Patent Publication Number: US-6709091-B1

Title: Ink ejection device and driving method therefor

Description:
BACKGROUND OF THE INVENTION 
     This application is a continuation-in-part of U.S. patent application Ser. No. 08/705,153 filed Aug. 29, 1996 and issued Sep. 8, 1998 now U.S. Pat. No. 5,805,177 entitled “Shear Mode Driving Method for an Ink Ejection Device That Accommodates Temperature Change” and assigned to the same assignee of the present application. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an ink ejection device for forming images on a recording medium by ejecting ink droplets from nozzles according to printing commands. The invention also relates to a driving method for the ink ejection device that forms. 
     2. Description of the Related Art 
     Non-impact type printing devices have recently taken the place of conventional impact type printing devices and are holding an ever-growing share of the market. Of these non-impact type printing devices, ink-ejecting type printing devices have the simplest operation principle, but are still capable of effectively and easily performing multi-gradation and color printing. Of these devices, a drop-on-demand type for ejecting only ink droplets which are used for printing has rapidly gained popularity because of its excellent ejection efficiency and low running cost. 
     A shear mode type printer using a piezoelectric actuator is one of the drop-on-demand types. Such a printer is disclosed in U.S. Pat. No. 4,879,568. One example of such type of printer is shown in FIGS.  1 ( a ) and  1 ( b ) in which FIG.  1 ( a ) is a cross-sectional view taken along line A—A in FIG.  1 ( b ) an FIG.  1 ( b ) is also a cross-sectional view taken along line B—B in FIG.  1 ( a ). 
     As shown in FIGS.  1 ( a ) and  1 ( b ), the shear mode type ink ejection device  600  includes a bottom wall  601 , a ceiling wall  602 , and elongated shear mode actuator walls  603  sandwiched therebetween. Each actuator wall  603  includes a lower wall  607  adhesively attached to the bottom wall  601  and an upper wall  605  adhesively attached to the ceiling wall  602 . The upper and lower walls  605 ,  607  are polarized in the directions indicated by arrows  609 ,  611 , respectively. Alternating pairs of actuator walls  603  form in alternation ink channels  613  therebetween or spaces  615 , which are narrower than the ink channels  613 . 
     Electrodes  619  and  621  are provided on both side surfaces of each actuator wall  603 . Specifically, the electrode  619  is provided in the ink channel  613  and the electrode  621  is provided in the space  615 . The electrode  621  is also provided on the outer side surface of each of the two outermost actuator walls  603 . The electrode  619  is covered by an insulating layer (not shown) to insulate it from the ink. The electrodes  621  are connected to ground  623 . The electrodes  619  are connected to a control unit  625  in a form of a silicon chip which applies voltages (driving signals) to the electrodes  619  as will be described later. 
     A nozzle plate  617  is fixedly secured to one end of the actuator walls  603 . The nozzle plate  617  is formed with nozzles  618  at positions corresponding to the ink channels  613 . An ink supplying source (not shown) is connected to the other end of the actuator walls  603  through a manifold  626 . The manifold  626  includes a front wall  627  formed with openings in positions corresponding to the ink channels  613 , and a rear wall  628  for sealing the space between the bottom wall  601  and the ceiling wall  602 . Ink from the ink supplying source is supplied to the manifold  626  or common ink chamber and distributed into the respective ink channels  613 . The front wall  627  prevents ink from the manifold  626  from entering the spaces  615 . 
     To eject droplets, a voltage from the control unit  625  is applied to the electrode  619  of each ink channel  613 . Pairs of the actuator walls  603  deform outward by the piezoelectric shear effect so that the volume of each ink channel  613  increases. In the example shown in FIG. 2, when a voltage E volts is applied to the electrode  619   c  of the ink channel  613   c , an electric field is developed in the actuator wall  603   e  in the direction indicated by the arrow  631 , and an electric field is developed in the actuator wall  603   f  in the direction indicated by the arrow  632 . Because the electric field directions  631  and  632  are at right angles to the polarization direction  609 ,  611 , the actuator walls  603   e ,  603   f  deform outward to increase the volume of the ink channel  613   c  by the piezoelectric shear effect, resulting in a decrease in the pressure in the ink chamber  613   c , including near the nozzle  618   c.    
     Application of the voltage E(V) is maintained for a duration of time T, during which time ink is supplied from the ink supplying source. A pressure wave occurring when the ink is supplied from the ink supplying source propagates in the lengthwise direction of the ink channel  613   c . The duration of time T corresponds to a duration of time required for the pressure wave to propagate once in the lengthwise direction of the ink channel  613   c . The duration of time T can be calculated by the following formula: 
     
       
         
           T=L/a 
         
       
     
     wherein L is the length of the ink channel  613 ; and 
     a is the speed of sound through the ink filling channel  613   c.    
     Theories on pressure wave propagation teach that at the moment the duration of time L/a elapses after the application of the voltage, the pressure in the ink channel  613   c  inverts to a positive pressure. The voltage application to the electrode  619   c  of the ink channel  613   c  is stopped in timed relation with this pressure inversion so that the actuator walls  603   e ,  603   f  revert to their initial shape shown in FIG.  1 ( a ). 
     The pressure generated when the actuator walls  603   e ,  603   f  return to their initial shape is added to the inverted positive pressure so that a relatively high pressure is generated in the ink channel  613   c . This relatively high pressure ejects an ink droplet  26  from the nozzle  618   c.    
     The inventor of the present invention developed a method for executing a remaining pressure wave canceling operation. In the canceling operation, pressure wave vibrations are generated in the ink of the ink channel  613  after execution of the ejection operation. The canceling operation is executed by applying the voltage E volts to the electrode  619   c  at a specified time, and subsequently returned to 0 volts in order to increase and then decrease the volume of the ink channel  613 . With this canceling operation, not only do the pressure wave vibrations converge at an early stage, thereby preventing unintentional ejection of ink due to residual pressure wave, but also the transition to process the next print command can be performed quicker. As a result, the printing device can form a more faithful image and printing speed can be improved. 
     However, the speed of sound a described above changes according to the temperature of the ink, as does the actual value of the time T required for a pressure wave to propagate once across the length of the ink channel  613 . Therefore, if the canceling operation is executed at a fixed timing regardless of the temperature of the ink, it is possible that the pressure wave vibrations will not be satisfactorily offset. In some cases, an ejection operation corresponding to the next print command may be executed before the pressure wave vibrations have converged, and the ejected ink may spray and scatter or the ink might not even be ejected. 
     Another problem exits in the remaining pressure wave canceling operation such that reliable cancellation of the pressure wave vibrations in the ink channels cannot be achieved. Because timing for executing the canceling operation has been set to an appropriate value through trial and error. In some cases, the ejection operation for the next print command is executed before the pressure wave vibrations have converged. As a result, the ejected ink can spray and scatter, or sometimes the ink does not eject at all. The canceling operation cannot always reliably cancel the pressure wave vibrations, particularly when driving the ink ejection device  600  at a rapid speed to support rapid printing, in which case the temperature of the ink rises, lowering the viscosity. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, it is an object of the present invention to provide an ink ejection device capable of executing a canceling operation to cancel pressure wave vibrations in the ink, regardless of the temperature of the ink. 
     It is another object of the present invention to provide an ink ejection device capable of forming faithful images by canceling pressure wave vibrations that exist within the ink chamber and capable of increasing the printing speed. 
     These and other objects of the present invention will be attained by an ink ejection device including nozzles from which ink is ejected; ink channels provided on the back of the nozzles for being filled with ink; an actuator for applying pressure wave vibrations to ink in the ink channels; and a control unit for executing an ejection operation by driving the actuator in response to printing commands to apply pressure wave vibrations to the ink in the ink channels and cause ink to eject from the nozzles, and for subsequently executing a canceling operation by driving the actuator at timings based on the ink temperature in the ink channels to order to eliminate as much as possible the pressure wave vibrations in the ink. 
     With an invention of this construction, the control unit drives the actuator according to print commands in order to execute the ejection operation in the following way. First, the actuator generates pressure wave vibrations in the ink of the ink channel, which pressure wave vibrations cause ink to be ejected from the nozzle. After the ejection operation, the control unit drives the actuator to execute a canceling operation for sufficiently canceling the pressure wave vibrations in the ink. Accordingly, the pressure wave vibrations are made to converge at an early period to prevent ink from being ejected in a undesirable location as a result of residual pressure wave vibrations, and also to quickly proceed to process the next print command. Moreover, the control unit executes the canceling operation at a timing corresponding to the temperature of the ink in the ink channel. For this reason, the canceling operation can be satisfactorily executed regardless of the temperature of the ink. Therefore, the ink ejection device of the present invention can create an extremely accurate image by preventing ink from spraying and scattering and from not ejecting properly. Further, since the pressure wave vibrations in the ink are converged at an early period, the printing speed can be increased. 
     The cancellation described above does not need to completely eliminate the pressure wave vibrations. For example, the canceling operation can be configured to only restrain the pressure wave vibrations to a sufficient degree that ink is not ejected from the nozzle. 
     According to another aspect of the present invention, the actuator varies the volume of the ink channel; and after executing the ejection operation, the control unit drives the actuator to increase and decrease the volumes of the ink channel at timings based on the ink temperature in the ink channel in order to eliminate as much as possible the pressure wave vibrations in the ink. 
     In the present invention, the actuator described above varies the volumes of the ink channel. Through these volume variations, pressure wave vibrations are generated in the ink, causing ink to be ejected from the corresponding nozzle. The actuator executes the canceling operation by increasing and decreasing the volume of the ink channel. Accordingly, the canceling operation can be extremely proficient in canceling pressure wave vibrations in the ink. Therefore, the ink ejection device of the present invention can even more satisfactorily cancel the pressure wave vibrations in the ink to form an even more accurate image. As a result, the printing speed can be improved even further. 
     According to still another aspect of the present invention, the control unit drives the actuator to first increase the volume of the specified ink channel and to then decrease the volume of the same to eject ink from the corresponding nozzle, and, following a time interval determined according to both the time required for the ink pressure wave vibrations to propagate one way through the ink channel and the temperature of the ink, subsequently executes a canceling operation by again driving the actuator to first increase and then decrease the volume of the ink channel. 
     In executing an ejection operation in the present invention, the control unit drives the actuator to first increase the volume of the ink chamber. At this time, the pressure inside the ink chamber decreases, allowing ink to flow into the chamber. Next, the control unit drives the actuator to decrease the volume of the ink chamber. Hence, the pressure inside the ink chamber becomes relatively high, causing ink to be ejected from the corresponding nozzle. After a specified time determined by both the time T required for pressure wave vibrations in the ink to propagate once across the length of the ink channel and the temperature of the ink, the control unit executes a canceling operation by again increasing the volume of the ink channel and then decreasing that volume. Accordingly, the canceling operation can be executed at an appropriate timing based on this time T and the temperature of the ink, and the pressure wave vibration in the ink can be offset very well. 
     Therefore, the ink ejection device of the present invention is even more proficient in canceling the pressure wave vibrations in the ink and forms an even more accurate image. Further, the printing speed can be increased even more. Since the temperature of the ink is referenced in the present invention, the time T required for pressure wave vibrations in the ink to propagate once across the length of the ink channel can be fixed according to specified temperature ranges, thereby greatly simplifying the process. 
     According to yet another aspect of the present invention, the control unit executes an ejection operation in response to a one-dot print command and executes a canceling operation after a time interval d 2 , wherein d 2  equals: 
     2.45 T, when the ink temperature in the ink chamber is between 0 and 10° C.; 
     2.50 T, when the ink temperature in the ink chamber is between 10 and 20° C.; 
     2.55 T, when the ink temperature in the ink chamber is between 20 and 30° C.; and 
     2.60 T, when the ink temperature in the ink chamber is between 30 and 40° C.; such that T is the time required for the ink pressure wave 
     vibrations to propagate one way through the ink channel at room temperature. The control unit performs these operations by driving the actuator to first increase the volume of the specified ink channel and, following an interval of about 1.0 T or an odd multiple thereof, to then decrease the volume of the same to eject ink from the corresponding nozzle. After a time interval of about 0.75 T, the control unit subsequently executes a canceling operation by again driving the actuator to first increase the volume of the ink channel and, following a time interval of about 1.0 T or an odd multiple thereof, to decrease the volume of the ink channel to again eject ink from the corresponding nozzle. 
     According to this configuration, the volume of the ink channel is first increased and subsequently decreased after approximately 1.0 T or an odd multiple thereof, thereby ejecting ink from the nozzle. After an interval of about 0.75 T, the volume of the ink channel is again increased and subsequently decreased after an interval of approximately 1.0 T or an odd multiple thereof, again causing ink to eject from the nozzle. 
     Ink ejection is very efficient when the volume of the ink channel is decreased approximately 1.0 T or an odd multiple thereof after the volume of the ink channel has been increased. Since the period of the pressure wave vibrations in the ink of the ink chamber is about 2 T, the timing in which the internal pressure of the ink channel increases after increasing the volume of the ink channel and the timing in which the internal pressure of the ink channel increases due to decreasing the volume of the ink channel coincide, thereby creating a great pressure within the ink channel. Since the control unit executes the ejection operation twice over an interval of about 0.75 T, two droplets of ink are ejected very efficiently for each one-dot print command, thereby forming a rich image. 
     After completing the ejection operation, the control unit executes a canceling operation after the pulse interval d 2 , determined according to the temperature of the ink in the ink channel, has elapsed. By executing a canceling operation a pulse interval d 2  after the above ejection operation has been completed, pressure wave vibrations in the ink can be very efficiently offset. 
     Therefore, the ink ejection device of the present invention is even more proficient in canceling the pressure wave vibrations in the ink and forms an even more accurate and richer image. Further, the printing speed can be increased even more. 
     According to another aspect of the present invention, the control unit increases or decreases the volume of the ink channel by applying a voltage to the actuator, and, moreover, applies the same voltage to the actuator both during an ejection operation and during a canceling operation. 
     Since the same voltage is applied to the actuator during both the ejection operation and the canceling operation in order to increase or decrease the volume of the ink channel, only one power source is necessary for supplying the drive signal, and, therefore, the construction of the control unit can be simplified. Further, the process for controlling the actuator is simplified by switching the applied voltage off and on. Hence, the construction and control of the ink ejection device can be even more simplified. 
     According to further another aspect of the present invention, the side walls of the ink channels in the actuator are formed of piezoelectric materials. 
     Since piezoelectric materials are used to construct the side walls of the ink channels, the volume of the ink channels can be changed by applying voltage to the piezoelectric materials. This type of actuator has a simple construction, is extremely durable, and is inexpensive. Therefore, an invention having this construction can simplify the construction, increase the durability, and further decrease the cost of the device. 
     The present invention also provides an ink ejection device including nozzles from which an ink is ejected; ink channels provided on the back of the nozzles for being filled with the ink; an actuator for varying volumes of the ink channels; and a driving device for executing an ejection operation by driving the actuator to generate pressure wave vibrations in the ink channels and cause the ink to eject from the nozzles, and for subsequently executing a canceling operation by driving the actuator to first increase and then decrease the volumes of the ink channels in order to eliminate as much as possible the pressure wave vibrations in the ink. The volume increases and decreases of the canceling operation are executed when the pressure wave vibrations cross the center of their vibration or the neutral pressure level, an odd number of times, that is, when the pressure changes from positive to negative. 
     With the construction described above, the control unit drives the actuator to vary the volume of the ink channels provided on the back of the nozzles, generating pressure wave vibrations in the ink channels and ejecting ink from those channels. 
     Subsequently, the control unit executes a canceling operation to cancel the pressure wave vibrations in the ink channels. In this canceling operation, the control unit drives the actuator to first increase the volume of the ink channels and subsequently decrease that volume. As a result, the pressure wave vibrations in the ink channels are quickly converged, thereby preventing ink from being ejected in an undesirable location by remaining pressure wave vibrations and quickly proceeding to the ejection operation corresponding to the next print command. Moreover, the control unit increases and decreases the volumes of the ink channels during the canceling operation at points when the frequency wave crosses the center of the vibration an odd number of times, that is, when the pressure changes from positive to negative. 
     Here, the inventors of the invention studied the relationship between the waveform of the pressure wave vibrations in the ink channels and the time for executing a cancel operation capable of most effectively canceling those pressure wave vibrations. As a result, the inventors discovered that the cancel operation is most effectively executed after the ejection operation when the pressure wave vibrations cross the center of the vibrations an odd number of times, particularly, three times. In this case, the pressure waves in the ink channels are converged at an extremely early period, thereby effectively preventing ink from ejected at an undesirable location and allowing the ink ejection device to proceed very quickly to the ejection process in response to the next print command. Moreover, the canceling operation demonstrates an ability to stabilize the pressure wave vibrations, regardless of various conditions. 
     Since the waveform shape of the pressure wave vibrations when crossing the center of the vibration a third times is similar to the waveform shape when crossing the center of the vibration in the other odd number of times, it is possible to assume that the effects of executing the cancel operation at these times are approximately the same. In other words, the pressure within the ink channel immediately after completion of the ejection operation has risen near the peak of the pressure wave. Afterward, the pressure wave vibrates periodically and, when crossing the center of the vibration an odd number of times, the pressure wave crosses the center in a declining direction at approximately the same slope. 
     In the present invention, the canceling operation is executed after the ejection operation and when the pressure wave vibration crosses the center of the vibration an odd number of times. Accordingly, the pressure wave vibrations in the ink channels are converged at an extremely early time, thereby effectively preventing ink from being ejected at an undesirable location and allowing the ink ejection device to proceed quickly to the ejection process corresponding to the next print command. Moreover, the effects of this invention demonstrate reliability. Therefore, the ink ejection device of the present invention forms an accurate image by reliably canceling pressure wave vibrations remaining in the ink channels and improving printing speed. 
     In the canceling operation described above it is not necessary to completely eliminate the pressure wave vibrations. For example, it is possible to restrain the pressure wave vibrations to the degree that ink is not ejected from the nozzles. 
     Preferably, the odd number of times is set to three. With this configuration, the invention can reliably cancel pressure wave vibrations. Moreover, it is possible to converge the pressure wave vibrations at an earlier time than when the above-described odd number of times is set to five, seven, or more. Accordingly, an even more accurate image is created by reliably canceling pressure wave vibrations at an even earlier time, thereby improving the print speed even further. 
     According to another aspect of the present invention, the control unit repeatedly executes the ejection operation a plurality of times in response to a one-dot print command and executes the canceling operation after all ejection operations are completed for the one-dot print command. 
     With the configuration described above, a plurality of ink droplets is ejected in response to a one-dot print command, thereby forming a richer image. By repeatedly executing the ejection process a plurality of times, the pressure wave vibrations in the ink channels become more complex, making it more difficult to set an appropriate timing for executing the cancel operation. In the present invention, this problem is overcome by executing the canceling operation at a time when the pressure wave vibrations have crossed the center of the vibration an odd number times, as described above. As a result, a timing for executing the cancel operation can be easily set. Moreover, it is possible to reliably cancel the pressure wave vibrations. Therefore, an even richer image can be formed, and costs for developing the ink ejection device can be further decreased by simplifying the settings for the device. 
     According to another aspect of the present invention, the time that elapses during the canceling operation after the volume of the ink channel is increased and until the volume is decreased is about 0.3 to 0.7 or about 1.3 to 1.7 times the length of time required for a pressure wave to propagate once across the length of the ink channel. 
     The inventor of the present invention conducted an experiment in which the time interval (hereinafter referred to as the “pulse width Wc”) in the cancel operation after the volume of the ink channel is increased until the volume of the ink channel is decreased was changed to various lengths, and studied the values of the pulse width Wc capable of most effectively canceling pressure wave vibrations in the ink channel. As a result, the inventor discovered that the pulse width Wc should be set to 0.3 to 0.7 or 1.3 to 1.7 times the time required for a pressure wave in the ink to propagate one direction along the ink channel (hereinafter referred to as the “time T”). 
     It is presumed that Wc is best set to these values for the following reason. When Wc=1.0 T, the peak of the pressure wave vibrations generated by increasing the volume of the ink channel and the increase in pressure generated by the decrease in the volume of the ink channel combine to eject ink from the nozzles. When Wc=2.0 T, the pressure wave vibrations caused by increasing the volume and the pressure wave vibrations generated by decreasing the volume cancel each other out, inviting the same effect as when not executing a canceling operation. Accordingly, by setting the pulse width Wc to a value between these values, such as 0.3 to 0.7 T or 1.3 to 1.7 T, it is thought that the canceling operation can be effectively executed. 
     Since in the present invention Wc is set at approximately 0.3 to 0.7 T or approximately 1.3 to 1.7 T, the canceling operation can be very effectively executed. Therefore, an even more accurate image can be formed by more effectively canceling the pressure wave vibrations, and the printing speed can be improved even further. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The particular features and advantages of the invention as well as other objects will become apparent from the following description taken in connection with the accompanying drawings, in which: 
     FIG.  1 ( a ) is a cross-sectional view taken along a line A—A in FIG.  1 ( b ), showing the configuration of a conventional ink ejection device; 
     FIG.  1 ( b ) is a cross-sectional view taken along a line B—B in FIG.  1 ( a ), showing the configuration of the conventional ink ejection device shown in FIG.  1 (a); 
     FIG. 2 is an explanatory diagram showing an example operation executed by the ink ejection device of FIGS.  1 ( a ) and  1 ( b ); 
     FIG. 3 is a circuit diagram for a control unit used in the ink ejection device according to the present invention; 
     FIG.  4 ( a ) is a timing chart showing pulse waves issued by a charge circuit of the control unit; 
     FIG.  4 ( b ) is a timing chart showing pulse waves issued by a discharge circuit of the control unit; 
     FIG.  4 ( c ) is a timing chart showing the voltage applied to an actuator; 
     FIG. 5 is an explanatory diagram showing the construction of the ROM in the control unit; 
     FIG.  6 ( a ) is an explanatory diagram showing an example drive waveform output from the control unit of the ink ejection device; 
     FIG.  6 ( b ) is an explanatory diagram showing the pressure wave vibration in the ink channel; 
     FIG.  7 ( a ) is an explanatory diagram showing an example of a drive waveform output from the control unit of the ink ejection device; 
     FIG.  7 ( b ) is an explanatory diagram showing the pressure wave vibration caused when the ejection pulse signal A rises; 
     FIG.  7 ( c ) is an explanatory diagram showing the pressure wave vibration caused when the ejection pulse signal A drops; 
     FIG.  7 ( d ) is an explanatory diagram showing the pressure wave vibration caused when the ejection pulse signal B rises; 
     FIG.  7 ( e ) is an explanatory diagram showing the pressure wave vibration caused when the ejection pulse signal B drops; and 
     FIG.  7 ( f ) is an explanatory diagram showing the pressure wave vibration combining the vibrations caused by the two ejection pulse signals A and B. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An ink ejection device according to preferred embodiments of the present invention will be described while referring to the accompanying drawings. A description of the mechanical parts in the ink ejection device  600  of the present embodiment will be omitted, as the construction of these parts is the same as the conventional device shown in FIGS.  1 ( a ) and  1 ( b ). 
     First the dimensions of the ink ejection device  600  will be described. The length L of the ink channel  613  is 7.5 mm. The diameter of the nozzles  618  on the nozzle plate  617   a  side is 40 μm. The diameter thereof on the ink channel  613  side is 72 μm. The length of the nozzles  618  is 100 μm. The ink supplied for the experiment described below has a viscosity of approximately 2 mPa·s at 25° C. and a surface tension of 30 mN/m. The ratio L/a, where L is the length L, described above and a is the speed of sound in the ink of the ink channel  613 , is 8 μsec. L/a equals the time T required for a pressure wave to propagate once across the length of the ink channel  613 . The value a for the speed of sound is the value at room temperature (25° C.). The ink ejection device  600  is mounted on a carriage that moves along a platen (not shown), forming a gap of 1-2 mm between the nozzle plate  617   a  and the recording paper (not shown) on the platen. 
     FIG. 3 is a circuit diagram showing the construction of the control unit  625  used in the ink ejection device  600  of the present embodiment. As shown in FIG. 3, the control unit  625  includes a charge circuit  182 , a discharge circuit  184 , and a pulse control circuit  186 . The piezoelectric materials and the electrodes  619  and  621  of the actuator wall  603  are represented by a capacitor  191 , where a terminal  191 A and a terminal  191 B of the capacitor  191  correspond to the electrode  619  and electrode  621 , respectively. In other words, the terminal  191 A is connected to the control unit  625 , while the terminal  191 B is connected to ground  623 . 
     An input terminal  187  provided on the charge circuit  182  and an input terminal  188  provided on the discharge circuit  184  receives pulse signals from the pulse control circuit  186  described later. In response to these pulse signals, a voltage of either E volts (for example, 20 volts) or 0 volts is applied to the electrode  619  (terminal  191 A) in the ink channel  613 . 
     The charge circuit  182  includes resistors R 101 , R 102 , R 103 , R 104 , and R 105 ; and transistors TR 101  and TR 102 . The base of the transistor TR 101  is connected to the input terminal  187  via the resistor R 101  and is grounded via the resistor R 102 . The emitter of the transistor TR 101  is directly grounded, while the collector thereof is connected to a positive power source  189  via the resistor R 103 . The base of the transistor TR 102  is connected to the positive power source  189  via the resistor R 104  and is connected to the collector of the transistor TR 101  via the resistor R 105 . The emitter of the transistor TR 102  is connected directly to the positive power source  189 , while the collector thereof is connected to the terminal  191 A via a resistor R 120 . 
     With this construction, if an ON signal (+5 volts) is applied to the input terminal  187  of the charge circuit  182 , the transistor TR 101  is rendered conductive, and current from the positive power source  189  flows from the collector in the transistor TR 101  toward the emitter. Accordingly, the voltage developed across the resistor R 104  increases, causing an increase in the base current of the transistor TR 102  and rendering the transistor TR 102  conductive. Then, a voltage E volts from the positive power source  189  is applied to the terminal  191 A via the emitter/collector junction of the transistor TR 102  and the resistor R 120 . 
     Next, the construction of the discharge circuit  184  will be described. The discharge circuit  184  includes a resistor R 106 , resistor R 107 , and a transistor TR 103 . The base of the transistor TR 103  is connected to the input terminal  188  via the resistor R 106  and is grounded via the resistor R 107 . The emitter of the transistor TR 103  is directly grounded, while the collector thereof is connected to the terminal  191 A via the resistor R 120  described above. With this construction, when an ON signal (+5 volts) is applied to the input terminal  188  of the discharge circuit  184 , the transistor TR 103  is rendered conductive, thereby grounding the terminal  191 A via the resistor R 120 . 
     Next, variations of the voltages applied to the actuator wall  603 , i.e., capacitor  191 , according to the charge circuit  182  and discharge circuit  184  will be described. 
     An input signal applied to the input terminal  187  of the charge circuit  182  is shown in FIG.  4 ( a ). Ordinarily, the signal is OFF. However, when ejecting ink, the signal is turned ON at a specified timing T 1  and turned OFF at a specified timing T 2 , described later. The signal is subsequently turned ON again at a timing T 3  and turned OFF at a timing T 4 . Once again, the signal is turned ON at a specified timing T 5  and turned OFF at a timing T 6 . An input signal applied to the input terminal  188  of the discharge circuit  184  is shown in FIG.  4 ( b ). This signal is turned OFF when the signal applied to the input terminal  187  is turned ON, that is, at T 1 , T 3 , and T 5 . The signal is turned ON when the signal applied to the input terminal  187  is turned OFF, that is, at T 2 , T 4 , and T 6 . 
     FIG.  4 ( c ) shows the voltage appearing at the terminal  191 A during this time. Normally, the voltage is maintained at 0 volts. Charging of the capacitor  191 , that is, the actuator wall  603 , starts at the timing T 1 . The voltage across the capacitor  191  reaches E volts after a charge time Ta determined by the transistor TR 102 , the resistor R 120 , and the electrostatic capacitance of the actuator wall  603  made from a shear mode type piezoelectric material. At the timing T 2 , discharging of the capacitor  191  begins, and the voltage drops to 0 volts after a discharge time Tb determined by the transistor TR 103 , the resistor R 120 , and the electrostatic capacitance of the actuator wall  603 . 
     The voltage E volts appears at the electrode  619  after the time delay Ta from the application of the ON signal to the input terminal  187  of the charge circuit  182 . Also, 0 volts appears at the electrode  619  after the time delay Tb from the stoppage of the application of the ON signal. Due to the delays Ta and Tb in the rising and falling edges in the voltage (hereinafter referred to as the “drive signal”) appearing at the electrode  619 , the points at which the voltage is a half of E volts (for example, 10 volts) is represented by rising timings AS, BS, and HS, and at falling timings AE, BE, and HE. The pulse control circuit  186  controls the timings T 1 -T 6  of the signals applied to the input terminals  187  and  188  to achieve desirable rising and falling timings described later. 
     Next, the pulse control circuit  186  will be described with reference to FIG.  3 . The pulse control circuit  186  is provided with a CPU  210  for performing various calculations; a RAM  212  for storing print and various other data; a ROM  214  for storing control programs for the pulse control circuit  186  and sequence data for generating ON and OFF signals at the timings T 1 -T 6  described above; pulse generators  220  and  222  for generating pulses to be applied to the input terminals  187  and  188 , respectively; a print data reception circuit  218  for receiving print commands from a host computer (not shown); and an I/O bus  216 . The I/O bus  216  transfers data between a temperature sensor  224  for sensing a temperature of ink, print data reception circuit  218 , pulse generators  220  and  222 , and CPU  210 . 
     As shown in FIG. 5, the ROM  214  includes an ink ejection device control program storage area  214 A and a drive waveform data storage area  214 B. The sequence data specifying the waveform of the drive signal is stored in the drive waveform data storage area  214 B. 
     The CPU  210  controls the pulse generators  220  and  222  based on the sequence data stored in the drive waveform data storage area  214 B. Therefore, by storing all the patterns of timings T 1 -T 6  in the storage area  214 B, a drive signal having a desired waveform can be applied to the actuator wall  603  in response to a 1-dot print command. The number of pulse generators  220  and  222 , charge circuits  182 , and discharge circuits  184  provided exactly equals the number of nozzles  618  in the ink ejection device  600 . The CPU  210  outputs a drive signal to the actuator wall  603  in response to print data to eject ink from the corresponding nozzle  618 . The temperature sensor  224  is a device well known in the art and functions to detect the temperature of ink in the ink channel  613 . 
     Next, an example waveform of the drive signal (hereinafter referred to as “drive waveform”) in an ink ejection device  600  according to the present embodiment will be described with reference to FIG.  6 ( a ). Further, FIG.  6 ( b ) illustrates pressure changes in the ink channel  613  in response to this drive waveform. 
     As shown in FIG.  6 ( a ), the drive waveform of the present example includes two ejection pulse signals A and B for ejecting ink and one non-ejection pulse signal C for canceling the residual pressure wave vibrations in the ink channel  613 . All of the pulse signals A, B, and C have a wave height (voltage) of E volts. Further, the pulse signals A, B, and C have respective pulse widths Wa, Wb, and Wc, which are set at 1.0 times, 1.0 times, and 0.5 times the time T (8 μsec) required for a pressure wave to propagate once across the length of the ink channel  613 . The pulse interval d 1  between the ejection pulse signals A and B is set at 0.75 T. 
     As described in the example of ink channel  613   c  of FIG. 2, when the ejection pulse signal A rises at the timing AS, an electric field is developed in the actuator wall  603 , causing the volume of the ink channel  613  to increase and the internal pressure of the same to decrease, including the area near the nozzle  618 . At this time, ink flows into the ink channel  613 , and pressure wave vibrations generated by the increased volume increase the internal pressure to a positive pressure, reaching a peak approximately after an interval of time T has elapsed. The ejection pulse signal A drops at the timing AE 1.0 T after the timing AS. At this time, the volume of the ink channel  613  decreases. The pressure generated by this decrease in volume adds to the positive pressure described above to generate a relatively high pressure near the nozzle  618 , causing ink to eject from the same. 
     The ejection pulse signal B rises at the timing BS 0.75 T after the timing AE. At the timing BE, an additional 1.0 T after the timing BS, a second droplet of ink is ejected from the nozzle  618  in the same manner as described above. Subsequently, the non-ejection pulse signal C is generated after the pulse interval d 2 . The center HC of this pulse signal C should be set to the point in time that the internal pressure of the ink channel  613  switches from positive to negative. 
     The pressure wave vibrations in the ink can be canceled in the following way. If the non-ejection pulse signal C rises at the timing HS before the internal pressure of the ink channel  613  switches from positive to negative, the still positive pressure can be quickly decreased. Further, if the non-ejection pulse signal C drops at the timing HE after the pressure has become negative, the negative pressure can be quickly increased. Accordingly, the pressure wave vibrations can be canceled, allowing the vibrations to quickly converge. As a result, it is possible to prevent unintentional ink ejection and to quickly proceed to processing the next print command. Therefore, an ink ejection device of the present invention not only can form very good images, but also can improve printing speed. The non-ejection pulse signal C functions to cancel pressure wave vibrations, as described above, and moreover, will not cause ink to eject, since the pulse width Wc is considerably different from an odd multiple of the time T. 
     However, the speed of sound within the ink of the ink channel  613  varies according to the temperature of the ink. Accordingly, the actual value L/a of the time T also varies. Further, the period of the pressure wave vibrations in the ink, shown in FIG.  6 ( b ), and an appropriate value of the pulse interval d 2  change according to the temperature of the ink. Therefore, the pulse interval d 2  is set in the following way. The inventor of the present invention performed an ink ejection experiment to study appropriate values for the pulse interval d 2  at various temperatures. The results of the experiment are shown in Table 1 below. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 d2 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Temp 
                 2.30 
                 2.35 
                 2.40 
                 2.45 
                 2.50 
                 2.55 
                 2.60 
                 2.65 
                 2.70 
                 2.75 
               
               
                   
               
             
            
               
                  0 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 X 
                 X 
               
               
                  5 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 X 
               
               
                 10 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 X 
               
               
                 15 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
               
               
                 20 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
               
               
                 25 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
               
               
                 30 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
               
               
                 35 
                 X 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                 40 
                 X 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                 45 
                 X 
                 X 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
               
               
                 50 
                 X 
                 X 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
               
               
                   
               
               
                 ◯ No deviation in trajectory/no scatter  
               
               
                 Δ Deviation in trajectory  
               
               
                 X  spray/no discharge  
               
            
           
         
       
     
     In Table 1, the pulse interval d 2  is a ratio to the time T at 25° C., and all temperatures are degrees Celsius. As shown in Table 1, a suitable value for the pulse interval d 2  to achieve a good ejection without deviation in trajectory or spray gradually increases as the temperature increases. If the value of the pulse interval d 2  deviates from an appropriate value, the pressure wave vibrations in the ink channel  613  will remain until ink is ejected in response to the next command. Hence, the trajectory speed of the ink droplet ejected next will not be appropriate, and deviation in trajectory will occur, in which the droplet is not deposited in a desirable location on the recording paper. If the disparity in the pulse interval d 2  becomes worse, the ejected ink may become spray, scattering on the recording paper. Further, the spray may be deposited on the nozzle plate  617   a , blocking discharge of the ink. 
     Therefore, the ink ejection device of the present embodiment sets the pulse interval d 2  based on the temperature of the ink, as shown in Table 2. The temperature of the ink is detected via the temperature sensor  224 . Further, the timings T 1 -T 6  described above are set according to this pulse interval d 2 . Accordingly, high quality printing can be achieved when the ink is at any temperature between 0 and 40° C., without the occurrences of deviation in trajectory and spray. In addition to being able to form very accurate images, the printing speed can be greatly improved by converging the pressure wave vibrations of the ink at an early stage. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Temperature (° C.) 
                 d2 (×T) 
               
               
                   
                   
               
             
            
               
                   
                  0 to 10 
                 2.45 
               
               
                   
                 10 to 20 
                 2.50 
               
               
                   
                 20 to 30 
                 2.55 
               
               
                   
                 30 to 40 
                 2.60 
               
               
                   
                   
               
            
           
         
       
     
     Next, another embodiment of the present invention will be described. In this embodiment, the drive waveform also includes two ejection pulse signals A and B for ejecting ink and one non-ejection pulse signal C for canceling the residual pressure wave vibrations in the ink channel  613  as in the previous embodiment. All of the pulse signals A, B, and C have a wave height (voltage) of E volts. Further, the pulse signals A, B, and C have respective pulse widths Wa, Wb, and Wc, which are set at 1.0 times, 0.75 times, and 0.5 times the time T (8 μsec) required for a pressure wave to propagate once across the length of the ink channel  613 . The pulse interval d 1  between the ejection pulse signals A and B is set at 0.85 T. 
     As described in the example of ink channel  613   c  of FIG. 2, when the ejection pulse signal A rises at the timing AS, an electric field is developed in the actuator wall  603 , causing the volume of the ink channel  613  to increase and the internal pressure of the same to decrease, including the area near the nozzle  618 . At this time, ink flows into the ink channel  613 , and pressure wave vibrations generated by the increased volume increase the internal pressure to a positive pressure (that is higher than the pressure at the center of the vibration), reaching a peak approximately after an interval of time T has elapsed. The ejection pulse signal A drops at the timing AE 1.0 T after the timing AS. At this time, the volume of the ink channel  613  decreases. The pressure generated by this decrease in volume adds to the positive pressure described above to generate a relatively high pressure near the nozzle  618 , causing ink to eject from the same. 
     The ejection pulse signal B rises at the timing BS 0.85 T after the timing AE. At the timing BE, an additional 0.75 T after the timing BS, a second droplet of ink is ejected from the nozzle  618  in the same manner as described above. Subsequently, the non-ejection pulse signal C is generated after the pulse interval d 2 . This pulse signal C should be set to overlap the point in time that the internal pressure of the ink channel  613  switches from positive to negative. 
     The inventor of the present invention investigated different settings for the pulse interval d 2  and discovered that the center HC of the non-ejection pulse signal C should be set to the point in time after the pressure wave vibrations cross the center of the vibration the third time after completion of the ejection operation according to ejection pulse signals A and B. In this case, the pressure wave vibrations in the ink channel  613  converge at an extremely early time, thereby efficiently preventing unintentional ink ejection and allowing the ink ejection device to proceed quickly to process the next print command. Moreover, the cancel operation can be reliably accomplished regardless of various other conditions. 
     Therefore, in the ink ejection device  600  of the present invention, the pulse interval d 2  is set based on a calculated point in time. This point in time is the point when the pressure wave vibrations generated by outputting ejection pulse signals A and B crosses the center of the vibration the third time, changing from positive to negative pressure. 
     Next, generation of the pressure wave vibrations will be described with reference to FIGS.  7 ( a ) through  7 ( f ). When an ejection pulse signal A rises at a timing AS, as shown in FIG.  7 ( a ), pressure within the ink channel  613  drops suddenly, as shown in FIG.  7 ( b ), and a sinusoidal pressure wave vibration having a period of about 2 T is subsequently generated. Hence, FIG.  7 ( b ) shows the pressure wave vibration component within the ink channel  613  that is caused when the ejection pulse signal A rises. 
     Similarly, FIG.  7 ( c ) shows the component of the pressure wave vibration caused when the ejection pulse signal A drops. Here, the pressure wave vibration rises suddenly when the ejection pulse signal A drops at a timing AE, and subsequently vibrates at a period of about 2 T. FIG.  7 ( d ) shows the component of the pressure wave vibration caused when the ejection pulse signal B rises. Here, the pressure wave vibration drops suddenly when the ejection pulse signal B rises at a timing BS, and subsequently vibrates at a period of about 2 T. FIG.  7 ( e ) shows the component of the pressure wave vibrations caused when the ejection pulse signal B drops. Here, the pressure wave vibration rises suddenly when the ejection pulse signal B drops at a timing BE, and subsequently vibrates at a period of about 2 T. The result of combining all components of the pressure wave vibrations is shown in FIG.  7 ( f ). The pressure wave vibration in FIG.  7 ( f ) is that which is actually generated in the ink channel  613  by the ejection pulse signals A and B. 
     Therefore, the inventor of the present invention calculated a point P signifying the point in time at which the pressure wave vibration of FIG.  7 ( f ) crosses the center of the vibration the third time after the timing BE at which the ejection operation is completed. In other words, the point P denotes the point that the pressure wave vibration changes from positive to negative pressure the second time after completion of the ejection operation. In the present embodiment, the pulse interval d 2  calculated based on the measured value for this point P is 2.51 T. By setting the pulse interval d 2  to this value, it is possible to efficiently cancel the pressure wave vibrations, as described above. 
     The inventor of the present invention conducted an ink ejection experiment using the ink ejection device  600 , in which experiment the pulse interval d 2  and the pulse width Wc of the non-ejection pulse signal C were changed to various values in order to determine the allowable range of values for the pulse interval d 2  and an appropriate value for the pulse width Wc. The results of this experiment are shown in Table 3 found at the end of the description. In Table 3, the deviation Δd 2  from the calculated value 2.51 T of the pulse interval d 2  and the pulse width Wc are written as ratios of the time T. 
     As indicated by Table 3, ejection is efficiently performed without generating spray or deviation in trajectory when the pulse interval d 2  is set such that Δd 2  is −0.3 to 0.3 T and when the pulse width Wc is set to 0.3 to 0.7 T or 1.3 to 1.7 T. If the value for d 2  or Wc deviates slightly from an appropriate value, the pressure wave vibrations in the ink channel  613  will remain until ink is ejected in response to the next command. Hence, the trajectory speed of the ink droplet ejected next will not be appropriate, and deviation in trajectory will occur, in which case the droplet is not deposited in a desirable location on the recording medium. If the disparity in the pulse interval d 2  or the pulse width Wc becomes worse, the ejected ink may become spray, scattering on the recording medium. Further, the spray may be deposited on the nozzle plate  617   a , blocking discharge of the ink. 
     The results of the above experiment show that the value for the pulse interval d 2  has an allowable error of about ±0.3. Also, the pulse width Wc should be set to 0.3 to 0.7 T or 1.3 to 1.7 T. The results for Wc are thought to be appropriate for the following reason. When Wc=1.0 T, the peak of the pressure wave vibrations generated by the increase in volume of the ink channel  613  (timing HS of FIG.  6 ( a )) and the increase of pressure caused by a decrease in the volume (timing HE of FIG.  6 ( a )) combine to eject ink from the nozzles. When Wc=2.0 T, the pressure wave vibrations caused by an increase in the volume of the ink channel and the pressure wave vibrations caused by a decrease in the volume cancel each other out, inviting the same effect as when a non-ejection pulse signal C is not generated. For this reason, it is thought that the cancel operation can be most effectively executed when the pulse width Wc is set between those values at 0.3 to 0.7 T or 1.3 to 1.7 T. 
     In the second embodiment described above, since the pulse interval d 2  is set to 2.51 T and the pulse width Wc is set to 0.5 T, the pulse width vibrations can be very effectively canceled by the non-ejection pulse signal C. Further, the effects of this cancel operation demonstrate a high reliability. Accordingly, a very accurate image can be reliably formed without generating spray or deviation in trajectory, and the pressure wave vibrations are quickly converged, allowing the print speed to be effectively improved. Further, in the embodiment described above, the deviation Δd 2  from the calculated value 2.51 T for the pulse interval d 2  is set to 0, while the pulse width Wc is set between the shorter appropriate range 0.3 to 0.7 T. Accordingly, an accurate image can be even more reliably formed, and the print speed can be improved even more effectively. 
     While the invention has been described in detail with reference to specific embodiments thereof, it would be apparent to those skilled in the art that many modifications and variations may be made therein without departing from the spirit of the invention, the scope of which is defined by the attached claims. For example, the value of the pulse interval d 2  can be set to a value other than that shown in Table 2, providing the value falls within the range indicated by a circle in Table 1, while achieving the same effects. 
     Further, it is possible to change the values for the pulse widths Wa and Wb and the pulse interval d 1 . For example, Wa, Wb, and d 1  can be modified according to the temperature of the ink to correspond to the actual value of the time T, thereby improving the quality of ink ejection. However, in this case, the value for pulse interval d 2  must also be changed. 
     As described in the embodiments above, two droplets of ink are ejected in response to each one-dot print command, but it is possible to only eject one droplet instead. However, as described above, consecutive ejection of a plurality of ink droplets (three or more droplets is also possible) per each one-dot print command can form a richer and easier to see image on the recording paper. 
     Further, it is possible to set various times T for each prescribed temperature range and execute an operation to cancel the pressure wave vibrations based on those times T. However, the control process is easier when multiplying the time T by a standard coefficient for each prescribed temperature range, as described above. 
     Further, it is possible to prevent ink from being ejected when canceling the pressure wave vibrations by applying a voltage lower than E volts or a negative voltage as the non-ejection pulse signal C. However, since the ejection and canceling operations in the first embodiment described above are executed by setting the pulse signals A, B, and C to fixed values and adjusting the output timings AS-HE, only one power source is needed for outputting all of the pulse signals, greatly simplifying both construction and control of the device. 
     The present invention can be applied to devices for ejecting ink by quickly reducing the volume of the ink channel  613 ; to devices for applying pressure wave vibrations to ink via means other than actuators formed with a piezoelectric material; and to line printers having an ink ejection device  600  fixed to the body of the printing device. However, when using an actuator formed from piezoelectric elements as described above, the device can be made simpler to construct, more durable, and less expensive to produce. 
     As a modification to the second embodiment of the invention, the values for d 2  and Wc can be set to any value within the range of values in Table 3 where the appropriate values are marked with circles. Although the reliability of the effects described above may degrade slightly if the values for d 2  and Wc are varied, the same approximate effects can be obtained. 
     It is also possible to change the pulse widths Wa and Wb and the pulse interval d 1  to other values. However, in this case, the value of the pulse interval d 2  is also changed to an appropriate value. Further, it is also possible to provide a pressure sensing device in the ink channel  613  in order to detect pressure wave vibrations after completion of an ejection operation and calculate the point P of FIG.  7 ( f ) and the pulse interval d 2 . In this case, ink having a different viscosity can be used according to the needs of the user, and the cancel operation can be effectively executed, even when changing the settings of Wa, Wb, and d 1 . 
     When repeatedly executing the ejection operation a plurality of times, the pressure wave vibrations in the ink channel  613  become complex. However, in the second embodiment described above, the timing for executing the canceling operation is set based on the time in which the pressure wave vibration crosses the center of the vibration, thereby simplifying setting of the device and reducing development costs. 
     The pressure wave vibrations when crossing the center of the vibration the third time is similar to those when crossing the center of the vibration an odd number of times other than three. Therefore, it is presumed that approximately the same effects can be obtained when executing the canceling operation based on this point in time, that is, when the pressure changes from positive to negative. To restate this idea, the pressure in the ink channel  613  has risen to approximately the peak immediately after the ejection operation, after which the pressure wave vibrates periodically. When the pressure wave vibration crosses the center of the vibration an odd number of times, the vibration crosses the center in a declining direction at approximately the same slope each time. If the cancel operation is executed when the pressure wave vibration crosses the center of the vibration on the fifth or seventh time, the processing time for one-dot of print data is longer. However, if the time T is sufficiently short, this method also has advantages. Further, in this case, it is possible to set the pulse width Wc to approximately 2.3 to 2.7 T. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Wc 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 d2 
                 0.2 
                 0.3 
                 0.4 
                 0.5 
                 0.6 
                 0.7 
                 0.8 
                 0.9 
                 1.0 
                 1.1 
                 1.2 
                 1.3 
                 1.4 
                 1.5 
                 1.6 
                 1.7 
                 1.8 
                 1.9 
                 2.0 
               
               
                   
               
             
            
               
                 −0.5 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
               
               
                 −0.4 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 X 
               
               
                 −0.3 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                 −0.2 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                 −0.1 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                   0.0 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                   0.1 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                   0.2 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                   0.3 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 ◯ 
                 Δ 
                 X 
               
               
                   0.4 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 X 
                 X 
                 X 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 Δ 
                 X 
               
               
                   0.5 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X