Abstract:
The present invention relates to a passive mass damper for broadband suppression of vibrations. The mass damper preferably includes a bob supported by nonlinear springs with high secant stiffness and low tangent stiffness. The mass damper is mounted on a machine or other source of vibration. The vibration generated by the machine is transmitted to the mass damper and induces off phase vibration of the bob which suppresses the inducing vibration.

Description:
This application is a continuation of and claims the benefit of U.S. patent application Ser. No. 09/082,616, filed May 20, 1998 now U.S. Pat. No. 6,035,981, which itself claims the benefit of U.S. Provisional Application No. 60/047,201, filed May 20, 1997, and U.S. Provisional Application No. 60/050,516, filed Jun. 23, 1997. 
    
    
     TECHNICAL FIELD 
     The present invention generally relates to a device for controlling vibration. More particularly, the present invention relates to a passive mass damper for conservative broadband suppression of vibrations. 
     BACKGROUND 
     In general, vibration originating from machines or other sources is most often undesirable and detrimental. For example, vibration in a precision machining tool may lead to faults and imperfections in work pieces produced on the tool. The vibration also may be transmitted through the floor and disrupt other tools. Additionally, the noise generally associated with machine vibration may be disruptive to workers. 
     Various methods and devices exist to reduce undesirable vibrations and may be generally categorized as vibration isolators or suppressors. Typically, vibration isolation devices operate locally to reduce transmissibility, wherein transmissibility is typically defined as the ratio of the transmitted force to the disturbing force. As such, vibration isolation devices are particularly suitable for reducing discrete and transient vibrations. For example, various reflexive and absorptive material, such as rubber, cork, foam and the like, may be placed in connective elements of a stamping machine, such as the stamping table and legs, to isolate the discrete vibrations associated with the stamping action of the machine. 
     In contrast, vibration suppression devices typically operate globally to suppress vibration. As such, vibration suppression devices are particularly suitable for reducing cyclic vibrations or vibrations which may be difficult to isolate to a particular element of a machine. For example, the motor of a machine generates cyclic vibrations. Rather than attempting to isolate the vibration transmitted through various connective elements of the machine, the entire machine may be mounted on a vibration suppression base. While the vibration suppression base may reduce the global vibration generated by the machine, local transmission of vibration may not be altered. In fact, certain vibration suppression devices may actually amplify local transmission of vibration. 
     Vibration mitigation devices may be categorized further as active or passive devices. Typically, active devices incorporate a feedback system which detects the amplitude and/or frequency of the disrupting vibration and responds accordingly to reduce or eliminate the vibration. Therefore, active devices are capable of broadband reduction of vibration. However, the complexity and cost of typical active devices often make them impractical for many applications. 
     In contrast, passive devices are typically mechanical devices which generally use various spring elements and damping elements to reduce or eliminate vibrations. However, conventional passive devices generally operate to reduce vibrations only in a fairly narrow bandwidth. Additionally, certain materials used in conventional passive devices, such as rubber and lubricating fluid, may be inappropriate for use in certain environments, such as clean room environments. 
     A spring damper device is one conventional passive vibration suppression device which is described in various mechanical textbooks and handbooks. In a spring damper device, a spring element and a damper element reduce vibration by removing the energy of a vibrating system through the damper element. However, the spring damper device typically operates at a narrow bandwidth determined by the stiffness of the spring element and the damper coefficient of the damper element. Typically, vibrations outside of this narrow preset bandwidth will not be effectively reduced. In fact, vibrations at certain frequencies will often produce increased responses with a peak response occurring when the frequency of the vibration is equal to the natural frequency of the spring damper system. Consequently, a spring damper device must often be precisely calibrated to match the frequency of the vibrating system. 
     In another conventional device, a spring element is used in combination with a beam-column element to reduce the transmission of vibration. See U.S. Pat. No. 5,178,357, issued on January 1993, to Platus and related U.S. Pat. No. 5,549,270, issued on August 1996, to Platus et al. More particularly, a spring and a beam-column are calibrated such that one element has a positive stiffness and the other element has an equal negative stiffness. In this manner, an object is supported with net-zero effective stiffness. However, a spring and beam-column pair is required for each axis to be isolated from vibration and each spring and beam-column pair must be precisely calibrated to achieve a net-zero effective stiffness in each axis. As such, this method is fairly complicated and difficult to calibrate and adjust. Additionally, as the requisite negative and positive stiffness are achieve through two separate elements, if one element wears at a rate different than that of the other, their stiffness will no longer match and a net-zero effective stiffness will not be achieved. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a device for broadband suppression of vibrations. According to a preferred embodiment of the present invention, a mass damper device includes a mass element and a plurality of nonlinear spring elements with high secant stiffness and low tangent stiffness. The mass damper is mounted on a vibration source which induces vibration of the mass element on the spring elements. The mass element vibrates off phase from the inducing vibration to suppress the inducing vibration. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING FIGURES 
     The present invention will hereinafter be described in conjunction with the appended drawing figures, wherein like numerals generally denote like elements, and: 
     FIG. 1 is perspective view of a mass damper in accordance with the present invention; 
     FIG. 2 is an exploded perspective view of a portion of the device shown in FIG. 1; 
     FIG. 3 is a cross-sectional view of another portion of the device shown in FIG. 1; 
     FIG. 4 is a cross-sectional view of a ball-in-recess assembly used in the device shown in FIG. 1; 
     FIG. 5 is a cross-sectional view of another ball-in-recess assembly used in the device shown in FIG  1 ; 
     FIG. 6 is a perspective view of a bob used in the device shown in FIG. 1; 
     FIG. 7 is a top view of another mass damper in accordance with the present invention; 
     FIG. 8 is a side view of a portion of the device shown in FIG. 1; 
     FIG. 9 is a cross-sectional view of a ball-in-recess assembly used in the device shown in FIG. 1; 
     FIG. 10 is another cross-sectional view of a ball-in-recess assembly used in the device shown in FIG. 1; 
     FIG. 11 is a perspective view of another mass damper in accordance with the present invention; 
     FIG. 12 is a top view of the device shown in FIG. 11; 
     FIG. 13 is a perspective cross-sectional view taken through line  1 — 1  of the device shown in FIG. 11; 
     FIG. 14 is a perspective view of yet another mass damper in accordance with the present invention; and 
     FIG. 15 is a perspective cross-sectional view taken through line  15 - 15  of the device shown in FIG.  14 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is preferably configured to reduce vibrations in systems such as machines, plants, tools, platforms, and the like which have multi-rotary or reciprocating parts and impact sources, particularly those with parts and sources which cannot be effectively isolated, which have less vibration modes than vibration sources, which require global rather than local transmission reduction, or in which the open loop vibration is substantially dominated by resonance. 
     For example, a mass damper in accordance with a preferred embodiment of the present invention is configured to operate with a Chemical Mechanical Planarization (“CMP”) tool used in the semiconductor industry to planarize and polish wafers to an extremely planar and smooth surface. As background, wafers in a CMP tool are typically held by carrier heads then lowered and pressed against a polishing pad, while a slurry is often added to aid in the CMP process. Additionally, the polishing pad and carrier heads are typically rotated at differential speeds while the carrier heads are typically oscillated back and forth. The multiple directional movement, the unmatched motor speeds and hydrodynamic fluctuation of the entrapped slurry typically creates a combination of high and low frequency vibrations which may result in wafer loss. Also, the resulting vibrations are commonly transmitted through the floor to other vibration sensitive machines and tools while the resulting noise may be detrimental to nearby workers. Although the present invention may be used in a CMP environment, the present invention also is configured to reduce vibration in various environments and systems. 
     With respect to the details of the device, FIG. 1 shows a mass damper in accordance with one embodiment of the present invention. Mass damper  10  has 6 degrees-of-freedom (“DOF”); 3 translational modes along x, y, and z axes, and 3 rotational modes about x, y and z axes. In a preferred embodiment, mass damper  10  preferably includes a plurality of ball-in-recess assemblies as nonlinear spring elements in combination with mass elements to substantially achieve broadband suppression of vibrations. 
     Base assembly  20  is preferably rigidly connected to a source of vibration, such as a machine tool. Base  20  preferably includes base plate  22  and a plurality of anchor bolts  24  and nuts  26 . Base plate  22  is preferably rigidly attached to the source of vibration by anchor bolts  24  and nuts  26  such that vibration is suitably transmitted to base plate  22  without substantial distortion. Base plate  22  is preferably formed from metal, ceramic, or other suitable rigid material. 
     Assembly  30  is preferably rigidly mounted on base plate  22 . Leveler studs  28  are preferably configured to level assembly  30  thereby defining the x-y plane of mass damper  10 . Assembly  30  preferably includes a plurality of ball-in-recess assemblies disposed between bottom plate  32  and top plate  34 . More particularly, with additional reference to FIG. 2, cone-shaped recesses  38 ,  40 ,  44  are suitably formed by known methods in bottom plate  32 . Substantially matching cone-shaped recesses  36 ,  42  and  46  are suitably formed by known methods in top plate  34  (recesses in top plate  34  are not shown). Balls  37 ,  41  and  45  are preferably disposed between recesses  36 ,  38 ,  40 ,  42 ,  44  and  46 , respectively. Balls  37 ,  41  and  45  preferably lie within holes formed in spacer  39  disposed between bottom plate  32  and top plate  34  to substantially ensure constant relative distance between balls  37 , 41 , and  45 . Spacer  39  is preferably formed from TEFLON® or other suitable low friction material to facilitate movement of bottom plate  32  relative to top plate  34 . 
     With additional reference to FIG. 3, tower  50  is preferably threaded into top plate  34  and counter locked by nut  52 . Various methods are known in the art for securing tower  50  to top plate  34 . For example, tower  50  can be welded to top plate  34 . 
     Coil spring  54  is preferably disposed within the vertical centerline of tower  50  to define the z axis of mass damper  10 . One end of coil spring  54  is preferably attached to bottom plate  32  and the other end is preferably attached to the top of tower  50 . More particularly, coil spring  54  is preferably attached to bottom plate  32  using spring anchor  64  and nut  66 . Coil spring  54  is preferably attached to dowel pin  60  by spring anchor  56  and nut  58 . Dowel pin  60  is preferably attached to the top of tower  50  by cotter pin  62 . The tension in coil spring  54  may be adjusted by adjusting either nut  52  or nut  66 . Coil spring  54  may be attached to bottom plate  32  and top of tower  50  using various methods known in the art. 
     Coil spring  54  exerts a compressive force on bottom plate  32  and top plate  34  through tower  50  to suitably pre-compress the ball-in-cone assemblies in assembly  30 . However, various methods are known in the art for suitably pre-compressing ball-in-cone assemblies. 
     With reference to FIG. 4, when mass-damper  10  is undisturbed by external vibrations or forces, ball  37  rests at the vertices of cone-shaped recesses  36  and  38  (for clarity only one ball-in-recess assembly is described). Similarly, balls  41  and  45  rest at the vertices of recesses  40 ,  42 ,  44  and  46 , respectively. Therefore, the weight of top plate  34  and assemblies attached to top plate  34  and the compressive force of coil spring  54  are substantially distributed between balls  37 , 41  and  45 . Accordingly, balls  37 ,  41  and  45  are preferably formed from metal or other high strength material. Although three ball-in-recess assemblies have been described, one skilled in the art will appreciate that any number of ball-in-recess assemblies may be used without deviating from the spirit and scope of the present invention. 
     Referring again to FIG. 1, assembly  70  preferably includes a first bob  72  and a second bob  74  suspended over assembly  30  on cover plate  68 . Cover plate  68  is preferably threaded on tower  50  and counter locked from underneath with a nut (not shown). Various methods are known in the art for securing cover plate  68  to tower  50 . For example, cover plate  68  can be welded to tower  50 . 
     Coil spring  76  is preferably disposed along a channel formed along the vertical center line of first bob  72 . The top end of coil spring  76  is preferably attached to spring anchor  78  which is preferably placed through a hole formed in cover plate  68  and secured by nut  80 . The bottom end of coil spring  76  is preferably attached to the bottom of first bob  72  by a spring anchor (not shown) and nut  52 . Second bob  74  is preferably secured to cover plate  68  in a substantially similar manner. Alternatively, bobs  72  and  74  may be secured to cover plate  68  using various methods known in the art. 
     With reference to FIGS. 5 and 6, a plurality of ball-in-recess assemblies are preferably disposed between tower  50  and bobs  72  and  74 . More particularly, cone-shaped raceways  82  and  86  are suitably formed around the circumference of tower  50 . Substantially matching cone-shaped raceways  80  and  84  are suitably formed around the inner surface of bob  72 . Balls  88  and  90  are preferably disposed between raceways  80 ,  82 ,  84  and  86 , respectively. Additionally, balls  88  and  90  lie within holes formed in curved spacer  92  to ensure constant relative distance between balls  88  and  90 . Spacer  92  is preferably formed from TEFLON® or other suitable low friction material to facilitate movement of bob  72  relative to tower  50 . In a similar manner, Bob  74  is suitably configured with cone-shaped raceways, balls, and curved spacer to facilitate movement of bob  74  relative to tower  50 . 
     Although bob  72  and  74  have been described as two mass elements, any number of mass elements may be used in accordance with the present invention. For example, with reference to FIG. 7, a mass damper is shown with three mass elements. 
     With reference to FIG. 1, a plurality of spring anchors  94  are preferably rigidly attached to tower  50  and a plurality of anchors  98  are preferably rigidly attached to bobs  72  and  74 . A plurality of springs  96  are preferably held in tension between spring anchors  94  on tower  50  and anchors  98  on bobs  72  and  74 . More particularly, with additional reference to FIG. 8, one of the plurality of springs  96  is preferably suitably attached to one of the plurality spring anchors  94  and to one of the plurality of spring anchors  98  by anchor  102  and nut  100 . A plurality of springs  104  held in compression between bores  106  formed in bobs  72  and  74  offset, in part, the force exerted by springs  96 . Bobs  72  and  74  may be suitably pressed against tower  50  using various methods known in the art. 
     Housing  120  substantially encloses assemblies  30  and  70  to protect these assemblies from corrosion or undesired access. Seal  122  substantially hermetically seals housing  120 , except for a hole in bottom plate  32  for coil spring  54  to pass. A plurality of bolts through tapped holes  124  suitably attach housing  120  to assembly  30 . 
     With additional reference to FIG. 9, vibration in the x-y plane suitably translates bottom plate  32  relative to top plate  34 . In response, ball  37  moves from the vertices of recesses  36  and  38  and onto the sloped perimeters of recesses  36  and  38  (for clarity, only one ball-in-recess assembly is described). 
     When ball  37  moves from the vertices of recesses  36  and  38 , a portion of the weight of top plate  34  and the assemblies attached to top plate  34  and the compression force of coil spring  54  is exerted as force P 1  normal to the sloped perimeters of recesses  36  and  38 . Force P 1  may be resolved into a vertical component V 1  and horizontal component H 1 . The horizontal component H 1  acts as a restorative force to translate top plate  34  and the assemblies attached to top plate  34  off phase relative to bottom plate  32 . 
     Moreover, as the slope of recesses  36  and  38  is substantially constant, the restorative force, horizontal component H 1 , is substantially constant for varying displacements of bottom plate  32 . As such, ball  37  and cone-shaped recesses  36  and  38  operate essentially as a nonlinear spring element with low tangential stiffness and high secant stiffness. Therefore, assembly  30  substantially provides broadband suppression of vibration in the x-y plane in the displacement range of the vibration source. Additionally, assembly  30  suitably provides soft support for small displacements in the x-y plane and stiff support for large displacements in the x-y plane. 
     The stiffness required to substantially achieve a broadband suppression of vibration in the x-y axis is a function of the mass of top plate  34  and the assemblies attached to top plate  34 , the mass of the vibration source, and the stiffness coefficient of the source. More particularly, the requisite stiffness is approximately the stiffness coefficient of the source times the ratio of the mass of top plate  34  and the assemblies attached to top plate  34  to the mass of the source. The mass of top plate  34  and the assemblies attached to top plate  34  largely consists of the mass of bobs  72  and  74 . The mass and stiffness coefficient of the vibration source may be measured using methods well known in the art. Alternatively, in the case of machine tools, the mass and stiffness coefficient may be provided by the manufacturers. 
     The effective stiffness provided by the ball-in-recess assemblies in assembly  30  is substantially a function of the forces applied to the balls, the diameter of the balls, and the geometry of the recesses. More particularly, the effective stiffness of a ball-in-recess assembly is approximately equal to the magnitude of the force applied to the ball divided by twice the difference between the radius of the rolling surfaces abutting the ball and the diameter of the ball. 
     The effective stiffness of the ball-in-recess assemblies in assembly  30  is sufficiently tuned such that the broadband response of assembly  30  is substantially centered on the frequency of the vibration. The stiffness of the ball-in-recess assemblies may be suitably tuned by appropriately altering the weight of top plate  34  and the assemblies attached to top plate  34 . Alternatively, the stiffness of the ball-in-recess assemblies may be suitably tuned more easily by appropriately altering the tension in coil spring  54  by adjusting nut  58  or nut  66  thus facilitating easy field tuning of the broadband response of assembly  30 . 
     With reference to FIG. 10, vibration in the x-z or y-z plane translates tower  50  vertically relative to bob  72 . Ball  88  moves from the vertex of cone-shaped raceways  80  and  82  and onto the sloped perimeter of raceways  80  and  82  (for clarity only one ball-in-recess assembly is described). 
     Springs  96  and  104  combine to exert a force P 2  normal to the sloped perimeters of raceways  80  and  82 . Force P 2  may be resolved into a horizontal component H 2  and vertical component V 2 . Vertical component V 2  operates to translate bob  72  off phase from tower  50 . 
     As the slopes of the perimeters of raceways  80  and  82  are substantially constant, vertical component V 2  is substantially constant for varying displacements. As such, ball  88  and raceways  80  and  82  operate essentially as a nonlinear spring element with low tangential stiffness and high secant stiffness. Therefore, assembly  70  substantially provides broadband suppression of vibration in the x-z and y-z planes for the displacement range of the vibration source. The broadband response of assembly  70  is suitably tuned to center the frequency of the vibration in a manner substantially similar to assembly  30 . Additionally, assembly  70  suitably provides soft support for small displacement in these planes and stiff support for large displacements in the x-z and y-z planes. 
     If vibration is substantially restricted to the x-z or y-z planes then bob  74  responds substantially synchronously with bob  72 . Bob  72  may suitably translate off-phase from bob  74  to oppose rotational vibration which may tend to rock tower  50 . Additionally, bobs  72  and  74  may suitably translate horizontally to oppose rotational vibration which may tend to roll tower  50 . 
     Multi-modal translational vibrations will result in multi-modal response by mass damper  10 . For example, vibration in the x-y plane combined with vibration in the x-z plane will be suitably opposed by multi-modal off phase vibration of mass damper  10  induced by the translational motion of bottom plate  32  relative to top plate  34  and translation motion of tower  50  relative to bobs  72  and  74 . 
     The requisite mass of bobs  72  and  74  largely is largely dependent on the specific application. The combined mass of bobs  72  and  74 , however, should be within a range of about 0.5 to 25 percent of the mass of the vibration source. A mass of less than about 0.5 percent of the mass of the source provides insufficient energy to effectively suppress the vibration. A mass of greater than about 25 percent, however, results in overshooting. 
     Friction associated with the various ball-in-recess assemblies does not contribute significantly to the response characteristic of mass damper  10 . Accordingly, mass damper  10  is a substantially conservative device. 
     With reference to FIGS. 11,  12  and  13 , a mass damper in accordance with another embodiment of the present invention is shown. Mass damper  200  also has 6 degrees-of-freedom (“DOF”); 3 translational modes along x, y, and z axes, and 3 rotational modes about x, y and z axes. Mass damper  200 , however, suitably incorporates known Bellevilles as nonlinear spring elements in combination with a mass element to substantially achieve broadband vibration suppression. 
     Mass damper  200  is preferably mounted on a vibration source, such as a machine tool, with cover  201  in contact with the source. Vibration is transmitted through housing  230  and base plate  202  to bob  208  suitably disposed within housing  230 . Various Belleville assemblies suitably vibrate bob  208  off phase from the vibration source to substantially suppress the vibration. 
     More particularly, bob  208  is preferably suspended on base plate  202  by a plurality of Belleville assemblies. In a preferred embodiment, three Belleville assemblies are preferably disposed at 120 degree increments around the bottom of bob  208  (for clarity only Belleville assembly  205  is described). 
     Belleville assembly  205  preferably includes seat  204 , needle support  206 , piston  214 , plurality of springs  222  and plug  216 . Seat  204  is preferably disposed within a recess formed in base plate  202 . The bottom end of needle support  206  suitably pivots on seat  204 . Similarly, piston  214  suitably pivots on the top end of needle support  206 . As bob  208  moves, piston  214  suitably slides within chamber  209  formed in bob  208 . Plug  216 , however, moves with bob  208 . Plurality of springs  222  are appropriately disposed between piston  214  and plug  216  such that relative motion between piston  214  and plug  216  suitably compresses and elongates springs  222 . 
     Additionally, bob  208  is suitably supported against housing  230  by a plurality of Belleville assemblies. In a preferred embodiment, three Belleville assemblies are preferably disposed at  120  degree increments around bob  208  (for clarity only Belleville assembly  211  is described). 
     Belleville assembly  211  preferably includes bolt  220 , plunger  212 , plurality of springs  224  and plug  210 . Bolt  220  is preferably threaded through housing  230 . Plunger  212  suitably pivots on bolt  220 . Plug  210  rests against recess  232  formed in bob  208 . Plurality of springs  224  are appropriately disposed between plunger  212  and plug  210  such that relative motion between plunger  212  and plug  210  suitably compresses and elongates springs  224 . 
     In a preferred embodiment, springs  222  and  224  are preferably Bellevilles appropriately configured to exhibit low tangential stiffness and high secant stiffness. Bellevilles are well known in the art and may be manufactured to provide the requisite stiffness characteristics. Alternatively, standard Bellevilles may be suitably configured in parallel and/or series to provide the requisite stiffness characteristics. However, various nonlinear spring elements may be used in mass damper  200  to provide broadband suppression of vibrations. For example, suitable EPDM rubber may be used to suitably provide the requisite stiffness characteristics. 
     The requisite mass of bob  208  and requisite stiffness of springs  222  and  224  are determined in substantially the same manner as in the prior embodiment. However, both parameters largely are dependent on the specific application. 
     With reference to FIGS. 14 and 15, a mass damper in accordance with yet another embodiment of the present invention is shown. Mass damper  300  has one degree-of-freedom (“DOF”) along the z axis. Mass damper  300  also uses Bellevilles as nonlinear spring elements in combination with a mass element to substantially achieve broadband suppression of vibration. 
     Mass damper  300  preferably includes base  302 , plurality of springs  304  and  306 , bob  308  and plug  310 . Housing  312  is preferably attached to base  302  by bolt  314 . Bob  308  is preferably suspended on springs  304  and  306  between base  302  and plug  310 . Vibration from a source is transmitted through housing  312  to base  302 . Springs  304  and  306  suitably vibrate bob  308  off phase from the vibration source to substantially suppress the vibration. 
     In a preferred embodiment, springs  304  and  306  are preferably Bellevilles with low tangential stiffness and high secant stiffness. However, as with the prior embodiment, various springs elements may be used with mass damper  300  to substantially achieve broadband suppression of vibration. 
     In a most preferred embodiment, a plurality of mass dampers  300  are preferably used to reduce planetary wobbling related to rotation of a heavy, large diameter, thick grinding head. Mass of bob  308  is about 2 to 8 percent of the grinding head. Ten mass dampers  300  are preferably disposed at about 36 degree increments around the grinding head. When the grinding head rotates at about 30 to 40 RPM, the wobbling vibration of the grinding head is substantially suppressed. 
     Although specific embodiments and parameters have been described, various modification may be apparent to one of ordinary skill in the art upon reading this disclosure. Therefore, it is to be understood that the embodiments described in this disclosure are merely illustrative of and not restrictive on the broad invention and that this invention is not limited to the specific embodiments shown and described herein.