Patent Publication Number: US-6659600-B2

Title: Inkjet recording head cartridge and inkjet recording apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an inkjet recording head cartridge and an inkjet recording apparatus. 
     2. Description of the Prior Art 
     An inkjet recording head cartridge (hereinafter referred to as cartridge) mounted in the carriage of conventional inkjet recording apparatuses is constructed to supply ink to a supply orifice of a head (head chip) through an ink supply passage from an ink tank. 
     The cartridge thus constructed has problems in (1) processing for bubbles generated in the ink supply passage and the head and (2) control of the fluctuation of ink supply pressure within the ink supply passage and the head. Various proposals are made to solve these problems. Hereinafter, a description will be made of several of these proposals. 
     The following four examples are proposed as measures against (1). 
     According to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 6-218945 (hereinafter referred to as conventional example 1), upon detecting bubbles generated in an ink supply passage, recording operation is stopped to prevent the bubbles from invading into a recording head. 
     Also, according to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 9-226142 (hereinafter referred to as a conventional example 2), an ink supply passage having a smaller cross-sectional area than that of a recording head opening part is provided to increase an ink flow velocity and thereby increase the ability to eliminate bubbles. 
     Furthermore, according to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 9-277552 (hereinafter referred to as a conventional example 3), a filter provided in an ink flow passage is provided with a bubble discharge part which discharges bubbles by pressuring the ink flow passage toward the outside. 
     According to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 9-131890 (hereinafter referred to as a conventional example 4), a wall outlined along a manifold is provided to discharge bubbles upward without depositing them on the wall face. 
     On the other hand, the following four example are proposed as measures against (2). 
     According to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 5-31904 (hereinafter referred to as a conventional example 5), bubbles are formed within a common liquid chamber by heating, and pressure waves are absorbed by transforming the bubbles to restrain pressure fluctuation caused by ink injection. 
     Also, according to the invention disclosed in Japanese Published Unexamined Patent Application No. Sho 55-128465 (hereinafter referred to as a conventional example 6), a minute hole for communication between the ink liquid passage and air is provided in part of the ink liquid passage to restrain pressure fluctuation. 
     Furthermore, according to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 7-125234 (hereinafter referred to as a conventional example 7), a gas holding part and a subheater for changing the volume of gas are provided to restrain pressure fluctuation caused by ink injection by changing the natural frequency of an ink supply system. 
     Furthermore, according to the invention disclosed in Japanese Published Unexamined Patent Application No. Hei 9-136415 (hereinafter referred to as a conventional example 8), plural gas holding parts for holding gas therein are provided in an ink supply passage to absorb pressure oscillation. 
     There are the following problems in the conventional examples 1 to 4. 
     In the conventional example 1, a bubble detection unit is required and it is questionable whether satisfactory bubble detection precision is obtained. Also, if a bubble is detected, recording must be temporarily halted. 
     In the conventional example 2, although it is possible to decrease the frequency of bubble-induced printing defects to some degree, it is impossible to completely eliminate printing defects. 
     In the conventional example 3, a pressurizing system for discharging bubbles is required, so that the apparatus becomes complicated. 
     In the conventional example 4, discharged bubbles accumulate under a filter and, if the accumulated bubbles spread throughout the manifold, printing would be disabled. 
     There are the following problems in the conventional examples 5 to 8. 
     In the conventional example 5, a heating unit in addition to an emission heater is required in the common liquid chamber, so that the mechanism becomes very complicated. Also, it is very difficult to control the size of bubbles generated by the heating unit. 
     In the conventional example 6, ink evaporation from the minute hole for communication with air and ink hardening in the minute hole are problematic. 
     In the conventional example 7, a heating unit is additionally required, so that the mechanism becomes complicated. Also, bubble size control is difficult. 
     In the conventional example 8, gas holding parts must be created, and therefore the construction of the ink supply passage becomes complicated. Also, gas in the gas holding parts may replace ink in the course of long-term preservation. 
     As described above, the conventional examples 1 to 8 have the problems that the structure of the mechanism is complicated or conventional problems cannot be completely solved. 
     SUMMARY OF THE INVENTION 
     Therefore, the present invention provides an inkjet recording head cartridge and an inkjet recording apparatus that have a simple structure and high reliability. 
     According to an aspect of the present invention, the inkjet recording head cartridge includes individual flow passages each having an ink emission orifice at one end thereof and an ink inflow orifice at another end thereof, an ink supply chamber communicating with the ink inflow orifices, and a heater face provided to be orthogonal to an ink emission face on which the ink emission orifices are formed, the heater face being part of the side of the ink supply chamber formed within an ink supplier. The ink supply chamber is formed to have a cross-sectional area allocated in an ink flow direction so that buoyancy acting on a bubble occurring in the ink supply chamber the size of which would cause a printing defect becomes larger than drag based on an ink flow velocity in the ink supply chamber when ink is emitted from all the ink emission orifices acting on the bubble, whereby the bubble moves away from the ink inflow orifices. 
     A bubble that occurring in the ink supply chamber due to printing operation or the like grows because of printing operation or the like and may hinder ink supply as a result of blocking the ink inflow orifices of the individual flow passages, causing a printing defect. In the present invention, the buoyancy that moves a bubble growing to such a size as to cause a printing defect away from the individual flow passages acts larger than drag based on the flow velocity of ink that flows toward the individual flow passages from the ink supply chamber. As a result, a bubble large enough to cause a printing defect is moved away from the individual flow passages (the ink inflow orifices) by the buoyancy, so that stable printing is achieved. Therefore, an ink suck mechanism or the like need not be used to discharge bubbles by sucking ink. In other words, highly reliable printing can be performed by preventing bubble-induced printing defects with a simple structure. 
     According to another aspect of the present invention, the following two expressions are satisfied for a given printing rate. 
     
       
         [( Q/S ) 2   ×Cd×ρ×π×d   2 ]/8&lt;(ρ× g×π×d   3 )/6; 
       
     
     and 
     
       
           d≧ 2 Np   
       
     
     where 
     Q: Average ink flow quantity during printing, 
     S: Minimum cross-sectional area in the ink flow direction within the ink supply chamber, 
     Cd: Resistance coefficient, 
     ρ: Ink density, 
     g: Gravitational constant, 
     Np: Individual flow passage (ink emission orifice) pitch, and 
     D: Bubble diameter. 
     A bubble within the ink supply chamber that has at least twice (=2Np) the diameter of individual flow passage pitch is difficult to discharge from one individual flow passage by ink emission. As a result, the individual flow passage remains blocked, causing a printing defect. Therefore, by having the ink supplier and the head chip so that buoyancy [(ρ×g×π×d 3 )/6] acting on the bubble (d≧2Np) is greater than drag [[(Q/S) 2×Cd×ρ×π×d   2 ]/8] produced by the flow velocity of ink that flows into the individual flow passage from the ink supply chamber, the bubble to cause the printing defect is moved away from the individual flow passage by the buoyancy. Therefore, bubble-induced printing defects can be prevented with a simple structure without having to provide a mechanism for discharging bubbles. 
     According to another aspect of the present invention, the ink supply chamber includes an ink tank part that communicates with the ink supply chamber and supplies ink to the ink supply chamber. 
     Since the ink tank part that supplies ink to the ink supply chamber is provided, an ink exchange interval is extended by supplying ink to the ink supply chamber from the ink tank part, improving the ease of use of the inkjet recording head cartridge. 
     According to another aspect of the present invention, a filter member intervenes between the ink supply chamber and the ink tank part. 
     Since a filter is provided between the ink supply chamber and the ink tank part, it can impede invasion into the head chip of foreign particles coming through the ink supply chamber from the ink tank part, increasing the reliability of printing. In other words, printing can be performed with high image quality. Moreover, since the filter member is provided, by exchanging only the ink tank part, the head can be used up to its operating life without discarding it at ink exchange. 
     According to another aspect of the present invention, the ink tank part is located upward in the gravity direction with respect to the ink supply chamber and holds ink in free condition. 
     Ink within the ink supply chamber is heated by printing operation and causes convection. Therefore, if the ink tank part is holding the ink in free condition, bubbles within the ink supply chamber are moved to the ink tank part by the convection, preventing the bubbles from growing in the ink supply chamber. As a result, the possibility that the bubbles cause a printing defect can be reduced. 
     According to another aspect of the present invention, an air lump of 1 mm 3  or more always exists in the ink tank part. 
     By sealing beforehand an air lump of 1 mm 3  or more in the ink tank part, bubbles occurring in the ink supply chamber are moved to the ink tank part by convection and grow integrally with the air lump within the ink tank part. In other words, it can be prevented that bubbles growing in the ink supply chamber impede ink supply from the ink tank part to the ink supply chamber. 
     According to another aspect of the present invention, the recording head cartridge is shipped with ink filled without bubbles existing in the ink supply chamber. 
     The recording head cartridge is shipped with ink filled without bubbles existing in the ink supply chamber. If a bubble exists in the ink supply chamber, when gas is deposited from the ink by printing operation or the like, the bubble already existing in the ink supply chamber grows mainly and impedes ink supply from the ink tank part to the ink supply chamber, possibly causing a printing defect. Accordingly, by shipping the recording head cartridge without bubbles existing in the ink supply chamber, bubble growth within the ink supply chamber is restrained and the above-described printing defect is prevented. 
     According to another aspect of the present invention, the sum of the capacity of the ink supply chamber and the initial capacity of ink in free condition in the ink tank part is greater than the total volume of ink emitted during one print job, defined in an ink temperature rise and cooling cycle in the recording head cartridge. 
     Ink temperature within the ink supply chamber rises because of printing operation and ink is moved to the ink tank part by convection, generating and growing a bubble. However, also in the ink supply chamber, air dissolved in the ink deposits as a bubble. Usually, the bubble dissolves in the ink again when the ink temperature has fallen after the termination of the print job. However, if printing operation is performed continuously, the bubble grows and no longer dissolves in the ink even if the ink has been cooled. 
     Data obtained experimentally shows that if the sum of the capacity of the ink supply chamber and the initial capacity of ink held in free condition in the ink tank part is greater than the total volume of ink emitted during one print job, air deposited by a rise in ink temperature dissolves in the ink again when the ink temperature has fallen. Therefore, the bubble generation and bubble growth in the ink supply chamber, caused by printing operation, can be restrained without fail. 
     According to another aspect of the present invention, the inkjet recording head cartridge includes an ink emission face on which ink emission orifices are formed, an ink supplier provided with an ink supplying chamber inside thereof; and a heater face orthogonal to the ink emission face, the heater face being part of the side of the ink supply chamber. The ink supply chamber is formed so as to have a cross-sectional area allocated in an ink flow direction so that pressure fluctuation within the ink supply chamber at the time of ink emission becomes an overattenuation mode or critical attenuation mode. 
     Since the ink supply chamber is formed so as to have a cross-sectional area in an ink flow direction so that pressure fluctuation within the ink supply chamber at the time of ink emission becomes an overattenuation mode or critical attenuation mode and, regardless of printing condition, it can be prevented without fail that the pressure fluctuation amplifies so that the ink refill of the ink emission orifices become imperfect, causing ink emission defects. 
     According to another aspect of the present invention, the inkjet recording head cartridge includes an ink emission face on which ink emission orifices are formed, an ink supplier provided with an ink supplying chamber inside thereof, and a heater face orthogonal to the ink emission face, the heater face being part of the side of the ink supply chamber. The relation of (R 1 +R 2 ) 2 ×(C 1 +C 2 )≧4×(L 1 +L 2 ) is satisfied, where L 1  is the inertance of the individual flow passage, L 2  is the inertance of the ink supply chamber, R 1  is the resistance value of the individual flow passage, R 2  is the resistance value of the ink supply chamber, C 1  is the capacitance of meniscus of the ink emission orifice, and C 2  is the capacitance of the ink supply chamber. 
     Since the present invention forms the ink supplier and the head chip so that the above-described relational expression is satisfied, for patterns of any image quality, pressure oscillation at the time of ink emission can be completely attenuated. Therefore, by appropriately designing the internal volume, cross-sectional area, and length of the ink supply chamber of the present invention, pressure fluctuation within the ink supply chamber at the time of ink emission can be attenuated without causing a bubble or communicating with the outside air, thereby providing increased printing reliability. 
     According to another aspect of the present invention, an ink jet recording apparatus including any of the above inkjet recording head cartridges is provided. 
     By mounting the inkjet recording head cartridge, without providing a special mechanism, bubble-induced printing defects, and printing defects caused by the resonance of pressure fluctuation within the ink supply chamber can be prevented. As a result, a reliable inkjet recording apparatus with a simple structure can be provided. 
     According to another aspect of the present invention, the inkjet recording apparatus includes: individual flow passages having each an ink emission orifice at one end thereof and an ink inflow orifice at another end; an ink supply chamber having open ink inflow orifices; an inkjet recording head cartridge having an ink tank part that supplies ink to the ink supply chamber through a filter member placed upward in the gravity direction of the ink supply chamber; a determination unit that determines whether, in one print job defined in temperature rise and cooling cycles of ink in the recording head cartridge, the total volume of ink emitted from the ink emission orifices exceeds the sum of the capacity of the ink supply chamber and the initial capacity of ink held in free condition in the ink tank part; and a printing control unit that, if the total volume of the ink exceeds the sum, halts printing during the print job, and resumes printing after the ink within the ink supply chamber is cooled to a predetermined temperature. 
     The ink temperature of the ink supply chamber rises because of printing operation and the ink is moved to the ink tank part by convection, generating and growing a bubble. However, also in the ink supply chamber, air dissolved in the ink deposits as a bubble. Usually, the bubble within the ink supply chamber dissolves in the ink again when the ink temperature has fallen after the termination of the print job. However, if printing operation is performed continuously, the bubble grows and does not dissolve again in the ink even if the ink has been cooled. 
     Accordingly, in the present invention, in the case where a determination unit determines that the total amount of emitted ink used by printing exceeds the sum of the capacity of the ink supply chamber and the initial capacity of ink held in free condition in the ink tank part, printing operation is temporarily halted to cool the ink, thereby preventing the bubble from growing to the extent that it cannot redissolve. This prevents printing defects caused by the growth of the bubble from reducing image quality. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Preferred embodiments of the present invention will be described in detail based on the followings, wherein: 
     FIG. 1 is a longitudinal sectional view of an inkjet recording head cartridge according to one embodiment of the present invention; 
     FIG. 2 is a schematic view of an inkjet recording apparatus according to one embodiment of the present invention; 
     FIG. 3A is a front perspective view of a head chip according to one embodiment of the present invention, and FIG. 3B is a back perspective view of the same; 
     FIG. 4 is a longitudinal sectional view of the inkjet recording head cartridge according to a comparative example; 
     FIG. 5 is a graph showing the relationship between ink flow velocity and the maximum diameter of bubbles flowing to the head; 
     FIG. 6 is a main flowchart showing bubble control; 
     FIG. 7 is a flowchart showing bubble control; 
     FIG. 8 is a graph showing the relationship between water temperature and air solubility; 
     FIG. 9 is a graph showing the relationship between bubble size in water and air solubility in the vicinity of bubbles; 
     FIG. 10 is a plan view showing individual flow passages of the inkjet recording head cartridge according to the present invention; 
     FIG. 11 is an explanatory view showing the dimension of an ink supply chamber of the inkjet recording head cartridge according to the present invention; 
     FIG. 12 is a drawing showing a fluid pressure electricity equivalent circuit of the inkjet recording head cartridge according to the present invention; 
     FIG. 13 is an explanatory view of line pairs; 
     FIG. 14 is a drawing showing the amplitude condition of an ink supply chamber of the comparative example; 
     FIG. 15 is a drawing showing the amplitude condition of the ink supply chamber of the embodiment example; and 
     FIG. 16 is a drawing showing an example of another inkjet recording head cartridge. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An inkjet recording apparatus and an inkjet recording head cartridge according to an embodiment of the present invention will be described with reference to FIGS. 1 to  16 . 
     An inkjet recording apparatus  10 , as shown in FIG. 2, is constructed so that an inkjet recording head cartridge (hereinafter referred to as cartridge)  14  held in a carriage  12  is scanned along a guide shaft  16  to perform printing on paper  18  carried in the direction of the arrow A. 
     A cartridge  14 , as shown in FIG. 1, basically includes a head chip  20  in which ink emission orifices  30  described later and other components are formed; an ink supplier  22  that supplies ink to the head chip  20 ; and a heat sink  24  that maintains the heat radiation capability of the head chip  20 . 
     As shown in FIGS. 3A and 3B, the head chip  20 , formed by a heat-generating substrate  26  and a flow passage substrate  28  being joined with each other, basically includes: plural ink emission orifices  30  formed on an end face (ink emission face) thereof; individual flow passages  32  that communicate with the ink emission orifices  30 ; a common liquid chamber  34  that communicates with all the individual flow passages  32  and extends in a nozzle array direction; and a heat generating element  36  (see FIG. 1) that is disposed in facing relation with the individual flow passage  32 . 
     The common liquid chamber  34  opens in the direction (the direction of arrow Y) in which the individual flow passages  32  extend and the direction (the direction of arrow Z) orthogonal to the individual flow passages  32  (hereinafter, the opening may be called an ink inflow orifice  35 ). 
     An electrical signal input/output terminal  38  is provided at both ends of the head chip  12  in the X direction. 
     The ink supplier  22  has the construction in which an opening is formed at one corner of the lower end of a housing of almost rectangular parallelepiped wherein the head chip  20  is attached to the opening through an elastic seal member  46 . The head chip  20  is integrated with the ink supplier  22 , whereby an ink tank chamber  42  and an ink supply chamber  44 , which are two parts of almost rectangular parallelepiped, divided by a filter  40 , are formed within the ink supplier  22 . 
     In other words, the side (the heater face)  28 A of the heat generating element substrate  28  that constitutes the common liquid chamber  34  of the head chip  20  servers as a part of the wall face  44 A of the gravity direction of the ink supply chamber  44  and the upper face  26 A of the flow passage substrate  26  serves as a part of the wall face  44 B of the ink supply chamber  42  orthogonal to the individual flow passages  32 . 
     Therefore, the common liquid chamber  28  serves as a part of the ink supply chamber  44  and the ink inflow orifices  35  of the individual flow passages  32  open directly to the ink supply chamber  44 . The ink supply chamber  44  is continuous in the direction (upward in the gravity direction) in which the individual flow passages  32  extend, and has a large cross-sectional area allocated in a direction (horizontal direction) orthogonal to the direction in which the individual flow passages  32  extend. 
     The ink supply chamber  44  is filled with ink so that no bubble exists in an initial state. Also, an air lump  48  of 1 mm 3  or more is introduced into the ink tank chamber in an initial state to grow a bubble in the ink tank chamber  42 . 
     To the ink tank chamber  42 , ink can be supplied from an external main ink tank and a secondary ink tank that can be freely mounted in and dismounted from the upper part of the cartridge  14  (a drawing is omitted). 
     In terms of bubble control described later, it is necessary that the cartridge  14  has at least the ink tank chamber  42 , the ink supply chamber  44 , and the ink emission orifices  30  (individual flow passages  32 ) placed in that order downward in the gravity direction. 
     A control unit not shown monitors the ink temperature and the total amount of emitted ink in the ink supply chamber  44 , halts temporarily printing operation if the total amount of emitted ink exceeds a predetermined quantity, waits until the ink temperature falls to a predetermined temperature, and then continues printing operation. 
     (Effect of the Present Embodiment) 
     A description will be made of the effect of the inkjet recording apparatus  10  (cartridge  14 ) thus constructed. There are three major points as the effect of the inkjet recording apparatus  10  (cartridge  14 ) of the present embodiment. Hereinafter, the three points will be described through comparison with a comparative example. 
     (Comparative Example) 
     First, a cartridge of a comparative example will be described with reference to FIG.  4 . Components shown in FIG. 4 that are almost identical to components shown in the present embodiment are identified by the same reference numerals, and detailed descriptions of them are omitted. 
     In a cartridge  114  of the comparative example, an ink supply orifice  116  formed in a common liquid chamber  34  of a head chip  20  and, an ink tank chamber  42  of an ink supplier  22  are communicated with each other by an ink pipeline  118  (equivalent to the ink supply chamber  44  of the present embodiment). 
     (First Effect) 
     The first effect of cartridge  14  is that a printing defect (hereinafter referred to as a bubble printing defect) caused when a bubble blocks the individual flow passages  32  can be satisfactorily prevented without having to perform maintenance. 
     Generally, a bubble-induced printing defect occurs when a large bubble flows into the head chip  20  and, as a result, ink supply to the ink emission orifices  30  (individual flow passages  32 ) is impeded. 
     Bubble-induced printing defects include those that are recovered when a bubble concerned is discharged from the ink emission orifices  30  by emitted ink, and those that are not recovered because the bubble is not discharged by emitted ink alone. Bubble-induced printing defects not recovered by emitted ink alone are particularly problematic. To recover the printing defects, the negative pressure maintenance is performed which brings a cap member into contact with the nozzle face of a head and applies negative pressure with a negative pressure pump to suck the bubble along with ink. 
     However, the negative pressure maintenance has the following two problems: first, since it requires a negative pressure pump, the maintenance apparatus is complicated with increased costs, and secondary, sucked ink becomes useless and wasted ink increases, so that the capacity of a tank for the wasted ink must be increased. 
     Accordingly, the inventor of the present invention proposes the following. That is, a cartridge is constructed so as to move a bubble to cause a printing defect away from the end of the individual flow passages  32  by means of buoyancy by blocking the end of the individual flow passages  32  so that a printing defect can be prevented without performing the negative pressure maintenance. 
     The cartridge  14  shown in FIG. 1 (hereinafter referred to as an embodiment example) functions as described below when buoyancy and drag acting on a bubble in the ink supply chamber  44  are taken into account. 
     Letting a minimum cross-sectional area of the ink supply chamber in ink flow direction be S; average ink flow quantity during printing be Q; ink density be ρ; gravity constants be g; resistance coefficient be Cd; emission orifice (individual flow passage) pitch be Np; and bubble diameter be d, drag acting on a bubble is represented by 
     
       
           F   1 =[( Q/S ) 2   ×Cd×ρ×π×d   2 ]/8  (1) 
       
     
     Also, buoyancy F 2  acting on a bubble is represented by 
     
       
           F   2 =(ρ× g×π×d   3 )/6  (2) 
       
     
     Therefore, if buoyancy F 2  acting on a bubble becomes greater than drag F 1  caused by ink flow (F 2 &gt;F 1 ), in other words, if the following expression 
     
       
         (ρ× g×π×d   3 )/6&gt;[( Q/S )2× Cd×ρ×π×d   2 ]/8  (3) 
       
     
     is satisfied, the bubble is moved up by buoyancy upward in vertical direction (in the present embodiment, in the direction from the individual flow passages  32  of the head to the filter  40 ). 
     When Reynolds number Re&lt;1, resistance coefficient Cd satisfies Cd=24/Re, and when ink viscosity is μ and ink flow velocity is v, because Reynolds number Re is represented as Re=ρ×v×d/μ, the expression (1) is arranged into 
     
       
           F   1 =3×π×μ× v×d   (4) 
       
     
     When the expression (4) is substituted into the expression (3) and the result is arranged by with respect to d, the following expression is obtained. 
       d &gt;[18×μ× v )/(ρ× g )] 1/2   (5) 
     This bubble diameter d indicates a bubble diameter at the time when buoyancy F 2  becomes larger than the drag F 1  of ink flow. Therefore, bubbles equal to or smaller than this diameter are made to flow in a head (individual flow passages  32 ) direction together with ink during printing. 
     In contrast, it is demonstrated from the result of observation that the bubble size to cause bubble-induced printing defects not recovered by ink emission alone is equal to or greater than a bubble size that causes plural individual flow passages  32  (ink inflow orifices  35 ) to be blocked. This indicates that, although bubbles of such a size as to block one individual flow passage  32  can be discharged from the ink emission orifices  30  by a pressure at the time of ink emission, bubbles of such a size as to block adjacent individual flow passages  32  also are difficult to discharge from the individual flow passages  32  (ink emission orifices  30 ) by transforming the bubbles by only the pressure at the time of ink emission. Therefore, when the pitch of the individual flow passages  32  is Np, a bubble diameter d to cause printing defects is represented as 
     
       
           d≧ 2 Np   (6) 
       
     
     Therefore, by creating the cartridge  14  so that the expressions (3) and (6) are satisfied, the cartridge  14  is freed from maintenance. 
     Referring to a comparative example, a detailed description will be made of how the cartridge  14  is constructed to achieve the above-described effect. 
     In a comparative example (see FIG.  4 ), the common liquid chamber  34  to which one end of the individual flow passages  32  is open, and the ink tank chamber  42  are connected by an ink pipeline  118  having a small cross-sectional area. Therefore, an ink flow velocity ((Q/S) in the expression (3)) of the ink pipeline  118  becomes high, so that bubbles (d≧2Np) to cause bubble defects cannot always rise. Therefore, if negative pressure maintenance is not performed, the bubbles may grow in the common liquid chamber  34 , causing printing defects. 
     On the other hand, in this enforcement example, a flow passage that connects the ink supply chamber  44  and the individual flow passages  32  is defined by a rectangular ink supply chamber  42  having a large cross-sectional area S. In other words, since the individual flow passages  32  are directly open to the large-capacity ink supply chamber  44  (the common liquid chamber  34  is a part of the ink supply chamber  44 ), an ink flow velocity (Q/S) at the time of ink emission is lower than that of the comparative example, decreasing drag F 1  acting on bubbles. As a result, bubbles (d≧2Np) of such a size as to cause printing defects can satisfy the expression (3). In other words, bubbles of such a size as to cause printing defects are made to rise without fail by buoyancy F 2  and deposit from the ink inflow orifice  35  located downward in the gravity direction within the ink supply chamber  44 . Therefore, without performing negative pressure maintenance, bubble-induced printing defects occurring when the ink inflow orifices  35  (individual flow passages  32 ) are blocked by bubbles can be prevented without fail. 
     (Test) 
     To confirm the aforementioned effect, printing operation was actually performed for the embodiment example and the comparative example to determine how many sheets had been printed until a bubble-induced printing defect occurred. 
     The printing specification of a head of a test example (the embodiment example, the comparative example) has a resolution of 800 dpi and 512 ink emission orifices (individual flow passages), and has a printing frequency of 20 kHz, a drop quantity of 5 pl, and a print speed of 5 ppm (sheet/minute) for A4-size paper. In this case, an average ink flow quantity Q during printing satisfies the relation of 0&lt;Q≦(ink flow quantity for printing rate 100%). In the test example, an ink flow quantity (maximum ink flow quantity) for printing rate 100% is estimated as 26 mm 3 /sec. 
     The cross-sectional area S of the ink supply chamber  44  in a flow direction in the embodiment example is 300 mm 2 , which is 300 or more times the cross-sectional area S(=0.8 mm 2 ) of the ink pipeline line  118  of the comparative example (corresponding to the ink supply chamber  44  of the embodiment example). 
     Ink used in the test example had an ink viscosity μ of 2.01 Pa.sec and an ink density ρ of 1050 kg/mm 3 . Also, an image used for printing evaluation had a printing rate 5 to 100%. 
     Test results are shown in Table 1. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 EMBODIMENT 
                 COMPARISON 
               
               
                   
                 EXAMPLE 
                 EXAMPLE 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 AVERAGE NUMBER 
                 NO IMAGE QUALITY 
                 300 SHEETS 
               
               
                 OF SHEETS HAVING 
                 DEFECT NOT 
               
               
                 BEEN PRINTED 
                 OBSERVED AFTER 
               
               
                 UNTIL A BUBBLE- 
                 THE PRINTOUT OF 
               
               
                 INDUCED IMAGE 
                 30,000 SHEETS 
               
               
                 QUALITY DEFECT 
                 (TRUNCATED DATA) 
               
               
                 OCCURRED (WITH 
               
               
                 COVERAGE OF 5%) 
               
               
                   
               
            
           
         
       
     
     In this way, the embodiment example caused no bubble-induced printing defect even after the printout of 30,000 sheets for the estimated life 10,000 sheets of head cartridge. In other words, it was confirmed that negative pressure maintenance for recovery was unnecessary. 
     In contrast, the comparative example causes a printing defect for printing of about 300 sheets and requires negative pressure maintenance each time the printing defect occurs. 
     To confirm this effect, values are assigned to the expression (5). For example, if a printing rate is 100%, an ink flow velocity in the ink supply chamber of the embodiment example is 0.087 mm/sec because of v=Q/S=26(mm 3 /sec)/300(mm 2 )=0.087 mm/sec, and an ink flow velocity in the ink pipeline of the comparative example is 33 mm/sec because of v=Q/S=26(mm 3 /sec)/0.8(mm 2 )=33 mm/sec. Similarly, by finding an ink flow velocity in a printing rate and assigning the value to the expression (5), the relationship between the diameter of bubble flowing into the head and, ink flow velocity was obtained (see FIG.  5 ). 
     When 1&lt;Re&lt;100, the expression (5) was compensated for by Cd=24/Re×(1×0.15×Re 0.687 ). 
     It is understood from FIG. 5 that, in the embodiment example, only bubbles having a diameter of up to 17 μm flow into the head in a flow velocity of a printing rate range of 5 to 100%. 
     In contrast, in the comparative example, since ink flow velocity is fast, bubbles as large as 76 to 430 μm flow into the head together with ink, in a flow velocity of a printing rate range of 5 to 100%. 
     In contrast, a bubble size to cause bubble-induced printing defects is decided by a individual flow passage pitch Np. In other words, because 800 dpi is used as Np in the test example, a pitch Np between adjacent individual flow passages  32  (ink emission orifices  30 ) is 31.75 μm because of Np=25400 μm/80=31.75 μm. Therefore, it is understood that a bubble size to cause bubble-induced printing defects is 62.5 μm or more. 
     Therefore, in the embodiment example, regardless of printing rates, since bubbles to cause bubble defects do not flow into the head (the bubbles rise within the ink supply chamber), bubble-induced printing defects will not occur. On the other hand, in the comparative example, since bubbles of 62.5 μm or more flow into the head with a certain probability without causing no printing defects, bubble-induced printing defect will occur for printout of about 300 sheets. 
     In this way, in the embodiment example, by increasing the cross-sectional area of the ink supply chamber  44  in the ink flow direction in comparison with the comparative example, ink flow velocity in the ink supply chamber at the time of printing is controlled below a predetermined value, bubbles of such a size as to cause bubble-induced printing defects are made to rise by buoyancy. Therefore, the occurrence of bubble-induced printing defects can be completely prevented without having to perform maintenance. 
     (Second Effect) 
     The second effect of the cartridge  14  is to prevent the situation in which bubbles within the ink supply chamber  44  grow, ink within the ink supply chamber  44  becomes empty, and ink to the individual flow passages  32  cannot be supplied, so that printing cannot be performed. 
     To achieve such purposes, the cartridge  14  is designed so that bubbles grow actively within the ink tank chamber  42  communicating to the ink supply chamber  44 , instead of growing them in the ink supply chamber  44 . 
     Generally, gas which deposits from a liquid grows a bubble integrally with a bubble that already exists in the liquid. Therefore, if a bubble exists in the ink supply chamber  44 , the gas deposited according to a rise in ink temperature accompanying printing operation grows the bubble. 
     Accordingly, the cartridge  14  is constructed so that no bubble exists in the ink supply chamber  44  at the time of shipment, and an air lump  48  having a capacity of 1 mm 3  or more is sealed in the ink tank chamber  42  which communicates with the ink supply chamber  44  through the filter  40  and in which ink is held in free condition. Therefore, the ink heated in the course of printing operation reaches the ink tank chamber  42  by convection and deposits air. As a result, the air lump  48  sealed beforehand is grown by the deposited gas, whereby the bubble occurrence and growth within the ink supply chamber  44  can be restrained. 
     If the capacity of an air lump sealed beforehand is below 1 mm 3 , because the diameter of the air lump (bubble) is small, the bubble may dissolve (disappear) because of a rise in ink temperature and the bubble may grow within the ink supply chamber  44 . 
     The present invention also intends to restrain bubble occurrence itself. 
     Generally, there are two kinds of causes of bubble occurrence within the cartridge  14 : (1) since the solubility of air to ink falls as ink temperature rises during printing, minute bubbles deposit in the ink and grow, result in occurrence of bubbles; and (2) there is always a pressure difference from the external atmosphere within the cartridge  14  because ink is supplied to the ink emission orifice  30  with negative pressure, and the pressure difference causes the phenomenon of gas transmission that surrounding air invades through members constituting the cartridge  14 , result in occurrence of bubbles. 
     The cartridge  14  uses noryl resin (or PPO (polyphenylene oxide)) for the ink supplier  22  and elastomer of a polystyrene system for an elastic seal member  46  that seals the head chip  20  and the ink supply chamber  44 . Since both of them have sufficiently small gas transmission constants and have inside-outside pressure difference as small as 1000 Pa, a gas transmission quantity (bubble occurrence of (2)) of surrounding air can be almost disregarded in the period of several years after start of use. 
     Therefore, bubble occurrence in the cartridge  14  is considered to be caused by a temperature rise (the cause of (1)) of ink. Generally, liquid, e.g., water decreases in the solubility of air as temperature rises (see FIG.  8 ). Therefore, air deposits from ink by a temperature rise accompanying printing operation. Of course, the bubble dissolves in ink upon a fall in ink temperature at the end of printing operation, but several bubbles exceeding a certain size do not dissolve. This is because the relationship between the size of a bubble and the solubility of liquid, e.g., water satisfies the relationship as shown in FIG.  9 . Therefore, bubble growth must be controlled so that bubbles that occurred in the ink supply chamber  44  dissolve in ink again when printing is halted. 
     To allow bubbles to dissolve in ink again when printing is halted (a fall in ink temperature), it was confirmed by a test described below whether printing should be halted when how much ink has been consumed. 
     (Test) 
     In the cartridge  14  of the embodiment example, by modifying the number of sheets of one job (the number of sheets that is continuously printed) to print 30,000 sheets of paper of A4 size, the condition that bubbles dissolve in ink was obtained. The internal volume of the ink supply chamber  44  was 3000 mm 3 . The capacity of ink of free condition in the ink tank chamber  42  before the cartridge  14  was used (hereinafter referred to as initial state) was 4000 mm 3  and head temperature during print job was about 55° C. The head temperature was naturally cooled to the room temperature 25° C. after each print job. 
     When printing was performed on paper of A4 size (210 mm×300 mm) with 800 dpi and a printing rate of 5%, the consumption of ink per page was estimated as 16 mm 3  from 5pl×800×800×(210/25.4×300/25.4)×0.05. 
     The number of a series of print jobs, and the quantity of bubbles that occurred in the ink supply chamber are shown in Table 2. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                 CAPACITY 
               
               
                   
                   
                   
                 OF AIR LUMP 
               
               
                 NUMBER OF 
                 TOTAL 
                 QUANTITY OF 
                 WITHIN INK 
               
               
                 PRINT JOBS 
                 VOLUME OF 
                 BUBBLES 
                 TANK 
               
               
                 (WITH 
                 EMITTED INK 
                 OCCURRING IN 
                 CHAMBER (1 
               
               
                 PRINTING 
                 FOR EACH 
                 INK SUPPLY 
                 to 10 mm 3  IN 
               
               
                 COVERAGE OF 
                 PRINT JOB 
                 CHAMBER 
                 INITIAL 
               
               
                 5%) 
                 (mm 3 ) 
                 (mm 3 ) 
                 STATE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 100 SHEETS × 
                 1600 
                 0 
                 3100 
               
               
                 300 JOBS 
               
               
                 200 SHEETS × 
                 3200 
                 0 
                 3200 
               
               
                 150 JOBS 
               
               
                 400 SHEETS × 
                 6400 
                 50 
                 3010 
               
               
                 75 JOBS 
               
               
                 500 SHEETS × 
                 8000 
                 400 
                 2500 
               
               
                 60 JOBS 
               
               
                 1000 SHEETS × 
                 16000 
                 1000 
                 1980 
               
               
                 30 JOBS 
               
               
                 3000 SHEETS × 
                 48000 
                 2000 
                 1000 
               
               
                 10 JOBS 
               
               
                   
               
            
           
         
       
     
     Ink temperature is about 20° C. under the environment of the room temperature 25° C. and the ink in the vicinity of the head rises in temperature to about 50 to 55° C. during printing. From, this, if the amount of deposited air per unit ink quantity is estimated on the basis of the difference of the solubility of air to water (see FIG.  8 ), the very large value of 75 mm 3  (amount of deposited air)/1000 mm 3  (printing ink quantity) is obtained. From this value, the amount of air generated per 30,000 sheets in Table 2 (the amount of air generated in the ink supply chamber and the ink tank chamber) is estimated as 3600 mm 3 . This matches well the result of Table 2. 
     It is understood from the test results that, for the total amount of emitted ink as small as the capacity (3000 mm 3 ) of the ink supply chamber  44 , bubbles (hereinafter referred to as residual bubbles) that do not dissolve in the ink will not occur in the ink supply chamber  44  even if it the temperature falls after the job comes to an end. On the other hand, in the ink tank chamber  42 , the air lump  48  grows, because the ink heated by convection invades from the ink supply chamber  44 . 
     Also, it was confirmed that residual bubbles occurred for the total amount of emitted ink of the vicinity of the sum (7000 mm 3 ) of the capacity of the ink supply chamber  44  and the initial ink capacity (4000 mm 3 ) in the ink tank chamber  42 . 
     Therefore, if the total volume of ink emitted from the ink emission orifices during one printing job is smaller than the sum (7000 mm 3 ) of the capacity of the ink supply chamber and the capacity of ink held in free condition, few bubbles occur within the ink supply chamber  44 . Therefore, by making the total amount of ink emitted during continuation printing smaller than the above-described sum, it becomes possible to eradicate bubbles that remain and grow in the ink supply chamber and establish the situation in which only the air lump  48  of the ink tank chamber  42  in free condition grows. 
     Based on such knowledge, the inkjet recording apparatus  10  performs the bubble occurrence prevention control as shown in FIG.  7 . Details are given referring to the flowcharts shown in FIGS. 6 and 7. 
     A control part (not shown) of the inkjet recording apparatus  10  detects ink temperature of the ink supply chamber  44  by a temperature sensor (not shown) until a printing signal is inputted (steps  200  and  202 ). 
     When the printing signal is inputted to the control part, a bubble control subroutine is started (step  204 ). 
     When the printing signal is input, the bubble control subroutine determines whether or not ink temperature in the ink supply chamber  44  is below a predetermined temperature T ° C. (T=25° C. in the present embodiment) (step  302 ). 
     When a detected temperature becomes below the predetermined temperature T ° C., by driving the heat generating element  36 , the subroutine emits ink from the ink emission orifices  30  and starts printing (step  304 ). 
     As soon as printing is started, a determination unit  1  counts the total number of printing dots that were emitted from all the ink emission orifices  30  constituting the cartridge  14  (step  306 ). By multiplying a drop quantity and the number of printing dots, the total amount of emitted ink is checked. 
     Next, the subroutine determines whether the number of printing dots exceeds a specified number N of dots (step  308 ). In the present embodiment, a value obtained by multiplying this specified number N of dots and the drop quantity is the number of printing dots equivalent to the total ink capacity of the ink supply chamber  44  and the ink tank chamber  42 . 
     If the number of printing dots is smaller than the specified number N of dots, the subroutine determines whether printing terminates (step  310 ). If a series of jobs terminate, the bubble control subroutine is terminated and control is again transferred to the monitoring of ink temperature of the ink supply chamber  44 . 
     On the other hand, if the jobs do not terminate, the above-described control is repeated until the number of printing dots exceeds the specified number N of dots. 
     A printing control unit  2  wherein if the number of printing dots exceeds the specified number N of dots, halts printing operation (ink emission) temporarily until the temperature of ink of the ink supply chamber  44  becomes below the predetermined temperature T ° C. (steps  312  and  314 ). This is done since if the total amount of emitted ink exceeds the sum of the capacity of the ink supply chamber  44  and the initial quantity of ink of free condition in the ink tank chamber  42 , an ink heating quantity becomes large, bubbles within the ink supply chamber grow excessively, and deposited bubbles do not disappear (not redissolve) after printing halt. In other words, by temporarily halting the printing to decrease the ink temperature, bubbles that deposited in the ink supply chamber  44  are redissolved regardless of a fall in the ink temperature to prevent the bubbles from remaining (occurring) in the ink supply chamber  44 . 
     If the number of printing dots exceeds the specified number N of dots, printing operation (ink emission) is temporarily halted until the temperature of ink of the ink supply chamber  44  becomes below the predetermined temperature T ° C. (steps  312  and  314 ). This is done since if the total amount of emitted ink exceeds the sum of the capacity of the ink supply chamber  44  and the initial quantity of ink of free condition in the ink tank chamber  42 , an ink heating quantity becomes large, bubbles within the ink supply chamber grow excessively, and deposited bubbles do not disappear (not redissolve) after printing halt. In other words, by temporarily halting the printing to decrease the ink temperature, bubbles that deposited in the ink supply chamber  44  are redissolved regardless of a fall in the ink temperature to prevent the bubbles from remaining (occurring) in the ink supply chamber  44 . 
     If a ink temperature in the ink supply chamber  44  becomes below the predetermined temperature T ° C., printing is resumed for remaining jobs (step  304 ), the number of printing dots is cleared, and counting is started again (step  306 ). This is because it is judged that the deposited air has dissolved in the ink again, if the ink temperature becomes below the predetermined temperature T ° C. 
     By controlling printing operation in this way, it can be prevented that bubbles deposit in the ink supply chamber, and the deposited bubbles grow without redissolving regardless of a fall in ink temperature and prevent ink supply. 
     In the present embodiment, if the total amount of emitted ink exceeds the sum of the capacity of the ink supply chamber  44  and the initial quantity of ink of free condition in the ink tank chamber  42 , printing is temporarily halted. However, by performing control so that printing is temporarily halted for a smaller quantity than the above-described sum, the occurrence of residual bubbles within the ink supply chamber can be prevented without fail. 
     (Third Effect) 
     A third effect of the cartridge  14  is to restrain fluctuations of ink meniscus interface of the ink emission orifices  30  at the time of ink emission and enable stable printing regardless of printing condition. 
     As shown in FIG. 10, the ink meniscus interface M oscillates by ink emission. This amplitude is amplified depending on printing condition (the pressure condition of the ink supply chamber  44 ) and the meniscus interface M migrates to the ink supply chamber  44  beyond the heat generating element  36 , so that an ink emission failure might occur. Accordingly, in the present embodiment, arrangements have been made so that the amplitude of the ink meniscus interface M caused by ink emission is not amplified regardless of printing condition to enable stable printing. 
     Since the oscillation of the ink meniscus interface M is determined by the pressure oscillation of the ink supply chamber  44 , control is performed so that the pressure oscillation does not amplify. 
     When a pressure pulse in the ink supply chamber  44  that occurs during ink emission is expressed by the function of E(t), a pressure electricity equivalent circuit is shown in FIG.  12 . Here, a flow passage resistance of the individual flow passages  32  is R 1 ; a capacitance by the ink meniscus interface of the ink emission orifices  30  is C 1 ; an inertance of the individual flow passages  32  is L 1 ; a flow passage resistance of the ink supply chamber  44  is R 2 ; a capacitance of ink supply chamber  44  is C 2 ; and an inertance of the ink supply chamber  44  is L 2 . 
     At this time, a fluid pressure oscillation equation can be expressed by the following expression, letting a pressure in the ink supply chamber be P. 
     
       
         ( L   1 + L   2 ) d   2   P/dt   2 +( R   1 + R   2 ) dP/dt+P/ ( C   1 + C   2 )= E ( t )  (7) 
       
     
     By solving this differential equation, a pressure P in the ink supply chamber  44  is found. 
     Since ink emission is cyclically repeated, an emission-induced pressure pulse E(t) that occurs in the ink supply chamber  44  is decided by ink emission. Also, fluid pressure oscillation in the ink supply chamber  44  is conceivable as a forced oscillation system because the excitation of ink emission is applied. 
     The characteristic of the forced oscillation system is that resonance is caused if an oscillation frequency of a pressure pulse E(t) outputted from the outside matches the natural frequency of the system. Especially in a system free of attenuation (flow passage resistance), a pressure amplitude is infinitely extended. 
     Also, in a system in which attenuation (flow passage resistance) exists, if attenuation ratio ζ is represented as 
     
       
         ζ=[( R   1 × R   2 )/2×{( C   1 + C   2 )/( L   1 + L   2 )] 1/2 , 
       
     
     amplitude X would be amplified to 1/{2×ζ×(1−ζ 2 ) 1/2 ] times. 
     Because of the amplitude amplification, in the case where, in the recording head cartridge of the comparative example, a pattern having a high printing rate (batch printing of 100%) is repeatedly printed at a certain period, a nonemission fault such as a white stripe occurred. 
     In the embodiment example, by satisfying a relational expression derived from a characteristic equation of an expression (7) 
      ( R   1 + R   2 ) 2 ×( C   1 + C   2 )≧4×( L   1 + L   2 )  (8) 
     pressure oscillation in the ink supply chamber during ink emission can be made into an overattenuation mode or critical attenuation mode. As a result, because the pressure oscillation in the ink supply chamber becomes nonoscillation type, the pressure fluctuation of the ink supply chamber  44  is not amplified even if a pressure pulse E(t) of any oscillation frequency is applied. 
     In the case where a construction as in the comparative example is taken, because the cross-sectional area S of the ink pipeline  118  is small, the value of L 2  becomes large and the expression (8) cannot be satisfied, and therefore pressure fluctuation will be amplified. Accordingly, to satisfy the characteristic equation, the amplification of pressure fluctuation was restrained, for example, by generating a bubble and sending it to the common liquid chamber  34  and increasing capacitance C 2  by the bubble. However, it was difficult to control the bubble sent to the common liquid chamber  34  and there was the possibility that the bubble grew in the course of printing operation and an emission defect might occur. 
     On the other hand, the embodiment example constructs the cartridge  14  by designing it so that the values of R 1 , R 2 , L 1 , L 2 , C 1 , and C 2  satisfy the expression (8) by adjusting the dimensions of the cartridge  14  described later. Thereby, very satisfactory printing can be achieved for any image quality pattern and a reliable recording head cartridge  14  can be formed. 
     For example, by increasing the cross-sectional area of the ink supply chamber  44 , pressure oscillation during ink emission can be completely attenuated, and very satisfactory printing can be achieved for any image quality pattern and a reliable recording head cartridge can be formed. 
     By the way, resistance R 1  in the individual flow passages, by circular tube approximation, is represented as 
     
       
           R   1 =8×μ× t   1 /(π r   4 ). 
       
     
     Herein, μ is ink viscosity; t 1  is the length of individual flow passage; and r is the cross-sectional radius of individual flow passage. The same is also true for the resistance R 2  of the ink pipeline line of the comparative example (1: the length of ink pipeline) (see FIG.  4 ). 
     On the other hand, the resistance R 2  of the rectangular ink supply chamber of the embodiment example can be obtained by applying circular tube approximation to the sectional shape. 
     Inertance L 1  in the individual flow passages, by circular tube approximation, is represented as 
     
       
           L   1 =ρ× t   1 /(π r   2 ). 
       
     
     Herein, ρ is ink density. The same is also true for the inertance L 2  of the ink pipeline of the comparative example (see FIG.  4 ). 
     On the other hand, inertance L 2  of the rectangular ink supply chamber  42  of the embodiment example is represented as 
     
       
           L   2 =ρ× t   2 / S.   
       
     
     Herein, t 2  is the length of the ink supply chamber, and S is the cross-sectional area of the ink supply chamber (see FIG.  11 ). 
     Capacitance C 2  of the ink supply chamber means acoustic capacity and is represented as 
     
       
           C   2 = V /(ρ× C   2 ). 
       
     
     Herein, V is the capacity of the ink supply chamber and C is acoustic velocity in the ink. The same is also true for the capacitance C 2  of the ink pipeline of the comparative example. 
     On the other hand, a capacitance C 1  by the ink meniscus interface of the ink emission orifice means a capacity by meniscus displacement and is represented as 
     
       
           C   1 = dV/PC.   
       
     
     Herein, dV is an ink drop volume and PC is a capillary tube pressure of the meniscus in the ink emission orifice. The capillary tube pressure PC is represented as 
     
       
           PC= 2γ cos θ/ r.   
       
     
     Herein, γ is an ink surface tension, θ is an emission orifice contact angle, and r is an emission orifice radius. 
     (Test Example) 
     Printing evaluation was made for the cartridge  14  (inkjet recording apparatus  10 ) of the embodiment example and the comparative example by printing line pairs each having a predetermined number of dots. Numeric values obtained from the embodiment example in the test example and the comparative example are shown in Table 3. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                 EMBODIMENT 
                 COMPARATIVE 
                   
               
               
                 CONSTANT 
                 EXAMPLE 
                 EXAMPLE 
                 UNIT 
               
               
                   
               
             
            
               
                 R2 
                 2.55 × 10 3   
                 1.38 × 10 9   
                 Pa•sec./m 3   
               
               
                 R1 
                 1.12 × 10 11   
                 1.12 × 10 11   
                 Pa•sec./m 3   
               
               
                 L2 
                 3.67 × 10 4   
                 2.34 × 10 7   
                 kg/m 4   
               
               
                 L1 
                 1.05 × 10 6   
                 1.05 × 10 6   
                 kg/m 4   
               
               
                 C2 
                 1.21 × 10 −15   
                 5.20 × 10 −18   
                 m 3 /Pa 
               
               
                 C1 
                 1.94 × 10 −16   
                 1.94 × 10 −16   
                 m 3 /Pa 
               
               
                 μ (AT ROOM 
                 2.01 × 10 −3   
                 2.01 × 10 −3   
                 Pa•sec. 
               
               
                 TEMPERATURE) 
               
               
                 μ (DURING 
                 1.00 × 10 −3   
                 1.00 × 10 −3   
                 Pa•sec. 
               
               
                 EMISSION) 
               
               
                   
               
            
           
         
       
     
     FIG. 13 is an explanatory drawing showing the line pairs used for the printing evaluation. Specifically, full width batch printing (printing rate 100%) of the recording head is performed with the printing pattern that a null part of x dots is formed after x dots are continuously emitted, at a printing spatial frequency 1/(2×x) times an emission frequency. 
     By printing the x-dot line pairs in the range in which x is from 1 to 20, printing evaluation was performed. Printing evaluation results and amplitude amplification factors are shown in Table 4. 
     The natural frequency F is a value obtained by an expression: 
     
       
           F =[1/(2π)]×[1/( LC )] 1/2 . 
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 EMBODIMENT 
                 COMPARATIVE 
               
               
                   
                 EXAMPLE 
                 EXAMPLE 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 (R1 + R2) 2  × 
                 1.32 × 10 7   
                 −9.53 × 10 7   
               
               
                 (C1 + C2) − 
               
               
                 4 × (L1 + L2) 
               
               
                 ATTENUATION 
                 2.01 
                 0.159 
               
               
                 RATIO ζ 
               
               
                 AMPLITUDE 
                 NOT AMPLIFIED 
                 3.18 TIMES 
               
               
                 AMPLIFICATION 
               
               
                 FACTOR 
               
               
                 NATURAL 
                 4072 
                 2282 
               
               
                 FREQUENCY OF 
               
               
                 INK SUPPLY 
               
               
                 SYSTEM Hz 
               
               
                 PRINTING 
                 NO PROBLEM 
                 WHITE DROPOUT 
               
               
                 EVALUATION 
                 OCCURRED AFTER 1- 
                 OCCURRED AFTER 4- 
               
               
                 RESULTS 
                 TO 20-DOT LINE 
                 TO 5-DOT LINE PAIRS 
               
               
                   
                 PAIRS WERE 
                 WERE REPEATEDLY 
               
               
                   
                 REPEATEDLY 
                 PRINTED AT 20 KHZ. 
               
               
                   
                 PRINTED AT 20 KHZ. 
               
               
                   
               
            
           
         
       
     
     It is understood from these results that the expression of (R 1 +R 2 ) 2 ×(C 1 +C 2 )−4×(L 1 +L 2 )&lt;0 is satisfied in the comparative example, indicating attenuation oscillation mode. Therefore, if input (4- to 5-dot line pairs at 20 kHz) having an oscillation frequency in the vicinity of the natural frequency of the ink supply system is repeated, the amplitude of pressure oscillation increases to 3.18 times the initial amplitude (see FIG.  14 ). 
     If the cartridge goes into such resonance condition, the refill of ink meniscus M formed in the individual flow passages  32  becomes unstable, eventually the ink is not emitted, and a printing defect such as white dropout occurs. 
     On the other hand, the embodiment example satisfies the expression of (R 1 ×R 2 ) 2 ×(C 1 +C 2 )−4×(L 1 +L 2 )&gt;0, indicating overattenuation mode. Therefore, because the amplitude of pressure oscillation does not increase and is almost the same as the input (see FIG.  15 ), reliable ink emission (printing) becomes possible. 
     Viscosity μ differs between at the time of ink emission and at the room temperature (standby). This is because the ink is heated during ink emission, with result that ink temperature in the vicinity of the individual flow passages rises and the viscosity decreases. 
     The cartridge  14  has the following effect, in addition to the aforementioned first to third effects. 
     That is, since the head chip  20  forms a part of the side of the ink supply chamber  44  and the individual flow passages  32  open directly to the large-capacity ink supply chamber  44 , the ink is easily diffused and the ink emission orifices  30  (individual flow passages  32 ) are not clogged because of dry ink after the cartridge  14  has been left unused for a long period of time. Therefore, the life of the cartridge  14  can be extended. 
     In this way, the present invention can offer the reliable cartridge  14  and inkjet recording apparatus  10  with a simple constitution. 
     Such a huge air lump of the ink tank chamber  42  described in the second effect as to block the upper part of the filter  40  can be prevented by exhausting air from the ink tank chamber  42  and providing an ink supply system to replace ink. 
     An example is shown in FIG.  16 . In other words, a cartridge  50 , which has an ink tank chamber  42  made up of two cells, includes a first ink chamber  42 A that communicates directly with an ink supply chamber  44  through a filter  40  and in which ink is held in free condition, a second ink chamber  42 B in which a porous member  52  impregnated with ink is disposed, and a secondary ink tank  54  that supplies ink to the first ink chamber  42 A. 
     The secondary ink tank  54  communicates with the first ink chamber  42 A through two communication tubes  56  and  58  different from each other in length. 
     The first ink chamber  42 A and a lower part of the second ink chamber  42 B are communicated with each other through clearances  64  of a communication member  60  (see FIG.  16 B). 
     With this constitution, when ink emission is started and the ink of the first ink chamber  42 A is consumed, air is introduced from the opening  62  of the second ink chamber  42 B, and the ink impregnated in the porous member  52  flows into the first ink chamber  42 A through the clearances  64  of the communication member  60 . When the ink surface of the second ink chamber  42 B drops to the location of the clearances  64  of the communication member  60 , air is introduced directly to the first ink chamber  42 A from the porous member  52 . In this condition, when the ink surface of the first ink chamber  42 A falls to a predetermined position, the ink of the secondary ink tank  54  replaces the air of the first ink chamber  42 A through the communication tubes  56  and  58 . 
     In this way, since the ink in the secondary ink tank  54  replaces the air in the first ink chamber  42 A, the air accumulated in the first ink chamber  42 A can be discharged. Therefore, it is possible to prevent a fault that the air accumulated in the first ink chamber  42 A grows excessively and blocks the filter  40 . 
     Also, since a liquid surface detection sensor provided in the first ink chamber  42 A detects the quantity of remaining ink in the first ink chamber  42 A and tells the replacement of the secondary ink tank, it is prevented without fail that too small a quantity of remaining ink in the first ink chamber  42 A promotes bubble occurrence and growth in the ink supply chamber  42 . 
     The inkjet recording apparatus and the inkjet recording head cartridge of the present invention prevent bubble-induced printing defects and can implement a reliable recording head. 
     Also, the fault that ink is not emitted because the ink supply chamber has been filled with bubbles can be prevented and the life of the head can be extended. 
     Furthermore, by optimally designing the internal volume, cross-sectional area, and length of the ink supply chamber, a pressure oscillation during ink emission can be completely attenuated, and satisfactory printing can be achieved for whatever image quality pattern. 
     As has been described above, by adopting the present invention, an inkjet recording head cartridge and an inkjet recording apparatus, both highly reliable and low-cost, can be achieved. 
     The entire disclosure of Japanese Patent Application No. 2000-223037 filed on Jul. 24, 2000 including specification, claims, drawings and abstract is incorporated herein by reference in its entirety.