Abstract:
A vibratory conveying apparatus includes a trough having a conveying surface connected via springs to a vibratory exciter. The springs are arranged on opposite sides of the exciter and compress against bracket plates of the trough. The springs are coil springs each having a rotationally non-symmetrical cross-section. Preferably, the springs each have an ovoid-shaped or rectangular cross section with an outside dimension being greater along the lateral axis than along the transverse axis.

Description:
TECHNICAL FIELD OF THE INVENTION  
         [0001]    The invention relates to a vibratory conveying apparatus, such as a vibratory feeder or conveyor. Particularly, the invention relates to a vibratory conveying apparatus having a spring system used between a vibratory exciter and a conveying trough of the vibratory conveying apparatus.  
         BACKGROUND OF THE INVENTION  
         [0002]    Vibratory feeders and conveyors are widely used in a variety of heavy to light industries for such purposes as the metering of bulk material, such as ore, stone, grain, various chemical powders and the like, from storage bins to other processing equipment, or to convey bulk material from one industrial process to another. Vibratory feeder designs generally consist of a trough member connected to one or more base members by means of spring mechanisms such as wound steel wire coil springs or stacked arrays of elastomer rubber blocks. A vibratory exciter generates vibratory motion. The vibratory exciter can be in the form of an electric motor that rotates eccentric weights mounted either on the motor shaft, or on a separate shaft inserted in bearing mounts. Some multi-mass feeder designs operate at a speed that is close to the natural frequency of the feeder mass/spring system to utilize the mechanical advantage due to the resonance phenomena.  
           [0003]    A typical prior art coil spring vibratory feeder  10  is depicted in FIG. 3. A feeder trough member  11  is fitted with a plurality of spring mounting blocks  14 , and coil spring mounting plate assemblies  16 . One or more reinforcing ribs  18  encircle the bottom of the feeder trough  11 . The feeder trough  11  is connected to a base member  22  by means of a plurality of leaf springs  24  bolted to the spring mounting blocks  14  located on both the feeder trough member  11 , and the base member  22 . Steel coil springs  26  are connected between the mounting plate assemblies  16  on the feeder trough member  11 , and mounting plate assemblies  28  welded to the feeder base member  22 . A vibratory exciter  30  is also connected to the base member  22 . Suspension hooks  32  and wire suspension cables  34  provide means to support the feeder at the operating site.  
           [0004]    An enlarged perspective view of a typical prior art wound steel coil spring  38  is depicted in FIG. 5. Lines representing the longitudinal axis A-A and the lateral axis B-B are shown in FIG. 5. The spring height is measured along the axis A-A and the spring width is measured along the axis B-B. The coil spring  38  is usually ground on the ends  42  so that they are flat and parallel to each other to facilitate proper mounting in the feeder.  
           [0005]    A typical heavy-duty coil spring of this design might be approximately 12 inches high, have a mean diameter of about 6 inches, and be wound from solid steel rod about ¾ of an inch in diameter. It would typically have a dynamic compressive (i.e. along the A-A axis) spring rate of about 1500 lbs/in., to be within the safe operating stress range of 10,000 to 12,000 psi.  
           [0006]    A two mass vibratory feeder, such as the example illustrated in FIG. 3, would have a dynamic spring rate requirement given by the relationship:  
         K   d     =         ω   o   2     ·     W   r       g                           
 
           [0007]    Where:  
           [0008]    K d =dynamic spring rate in lbs./in.  
           [0009]    ω o =natural frequency in radians/sec. (2πf o )  
           [0010]    W r =resultant weight of the feeder in lbs.  
           [0011]    g=acceleration due to gravity (386 in./sec. 2 )  
           [0012]    For example, a vibratory feeder having a desired natural frequency of 20 Hz. (1200 cpm.), and a resultant weight of 500 lbs., would have a dynamic spring rate of:  
         K   d     =             (     2                   π   ·   20       )     2     ·   500     386     ≈     20        ,        455                     lbs   .     /     in   .                                 
 
           [0013]    Using the above described coil springs rated at 1500 lbs./in. each, it would require at least 14 (20,455/1500=13.63) individual springs operating in parallel to make up the required total spring rate.  
           [0014]    In designing the coil spring, it is important to maintain a certain relationship between its height and diameter (such as &lt;2:1). This is referred to as “column stability.” Sufficient column stability is required, otherwise any slight off vertical axis loading might cause the spring to buckle or move sideways.  
           [0015]    Referring once again to FIG. 5, it is noted that the coil spring  38  has a relatively low spring rate along the lateral axis B-B. If the spring is applied such that the longitudinal axis A-A was other than vertical, such as shown in FIGS. 3 and 4, the off axis loading, due to the weight of the base members, i.e., the base member  22  and the exciter  30  in FIG. 3, or the exciter  30  and a drive motor  46  in FIG. 4, would cause the springs  54  to sag or bend in the direction of the lateral axis B-B. The feeder would not function correctly. The prior art vibratory equipment used the additional leaf springs  24  as shown in FIG. 3, to provide the required support between the trough and base members. The leaf springs  24 , do not allow the coil springs  26  to sag or bend, while maintaining the desired motion of the feeder. This configuration also places constraints on the size and geometry of the feeder design, affecting the cost of equipment and its installation.  
           [0016]    Another consideration in spring design concerns the dynamic stress the spring undergoes during operation. Generally, material composition and the physics involved impose limitations on the operating stress. Unfortunately, normal manufacturing methods and processes add stresses to further restrict operating limits. For example, springs that material and physical considerations indicate should operate with long life at stress levels of 20,000 to 25,000 psi, from a practical standpoint, can only be operated at levels of 10,000 to 12,000 psi to meet acceptable life expectation. Such limitations usually mean that smaller wire sizes have to be used for the springs, and result in a large number of springs required for a given application, affecting the size and geometry of the feeder.  
           [0017]    One way of avoiding the above-mentioned design limitations is to substitute elastomer blocks, such as rubber blocks, for the wound steel coil springs. The characteristics of the rubber blocks are such that very large amounts of energy can be stored per given volume when compared to the steel coil springs. Also, the rubber blocks can be of rectangular shape, allowing the blocks to provide sufficient stiffness along a transverse axis for supporting the weight of vibratory drives.  
           [0018]    A prior art vibratory feeder design using elastomer rubber springs is depicted in FIG. 4. A side view of the feeder is shown with a section of a wing plate member  52  removed, and with only the rear portion of the feeder visible. The trough member  11  is shown connected to the wing plate member  52 . One of a plurality of reinforcing ribs  18  is shown surrounding the bottom of the trough  11  and connected to the wing plate member  52 . The vibratory exciter member  30  is positioned between a spring mounting plate  56  and a back plate  58  and held in place by the elastomer springs  54 , which are bonded to mounting plates  63 . The springs mounting plates  63  are bolted to the coil spring mounting plate  56  and the vibratory exciter member  30  at the front end, and to the vibratory exciter member  30  and the back plate  58  at the rear end. The drive motor  46  is mounted to the base of the vibratory exciter member  30 , and rotates the shaft  66  by means of the drive belt  68  and the pulleys  70  and  72 . Eccentric weights (not shown) mounted on the shaft  66 , generate vibratory motion of the feeder as the shaft  66  is rotated.  
           [0019]    The back plate  58  is bolted to the ends of the wing plate members  52  such that the elastomer spring members  54  are compressed by a known amount, determined by the dimension between the spring mounting plate  56 , and the end of the wing plate members  52 . Reinforcing ribs  76  are welded to the back plate  58  for stiffening the back plate  58  due to the compression loading of the elastomer springs  54 . Suspension hooks  32  and wire suspension cables  34  provide means to install the feeder at the operating site.  
           [0020]    Apparatus manufactured at FMC Technologies in Homer City Pa. have utilized springs made from an elastomer material such as polyisoprene rubber. The two mass vibratory feeder design illustrated in FIG. 4 is an example of the application of such rubber springs. Typically, in order to achieve the required deflection, each spring element  54  is comprised of about four rubber blocks sandwiched between thin aluminum heat dissipating plates. Utilizing typical rubber blocks 6 inches long by 4 inches wide, and 1.5 inches thick, each spring element  54  would have a spring rate of approximately 3700 lbs./in. Using the spring rate requirement for the example feeder calculated above, only 6 spring elements  54  (20,455/3700=5.528) would be needed compared to the 14 steel coil springs.  
           [0021]    Furthermore, mounting the spring elements  54  with the long dimension of the rubber block parallel to the vertical axis of the vibratory exciter  30  provides mechanical support for the exciter  30 , while maintaining linear motion along the drive axis A-A, thus eliminating the need for the leaf springs  24  of FIG. 3. Also, due to the large difference between the spring rates of the rubber blocks in the shear direction as compared to the compression direction, the natural frequency in the shear and compression direction differs by a factor of two or more. Accordingly, the operating speed of the feeder, selected to be close to the natural frequency of the spring/mass system in the compressive direction to take advantage of resonance, does not resonate with the spring/mass system in the shear direction, allowing the use of a single shaft eccentric weight exciter design, while maintaining linear motion. In contrast, the feeder design of FIG. 3 often requires the use of a two eccentric weight shaft exciter, each shaft rotating in opposite directions to produce linear motion, as a means to avoid such resonance and motion problems. These advantages represent a considerable savings in overall size requirement, design flexibility and initial cost.  
           [0022]    Unfortunately, manufacturing elastomer springs is difficult as the processes are hard to control to obtain consistent results in spring rates and material stability. High levels of material science, practical experience and strict process quality control are required for a manufacturer to make engineering grade rubber products. This of course greatly affects the cost of the spring elements.  
           [0023]    An initial application problem with elastomer springs is that the amount of allowed deflection per elastomer block is a function of the thickness and dimensions of the rubber element. If the rubber element is too thick, or the ratio of thickness to length dimensions too great, the internal heat, generated by hysteresis as the elastomer is deflected, can become hot enough to actually melt the elastomer. Therefore, it is a customary practice to stack several thinner, properly proportioned, elastomer blocks in series, separated by aluminum plates that dissipate the heat (See FIG. 4). Using this design, the required machine deflection can be obtained, and by arranging a plurality of these stacks together in a parallel relationship, the required spring rate for a given feeder design can also be obtained. The individual elastomer blocks are bonded to the aluminum plates in an exacting process requiring chemical preparation, adhesive application, clamped assembly fixtures, and precise thermal curing. Therefore, the elastomer spring arrays are relatively expensive to manufacture.  
           [0024]    A further drawback of elastomer block springs, resulting in increased cost, is the fact that the elastomer block spring elements tend to vary in spring rate for a given size even from the best and most careful manufacturers. This means the elements must be graded into spring rate groups for practical use in selecting required spring system rates and to avoid over heating individual out-of-range spring elements due to overstress. Also, as the elastomer spring elements are worked during operation, some further curing of the elastomer may take place over time, changing its rate. If a sufficient number of spring elements change rate this way in a tuned feeder design, referred to as “aging,” it becomes necessary to either replace the spring elements or to change the operating speed of the feeder, another costly proposition.  
           [0025]    The present inventors have recognized the desirability of providing a vibratory conveying apparatus design that overcomes the drawbacks associated with prior art drive springs that typically utilize round wound steel wire coil springs or stacked arrays of elastomer blocks. Furthermore, the present inventors have recognized that through the elimination of such drawbacks, cost is dramatically reduced. Cost is reduced by enabling simple, efficient spring designs, and by the simplification of manufacturing processes. Also, the present inventors have recognized the desirability of providing more stable and reliable products using such spring designs.  
         SUMMARY OF THE INVENTION  
         [0026]    The present invention provides a vibratory conveying apparatus, such as a feeder or conveyor, having a conveying trough, an exciter and a drive spring system driven by the exciter to vibrate the trough. The spring system comprises substantially rectangular or ovoid-shaped springs that provide spring rates and deflections comparable to that of elastomer spring systems. The spring system also provides sufficient stiffness along the transverse loading axis of the springs to support the weight of the exciter of the apparatus where the exciter is supported from the trough by opposing springs of the drive spring system.  
           [0027]    A vibratory conveying apparatus according to the invention includes the trough having a conveying surface, the vibratory exciter, and a first coil spring arranged to be compressed between a first portion of the trough and a first portion of the exciter. The first coil spring has a longitudinal axis around which the first coil spring is wound, a transverse axis and a lateral axis, the transverse axis and the lateral axis being perpendicular and in a plane that is perpendicular to the longitudinal axis. An outside dimension of the first coil spring is greater along the lateral axis than along the transverse axis. The greater outside dimension along the lateral axis allows the first coil spring to support greater weight when the longitudinal axis is arranged in a non-vertical orientation.  
           [0028]    The apparatus can further include a second coil spring arranged to be compressed between a second portion of the trough and a second portion of the exciter, the second coil spring also having a longitudinal axis around which the second coil spring is wound, a transverse axis and a lateral axis, the transverse axis and the lateral axis being perpendicular and in a plane that is perpendicular to the longitudinal axis. An outside dimension of the second coil spring is also greater along the lateral axis than along the transverse axis. The greater outside dimension along the lateral axis allows the second coil spring to support greater weight when the longitudinal axis is arranged in a non-vertical orientation. The first and second portions of the exciter are preferably on opposite sides of the exciter and the first and second coil springs are arranged to be compressed and unloaded in opposition during operation of the conveying apparatus.  
           [0029]    The trough preferably includes a trough bracket assembly having a front plate and a back plate. The first portion of the trough is located on the front plate and the second portion of the trough is located on the back plate.  
           [0030]    To achieve the desired overall spring rate for the conveying apparatus, multiple coil springs of the above-described shape can be arranged on opposite sides of the exciter to be compressed against the front and back plates.  
           [0031]    Numerous other advantages and features of the present invention will become readily apparent from the following detailed description of the invention and the embodiments thereof, and from the accompanying drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0032]    [0032]FIG. 1 is a perspective view of a vibratory feeder incorporating ovoid-shaped coil springs of the invention.  
         [0033]    [0033]FIG. 1 a  is an enlarged perspective view of an ovoid-shaped coil spring from FIG. 1 with the longitudinal, lateral and transverse axis indicated by dashed lines.  
         [0034]    [0034]FIG. 2 is a side view of the vibratory feeder of FIG. 1, with a portion of the wing plate removed to view the ovoid-shaped coil springs.  
         [0035]    [0035]FIG. 3 is a side view of a prior art vibratory feeder utilizing standard coil springs.  
         [0036]    [0036]FIG. 4 is a side view of a prior art vibratory feeder utilizing stacked elastomer rubber springs.  
         [0037]    [0037]FIG. 5 is perspective view of a typical wound steel coil spring of the prior art. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0038]    While this invention is susceptible of embodiment in many different forms, there are shown in the drawings, and will be described herein in detail, specific embodiments thereof with the understanding that the present disclosure is to be considered as an exemplification of the principles of the invention and is not intended to limit the invention to the specific embodiments illustrated.  
         [0039]    A conveying apparatus  100  according to the invention is shown in FIG. 1. A trough or pan member  111 , having a conveying surface  112 , includes a trough bracket assembly  113 . The bracket assembly  113  includes wing plate members  114  sized and positioned such that a discharge lip  116  of the trough or pan member  111  extends beyond the wing plate members  114  at the front end of the vibratory feeder. The wing plate members  114  extend beyond the trough inlet  121  at the rear of the feeder. A coil spring mounting plate  124  is welded in place between the wing plate members  114  located below but near the trough inlet  121  towards the rear of the feeder.  
         [0040]    A vibratory exciter mechanism  130  is positioned between the wing plate members  114  that extend beyond the trough inlet  121  at the rear of the feeder. The vibratory exciter mechanism  130  is held in place by means of two sets of ovoid-shaped coil springs  134  (as shown in FIG. 1) or rectangular coil springs (not shown). The coil ends of each set of ovoid-shaped coil springs  134  are typically placed over spring seats  135  which are welded to end plates  136 . One set of coil springs/end plates is then fastened between the coil spring mounting plate  124  and the vibratory exciter mechanism  130 , while the remaining set of coil springs/end plates is fastened between the vibratory exciter mechanism  130 , and a back plate  140 . The back plate  140  is bolted to the ends of the wing plate members  114 , compressing the coil springs  134  by a specified amount set by the distance between the coil spring mounting plate  124  and the ends of the wing plate members  114 . Reinforcing ribs  144  are welded to the back plate  140  to stiffen the structure due to the compression load of the coil springs  134 . Ribs  150  are usually added to the trough or pan member  111  to provide stiffness and structural integrity. Suspension hooks  154  are welded to the trough structure  111  and/or the wing plate structure  114  to facilitate installation of the feeder at the operation site where it is typically hung or suspended by means of wire cables under the discharge end of a supply hopper.  
         [0041]    [0041]FIG. 1 a  is a close up perspective view of an ovoid-shaped coil spring  134 , the ends  160  of which have been ground flat and parallel to each other to facilitate welding between the end plates  136 . For reference, a line A-A is shown along the longitudinal axis of the coil spring  14 , a line B-B is shown along a “lateral” axis, and a line C-C is shown along a “transverse” axis. The height of the spring is measured along the A-A axis, the major diameter along the B-B axis, and the minor diameter along the C-C axis.  
         [0042]    Although ovoid-shaped springs are somewhat easier to manufacture, springs closer to true rectangles can also be used, as sold by DRACO Spring Mfg. Co. of Houston, Tex., U.S.A. The DRACO springs are manufactured according to a process such that the spring can be utilized at higher stress levels, making it competitive in dimension to the elastomer spring arrays. The details of this spring and the manufacturing process thereof have been disclosed in a separate patent application now pending, U.S. Ser. No. 10/124,497, filed Jul. 3, 2002, herein incorporated by reference.  
         [0043]    [0043]FIG. 2 is a side view of the feeder of FIG. 1 with a section of the wing plate member  114  removed. The trough member  111 , having the discharge lip  116 , is shown connected to the wing plate member  114 . The reinforcing ribs  150  are seen surrounding the bottom of the trough  111  and connected to the wing plate member  114 . The vibratory exciter member  130  is positioned between the coil spring mounting plate  124  and the back plate  140  and held in place by the ovoid-shaped coil springs  134  that are placed over the spring seats  135  which are welded to the coil spring end plates  136 . The end plates  136  are bolted to the spring system mounting plate  124  and the vibratory exciter member  130  at the front end, and the vibratory exciter member  130  and the back plate  140  at the rear end.  
         [0044]    A drive motor  176  is mounted to the base of the vibratory exciter member  130 , and rotates a shaft  178  by means of a drive belt  180  and pulleys  182  and  184 . Eccentric weights (not shown) mounted on the shaft  178 , generate vibratory motion of the feeder as the shaft  178  is rotated. The back plate  140  is bolted to the ends of the wing plate members  114  such that the ovoid-shaped coil springs  134  are compressed by a known amount, determined by the dimension between the coil spring mounting plate  124 , and the end of the wing plate members  114 . Reinforcing ribs  144  are welded to the back plate  140  for stiffening due to the compression loading of the coil springs  134 . The suspension hooks  154  and wire suspension cables  192  provide means to install the feeder at the users site. An imaginary drive line  200  is shown at a specific angle to the bottom  112  of the trough member  111 , and along the line of force generated by the vibratory exciter  130 , such that it passes through or close to the center of gravity  210  of the entire feeder assembly thereby minimizing or eliminating, off-axis motion of the feeder during operation.  
         [0045]    The spring system of the invention provides a steel coil spring that has a stiff rate in the shear direction to support the weight of the vibratory exciter mechanism, while having a compressive spring rate comparable to that of the elastomer rubber spring element  54  of FIG. 4.  
         [0046]    The ovoid-shaped spring described in this disclosure is a preferred embodiment of the spring design, but other embodiments that are more or less rectangular in shape may be manufactured using the methods, equipment and techniques required for the ovoid shape. The ovoid shape provides exemplary performance, ease of manufacturing, and reasonable cost.  
         [0047]    One exemplary ovoid-shaped spring  134  as shown in FIG. 1 a  includes a wire diameter, coil height (the length along the A-A axis), coil diameter (measured along the C-C axis) chosen to result in a spring design that has a spring rate of approximately 4000 lbs/in., and, at a design deflection of approximately ⅜ inch, a working stress up to 16000 psi. The precision manufacturing methods, and techniques used to produce the ovoid-shaped spring result in being able to work the spring at higher stress levels in demanding applications such as vibratory feeders and conveyors. The ends  160  of the ovoid-shaped spring have been ground flat and squared such as to be parallel to each other to facilitate installation in the vibratory feeder. The overall dimensions and spring rate of the resultant spring design herewith described are close to those of the elastomer spring element  54  of FIG. 4, the prior art vibratory feeder described above. This enables a direct substitution of spring elements thus only requiring minor accommodation modifications to a proven vibratory feeder design. The spring rate along the B-B axis, the shear direction of the ovoid, is much greater than that along the A-A axis as can readily be imagined from observing FIG. 1 a , perhaps as much as 4 times greater, making the rate of the example spring 16,000 lbs./in. along this B-B axis.  
         [0048]    Also, installing the spring elements  134  with the long, lateral axis dimension of the ovoid-shaped spring substantially parallel to the vertical axis of the vibratory exciter  130  (as shown in FIGS. 1 and 2), provides more than sufficient mechanical support for the exciter  130 , as each link of the ovoid-shaped springs acts as if it were a small, stiff, vertical torsion bar primarily deflecting only at the ends in the direction of the A-A axis. Such support maintains linear motion along the drive axis A-A, and eliminates the need for the leaf springs  24  of FIG. 3.  
         [0049]    Using the example vibratory feeder described above, having a resultant weight of 500 lbs., and 6 ovoid-shaped spring elements, the total dynamic spring rate would be 6×4,000=24,000 lbs./in. The above equation for calculating dynamic spring rate K d :  
         K   d     =         ω   o   2     ·     W   r       g                           
 
         [0050]    can be rearranged to calculate the natural frequency f o  of the feeders spring mass system along the A-A axis. Since ω o  is the same as 2πf o  then:  
         f   o     =       1     2                 π       ·           K   d     ·   g       W   r                                 
 
         [0051]    Using the values of 24,000 lbs./in. for K d  and 500 lbs. for W r  we get:  
         f       o                 A     -   A       =         1     2   ×   3.14159       ·         24000   ×   386     500         ≈     21.66                 Hz                             
 
         [0052]    If the spring rate along the B-B axis were 4 times greater than that along the A-A axis then the natural frequency in the B-B direction would be:  
         f       o                 B     -   B       =         1     2   ×   3.14159       ·         96000   ×   386     500         ≈     43.33                 Hz                             
 
         [0053]    Accordingly, if the operating frequency of the feeder was 19 Hz (1140 cpm), the dimensionless ratio of the operating frequency divided by the natural frequency (N/N o ), often referred to as lambda (λ), would be 0.88 along the A-A axis and 0.44 along the B-B axis. The ratio “lambda” represents a figure of operational merit or amplification due to the resonance phenomena, the amplification factor being expressed by the relationship 1/1−α 2 . The ratio “lambda” at resonance, where the operating frequency and the natural frequency are equal (N=N o ), would therefore be 1 and the amplification factor theoretically would be infinite. At λ=0.999999 the amplification factor would be 500,000, at λ=0.9, it would be 4.78, at λ=0.88 it would be 4.433, and at λ=0.44 it would be 1.24. The amplification factor has a direct bearing on the force requirements to produce the desired amplitude of vibration on the feeder trough.  
         [0054]    In our example feeder, a single rotating shaft with an eccentric weight mounted on it would produce sufficient force to generate the vibration amplitude of 0.375 in. along the A-A axis, but only a fraction of that amplitude along the B-B shear axis. This assures a relatively linear trough motion back and forth along the A-A axis, and consequently along the drive line  200  of FIG. 2, which it parallels, passing through the center of gravity  210  of the feeder, to eliminate undesirable off axis motion.  
         [0055]    The ovoid-shaped spring therefore compares favorably to the elastomer spring, having the same advantages of a high spring rate, and being stiff enough in the shear direction to support the exciter without the need for additional support springs, while maintaining a desirable vibratory motion pattern. The ovoid-shaped spring also retains the advantageous features of the steel coil spring in that it has a consistent, repeatable spring rate, an effectively infinite shelf life allowing the springs to be mass produced and held in inventory. Since the material, manufacturing methods, and techniques allow the manufacturer to produce springs having dimensions and spring rates held within close tolerances, only one basic spring element design is required, and therefore, the need for the expensive testing and grading required for elastomer springs is obviated, as is the need to carry multiple spring elements in inventory.  
         [0056]    The ovoid-shaped springs  134  in FIGS. 1 and 2, in a preferred embodiment of the invention, are mounted between mild steel spring end plates  136 , fitting over rectangular shaped mild steel spring seats  135 , which have been welded in a symmetrically spaced array to the spring end plates  136 , forming a feeder drive spring assembly. For vibratory feeders of standard size and weight, such assemblies may be made in advance of feeder production and held in inventory. Such inventory may also be used to replace a spring assembly in a feeder at a customers site should a spring element break due to some unforeseen event.  
         [0057]    The top and bottom dead turns of the spring elements may be tack welded in place to the end plates  136  if desired, to facilitate assembly to the feeder and to make inventory storage easier. According to FIG. 1, two sets of spring assemblies are provided for each feeder, one set bolted between the spring assembly backing plate  124  which is welded between the feeder wing plates  114 , and one side of the vibratory exciter  130 , and the other set bolted between the exciter  130  and the feeder back plate  140 . When the feeder back plate  140  is bolted to the ends of the wing plates  114 , the spring assemblies are compressed by a known amount set by the space between the spring assembly backing plate  124 , and the feeder back plate  140 . The amount of compression on each assembly is predetermined to be a little more than the total stroke of the feeder (i.e., the trough stroke plus the exciter stroke [A T +A M ]), such that in operation the spring elements  134  never go into tension. Therefore, even if the spring elements  134  were not welded in place, they would remain tightly positioned between their respective mounting plates during operation of the feeder.  
         [0058]    The following methodology outlines the design process to configure a conveying apparatus of the invention:  
         [0059]    Determine the dimensions of the vibratory feeder trough based on application information, and calculate the weight of all of the trough side members, plus an estimate of the weight of half of the spring assemblies.  
         [0060]    Select an exciter from a number of available standard units and calculate the weight of all of the exciter side members, which include the drive motor and its components, plus an estimate of the weight of half of the spring assemblies.  
         [0061]    Select goals for the operating speed of the feeder (N), and for lambda λ, to determine the natural frequency (N o ) of the feeder. Also select the trough stroke (A T ) that will be required to produce a determined feed rate.  
         [0062]    Using the equation in the disclosure, calculate the required spring rate (K d ) for the feeder using the weights calculated from the previous steps, and the natural frequency (N o ) determined above.  
         [0063]    Using an ovoid or rectangular spring element designed to have a spring rate of 4000 lbs./in., a deflection of at least 0.375 in., and a spring rate along its transverse shear axis of at least four times that of its compressive rate, determine the number of spring elements required in parallel to meet the feeders spring rate (K d ) by dividing it by 4000 (i.e., S n =K d /4000). If the answer is fractional or uneven, round the number of springs up or down to the next even number of springs and recalculate the feeder&#39;s design parameters, adjusting the operating speed of the feeder (N), and/or the trough stroke (A T ) as necessary to meet the application requirements of the feeder.  
         [0064]    Design the feeder such that the space between the spring assembly backing plate  124 , and the feeder back plate  140 , is the width of the exciter assembly  130 , plus the width of two spring assemblies, minus a little more than twice the total stroke of the feeder (i.e. twice the trough stroke plus the exciter stroke [2•(A T +A M )]).  
         [0065]    Divide the ovoid springs into two even sets and assemble each set between two mild steel spring end plates  136 , fitting them over the rectangular shaped mild steel spring seats  135 , which have been welded in a symmetrically spaced array to the spring end plates  136 , to form two feeder drive spring assemblies. Tack-weld the ovoid springs to the end plates  136  if desired, to facilitate assembly to the feeder.  
         [0066]    Manufacture the feeder as designed; bolt one of the spring assemblies to the spring assembly backing plate  124 , and to the front face of the exciter assembly  130 , then bolt the other spring assembly to the back face of the exciter assembly  130 , and to the feeder back plate  15 . Bolt the feeder back plate  140  to the ends of the wing plates  114 , compressing the spring assemblies to twice the trough stroke plus the exciter stroke [i.e., [2•(A T +A M )].  
         [0067]    From the foregoing, it will be observed that numerous variations and modifications may be effected without departing from the spirit and scope of the invention. It is to be understood that no limitation with respect to the specific apparatus illustrated herein is intended or should be inferred.