Patent Publication Number: US-2021162493-A1

Title: Method of three-dimensional printing and a conductive liquid three-dimensional printing system

Description:
DETAILED DESCRIPTION 
     Field of the Disclosure 
     The present disclosure is directed to a method of three-dimensional printing using a laser beam for heating a build surface. A conductive liquid three-dimensional printing system that includes a laser is also disclosed. 
     BACKGROUND 
     Conductive liquid three-dimensional printers for building 3D parts from molten aluminum alloys are known in the art. An example of such a system is disclosed in U.S. Pat. No. 9,616,494. The system works by using a DC pulse applied by an electromagnetic coil to expel molten aluminum drops in response to a series of pulses. The platen to which the drops are targeted translates to allow for the drops to be connected and built up to produce a three-dimensional part. 
     However, the drops of molten aluminum sometimes do not combine smoothly or with sufficient bonding strength. Further, the 3D part can have an undesirable degree of porosity, as well as uneven build surfaces during fabrication, unwelded drops, and shape inconsistencies. All of these lead to degraded physical properties such as fatigue strength and tensile strength, as well as appearance issues, with the final part. 
     Therefore, methods and systems for improving the quality of three-dimensional parts made from conductive liquid three-dimensional printers would be a step forward in the art. 
     SUMMARY 
     An embodiment of the present disclosure is directed to a method of three-dimensional printing. The method comprises heating a first portion of a build surface on a platform by impinging a laser beam on the build surface so as to provide a preheated drop contact point having a first deposition temperature. A first drop of a liquid print material is ejected from a printhead of a 3D printer so as to deposit the first drop on the preheated drop contact point at the first deposition temperature. 
     Another embodiment of the present disclosure is directed to a conductive liquid three-dimensional printing system. The system comprises a platform; a printhead for ejecting drops of a conductive liquid print material at drop contact points on the platform; and a laser configured to direct a laser beam at the drop contact points. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present teachings, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrates embodiments of the present teachings and together with the description, serve to explain the principles of the present teachings. 
         FIG. 1  shows a flowchart of a method of heating a build surface for three-dimensional printing, according to an embodiment of the present disclosure. 
         FIG. 2  shows a perspective view of a conductive liquid three-dimensional printing system, according to an example of the present disclosure. 
         FIG. 3  shows an exploded view of the internal components a build nozzle. 
         FIG. 4  shows a schematic side view of a build nozzle and laser, according to an embodiment of the present disclosure. 
         FIG. 5  shows a cross-sectional view taken along line  5  of the build nozzle of  FIG. 4  that illustrates the internal components of the build nozzle. 
         FIG. 6  shows a cross sectional view of the printhead, according to an embodiment of the present disclosure. 
         FIG. 7  shows a cut away, cross sectional perspective view of the nozzle pump containing liquid conductive material and the build surface with a perspective view of the laser, according to an embodiment of the present disclosure. 
         FIG. 8  shows a schematic cross sectional view of liquid conductive material in the pump chamber, including the flow of liquid material out of the pump chamber and the electromagnetic coil. 
         FIG. 9  shows a perspective view of the nozzle pump producing drops forming a 3D object, according to an embodiment of the present disclosure. 
         FIG. 10  illustrates an image of a laser beam incident on a build surface. 
         FIG. 11  shows a graph of temperature date, according to an example of the present disclosure. 
     
    
    
     It should be noted that some details of the figure have been simplified and are drawn to facilitate understanding of the embodiments rather than to maintain strict structural accuracy, detail, and scale. 
     DESCRIPTION OF THE EMBODIMENTS 
     Reference will now be made in detail to embodiments of the present teachings, examples of which are illustrated in the accompanying drawings. In the drawings, like reference numerals have been used throughout to designate identical elements. In the following description, reference is made to the accompanying drawing that forms a part thereof, and in which is shown by way of illustration a specific exemplary embodiment in which the present teachings may be practiced. The following description is, therefore, merely exemplary. 
     During the printing process of molten metal by a conductive liquid three-dimensional printer, the temperature differential between a molten drop ejected from the printer and a build surface causes inconsistencies with the build strength, porosity and surface finish of the final build part. Testing has shown that to properly fuse the molten metal to the base build material the receiving surface temperature can be controlled to a deposition temperature. For example, for aluminum and aluminum alloys this temperature is about 400° C. to about 550° C., or higher. The conductive liquid three-dimensional printer system uses a heated base plate set to, for example, about 400° C., to heat the initial layers. However, as the part continues to grow from the base plate, the heating from the base plate is unable to maintain the higher temperatures on the upper surface so as to ensure a good bond between the molten drop and the cooled top surface. 
     A laser system employed in conjunction with the conductive liquid three-dimensional printer provides for a hybrid system that allows for the lower cost molten drop deposition system to control the temperature at the target location on the build surface where the drops are deposited to provide a strong, cohesive and/or uniform bond of the drop to the build part and/or reduced porosity of the part. 
     Thus, embodiments of the present disclosure are directed to a hybrid conductive liquid three-dimensional (3D) build system wherein conductive liquid drops are deposited on a build surface while employing a laser pre-heat system to adjust the build surface temperature in the area where the drops come into contact with the build surface. By raising the temperature in a localized area at the drop contact point, a more complete and controlled bonding of the drop to the build surface can be achieved, leading to better build quality and improved material properties across the bond and throughout the finished part. Increasing the temperature of the build surface just before and during the deposition of the drop can improve coalescence of the drop with the previously deposited layer compared to the same process in which the temperature of the build surface is not increased to the desired temperature. 
     Advantages of the method and system of the present disclosure include one or more of the following: an interactive laser system that can increase performance of build based on time, energy and part structure to improve additive material performance; targeted heating to raise temperature a precise amount in a limited zone to improve part structure in a conductive liquid three dimensional printer; improved part properties, such as lower porosity, higher yield strength, higher fatigue cycles and/or surface quality, among other things; the ability to adjust the localized temperature to improve material bonding during the 3D print; the ability to adjust the localized temperature based on object shape, size and/or material to improve build properties, such as surface appearance and other part properties; allow for heating at the point of impact of the liquid metal with changes in direction of the part during the build process; localized pre-heat can reduce impact to geometric integrity; areas around the heated zone can act as support boundries; the ability to control energy to part based on part geometry by using slicing data; allowance for higher temperature latitude at a focused location (e.g., a voxel), which is something that cannot be attained by conventional surface heating (e.g., radiant or induction heating) 
     Method of Three-Dimensional Printing 
     An embodiment of the present disclosure is directed to a method of three-dimensional printing. As shown by the flowchart of  FIG. 1 , the method comprises heating a first portion of a build surface on a platform by impinging a laser beam on the build surface so as to provide a preheated drop contact point having a first deposition temperature. A first drop of a liquid print material is ejected from a printhead of a 3D printer so as to deposit the first drop on the preheated drop contact point at the first deposition temperature. 
     The processes of heating a portion of the build surface and ejecting a drop of liquid print material can be repeated any number of times so as to deposit a plurality of drops until the 3D part is completed. For example, the method can include heating a second portion of the build surface that is different from the first portion by impinging a laser beam at the build surface, thereby providing a second preheated drop contact point having a second deposition temperature; and ejecting a second drop of the print material from the printhead to deposit the second drop on the preheated drop contact point at the second deposition temperature. The method further includes adjusting the position of the laser beam relative to the build surface so as to heat the drop contact points on which each successive drop is deposited. 
     In an embodiment, the drops, (e.g., the first drop, second drop and successively deposited drops) comprise a molten metal. As examples, the molten metal can comprise at least one metal chosen from aluminum (e.g., pure aluminum or aluminum alloys), copper (e.g., pure copper or copper alloys such as bronze), and silver (e.g., pure silver or silver alloys). Examples of aluminum alloys include the 6000 series of alloys such as A1 6061, as well as 300 series such as 356, 7000 series such as 7075, and 4000 series such as 4043. Any other aluminum alloys or other metals that can be printed using liquid 3D printing techniques can be employed. The metal can be supplied to the 3D printer in any desired form, such as wire (e.g., wire comprising any of the metals described herein) or other forms, as described in more detail below. 
     The deposition temperature of the build surface will depend on the type of material being 3D printed. As an example, for aluminum and aluminum alloys, the deposition temperature may range from about 400° C. to about 800° C., such as about 400° C. to about 600° C., or about 400° C. to about 550° C. Depending on the metal being deposited, temperatures outside these ranges may also be employed. At appropriate deposition temperatures, such as those listed above, the molten drops combine with the build part in a uniform way that produces bonds that create a strong and consistent build structure. On the other hand, when the build surface temperatures fall below about 400° C. for aluminum and aluminum alloys, the drops do not combine as smoothly or with the desired bonding strength. This can result in porosity in the part, uneven build surfaces, unwelded drops, and shape inconsistencies, which in turn, may lead to degraded physical properties, such as fatigue strength and tensile strength as well as appearance issues with the final part. However, if the temperature of the build surface is 400° C. or greater the build quality is more controlled. By targeting the surface with a laser the temperature of the build surface may be controlled and raised to the level that produces an improved bond between the molten drop and the build surface compared to the bond that would otherwise occur if lower build surface temperatures are employed. The laser allows for the surface to be heated as the part is moved through an x, y and z axes build pattern to create the surface layer. The focused energy of the laser allows for a controlled energy delivery to a localized area to be heated (e.g., an area that includes where each of the molten drops directly contact the build surface). This allows for heating the surface of the part as it traverses under the incoming molten drops. 
     The build surface can be whatever surface on which the drops are deposited. For example, the build surface can be the surface of the platform, sometimes referred to a build plate. In another embodiment, the build surface is a surface portion of a 3D part being built on the platform. 
     The platform can also be heated by a secondary means other than the laser beam, such as a heating element, radiative heating and so forth. For example, the platform can be heated to a base temperature using the secondary heating means, followed by additional heating with the laser beam. The base temperature can be any desired temperature, such as a temperature ranging from about 300° C. to about 500° C., or about 350° C. to about 450° C., or about 380° C. to about 420° C. 
     The portion of the build surface radiated by the laser beam is heated, thereby forming a localized hotspot having a temperature that increases compared to the temperature of the surrounding build surface that is not radiated. A molten metal drop ejected onto this hotspot can have improved deposition properties and/or result in a final part with improved characteristics, as described herein.  FIG. 10  illustrates an image of a laser beam  125  incident on a build surface prior to deposition of drops  120 . 
     The molten metal drops ejected from the printer can have a diameter of any suitable size prior to deposition on the build surface, such as a diameter ranging from about 0.05 mm to about 2 mm, or about 0.1 mm to about 1 mm, or about 0.5 mm. After deposition, the drops may spread to have a wider dimension. For example, a drop with a diameter of 0.5 mm may spread to cover an area of about 0.7 mm upon impact with the build surface. 
     As shown, for example, in  FIG. 4 , the laser beam  125  is at an angle, e, relative to a top surface of the platform  112 . The angle can be any suitable angle that will allow the laser to be incorporated into the system and that will provide effective heating of the build surface by the laser beam. In an embodiment, the angle ranges from about 10 degrees to about 45 degrees, such as about 20 degrees to about 40 degrees, or about 30 degrees. 
     Any 3D printing technique that ejects molten metal drops can be employed in the methods of the present disclosure. In an embodiment, the 3D printer employs a DC pulse applied by an electromagnetic coil to eject the first drop, as described in greater detail below. The method can include depositing the drops on the build surface at any desired rate. For example, the plurality of drops can be ejected at a frequency ranging from about 0.1 Hz to about 2000 Hz, such as about 1 Hz to about 1200 Hz, or about 10 Hz to about 1000 Hz, or about 100 Hz to about 1000 Hz. 
     As mentioned above, the method of the present disclosure includes adjusting the position of the laser beam relative to the build surface and repeating the processes of heating portions of the build surface on which the molten metal drops are deposited. The position of the laser beam can be adjusted relative to the build surface by moving the laser, the build surface or both. In an example, as described in greater detail below, the position of the laser beam comprises moving the laser beam and the printhead along a z-axis; and moving the platform along an x-axis, a y-axis or both the x-axis and the y-axis. The movement of the laser beam and the platform can occur simultaneously or at different times. 
     In an embodiment, the method further comprises determining an amount of heat energy to be applied to the portion of the build surface to achieve the deposition temperature at the drop contact point. The amount of heat energy can be determined based on a number of factors, such as one or more of a geometry of the portion of the build surface, the distance, “X”, that the portion of the build surface being radiated is from the platform  112  ( FIG. 4 ), the temperature of the platform and the temperature of the portion of the build surface being radiated. The laser beam can then be controlled based on the amount of heat energy to be applied to the portion of the build surface. For example, the length of time the portion of the build surface is radiated can decreased or increased to provide the desired temperature at the drop contact point. 
     The build surface can be radiated with the laser to the desired temperature prior to deposition of the drop contact point. It may sometimes be desirable to continue heating the drop contact point for a period of time after the drop is deposited thereon. In an embodiment, application of laser irradiance occurs just before and during the deposition of drop to provide for good coalescence of the drop with the previously deposited layer of the part. In an alternative embodiment, the heating of the build surface at the drop contact point with the laser may stop prior to the drop being deposited on the drop contact point. 
     Conductive Liquid Three-Dimensional Printing System 
     An embodiment of the present disclosure is directed to a conductive liquid three-dimensional printing system that can be used to carry out the three-dimensional printing method described herein. The system comprises a platform and a printhead for ejecting drops of a conductive liquid print material at drop contact points on the platform. A laser is configured to direct a laser beam at the drop contact points. 
       FIG. 2  illustrates an example of a conductive liquid three-dimensional printing system, referred to herein as a liquid metal 3D printer  100 . Drops of liquid metal that are used to form a three-dimensional metal object are produced by a printhead  102  supported by a tower  104 . The printhead  102  is affixed to vertical z-axis tracks  106   a  and  106   b  and can be vertically adjusted, represented as movement along a z-axis, on tower  104 . Tower  104  is supported by a frame  108  manufactured, for example, from steel tubing or any other suitable material. 
     Proximate to frame  108  is a base  110 , formed of, for example, granite or other suitable material. Base  110  supports a platform  112  upon which a 3D object is formed. Platform  112  is supported by x-axis tracks  114   a  and  114   b , which enable platform  112  to move along an x-axis. X-axis tracks  114   a  and  114   b  are affixed to a stage  116 . Stage  116  is supported by y-axis tracks  118   a  and  118   b , which enable stage  116  to move along a y-axis. 
     As drops of molten metal (e.g., molten aluminum)  120  fall onto platform  112 , the programmed horizontal movement of platform  112  along the x and y axes results in the formation of a three-dimensional object. The programmed movement of stage  116  and platform  112  along x-axis tracks  114   a  and  114   b , and y-axis tracks  118   a  and  118   b  can be performed by means of, for example, an actuator  122   a  and  122   b , as would be known to a person of ordinary skill in the art. Liquid metal 3D printer  100  was designed to be operated in a vertical orientation but other orientations could also be employed. 
       FIG. 2  also shows a source of aluminum  132  and aluminum wire  130 . Alternative embodiments may utilize aluminum in bar, rod, granular or additional forms. In alternative embodiments, any sufficiently conductive liquid or colloidal mixture could be used in place of aluminum with the proper adjustments to the system, as would be understood by one of ordinary skill in the art. 
     Printhead  102  includes a nozzle pump  300  and a laser  124 . For example, as illustrated in  FIG. 2 , laser  124  can be disposed within the printhead  102  and configured in a manner that allows a laser beam  125  to travel through an orifice  128  and radiate the build surface (e.g. platform  112  or the three-dimensional part being fabricated thereon). Liquid metal 3D printer  100  and the method of operating the printer are described in greater detail in U.S. Pat. No. 9,616,494, the disclosure of which is incorporated herein by reference in its entirety. 
     The laser can be any suitable type of laser that can achieve the desired irradiance. The irradiance can vary depending on, for example, the type of metal being deposited and the deposition rate. Generally speaking, the faster the drops are ejected onto the build surface the higher the desired irradiance. Examples of desired irradiance ranges are from about 1000 W/cm 2  to about 10,000 W/cm 2 , such as about 1500 W/cm 2  to about 5,000 W/cm 2 , or about 2000 W/cm 2  to about 3,000 W/cm 2 . In an example, the laser can provide a laser beam having an irradiance of 1800 W/cm 2  or more, such as 2000 W/cm 2  or more. A laser having any combination of power and optical configuration, including collimated and non-collimated lasers, that can achieve the desired irradiance can be employed. 
       FIG. 3  shows an exploded view of certain internal components of printhead  102 , including nozzle pump  300 . An upper pump housing  210 , pump partition  204 , and lower pump housing  214  together form a first chamber, herein referred to as a pump chamber  220 . The internal components shown in  FIG. 3  are manufactured from a non-conductive material, such as, for example, boron nitride. 
       FIG. 4  illustrates internal components of printhead  102  assembled. Upper pump housing  210 , pump partition  204  (shown in  FIG. 3 ), and lower pump housing  214  are assembled together to form nozzle pump  300 . 
       FIG. 5  is a cross-sectional view taken along line  5  of  FIG. 4 , including the assembled components of nozzle pump  300 .  FIG. 5  shows a channel  404  extending from a first end where aluminum wire  130  enters printhead  102  and a second end where liquid aluminum leaves channel  404  and enters pump chamber  220 . Pump chamber  220  is adjacent to nozzle  410 . Surrounding channel  404  is a tundish  402 . 
       FIG. 6  illustrates a cross-sectional view of a portion of printhead  102 , which includes a cooled wire inlet  608 , an outer sleeve  606 , and the nozzle pump  300  enclosed by electromagnetic coil  510 . In an embodiment, aluminum wire  130  is fed into cooled wire inlet  608  and a wire guide and gas seal  610  made of copper. The aluminum wire  130  then passes through an insulating coupler  604 , made, for example, of Macor ceramic, where inert gas  142  is supplied through the melt shield gas inlet port  602 , also made of, for example, Macor ceramic, to apply a protective inert gas  142  shield before the aluminum is melted. 
     Melted aluminum, or other electrically conductive liquid, flows downward under gravity and positive pressure exerted by inert gas  142  along a longitudinal z-axis to nozzle pump  300 . Electrical heating elements  620   a  and  620   b , made of, for example, nichrome, heat the interior of a furnace  618 , made of, for example, firebrick, to above the 660° C., which is the melting point of aluminum. The thermally conductive tundish  402  transmits heat to aluminum wire  130 , as supplied from a source of aluminum  132 , causing it to melt as it enters nozzle pump  300 . Tundish  402  can comprise, for example, boron nitride or other suitable thermally conductive material. 
       FIG. 7  shows molten aluminum flowing downward through upper pump housing  210  around pump partition  204  to form a charge of molten aluminum  710 . Charge of molten aluminum  710  is contained primarily within the pump chamber  220 , with a small amount of the molten aluminum contained in upper pump housing  210  to keep pump chamber  220  fully primed. An excess of molten aluminum in the upper section of pump chamber  220  would increase the inertia of the charge of molten aluminum  710  and cause an undesirable decrease in the firing rate of nozzle pump  300 . In alternative embodiments the number of dividers in the pump partition  204  may be varied. 
     Electromagnetic coil  510  is shaped to surround nozzle pump  300 . The pressure on the inert gas  142  inside nozzle pump  300  is adjusted to overcome much of the surface tension at the nozzle  410  in order to form a convex meniscus  810 . The pre-pressure within pump chamber  220  prior to a pulse is set by inert gas  142  to create convex meniscus  810  with a spherical cap that is less than the radius of nozzle orifice  440 . This pressure is determined by Young&#39;s law as P=2×surface tension/orifice  440  radius. 
       FIG. 8  is a simplified 3D section through nozzle pump  300  showing only the electromagnetic coil  510  and the charge of molten aluminum  710 . Charge of molten aluminum  710  is shown at an appropriate level in pump chamber  220  for operation. The shape of the upstream portion of charge of molten aluminum  710  conforms to pump partition  204  and partition dividers  206 . 
       FIG. 8  further shows electromagnetic coil  510  shaped around nozzle pump  300  in such a way as to focus magnetic field lines  940  vertically through the charge of molten aluminum  710 . Nozzle pump  300  is transparent to the magnetic field. The electromagnetic coil  510  applies forces to the charge of molten aluminum  710  to pump liquid metal based on the principles of magnetohydrodynamics. A step function direct current (DC) voltage profile applied to the electromagnetic coil  510  causes a rapidly increasing applied current  900  to electromagnetic coil  510 , thereby creating an increasing magnetic field that follows the magnetic field lines  940 . The optimal range of voltage for the pulse and current strength, as well as the range of time durations for the pulse, for effective operation vary depending on the electrical resistivity of the fluid, viscosity and surface tension. The possible effective range is wide, where alternative embodiments could optimally range from 10 to 1000 volts (V) and 10 to 1000 amperes (A). 
     According to Faraday&#39;s law of induction, the increasing magnetic field causes an electromotive force within the pump chamber  220  which in turn causes an induced current  930  in molten aluminum  710  to flow along circular paths through the charge of molten aluminum  710 . The induced current  930  in molten aluminum  710  and the magnetic field produce a resulting radially inward force  920  on molten aluminum, known as a Lorenz force, in a ring shaped element through the charge of molten aluminum  710 . The radially inward force on molten aluminum  920  is proportional to the square of the DC voltage applied. 
     A peak pressure occurring at the inlet to the nozzle  410  is also proportional to the square of the DC voltage applied. This pressure overcomes surface tension and inertia in the molten aluminum to expel the drop of molten aluminum. At the same time, the computer causes stage  116  to move to deposit the drop of molten aluminum in the desired location on platform  112 . 
     In alternative embodiments of the present invention, the shape of the nozzle may be varied to achieve a smooth inlet bell. In one embodiment, an efficient intrinsic electromagnetic heating mode is possible by pulsing the electromagnetic coil at approximately 20 us, 300 amps and 1500 Hz. This creates sufficient heat to maintain the housing and aluminum at 750 C thereby melting the aluminum. The heat is created through resistive losses in the electromagnetic coil and inductive heating within the aluminum. Use of this heating mode eliminates the need for any external heating system. 
       FIG. 9  illustrates nozzle pump  300  producing a drop of molten aluminum  120  during formation of a 3D printed object  1100  on platform  112 . The 3D printed object  1100  is the location to which molten metal droplets are directed from nozzle  410 . As each drop of molten aluminum  120  is deposited, it solidifies, thereby increasing the volume of 3D printed object  1100 . The proper orientation of 3D printed object  1100  is maintained by computer programs that control and coordinate the movement of platform  112 . 
     EXAMPLES 
     A thermocouple was buried roughly at the center within an aluminum part having a volume of about 500 mm 3 . The part was made by 3D printing using a conductive liquid three-dimensional build system similar to that shown in  FIG. 2 . A surface of the part was pre-heated using a 150 W 976 nm Fiber-Couple Laser Diode, targeting the surface with the emitted laser beam at an acute angle of about 30° relative to the build surface. The laser beam had a 3 mm diameter and an irradiance level of ˜2000 W/cm 2 . 
     The temperature of the 3D printed metal part was recorded with time and the results are shown in the graph of  FIG. 11 . The two curves in the  FIG. 11  plot are the measured temperature results from two different sides of the part. A smooth side, which has relatively good coalescence and a build side, which has relatively poor coalescence. The results indicate that even a relatively low power laser can effectively heat an aluminum part. Heating time of the part may be reduced significantly by optimization of, for example, laser type, power, beam diameter, and angle can be adjusted optimize energy transfer. 
     Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Moreover, all ranges disclosed herein are to be understood to encompass any and all sub-ranges subsumed therein. 
     While the present teachings have been illustrated with respect to one or more implementations, alterations and/or modifications can be made to the illustrated examples without departing from the spirit and scope of the appended claims. In addition, while a particular feature of the present teachings may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular function. Furthermore, to the extent that the terms “including,” “includes,” “having,” “has,” “with,” or variants thereof are used in either the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” Further, in the discussion and claims herein, the term “about” indicates that the value listed may be somewhat altered, as long as the alteration does not result in nonconformance of the process or structure to the illustrated embodiment. Finally, “exemplary” indicates the description is used as an example, rather than implying that it is an ideal. 
     It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompasses by the following claims.