Abstract:
An improved suspension apparatus and method for damping vibration arising in liquid vortex mixers of the type pivotably supporting a mixing frame assembly and suspending the assembly by at least one spring for mixing a liquid coating using both spin and orbital rotational movements. A pivoting support is located between the mixing frame assembly and a base. A damper in the form of an annular ring is used to damp pivoting movement of the mixing frame assembly. Various pivoting mounts may be used to pivotably support the mixing frame on a base. A bushing provides accommodation of a misaligned spring mounting end turn using a V-groove to retain the spring mounting end turn, and may include an eccentric feature to allow adjustment of the spring mounting length.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a Continuation-In-Part of U.S. application Ser. No. 10/891,446, filed Jun. 30, 2004, now U.S. Pat. No. 7,182,506 B2, the entire contents of which are hereby expressly incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     In the past, vortex mixers have been used to mix pigment and vehicle in liquids such as paint, typically in 5 gallon cylindrical containers. Such vortex mixers achieved mixing by spinning the container on its cylindrical axis, while that axis was positioned at an angle to a central orbit axis about which the container was simultaneously orbited as well as spun. While such vortex mixers have enjoyed a degree of popularity, they have also been subject to a certain amount of imbalance, caused by a range of density and viscosity in the materials (typically liquids) being mixed. While a vortex was created in the material being mixed, the vortex assumed different shapes and positions within the container, depending upon the density and viscosity of the material being mixed and the spin and orbit speeds of the mixer. While most applications of the present invention contemplate that the materials to be mixed are liquid, other materials may be considered, and, in the event of non-liquid materials (such as granular materials) a concept of apparent or equivalent viscosity would be relevant thereto. 
     Some prior art mixers had a center of volume offset from the center of rotation such that the center of mass was displaced in one direction with an empty machine, and the center of volume was displace in an opposite direction, such that adding a mass of material to be mixed brought the rotating elements somewhat into balance. However, such balance was only achieved with one volume, density and viscosity of material to be mixed. 
     Imbalance in prior art mixers manifested itself in vibration of the mixer, sometimes resulting in the mixer “walking” or moving laterally across the surface upon which it was supported. Such walking is undesirable, particularly when the mixer is located on a surface elevated above a floor, as for example, when the mixer is “stacked” on top of other equipment as is sometimes done in paint mixing facilities. 
     The present invention relates to various aspects of and improvements to the suspension shown and described in copending application Ser. No. 10/891,446, assigned to the same assignee hereof. The suspension provides improved performance for vortex mixers of the type described herein. In alternative embodiments, various pivoting support embodiments may be found useful in the practice of the present invention, along with an annular damper formed of visco-elastic polymer, which has been found to be a desirable embodiment and is included herein. Improved spring mounting arrangements are also included herein. 
     SUMMARY OF THE INVENTION 
     In one aspect the present invention includes an improved suspension system in the form of apparatus and method for a mixer of the type having a mixing frame assembly mounted by a pivoting support to the base of the mixer and thereby supported for angular movement about the pivot. More particularly, the improvement includes at least one damper element, preferably in an annular concentric orientation to the pivot. The damper element may, but need not be in the form of a damper pad or ring. 
     In a further aspect, the present invention includes providing a predetermined preload to the at least one damper element. The preloading may be chosen to provide additional damping effectiveness; furthermore, preloading may also (or alternatively) be used to provide self-leveling for the mixing frame when it is at rest. 
     In a further aspect, the present invention includes an indexing structure associated with the pivot to positively orient the mixing frame assembly to the base. The indexing structure may be formed integral with the pivoting support or may be a separate part attached to the pivoting support. 
     In a further aspect, the present invention includes an improved spring mounting bushing arrangement having a bushing with a V-groove accepting an end turn of a helically wound tension spring, with an included angle of the V-groove allowing a relatively loose fit of the end turn in the V-groove. Providing such a loose fit enhances the ability of the spring mounting bushing to react to and recover from misalignment of the spring end turn and the bushing, returning the end turn into proper alignment after the end turn is dislodged from the bushing as a result of a shock load. In one embodiment the bushing is free to rotate, and in another embodiment, the bushing is fixed against rotation. In a further aspect, the fixed bushing may include an eccentric adjustment feature to allow selection from among a plurality of mounting lengths for the springs of the present suspension. In a still further aspect, the present invention provides the convenience of a degree of self-leveling of the mixing frame assembly when it is at rest. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an assembly view of an embodiment of the present invention in the form of a vortex mixer with single pivot support and with an enclosure shown in phantom. 
         FIG. 2  is an exploded view of the vortex mixer of  FIG. 1  with parts omitted for clarity. 
         FIG. 2A  is an exploded view of an alternative embodiment of the vortex mixer of  FIG. 1  with parts omitted for clarity. 
         FIG. 3  is a fragmentary detail view of a single pivot support useful in the practice of the present invention. 
         FIG. 3A  is a simplified 3 dimensional force diagram to illustrate certain aspects of the present invention. 
         FIG. 4  is an alternative embodiment of the present invention with part removed to show certain details of the suspension system for a vortex mixer useful in the practice of the present invention. 
         FIG. 5  is a top plan view of suspension parts for the vortex mixer according to  FIG. 4 , illustrating certain details of the present invention. 
         FIG. 6  is a side elevation section view of the parts shown in  FIG. 5 , taken along line VI-VI of  FIG. 5 . 
         FIG. 7  is a perspective view of the parts shown in  FIG. 6 , along with the section plane VI. 
         FIG. 8  is a front elevation view of the mixer parts shown in  FIG. 5 . 
         FIG. 9  is an elevation section view of the parts shown in  FIG. 5 , taken along line IX-IX of  FIG. 5 . 
         FIG. 10  is a perspective view of the parts shown in  FIG. 9 , along with the section plane IX. 
         FIG. 11  is a perspective view of a section of parts shown in  FIG. 5 , taken along a section plane XI conforming to a plane of triangle XI in  FIG. 4 . 
         FIG. 12  is a perspective view of a section of parts shown in  FIG. 5 , taken along a section plane XII conforming to line XII-XII in  FIG. 4 . 
         FIG. 13  is a perspective view of an alternative embodiment for a pivoting support using an elastomeric isolator in the practice of the present invention. 
         FIG. 14  is a side view of the pivoting support of  FIG. 13 . 
         FIG. 15  is a section view in perspective of the pivoting support taken along line XV-XV of  FIG. 13 . 
         FIG. 16  is a side elevation view of another alternative embodiment for a pivoting support using a U-joint in the practice of the present invention. 
         FIG. 17  is a section view of an alternative embodiment of a mixer (without a cover) useful in the practice of the present invention. 
         FIG. 18  is a top view of the mixer of  FIG. 17 . 
         FIG. 19  is an enlarged and simplified view of detail XIX of  FIG. 17 . 
         FIG. 20  is a perspective section view similar to that of  FIG. 19 . 
         FIG. 21  is a plan view of a damper useful in the practice of the present invention. 
         FIG. 22  is a side view of the damper of  FIG. 21 . 
         FIG. 23  is a side view of an alternate pivoting support. 
         FIG. 24  is a plan view of one side of the pivoting support of  FIG. 23 . 
         FIG. 25  is a perspective view of one side of the pivoting support of  FIG. 23 . 
         FIG. 26  is a perspective view of the other side of the pivoting support of  FIG. 23 . 
         FIG. 27  is a plan view of the other side of the pivoting support of  FIG. 23 . 
         FIG. 28  is a section view taken along line XXVIII-XXVIII of  FIG. 27 . 
         FIG. 29  is a side view of an alternate pivoting support. 
         FIG. 30  is a plan view of one side of the pivoting support of  FIG. 29 . 
         FIG. 31  is a perspective view of one side of the pivoting support of  FIG. 29 . 
         FIG. 32  is a perspective view of the other side of the pivoting support of  FIG. 29 . 
         FIG. 33  is a plan view of the other side of the pivoting support of  FIG. 29 . 
         FIG. 34  is a section view taken along line XXXIV-XXXIV of  FIG. 33 . 
         FIG. 35  is a side view of an alternate pivoting support. 
         FIG. 36  is a plan view of one side of the pivoting support of  FIG. 35 . 
         FIG. 37  is a perspective view of one side of the pivoting support of  FIG. 35 . 
         FIG. 38  is a plan view of the other side of the pivoting support of  FIG. 35 . 
         FIG. 39  is a section view taken along line XXXIX-XXXIX of  FIG. 35 . 
         FIG. 40  is a detail section view taken along line XL-XL of  FIG. 18 . 
         FIG. 41  is a side view of a spring attachment ring useful in the practice of the present invention. 
         FIG. 42  is a plan view of the spring attachment ring of  FIG. 41 . 
         FIG. 43  is an exploded view of a spring attachment ring and associated parts from  FIG. 40 . 
         FIG. 44  is a side section view of an alternative suspension, mixing frame and base useful in the practice of the present invention. 
         FIG. 45  is an enlarged section view of an alternative pivoting support. 
         FIG. 46  is a perspective view of the pivoting support of  FIG. 45 . 
         FIG. 47  is a plan view from one side of the pivoting support of  FIG. 45  with an indexing structure removed. 
         FIG. 48  is a side view of the pivoting support of  FIG. 47 . 
         FIG. 49  is a plan view of the other side of the pivoting support of  FIG. 47 . 
         FIG. 50  is a side section view along line L-L of  FIG. 47 . 
         FIG. 51  is a side view of the indexing structure of the pivoting support of  FIG. 45 . 
         FIG. 52  is a bottom plan view of the indexing structure of  FIG. 51 . 
         FIG. 53  is a perspective view of the indexing structure of  FIG. 51 . 
         FIG. 54  is an enlarged fragmentary view of a spring and spring mounting tower with an alternative spring mounting bushing from  FIG. 44 . 
         FIG. 55  is an enlarged fragmentary section view taken along line LV-LV of  FIG. 18 . 
         FIG. 56  is a first side view of the alternative mounting bushing of  FIGS. 44 and 54 . 
         FIG. 57  is a perspective view of the alternative mounting bushing of  FIG. 56 . 
         FIG. 58  is an end view of the alternative mounting bushing of  FIG. 56 . 
         FIG. 59  is a second side view of the alternative mounting bushing with the bushing rotated 90 degrees about a cylindrical axis thereof with respect to the view shown in  FIG. 56 . 
         FIG. 60  is a section view along line LX-LX of  FIG. 58 . 
         FIG. 61  is a perspective view of another embodiment of the pivoting support 
         FIG. 62  is a plan view from one side of the pivoting support of  FIG. 61 . 
         FIG. 63  is a perspective view of the pivoting support of  FIG. 61 . 
         FIG. 64  is an exploded perspective view of the pivoting support of  FIG. 61 . 
         FIG. 65  is a side section view along line LXV-LXV of  FIG. 62 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is directed to design goal of improving suspension of a mixing frame assembly in a mixing machine. 
     It has been found preferable to decrease a gear reduction ratio between an electric motor driving the mixer to increase both the spin and orbit rotational speeds resulting in improved mixing action. However, when this is done, it is also desirable to increase machine stability. 
     A deficiency in some prior art designs was that the machine was not balanced in certain conditions. 
     The mixer of the present invention has been designed to seek balance for the mixing machine in all configurations, including i) empty, ii) loaded with 5 gallon bucket, and iii) loaded with 1 gallon can using an adapter. Balance is achieved in the empty state by balancing all rotating components. The best balance in the other configurations is achieved by positioning the paint container average center of mass on both a spin axis and an orbit axis. 
     Because paint is approximately homogeneous, positioning the center of volume also generally positions the center of mass. It has been found, however, that rotational balance is dependent on the density and viscosity of the paint or other material to be mixed. As used herein, the term “paint” is understood to include paint and all other similar liquid coatings requiring mixing, typically to blend pigment and vehicle. 
     Another aspect of the mixer disclosed herein improves machine isolation by decreasing machine resonance frequencies in the 3 rotational degrees of freedom (DOF) (rotation around three mutually orthogonal x, y, and z axes). The resonance frequency or frequencies are decreased to a point substantially less than the driving frequencies which correspond to the rotational velocities of the spin and orbit motions. It has been found that reducing the resonance frequency to be less than or equal to 1/√{square root over (2)} times the lowest driving frequency or approximately 0.7 times the lowest driving frequency is desirable. 
     A machine&#39;s natural frequency is a function of mass and spring rate. Because the mass of the coating liquid load varies, the machine&#39;s natural frequency varies. A deficiency of some prior art designs was that the spring rate(s) of the isolators was very stiff, resulting in the machine operating at or near resonance with certain liquid product weights. Decreasing the spring rate significantly in the present invention brings the natural frequency (with and w/o product) much below the operating frequency. 
     A decrease in the spring rate in all 6 degrees of freedom (DOF) is not particularly desirable due to issues with loading (the can holder is not stable, and tends to move when the operator bumps the holder while loading). In addition, shipping the machine is complicated when all 6 DOF are left ‘loose’. 
     In connection with the present mixer, it has been determined that it is desirable to isolate the rotational DOF, while the translational DOF can be ignored (or positively restrained). Using a pivoting support such as a ball joint between a base of the machine and a mixing frame assembly carrying the paint container holder to allow rotational movement, but restricting translation between the mixing frame assembly and the base, allows more stability when loading liquid product into the mixer, and makes the mixer easier to prepare for shipment. 
     It has also been found desirable to add one or more dampers to decrease transmissibility when the machine spins up, and down (passing through resonance). 
     It has been found convenient, (but not essential) to match resonance frequencies in the 3 rotational degrees of freedom, to result in fewer natural frequencies. 
     It has also been found convenient, but not essential, to balance the mass cross the center plane running vertically along the lateral centerline of the machine (dividing the machine left-right). 
     Referring to the Figures, and most particularly to  FIG. 1 , a vortex mixer  10  embodying the present invention may be seen. Mixer  10  has a paint container holder  12  in the form of cylindrical bucket adapted to receive a paint container, typically cylindrical. The mixer  10  shown is sized to mix paint in a 5 gallon container, but it is to be understood that the present invention is not limited to any particular size of paint container. To mix the paint, the mixer  10  rotates the holder  12  about a spin axis  14  and an orbit axis  16 . 
     Referring now also to  FIG. 2 , an electric motor  18  operates through a tight angle gear reducer  20  to rotate an orbit shaft  22  carrying a counterweight  24  and a rotating arm  26  on which the holder  12  is mounted using a spin shaft  28  supported for rotation about a stationary bevel ring gear  30  via a pinion gear  32 . Gear  30  is supported by a top mix frame element  34  which is fastened to a bottom mix frame member  36 . The components of the holder  12  through the bottom mix frame member  36  make up a mixing frame assembly or paint container holder assembly  38 , which may or may not also include the liquid paint and container (not shown). 
     Mixing frame assembly  38  is supported by a single pivoting support  40  on a base  42 . Support  40  permits the mixing frame assembly to pivot about base  42  in at least two directions (and in some embodiments, three directions), and may prevent substantial lateral or linear motion between assembly  38  and base  42 . For convenience, three mutually orthogonal axes  16 ,  44 , and  46  are shown in  FIG. 1 , with conventions assigned as follows: axis  16  is a “z” axis, axis  44  is an “x” axis, and axis  46  is a “y” axis. The pivoting or rotational directions of yaw, pitch and roll about the z, x and y axes are indicated, respectively by arrows  48 ,  50 , and  52 . It is to be understood that these conventions are arbitrary and not limiting. Furthermore, the directional arrowheads on arrows  48 ,  50 , and  52  are arbitrary and not to be taken as limiting. (Corresponding rotational directional arrows  48 ′,  50 ′, and  52 ′ in the following drawings are to be understood to be bidirectional.) 
     A plurality of elastomeric bumpers  59  are provided to act as cushions at the end of travel for the movement of the mixing frame assembly  38  when it comes into contact with base  42 , for example, while loading or unloading the paint container from the holder. 
     Referring now to  FIG. 2A , an exploded view of an alternative embodiment  10 ′ of the mixer  10  shown in  FIGS. 1 and 2  may be seen. This embodiment has the same electric motor  18  operating through the right angle gear reducer  20  to rotate the orbit shaft  22  carrying a counterweight  24 ′ and the rotating arm  26  on which a holder  12 ′ is mounted using the spin shaft  28  supported for rotation about the stationary bevel ring gear  30  via the pinion gear  32 . Holder  12 ′ may be the same as holder  12 , if desired. The embodiment  10 ′ of  FIG. 2A  differs from that shown in  FIG. 2  in that the top mix frame element  34  has been replaced by a gear support plate  34 ′ mounted to the pair of brackets  35  for gear reducer  20 . In this embodiment, gear  30  is mounted to gear support plate  34 ′. The brackets  35  are fastened to a modified bottom mix frame member  36 ′. The components of the holder  12 ′ through the bottom mix frame member  36 ′ make up a modified mixing frame assembly or paint container holder assembly  38 ′, which may or may not also include the liquid paint and container (not shown in  FIG. 2A ). 
     In this embodiment, modified mixing frame assembly  38 ′ is preferably supported by an improved pivoting support  240  on a modified base  42 ′. Similar to the embodiment shown in  FIG. 1 , support  240  permits the mixing frame assembly to pivot about the base in at least two directions, (while limiting or substantially preventing rotation about the z or orbit axis  16  which is coincident with an axis of shaft  22 ). Support  240  also preferably prevents substantial lateral or linear motion between assembly  38 ′ and base  42 ′. It is to be understood that the three mutually orthogonal axes  16 ,  44 , and  46  shown in  FIG. 1  (together with conventions assigned thereto) are applicable to the embodiment shown in  FIG. 2A . As with respect to  FIG. 1 , it is to be understood that the conventions and arrowheads are arbitrary and not limiting, with corresponding rotational directional arrows  48 ′,  50 ′, and  52 ′ in the following drawings being understood to be bidirectional. 
     In the embodiment shown in  FIG. 2A , a plurality of elastomeric bumpers  59 ′ are provided on base  42 ′ to act as cushions at the end of travel for the movement of the mixing frame assembly  38 ′ when approaches contact with the base, for example, while loading or unloading the paint container from the holder. It is also to be noted that in the embodiment of  FIG. 2A , the spring mounting arrangements, including the towers  92 ′ and end mounting bushings  406  are different from those shown in  FIG. 2 , and are described in more detail infra. Also as will be described in more detail infra, the functions of dampers  84 ,  85  and  89  have are accomplished using a visco-elastic ring  212 . 
       FIG. 3  is an enlarged fragmentary view of an alternative pivoting support  40  using a spherical bearing  54  with a bearing retainer block  56  and a U-shaped flange  58 , secured together by a machine screw  60 , nut  62 , and spacers  64 . Flange  58  is preferably welded to the underside of bottom mix frame weldment plate  36 , and retainer block  56  is preferably secured to base  42  by a pair of machine screws  66  (see  FIG. 6 ). It is to be understood that other structures may be used for the pivoting support, such as a clevis and pin arrangement, a universal joint, or an elastomeric mounting device. Furthermore, it is to be understood that in the practice of the present invention, the roll, pitch and yaw axes do not necessarily need to pass through a single point, but may in fact be displaced, if desired. However, one desirable aspect of a paint mixer is to reduce the height to which a paint container must be lifted to be inserted into the holder  12 , and consequently, it has been found desirable to have the height of the pivoting support  40  be minimized to the extent practicable. 
       FIG. 3A  is a simplified 3 dimensional force diagram to illustrate certain aspects of the present invention. An idealized or simplified conceptual model  80  includes three pair  74 ,  76 ,  78  of springs perpendicular to each of the x, y and z axes  44 ,  46 ,  16 . 
     The equivalent moment arm or radius that each pair of springs acts through is indicated by dimensions or radii  68 ,  70 , and  72 . Roll springs  74  act through the roll radius  68 , to react to roll motion in the roll rotational directions indicated by arrow  50 ′. Pitch springs  76  act through the pitch radius  70  to react to pitch motion in the pitch rotational directions indicated by arrow  52 ′. Yaw springs  78  act through the yaw radius  72  to react to yaw motion in the yaw rotational directions indicated by arrow  48 ′. The equivalent mass and mass moment of inertia for each of the three rotational directions or degrees of freedom are to be understood to be centered at the origin  82  of model  80 . It is to be understood that the origin  82  corresponds to one or more pivot points in the pivoting structure, whether one or more than one pivot point (i.e., there may be separate or congruent pivot points for each axis of rotation) exists in the pivoting structure. 
     Each of the x, y and z (roll, pitch and yaw) axes may be characterized by a plane perpendicular to the respective axis, and a two dimensional model for determining the natural frequency in each of the planes may be represented by Equation (1):
 
ω n =( k   t   /J ) 1/2   (1)
 
where ω n  is the natural frequency, k t  is an effective torsional spring constant, and J is the mass moment of inertia about the rotational axis of interest (of the mixing frame assembly  38 ) taken with respect to the pivot point for that axis in the pivoting structure.
 
     In the simple model, if damping is present,
 
ζ=λ/2( k   t    J ) 1/2   (2)
 
where ζ is the damping coefficient and λ is the scalar coefficient of a damper according to:
 
 F=λdL/dt   (3)
 
where F is the force produced by the damper, and dL/dt is the velocity at which parts on either side of the damper move. It is to be understood that one or more equivalent dampers may be added to one or more of the axes in parallel with one or more of the springs  74 ,  76 ,  78 , it being understood that each damper may be located at a different radius than its corresponding spring, with consequent difference in leverage with respect to the respective axis on which it acts. In  FIG. 3A , a roll damper  84  is illustrated at a damper radius of dimension  86  to damp roll motion  50  about the x or roll axis  44 . Similarly, a pitch damper  85  is illustrated at a pitch damper radius  87  to damp pitch motion about the y or pitch axis  46 . A yaw damper  89  is shown schematically at a yaw damper radius  91  to retard yaw rotational motion about the z or yaw axis  16 .
 
     The frequency at which a forcing function will result in an undamped or underdamped system exhibiting its peak amplitude response is the resonant frequency. For undamped systems, the resonant frequency and natural frequency are the same. For underdamped systems with damping (i.e., ζ&lt;1) the resonant frequency is related to the natural frequency through the damping coefficient ζ by equation (4):
 
ω resonance =ω n (1−ζ 2 ) 1/2   (4)
 
Thus it can be seen that the resonant frequency is less than the natural frequency for such underdamped systems, but as damping is reduced, the resonant frequency converges to the natural frequency.
 
     In the model illustrated in  FIG. 3A , the springs and damper are shown located perpendicular to the moment arms (radii) through which they act on the mass having its respective polar moments of inertia centered at  82 . However, in practice, it has been found desirable to reposition the springs (and dampers if any) to react with the mass and respective rotational inertial components of the mixing frame assembly, both to reduce the volume that would otherwise be needed (if the springs and dampers were perpendicular to the moment arms as shown in  FIG. 3A ) and also because it has been found desirable to have the individual actual springs and damper or dampers react to rotation motion in more than one direction or DOF. In other words one actual spring can serve as an effective spring in two or three rotational dimensions. Similarly, one actual damper can serve as an effective damper in multiple dimensions. For symmetry and balance, however, it has been found preferable to have the springs operate in pairs on opposite sides of the pivoting support. 
     It is also desirable to have a compact “footprint” or small plan view area for vortex paint mixers, to make efficient use of the space needed for the mixer. To that end, the suspension system of the present invention is “folded” or collapsed to reduce the mixer footprint. While the “unfolded” condition of the suspension system is shown in  FIG. 3A , in practice it is desirable to reduce the size of the space required by the suspension system of the present invention. Furthermore, by realigning the springs and damper or dampers in the practice of the present invention, one actual spring can be made to deliver forces equivalent to two or more theoretical springs illustrated in FIG.  3 A., thus reducing the cost as well as the size of the mixer embodying the present invention. 
     Referring now most particularly to  FIGS. 4-7 , certain views of the base  42  and suspension  88  for the mixing frame assembly  38  of the present invention may be seen. It is to be understood that the design of suspension  88  is symmetric about line VI-VI in  FIG. 5 , but such symmetry is not required in the practice of the present invention. Comparing the embodiment shown in these Figures with that of  FIGS. 1 and 2 , it may be seen that in the practice of the present invention, either individual towers  90  may be used or combined towers or upright members  94  may be used for the springs. In  FIGS. 1 and 2 , each spring is supported by a separate tower  90 , forming a first plurality of towers. Using such an arrangement allows each spring to be individually oriented to the mixing frame assembly  38  as desired. In the embodiment shown in  FIGS. 4-12 , a pair of towers or upright members  94 ,  96  may each be used to support a pair of springs. More particularly, a front member  94  supports a first pair of springs  98 ,  100  at the front of mixer  10 , and a rear member  96  supports a second pair of springs  102 ,  104  towards a rear of mixer  10 . It is to be understood that side members may be used instead of front and rear members in an alternative embodiment (not shown) in the practice of the present invention. Furthermore, various other combinations of spring and damper supports may be used, for example, a single upright member (not shown, but similar to a combined version of members  94  and  96 ) while remaining with the scope of the present invention. 
     Since the design shown in  FIGS. 4-12  is symmetric about line VI-VI, only one side will be described, it being understood that the following description applies equally to parts for the other side. Front spring  98  is angled towards the mixing frame assembly in three dimensions (i.e., it is not aligned parallel to any of the x, y, or z axes as shown, for purposes which will be described infra. Spring  102  is shown generally parallel to the x-z plane, but may be angled, as indicated by dashed line  106 , if desired, while still remaining within the scope of the present invention. If used, a damper  108  may be oriented in a two or three dimensional angle, again according to principles described infra. 
     In  FIG. 5 , viewing the mixer parts perpendicular to the x-y plane, it may be seen that vector components of the respective forces of springs  100  and  104  will exist in the x-y plane along dashed lines  110  and  112  to counteract a yaw rotational movement  48 ′ of the mixing frame assembly  38 . 
     In  FIG. 6 , viewing the mixer parts perpendicular to the x-z plane, it may be seen that vector components of the respective spring forces of springs  98  and  102  will exist in the x-z plane along dashed lines  114  and  116 , respectively, to counteract pitch rotational movement  50 ′ of the mixing frame assembly  38 , because springs  98  and  102  are positioned at angles  118 ,  120 , respectively. A similar effect will be produced for roll rotational movement. It may be noted that the vector components along the dashed lines mentioned correspond to certain of the springs shown in the model of  FIG. 3A , and the dot dashed lines  122  extending from the dashed lines in  FIG. 6  correspond to the radii in  FIG. 3A  through with the spring forces act to counter various rotational movements caused by imbalance of the load on mixing frame assembly  38 . Similarly, the dot dashed lines  123  in  FIG. 5  illustrate radii through which springs  100  and  104  act, although lines  123  are not aligned with the x, y, z coordinate system. The springs may be connected through rollers  123  secured by an axle  124  through ears  126  integrally formed in members  94 ,  96  at one end of the springs, and through ears  128  welded to the top mix frame weldment  34  at the other end of the springs. When used, dampers may have threaded mounting rods  130  carried by ball joints  132  and secured with nuts (not shown) either to towers  92  or to upright members  94  and  96 . 
     Referring now to FIGS.  6  and  8 - 10 , when desired, one or more dampers  108  may be used. Damper  108  is mounted at a three dimensional angle, as may be most clearly seen in  FIGS. 6 and 8 . Angle  134  is in the x-z plane of  FIG. 6  and angle  136  in  FIG. 8  is in the y-z plane, which is also the section plane in  FIGS. 6 ,  8 ,  9  and  10 . Because damper  108  (and its partner  109 ) are oriented primarily upright (or generally aligned with the z axis  47 ), primary damping will be for roll and pitch motions  50 ′ and  52 ′, with secondary damping (because of angles  134  and  136 ) of yaw motion  48 ′. 
     Referring now to  FIG. 11  and also back to  FIG. 4 , a section XI through an axis  138  of spring  98  and a line  140  to the pivot may be seen in  FIG. 11 . The view shown in  FIG. 11  is taken through the axis  138  of spring  98  and the center of the pivoting support  40 . It is to be understood that line  140  in  FIG. 4  is aligned with dot dashed line  142  in  FIG. 11 , when viewing perpendicular to the x-y plane. Line  142  corresponds to a radius or moment arm through which spring  98  acts on the mixing frame assembly  38 . 
     Referring now to  FIG. 12  and also back to  FIG. 4 , a section XII through line XII-XII may be seen in  FIG. 12 . The view shown in  FIG. 12  is a section through an axis  144  of spring  104  and the center of pivoting support  40 . It is to be understood that dot dashed line  146  corresponds to a radius or moment arm through which spring  104  acts on the mixing frame assembly  38 . 
     One way of carrying out the design for the mixer is as follows. The mixing frame assembly (or pivotably mounted corresponding structure) is modeled using a dynamics analysis modeler computer program. One such program suitable for this purpose is Visual Nastran 4D, available from MSC.Software, 500 Arguello Street, Suite 200, Redwood City, Calif. 94063. 
     The three rotational resonant modes are preferably matched to get the response to the forcing functions as clean as possible. Using equation (1) the springs are selected and oriented to achieve at least pitch and roll natural frequencies substantially below the lower of the spin and orbit forcing function frequencies corresponding to the spin and orbit rpms. For convenience, one pair of springs (e.g., the rear springs  102  and  104 ) may be oriented generally vertically in the y-z plane, and another pair of springs (e.g., the front springs  98  and  100 ) may be used to adjust yaw response by angling each spring of that pair out of the x-z plane. Desirably each fundamental or lowest natural frequency or resonant frequency in the x, y and z rotational directions is less than 0.707 times the lowest forcing frequency that can excite such resonant frequency or frequencies. The spring constant or spring rate and/or the effective radius to the pivot location are preferably adjusted to obtain the desired matching of resonant frequencies and frequency difference(s) from the closest forcing function frequency. Normally, this is carried out using an empty mixer, since that condition will result in the highest resonant rotational frequencies, with little or no change in the forcing function frequencies between empty and loaded mixer conditions. It will be found that an angle and radius may be selected to balance or match the three lowest rotational resonance frequencies. However, it may be found unnecessary or not desirable (for example, due to space considerations in the mixer) to exactly balance all three rotational resonance frequencies. Alternatively, it may not be necessary to match, for example, the yaw resonant frequency, if yaw motion at resonance is not significant. 
     It is to be understood that the first set or pair of springs may in the alternative or in addition be angled, as well, if desired.  FIG. 5  illustrates this option for the present invention at dashed line  106 . 
     To address the roll motion, one may, for convenience, hold the spring constant fixed and adjust the working radius and angle of the spring to get an effective spring rate (i.e., corresponding to a spring perpendicular or orthogonal to the working radius) while remaining within the physical constraints of the mixer environment. With the arrangement shown, it is to be understood that moving springs laterally apart will increase the roll natural frequency, with all other parameters held constant, because of an increase in the effective radius. 
     Similarly, moving springs apart along the roll axis  44  will result in a higher pitch rotational resonance, since the effective moment arm or radius will increase, assuming all other parameter are held constant. 
     Starting with a vertical spring orientation and angling the spring from the vertical will increase the effect on yaw, while reducing the effect on one or both of roll and pitch (depending upon the direction of angling). In the design shown, the two front springs  98  and  100  have been angled to increase effect on yaw motion. 
     Adding dampers to the system is analogous to the design effort carried out for the springs. Orienting the dampers vertically results in no yaw damping, while angling the dampers will increase yaw damping, while reducing damping in one or both of the roll and pitch rotational directions. It has been found satisfactory to use only two dampers, angled to achieve sufficient damping in all three rotational directions. Alternatively, an annular damper element, described infra, has been found desirable for the practice of the present invention. 
     Referring now to  FIGS. 13 ,  14 , and  15 , an alternative embodiment  40 ′ for the pivoting support  40  may be seen. This embodiment of a pivoting support  40 ′ may utilize an isolator  146  which is commercially available. In this embodiment, the elastomeric shock mount isolator  146  has a steel mounting plate  148  embedded within an elastomeric body  150 , made of, for example, synthetic or natural rubber. Preferably a rigid tube  152 , which may also be made of steel, is molded in body  150 . In use, one of the plate and tube  148 ,  152  is secured to the base  42  and the other of the plate and tube  148 ,  152  is secured to the mixing frame assembly  38 , preferably at the bottom mix frame weldment  36 . 
     As mentioned above, it is within the practice of the present invention to have a pivoting support which does not permit yaw motion. Furthermore, it is also within the scope of the present invention to have a pivoting support which has offset pivot points or locations for the respective rotational axes, in which case, the effective radii will be with respect to different planes containing the respective pivot point addressed. 
     One still further alternative embodiment  40 ″ of the pivoting support  40  is shown in  FIG. 16  as a conventional U-joint  154 . In use, U-joint  154  is connected between the base  42  and the mixing frame assembly  38 , preferably at the bottom mix frame weldment  36 . 
     Referring now to  FIGS. 17-40 , and most particularly to  FIGS. 17-22 , an alternative embodiment  210  of the mixer  10  may be seen. Like mixer  10 , mixer  210  has a suspension system  288  utilizing a pivoting support  240  and a plurality of springs  298 , and generally operates in the same way and according to generally the same principles as described for mixer  10 . Mixer  210  has a damper  208  preferably in the form of an annular member or ring  212  formed of commercially available viscoelastic polymer material. In the practice of the present invention, it has been found desirable to use a ring having a 70 durometer (shore 00) but it is to be understood that other geometries and durometers may be used in the practice of the present invention for damper element  208 . Furthermore, various shapes for one or more dampers or damper elements may be used, although, as is illustrated in  FIGS. 21 and 22 , a ring having dimensions of 1.00 inches thickness, 5.00 inches OD, and 2.81 inches ID has been found preferable for use herein. 
     While it is preferable to have the damper element  208  extend substantially completely around the pivot  240 , an alternative within the present invention is to have a damper element extending only partially around the pivot. A still further alternative within the present invention is to have at least one and preferably a plurality of damper elements located at one or more predetermined distances (or, equivalently, at a predetermined effective radius) from the pivot. In all embodiments or alternatives, the damper element is located between a mixing frame assembly  238  and a base  242  of the mixer  210 . The damper element  208  acts as an energy absorber when the mixing frame assembly  238  pivots with respect to the base  242  and deforms the damper element  208 . The damper element or elements may be arranged anywhere between the mixing frame assembly and the base, while still remaining within the scope of the present invention. Preferably, the mixing frame assembly has a generally planar support member  236  and the base  242  is also generally planar, in which case the damper element is preferably located between the generally planar support member  236  and the base  242 . 
     It has also been found preferable to provide a predetermined preload for the damper element, to obtain more effective or efficient use of the viscoelastic material forming the damper element. It is also to be recognized that the viscoelastic material of the damper element will act as a spring in addition to acting as an energy absorber, and the spring effect of viscoelastic material must be taken into account in the design and construction of the suspension system of the present invention. In one embodiment of the present invention with a mixing frame assembly having a weight of approximately 100 pounds (without a paint container), a total preload of about 350 pounds on the damper element has been found desirable, resulting in sufficient deformation (which may, but need not be in the form of compression) of the damper element to achieve the desired spring action. It is to be understood to be within the scope of the present invention to have deformation of the damper element other than compression, such as tension or shear or a combination thereof. However, in a preferred embodiment, the preload is achieved by applying a compressive load across the pivoting support  240 . In another aspect, the predetermined preload may be chosen (additionally or alternatively) to be an amount sufficient to provide a substantial degree of leveling for the mixing frame assembly when it is at rest. 
       FIGS. 19 and 20  show one form of pivoting support  240 . Other variations for the pivoting support  240  may be seen in  FIGS. 23-39 . In the embodiment shown in  FIG. 19 , the pivoting support  240  is located between the mixing frame assembly  38  and the base  42 . A first metal mounting structure or first flange  248  is located peripherally of an elastomer element  250 . A second metal mounting structure  252  is located centrally of the elastomer element  250 , with the first and second metal mounting structures preferably bonded to the elastomer element. An insert  258  is received in structure  252  and secured therein by a machine screw  259 . Insert  258  is secured to a flange  254  by welding. Flange  254  is mounted to the mixing frame assembly  38  by three bolts  256 . A spacer ring  260  may be used to locate the damper ring  212  in a concentric relationship to the pivoting support  240 . 
     It is to be understood, however, that other arrangements may be used to locate the damper element at a predetermined radius from the pivot, for example, and not by way of limitation, either (or both) the damper element or pivot may be resized to closely interfit with each other, without the need for the spacer ring  260 , keeping in mind that resizing the damper element will affect the damping and spring properties thereof. 
     Referring now most particularly to  FIGS. 23-28 , an alternative pivoting support  340  may be seen. Support  340  is similar to support  240  (corresponding to support  40 ′ shown in  FIGS. 13-15 ), except that support  340  has a round periphery for flange  348  where supports  40 ′ and  240  each have a generally square periphery for plates  148  and  248 . In addition, support  340  preferably has a keyed surface  358  on a cylindrical rod or extension  352  passing through an elastomer body  350 , it being understood that both flange  348  and rod  352  are permanently bonded to elastomer body  350 . Support  340  may have apertures  354  in flange  348  or alternatively apertures  354  may be replaced by threaded studs  356 . 
     Referring now most particularly to  FIGS. 29-34 , a further alternative pivoting support  440  may be seen. Support  440  has the square periphery plate or flange  148  bonded to elastomer element  350  which in turn is bonded to rod  352  having keyed surface  358  thereon. 
     Referring now most particularly to  FIGS. 35-39 , a still further alternative pivoting support  540  may be seen. Support  540  is similar to the supports described above in that it has the generally square peripheral flange  148  as a first metal mounting structure bonded to an elastomer body  550  which is also bonded to a second metal mounting structure  552  in the form of a rod or tube with a second flange  554  integral therewith, the second flange having apertures  556  therein. The apertures in flange  554  serve as an indexing structure formed integrally with the second metal mounting structure to positively orient the base and mixing frame assembly with respect to each other. It is to be understood that the indexing structure preferably orients the mixing frame assembly to the base in the xy plane, i.e., a plane perpendicular to the z axis. 
     Referring now to  FIGS. 17 ,  18  and  40 - 43 , another aspect of the improved suspension of the present invention may be seen. In this aspect, the mixer  210  has one or more (preferably four) helical extension springs  298  connected between the mixing frame assembly  238  and the base  242 .  FIG. 40  is a view, partly in section along line  40 - 40  of  FIG. 18  showing the arrangement for springs  203  and  202 , although it is to be understood that the same arrangement described infra may and preferably is used for springs  200  and  204 . Each spring is preferably formed as a helix  300 , with each end of the spring having an end turn  302  formed from the helix  300 , which itself is generally cylindrical (see  FIGS. 17 ,  18  and  40 ). In the process of forming end turns, it is not easy to maintain parallelism of the end turns at opposite ends of the spring. Furthermore, each end turn  302  is a portion of the helix  300  and thus has a spiral shape itself. Finally, in one variation (shown in  FIG. 40 ), a primary axis  301  of the spring  298  (more particularly, the cylindrical axis of the helix  300 ) may not be perpendicular to a mounting axis  307  of a bushing  306  to which the spring is mounted, exacerbating the challenge of aligning the spring and its mounting bushing. Nevertheless, this aspect of the present invention is still useful even when the primary axis of the spring is perpendicular to the cylindrical axis of the bushing, as shown and described infra, with respect to  FIG. 55 . 
     In attaching end turns  302  of springs in the assembly of the mixer suitable for the present invention, it has been found that a circumferential U-shaped groove closely matching the wire diameter  304  of the spring allows the end turn to jump out of the groove when tension is relieved on the spring, as may happen as a result, e.g., of shock loading, in shipping, handling or even operating the mixer. Even partial unmounting of one or more end turns has been found undesirable. Accordingly it has been found advantageous to provide the bushing  306  with a circumferential V-groove  308  formed therein to receive end turn  302 . The V-groove  308  desirably has an included angle  310  sufficiently large enough to permit some misalignment of the end turn in the V-groove when the end turn of the spring is received in the bushing. Preferably the included angle  310  is about 90 degrees. It is to be understood that the wire forming the end turn typically will have a characteristic wire diameter and the V-groove preferably will have an entry dimension or width  305  at the top of the V-groove substantially greater than the wire diameter  304  of the end turn received in the V-groove. 
     The V-groove  308  may have a contoured surface  312  replacing the vertex of the included angle  310 , with the contoured surface  312  preferably in the form of an arc with a radius equal to half the diameter  304 . Providing the bushing  306  with the V-groove  310  guides the end turn  302  back into engagement with the bushing in the event that tension is relieved on the spring, so that the chances of complete disengagement of the spring from the spring mount or misalignment of the end turn in contact with the bushing are reduced. 
     Referring now most particularly to  FIGS. 40 and 43 , various details of the spring mounting arrangement of the suspension of the present invention (which includes the improved bushing  306 ) may be seen. In the suspension of the present invention, each spring is mounted between the mixing frame assembly  238  and a respective spring tower, with tower  314  for spring  203  shown in section and tower  316  for spring  202  shown partially obscured in  FIG. 40 . As perhaps may be seen most clearly in  FIGS. 17 and 40 , each tower is preferably identical, with a lower mounting hole  318  for front springs  200 ,  203  and an upper mounting hole  320  for rear springs  202 ,  204 . 
     Washers  322  are located on each side of bushing  306 , separated by a first spacer  324  to allow clearance for bushing to turn. A second spacer  326  distances bushing  306  from the side of the tower to allow clearance for the spring. A machine bolt  328  is received through either hole  318  or  320 , with a backing washer  330  and lock nut  332  securing the spring mounting assembly to the tower. 
     Referring now to  FIGS. 44-60 , an alternative suspension system  488  for the practice of the present invention may be seen. Suspension system  488  is similar to suspension systems  88  and  288  described supra, except that it uses an alternative pivoting support  440  and an alternative spring mounting in the form of an alternative bushing  406 . System  488  preferably uses the same damper element  208  described supra positively located by and concentric to pivoting support  440 . Bushing  406  is a fixed, non-rotating type, used with both top and bottom end turns on springs  298 . As shown, bushings  406  located at the top of towers  492  are adjustable to one of a plurality of settings, more particularly, to LOW, MEDIUM or HIGH settings or positions, as will be described more fully infra. Similar to suspensions  88  and  288 , the suspension system embodiment shown in  FIG. 44  may have elastomeric bumpers  459  to cushion the limit of pivoting motion of mixing frame  438  as it approaches base  442 . 
     Referring now most particularly to  FIGS. 45-53 , pivoting support  440  is similar to support  240 , except that a square cross section hole  445  is broached in tube  252 . The square hole is sized to closely receive a square cross section extension  446  of a T-shaped indexing structure  448 . Structure  448  preferably has an integrally formed cross bar  450  with a pair of threaded apertures  452  to secure structure  448  to the mixing frame  438 , using conventional threaded fasteners, as shown in  FIG. 44 . Using this arrangement will positively align the mixing frame  438  to the base  442 . Optionally spacer ring  260  may be used with support  440 , as shown in  FIGS. 20 and 46 , to positively locate damper element  208  concentrically with respect to the pivoting support  440 . The remaining features of pivoting support  440  may be the same as those of support  240 , described supra. 
     Referring now most particularly to  FIGS. 42 ,  43  and  54 - 60 , the bushing  406  may be seen to have a circumferential groove  410 , which is preferably a V-groove. Groove  410  is preferably the same as the V-groove in bushing  306  described supra. Bushing  406  differs from bushing  306  in that bushing  406  is fixed and eccentric, and positionable to a selected one of a predetermined number of positions (four are shown) while bushing  306  is free to rotate and is concentric to its mounting. In bushing  406 , a through bore  412  is located eccentrically to the circumferential groove  410 . At least one and preferably two projections  414 ,  416  extend out from a mounting surface  418  of bushing  406 , where the mounting surface is generally perpendicular to a cylinder axis of the circumferential groove  410  and bore  412 , which are preferably parallel to each other. 
     Each tower  492  preferably has identical upper and lower hole patterns  494 ,  496 , each made up of five apertures, with a central aperture  498  for receiving a threaded fastener  500  and four positioning apertures  502 ,  504 ,  506  and  508  having centers located on a circle sized to receive projections  414  and  416 . More or fewer positioning apertures may be provided, if desired, while still remaining within the scope of the present invention. Bushing  406  may be adjusted to accommodate variations in the length of springs  298  which may result from manufacturing tolerances for the springs. If projection  414  is received in positioning aperture  502 , bushing  406  will be located for a minimum spring extension length. If projection  414  is located in positioning aperture  506 , bushing  406  will be located for a maximum spring extension length. If projection  414  is located in either of positioning apertures  504  or  508 , bushing  406  will be positioned for a “medium” spring extension length, about half way between the minimum and maximum. It is to be understood that the projection  416  will be automatically received in the positioning aperture which is diametrically opposite the positioning aperture in which projection  414  is received. 
     Referring again to  FIG. 44 , tower  492  to the left is a “front” tower and has the bushing  406  attached using the lower hole pattern  496 , while the tower to the right is a “rear” tower and has the bushing  406  preferably attached using the upper hole pattern  494 . It has been found to desirable to increase the spring extension length by the distance between the hole patterns  494  and  496  because of the additional weight (most notably caused by the motor) towards the rear of the mixing frame assembly. It has been found preferable to use bushing  406  for the lower end turn of each of springs  298 , and to provide only “medium” positioning apertures  504  and  508  for lower end turns. However, it is within the scope of the present invention to provide more positioning apertures for the lower end turns of springs  298 , if desired. The lower end turns of springs  298  are each secured to the mixing frame assembly by brackets  426  holding bushings  406 . 
     In  FIG. 55 , further details for the mounting arrangement of bushing  406  may be seen. It is to be understood that in this arrangement, the primary axis  301  of the spring  203  is perpendicular to a cylindrical axis  436  of the bushing  406 . Axis  301  is parallel to the plane  490  of an angled upper surface  491  of tower  492 . Angling surface  491  provides improved alignment of the spring with the bushing, more particularly, improved alignment of the end turn of the spring with the groove  308  of the bushing  406 . A pair of washers  420  are received on threaded fastener  550 , and a lock nut  510  secures the assembly shown in  FIG. 55  together, holding the bushing  406  in a “maximum” position (i.e., a position in which a distance to the end turn is maximized) with projection  414  received in aperture  508  and projection  416  received in aperture  504 . The width  405  of the entry to the circumferential groove  410  is to be understood to be substantially wider than the wire diameter of the end turn of the spring to be received in the groove  410 . 
     Returning now to  FIGS. 56 ,  57  and  59 , visible indicia may be provided on bushing  406  in the form of one or more arrows  428 ,  430 , with each of the arrowheads pointing toward each other. With the arrows pointing down, the bushing  406  is in the minimum position. With the arrows pointing up, the bushing is in the maximum position, and with the arrows pointing either left or right horizontally (as shown in  FIG. 18 ), the bushing is in a “medium” position. 
     Bushings  306  and  406  may be made of an appropriate polymer, such as nylon or polyurethane, to provide for improved wear resistance and quiet operation of the mixer as it pivots. The respective spring end turn may be installed on bushing  406  by placing the end turn against a sloping conical section wall  432  on the bushing and urging the end turn into the V-groove. The groove  410  of bushing  406  has a short radial section  434  extending generally perpendicularly to the cylindrical axis  436  to retard the spring from disengaging itself from the groove  410 . Bushing  406  also has an enlarged diameter shoulder  444  between groove  410  and mounting surface  418  to retard the spring from “walking” or moving out of groove  410  and towards the mounting surface  418 . 
     Referring now to  FIGS. 61 through 65 , another alternative embodiment  640  for the pivoting support may be seen. Pivoting support  640  includes a plate  648  around which a support element  646  is formed, preferably by molding element  646  to plate  648 . Support element  646  may include an elastomeric body  650  with an integrally molded tube  652  formed therein, with tube  652  having a square cross section hole  645  extending therethrough. Plate  648  may have threaded studs  653  extending therefrom. An indexing structure  662  may be formed by a second plate  654  welded to a square cross section projection  656  having internal threads  658  therein. A conventional threaded fastener  660  may be used to secure structure  662  to support element  646 . Plate  654  may have a plurality of threaded holes  664  therein to receive and secure the mixing frame assembly as with previously described embodiments for the pivoting structure of the present invention. This embodiment may be seen to have conically shaped projections  666 ,  668  of the elastomeric element  650  projecting on opposite sides of plate  648 . It has been found that providing the conically shaped projection  666  in the body  650  on the side facing the indexing structure  662  eliminates or reduces a stress riser that otherwise may precipitate and propagate one or more stress-induced cracks in the body, as for example, may occur with repetitive cycles of flexing the elastomeric body of the pivoting support. 
     This invention is not to be taken as limited to all of the details thereof as modifications and variations thereof may be made without departing from the spirit or scope of the invention. For example and not by way of limitation, it is within the scope of the present invention to provide or use the various aspects of the suspension system claimed herein with other mixers suitable to mix materials other than paints or similar coatings in cylindrical and non-cylindrical containers, with appropriate modifications, if and when needed.