Abstract:
A system and method for adjusting the gap between a horn and an anvil in an ultrasonic welding system includes the act of positioning a horn proximal to an anvil, so that a gap is established between the horn and the anvil. A force is applied to the horn, so as to urge the horn toward the anvil. A deformable stop is positioned at a location, such that application of the urging force causes a member operatively connected to the horn to abut the deformable stop, and to deform the stop. The urging force is iteratively adjusted during operation of the horn, so as to adjust the extent of the deformation of the deformable stop, and to maintain the gap between the horn and the anvil substantially constant.

Description:
RELATED APPLICATIONS  
       [0001]     This application claims priority from provisional application Ser. No. 60/640,978, entitled “FREQUENCY BASED CONTROL OF AN ULTRASONIC WELDING SYSTEM,” filed Jan. 3, 2005, and from provisional application Ser. No. 60/641,048, entitled “GAP ADJUSTMENT FOR AN ULTRASONIC WELDING SYSTEM”, filed Jan. 3, 2005, both of which are incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates to a method and system for determining a gap between a vibrational body and a fixed point, and more particularly to a system and method arriving at such a determination based upon the resonant frequency of the vibrational body.  
       BACKGROUND  
       [0003]     In ultrasonic welding (sometimes referred to as “acoustic welding” or “sonic welding”), two parts to be joined (typically thermoplastic parts) are placed proximate a tool called an ultrasonic “horn” for delivering vibratory energy. These parts (or “workpieces”) are constrained between the horn and an anvil. Oftentimes, the horn is positioned vertically above the workpiece and the anvil. The horn vibrates, typically at 20,000 Hz to 40,000 Hz, transferring energy, typically in the form of frictional heat, under pressure, to the parts. Due to the frictional heat and pressure, a portion of at least one of the parts softens or is melted, thus joining the parts.  
         [0004]     During the welding process, an alternating current (AC) signal is supplied to a horn stack, which includes a converter, booster, and horn. The converter (also referred to as a “transducer”) receives the AC signal and responds thereto by compressing and expanding at a frequency equal to that of the AC signal. Therefore, acoustic waves travel through the converter to the booster. As the acoustic wavefront propagates through the booster, it is amplified, and is received by the horn. Finally, the wavefront propagates through the horn, and is imparted upon the workpieces, thereby welding them together, as previously described.  
         [0005]     Another type of ultrasonic welding is “continuous ultrasonic welding”. This type of ultrasonic welding is typically used for sealing fabrics and films, or other “web” workpieces, which can be fed through the welding apparatus in a generally continuous manner. In continuous welding, the ultrasonic horn is typically stationary and the part to be welded is moved beneath it. One type of continuous ultrasonic welding uses a rotationally fixed bar horn and a rotating anvil. The workpiece is fed between the bar horn and the anvil. The horn typically extends longitudinally towards the workpiece and the vibrations travel axially along the horn into the workpiece. In another type of continuous ultrasonic welding, the horn is a rotary type, which is cylindrical and rotates about a longitudinal axis. The input vibration is in the axial direction of the horn and the output vibration is in the radial direction of the horn. The horn is placed close to an anvil, which typically is also able to rotate so that the workpiece to be welded passes between the cylindrical surfaces at a linear velocity, which substantially equals the tangential velocity of the cylindrical surfaces. This type of ultrasonic welding system is described in U.S. Pat. No. 5,976,316, incorporated by reference in its entirety herein.  
         [0006]     In each of the above-described ultrasonic welding techniques, the workpieces to be joined are disposed between the horn and the anvil, during the welding process. One way to weld is by fixing a gap between the horn and the anvil. The gap between the horn and anvil creates a pinching force that holds the workpieces in place while they are being joined. For the sake of yielding a uniform and reliable welding operation, it is desirable to maintain a constant gap between the horn and the anvil.  
         [0007]     During operation, one or more components of the horn stack, including the horn, itself, generally experience an elevation in temperature. Thus, the horn stack generally experiences thermal expansion. As the horn stack expands, the gap between the horn and the anvil is decreased—a result inimical to the aforementioned goal of yielding a uniform and reliable welding operation.  
         [0008]     As the foregoing suggests, presently existing ultrasonic welding schemes exhibit a shortcoming, in that the gap between the horn stack and the anvil grows narrower, during successive welding operations.  
       SUMMARY OF THE INVENTION  
       [0009]     Against this backdrop, the present invention was developed. A method includes positioning a horn proximal to an anvil, so that a gap is established between the horn and the anvil. A force is applied to the horn, so as to urge the horn toward the anvil. A deformable stop is positioned at a location, such that application of the urging force causes a member operatively connected to the horn to abut the deformable stop, and to deform the stop. The urging force is iteratively adjusted during operation of the horn, so as to adjust the extent of the deformation of the deformable stop, and to maintain the gap between the horn and the anvil substantially constant.  
         [0010]     According to another embodiment, a system includes a mount including a translation member and a fixed elastic deformable stop. A horn is coupled to a source of ulstrasonic energy. The horn is operatively connected to the translating member. An anvil is separated from the horn by a gap. A force applicator is configured to urge the horn toward the anvil, and to cause a member operatively coupled to the horn to contact and deform the elastic deformable stop by varying degrees, so that the gap between the horn and the anvil remains substantially constant during operation of the system.  
         [0011]     According to yet another embodiment, a system includes a horn separated from an anvil by a mounting system. A source of ultrasonic energy is coupled to the horn. The system also includes a means for substantially maintaining the separation at a constant length, while the horn experiences thermal expansion. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  depicts an embodiment of a simple ultrasonic welding horn stack coupled to an energy source.  
         [0013]      FIG. 2  depicts an embodiment of a mounting system coupled to the ultrasonic welding horn stack of  FIG. 1 .  
         [0014]      FIG. 3  depicts an embodiment of a system for determining a length of a gap between a horn and an anvil.  
         [0015]      FIG. 4A  depicts an exemplary embodiment of a table that may be used as a part of a gap-determining unit.  
         [0016]      FIG. 4B  depicts an exemplary embodiment of a method of determining a gap length.  
         [0017]      FIG. 5A  depicts an embodiment of a simple rotary ultrasonic welding horn for use in a continuous ultrasonic welding operation.  
         [0018]      FIG. 5B  depicts an exemplary embodiment of a method of determining a gap length.  
         [0019]      FIG. 6  depicts an exemplary embodiment of a system for maintaining a substantially constant gap between a welding horn and an anvil.  
         [0020]      FIG. 7  depicts an exemplary embodiment of a system for adjusting a gap between a horn and an anvil in an ultrasonic welding system.  
         [0021]      FIG. 8A  depicts an exemplary embodiment of a system for maintaining a susbtantially constant gap between a horn and an anvil in an ultrasonic welding system.  
         [0022]      FIG. 8B  depicts another exemplary embodiment of a system for maintaining a susbtantially constant gap between a horn and an anvil in an ultrasonic welding system.  
         [0023]      FIG. 9A  depicts an exemplary embodiment of a force-determining unit.  
         [0024]      FIG. 9B  depicts another exemplary embodiment of a force-determining unit.  
         [0025]      FIG. 10  depicts an exemplary embodiment of a system for adjusting a gap between a horn and an anvil in an ultrasonic welding system.  
         [0026]      FIG. 11A  depicts the surface of a horn driven by an acoustic signal propagating along the longitudinal axis of the horn.  
         [0027]      FIG. 11B  depicts the surface of a horn driven by an acoustic signal of smaller magnitude than that of  FIG. 11A , as that signal propagates along the longitudinal axis of the horn.  
         [0028]      FIG. 12A  depicts an exemplary embodiment of a system for controlling the gap between a horn and an anvil.  
         [0029]      FIG. 12B  depicts another exemplary embodiment of a system for controlling the gap between a horn and an anvil.  
         [0030]      FIG. 13  depicts an exemplary embodiment of a method for combining the operations of an adjustor and an amplitude determination module.  
         [0031]      FIG. 14  depicts another exemplary embodiment of a method for combining the operations of an adjustor and an amplitude determination module. 
     
    
     DETAILED DESCRIPTION  
       [0032]     Various embodiments of the present invention will be described in detail with reference to the drawings, wherein like reference numerals represent like parts and assemblies throughout the several views. Reference to various embodiments does not limit the scope of the invention, which is limited only by the scope of the claims attached hereto. Additionally, any examples set forth in this specification are not intended to be limiting and merely set forth some of the many possible embodiments for the claimed invention.  
         [0033]      FIG. 1  depicts an example of a simple horn stack  100  that is coupled to an AC source of electrical energy  102 . As can be seen from  FIG. 1 , the horn stack  100  includes a converter  104 , a booster  106 , and an ultrasonic welding horn  108 . During operation, the AC source supplies electrical energy to the converter  104 , which responds thereto by compressing and expanding at a frequency equal to that of the AC signal. Therefore, acoustic waves travel through the converter  104  to the booster  106 . As the acoustic wavefront propagates through the booster  106 , it is amplified, and is received by the welding horn  108 . (In some embodiments, the horn  108  is designed to achieve a gain, eliminating the need for a booster  106 .) Finally, the wavefront propagates through the horn  108 , whereupon it is imparted to workpieces (not depicted in  FIG. 1 ) that are positioned between the welding horn  108  and an anvil  110 . Other examples of horn stacks are known in the art, and function with the following systems, schemes, and methods disclosed herein.  
         [0034]     The horn  108  is separated from the anvil  110  by a distance labeled “Gap” in  FIG. 1 . The process of imparting frictional energy to the workpieces causes the various elements of the horn stack  100  to elevate in temperature. As the elements of the horn stack  100  elevate in temperature, they exhibit thermal expansion, meaning that the gap between the horn  108  and the anvil  110  is likely to change in dimension, depending upon the particular manner in which the horn stack  100  is mounted.  
         [0035]      FIG. 2  depicts a simplified exemplary mounting scheme for the horn stack  100  of  FIG. 1 . The mounting scheme makes use of a rigid, generally tripartite, frame  200 . The frame  200  includes a first portion  202  upon which the anvil  110  is mounted, and a second portion  206  that is adjoined to a nodal point on the horn stack  100 . For example, the second portion  206  of the frame is depicted in  FIG. 2  as being coupled to the midpoint  208  of the booster  106 . A third portion  204  of the frame  200  extends between the first and second portions  202  and  206 .  
         [0036]     The mounting system  200  maintains a substantially fixed distance between a workpiece-supporting surface  210  of the anvil  110  and a portion of the horn stack  100 . In this case, the mounting system  200  maintains a substantially fixed distance between the upper surface  210  of the anvil  110  and the midpoint/nodal point  208  of the booster  106 . Therefore, should the horn stack  100  expand during operation, the horn stack  100  expands outwardly from the midpoint  208  of the booster  106 , along the longitudinal axis of the stack  100 , as indicated by the arrows labeled “Expansion” in  FIG. 2 . It is understood that a variety of other mounting systems may also maintain a substantially fixed distance between the upper surface  210  of the anvil  110  and a portion of the horn stack  100 , and such other mounting systems are within the scope of the present application.  
         [0037]     Given the mounting arrangement of  FIG. 2 , thermal expansion of the converter  104  and upper portion of the booster  106  produces no effect on the gap length (because of the position of these elements relative to the point  208  at which the frame  200  joins the stack  100 , these elements are free to expand upwardly, i.e., away from the anvil  110 ). On the other hand, the gap length is affected by expansion of the lower portion of the booster  106  and by expansion of the horn  108 —as these elements expand, they expand toward the anvil  110 , and the gap contracts.  
         [0038]     According to one embodiment, the converter  104  and booster  106  are maintained at a substantially constant temperature. For example, the converter  104  and booster  106  may be cooled by a cooling system, such as by one or more fans that circulate relatively cool air to the surfaces of the converter  104  and booster  106 , so as to substantially maintain their temperatures, and to thereby substantially suppress their thermal expansion. Therefore, according to such an embodiment, any change in length of the horn stack  100  may be considered as being substantially due to expansion of the welding horn  108 .  
         [0039]     Furthermore, according to some embodiments, the horn  108  is cooled by a cooling system, so as to suppress or reduce its propensity to heat up during operation. Generally, such a scheme does not totally eliminate thermal expansion of the horn  108 , meaning that it still exhibits some degree of thermal expansion, which should be accounted for, if the gap length is to be maintained substantially constant.  
         [0040]     It is known that the length of a given body is inversely proportional to the given body&#39;s resonant frequency. Stated another way, as a body grows in length, it exhibits a lower resonant frequency. Therefore, as the horn stack  100  grows in length, as occurs, for example, by virtue of thermal expansion, it exhibits a lower resonant frequency. Specifically, the length of a body, l, is related to its resonant frequency, f by the following equation:  
         l   ≈         E   /   ρ         2   ⁢   f         ,       
 
 where E represents the modulus of elasticity of the object, and where ρ represents the density of the object. If the object is compound (e.g., is made up of multiple parts or has various sections made from different materials, etc.), E and ρ may be assigned values representing the behavior of the materials, considering its various parts (e.g., may be a weighted average, etc.). 
 
         [0041]     According to some embodiments, the energy source  102  detects the resonant frequency, f, of the horn stack  100 , in order to generate an AC signal equal in frequency thereto. For example, the energy source  102  may deliver a sinusiodal signal exhibiting a particular peak-to-peak voltage (or root-mean-square voltage) to the horn stack  100 . While keeping the peak-to-peak (or RMS) voltage of the sinusoidal signal constant, the energy source  102  adjusts the frequency of the signal, and seeks out the frequency at which the least current is drawn by the horn stack  100 —this frequency is the resonant frequency of the horn stack  100 . Accordingly, per such embodiments, the resonant frequency of the stack  100  may be obtained from the energy source  102 . According to other embodiments, the resonant frequency of the stack  100  may be detected by observation of the stack  100  with a detector.  
         [0042]     Upon obtaining the resonant frequency of the horn stack  100 , the overall length of the stack  100  may be obtained by relating, in a manner similar to the aforementioned physical principles, resonant frequency to horn stack length. Given that the converter  104  and booster  106  are cooled, so as to substantially suppress the effects of thermal expansion thereupon, the length of the horn stack  100  can be related to the gap length. For example, according to the scheme of  FIG. 2 , the gap length and the length of the horn  108 , l, are related by the following equation: 
 
gap length≈ D−l,  
 
 where D is an approximately constant value that represents the length between the top of the horn  108  and the workpiece-supporting surface  210  of the anvil  110 . 
 
         [0043]      FIG. 3  depicts a system for determining the length of the gap between a welding horn  108  and the workpiece-supporting surface  210  of the anvil  110 . The system of  FIG. 3  includes an ultrasonic power supply  300  (e.g., an electrical power supply that delivers an AC signal to converter, which, in turn, transduces the signal into an acoustic wave) that delivers an acoustic signal to a horn (and booster)  302 . The ultrasonic power supply  300  is controlled by a controller circuit, such as by a processor in data communication with a memory device that stores firmware/software controlling the operation of the ultrasonic power supply  300 . Alternatively, the controller circuit may be embodied as a hardware-based control loop. In either event, the controller of the ultrasonic power supply  300  identifies the resonant frequency of the horn stack, and commands power supply signal generation circuitry therein to cooperate with the converter to yield an acoustic signal equal in frequency thereto. The controller within the power supply  300  may interface to a gap-determining unit  304 .  
         [0044]     The gap-determining unit  304  receives the resonant frequency of the horn stack, and generates a quantity standing in known relation to the gap length. According to one embodiment, the gap-determining unit  304  is a software module executing upon a processor coupled to a memory unit. The gap-determining unit  304  may execute upon the same processor upon which the firmware controlling the ultrasonic power supply  300  executes. Alternatively, it may execute upon a different processor that is in data communication therewith. In either event, the software/firmware executed by the gap-determining unit  304  may function according to the schemes (below) discussed with reference to  FIGS. 4A-5B .  
         [0045]     According to an alternative embodiment, the gap-determining unit  304  may receive the resonant frequency of the horn stack from a source other than the ultrasonic power supply  300 . For example, the system may include a detector  306  that observes the horn stack, measures the resonant frequency thereof, and communicates the resonant frequency to the gap-determining unit  304 . In the discussion that follows, it is assumed that the resonant frequency originates from the ultrasonic power supply  300 , for the sake of example only.  
         [0046]      FIG. 4A  depicts a scheme by which the gap-determining unit  304  may operate. The gap-determining unit  304  may include a table  400  stored in a memory device. The table  400  is organized according to resonant frequency, and relates a gap length G to a resonant frequency, f. Thus, upon receiving a resonant frequency, f, the gap-determining unit  304  uses the resonant frequency to access the table  400 , and to determine a gap length G corresponding to the resonant frequency, f. For example, assuming that the gap-determining unit  304  receives a frequency of f 2  as an input, the unit  304  responds by accessing the table  400  to identify a row corresponding to frequency f 2 . Upon identification of the row, the gap length entered therein, G 2 , is returned. Optionally, the table  400  may be accessed to determine the length of the horn stack  100 , L, or to determine any other quantity standing in known relation to the gap length. Assuming that the gap-determining unit  304  receives a value f x  as an input, and assuming that f x  falls between successive table entries (i.e., f i &lt;f x &lt;f i+1 ), then the gap-determining unit  304  may access the table  400  to obtain gap length values G i  and G i+1 , and may interpolate between the two values to arrive at a gap length corresponding to the resonant frequency, f x .  
         [0047]     The various entries in the table  400  may be populated ex ante by a heuristic process, in which the length of the horn stack  100  and the length of the gap are recorded for each frequency, f, within the table  400 . Alternatively, the various entries in the table  400  may be populated by theoretical calculation, in a manner similar to that described above.  
         [0048]      FIG. 4B  depicts another scheme by which the gap-determining unit  304  may operate, theoretical computation. For example, the gap-determining unit  304  may begin its operation by receiving the resonant frequency of the horn stack  100 , f, as shown in operation  402 . Thereafter, the unit  304  responds by calculating the length of the horn  108 , L, based upon the resonant frequency, such as by use of an equation based upon the physical principles underlying the equation shown in operation  404 . Finally, as shown in operation  406 , the unit  304  may relate the length, L, determined in operation  404 , to a gap length, based upon knowledge of the particular geometric constraints arising from the mounting scheme employed. For example, in the context of the the mounting scheme of  FIG. 2 , the gap length may be found as: 
 Gap Length= D−L,    
 where D represents the distance between the top of the horn  108  and the workpiece-supporting surface  210  of the anvil  110 , and L represents the length of the horn. 
 
         [0049]      FIG. 5A  depicts an example of a welding horn  500  that is used for continuous ultrasonic welding. The horn  500  therein includes a longitudinal axis  502  about which the horn  500  may rotate. The horn  500  is constrained by a mounting system (not depicted in  FIG. 5A ), so that a gap is maintained between the horn and the anvil  504 . The horn stack may be mounted at any nodal point on the system. The longitudinal axis  502  of the horn is substantially parallel to the workpiece-supporting surface  506  of the anvil  504 .  
         [0050]     The aforementioned principle of determining the length of the gap between a horn and an anvil based upon the resonant frequency of the horn stack is applicable to the horn  500  of  FIG. 5 . As materials expand thermally, they do so in equal proportions in all directions. Therefore, the following technique, depicted in  FIG. 5B , may be used to determine the length of the gap between the horn and the anvil.  
         [0051]     Initially, as shown in operation  508 , the resonant frequency of the horn stack is received. Thereafter, the length of the horn  502 , L, is determined based upon the frequency, in like manner as described above (operation  510 ). As before, the horn stack of  FIG. 5A  is cooled so that the converter (not depicted in  FIG. 5A ) and booster (not depicted in  FIG. 5A ) remain at substantially constant temperatures during operation, thereby suppressing their thermal expansion and the effects on the system resonant frequency.  
         [0052]     Since the horn  500  expands proportionally in all dimensions, the ratio between its length, L, and its radius, B, remains constant. Therefore, after calculation of the length of the horn  502 , its radius may be arrived at by multiplication of the length by the aforementioned ratio, B, as shown in operation  512 . Finally, the length of the gap may be determined by subtracting the radius from the distance, D, between the longitudinal axis of the horn  500  and workpiece-supporting surface  506  of the anvil  504 , as shown in operation  514 .  
         [0053]     It should be noted that the results of the method described with respect to  FIG. 5B  may be stored within a table, as described with reference to  FIG. 4A . Thus, the gap length, or any value standing in known relation thereto, may be obtained by virtue of accessing such a table, based upon the resonant frequency of the horn stack.  
         [0054]      FIG. 6  depicts a control system for maintaining a substantially constant gap between a horn and an anvil, based upon observation of the resonant frequency of the horn stack. The system includes a horn stack  600  and a power supply  602  coupled thereto. According to one embodiment, the power supply  602  determines the resonant frequency of the horn stack  600 , as described above.  
         [0055]     Coupled to the horn stack is a position adjustor  606 . The position adjustor  606  adjusts the horn stack  600 , either toward or away from the anvil, under the control of an input signal. A known relationship exists between the input signal delivered to the adjustor  606  and its response thereto. The position adjustor  606  is in data communication with a control signal generator  604 . The control signal generator  604  receives the resonant frequency of the horn stack as an input, and generates a control signal that is delivered to the position adjustor  606 . The control signal generator  604  yields a control signal that maintains a substantially constant gap between the anvil and the horn, given the resonant frequency of the horn stack  600  and the relationship between the response of the position adjustor  606  and its input signal.  
         [0056]     The control signal generator  604  may be embodied as a controller circuit, such as a processor in data communication with a memory device that stores firmware/software in accordance with the aforementioned principles. It may alternatively be embodied as an ASIC yielding the aforementioned control signal so as to maintain a substantially constant gap. In the following portion of the disclosure, a particular embodiment of a position adjustor is disclosed. It is not necessary to use the position adjustor disclosed below for practice of the invention. Also, the preceding portion of the specification was directed toward particular methods of determining the length of a horn or the length of a gap, based upon the resonant frequency of the horn stack. According to other embodiments, such determinations may be arrived at by measurement of the temperature of the horn stack, or of its various components.  
         [0057]      FIG. 7  depicts an exemplary embodiment of a system for adjusting the gap between a horn and an anvil. The system therein includes a horn  700  oriented above a workpiece-supporting surface  702  of an anvil  704 . The horn  700  is rigidly coupled to a frame  706 . The frame  706  includes a slide  708  that engages a receiver  710 , so that the frame  706  and horn  700  may translate vertically.  
         [0058]     The frame  706  also includes a force-receiving plate  712  that is coupled to the frame  706  by a pair of members  714 . A force is applied to the force-receiving plate  712  by a force applicator (not depicted in  FIG. 7 ). The force urges the horn  700  toward the anvil  704 . The direction of the force is indicated by the arrow  713 . The force has the effect of causing a contact surface  716  to abut an elastic deformable stop  718 . The force exerted upon the elastic deformable stop  718  causes the stop  718  to deform, and to thereby exhibit a downward deflection (i.e., a deflection in the direction of the anvil  704 ). Generally, the greater the force applied to the plate  712 , the greater the downward deflection exhibited by the stop  718 . The greater the deflection exhibited by the stop  718 , the smaller the gap between the horn  700  and the anvil  704 .  
         [0059]     To maintain a constant gap between the horn  700  and the anvil  704 , the following scheme may be employed. While the horn  700  is at its unelevated temperature, an initial force is applied to the plate  712 , to cause the gap between the horn  700  and the anvil  704  to be established at an “ideal” length. As the horn  700  thermally expands during operation, the gap grows smaller. To counteract this effect, the force applied to the plate  712  is reduced, causing the stop  718  to exhibit a lesser deflection, meaning that the horn  700  and frame are translated upwardly (i.e., away from the anvil). Thus, the gap between the horn  700  and the anvil  704  may be maintained substantially constant by controlled application of force to the plate  712 . To ensure the functionality of this scheme the initial force applied to the plate  712  should be of sufficient magnitude to cause the stop  718  to exhibit a deflection at least as great in extent as the expected thermal expansion to be counteracted.  
         [0060]     The deformable stop  714  is elastic, and preferably has a relatively high modulus of elasticity. By selection of a material having a relatively high modulus of elasticity, a circumstance is set up in which the force required to deflect the stop  714  is relatively great compared to the process force (i.e., the force exerted by the horn on the workpiece). Such an arrangement provides for ease of control design. According to one embodiment, the stop  714  may be made of steel, or another suitable material. According to one embodiment, the force exerted upon the stop  714  does not cause the material therein to exit its elastic range (i.e., the stop  714  will return to its original shape upon withdrawal of the force). Further, according to one embodiment, the stop  714  exhibits a deflection that is proportional to the force applied thereto, i.e., there exists a linear relationship between the force applied to the stop  714  and the extent of deflection exhibited thereby.  
         [0061]      FIG. 8A  depicts an example of a control system for use with the exemplary adjustment system of  FIG. 7 . (The various units  804 - 810  of  FIG. 8A , dicussed below, may be embodied as software modules stored in a computer-readable medium and executed by a processor, or may be embodied as dedicated hardware, such as one or more application-specific integrated circuits, or as a field-programmable gate array. Further, the units  804 - 810  may be combined or divided as a matter of design choice.) As can be seen from  FIG. 8A , the system includes a horn  800  that is coupled to a source of ultrasonic power  802 . A gap-determining unit  804  determines the gap between the horn  800  and an anvil (not depicted in  FIG. 8 ). According to one embodiment, the gap-determining unit  804  obtains the resonant frequency of the horn stack from the power source  802 , and determines the gap therefrom. According to another embodiment, the gap-determining unit  804  detects the resonant frequency of the horn  800  by observation thereof. According to yet another embodiment, the gap determining unit  804  arrives at the gap length by measurement of the temperature of the horn, inferring horn length therefrom, and arriving at the gap length on the basis of the horn length.  
         [0062]     The gap length arrived at by the gap-determining unit is supplied to a force-determining unit  806 . The force-determining unit  806  determines the force to be exerted upon the frame (e.g., plate  712  in  FIG. 7 ), in order to maintain the gap at a substantially constant length. The force arrived at by the gap-determining unit  806  is supplied to a control signal generator  808 . The control signal generator  808  develops a control signal, and communicates that control signal to a force applicator  810 . The force applicator  810  exhibits a known relationship between the received control signal and the force it exerts. Thus, the control signal generator  808  develops the control signal in light of that relationship.  
         [0063]      FIG. 8B  depicts exemplary embodiments of the gap determining unit  804  and force determining unit  806 . (As was the case with the units of  FIG. 8A , the various units of  FIG. 8B , dicussed below, may be embodied as software modules stored in a computer-readable medium and executed by a processor, or may be embodied as dedicated hardware, such as one or more application-specific integrated circuits, or as a field-programmable gate array. Further, the units of  FIG. 8B  may be combined or divided as a matter of design choice.) As can be seen from  FIG. 8B , the gap determining unit  804  includes a length determining unit  812  and a gap finding unit  814 . The length determining unit  812  receives the resonant frequency of the horn stack, and applies one of the methods described with reference to  FIGS. 4A and 4B  to find the length of the horn. Thereafter, the length of the horn is received by the gap finding unit  814 . The gap finding unit  814  arrives at the gap length, by virtue of knowledge of the length of the horn and the particular geometry imposed by the mounting scheme (e.g., the gap length may be equal to the difference between the length from the top of the horn to the workpiece-supporting surface and the horn length, Gap=D−L).  
         [0064]     After arrival at the gap length, this value is provided to the force-determining unit  806 . The force-determining unit  806  arrives at the force to be applied to the frame, in order to keep the gap substantially constant. The force arrived at is a function of, amongst other things, the length of the stop, L stop , the modulus of elasticity of the stop, E, the cross-sectional area of the stop, A, the difference between the initial gap length and the gap length as arrived at by the gap determining unit  804 , Δ, and the assembled system deflection.  
         [0065]      FIG. 9A  depicts a scheme by which the force-determining unit  806  may operate. The force-determining unit  806  may include a table  900  stored in a memory device. The table  900  is organized according to resonant gap length, G, and relates a force F to a gap length, G. Thus, upon receiving a gap length, G, the force-determining unit  806  uses the gap length to access the table  900 , and to determine a force F corresponding to the gap length, G. For example, assuming that the force-determining unit  806  receives a gap length of G 2  as an input, the unit  806  responds by accessing the table  900  to identify a row corresponding to gap length G 2 . Upon identification of the row, the force entered therein, F 2 , is returned. Optionally, the table  900  may be accessed to determine the control signal, C, to be delivered to the force applicator  810 , or to determine any other quantity standing in known relation to the force to be exerted on the frame. Assuming that the force-determining unit  806  receives a value G x  as an input, and assuming that G x  falls between successive table entries (i.e., G i &lt;G x &lt;G i+1 ), then the force-determining unit  806  may access the table  900  to obtain force values F i  and F i+1 , and may interpolate between the two values to arrive at a force corresponding to the gap length, G x .  
         [0066]     The various entries in the table  900  may be populated ex ante by a heuristic process, in which the force to be applied to the frame and the control signal corresponding thereto are expirementally determined for each gap length, G, within the table  900 . Alternatively, the various entries in the table  900  may be populated by theoretical calculation, in a manner similar to that described below with reference to  FIG. 9B .  
         [0067]      FIG. 9B  depicts another scheme by which the force-determining unit  806  may operate, theoretical computation. For example, the force-determining unit  806  may begin its operation by receiving the gap length calculated by the gap determining unit  804 , CG, as shown in operation  902 . Thereafter, the unit  806  responds by calculating the difference between the initial gap, IG, and the calculated gap, CG, as shown in operation  904 . This difference, Δ, refers to the amount by which the deflection of the stop must be reduced in order to return the gap to its initial length. Thus, in operation  906 , the new force to be applied to the frame, F new , may be arrived at by solving for F new  in the equation shown therein.  
         [0068]      FIG. 10  depicts another exemplary embodiment of a system for adjusting the gap between a horn and an anvil. Welding system  1010  has a welding system  1030  fixed to support surface  1017  and an anvil  1021  fixed to support surface  1018 . Welding system  1030  includes horn  1032 , which is supported by horn support  1020  and is moveable in relation to surface  1017 , a fixed stop  1055  having support plate  1056 , which are fixed in relation to surface  1017 , and an expandable pneumatic bladder  1061 .  
         [0069]     Bladder  1061  is used to apply the force to move horn support  1020  and horn  1032  toward anvil  1021 ; the force is controlled by adjusting the air pressure in bladder  1061 . As surface  1025  contacts fixed stop  1055 , support plate  1056  deflects slightly under the applied force.  
         [0070]     In one specific example, the minimum allowable force to weld a desired product is 600 pounds (about 272 kg), which is generated by 30-psig (about 207 kPa) air pressure in bladder  161 . The desired fixed gap is 0.0020 inch (about 0.05 mm).  
         [0071]     In operation with a titanium horn, it was determined that the temperature will increase from room temperature by a maximum of 50° F. (about 27.7° C.), which will increase the horn length by 0.0010 inch (about 0.025 mm). As a result, the gap between horn  132  and anvil  121  is reduced to 0.0010 inch (about 0.025 mm), if no compensation is made. The deflection of support plate  156  is known to be 0.0010 inch (about 0.025 mm) per 675 pounds force (about 306 kg-force). Therefore, the applied force with a room temperature horn must be at least 1125 pounds (about 510 kg), or 60 psig (about 414 kPa). As the horn operates and increases in length, the applied air pressure is reduced from 60 psig (about 414 kPa) to 30 psig (about 207 kPa) to keep the gap between horn and anvil constant.  
         [0072]     A welding apparatus, generally configured to control the distance between the anvil and the horn by utilizing a deformable stop assembly, includes an anvil with a fixed stop, a horn, and a force applicator mounted so as to be able to apply force to press the horn against the fixed stop such that elastic deformation of the fixed stop provides fine control over the gap between the horn and the anvil. The apparatus may include a sensing system to monitor a specific property of the horn and control the force applied to the horn so as to hold the gap between the horn and the anvil at a fixed value despite changes in the specific property. The property monitored could be, for example, temperature, length, or vibration frequency of the horn.  
         [0073]     The use of a deformable, yet fixed stop to compensate for the horn length increase, due to thermal expansion, can be used with a rotary anvil, stationary anvil, rotary horn, stationary horn, or any combination thereof.  
         [0074]     In use, the workpieces to be joined would be positioned between the horn and the anvil, energy would be applied to the horn and the horn would be energized, and a force would be applied to the horn to urge the horn against the fixed stop such that elastic deformation of the fixed stop provides fine control of the gap between the horn and the anvil.  
         [0075]     To employ the methods discussed above, one can determine data for a system, and then fit it into equations that can be used in the control system for a particular unit. Applicants have used the following method for the system described above, but this method can be applied to other systems of different configurations. The equations were can be derived using engineering principles or using measured data from an individual system.  
         [0076]     Equations 2-5 were best fits to linear systems of the two variables. The slope and intercept of the equations were determined empirically from best fitting measured data of the system. Measuring the relationship between the variables can similarly yield the slope and intercept of any particular system. It is preferred that the systems behave linearly in the operating regions, but if the systems are non-linear, a second order or higher equation can be used.  
         [0077]     Applicants have developed and used the method described following for control of a gap during ultrasonic welding.  
         [0078]     First, for a rotary ultrasonic system as described above, the following parameters were determined.  
         [0079]     (1) Horn diameter=6.880″ 
         [0080]     (2) Ambient temp. ° F.=65° F.  
         [0081]     (3) Frequency at ambient temp.=19.986 KHz  
         [0082]     (4) Pressure at which gap is set at=72.5 psig.  
         [0083]     (5) Gap set point for the process=2 mils (1 mil=0.001 inch).  
         [0084]     The material properties of the horn are also known,  
         [0085]     (6) Coefficient of Thermal Expansion, α
 
α Titanium =5.4×10 −6  deg F./inch/inch 
 
α Aluminum =5.4×10 −5  deg F./inch/inch 
 
         [0086]     When the system is energized and operating, the horn will increase in temperature. So next, one determines what would be the temperature, T final , at which there will be no gap left (i.e., 2.0 mil gap goes to zero, e.g., contact between horn and anvil) when welding continuously. This temperature is found by solving Equation 1:  
               T   final     =     (       2   *   IG   *     10     -   3           D   *   α       )             (     Equation   ⁢           ⁢   1     )             
 
         [0087]     In Equation 1, T final  is the temperature at which the Gap vanishes, IG is the initial gap (in mils) set and measured when the system is set-up and not in operation, D is the outer diameter of the rotary horn, and α is the coefficient of thermal expansion of the horn material. Solving Equation 1 using the above inputs for an aluminum horn gives a temperature of 172.7 deg F. where the gap will go to zero based on heating of the horn during operation. Thus, if the horn heats to 172.67° F., then there will be no gap left. Hence there is an upper bound for temperature. The upper bound for any given system can be found using equation 1 for a rotary system. One of ordinary skill in the art will also appreciate that a similar equation can also be derived for other geometries, and an upper operating temperature for avoiding a vanishing gap can be determined.  
         [0088]     As it is difficult to measure the temperature on a dynamic resonating state of a horn, Applicants developed using a surrogate that gives an indirect, but accurate, measurement of temperature. Instead of directly measuring temperature, the frequency of the horn is determined by measuring the frequency of the horn during operation, and then determining temperature by using Equation 2 following: 
 
λ min =−0.0017 *T   final +20.096  (Equation 2) 
 
         [0089]     In Equation 2, λ min  is the minimum frequency at which the horn can be operated before the gap goes to zero, and the coefficients of the linear equations have been determined empirically by experiment. Solving Equation 2 for the input parameters, the gap will go to zero when the frequency of the horn drops to less than 19,802 Hertz. Since the frequency of the horn is a parameter than can be measured easily using standard equipment commonly used by those of ordinary skill in the art, one can determine using Equations 1 and 2 the minimum operating frequency of a rotary system that will keep the gap from closing, which can result in product damage and also damage the horn and/or anvil due to the contact.  
         [0090]     Using Equations 1 and 2, one now has the ability to relate gap to temperature and temperature to frequency. Hence, one can relate the gap to frequency. During normal operation, when the material is in the gap (or nip), it is difficult to measure the gap, but using the above principles, the frequency can be used to determine the gap. The relationship between the frequency of the horn and the gap between the horn and anvil can be determined using Equation 3 (which can be solved for either the gap as a function of frequency or vice versa) following: 
 
λ=0.0965*Gap+19.7925  (Equation 3) 
 
         [0091]     In Equation 3, λ is the horn frequency and the Gap is measured in mils (1 mil=0.001 inches). Solving Equation 3 for a gap of 1 mil gives a frequency of 19,889 Hertz. Note that there is now a way to determine the gap change as a function of frequency. Using the information thus determined by Equations 1-3, the force applied to the horn/anvil arrangement can be controlled to keep the operating gap constant as the temperature and frequency of the horn change during operation of the welding assembly.  
         [0092]     To control the gap and keep it a constant operating value, the pressure applied to the system is controlled, thereby compensating for thermal expansion of the horn as it heats during operation. Referring back to the example above, when the gap is reduced to 1 mil, one needs to reduce the pressure exerted on the system so that the system can keep or get back to original gap setting of 2 mils. Hence, to compensate for the thermal expansion, the pressure is reduced to get the gap to go back to 2 mils.  
         [0093]     To reduce the pressure properly, one first needs to determine the relationship between pressure and frequency, as shown by Equation 4 following: 
 
 P   compensation =−367.3404*λ+7412.7731− P   setpoint   (Equation 4) 
 
         [0094]     where P compensation  is the reduction in pressure (in pounds per square inch gage) on the system, λ is the frequency determined from Equation 3, and P setpoint  is the pressure at the initial gap set point.  
         [0095]     For example, using the above parameters, one can determine the pressure reduction needed to move restore an initial gap of 2 mils when the horn expands 1 mil due to thermal expansion. 
    Example: What is the pressure compensation needed if the gap changed to 1 mil?   
 
         [0097]     First calculate the frequency for gap at 1 mil from Equation (3) (that value is 19.889 KHz, as previously determined). Then substituting the values into Equation 4 yields,  
               P   compensation     =         -   367.3404     ⁢     (   19.889   )       +   7412.7731   -   72.5                 =     106.7399   -   72.5               
         P   compensation     =     34.24   ⁢           ⁢     psig   ⁡     (     reduction   ⁢           ⁢   in   ⁢           ⁢   operating   ⁢           ⁢   pressure     )             
 
         [0098]     After the pressure has been determined, to compensate for thermal expansion, it can be verified what is the gap at that pressure compensation. This gap should be roughly equal to initial gap plus the gap change due to thermal expansion. To verify, first the relationship between the Pressure and Gap is determined by Equation 5 following: 
 
 P   Compensation =35.461*(Gap@Pressure Compensation)+142.205  (Equation 5) 
 
         [0099]     For example, at a pressure compensation of 34.24 psig (from Equation 4), one can rearrange Equation 5 and solve for the Gap: 
 
Gap@Pressure Compensation=(34.24−142.205)/−35.461=3.045 mils 
 
         [0100]     Thus, one can validate the model because the Initial Gap was set at 2.0 mils and the gap change was 1 mil. Therefore, to compensate for a 1 mil expansion due to heating of the horn during operation, one would open the gap by 1 ml, thereby restoring the original 2.0 mil gap.  
         [0101]     Thus, using the equations (or deriving their equivalents for linear horns or other geometries) discussed above for determining the operating parameters, one can determine the operating limits for a rotary ultrasonic welding process. For example, the operating temperature limit is found using Equation 1 and value of Gap set point (target). The operating frequency limit of the ultrasonic horn is found using Equation 2 and using the value of Temperature limit from Equation 1. The frequency at gap change is found using Equation 3 and using the value of the gap as input. The temperature at gap change is found using Equation 2, but using the value of frequency determined from Equation 3. The Pressure Compensation for Gap change is found using Equation 4 but using value of Frequency from Equation 3. The Gap at Pressure Compensation (at Ambient Temperature) is found using Equation 5, but using the value of Pressure Compensation from Equation 4.  
         [0102]     There exists yet another scheme by which the gap between a horn and an anvil may be controlled. As mentioned previously, in the context of ultrasonic welding, a horn is driven by an acoustic signal, generally in the realm of 20,000 to 40,000 Hz.  FIG. 11A  depicts the surface  1100  of a horn, as an acoustic wave propagates along its longitudinal axis. The direction of propagation of the acoustic wave is depicted by the arrow  1102 . As can be seen from  FIG. 11A , as an acoustic wave propagates along the longitudinal axis of the horn, the surface  1100  of the horn is perturbed, and exhibits a standing waveform  1104  thereupon. The standing waveform  1104  exhibits a peak-to-peak amplitude, referred to as the “displacement” exhibited by the horn surface. The peak-to-peak amplitude, or surface displacement, is a function of the amplitude of the acoustic signal propagating along the horn. Of course, the amplitude of the acoustic signal is a function of the amplitude of the electrical signal supplied to the converter coupled to the horn. Thus, the displacement exhibited by the surface  1100  of the horn is a function of the amplitude of the electrical signal delivered to the converter. Typically, the greater the amplitude of the electrical signal delivered to the converter, the greater the amplitude of the acoustic signal propagating along the horn; the greater the amplitude of the acoustic signal, the greater the displacement exhibited on the surface  1100  of the horn.  
         [0103]     As can be seen from  FIG. 11A , the gap between the surface  1100  of the horn and the surface of the anvil  1106  is a function of the displacement. As the horn exhibits greater surface displacement, the gap between the surface of the horn and the surface of the anvil diminishes.  
         [0104]     Before proceeding further, it is pointed out that  FIGS. 11A and 11B  are not drawn to scale, and that some features therein, such as the surface displacement have been exaggerated for the sake of illustration. (A typical horn may exhibit a surface displacement of approximately 2-3 mils, when operating under normal conditions, for example.)  
         [0105]     For the sake of discussion, the amplitude of the voltage signal stimulating the surface displacement shown in  FIG. 11A  is termed Amplitude 1 .  FIG. 11B  depicts the horn surface  1100  of  FIG. 11A , as it appears when stimulated by a voltage signal having an amplitude of Amplitude 2  (Amplitude 2  is less than Amplitude 1 ). As can be seen from comparison between  FIGS. 11A and 11B , the gap between the surface of the horn  1100  and the anvil  1106  grows when the amplitude of the voltage signal stimulating the horn diminishes, because the surface of the horn  1100  is not so greatly displaced toward the anvil.  
         [0106]     As mentioned previously, during a typical welding operation, a horn may exhibit a surface displacement on the order of 3 mils, for example. However, the welding operation may yield satisfactory product, even if the surface displacement is reduced by, for example, 33%. Thus, per the aforementioned example, the welding operation may be performed with the horn exhibiting a displacement of as little as 2 mils. It follows, then, that the welding operation may be initiated using an electrical signal of sufficient amplitude to stimulate a surface displacement of 3 mils. During operation, the horn experiences thermal expansion, meaning that the gap between the horn and the anvil diminishes as the horn expands towards the anvil. To counteract this effect, the amplitude of the electrical signal stimulating the horn may be attenuated, so as to yield a surface displacement less than the original 3 mils, thereby maintaining a substantially constant gap. Of course, in the context of an operation that requires at least 2 mils of displacement to produce an appropriate product, the electrical signal should not be attenuated to such an extent that the surface of the horn exhibits less than the required 2 mils of displacement.  
         [0107]     An exemplary embodiment of a system for controlling the gap between a horn and an anvil is depicted in  FIG. 12A . As can be seen from  FIG. 12A , the system includes a horn  1200  (which, in turn, includes the converter and booster), which is supplied with an AC electrical signal from a power supply  1202 . The power supply  1202  communicates the resonant frequency of the horn  1200  to a gap determining module  1204 . (As described previously, the power supply  1202  detects the resonant frequency of the horn stack and drives the horn stack at that frequency.)  
         [0108]     The gap determining module  1204  determines the length of the gap (or, may determine the change in the gap, or may determine any other value standing in known relation to the length of the horn), based upon the resonant frequency, as described previously. Thereafter, the gap length (or change therein) is supplied to an amplitude determining module  1206 . In response, the amplitude determining module identifies the proper amplitude of the electrical signal to be delivered by the power supply, in order to maintain the gap substantially constant. The amplitude may be retrieved from a look-up table, or may be arrived at by calculation. The amplitude determined thereby is communicated to a control signal generation module  1208 , which generates an appropriate command or control signal to cause the power supply  1202  to adjust the amplitude of the signal to that selected by the amplitude determination module  1206 .  
         [0109]     As described previously, each of the modules  1204 - 1208  may be embodied as dedicated hardware, such as one or more ASICs cooperating with one another. Alternatively, the modules  1204 - 1208  may be embodied as software/firmware stored in a memory, and executed by a processor in communication therewith. If embodied as firmware/software, the instructions making up the modules  1204 - 1208  may be executed by the same processor, or may be executed by a plurality of processors, as a matter of design choice.  
         [0110]     Another exemplary embodiment of a system for controlling the gap between a horn and an anvil is depicted in  FIG. 12B . The system of  FIG. 12B  takes advantage of two different schemes by which the gap may be adjusted: (1) controlling the position of the horn, itself; and (2) controlling the amount of surface displacement exhibited by the horn. As can be seen from  FIG. 12B , the system includes a horn  1210  (which, in turn, includes the converter and booster), which is supplied with an AC electrical signal from a power supply  1212 . The power supply  1212  communicates the resonant frequency of the horn  1210  to a gap determining module  1214 . (As described previously, the power supply  1212  detects the resonant frequency of the horn stack and drives the horn stack at that frequency.)  
         [0111]     The gap determining module  1214  determines the length of the gap (or, may determine the change in the gap, or may determine any other value standing in known relation to the length of the horn), based upon the resonant frequency, as described previously. Thereafter, the gap length (or change therein) is supplied to an amplitude determining module  1216  and to an adjustor  1220 . The adjustor  1220  is a system that can alter the position of the horn, such as the adjusting systems shown in  FIGS. 7 and 10 , which adjust the position of the horn by varying the deformation of an elastic stop by varying degrees. As was the case in the embodiment of  FIG. 12A , the amplitude determining module  1216  identifies the proper amplitude of the electrical signal to be delivered by the power supply, in order to maintain the gap substantially constant. However, the amplitude determining unit  1216  cooperates with the adjustor  1220  to jointly adjust the position and/or adjust the amplitude of the AC signal delivered by the power supply  1212 , in order to achieve the end goal of substantially maintaining a constant gap.  
         [0112]     For example, according to one embodiment, the amplitude determination unit  1216  and adjustor  1220  operate according to the method depicted in  FIG. 13 . As shown therein, both modules  1216  and  1220  receive the gap length, or change therein, from the gap determining unit  1214 , as shown in operation  1300 . Thereafter, (assuming the embodiment in which the adjustor  1220  comprises a force applicator that forces the horn against a deformable elastic stop), the amplitude determination unit  1216  receives from the adjustor  1220  the force applied thereby (operation  1302 ). Next, as shown in operation  1304 , the force is compared to the lower limit of the acceptable force for the welding operation. If the force is still above the limit, then the adjustor  1220  determines the new force required for application, and adjusts the force accordingly (operation  1306 ). On the other hand, if the force has reached the lower limit, then the force should not be reduced any further, and control is passed to operation  1308 , in which it is determined whether the amplitude of the surface displacement has reached its lower limit. If not, control is passed to operation  1310 , whereupon the amplitude determining module  1216  identifies the proper amplitude of the electrical signal to be delivered by the power supply, in order to maintain the gap substantially constant. The amplitude determined thereby is communicated to a control signal generation module  1218 , which generates an appropriate command or control signal to cause the power supply  1212  to adjust the amplitude of the signal to that selected by the amplitude determination module  1216 . On the other hand, if the amplitude of the surface displacement has reached its lower limit, then control is passed to operation  1312 , and an alarm is generated to indicate that the gap cannot be maintained at a constant length without either reducing the process force beneath its acceptable limit, or reducing the surface displacement of the horn beneath its acceptable limit.  
         [0113]     Although the operations of  FIG. 13  are described as being performed by amplitude determination module  1216 , the operations may be performed by any of the modules depicted in  FIG. 12B , or may be performed by another module dedicated to coordinating the operations of the amplitude determination module  1216  and the adjustor  1220 .  
         [0114]     Further, it is to be noted that, in operation  1302 , the adjustor  1220  may communicate the position of the horn to the module performing the method of  FIG. 13 . Then, in operation  1304 , the position of the horn may be compared to a positional limit expressing the capacity of the adjustor  1220  to withdraw the horn from the anvil. In other words, in operation  1304 , it is determined whether the adjustor  1220  has withdrawn the horn from the anvil as the adjust  1220  is able to do so.  
         [0115]     According to another embodiment, the amplitude determination unit  1216  and adjustor  1220  operate according to the method depicted in  FIG. 14 . As shown therein, both modules  1216  and  1220  receive the gap length, or change therein, from the gap determining unit  1214 , as shown in operation  1400 . Thereafter, (again assuming the embodiment in which the adjustor  1220  comprises a force applicator that forces the horn against a deformable elastic stop), the amplitude determination unit  1216  receives from the adjustor  1220  the force applied thereby (operation  1402 ). Next, as shown in operation  1404 , whereupon it is determined whether the amplitude of the surface displacement has reached its lower limit. If not, control is passed to operation  1406 , whereupon the amplitude determining module  1216  identifies the proper amplitude of the electrical signal to be delivered by the power supply  1212 , in order to maintain the gap substantially constant. The amplitude determined thereby is communicated to a control signal generation module  1218 , which generates an appropriate command or control signal to cause the power supply  1212  to adjust the amplitude of the signal to that selected by the amplitude determination module  1216 . On the other hand, if the amplitude of the surface displacement exhibited by the horn has reached the lower limit, then the force should not be reduced any further, and control is passed to operation  1408 , in which it is determined whether the force value received during operation  1402  is at the lower limit of the acceptable force for the welding operation. If the force is still above the limit, then the adjustor  1220  determines the new force required for application, and adjusts the force accordingly (operation  1410 ). On the other hand, if the force has reached the lower limit, then control is passed to operation  1412 , and an alarm is generated to indicate that the gap cannot be maintained at a constant length without either reducing the process force beneath its acceptable limit, or reducing the surface displacement of the horn beneath its acceptable limit.  
         [0116]     Although the operations of  FIG. 14  are described as being performed by amplitude determination module  1216 , the operations may be performed by any of the modules depicted in  FIG. 12B , or may be performed by another module dedicated to coordinating the operations of the amplitude determination module  1216  and the adjustor  1220 .  
         [0117]     Further, it is to be noted that, in operation  1402 , the adjustor  1220  may communicate the position of the horn to the module performing the method of  FIG. 14 . Then, in operation  1408 , the position of the horn may be compared to a positional limit expressing the capacity of the adjustor  1220  to withdraw the horn from the anvil. In other words, in operation  1408 , it is determined whether the adjustor  1220  has withdrawn the horn from the anvil as the adjust  1220  is able to do so.  
         [0118]     Upon reading and understanding the foregoing process for controlling an ultrasonic welding system, one of ordinary skill in the art will appreciate that gap control for a system can be achieved by measuring the operating frequency of the horn, and then adjusting the force, for example, pressure, that controls the gap. The specific equations can be derived or determined empirically for any horn geometry, including linear and rotary horns.  
         [0119]     The various embodiments described above are provided by way of illustration only and should not be construed to limit the invention. Those skilled in the art will readily recognize various modifications and changes that may be made to the present invention without following the example embodiments and applications illustrated and described herein, and without departing from the true spirit and scope of the present invention, which is set forth in the following claims.