dividing this value by C _f at block 118 and by integrating at time t at block 119, the above-mentioned temperature T is obtained. Incidentally, flicker so liable to occur when the power is turned on the filament 14 is fully coldest, the ambient temperature T ₀ of the filament 14 may be substituted at room temperature T _a.

  Further, the above resistance value R is obtained by multiplying T by the power of 1.2 in the block 121 and further multiplying by α in the block 122. The resistance value R is also input to the power supply block 130 as Rhalogen as shown in FIG.

  FIG. 9 is a block diagram showing the configuration of the power supply block 130 in detail. First, the power supply block 130 includes a zero-cross power supply block 131 shown in detail in FIG. As shown in FIG. 10, the zero cross power supply block 131 includes an AC power supply model 132 that generates an AC waveform of 50 Hz. Is output as Vsrc.

  The zero-cross power supply block 131 includes a zero-cross block 134. The zero-cross block 134 converts the ON / OFF pulse signal input from the block 90 into a pulse signal that is turned ON / OFF when the AC waveform crosses zero. To do. That is, this simulation model assumes a device that reduces flicker by switching ON / OFF of the halogen lamp heater 12 in synchronization with the timing when the AC waveform crosses zero. A value obtained by multiplying the output from the zero cross block 134 and the output from the block 133 in the block 135 is output as Vout.

Returning to FIG. 9, another configuration of the power supply block 130 corresponds to the above-described simultaneous differential equation (Equation 5) as follows. That is, the value obtained by multiplying _Rh and I described above at block 141 and the value obtained by multiplying I by R _s at block 142 are subtracted from Vout at block 143. That is, in block 143, L · dI / dt is calculated. This value is integrated over time at block 145 and divided by L at block 146 to obtain I described above.

Further, the flicker meter model 200, R _s · I outputted from the block 142, and the L · dI / dt, which is output from the block 143, a value obtained by subtracting from Vsrc at block 147 is entered. That is, the halogen lamp heater 12 is inputted as it is as V (t) is V _s when OFF, the when the halogen lamp heater 12 is ON assuming a model voltage across the filament 14 is input as V (t) (See FIG. 4).

The above is the configuration of this simulation model. By using such a simulation model, as shown in FIG. 11, the current I flowing through the filament 14, the voltage Vd input to the flicker meter (corresponding to V (t) described above), the output (ie, power), Changes in temperature, resistance value R, and voltage V across the filament 14 can be simulated. In FIG. 11, a portion where the voltage Vd slightly decreases in response to the first rise of the current I is detected as flicker.
<Coefficient α, β, C _f , h setting processing>
Next, a coefficient setting process for setting the various coefficients α, β, C _f , h used in the simulation model based on actual measurement values will be described. FIG. 12 is a flowchart showing the coefficient setting process executed by the personal computer 70 equipped with Simulink or the like.

When the processing is started, first, in S1 (S represents a step: the same applies hereinafter), the change in the current I (transient current measurement value) measured at a predetermined sampling interval from the start of energization of the filament 14 is started. Is read. In subsequent S2, initial values of α, β, C _f and h are set based on the operation of the keyboard 73 by the operator. Then, in subsequent S3, the change of the current I in the simulation model is calculated by applying this initial value to the above-mentioned simulation model.

In subsequent S4, the sum of squares of the difference between the value of current I calculated in S3 and the actually measured value read in S1 is calculated, and in S5, the sum of squares is less than a preset predetermined value. It is determined whether or not there is. If the sum of squares is less than a predetermined value (S5: Y), the values of the set coefficients α, β, C _f , h are assumed to be appropriate, and the values are determined to be α, β, C _f and h are determined, and the process ends.

On the other hand, if the sum of squares is equal to or greater than the predetermined value (S5: N), the values of α, β, C _f , and h are changed in S7, and the process proceeds to S3 again. As this changing method, various mathematically known methods such as a simplex method can be adopted. And thus alpha, beta, C _f, processing S3~S5 while changing the values of h are repeated, the square sum is less than the predetermined value alpha, beta, C _f, values of h Is found (S5: Y), the values are determined as α, β, C _f , and h in S6, and the process ends.

A specific example of this processing is shown in FIG. In FIG. 13, ◯ is an actual value read in S1, and a dotted line is a current value calculated in S3 based on the initial values of α, β, C _f , and h input in S2. By repeating the processes of S3 to S5 so that the square sum is less than the predetermined value, the change in the current value calculated from the values of α, β, C _f and h determined in S6 is as shown in FIG. As shown by a solid line in FIG.

By setting α, β, C _f , and h in this way, the flicker value calculated from the simulation model agrees very well with the flicker value measured from the actual halogen lamp heater 12. FIGS. 14A and 14B are experimental examples showing this, and are calculated using the experimental value (actual value) of the flicker value measured using the actual halogen lamp heater 12 and the simulation model. The calculated flicker value agrees very well. 14A shows an example in which the flicker value is measured and calculated while changing the cycle with the duty ratio of 6.25%, and FIG. 14B shows the ON / OFF of the pulse signal. In this example, the flicker value is measured and calculated by changing the cycle with OFF as the duty ratio of 12.5%.

As described above, in this simulation model, various physical quantities (temperature T, current I, resistance value R) of the filament 14 can be simulated very well, and flicker flicker caused by energization of the filament 14 can be achieved. The value can also be simulated well. In this simulation model, the process executed in blocks 118 and 119 corresponds to a heat amount calculation process, the process executed in blocks 112 and 113 corresponds to a heat release amount calculation process, and is executed in blocks 115 and 116. This process corresponds to the heat conduction calculation process, and the process executed in the blocks 121 and 122 corresponds to the resistance value calculation process.
<Application of simulation model to design (1)>
Next, processing when the simulation model is applied to the design of the fixing device 51 and its control system will be described. FIG. 15 is a flowchart showing a flicker value calculation process executed by the personal computer 70 when designing the form of the control signal to the halogen lamp heater 12, such as the ON / OFF duty ratio of the pulse signal.

In this process, first, in S11, the coefficients α, β, C _f , h set by the coefficient setting process described above are read out. In subsequent S12, a control signal for driving the halogen lamp heater 12 is appropriately set based on the operation of the keyboard 73 by the operator.

Then, in subsequent S13, the power supply voltage fluctuation V (t) is calculated using the simulation model. In the subsequent S14, the flicker value is calculated by the flicker meter model 200 of the simulation model based on the power supply voltage fluctuation V (t) calculated in S13, and the process ends. With the above processing, it is possible to predict well what kind of flicker will occur when setting what kind of control signal, and it can be applied well to the design of the control system of the fixing device 51.
<Application of simulation model to design (2)>
FIG. 16 is a flowchart showing a flicker value calculation process executed by the personal computer 70 when designing the temperature control mode of the halogen lamp heater 12 such as various control coefficients in the case of feedback control of the temperature T of the filament 14. It is.

Also in this process, first, the coefficients α, β, C _f , h set by the above-described coefficient setting process or the like are read in S21. In the subsequent S22, the temperature control mode of the halogen lamp heater 12 is calculated based on various control coefficients and the like appropriately input by the operation of the keyboard 73 by the operator.

Then, in subsequent S23, the power supply voltage fluctuation V (t) is calculated using the simulation model. In the subsequent S24, the flicker value is calculated by the flicker meter model 200 of the simulation model based on the power supply voltage fluctuation V (t) calculated in S23, and the process ends. With the above processing, what kind of flicker is generated when what temperature control is set can be predicted well, and can be favorably applied to the design of the control system of the fixing device 51.
<Configuration of Simulation Model Modification>
In the simulation model, only the temperature T of the filament 14 is taken into account, but in practice, feedback control is often performed based on a detection signal of the thermistor 13 (see FIG. 2) provided in the heat roller 1. . In this case, it is necessary to consider heat transfer from the roller body 11 to the pressure roller 53 and heat transfer from the roller body 11 and the pressure roller 53 to the sheet. FIG. 17 is a block diagram showing an overall image of a simulation model considering such heat transfer.

In this simulation model, a signal is input from the block 900 to the halogen lamp heater model 100 configured similarly to the previous simulation model. This block 900 controls a signal to be input to the halogen lamp heater model 100 based on a signal from the thermistor model 300 corresponding to the thermistor 13. In this simulation model, the thermistor model 300 is a first-order lag system that transmits the temperature T _HR of the roller body 11 with a time constant τ _S.

A fixing device model 500 that simulates heat transfer in the fixing device 51 includes a heat roller model 510 that simulates heat transfer to the roller body 11, a pressure roller model 530 that simulates heat transfer to the pressure roller 53, and the heat roller 1. A nip model 550 that simulates heat transfer to the nip with the pressure roller 53 is provided. Further, the heat roller model 510, a pressure roller model 530, the nip model 550, room temperature T _a, which is set in the block 570 is entered.

  The roller main body 11 is supplied with energy Radiation Energy (corresponding to the output of the block 113 in FIG. 8) radiated from the halogen lamp heater 12, and a predetermined energy QfromHR (a nip part model 550 as will be described later) via the nip part. Is calculated). Therefore, in this simulation model, a value obtained by subtracting QfromHR from Radiation Energy (referred to as Q) in block 580 is input to the heat roller model 510.

  Further, the heat transfer in the nip portion is affected by the presence or absence of rotation of the heat roller 1 and the pressure roller 53 (hereinafter also referred to as “rotating”) and the presence or absence of paper. For this reason, the nip portion model 550 is input with signals from the block 600 in which the presence / absence of rotation is set and the block 700 that generates a signal indicating the sheet insertion timing.

  Next, the configuration of each part constituting the fixing device model 500 will be described in detail. Note that each part of the fixing device model 500 is configured such that the energy (amount of heat) moving between two members in contact is proportional to the temperature difference between the two members.

Accordingly, the energy Q _{airHR radiated} from the roller body 11 into the air is Q _airHR = H _air (T _HR −T _a , where T _a is the room temperature, T _{HR is} the temperature of the roller body 11, and the proportional coefficient is H _air. ). The energy Q-Q _airHR that contributes to the temperature rise of the roller body 11 is equal to a value obtained by multiplying the temperature change dT _HR / dt of the roller body 11 by the heat capacity C _HR of the roller body 11, so the heat balance in the roller body 11 is It is expressed by the following formula.

そこで、ヒートローラモデル５１０は、図１８に示すように構成されている。すなわち、ブロック５１１によりＴ_HRからＴ_a を減算した値がブロック５１２にてＨ_air 倍され、その値がブロック５１３にてＱから減算される。すなわち、ブロック５１３では、Ｃ_HR・ｄＴ_HR／ｄｔが算出される。この値を、ブロック５１４にてＣ_HRで割り、更にブロック５１５にて時間ｔで積分することにより、前述のＴ_HRが得られる。

Therefore, the heat roller model 510 is configured as shown in FIG. That is, the value obtained by subtracting the T _a from T _HR by block 511 is H _air multiplied at block 512, the value is subtracted from Q at block 513. That is, in block 513, C _HR · dT _HR / dt is calculated. By dividing this value by C _HR at block 514 and further integrating at time t at block 515, the aforementioned T _HR is obtained.

Next, the energy Q _{airPR radiated} from the pressure roller 53 into the air is also Q _airPR = H _a (T, where the temperature of the pressure roller 53 is T _PR and the proportionality coefficient is H _a , similar to the above-described Q _{airHR. PR−} T _a ) Further, the energy Q _PR deprived by heat conduction from the pressure roller 53 via the shaft 53a is to assume that the temperature of the shaft 53a matches the room temperature T _a, by a proportional coefficient and H _pr, Q _PR = H _pr It is expressed by (T _PR −T _a ).

Furthermore, if the heat energy to be supplied to the pressure roller 53 and Q _{an nip,} the energy contributes to raising the temperature of the pressure roller ₅₃ Q _nip -Q airPR -Q _PR is the pressure in the temperature change dT _PR / dt of the pressure roller 53 Since it is equal to the value obtained by multiplying the heat capacity C _PR of the roller 53, the heat balance in the pressure roller 53 is expressed by the following equation.

そこで、圧力ローラモデル５３０は、図１９に示すように構成されている。すなわち、ブロック５３１によりＴ_PRからＴ_a を減算した値を更にブロック５３２にてＨ_a 倍した値、及び、ブロック５３３によりＴ_PRからＴ_a を減算した値を更にブロック５３４にてＨ_pr倍した値が、ブロック５３５にてＱ_nip から減算される。すなわち、ブロック５３５では、Ｃ_PR・ｄＴ_PR／ｄｔが算出される。この値を、ブロック５３６にてＣ_PRで割り、更にブロック５３７にて時間ｔで積分することにより、前述のＴ_PRが得られる。

Therefore, the pressure roller model 530 is configured as shown in FIG. That further value H _a multiplied at block 532 the value obtained by subtracting T _a from T _PR by the block 531, and were H _pr multiplied by T _PR further a value obtained by subtracting T _a from block 534 by block 533 The value is subtracted from Q _nip at block 535. That is, in block 535, C _PR · dT _PR / dt is calculated. By dividing this value by C _PR at block 536 and further integrating at time t at block 537, the aforementioned T _PR is obtained.

Next, consideration will be given to the entry and exit of thermal energy at the nip. When there is no paper in the nip portion, when neither the roller body 11 nor the pressure roller 53 is rotating, the heat energy in / out is estimated to be 0, and when rotating, the proportionality coefficient is set as H _nip and Q Calculate _nip (also called QtoPR). In this case, Q _nip = QfromHR.

Q _nip = H _nip (T _HR -T _PR )
When paper is present in the nip portion, the paper temperature is T _paper , the energy to move from the roller body 11 to the paper is Q _paperHR , the proportional coefficient of the heat transfer is H _paperHR , and the energy to move from the pressure roller 53 to the paper is By _setting Q _paperPR and the proportional coefficient of the heat transfer as H _paperPR , the following equation is obtained.

Q _paperHR = H _paperHR (T _HR -T _Paper )
_{Q paperPR = H paperPR (T PR} -T Paper)
Therefore, the nip model 550 is configured as shown in FIG. In the nip model 550, QfromHR corresponding to the energy taken from the roller body 11 via the nip and QtoPR corresponding to the energy supplied to the pressure roller 53 via the nip are calculated.

When there is no paper and the paper is not rotated (rot), the constant “0” set in the block 551 is calculated as QfromHR through the blocks 552 and 553, and “0” is also set in the block 552. QtoPR is calculated via 554. No paper, if the idle rotation is performed, a value obtained by subtracting the T _PR from T _HR at block 555, the value H _{an nip} times further at block 556, QfromHR, is calculated as QtoPR.

Furthermore, has assumed the the nip Model 550 T _paper = T _a, when there is a sheet, with or without idle rotation, the value obtained by subtracting T _a from T _HR at block 561, further blocks ₅₆₂ H paperHR multiplied value is outputted as QfromHR at a value obtained by subtracting T _a from T _PR at block 563, further values -H _PaperPR multiplied at block 564 is calculated as QtoPR.

In the simulation model configured as described above, actual feedback control is performed in consideration of heat transfer from the roller body 11 to the pressure roller 53 and heat transfer from the roller body 11 and the pressure roller 53 to the sheet. Can be simulated.
<Application to feedback control>
Next, an example in which the halogen lamp heater 12 of the fixing device 51 is feedback controlled using the simulation model will be described. FIG. 21 is a block diagram showing the configuration of the control system.

  As shown in FIG. 21, the temperature control unit 990 is configured as a microcomputer including a CPU 991, a ROM 992, and a RAM 993, and inputs control signals to the halogen lamp heater 12. The temperature of the fixing device 51 (more precisely, the temperature of the roller body 11) heated by the heat radiation of the halogen lamp heater 12 is detected by the thermistor 13, and the detection signal is input to the temperature control unit 990.

  The temperature control unit 990 includes a halogen lamp heater model 100, a flicker meter model 200, and a fixing device model 500, which are similar to the simulation model described above. These simulation models are virtually configured by the CPU 991 executing the program recorded in the ROM 992, but in FIG. 21, these simulation models are described outside the block of the temperature control unit 990 for convenience of explanation. did.

  Next, FIG. 22 is a flowchart showing a feedback control process executed by the temperature control unit 990. When this process is started, first, in S31, a preset control signal is output to the halogen lamp heater 12, and at the same time, a similar control signal is also output to the halogen lamp heater model 100.

In S32, the halogen lamp heater model 100 calculates the temperature T, resistance value R, current I, and power supply voltage fluctuation V (t) of the filament 14 as described above. In subsequent S33, the fixing device model 500, the temperature T _PR temperature T _HR and pressure roller 53 of the roller body 11 as described above is calculated, in S34, the flicker value is calculated by the flicker meter model 200.

Subsequently, in S35, the detection value of the thermistor 13 is read. In subsequent S36, the temperature T of the filament 14 read in the process, the resistance value R, the current I, supply voltage variation V (t), the temperature T _HR of the roller body 11, the temperature T _PR of the pressure roller 53, the flicker value A control signal is generated based on the detection value of the thermistor 13 and is output to the halogen lamp heater 12 and the halogen lamp heater model 100, and the process proceeds to S32.

  Conventionally, feedback control is performed based only on the detection value of the thermistor 13, but more accurate control is executed by performing feedback control in consideration of various calculated values using a simulation model. be able to.

  The present invention has been described with reference to the embodiment. However, the present invention is not limited to the above embodiment, and can be implemented in various forms without departing from the gist of the present invention. For example, the simulation may be performed by adding factors such as humidity (that is, thermal conductivity of air).

  In each of the simulation models, the flicker value is simulated based on the power supply voltage fluctuation V (t) calculated from the resistance value R of the filament 14, but the temperature T and current I of the filament 14 obtained by the simulation are simulated. From the above, the flicker value may be simulated. Furthermore, a program for causing a personal computer, a microcomputer, etc. to execute the various processes described above can be recorded on various recording media such as a flexible disk, a compact disk, and a web server on the Internet in addition to elements such as a ROM. Needless to say.

1 is a cross-sectional view illustrating a configuration of a printer to which the present invention is applied. It is sectional drawing showing the structure of the fixing device of the printer. It is explanatory drawing showing the energy in / out in the filament of the fixing device. It is explanatory drawing showing the power supply impedance for flicker simulation. It is explanatory drawing showing the structure of the personal computer which performs simulation. It is a block diagram showing the whole image of a simulation model. It is a block diagram showing the detail of the halogen lamp heater model of the model. It is a block diagram showing the detail of the halogen block of the model. It is a block diagram showing the detail of the power supply block of the model. It is a block diagram showing the detail of the zero cross power supply block of the block. It is explanatory drawing showing the effect of the said simulation model. It is a flowchart showing the coefficient setting process which sets each coefficient of the model. It is explanatory drawing showing the specific example of the coefficient setting process. It is explanatory drawing showing the effect of the coefficient setting process. It is a flowchart showing the application to the design of the control signal of the model. It is a flowchart showing the application to the design of the temperature control of the said model. It is a block diagram showing the whole picture of the modification of the model. It is a block diagram showing the detail of the heat roller model of the modification. It is a block diagram showing the detail of the pressure roller model of the modification. It is a block diagram showing the detail of the nip part model of the modification. It is a block diagram showing the structure of the control system using the modification. It is a flowchart showing the feedback control process in the control system.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Heat roller 11 ... Roller main body 12 ... Halogen lamp heater 13 ... Thermistor 14 ... Filament 51 ... Fixing device 53 ... Pressure roller 70 ... Personal computer 100 ... Halogen lamp heater model 110 ... Halogen block 130 ... Power supply block 200 ... Flicker meter model DESCRIPTION OF SYMBOLS 300 ... Thermistor model 500 ... Fixing device model 510 ... Heat roller model 530 ... Pressure roller model 550 ... Nip part model 990 ... Temperature control part

Claims (14)

A heater simulation method for numerically analyzing a change in temperature of a filament of a heater having a filament that generates heat in response to energization,
A calorific value calculation process for calculating energy stored as heat in the filament;
A heat dissipation amount calculation process for calculating energy dissipated from the filament,
Heat conduction calculation processing for calculating energy taken away from the filament by heat conduction;
A resistance value calculation process for calculating the resistance value of the filament according to the temperature of the filament;
A heater simulation method comprising the steps of: A heater simulation method for numerically analyzing a change in a current flowing through a filament of a heater having a filament that generates heat in response to energization,
A calorific value calculation process for calculating energy stored as heat in the filament;
A heat dissipation amount calculation process for calculating energy dissipated from the filament,
Heat conduction calculation processing for calculating energy taken away from the filament by heat conduction;
A resistance value calculation process for calculating the resistance value of the filament according to the temperature of the filament;
A heater simulation method comprising the steps of: A heater simulation method for numerically analyzing a change in resistance value of a filament of a heater including a filament that generates heat in response to energization,
A calorific value calculation process for calculating energy stored as heat in the filament;
A heat dissipation amount calculation process for calculating energy dissipated from the filament,
Heat conduction calculation processing for calculating energy taken away from the filament by heat conduction;
A resistance value calculation process for calculating the resistance value of the filament according to the temperature of the filament;
A heater simulation method comprising the steps of: In the calorific value calculation process, the energy is calculated by the formula C _f · dT (t) / dt (where T (t) is the filament temperature (K) and C _f is the heat capacity of the filament),
In the heat dissipation amount calculation process, the energy is calculated by an expression β · T ⁴ (t) (where β is a coefficient determined according to the heater),
In the heat conduction calculation process, the energy is calculated by an expression h (T (t) −T ₀ ) (where T ₀ is the filament ambient temperature (K), h is a coefficient determined according to the heater),
4. The resistance value calculation process according to claim 1, wherein the resistance value is calculated by an equation of α · T ^1.2 (t) (where α is a coefficient determined according to the filament). The heater simulation method described. The relationship between the applied voltage V (t) to the filament, the current I (t) flowing through the filament, and the temperature T (t) of the filament is calculated by the following equation. The heater simulation method according to claim 1.

6. The heater simulation method according to claim 4, wherein the C _f , β, h, and α are set based on actual measurement values. The heater simulation method according to claim 6, wherein the C _f , β, h, and α are set based on actual measurement values from the start of energization of the filament.   The heater simulation method according to claim 1, further comprising a process of numerically analyzing a flicker value based on the analyzed temperature, resistance value, or current change.   9. The heater simulation method according to claim 1, wherein the heater is a halogen lamp heater.   10. The heater simulation method according to claim 1, wherein the heater is a fixing heat source for image formation by electrophotography.   The program for making a computer perform each said process in any one of Claims 1-10.   12. A recording medium on which the program according to claim 11 is recorded so as to be readable by a computer. Image forming means for forming an image on a recording medium by an electrophotographic method;
Fixing means for fixing the image formed by the image forming means using the heater as a heat source;
An image forming apparatus comprising:
An image forming apparatus comprising the program according to claim 11 or the recording medium according to claim 12 incorporated therein. Image forming means for forming an image on a recording medium by an electrophotographic method;
Fixing means for fixing the image formed by the image forming means using the heater as a heat source;
An image forming apparatus comprising:
An image forming apparatus, which is designed based on an analysis result using the heater simulation method according to claim 1.

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