Abstract:
An apparatus and method for automatic balancing and inertial damping of vibrations in a rotor are disclosed. According to one embodiment, a rotor drive shaft is adapted to mount a rotor and rotate the rotor. A lower drive shaft connects to a source of rotation. A flexible coupling attaches the rotor drive shaft to the lower drive shaft and transfers a rotational force applied by the source of rotation to the rotor while permitting relative lateral motion between the rotor drive shaft and the lower drive shaft. An inertial coupling is coupled to the rotor drive shaft and provides inertial resistance to the relative lateral motion. A clamping collar is coupled to the inertial coupling to couple the inertial coupling to a chassis and permit the relative lateral motion between the rotor drive shaft and the lower drive shaft.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to an automatic balancing centrifuge that does not require load balancing of tubes placed in the centrifuge. More specifically, the present invention provides automatic critically-damped inertial mass centering of a centrifuge rotor to accommodate unbalanced loads without imparting significant vibration on the centrifuge chassis. 
       BACKGROUND OF THE INVENTION 
       [0002]    A centrifugation device, often referred to as centrifuge, is used to separate laboratory specimen samples into component parts. For example, blood includes liquid, cells and other components. By spinning the specimen samples within the centrifuge at high velocity, such as 3,000 revolutions per minute (RPM), the samples are separated into the respective component parts based upon relative specific gravity of the components within the samples. When a sample includes components with differing specific gravities, the heavier components are forced to the bottom of the centrifuge tube when processed within the centrifuge. The separation of samples into component parts allows scientists and laboratory technicians to determine the relative quantities, through both qualitative and quantitative analysis, of the component parts within the samples, as well as providing an opportunity to further process the respective component parts. 
         [0003]    A centrifugation device includes a rotor and a drive system that causes the rotor to rotate. The rotor is typically disk-shaped and intended to support specimen samples at its outer peripheral edge. The rotor possesses sufficient centripetal properties to retain the specimen samples against elevated gravitational forces generated when the rotor is rotated at high velocity. 
         [0004]    With conventional centrifuge designs, the rotor support mechanism, excluding the drive motor (referred to herein as the gyro), can be little more than a bearing to support the rotor and a shaft connecting the rotor to the prime mover. If this rotor is sufficiently balanced, no apparent vibrational energy is translated to the support chassis as the rotor approaches operational speeds, referred to as “slew” speeds. However, in actual practice, there is at least some variation in specimen volume, and this mass differential alone can cause rotor imbalance to a greater or lesser extent. This rotor imbalance can cause significant vibration within a conventional centrifugation device. 
         [0005]    To further explain the effect of an unbalanced centrifuge,  FIG. 1  illustrates an exemplary trapezoidal velocity-time plot for a conventional centrifuge with time on the X-axis and velocity on the Y-axis. As can be seen from  FIG. 1 , the centrifuge rotor velocity appears as an ascending slope A with the angle dependent on acceleration rate after the centrifuge is activated. The plot then transitions to a flat line B as the rotor maintains constant velocity for a period of centrifugation time. The flat line B is referred to as the slew speed for the centrifugation process. The plot then has a descending slope C with the angle dependent on deceleration rate after the centrifuge is deactivated. 
         [0006]      FIG. 1  also illustrates a phenomenon known as resonance. Resonance occurs within all rotational centrifugation devices as a result of forces which act upon the rotor as it speeds up and slows down. All rotors transition through resonance as they accelerate and likewise transition through resonance again as they decelerate. 
         [0007]    As can be seen from  FIG. 1 , resonance occurs on the ascending slope A during acceleration and on the descending slope C during deceleration. Resonance is a function of the total rotational mass, any imbalanced mass, and the spring rate of the mechanical coupling (e.g., gyro) between the rotor and the chassis. Conventional rigid rotor/chassis couplings produce relatively high resonance speeds, typically occurring close to slew speeds. 
         [0008]    In centrifuge rotors, energy is a function of the square of the velocity. As such, twice the velocity equals four times the energy. Accordingly, the high resonance speeds of conventional centrifugation devices produce significant accumulated energy at resonance and impart significant vibration to the chassis of the centrifuge. 
         [0009]    Because of the high speeds and high accumulated energy at resonance, conventional centrifugation devices are particularly sensitive to unbalanced loading. An unbalanced load within a conventional centrifuge can result in significant imbalance of the forces at resonance. The additional forces caused by the unbalanced load at resonance can result in the rotor/gyro systems becoming violently unstable during resonance and cause them to physically crash into internal mechanical stops or exceed preset vibration limit switches, thus removing drive power. 
         [0010]      FIGS. 2A-2C  illustrate force vectors associated with centrifugation devices during an acceleration sequence. As can be seen from  FIG. 2A , when counter-clockwise acceleration begins, a force vector D is in relative alignment with a motion vector E. The force vector D represents radial forces (e.g., stress) on the rotor and the motion vector E represents rotational movement (e.g., strain) of a centrifuge rotor. Throughout acceleration, the direction of the vectors changes continually and the motion vector E begins to lag behind the force vector D. This lag results from the fact that the force vector D is continually applied in a new direction throughout acceleration, which is ahead of the induced motion vector E. The angle quantifying the lag of the motion vector E behind the force vector D is termed phase angle. The phase angle is zero at zero RPM, approximately 90 degrees at resonance, and approximately 180 degrees at high speeds. The frequency of rotation divided by the resonant frequency is generally termed the frequency ratio.  FIG. 2B  shows that the motion vector E lags the force vector D by approximately 90 degrees at resonance. This 90 degree lag results in the violent instability of conventional centrifuge devices if loaded with an unbalanced load.  FIG. 2C  shows that the motion vector E lags the force vector D by approximately 180 degrees at slew speeds. When the vectors are at equal magnitude and opposite in direction, they effectively cancel one another and the centrifuge rotates smoothly without imparting vibration to the chassis. Any change in magnitude or phase angle may result in some vibration imparted to the chassis. Accordingly, as described above, if a conventional centrifuge is imbalanced, it may never reach slew speeds due to the high rotational energy accumulated by the time the rotor reaches resonance. 
         [0011]    A previous solution has employed a flexible coupling between the prime mover and the rotor to allow lateral movement of the center of mass to automatically balance an unbalanced centrifuge. Frictional damping is used to limit lateral movement of the rotor. However, this causes vibration in the rotor and chassis of the centrifuge device, which is undesirable. 
         [0012]    Accordingly, there exists a need to provide a device and system capable of automatically balancing centrifuge rotors that does not require load balancing of tubes placed in the centrifuge, and particularly for automatic critically-damped inertial mass centering of a centrifuge rotor to accommodate unbalanced loads without imparting significant vibration on the centrifuge chassis and without lateral frictional damping. 
       SUMMARY OF THE INVENTION 
       [0013]    The present invention is a device and method for automatically balancing centrifuge rotors. More specifically, the present invention provides automatic critically-damped inertial mass centering of a centrifuge rotor to accommodate unbalanced loads without imparting significant vibration on the centrifuge chassis and without lateral frictional damping. A centrifuge rotor shaft is “softly coupled” to a motor drive shaft using a flexible coupling or bellows to allow the rotor to automatically adjust its spin axis from its center of geometry to its new rotational center of mass (e.g., mass centering) in the presence of an unbalanced load. However, the lateral motion needed to mass center the unbalanced load results in lateral energy within the rotor. This lateral motion can impart significant vibration to the centrifuge chassis as a result of overshoot and oscillations (e.g., an under-damped condition) during mass centering if it is not damped. Thus, the present invention also provides an inertial coupling mounted, via a bearing, on the rotor shaft between the rotor and the flexible bellows. This provides inertial critical damping of the mass centering action of the rotor and provides “virtual mass” to the rotor without increasing the polar moment of inertia (e.g., resistance to turning) of the rotor. The movable relatively high mass inertial coupling, in conjunction with the flexible bellows coupling, also enables a lower resonance speed for the centrifuge rotor, thus allowing the centrifuge rotor to transcend resonance with lower energy. As a result, the inertial coupling, and thus the rotational center or mass of the rotor, is free to move laterally without imparting significant vibration on the centrifuge chassis and without imparting vibration that prevents the velocity of the rotor from passing through resonance and reaching slew. 
         [0014]    According to one embodiment of the present invention, the inertial coupling distributes its mass in close vertical proximity to the rotor and is attached via a bearing to the rotor shaft. This allows the inertial coupling to provide virtual mass to the rotor without turning at the same velocity and, thereby, without increasing the polar moment of inertia of the rotor. The inertial coupling is further attached via a clamping collar to a circular horizontal flange of the centrifuge chassis. Ball bearings are provided within bearing races in the inertial coupling and the clamping collar and are compressed against the circular horizontal flange by the clamping collar attachment to the inertial coupling. The ball bearings allow the inertial coupling to move horizontally with inertial resistance and to limit the effects of vertical force vectors and cantilevered moments. The clamping collar provides horizontal travel limiting to bound movement of the inertial coupling. An elastomeric cushion is also provided to soften the impact of the inertial coupling when it comes into contact with the chassis of the centrifuge. The elastomeric cushion absorbs energy during mass centering without imparting a rebound force to the inertial coupling and reduces vibration that may be imparted to the chassis of the centrifuge upon contact of the inertial coupling with the chassis. The elastomeric cushion may be made of a low-density open or closed cell foam of a monomer such as polyurethane. 
         [0015]    According to another embodiment of the present invention, rotational frictional damping of the inertial coupling is provided by use of rods made of a low friction monomer, such as polytetrafluoroethylene (PTFE) or olefin. The rods are placed in contact with a surface of the inertial coupling to lightly inhibit rotation of the inertial coupling. The rods may be pressed against the inertial coupling, for example, using force provided by compressed springs. Alternatively, higher friction materials, such as polyurethane, may be used for tuning purposes where higher frictional damping may be required. Additionally, materials, such as high-density wool felt in conjunction with silicone oil and polyetheretherketone (PEEK), may also be used. Reliability of the centrifuge may be improved by decreasing excessive rotation of the inertial coupling using the rods. 
         [0016]    Those skilled in the art will appreciate the scope of the present invention and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]    The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the invention, and together with the description serve to explain the principles of the invention. 
           [0018]      FIG. 1  illustrates an exemplary trapezoidal velocity-time plot for a conventional centrifuge with time on the X axis and velocity on the Y axis; 
           [0019]      FIG. 2A  illustrates exemplary force vectors associated with a centrifugation device as the rotor begins to rotate; 
           [0020]      FIG. 2B  illustrates exemplary force vectors associated with a centrifugation device at resonance; 
           [0021]      FIG. 2C  illustrates exemplary force vectors associated with a centrifugation device at slew speeds; 
           [0022]      FIG. 3  illustrates an exemplary embodiment of a centrifuge that does not require load balancing and that provides automatic critically-damped inertial mass centering to accommodate unbalanced loads without imparting significant vibration on a chassis, according to an embodiment of the subject matter described herein; 
           [0023]      FIG. 4  illustrates an exemplary cross-sectional view of a centrifuge at rest and shows details related to the automatic critically-damped inertial mass centering capabilities of the centrifuge, according to an embodiment of the subject matter described herein; 
           [0024]      FIG. 5  illustrates an exemplary top view of a centrifuge at rest and loaded with seven sample tubes, according to an embodiment of the subject matter described herein; 
           [0025]      FIG. 6  illustrates an exemplary top view of a centrifuge while spinning at slew speeds and loaded with seven sample tubes to provide an unbalanced load, according to an embodiment of the subject matter described herein; 
           [0026]      FIG. 7  illustrates an exemplary front cross-sectional view of  FIG. 6  with the rotor spinning at slew speeds after a mass centering action has occurred and illustrates how the inertial coupling provides the inertial critical damping of the mass centering action of the rotor, according to an embodiment of the subject matter described herein; 
           [0027]      FIG. 8  illustrates an exemplary trapezoidal velocity-time plot for a centrifuge and represents the lower resonance speed provided, according to an embodiment of the subject matter described herein; 
           [0028]      FIG. 9  illustrates an alternate embodiment of a centrifuge which includes frictional rotational damping, according to an embodiment of the subject matter described herein; and 
           [0029]      FIG. 10  illustrates an exemplary top view of a centrifuge without a rotor attached and shows three rods placed at 120 degrees relative to one another around the periphery of the chassis of the centrifuge to provide rotational frictional damping, according to an embodiment of the subject matter described herein. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0030]    The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the invention and illustrate the best mode of practicing the invention. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the invention and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
         [0031]    The present invention is a device and method for automatically balancing centrifuge rotors. More specifically, the present invention provides automatic critically-damped inertial mass centering of a centrifuge rotor to accommodate unbalanced loads without imparting significant vibration on the centrifuge chassis. A centrifuge rotor shaft is “softly coupled” to a motor drive shaft using a flexible coupling or bellows to allow the rotor to automatically adjust its spin axis from its center of geometry to its new rotational center of mass (e.g., mass centering) in the presence of an unbalanced load. However, the lateral motion needed to mass center the unbalanced load results in lateral energy within the rotor. This lateral motion can impart significant vibration to the centrifuge chassis as a result of overshoot and oscillations (e.g., an under-damped condition) during mass centering if it is not damped. Thus, the present invention also provides an inertial coupling mounted, via a bearing, on the rotor shaft between the rotor and the flexible bellows. This provides inertial critical damping of the mass centering action of the rotor and provides “virtual mass” to the rotor without increasing the polar moment of inertia (e.g., resistance to turning) of the rotor. The movable relatively high mass inertial coupling, in conjunction with the flexible bellows coupling, also enables a lower resonance speed for the centrifuge rotor, thus allowing the centrifuge rotor to transcend resonance with lower energy. As a result, the inertial coupling, and thus the rotational center or mass of the rotor, is free to move laterally without imparting significant vibration on the centrifuge chassis and without imparting vibration that prevents the velocity of the rotor from passing through resonance and reaching skew. 
         [0032]      FIG. 3  illustrates an embodiment of a centrifuge  10  that does not require load balancing and that provides automatic critically-damped inertial mass centering to accommodate unbalanced loads without imparting significant vibration on a chassis  12 . Details related to the automatic critically-damped inertial mass centering will be described beginning with  FIG. 4  below. In general, as illustrated in  FIG. 3 , a rotor  14  is illustrated with an exemplary fifteen buckets  16 . The buckets  16  are secured to the rotor  14  by trunion mounts  18 . The trunion mounts  18  allow the buckets  16  to pivot to a horizontal position when the rotor  14  spins at slew speeds. It should be noted that many other rotor styles exist and all are considered within the scope of the subject matter described herein. Furthermore, it is understood that the description herein may be applied to any field within which an unbalanced load may be rotated within a rotor without limitation. 
         [0033]    Seven specimen tubes  20  are illustrated to be sequentially placed within seven of the buckets  16 . By sequentially placing the seven specimen tubes  20  within seven of the fifteen buckets  16 , an unbalanced rotor is provided to the centrifuge, for the example of the centrifuge as described herein. One skilled in the art will recognize that this presents a significantly imbalanced load to the centrifuge  10 . 
         [0034]      FIG. 4  illustrates an exemplary cross-sectional view of the centrifuge  10  at rest and shows details related to the automatic critically-damped inertial mass centering capabilities of the centrifuge  10 . As will be described in more detail below, the centrifuge  10  has a significantly lower resonance speed when compared to conventional centrifugation devices without a need for sensors, tolerance prone passive lateral frictional damping, or active damping members (e.g., solenoids). The centrifuge  10  also places additional “virtual” mass in very close vertical proximity to the rotor  14  without increasing the polar moment of inertia (e.g., resistance to turning) of the rotor  14 . Furthermore, gyro reliability and manufacturing costs may be improved when compared to conventional centrifugation devices, thereby providing increased commercial opportunity for the centrifuge  10 . 
         [0035]    As can also be seen from  FIG. 4 , the centrifuge  10  is not yet spinning. As such, the fifteen buckets  16 , as secured by the trunion mounts  18 , are resting vertically on the trunion mounts  18  at approximately 90 degrees relative to horizontal. Characteristics of the centrifuge  10  during a centrifugation cycle with the rotor  14  spinning will be described below beginning with  FIG. 6 . One skilled in the art will realize that there are many different types of rotors and that the rotor  14  is but one possible variant. Accordingly, different resting angles for the buckets  16  are possible. Additionally, rotors exist which allow the buckets  16  to rotate to angles other than horizontal (e.g., 45 degrees relative to horizontal) during centrifugation. Furthermore, rotors exist that hold the sample tubes  20  at a fixed angle throughout centrifugation. All rotors are considered to be within the scope of the subject matter described herein. 
         [0036]    A centrifuge rotor shaft  28  is “softly coupled” to a motor drive shaft  30  using a flexible bellows  32 . Rotational force applied to the motor drive shaft  30  is transferred to the rotor shaft  28  via the flexible bellows  32 . The flexible bellows  32  flexes during transfer of the rotational force from the motor drive shaft  30  to the rotor shaft  28 . The soft coupling provided by the flexible bellows  32  allows the rotor  14  to automatically adjust its spin axis from its center of geometry to its new center of mass when torque is applied to “mass center” an unbalanced load. The flexible bellows  32  also provides the lower resonance speed for the centrifuge  10  due to the soft coupling between the rotor shaft  28  and the motor drive shaft  30 . The flexible bellows  32  may be fastened to both the rotor shaft  28  and the motor drive shaft  30  via any device capable of securely fastening the flexible bellows  32  to both the rotor shaft  28  and the motor drive shaft  30 , such as one or more set screws (not shown). 
         [0037]    As will be described in more detail below in association with  FIG. 7 , the flexible bellows  32  is configured to offer flexibility for lateral displacement of the rotor  14  in the presence of an unbalanced load, while providing sufficient centering forces to move the rotor  14  back to the geometric center of the centrifuge  10  in a static mode (e.g., while not rotating). 
         [0038]    A vertical axis/plane M represents the center of mass of the centrifuge  10  and a vertical axis/plane G represents the center of geometry of the rotor  14 . As can be seen from  FIG. 4 , the vertical axis/plane M and the vertical axis/plane G approximately coincide when the rotor  14  is not spinning. It should be noted that, in addition to when the rotor  14  is not spinning, when the rotor  14  is spinning with a balanced load, the center of mass of the centrifuge  10  will also approximately coincide with the center of geometry of the rotor  14 , represented by the vertical axis/plane M and the vertical axis/plane G, respectively. However, as will be described in more detail in association with  FIGS. 5-7 , during operation when an unbalanced load is placed within the rotor  14 , the rotor  14  will mass shift when it begins to rotate, such that the center of mass of the unbalanced rotor  14  will align axially with the center of mass of the centrifuge  10  represented by the vertical axis/plane M, but the center of geometry of the rotor  14  represented by the vertical axis/plane G will shift to a different vertical alignment that will vary depending upon the imbalance of the load. 
         [0039]    The motor drive shaft  30  couples to a chassis base  34  via a bearing  36 . The bearing  36  may be any type of bearing, such as a ball bearing, that allows the motor drive shaft  30  to move freely relative to the chassis base  34  when a drive force from a motor (not shown) is applied to the motor drive shaft  30 . The chassis base  34  is mounted to the chassis  12  via fasteners  38 . The fasteners  38  may be any fastening device capable of securely mounting the chassis base  34  to the chassis  12 , such as a bolt or bolt assembly. 
         [0040]    An important aspect of the present invention is an inertial coupling  40  that is mounted, via a bearing  42 , on the rotor shaft  28  between the rotor  14  and the flexible bellows  32 . While the flexible bellows  32  provides the capability for the rotor  14  to mass center, the automatic inertial critical damping of the rotor  14  is provided by the mass of the inertial coupling  40 . 
         [0041]    As described above, the lateral motion needed to mass center an unbalanced load within the rotor  14  results in lateral energy within the rotor  14 . This lateral motion can impart significant vibration to the centrifuge chassis  12  as a result of overshoot and oscillations (e.g., an under-damped condition) during mass centering if it is not damped. 
         [0042]    The mass of the inertial coupling  40  provides inertial resistance to lateral motion of the rotor  14  and damps the lateral motion. However, as will be described in more detail below, the inertial coupling  40  does not rotate at the rate of the rotor  14 . As such, the inertial coupling  40  provides inertial critical damping of the lateral mass centering action of the rotor  14  and provides its mass as a “virtual mass” to the rotor  14  without increasing the polar moment of inertia (e.g., resistance to turning) of the rotor  14 . By imparting virtual mass to the rotor  14  without increasing the polar moment of inertia, the rotor  14  may have less mass than conventional rotors. A rotor  14  having less mass requires less energy to start and is consequently less dangerous, because less rotational energy is present within the rotor  14  at resonance and slew speeds. 
         [0043]    The inertial resistance to lateral motion provided by the inertial coupling  40  in conjunction with the soft coupling provided by the flexible bellows  32  allows the inertial coupling  40  to move laterally without imparting significant vibration to the centrifuge chassis  12  and without imparting vibration that prevents the velocity of the rotor  14  from passing through resonance to reach slew speeds. It should be noted that no frictional lateral damping is provided within the centrifuge  10 . 
         [0044]    Because the inertial coupling  40  is mounted to the rotor shaft  28  via the bearing  42 , the inertial coupling is not driven to turn at the rate of the rotor  14  and only turns incidentally due to friction within the bearing  42  and windage induced by the spinning rotor  14 . An additional force known as harmonic drive also contributes to inertial coupling rotation, especially during significantly unbalanced rotor conditions. The rotation of the inertial coupling  40  may be on the order of 40-100 revolutions per minute (RPM), while the rotor  14  rotates at speeds of approximately 3,000 RPM. Rotational damping may be provided to further reduce any rotation that is imparted to the inertial coupling  40 .  FIG. 9  below describes an alternative embodiment that includes rotational frictional damping to limit rotation of the inertial coupling  40 . 
         [0045]    An exemplary mass ratio between the inertial coupling  40  and the rotor  14  is 1:1. By providing approximately equivalent mass between the inertial coupling  40  and the rotor  14 , critical damping of the mass centering action of the rotor  14  may be achieved. Alternatively, mass ratios between the inertial coupling  40  to the rotor  14  are scalable and may be larger or smaller than 1:1 to tune the critical damping action of the inertial coupling  40 . In one embodiment of the present invention, the mass of the inertial coupling  40  and the mass of the rotor  14  are approximately equal, or approximately 4.5 pounds in a particular example. In another embodiment, the mass of the inertial coupling  40  and the mass of the rotor  14  are approximately equal, or approximately 5 pounds in a particular example. 
         [0046]    The inertial coupling  40  is configured and mounted to place its vertical center of gravity into very close physical proximity to the vertical center of gravity of the rotor  14 . This minimizes the cantilevered moment between the rotor&#39;s  14  applied lateral forces and the inertial coupling  40 , thereby imparting those forces more directly to the inertial coupling  40 . In effect, the vertical center of gravity of the inertial coupling  40  and the vertical center of gravity of the rotor  14  approach the same vertical plane, which assists with the mass centering action of the rotor  14  and the critically-damped inertial action of the inertial coupling  40 . 
         [0047]    As previously described, resonance speed of a rotor, such as the rotor  14 , is a function of total mass, exocentric mass, and coupling stiffness. As discussed above, the inertial coupling  40  effectively doubles the rotor&#39;s  14  total mass, but does not rotate at the rate of the rotor  14 , thereby not increasing the rotor&#39;s  14  polar moment of inertia (e.g., resistance to turning). This effective mass increase of the rotor  14  without increased polar moment of inertia effectively lowers the resonance speed of the rotor  14  without penalizing acceleration/deceleration rate and without penalizing the total rotational kinetic energy of the rotor  14 . 
         [0048]    The inertial coupling  40  is also “softly” coupled to the chassis  12  by use of a clamping collar  44 . The soft coupling of the inertial coupling  40  to the chassis  12  by use of the clamping collar  44  allows the inertial coupling  40  to move laterally with the rotor  14  during mass centering actions without imparting vibration to the chassis  12  and also helps to minimize the cantilevered moment between the rotor&#39;s  14  applied lateral forces and the inertial coupling  40 . 
         [0049]    The clamping collar  44  fastens to the inertial coupling  40  via threaded connectivity at locations  46  and is maintained at torque by three set screws  48  (one shown) that are spaced by 120 degrees around the circumference of the inertial coupling  40 . It should be noted that any other number or arrangement of the set screws  48  may be used, such as six set screws  48  spaced by 60 degrees or any other combination, which provides a balanced fastening mechanism to maintain the torque between the inertial coupling  40  and the clamping collar  44  without providing horizontal rotational imbalance. 
         [0050]    The soft coupling between the inertial coupling  40  and the clamping collar  44  to the chassis  12  is further accomplished by the use of ball bearings  50  within bearing races  52 . When the clamping collar  44  is secured to the inertial coupling  40 , the ball bearings  50  are compressed or pre-loaded against a circular flange  54  of the chassis  12 . The ball bearings  50 , operating under this pre-load compression, allow the inertial coupling  40  and rotor  14  to move laterally relative to the circular flange  54  during critically-damped inertial mass centering, while constraining vertical and angular forces that are generated by the spinning rotor  14 . Constraining the vertical and angular forces minimizes the effect of these force vectors and any cantilevered moments generated relative to the lateral forces applied to the rotor  14 , thereby imparting those forces more directly to the rotor  14 . Additionally, by allowing the ball bearings  50  to roll when the inertial coupling  40  moves laterally, flat spots may be avoided on the ball bearings  50 . An exemplary material from which the ball bearings  50  may be made is a plastic, such as Torlon (e.g., polyamide-imide). 
         [0051]    It should be noted that the bearing races  52  are themselves circular and are located against the bottom and top surfaces of the inertial coupling  40  and the clamping collar  44 , respectively. As such, when the inertial coupling  40  and the clamping collar  44  moderately rotate, as described above, the ball bearings  50  will be generally free to rotate within the bearing races  52  against the surfaces of the circular flange  54 , the inertial coupling  40 , and the clamping collar  44 . However, during lateral motion of the inertial coupling  40  and the clamping collar  44 , the ball bearings  50  will not rotate as freely due to friction at the sides of the bearing races  52 . As such, the bearing races  52  in contact with the ball bearings  50  may provide additional damping of and resistance to lateral motion to further assist with the damping provided by the mass of the inertial coupling  40 . Accordingly, the critically-damped inertial mass centering provided by the inertial coupling  40  may be assisted by frictional damping of the ball bearings  50  against the sides of the bearing races  52 . Furthermore, this additional frictional damping may further reduce vibration as the rotor  14  passes through resonance, and may also be predictable and proportional to the lateral excursion, such that, in the presence of a higher lateral excursion, a higher frictional damping may be provided. 
         [0052]    As can be seen from  FIG. 4 , spaces  56  are provided between an outer periphery of the circular flange  54  and an inner surface of the clamping collar  44 . The spaces  56  provide lateral travel limiting for the inertial coupling  40  relative to the chassis  12 . The clamping collar  44  has a circular cutout  58 , which allows the clamping collar  44  to move laterally without coming into contact with the chassis  12 . However, acting as hard stops to lateral movement, an impact of the clamping collar  44  against the circular flange  54  during a critically-damped inertial mass centering activity or due to an external impact may cause vibration to be imparted to the chassis  12 . Additionally, if the chassis  12  is bumped or moved by external forces while rotating, the rotor  14  and inertial coupling  40  acting gyroscopically are moved against these otherwise internal hard stops. This may cause precipitous unacceptable vibration to the chassis  12 . 
         [0053]    As described above, with the rotor  14  spinning, at slew speeds in particular, the only force that constrains the inertial coupling  40  to the center of mass of the chassis  12  as depicted by the vertical axis/plane M is the relatively low spring force of the flexible bellows  32 . As such, the mass centering action of the rotor  14  and the inertial coupling  40  may impart some vibration to the chassis  12 , as described above. A circular elastomeric cushion  60  is attached to a circular vertical collar  62  of the inertial coupling  40  to compensate for and reduce any such vibration. The circular elastomeric cushion  60  absorbs contact energy as the inertial coupling  40  comes into contact with the inside surface of the chassis  12  without rebound and reduces any vibration that may be imparted to the chassis  12  upon impact. 
         [0054]    Spaces  64  provide lateral travel limiting of the circular elastomeric cushion  60  relative to an inside surface of the chassis  12 . As can be seen from  FIG. 4 , the travel limiting provided within spaces  64  is slightly smaller than the travel limiting provided within spaces  56 . Accordingly, the circular elastomeric cushion  60  will come into contact with the inside surface of the chassis  12  and slightly compress before the inside of the clamping collar  44  comes into contact with the circular flange  54  of the chassis  12  within the spaces  56 . The circular elastomeric cushion  60  may be made of a low durometer open or closed cell foam of a monomer, such as polyurethane. It should be noted that the circular elastomeric cushion  60  may be alternatively fastened to the inside surface of the chassis  12  without departure from the scope of the subject matter described herein. 
         [0055]      FIG. 5  illustrates an exemplary top view of the centrifuge  10  at rest and loaded with seven sample tubes  20 . As such, an unbalanced rotor  14  is provided to the centrifuge  10  for centrifugation. Furthermore, one skilled in the art will recognize that this presents a massively unbalanced load to the centrifuge  10 . The clamping collar  44  can be seen through voids  70  in the rotor  14 . The voids  70  allow the buckets  16  to rotate at the trunion mounts  18  to a horizontal plane during centrifugation. The chassis  12  and the circular flange  54  are illustrated in dashed lines. As can be seen from  FIG. 5 , the center of mass represented by the vertical axis/plane M is aligned with the center of geometry of the rotor  14 , represented by the vertical axis/plane G. 
         [0056]      FIG. 6  illustrates an exemplary top view of the centrifuge  10  while spinning at slew speeds and loaded with seven sample tubes  20  to provide an unbalanced load. As can be seen from  FIG. 6 , the voids  70  have allowed the buckets  16  to rotate at the trunion mounts  18  to a horizontal plane during centrifugation. The rotor  14  has mass centered by moving to the right and a new center of mass has become the spin axis to offset the unbalanced load that has been presented by the seven sample tubes  20 . As can be seen by the dashed line representations, the new center of mass of the rotor  14  is illustrated to be aligned with the center of mass of the centrifuge  10 , represented by the vertical axis/plane M. However, as a result of the mass centering action, the center of geometry of the rotor  14 , as represented by the vertical axis/plane G, has shifted to the right. The clamping collar  44  can be seen through the voids  70  in the rotor  14  to have moved with to the rotor  14  and is also aligned with the center of geometry of the rotor  14  on the vertical axis/plane G. More details of the mass centering action of the centrifuge  10  will be described below in association with  FIG. 7 . 
         [0057]      FIG. 7  illustrates an exemplary front cross-sectional view of  FIG. 6  with the rotor  14  spinning at slew speeds after a mass centering action has occurred and illustrates how the inertial coupling  40  provides the inertial critical damping of the mass centering action of the rotor  14 . The buckets  16  are illustrated with dashed lines and rotated at the trunion mounts  18  to a horizontal plane during centrifugation. The sample tubes  20  are also illustrated with dashed lines. As described above in association with  FIG. 6 , the flexible bellows  32  has allowed the rotor  14  to shift its spin axis to its center of mass and has aligned this center of mass with the vertical axis/plane M, which also aligns with the center of geometry of the centrifuge  10 . The center of geometry of the rotor  14 , as represented by the vertical axis/plane G, is shown shifted to the right and aligned along the rotor shaft  28 . 
         [0058]    The flexible bellows  32  is shown flexed into an “S” shape toward the right within  FIG. 7 . The low-spring rate resistance of the flexible bellows  32  to lateral motion combined with the “soft coupling” of the rotor shaft  28  to the motor drive shaft  30  enables mass centering of the rotor  14 . Additionally, the flexible bellows  32  provides enough resistance to movement to return the center of geometry of the rotor  14  (e.g., the vertical axis/plane G) to the center of mass of the centrifuge  10  when rotation stops (e.g., to the vertical axis/plane M). As such, the flexible bellows  32  provides angular torque fidelity to the rotor  14  without inhibiting lateral motion. 
         [0059]    The lateral displacement of the flexible bellows  32  as it is flexed into the “S” shape may be measured by the distance between the vertical axis/plane M and the vertical axis/plane G. This distance is additionally illustrated within  FIG. 7  at the top left of the flexible bellows  32  and in the magnified section to the left within  FIG. 7 . As can be seen from these additional illustrations, the flex of the flexible bellows  32  is measured as a distance “d,” which may vary depending upon the magnitude of imbalance of the load within the centrifuge  10  and upon the material used for the circular elastomeric cushion  60 . 
         [0060]    The soft coupling provided by the flexible bellows  32  allows the rotor  14  to automatically adjust its spin axis from its center of geometry to its new center of mass (i.e., different from center of geometry) when torque is applied to “mass center” the unbalanced load presented by the seven sample tubes  20 . The soft coupling of the rotor  14  provided by the flexible bellows  32  also transitions the rotor  14  through resonance at a relatively low energy, thereby enabling the mass centering action to occur. 
         [0061]    As described above, a key aspect of the present invention is that the inertial coupling  40  critically damps the mass centering action without the need of real-time feedback, active damping devices, sensors, or solenoids that may be found in other rotor balancing systems. Additionally, by contributing its mass to the rotor  14  as a virtual mass without increasing the polar moment of inertia of the rotor  14 , the inertial coupling  40  allows the lower resonance speed to be achieved without penalizing the acceleration/deceleration rate of the rotor  14  and may do so without penalizing the total rotational kinetic energy of the rotor  14 . 
         [0062]    As can be seen from  FIG. 7 , the circular elastomeric cushion  60  has moved to the right with the inertial coupling  40  and is in contact with the inner surface of the chassis  12 . The space  64  on the left is larger as a result of the inertial coupling  40  moving to the right. Additionally, the space  56  on the left is smaller than the space  56  on the right, illustrating that the flange is closer to the left inner surface of the clamping collar  44 . It should be noted that the circular elastomeric cushion  60  is compressible to a varying degree depending upon the material used for fabrication. As such, while  FIG. 7  illustrates the circular elastomeric cushion  60  as it contacts the right inner surface of the chassis  12 , it should be noted that the circular elastomeric cushion  60  may be compressed and lateral displacement of the inertial coupling  40  is limited by the physical stop provided by the circular flange  54  against the inside surface of the clamping collar  44 . 
         [0063]    Exocentric forces may act against the inertial coupling  40 . The inertial coupling  40  is free to move laterally via the bearings  50  within the bearing races  52 . However, as described above in association with  FIGS. 2A and 2B , the motion vector E direction quickly begins to lag behind exocentric force vectors D. Exocentric force vectors D can and do move the inertial coupling  40 , but these forces are quickly re-applied in a new direction, thereby dynamically canceling previous force vectors D. In conjunction with the low spring rate of the flexible bellows  32 , the inertial coupling  40  dramatically lowers effective resonance speed of the rotor  14  and rotational energy accumulated therein. 
         [0064]    For a more theoretical understanding of the mass centering and critical inertial damping of the centrifuge  10 , low rotational speeds cause exocentric forces to move the mass of the rotor  14  and the inertial coupling  40  physically in the direction of the force. As rotational speed increases, the motion direction begins to lag behind the force direction. The static center of gravity of the rotor  14  is offset from the geometric center of the centrifuge  10  as a consequence of exocentric imbalance. At high frequency ratios, the amount of resulting displacement of the rotor  14  approaches the amount of offset of the center of gravity. Since the phase angle is nearly 180 degrees (force opposite motion) at slew speeds, the center of gravity ends up at the geometric center of the centrifuge  10 . This is mass centering and can only happen at high frequency ratios (e.g., slew speed greater than resonance). 
         [0065]      FIG. 8  illustrates a trapezoidal velocity-time plot for the centrifuge  10  and represents the lower resonance speed provided. As can be seen from  FIG. 8  and as described above, the flexible bellows  32  and the inertial coupling  40  allow the rotor  14  to mass center in an inertial critically-damped fashion at a rotational speed that is considerably lower than for conventional centrifugation devices. As described above, no lateral frictional damping is provided and the lateral damping is provided in an inertial fashion by the inertial coupling  40 . As an example of the difference in resonance speed between a conventional centrifugation device and the centrifuge  10 , the centrifuge  10  may have a resonance speed of approximately 350 RPM, whereas a conventional centrifugation device may have a resonance speed of approximately 2680 RPM. This significant decrease in resonance speed also provides significantly lower rotational energy at resonance for the centrifuge  10  when compared to a conventional centrifugation device. 
         [0066]      FIG. 9  illustrates an alternate embodiment of the centrifuge  10  which includes frictional rotational damping. The centrifuge  10  illustrated in  FIG. 9  is shown without the rotor  14  attached for ease of illustration. As described above, the inertial coupling  40  may rotate at a rate of approximately 40-100 RPM as a result of friction within the bearing  42  and windage from the rotor  14  as the rotor  14  spins. Some rotation of the inertial coupling  40  is useful in addition to the lateral movement during mass centering to allow the ball bearings  50  to rotate within the ball bearing races  52 . Ball bearings need to rotate to distribute loads evenly over their surfaces and to prevent the development of flat spots. Additionally, allowing the ball bearings  50  to rotate distributes lubricant evenly over their surfaces and their mating flat surface contact points within the ball bearing races  52 . 
         [0067]    Because the rotation of the inertial coupling  40  is induced over time due to friction in the ball bearings  42  and windage from the rotor  14 , the effects of the rotation of the inertial coupling  40  are not experienced during acceleration. However, this is not true during deceleration. As such, the rotation of the inertial coupling  40  may induce additional wobble as resonance is traversed during the deceleration phase of the centrifuge  10 . This wobble results from the rotational energy of the inertial coupling  40  which imparts a polar moment of inertia to the rotor  14 . 
         [0068]    As such, the exemplary embodiment illustrated in  FIG. 9  provides rotational frictional damping for the inertial coupling  40 . A frictional damping rod  70  is illustrated within a cavity  72  of the chassis  12 . A spring  74 , which is compressed within the cavity  72  below the rod  70 , applies force to the rod  70  sufficient to limit rotation of the inertial coupling  40 . However, as described above, rotation of the inertial coupling  40  resulting from the friction in the ball bearings  42  and windage from the rotor  14  is not prevented, but is reduced by the rotational frictional damping of the rod  70 . 
         [0069]    Though only one rod  70  is depicted within  FIG. 9 , it should be noted that any number of rods may be placed around the perimeter of the chassis  12  depending upon the material of the rod  70  and the force applied to it by the spring  74 . For example, three rods  70  may be placed at 120 degrees relative to each other around the perimeter of the chassis  12  to provide three points of contact for the rotational frictional damping. 
         [0070]    The material used to construct the rod  70  may be a material such as polytetrafluoroethylene (PTFE) or olefin. Alternatively, higher friction materials, such as polyurethane, may be used for tuning purposes where higher frictional damping may be desired. The rods  70  may also be made of graphite or a high-density wool felt. When high-density wool felt is used, oil, such as a silicone oil, may be placed within the cavity  72  of the chassis  12 . A silicone oil, such as  200  centipoise oil, may be used. The high-density wool felt may act as a wick to draw the lubricant onto the surface of the inertial coupling  40 . The use of high-density wool felt may improve the usable life and reliability of the rods  70 . Polyetheretherketone (PEEK) is another alternative material that may be used for the rods  70 . PEEK is a low friction/high temperature thermo plastic. Reliability of the centrifuge  10  may be improved by decreasing excessive rotation of the inertial coupling  40  by use of the rods  70 . 
         [0071]      FIG. 10  illustrates a top view of the centrifuge  10  without the rotor  14  attached and shows three rods  70  placed at 120 degrees relative to one another around the periphery of the chassis  12  of the centrifuge  10  to provide rotational frictional damping. The inertial coupling  40  and the clamping collar  44  are illustrated with solid lines. The chassis  12  and the three rods  70  placed at 120 degrees relative to one another are illustrated with dashed lines. As described above, any combination of rods  70  may be used depending upon the materials and design preferences for the rotational frictional damping thereby provided. 
         [0072]    Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present invention. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.