System and method for balancing centrifuge rotor

Abstract

A rotor for use in a centrifuge and a method for balancing the rotor are disclosed. The rotor includes a plurality of apertures circumferentially arranged about an axis of rotation of the rotor, each aperture configured to selectively receive a weight. A critical speed of the rotor is determined, and an imbalance of the rotor at a test speed lower than the critical speed is determined. A test weight is installed in the reference aperture and another imbalance at the test speed is determined. The test weight is repeatedly moved to another orifice that is angularly displaced from the previous orifice, and the imbalance at the test speed is measured until a predetermined number of imbalance measurements are obtained. A target mass and a target position for balancing the rotor are determined from the imbalance measurement, and a counterweight is mounted in the aperture based on the target mass and the target position. The balancing process may be repeated for multiple critical frequencies.

Description

[0001] This divisional patent application is a divisional application of a patent application with international application number PCT / US2021 / 016557, international filing date February 4, 2021, and national stage entry application number 202180012157.4, titled "Systems and Methods for Balancing Centrifuge Rotors".

[0002] Cross - reference to related applications

[0003] This application claims the benefit of co-pending U.S. Provisional Application Serial No. 62 / 969,932, filed February 4, 2020, and co-pending U.S. Provisional Application Serial No. 63 / 112,018, filed November 10, 2020, the disclosures of which are hereby incorporated by reference in their entirety. Technical Field

[0004] The present invention generally relates to centrifuge rotors, and more particularly to balancing rotors for use with centrifuges. Background Art

[0005] Rotors are commonly used in laboratory centrifuges to hold samples during centrifugation. Although rotors can vary significantly in construction and size, one common rotor configuration is a fixed-angle rotor with a solid rotor body having a plurality of cavities radially distributed within the rotor body and symmetrically arranged about the axis of rotation. In this type of rotor, samples are placed in the cavities such that multiple samples are subjected to centrifugation.

[0006] Conventional fixed-angle rotors can be made of metal or various other materials. However, compression molding and filament winding processes can also be used to construct rotors, where the rotors are made of a suitable material such as composite carbon fiber. For example, a fixed-angle rotor can be compression molded from layers of resin-coated carbon fiber laminate. Examples of composite rotors are described in U.S. Patent Nos. 8,147,392, 8,273,202, 8,323,169, and 10,086,387.

[0007] A centrifuge can be characterized by a rigid rotor shaft or spindle that imparts rotational torque to a rotor mounted on the spindle within the centrifuge. However, for high-speed centrifuges, such as ultracentrifuges that can rotate a rotor at a rotational speed of 50,000 revolutions per minute (RPM) or higher, a flexible shaft is typically used instead of a rigid shaft. The flexible shaft limits the transmission of vibrations due to any imbalance of the rotor or uneven distribution of the sample load within the centrifuge to the centrifuge frame.

[0008] Care must be taken to balance the rotors used in high-speed applications, such as at speeds exceeding tens of thousands of revolutions per minute, in order to reduce the tendency of the rotors to cause vibrations during high-speed rotation. When the rotor operates at high speed, changes in the mass of the rotor load can cause undesirable force imbalances. Such force imbalances can strain the spindle and may lead to centrifuge damage, inefficiency, excessive wear, and undesirable noise. Conventional balancing techniques for rotors operating with a rigid spindle use a combination of samples and balance tubes all having the same heavy body or various other balancing modes without adding balance tubes.

[0009] Diagnostic devices or balancing machines, such as those commercially sold by American Hofmann Corporation of Lynchburg, Virginia or Schenck Corporation of Deer Park, New York, can be used to detect rotor imbalance in rotors typically mounted on a rigid spindle and can also be used to identify the specific locations on the rotor body where additional heavy bodies are needed to balance the rotor. Then, holes are manually drilled in the rotor body at the identified locations, and the heavy bodies are press-fitted into the holes based on the information provided by the diagnostic device. The heavy bodies can be, for example, cylindrical metal bodies each having a specific mass to compensate for the imbalance detected by the diagnostic device.

[0010] It may be necessary to rebalance the rotor multiple times throughout the life of the rotor. For example, as the rotor ages and wears, the mass distribution of the rotor may change, making it necessary to rebalance the rotor. When this occurs, the previously installed heavy bodies must typically be removed from the previously drilled holes. New holes are then drilled in the rotor body, and the heavy bodies are press-fitted into the new holes. Thus, the previously drilled holes are rendered unusable. For structural and / or aesthetic purposes, it is generally desirable to plug the previously drilled holes, which requires repairing the rotor body. Each time the rotor is rebalanced, the cycle of drilling new holes in the rotor body and repairing the rotor body to plug the previously drilled holes is repeated.

[0011] Accordingly, it would be desirable to provide improved systems and methods for balancing rotors that address these and other problems associated with conventional rotors, particularly for rotors used in high-speed centrifuges such as ultracentrifuges. Summary of the Invention

[0012] In one embodiment of the present invention, a rotor is provided. The rotor includes: a rotor body having a rotational axis; and a plurality of balance orifices circumferentially arranged about the rotational axis. Each of the balance orifices is configured to selectively receive a heavy body.

[0013] In one aspect of the present invention, the rotor body may further comprise a plurality of circumferentially spaced tubular cavities and a lid in which the balance orifices are formed. Each tubular cavity may have an open end configured to receive a sample container. The lid may be supported by the rotor body and configured to cover the open end of the tubular cavity when the lid is positioned on the rotor body.

[0014] In another aspect of the present invention, the lid may further comprise a top surface and a bottom surface opposite the top surface, and the balance orifice may be formed in one of the top surface or the bottom surface.

[0015] In another aspect of the present invention, at least one of the balance orifices may receive at least one weight body.

[0016] In another aspect of the present invention, the at least one weight body may be a screw including a threaded outer surface, and each of the balance orifices may include a threaded inner surface configured to threadedly engage the weight body.

[0017] In another aspect of the present invention, the radial distance of each balance orifice from the axis of rotation may be the same as the radial distance of the other balance orifices from the axis of rotation.

[0018] In another aspect of the present invention, each balance orifice may be spaced apart from each of the circumferentially adjacent balance orifices by the same circumferential distance.

[0019] In another aspect of the present invention, the balance orifices may be coplanar.

[0020] In another aspect of the present invention, the rotor body may further comprise an upper surface and a lower surface opposite the upper surface, wherein the upper surface includes a first annular groove. The rotor may further comprise a balance ring positioned in the first annular groove, and the balance ring may include an upper surface of the balance ring in which the balance orifices are formed.

[0021] In another aspect of the present invention, the rotor body may include an elongated bore that extends along the axis of rotation between the upper surface and the lower surface of the rotor body, and the rotor may further include a drive hub, a cap screw, a cap, and an elastic member. The drive hub may be mounted within the elongated bore and may include a cylindrical shaft that projects upwardly through the elongated bore and an upper portion having a threaded outer surface. The cap screw may include a lower bore and a cap screw flange, the lower bore having a threaded inner surface configured to threadedly engage the threaded outer surface of the drive hub, the cap screw flange extending radially outwardly from the lower end of the cap screw. The cap may include a wall portion that extends radially outwardly and has a lower surface with a third annular groove. The elastic member may be positioned within the third annular groove and may bear against the upper surface of the balance ring in response to the threaded engagement of the cap screw with the drive hub.

[0022] In another aspect of the present invention, the first annular groove may include a shoulder, and the balance ring may include a balance ring flange that projects radially inwardly to engage the shoulder.

[0023] In another aspect of the present invention, the rotor body may include a circumferential sidewall, and the rotor may further include a reinforcement that extends around the circumferential sidewall.

[0024] In another aspect of the present invention, the reinforcement may extend around and above the circumferential sidewall of the rotor body to define a channel having the first annular groove, and the balance ring may be positioned within the channel.

[0025] In another aspect of the present invention, the circumferential sidewall may include a circumferential recess, and the reinforcement may conform to the circumferential recess.

[0026] In another aspect of the present invention, the balance ring may be operatively connected to the first annular groove by an adhesive, a shrink fit, or both the adhesive and the shrink fit.

[0027] In another aspect of the present invention, the rotor body may be constructed of a polymer composite, a carbon fiber material, or both the polymer composite and the carbon fiber material.

[0028] In another aspect of the present invention, a method for balancing a rotor that includes a plurality of orifices, each orifice being configured to selectively receive a weight, is provided. The method includes detecting an imbalance of the rotor when the rotor is rotated in a centrifuge, and in response to detecting the imbalance, selectively mounting balance weights in selected balance orifices.

[0029] In one aspect of the present invention, detecting the imbalance can include identifying the critical speed of the rotor and determining the imbalance in the rotor at a test speed less than the critical speed.

[0030] In another aspect of the present invention, the critical speed can be one of a plurality of critical speeds, and the imbalance of the rotor can be determined for each of a plurality of test speeds, where each test speed is a fraction of the corresponding critical speed among the plurality of critical speeds.

[0031] In another aspect of the present invention, identifying the critical speed can include: rotating the rotor at a plurality of rotational speeds; applying an external force to the rotor while the rotor is rotating at the rotational speed; measuring and recording the vibration response of the rotor to the external force; and determining the natural frequency of the rotor based on the vibration response. The method can then identify one or more critical speeds of the rotor based on the natural frequency.

[0032] In another aspect of the present invention, selectively mounting the balance weights in the selected balance apertures can include measuring the imbalance of the rotor at a first test speed; mounting a trial weight in a balance aperture at a reference location; and measuring the imbalance of the rotor at the first test speed with the trial weight mounted at the reference location. The method can then include repeatedly moving the trial weight to the next balance aperture that is a predetermined angular distance away from the current balance aperture and measuring the imbalance of the rotor at the first test speed until the next balance aperture will be at or beyond the reference location. Based on the measured imbalances, the method can then determine a first target location and a first target mass to be added at the first target location to balance the rotor.

[0033] In another aspect of the present invention, the method can further include: determining a first balance vector provided by the first target mass at the first target location, selecting a first balance aperture located on one side of the first target location and a second balance aperture located on the other side of the first target location; and determining a first balance mass and a second balance mass that provide a second balance vector equivalent to the first balance vector when placed in the first balance aperture and the second balance aperture, respectively.

[0034] In another aspect of the present invention, the method may further comprise: mounting a first heavy body having the first balancing mass in the first balancing aperture; mounting a second heavy body having the second balancing mass in the second balancing aperture; and measuring the unbalance at the first test speed with the first heavy body mounted in the first balancing aperture and the second heavy body mounted in the second balancing aperture.

[0035] In another aspect of the present invention, the method may further comprise: measuring the unbalance of the rotor at a second test speed higher than the first test speed; mounting the test heavy body in the balancing aperture at the reference position; and measuring the unbalance of the rotor at the second test speed with the test heavy body mounted at the reference position. The method may further comprise repeatedly moving the test heavy body to the next balancing aperture spaced the predetermined angular distance from the current balancing aperture and measuring the unbalance of the rotor at the second test speed until the next balancing aperture will be at or beyond the reference position. Based on the measured unbalance, the method may then determine a second target position and a second target mass to be added at the second target position to balance the rotor.

[0036] In another aspect of the present invention, the method may further comprise: determining a second balancing vector of a combination of the first target mass at the first target position and the second target mass at the second target position; and determining a third target mass and a third target position, the third target mass and the third target position providing a third balancing vector equivalent to the second balancing vector.

[0037] In another aspect of the present invention, the method may further comprise: selecting a third balancing aperture on one side of the third target position and a fourth balancing aperture on the other side of the third target position; and determining a third balancing mass and a fourth balancing mass, the third balancing mass and the fourth balancing mass providing a fourth balancing vector equivalent to the third balancing vector when respectively placed in the third balancing aperture and the fourth balancing aperture.

[0038] In another aspect of the present invention, the method may further comprise: mounting a third heavy body having the third balancing mass in the third balancing aperture; mounting a fourth heavy body having the fourth balancing mass in the fourth balancing aperture; measuring the unbalance at the second test speed with the third heavy body mounted in the third balancing aperture and the fourth heavy body mounted in the fourth balancing aperture; and comparing the unbalance measured at the second test speed with the unbalance measured at the first test speed.

[0039] The above Summary of the Invention presents a simplified overview of some embodiments of the present invention to provide a basic understanding of certain aspects of the present invention discussed herein. The Summary of the Invention is not intended to provide a broad overview of the present invention, nor is it intended to identify any key or critical elements or delineate the scope of the present invention. The sole purpose of the Summary of the Invention is merely to present some concepts in a simplified form as an introduction to the Detailed Description presented below. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings incorporated in and forming a part of this specification illustrate embodiments of the present invention and, together with the general description of the present invention given above and the detailed description given below, serve to explain the present invention.

[0041] Figure 1 is a perspective view of a centrifuge including a rotor having a lid according to an exemplary embodiment of the present invention.

[0042] Figure 2 is Figure 1 a perspective view of the rotor of

[0043] Figure 3 is Figure 2 an exploded perspective view of the rotor of

[0044] Figure 4 - 4D is Figure 1 - 3 a bottom perspective view of the lid of

[0045] Figure 5 is Figure 2 a cross-sectional view of the rotor of

[0046] Figure 6 is Figure 5 a detailed view of a part of the rotor of

[0047] Figure 7 is Figure 4 a perspective view of an alternative embodiment of the lid of

[0048] Figure 8 is Figure 7 a detailed view of a part of the rotor of

[0049] Figure 9 is a flowchart showing an exemplary method that can be performed to balance a rotor according to an embodiment of the present invention.

[0050] Figure 9A - 9C is showing that can be through Figure 9Flowchart of an exemplary sub - method implemented by the method.

[0051] Figure 10 Is a perspective view of a rotor according to another exemplary embodiment of the present invention.

[0052] Figure 11 Is Figure 10 An exploded perspective view of the rotor, which shows the rotor body, the balance ring, the drive hub, and the cover of the rotor.

[0053] Figure 12 Shows Figure 11 Additional details of the cover.

[0054] Figure 13 Shows Figure 11 Additional details of the rotor body in a top perspective view.

[0055] Figure 14 Shows Figure 11 Additional details of the rotor body and the drive hub in a bottom perspective view.

[0056] Figure 15 Is Figure 10 A cross - sectional view of the rotor.

[0057] Figure 16 Is Figure 15 An exploded cross - sectional view of a part of the rotor, which shows additional details of the cover, the balance ring, and the rotor body.

[0058] Figure 17 And 18 Is Figure 10 A top view of the rotor with the cover removed.

[0059] Figure 19 Is a curve view showing the vibration data of a mode - balanced rotor according to an embodiment of the present invention.

[0060] Figure 20 Is for generating Figure 19 The data of the rotor.

[0061] Figure 21 - 24 Is a graphical view showing the vibration data of an unbalanced rotor, a rotor balanced conventionally, and a mode - balanced rotor.

[0062] Figure 25 Is a schematic view of a computer according to an embodiment of the present invention that can be used to implement one or more methods. Detailed description

[0063] Figures 1 to 6Depicts an exemplary lid 212 of a rotor 102 (e.g., an 8 x 100 mL capacity fixed angle rotor) according to an embodiment of the present invention. The lid 212 includes a plurality of balance orifices 432, each balance orifice being configured to selectively receive a test weight 433 or a balance weight 436 that can removably engage the lid 212. As described in more detail below, the balance weights 436 can be selectively positioned in a plurality of predetermined positions on the lid 212 to balance the rotor 102 according to a modal balancing method.

[0064] Figure 1 Depicts an exemplary centrifuge 100 according to an embodiment of the present invention. The centrifuge 100 includes a housing 101, a drive motor 106, a rotor drive shaft or spindle 104, and a rotor 102 mounted on the spindle 104. In operation, the drive motor 106 rotates the spindle 104, which in turn provides rotational torque to the rotor 102 to cause the rotor 102 to rotate at a desired speed.

[0065] Depending on the type of centrifuge 100 used, such as a centrifuge operating at a maximum speed of up to 15,000 RPM, over 15,000 RPM up to 40,000 RPM, over 40,000 RPM up to 90,000 RPM, or over 90,000 RPM, the spindle 104 can be rigid or flexible. A rigid spindle 104 can be used for low-speed centrifuges 100. However, for those centrifuges 100 operating at high speeds, such as 50,000 RPM or higher, a flexible spindle 104 can be used to reduce the transmission of vibration during centrifugation. A sensor 108, such as an accelerometer, can be operatively coupled to the centrifuge 100 or its components and can be configured to measure vibration. For example, the sensor 108 can be attached to the motor 106 at a bearing that supports the rotating spindle 104. The sensor 108 can be placed as close as possible to the bearing and can preferably be in the same plane as the bearing in order to obtain an accurate measurement of the vibration signal at the bearing during rotation of the rotor 102.

[0066] Figure 2 、 3Figs. 0 and 5 depict an exemplary rotor 102 in accordance with an embodiment of the present invention. The rotor 102 includes a rotor body 210 and a rotor hub 322. The rotor hub 322 is configured to transfer torque from a main shaft 104 to the rotor body 210. The rotor hub 322 may be constructed of a metallic material such as titanium and includes a head portion 548 and an elongated shaft portion 546 extending axially upward from the head portion 548. The shaft portion 546 includes a threaded outer surface 550, a threaded inner surface 552, and an inward-facing circumferential surface 544. The inward-facing circumferential surface 544 may taper radially inward and downward along a portion of the length of the rotor hub 322. The rotor hub 322 may be fixed to the rotor body 210 by a hub retainer 320 that is operatively coupled to the threaded outer surface 550 of the shaft portion 546 of the rotor hub 322. After the rotor hub 322 is inserted through the rotor body 210, the hub retainer 320 may be threaded onto the threaded end of the shaft portion 546.

[0067] The rotor 102 also includes an exemplary cover 212 that is removably coupled to the rotor hub 322 to cover the rotor body 210. The cover 212 is generally disk-shaped and includes a central bore 551 and an annular outer peripheral groove 429 for receiving an O-ring 430. When the cover 212 is removably coupled to the rotor body 210, the O-ring 430 may provide a fluid seal between the cover 212 and the rotor body 210. The cover 212 may be constructed of a carbon fiber material, a metallic material, or any other suitable material. For example, the cover 212 may be compression molded from a resin-coated carbon fiber laminate. The rotor body 210 and the cover 212 may also include corresponding indicia (e.g., arrows 438, 440) indicating a designated reference position 213. The reference position 213 may specify a particular location on the rotor body 210 and the cover 212 such that the cover 212 may be aligned with the rotor body 210 at the same reference position 213. The reference position 213 may be identified on both the rotor body 210 and the cover 212 with a marker or indicia. Although reference arrows are depicted in Figure 2 , it should be understood that the reference position 213 may be identified on the rotor body 210 and the cover 212 in any suitable manner that indicates to the user where to align the rotor body 210 and the cover 212.

[0068] As Figure 3 , 5, as shown in FIGS. 6 and 8, the cover 212 can be removably coupled to the rotor body 210 by cover screws 214. Exemplary cover screws 214 include an upper flange 554, a threaded lower outer surface 556, and a multi-stage bore 558 that axially extends through the cover screw 214. The cover screw 214 can include an outward-facing circumferential surface 542 that radially inwardly and downwardly tapers along a partial length of the cover screw 214. The circumferential surface 542 can thus be configured to face an inward-facing circumferential surface 544 of the rotor hub 322 when the cover screw 214 engages the rotor body 210. As shown, the threaded lower outer surface 556 can be received by and threadedly engaged with a threaded inner surface 552 of the hub 322 such that the upper flange 554 presses the washer 316 against the cover 212. The retaining clip 318 can hold the cover screw 214, the washer 316, and the cover 212 together by clamping the cover 212 between two washers 316. When coupled to the rotor body 210 by engagement of the cover screw 214 with the hub 322 and engagement of the retaining clip 318 with the cover 212, the cover 212 can cover a plurality of tubular cavities 540 and sample containers received therein. The cover 212 can thus prevent access to the sample containers held in the cavities 540, such as during high-speed rotation. Each of the rotor mounting assemblies described above can be made of any suitable metal or non-metal material.

[0069] Figure 4 FIG. 4 depicts an exemplary cover 212 having a test weight 433 mounted in accordance with an embodiment of the present invention. The cover 212 can be supported by the rotor body 210 and is configured to cover the top of the rotor body 210, as Figure 5 best shown in FIG. 6. The cover 212 includes a top surface 426, a bottom surface 424 opposite the top surface 426, and an outward-facing circumferential sidewall 428 that extends between the top surface 426 and the bottom surface 424. The circumferential sidewall 428 radially inwardly and downwardly tapers from proximal to the top surface 426 of the cover 212. The circumferential sidewall 428 can taper at a cone angle ranging from about 10° to 30° relative to the top surface 426 of the cover 212. Preferably, the circumferential sidewall 428 can taper at a cone angle of about 10° relative to the top surface 426 of the cover 212. The cover 212 can also include an O-ring 430 supported by the circumferential sidewall 428 of the cover 212. The cover 212 can also include an annular ridge 434 that extends from the top surface 426 and the bottom surface 424 of the cover 212 to define a cavity configured to receive the washer 316.

[0070] The cover 212 may further include a plurality of balance orifices 432 circumferentially spaced apart from each other on the cover 212. Each balance orifice 432 may include a threaded inner surface and have a uniform configuration. That is, each of the balance orifices 432 may have, for example, the same depth, cross-sectional dimensions, or thread pitch. Thus, each of the balance orifices 432 may be configured to threadedly receive the same type of balance weight 436 or test weight 433. The balance orifices 432 may be located on the bottom surface 424, top surface 426, or both surfaces 424, 426 of the cover 212.

[0071] Figure 4 The exemplary embodiment best shown in [FIGURE] includes twenty-four balance orifices 432 located on the bottom surface 424 of the cover 212. The balance orifices 432 are circumferentially spaced apart from each other at equal circumferential intervals around a central bore 551. Thus, the balance orifices 432 define predetermined positions on the cover 212 for receiving the balance weights 436 or test weights 433. However, any suitable number of balance orifices 432 at any suitable spacing may be used. Thus, the lateral dimension of the cover 212 may affect the available surface area for the balance orifices 432 and may be increased to provide additional surface area to accommodate a greater number of balance orifices 432. It should be understood that the number of balance orifices 432 may be related to the number of options for mounting the balance weights 436 or test weights 433. Thus, the number of balance orifices 432 may be related to the degree of control over the center of gravity of the cover 212, which may affect the stability of the rotor 102. Figure 4 A single test weight 433 mounted in a balance orifice 432 referred to as the reference position 213 is depicted. It should be further understood that the number of balance weights 436 mounted in the cover 212 may vary depending on the amount of imbalance of the rotor 102 to be corrected.

[0072] Imbalance may occur whenever the center of gravity of the rotor 102 does not coincide with the axis of rotation. The force generated by the imbalance may be characterized as:

[0073] F 不平衡 = M × ε × ω 2

[0074] where M is the mass of the rotor, ε is the radial offset (or "eccentricity") of the center of gravity from the axis of rotation of the rotor, (M × ε) is the imbalance, F 不平衡 is the force caused by the imbalance, and ω is the rotational speed in radians per second. The rotational speed ω is given by:

[0075]

[0076] where N = rotational speed, in RPM. The imbalance vector is guided outwards from the axis of rotation by the center of gravity and thus rotates around the axis of rotation synchronously with the rotor 102. Therefore, the rotor 102 can be balanced by adding a certain amount of mass to the rotor in one or more positions where the balance vector is generated. That is, in order to completely balance the rotor 102, the balance vector should be equal in magnitude to the unbalance vector and opposite in phase.

[0077] In Figure 4 - 4D the illustrated embodiment, it should be understood that the reference position 213 can correspond to the Figure 1 - 3 reference position 213 described in Figure 4A and 4B but is located on the directly opposite side (bottom surface 424) of the cover 212. Figure 3 depicts a bottom perspective view of the cover 212 of Figure 4A depicts a test weight 433 installed in a balance orifice 432 located 120 degrees (θ) from the reference position 213 of the test weight 433 installed in Figure 4 In Figure 4B depicts a test weight 433 installed in a balance orifice 432 located 240 degrees (2θ) clockwise from the position of the test weight 433 installed in Figure 4 or 120 degrees (θ) clockwise from the reference position 213 of the test weight 433 installed in Figure 4A In

[0078] Figure 4C and 4D each depict a bottom perspective view of the cover 212 of Figure 3 In Figure 4C shows a balance weight 436 installed in a balance orifice 432, and Figure 4D shows two balance weights 436 installed in adjacent balance orifices 432. The number of balance weights 436 installed in the balance orifices 432 of the cover 212 can depend on the amount of unbalance of the rotor 102. The number of balance weights 436 installed can vary, from almost none to as many as the number of balance orifices 432 present on the cover 212.

[0079] Each balancing weight or test weight may include a positioning screw having a threaded outer surface, a proximal end, and a distal end. The distance between the proximal end and the distal end of the positioning screw may define the length of the weight. A hex socket or other suitable keyed bore may be provided at the proximal end to receive a tool, such as an Allen wrench, to assist in pushing the weight into or out of one of the balance ports 432. The threaded outer surface of the weight may allow the weight to be inserted into or removed from any of the balance ports 432 in the balance port 432 without damaging the cover 212. Although the weights 433, 436 and the balance ports 432 are depicted herein as threaded such that the weights may be removably engaged with one or more of the balance ports 432, embodiments of the present invention are not so limited. Thus, the weights 433, 436 may be removably engaged with the cover 212 in any suitable manner. In some embodiments, a plurality of balancing weights 436 having various different lengths or masses may be provided such that balancing weights 436 having different balancing characteristics may be selectively positioned in specific balance ports 432 to achieve a customized balance. It should be understood that other suitable devices, such as press-fit dowel pins, may also be employed. Accordingly, embodiments of the present invention are not limited to the exemplary test weights and balancing weights depicted.

[0080] Although the balancing weights 436, test weights 433, and corresponding balance ports 432 have been described relative to the illustrated cover 212 and rotor 102, the balancing weights 436, test weights 433, and balance ports 432 may be incorporated into any suitable cover. In alternative embodiments, the balance ports 432 may be included in the rotor body 210, such as in the top annular surface 437 of the annular edge 439 of the rotor body 210. The balancing weights 436, test weights 433, and balance ports 432 may also be incorporated into other carbon fiber rotors of various designs or rotors constructed of different materials.

[0081] Figure 5 A side cross-sectional view of a rotor 102 in accordance with an embodiment of the present invention is depicted. The rotor 102 includes a rotor body 210 that is symmetric about a rotational axis defined by a rotor hub 322. A sample contained in a sample container (not shown) may be positioned within the rotor body 210 about the rotational axis and centrifuged. The illustrated rotor body 210 includes a central bore 560 for receiving a rotor insert 562 that may be co-molded with the rotor body 210. The rotor insert 562 includes a threaded central bore 564 configured to at least operatively engage a threaded shaft portion 550 of the hub 322 to seat the rotor body 210 securely on the hub 322.

[0082] The rotor body 210 can include a plurality of cavities 540. In one embodiment of the present invention, the plurality of cavities 540 can include a plurality of circumferentially spaced tubular cavities, each tubular cavity having an open end configured to receive a sample container. Each of the plurality of cavities 540 can extend into the rotor body 210 from an upper cavity and can be appropriately sized and shaped to receive at least one of the sample containers in the sample container for centrifugal rotation about the axis of rotation. Although Figure 1 - 3 the exemplary rotor 102 depicted in FIGS. 5, 6, and 8 has eight cavities 540 each sized to receive a 100 mL sample container, it should be understood that any suitable number of cavities 540 can be used and the cavities 540 can be configured to fit sample containers of various sizes. As used herein, the term "tubular" can refer to any suitable cross-sectional shape, including for example but not limited to circular shapes (e.g., oval, round, or conical), quadrilateral shapes, regular polygon or irregular polygon shapes, or any other suitable shape. Thus, the term "tubular" is not intended to be limited to the generally circular cross-sectional profile of the exemplary cavities 540 shown in the figures.

[0083] In one embodiment, the rotor body 210 can be constructed of a polymer composite. For example, the rotor body 210 can be compression molded from a resin-coated carbon fiber laminate. It should be understood that the rotor body 210 can also be formed using a variety of other materials and by a variety of other methods. For example, the rotor body 210 can be compression molded from a combination of discontinuous resin-coated carbon fiber sheets or discontinuous carbon fiber sheets and stacked carbon laminates.

[0084] In the case where the rotor body 210 is operatively engaged with the rotor hub 322, the hub retainer 320 can be removably fastened to the hub 322 to further facilitate holding the rotor body 210, the rotor hub 322, and the insert 562 in position relative to each other. In this regard, the hub retainer 320 can include an internal threaded bore 326 for receiving and threadedly engaging at least the threaded outer surface 550 of the shaft portion 546 of the hub 322.

[0085] Figure 6 is depicted Figure 5Detailed view of a portion of the rotor 102, which shows the interface between the cover 212 and the rotor body 210. The cover 212 may include an O-ring 430 seated in a circumferential outer groove 429 in the circumferential sidewall 428 of the cover 212. The cover 212 may be configured to fit within the inward-facing circumferential sidewall 538 of the rotor body 210 such that the cover 212 rests against the circumferential sidewall 538. Preferably, the cover 212 may be formed such that when the cover 212 rests against the circumferential sidewall 538 of the rotor body 210, there is a sliding contact between the cover 212 and the circumferential sidewall 538 that does not impede the removal of the cover 212. To create a tight seal, the cover 212 may be forced downward against the circumferential sidewall 538 by the cover screw 214 as previously described. In response to being compressed, the O-ring 430 may expand radially such that it presses against the circumferential sidewall 428 of the cover 212 and the circumferential sidewall 538 of the rotor body 210, thereby creating a seal. The cover 212 may thus be securely sealed proximal to the upper end of the rotor body 210 but may be easily removed by unscrewing the cover screw 214 to release the downward force applied to the cover 212. When the force applied by the cover screw 214 is released, the O-ring 430 may retract from the circumferential sidewall 538 of the rotor body 210 such that there is only a sliding contact between the cover 212 and the circumferential sidewall 538 of the rotor body 210. The cover 212 may then be easily removed.

[0086] Figure 6 Also shown is the orientation of the balance weight 436 within the balance orifice 432 of the cover 212. In the depicted embodiment, the balance orifice 432 is located on the bottom surface 424 of the cover 212. Therefore, the balance weight 436 must be installed in the balance orifice 432 of the cover 212 before the cover 212 is fixed to the rotor body 210. To add, remove, or move the balance weight 436 or the test weight 433 in the cover 212, the cover 212 must be removed. Figure 7 An alternative embodiment of the cover 212 is depicted, where the balance orifice 432 is located on the top surface 426 of the cover 212. In this embodiment, it may not be necessary to remove and replace the cover 212 during the modal balancing process.

[0087] Figure 8 Depicted is an Figure 7 embodiment of the rotor 102 featuring the cover 212, where the balance orifice 432 is located on the top surface 426 of the cover 212. The detailed view shows the interface between the cover 212 and the rotor body 210 and the orientation of the balance weight 436 within the balance orifice 432 of the cover 212.

[0088] Figure 9Depicts a flowchart showing an exemplary modal balancing method 945 for balancing rotor 102 in centrifuge 100. The centrifuge can have natural harmonic resonance frequencies that create standing wave patterns at certain critical speeds. These standing wave modes are commonly referred to as "critical modes". Advantageously, by minimizing the imbalance in the rotor, it may be possible to pass through these critical modes without interruption and achieve smooth operation of the centrifuge at high speeds. Method 945 can detect the imbalance in rotor 102 that occurs at the identified critical modes and identify at least one target reference position on cover 212 and at least one corresponding target quantity of heavy bodies whose addition at the target reference position helps to properly balance rotor 102. Although the illustrated method 945 can be used to balance rotor 102, including Figures 4 - 8 any of the various embodiments of cover 212 shown in

[0089] In block 946, method 945 determines one or more critical modes in which rotor 102 may be unbalanced. Method 945 can then proceed to block 956 and rotate rotor 102 in centrifuge 100 at a certain test speed, e.g., a fraction of the lowest critical speed, where the certain test speed is a fraction (e.g., 3 / 4 or 75%) of the critical speed at which centrifuge 100 enters one of the critical modes identified in block 946. The test speed may be less than the critical speed because rotating rotor 102 at the critical speed may damage centrifuge 100 due to the intensity of the imbalance experienced while in the critical mode. There can be a range of acceptable values for the test speed at which rotor 102 rotates. For example, rotor 102 can rotate at a speed between 70% and 95% of the critical speed. For example, rotor 102 can rotate at 70% or 85% of the critical speed.

[0090] In block 958, method 945 can correct the imbalance of rotor 102 at the test speed at which rotor 102 rotates in block 956. Correcting the imbalance determined at the test speed can allow rotor 102 to rotate at a higher speed than before the imbalance was corrected.

[0091] In block 982, method 945 can rotate rotor 102 in centrifuge 100 at another test speed, where the another test speed is a fraction of another (e.g., higher) critical speed determined in block 946. As previously described, rotor 102 can rotate at this other test speed that is lower than the other critical speeds to avoid damaging centrifuge 100. In block 984, method 945 can correct the imbalance of rotor 102 at the other test speed at which rotor 102 rotates in block 982.

[0092] In block 986, method 945 may rotate rotor 102 at yet another test speed that is a fraction of yet another critical speed determined in block 946 (i.e., a critical speed higher than the previous critical speed), provided that another critical speed is available. In block 988, method 945 may again correct for the imbalance of rotor 102 at the test speed at which rotor 102 is rotated in block 986. Thus, method 945 may iteratively rotate the rotor to a fraction of the critical speed, correct for any imbalance occurring at that speed, and then select another critical speed at which to balance the rotor. This method may continue until a desired balance level is achieved. It should be understood that the number of balancing runs may vary (e.g., there may be fewer or more than three runs). For example, in some cases, method 945 may only need to perform one balancing run to achieve the desired balance level.

[0093] In block 990, method 945 may evaluate the balance of rotor 102 in centrifuge 100 at the target speed. The target speed may preferably be the rotational speed at which a user would typically operate centrifuge 100. In an alternative embodiment, the target speed may be the maximum operating speed of centrifuge 100, which may depend on the type of centrifuge 100 being used.

[0094] Figure 9A A flowchart depicting an example sub - method 947 that may be used to determine the critical modes of the rotor system in block 946 is shown. In block 948, sub - method 947 may apply an external force to a component of centrifuge 100, such as motor 106. The external force may include frequencies in a predetermined frequency band. One way to apply the external force may be to operatively couple a chirp or sine sweep signal generated by a modal shaker to motor 106. In an alternative embodiment, the external force may be provided by a pulse load impact delivered by an instrumented hammer to motor 106. Other ways of applying an external force to motor 106 or other components of centrifuge 100 having frequency components in a predetermined frequency band may also be used.

[0095] In block 950, sub - method 947 may measure the vibration response of rotor 102 to the applied external force. The vibration response may be measured at the motor bearings that support the rotating main shaft 104 while rotor 102 is rotating in centrifuge 100. The measurement results of the vibration response may be extracted at selected rotational speeds of rotor 102. For example, the measurement results of the vibration response may be extracted at intervals from 1,000 RPM up to the typical or maximum operating speed of centrifuge 100. The vibration response of the bearing to the external force may be measured at each of the selected rotational speeds by sensor 108. The output of sensor 108 is operatively coupled to a suitable device for analyzing the output signal, such as a computer running dynamic signal analyzer or digital data recorder software.

[0096] In block 952, sub-method 947 may plot or otherwise analyze the measured vibration response data obtained in block 950 as a function of both the rotational speed of rotor 102 at which the vibration response was recorded and the frequency of the applied force. Data for generating the plot may be obtained, for example, by using a modal shaker to generate an external force by chirping or sine-wave sweeping across a predetermined frequency band. The plot may be a waterfall plot of the experimentally measured vibration response of the rotor as a function of rotational speed and excitation frequency, which is commonly referred to as a Campbell diagram. A Campbell diagram typically contains multiple slices, each corresponding to the rotational speed of rotor 102 and depicting the frequency power spectrum of the vibration detected at that rotational speed. Each slice may contain peaks corresponding to the eigenfrequencies of the rotor at that rotational speed. As the rotational speed approaches a critical mode, the intensity of the vibration at the eigenfrequency may increase.

[0097] In block 954, sub-method 947 may identify one or more critical rotational frequencies (i.e., critical speeds) of rotor 102 based on the Campbell diagram. In an exemplary embodiment of the present invention, critical speeds may occur at 5,000 RPM, 37,000 RPM, and 55,000 RPM. Based on the eigenfrequencies of rotor 102, the critical modes of rotor 102 may be identified by computer analysis. The critical modes of rotor 102 may occur at the rotational speeds at which the vibration at the bearings is most severe. It is at these rotational speeds that the imbalance of rotor 102 may be greatest. Therefore, these rotational speeds are the rotational speeds at which rotor 102 will need to be further balanced. Given the speeds at which the balance of rotor 102 needs to be corrected, method 945 may proceed to determine where to place balance weights 436.

[0098] Figure 9B Depicted is a flowchart showing an exemplary imbalance correction sub-method 963, which may be used to correct rotor imbalance at fractions of critical speeds, such as fractions of 5,000 RPM, 37,000 RPM, or 55,000 RPM, in blocks 958, 984, and 988 of method 945. Each time sub-method 963 is used to correct rotor imbalance at a subsequent critical speed (e.g., 37,000, 55,000), the correction actions may differ in at least one detail based on the results determined at the initial or previous critical speed (e.g., 5,000 RPM), as described in detail below.

[0099] In block 960, sub-method 963 may cause rotor 102 to rotate at an initial test speed that is a fraction of the initial critical speed. Advantageously, by using a test speed that is a fraction of the initial critical speed, sub-method 963 may avoid damaging centrifuge 100 due to the intensity of the imbalance levels that may be experienced when operating in the critical mode.

[0100] In block 962, sub-method 963 may measure and record the imbalance of rotor 102 as rotor 102 rotates at the initial test speed. The imbalance of rotor 102 may be measured, for example, by sensor 108. To this end, sub-method 963 may determine the root mean square (“RMS”) value of the power spectral density of the measured vibration response. The RMS value of the power spectral density may be recorded and may be a preferred measurement result parameter for determining the imbalance of the rotor.

[0101] In block 964 of sub-method 963, a test weight 433 of known mass may be installed in a balance orifice 432 at a reference position 213 on the cover 212. Preferably, test weight 433 may be similar in mass to balance weights 436 used to balance rotor 102. Reference position 213 may be the position of any balance orifice in balance orifices 432 circumferentially located around the edge of cover 212. Once reference position 213 is selected, the same reference position 213 should be used, and cover 212 should be kept in a consistent circumferential orientation relative to rotor body 210 for the remainder of the balancing process.

[0102] In block 966, sub-method 963 again rotates rotor 102 at a fraction of the initial critical speed with test weight 433 in place. Once rotor 102 reaches speed, sub-method 963 proceeds to block 968 and again measures and records the imbalance of rotor 102 as rotor 102 rotates at this speed. Sub-method 963 may then determine and record the RMS value of the power spectrum of the measured vibration response.

[0103] In block 970 of sub - method 963, the test weight 433 can be moved from the reference position 213 to another balance orifice 432. In one embodiment, the test weight can be moved to a balance orifice that is 120 degrees clockwise offset from the previous position on the cover 212. Moving the test weight 120 degrees can allow sub - method 963 to correct rotor imbalance in three runs. In an alternative embodiment, the test weight 433 can be moved 60° clockwise each time, in which case sub - method 963 may need to perform six runs. In yet another embodiment, the test weight 433 can be moved 90 degrees clockwise each time, in which case sub - method 963 can include four runs. Embodiments of sub - method 963 that move the test weight 433 in smaller increments and perform more runs can have more data for deciding where to place the selected balance weight 436. However, it has been determined that three measurements with a 120 - degree radial displacement are generally sufficient to determine the positioning and mass of the selected balance weight 436.

[0104] In response to the test weight 433 being moved, sub - method 963 can proceed to block 972 and rotate the rotor 102 at a fraction of the critical speed. Once the rotor 102 reaches speed, sub - method 963 can proceed to block 974, measure and record the imbalance of the rotor 102, determine the RMS value of the power spectral content of the vibration, and record the RMS value.

[0105] Sub - method 963 can return to block 970 and iteratively repeat moving the test weight 433, rotating the rotor 102, and measuring and recording the imbalance data until the test weight has been placed in each of the multiple positions in the cover 212. For a 120 - degree incremental offset angle, one additional run can be performed such that the test weight 433 is moved another 120 degrees from its previous position on the cover 212, i.e., 240 degrees from the original reference position 213. Each run provides an additional imbalance data point. The imbalance data from the test weight 433 at three positions mounted on the cover 212, together with the initial imbalance information of the cover 212 without the test weight 433, can provide the user with the information needed to determine where the balance weight 436 should be installed on the cover 212 and what mass the balance weight 436 should have to counteract the inherent imbalance of the rotor 102. The incremental offset angle θ can be chosen such that 360 degrees is an integer multiple of the offset angle θ. That is, the incremental offset angle θ = 360 / n, where n is an integer greater than one.

[0106] After sufficient imbalance data has been collected, sub - method 963 can proceed to block 976 and solve a system of equations to determine where the balance weight 436 should be installed on the cover 212 and what mass the balance weight 436 should have. In one embodiment, the system of equations to be solved can include the following three equations:

[0107]

[0108] where α is defined as the influence coefficient, which is the ratio of the balance weight 436 to the test weight 433, and U = ε·M is defined as the imbalance, ε is the eccentricity of the mass with respect to the centerline of rotation, and M is the mass of the rotor 102. The imbalance of the rotor 102 can be represented as a vector having a certain magnitude and phase. In vector form, the imbalance of the rotor 102 can be written as:

[0109]

[0110] For example, the initial imbalance value of the rotor 102 can be represented in vector form using the above-mentioned equation, such as: As shown in the equation, the imbalance vector can be decomposed into its components - the magnitude of the imbalance |A0| and the phase of the imbalance with respect to the selected reference position 213 For each case of introducing the test weight 433 into the rotor 102, the same operation can be performed on the imbalance value. However, for each case of introducing the test weight 433 into the rotor 102, the initial imbalance value inherent in the rotor 102 itself can be subtracted in order to determine the additional "amount" of imbalance added to the rotor 102 by adding the test weight 433 at the specified position. By writing each imbalance vector in the imbalance vector in the form of Equation 4 (i.e., in terms of magnitude and direction) and solving the system of equations shown in Equations 1 - 3, the radius (R) and phase (Φ) of the required balance weight 436 can be determined. According to the determined radius (R), the following equation can be used to determine the weight of the balance weight 436 required:

[0111]

[0112] where W c is the mass of the balance weight 436, and T W is the mass of the test weight 433 used to test the rotor 102. The phase (Φ) determined above represents the angle with respect to the selected reference position 213 where the balance weight 436 is to be installed. The mass W c of the correction weight represents how heavy the balance weight 436 to be installed should be in order to balance the rotor 102 in a specific mode.

[0113] For example, assume the following measurement results are extracted while measuring and recording the imbalance of the rotor 102 by sub-method 963:

[0114] A0 = 0.225

[0115] A1 = 0.357

[0116] A2 = 0.184

[0117] A3 = 0.395

[0118] T W = 1.01 grams

[0119] Inserting these measured quantities into the equations provided above gives the following results:

[0120] |R| = 0.178

[0121]

[0122] Taking the value of the determined radius (R) and substituting it into the equations provided above gives:

[0123] W c = 1.44 grams

[0124] Therefore, the balancing weight 436 required to balance the rotor 102 in the particular selected critical mode should weigh 1.44 grams and should be placed in a balancing aperture that is 109.57° from the previously selected reference position 213.

[0125] Referring again to Figure 9B , in block 978 of sub-method 963, the identified balancing weight 436 can be installed at the designated position determined by the modal balancing method. Then a suitable balancing aperture 432 corresponding to the target position, and a balancing weight 436 whose weight is relatively close to the target amount of the weight determined by the modal balancing method, can be selected. Generally, the user can take a balancing weight 436 of appropriate mass and install it in the balancing aperture 432 corresponding to the designated position. Referring back to the above example, if the cover 212 in use has a balancing aperture 432 that is 109.57° from the reference position 213, the user can simply install a balancing weight 436 of appropriate mass in the particular balancing aperture 432.

[0126] If the cover 212 does not have balance orifices 432 specifically located at the positions determined by the modal balancing method, the vector calculation results can be used to determine the approximate positions where the balance weights 436 are to be placed. The combined balance vector of multiple balance weights 436 can be equivalent to the balance vector of a single balance weight 436 at a specified position. Referring back to the above example, if the cover 212 does not have balance orifices 432 that are 109.57 degrees from the reference position 213, the vector calculation results can be used to determine the positions near the 109.57° mark; for example, the masses of the balance weights 436 required at the two balance orifices 432 closest to the target position. For a cover 212 having 24 balance orifices 432 circumferentially spaced 15 degrees apart from each other around the edge of the cover 212 (as Figure 4 shown), the selected balance orifices 432 can be located at 105 degrees and 120 degrees, and the selected balance orifices are the balance orifices 432 on either side of the position where the 109.57 degree mark would be located. The vectors generated by placing the balance weights 436 at 105 degrees in the balance orifices 432 and at 120° in the balance orifices 432 can be calculated. In this example, the combined vector from one balance weight 436 weighing 1.01 grams at the balance orifice 432 that is 105 degrees clockwise from the reference position 213 and one balance weight 436 weighing 0.44 grams at the balance orifice 432 that is 120 degrees clockwise from the reference position 213 will provide a vector equivalent to the vector of a 1.44 gram balance weight 436 that is 109.57 degrees from the reference position 213. In certain embodiments of the present invention, the balance weights 436 can be selected to have a predetermined mass close to the calculated mass to provide an optimal balance vector. For example, in the above case, weights of 1.00 grams and 0.50 grams can be selected from a set of balance weights having a predetermined mass increment of 0.25 grams. In any case, the method of calculating the combined vector equivalent to the determined correction weight W c and phase Φ can be generalized and used to determine the appropriate number, mass, and position of the balance weights 436.

[0127] In block 980, the sub-method 963 can test the rotor 102 with the balance weights 436 installed in the appropriate balance orifices 432 to determine if the balance is satisfactory. To do this, the rotor 102 can be rotated to a fraction of the previously determined critical speed, the vibration response can be measured, and the RMS value of the power spectral content of the vibration response can be determined and recorded. Before starting the sub-method 963, this RMS value can be compared with the RMS value of the imbalance of the rotor 102. If the balancing is performed correctly, the RMS value of the imbalance after balancing should be less than the RMS value of the imbalance before modal balancing. Additionally, the imbalance after balancing should fall within the acceptable tolerance for the operation of the centrifuge 100.

[0128] Referring again toFigure 9 , if the target speed for the rotor 102 is greater than the initial critical speed, the method 945 can proceed to block 982 and rotate the rotor 102 to a fraction of another (e.g., the next incrementally higher) critical speed. In block 984, the method 945 can correct the imbalance as described above with respect to the sub-method 963, except that the balancing weights 436 previously added to the cover 112 of the rotor 102 (as Figure 4C shown) or the balancing weights 436 (as Figure 4D shown) remain in the indicated balance orifices 432 during the modal balancing process.

[0129] Thus, in block 964 of the sub-method 963, the trial weight 433 can be installed at the reference location 213 of the cover 212, where the cover 212 has a balancing weight 433 installed substantially as Figure 4C or Figure 4D shown. In block 966, the sub-method 963 can rotate the rotor 102 at a fraction of the next (e.g., higher) critical speed. In block 970, the trial weight 433 can be moved clockwise by an incremental offset angle θ, e.g., 120 degrees to the Figure 4A shown position. During this iteration of the imbalance correction sub-method 963, one or more balancing weights 436 from the previous modal balancing process remain in place. The sub-method 963 can then proceed to block 972 and again rotate the rotor 102 at a fraction of the currently selected critical speed. The sub-method 963 can thus repeat the balancing process described above with respect to the initial critical speed, but at the currently selected critical speed and with one or more weights 436 from the previous balancing run still in place. Then the positioning and weight analysis required to correct the measured imbalance as described above with respect to Figure 4C the initial modal balance can be repeated for the current modal balance.

[0130] If the primary concern is modal balancing at or near the second critical speed, the sub-method 963 can proceed to block 978 and install all of the identified amount of balancing weights 436 at the identified one or more locations. The sub-method 963 can then proceed to block 980 and estimate and test the amount of possible imbalance at or near the initial critical speed. The testing can include performing a test balance at defined fractions of both the initial critical speed and subsequent critical speeds. If the amount of imbalance at or near the initial critical speed becomes too large, the mass of the balancing weights 436 can be reduced and the balance at both critical speeds re-tested to determine if the imbalance is at an acceptable level for each rotational speed.

[0131] Referring again toFigure 9 If there are one or more higher critical speeds within the desired operating range of the rotor 102, the modal balancing method 945 can proceed to block 988 and repeat the imbalance correction sub-method 963 described above, but starting from each previous iteration of the imbalance correction sub-method 963 with the balance weights 436 in place. Thus, the method of correcting the imbalance can be performed on one or more critical modes until the rotor 102 is balanced in such a way as to optimize the operation of the centrifuge within the desired operating range of the rotational speed.

[0132] Reference has been made in the foregoing description where additional balance weights 436 were added during the modal balancing method 945 while leaving the balance weights 436 from the previous iteration of the imbalance correction sub-method 963 in place. However, it should be understood that the same result can be achieved by calculating and then implementing an equivalent balance vector using a smaller number of balance weights 436 after removing the previously installed balance weights 436.

[0133] Figure 9C A flowchart of a balance evaluation sub-method 991 that can be performed by the modal balancing method 945 in block 990 is depicted. The balance evaluation sub-method 991 can be used to evaluate the balance of the rotor 102 at a target speed. In block 992, the sub-method 991 can cause the centrifuge 100 to rotate the rotor 102 at the target speed. The target speed can be the rotational speed at which the user intends to operate the centrifuge 100. Alternatively, the target speed can be the maximum operating speed of the centrifuge 100. The maximum speed of the centrifuge 100 can depend on the type of centrifuge 100 being used and how well the rotor 102 is balanced.

[0134] In block 994, the sub-method 991 can measure and record the imbalance of the rotor 102 experienced when the rotor 102 rotates at the target speed within the centrifuge 100, as described above. The sub-method 991 can then proceed to block 996 and compare the recorded imbalance at the target speed after balancing with the recorded imbalance at the initial critical speed. To do this, the RMS value of the imbalance at the target speed can be compared with the RMS value of the imbalance at a fraction of the initial critical speed after balancing the rotor 102 at that speed.

[0135] In block 998, sub-method 991 can determine whether the level of balance is sufficient. For example, if the RMS value of the imbalance at the target speed is approximately equivalent to the RMS value of the imbalance at a fraction of the initial critical speed immediately following balancing the rotor 102 at that speed, the balance can be considered to have been sufficiently performed. That is, before any further iteration of the imbalance correction sub-method 963. Approximately equal RMS values can demonstrate that balancing the rotor 102 at subsequent critical speeds will not interfere with the balance of the rotor 102 at previous critical speeds. In other words, balancing the rotor 102 at subsequent critical speeds does not undo the balance previously performed at the initial critical speed. Further, the imbalance of the rotor 102 after balancing should fall within the acceptable tolerance of operation of the centrifuge 100.

[0136] Subsequently, the rotor 102 can be rebalanced by, for example, detecting a new imbalance in the rotor 102 and disengaging one or more balance weights 436 from their respective balance apertures 432 in a threaded manner, repositioning the removed balance weights 436 to different balance apertures 432, engaging one or more different balance weights 436 with one or more different balance apertures 432 in a threaded manner or replacing the removed balance weights 436 with one or more balance weights 436 having different lengths and / or masses. Using the balance weights 436 and balance apertures 432 can eliminate the need to drill holes in the rotor body 210 or plug such drilled holes during rebalancing, which would otherwise become obsolete and repetitive.

[0137] Figures 10 - 18 An exemplary rotor 1010 (e.g., a 12×1.5 mL fixed angle rotor) according to another exemplary embodiment of the present invention is depicted. The rotor 1010 includes a rotor body 1012, a reinforcement 1014, a balance ring 1016, a cover 1018, a drive hub 1020, and cover screws 1022. The rotor 1010 has a rotational axis 1024 about which the rotor 1010 is configured to rotate when used in a centrifuge and about which the components of the rotor 1010 are concentrically arranged.

[0138] The rotor body 1012 can be made of a carbon fiber composite material or other suitable lightweight rigid material and includes an upper surface 1026, a lower surface 1028, a circumferential sidewall 1030, and an elongated bore 1032 passing through the upper surface 1026 and the lower surface 1028. The elongated bore 1032 can be axially aligned with the rotational axis 1024 and intersects an upper recess 1034 in the upper surface 1026 of the rotor body 1012 and a lower bore opening 1036 in the lower surface 1028. As described in more detail below, the lower bore opening 1036 can have a horizontal cross-sectional shape that is keyed to the drive hub 1020 to prevent rotation of the rotor body 1012 relative to the drive hub 1020.

[0139] The upper surface 1026 of the rotor body 1012 may include an annular surface 1038, a central surface 1040 that is axially downwardly recessed relative to the annular surface 1038, and an annular groove 1042. The annular groove 1042 may define an outer perimeter 1044 of the annular surface 1038 and an upper edge 1046 of the circumferential sidewall 1030. The annular groove 1042 may be defined by an upper notch 1048 and a lower notch 1050 that overlap to define a shoulder 1052. The central surface 1040 may be connected to the annular surface 1038 by a connecting surface 1054. The connecting surface 1054 may extend axially upwardly and radially outwardly from the outer perimeter of the central surface 1040 to the inner perimeter of the annular surface 1038. The connecting surface 1054 may be oriented such that it faces axially upwardly and radially inwardly, and may include a lower portion 1056 and an upper portion 1058. The upper portion 1058 of the connecting surface 1054 may rise above the lower portion 1056 in a direction perpendicular to the connecting surface 1054.

[0140] The rotor body 1012 may further include a plurality of cavities 1060 (e.g., 12 cavities), each cavity extending axially downwardly and radially outwardly from the lower portion 1056 of the connecting surface 1054 and into the rotor body 1012. In one embodiment of the present invention, the plurality of cavities 1060 may include a plurality of circumferentially spaced tubular cavities, each tubular cavity having an open end configured to receive a sample container. Each cavity 1060 may have a central axis perpendicular to the connecting surface 1054 and be sized and shaped appropriately to receive a sample container 1062. Each cavity 1060 may be configured to hold its corresponding sample container 1062 in a proper position and orientation for centrifugation, e.g., at an angle of 45 degrees relative to the axis of rotation 1024.

[0141] Each sample container 1062 can be configured to hold a quantity of sample suspension (e.g., 1.5 ml) and include a cap 1064 that seals the sample container 1062 when pressed into a closed position. The cap 1064 can include a tab 1066 configured to facilitate opening of the sample container 1062. The cavity 1060, the sample container 1062, and the cap 1064 can be configured such that when the sample container 1062 is fully inserted into its corresponding cavity 1060, the tab 1066 is supported by the upper portion 1058 of the connection surface 1054. The top portion of the cavity 1060 can also include a counterbore 1067 configured to receive the cylindrical skirt of the cap 1064. Advantageously, the counterbore 1067 and the pressure on the top surface of the cap 1064 from the bottom surface of the lid 1018 can provide sufficient support to prevent any deformation of the cap 1064 under the high g-forces generated by centrifugation. Thus, these features can prevent the seal between the cap 1064 and the body of the sample container 1062 from being compromised or prevent damage to the sample container 1062 itself.

[0142] The reinforcement 1014 can include one or more helical coils that extend around and above the circumferential sidewall 1030 of the rotor body 1012. The inner surface 1068 of the reinforcement 1014 can cooperate with the annular groove 1042 of the rotor body 1012 to define a channel 1070 in which the balance ring 1016 is positioned. The reinforcement 1014 can be formed using a suitable material (such as epoxy-coated carbon fiber) by a filament winding process followed by a compression molding process. For example, after placing a layer of resin-coated carbon fiber laminate or winding one or more carbon fiber tows around the outward-facing surface of the circumferential sidewall 1030, the reinforcement 1014 can be compression molded into the rotor body 1012 and the balance ring 1016.

[0143] To prevent the reinforcement 1014 from moving axially, the circumferential sidewall 1030 can include an inward taper that defines a circumferential recess 1072 in the circumferential sidewall 1030. The inner surface 1068 of the reinforcement 1014 can mate with the circumferential recess 1072 such that the reinforcement 1014 resists axial movement relative to the rotor body 1012. The reinforcement 1014 can be configured to carry most of the centrifugal force applied to the rotor 1010. A method of forming a reinforcement for a centrifuge rotor using a filament winding process is described in detail in U.S. Patent No. 8,323,169, published on December 4, 2012, the disclosure of which is incorporated herein by reference in its entirety.

[0144] The balance ring 1016 can include a body 1074 having a rectangular cross-section and a flange 1076. As Figure 15As best shown, the flange 1076 can project radially inwardly from the top portion of the body 1074 of the balance ring 1016 and can be configured to engage the shoulder 1052 of the rotor body 1012. In one embodiment of the present invention, the balance ring 1016 can have an outer diameter that is equal to or slightly larger than the diameter of the inner surface 1068 of the reinforcement 1014. In this embodiment, the balance ring 1016 can be operatively coupled to the rotor 1010 by cooling the balance ring 1016 to a temperature below ambient such that the balance ring 1016 contracts sufficiently to make its outer diameter smaller than the diameter of the inner surface 1068 of the reinforcement 1014. The balance ring 1016 can then be placed in the channel 1070 and allowed to warm back up to ambient temperature. As it warms, the balance ring 1016 can expand until it presses against the inner surface 1068 of the reinforcement 1014 such that it is held firmly in place. In an alternative embodiment of the present invention, the balance ring 1016 can be heated such that the balance ring expands before being placed on the annular groove 1042 and the balance ring is cooled in place such that the balance ring is held to the rotor body 1012 by a shrink fit. In this case, the balance ring 1016 can be placed in the annular groove 1042 of the rotor body 1012 before the reinforcement 1014 is formed. In either case, the reinforcement 1014 can hold the balance ring 1016 in place. An adhesive can also be used to operatively couple the balance ring 1016 to the annular groove 1042 of the rotor body 1012.

[0145] The balance ring 1016 can include a plurality of balance apertures 1078, each balance aperture being configured to receive a balance weight 1080. One or more balance weights 1080 can be selectively positioned in one or more of the balance apertures 1078 of the balance ring 1016 to facilitate balancing of the rotor 1010. In one embodiment of the present invention, each balance weight 1080 can include a threaded shank 1082 and a head 1084. Each balance aperture 1078 can include a threaded bore 1086 configured to receive the threaded shank 1082 of the balance weight 1080 and a receiving portion 1088 (e.g., a countersunk conical hole, a countersunk bore, etc.) configured to receive the head 1084 of the balance weight 1080. The receiving portion 1088 can thus allow the top of the balance weight 1080 to be flush with or recessed below the top surface 1090 of the balance ring 1016 when the balance weight 1080 is fully inserted into the balance aperture 1078.

[0146] The balance ring 1016 can be angularly positioned relative to the rotor body 1012 about the axis of rotation 1024 such that the balance orifices 1078 of the balance ring 1016 are symmetrically positioned relative to the cavities. This symmetry can cause each of the two balance orifices 1078 of the corresponding cavity 1060 closest to the rotor body 1012 to be equidistant from and on opposite sides of a line extending radially outward from the axis of rotation 1024 and passing through the central axis of the cavity 1060. This angular positioning of the balance ring 1016 can provide such an orientation for the ring that each cavity 1060 of the rotor body 1012 is angularly centered between the two balance orifices 1078 of the balance ring 1016 closest to the cavity 1060 and ensures the positioning symmetry between the cavities 1060 of the rotor body 1012 and the balance orifices 1078 of the balance ring 1016.

[0147] The balance ring 1016 can be made of aluminum or any other suitable lightweight rigid material. One or more balance weights 1080 can be selectively placed into the corresponding balance orifices 1078 to counterbalance the imbalance in the rotor 1010. For example, balance weights 1080 can be added to align the center of mass of the rotor 1010 with the axis of rotation 1024 (i.e., achieve static balance), to align the principal axis of the moment of inertia of the rotor with the axis of rotation 1024 (i.e., dynamic balance), or to make the rotor 1010 both statically balanced and dynamically balanced. Balance weights 1080 can also be added to the balance ring 1016 during the modal balancing method described above Figures 9 - 9C described.

[0148] The cover 1018 of the rotor 1010 can include an annular wall portion 1092, a central wall portion 1093, and a tapered wall portion 1094, and can be made of a carbon fiber composite, aluminum, or any other suitable rigid low-mass material. The tapered wall portion 1094 of the cover 1018 can connect the inner edge 1095 of the annular wall portion 1092 to the outer edge 1096 of the central wall portion 1093. The tapered wall portion 1094 can connect to each of the central wall portion 1093 and the annular wall portion 1092 of the cover 1018 at an obtuse angle such that the annular wall portion 1092 is axially offset from the central wall portion 1093 and parallel to the central wall portion. The resulting shape of the cover 1018 can generally conform to the shape of the upper surface 1026 of the rotor body 1012.

[0149] The annular wall portion 1092 of the cover 1018 can include a lower surface 1098 having an annular groove 1100 configured to receive an elastic member 1102, such as an O-ring. The elastic member 1102 can be made of any suitable material (e.g., silicone) and can be configured to engage the top surface 1090 of the balance ring 1016 when the cover 1018 is operatively coupled to the rotor 1010.

[0150] The central wall portion 1093 of the lid 1018 may include an upper surface 1104, a central bore 1106, and a lid-lifting handle 1108 that projects axially upward from the upper surface 1104. The central bore 1106 may have the same diameter as the elongated bore 1032 of the rotor body 1012 such that the bores are axially aligned through the drive hub 1020. The lid-lifting handle 1108 may include a cylindrical wall 1109 and a flange 1112. The cylindrical wall is connected to the lid 1018 at the lower end of the cylindrical wall and has an inner surface 1110. The flange projects radially outward from the upper portion of the lid-lifting handle 1108 at the free end of the cylindrical wall 1109 remote from the central wall portion 1093 of the lid 1018. The flange 1112 of the lid-lifting handle 1108 may provide a grip for grasping the rotor 1010. This grip may improve the ergonomics of mounting the rotor 1010 in and removing the rotor 1010 from a centrifuge as compared to a rotor lacking this feature. The inner surface 1110 of the cylindrical wall 1109 may include a neck 1114 that is close to or adjacent to the upper surface 1104. The diameter d1 of the neck 1114 may be less than the diameter d2 of the main portion of the inner surface 1110. The main portion of the inner surface 1110 may be connected to the neck 1114 by a bevel 1116.

[0151] The drive hub 1020 may include a shaft 1120, a flange 1122 that projects radially outward from the bottom portion of the shaft 1120, and a central bore 1124 that extends axially into the bottom end of the shaft 1120. The central bore 1124 of the drive hub 1020 may be axially aligned with the rotational axis 1024 of the rotor 1010, may include a bottom surface 1130, and may be configured to receive the main shaft (not shown) of a centrifuge. The upper portion 1126 of the shaft 1120 may be configured to receive the lid screw 1022. To this end, the upper portion 1126 of the shaft 1120 may include a threaded outer surface 1128 that is configured to threadedly engage the lid screw 1022.

[0152] A portion of the shaft 1120 adjacent to and below the threaded outer surface 1128 may have a reduced radius (e.g., an undercut) for providing thread relief. This thread relief can ensure that the lower surface 1148 of the flange 1146 is not interfered with by the shaft 1120 when the cover screw 1022 is threadedly engaged with the drive hub 1020 and engages the upper surface 1104 of the central wall portion 1093 of the cover screw 1018. The upper portion 1126 of the shaft 1120 may include a protruding end 1129 at its top. The protruding end 1129 may have a diameter approximately the same as the small diameter of the threaded outer surface 1128 and may extend a distance of 1.5 to 2.5 thread widths beyond the threads of the threaded outer surface 1128. The drive hub 1020 may be manufactured from a solid metal blank using a computer numerical control (CNC) machine or any other suitable process.

[0153] To prevent the drive hub 1020 from rotating relative to the main shaft, one or more drive pins 1132 may axially extend downward from the bottom surface 1130 of the central bore 1124. Each drive pin 1132 may be configured to engage a corresponding receiving portion in the main shaft of the centrifuge. Each drive pin 1132 may include a rod 1134 inserted into a corresponding bore 1136 that axially extends into the bottom surface 1130 of the central bore 1124. Each bore 1136 may be radially offset from the central axis of the central bore 1124 such that the drive pins 1132 will be subjected to shear forces in response to the main shaft applying a torque to the rotor 1010 sufficient to cause slippage between the main shaft and the drive hub 1020 in the absence of the drive pins 1132.

[0154] The drive portion 1138 of the hub 1020 may axially extend upward from the flange 1122 and radially outward from the shaft 1120. The drive portion 1138 of the hub 1020 may have a horizontal cross-sectional shape that is keyed or otherwise complementary to the horizontal cross-sectional shape of the lower bore opening 1036 of the rotor body 1012. Keying the drive portion 1138 to the lower bore opening 1036 can prevent angular misalignment of the rotor body 1012 relative to the drive hub 1020 under angular acceleration. To this end, the cross-sectional shape of the drive portion 1138 may be the same as the cross-sectional shape of the lower bore opening 1036, i.e., a shape that fits within the lower bore opening 1036 and has one or more faces 1139 that engage corresponding faces 1141 in the sidewalls of the lower bore opening 1036 or otherwise a different shape that is keyed to the cross-sectional shape of the lower bore opening 1036.

[0155] For example, the cross-sectional shape of the drive portion 1138 can be polygonal (e.g., square), having the same number of faces 1139 or more faces 1139 as the shape of the lower bore opening 1036. For example, for the lower bore opening 1036 having a square-shaped horizontal cross-section, the drive portion 1138 can have a square shape, an octagonal shape, or other cross-sectional shapes having one or more faces 1139 complementary to the faces 1141 of the lower bore opening 1036. The lower bore opening 1036 can also include one or more axially aligned channels 1143 positioned where the vertices of the faces 1141 would otherwise facilitate insertion of the drive portion 1138 of the drive hub 1020 into the lower bore opening 1036.

[0156] The cover screw 1022 can be made of any suitable material (e.g., aluminum) and includes a cylindrical body having an outer surface 1140, an upper bore 1142, a lower bore 1144, and a flange 1146 that projects radially outward from the lower end of the cylindrical body. The outer diameter of the flange 1146 can be the same as or slightly less than the diameter d1 of the neck 1114. When the flange 1146 is inserted into the lid lifting handle 1108 and the cover screw 1022 is threaded onto the drive hub 1020, the inclined surface 1116 can guide the flange 1146 into the neck 1114. The neck 1114 and the inclined surface 1116 can thus cooperate with the flange 1146 to concentrically position the cover screw 1022 with respect to the cover 1018 and the drive hub 1020, thereby aligning the cover 1018 with the rotational axis 1024 of the rotor 1010 during engagement of the cover screw 1022 with the drive hub 1020. The final alignment between the cover 1018 and the rotational axis 1024 of the rotor 1010 can be defined by the engagement of the shaft 1120 of the drive hub 1020 and the central bore 1106 of the cover 1018.

[0157] The flange 1146 can include a lower surface 1148 having an annular groove 1150 configured to receive an elastic member 1152. The elastic member 1152 can be an O-ring or other type of gasket made of a suitable material such as silicone. The elastic member 1152 can press against the upper surface 1104 of the central wall portion 1093 of the cover 1018 in response to tightening the cover screw 1022 against the drive hub 1020. The elastic member 1152 can thus urge the cover 1018 into operative engagement with the rotor 1010.

[0158] The cover screw 1022 may further include one or more pairs of radially aligned holes 1156 located on opposite sides of the upper bore 1142. The radially aligned holes 1156 may be configured to receive a rod or other tool for applying torque to the cover screw 1022. The radially aligned holes 1156 may thus facilitate tightening the cover screw 1022 onto the drive hub 1020 and loosening the cover screw 1022 from the drive hub 1020.

[0159] The lower bore 1144 of the cover screw 1022 may include a threaded inner surface 1158 configured to threadedly engage the threaded outer surface 1128 of the drive hub 1020. By providing a clean start to the engagement between the threaded outer surface 1128 of the shaft 1120 and the threaded inner surface 1158 of the lower bore 1144, the protruding end 1129 of the shaft 1120 may facilitate such threaded engagement between the drive hub 1020 and the cover screw 1022. Threadedly engaging the cover screw 1022 with the drive hub 1020 may push the cover 1018 against at least a portion of the upper surface 1026 of the rotor body 1012. The cover screw 1022 may also push the cover 1018 against the cap 1064 of the sample container 1062, thereby maintaining the cap 1064 fully seated on the sample container 1062. In this way, the cover 1018 may also hold the sample container 1062 in a fully seated position within the respective cavity 1060 of the sample container by applying a nominal force to the surface of each cap 1064.

[0160] Embodiments of the present invention that include balance rings may use a modal balancing method 945 to balance in a manner similar to that described above with respect to Figures 9 - 9C That is, the method 945 may determine one or more critical modes of the rotor 1010 by applying an external force to the rotor 1010 as the rotor 1010 rotates at each of a plurality of rotational speeds. The method 945 may measure and record the vibration response at each rotational speed. Based on this data, the method 945 may determine the severity of the vibration at each rotational speed. The method 945 may then identify the rotational speed at which the vibration is most severe as the critical speed.

[0161] Once the critical speed has been identified, the method 945 may rotate the rotor 1010 in the centrifuge 100 at an initial test speed that is a fraction of one of the critical speeds, e.g., the lowest critical speed. The method 945 may measure and record the imbalance of the rotor 1010 experienced as the rotor 1010 rotates at the initial test speed, e.g., as the RMS value of the power spectral density of the vibration detected at a component of the centrifuge 100, e.g., the motor bearing.

[0162] A test weight of known mass can then be installed in the balance orifice 1078 at a reference location on the balance ring 1016, which can be the location of the balance orifice in the balance orifice 1078 of the balance ring 1016, provided that the same balance orifice 1078 is used as the reference aperture for the remainder of the balancing method. To facilitate consistent placement of the weight in the balance ring 1016, one or both of the rotor body 1014 and the balance ring 1016 can include reference marks proximate to one of the balance orifices 1078. One or more reference marks can also be included on the cover 1018 and the rotor body 1014 to facilitate installation of the cover 1018 in the same orientation relative to the rotor body 1014 during use of the rotor 1010.

[0163] The balancing method 945 can then rotate the rotor 1010 at an initial test speed and measure and record the imbalance of the rotor 1010 with the test weight in place, e.g., by determining and recording the RMS value of the power spectrum of the measured vibration response. The test weight can then be moved to another balance orifice 1078 and the resulting imbalance measured and recorded as described above. The process of moving the test weight and measuring the rotor imbalance can be repeated until imbalance measurements have been recorded sufficient to determine where the correction mass should be installed in the balance ring 1016 and how large the correction mass should be to counteract the inherent imbalance of the rotor 1010. One or more balance weights 1080 can then be installed in the corresponding balance orifices 1078 of the balance ring 1016, which, e.g., using the equations described above for adding balance weights 436 to the cover 212 provides a balance mass that is close to or equivalent to the correction mass.

[0164] The method of installing a test weight in the balance orifice 1078 of the balance ring 1016, rotating the rotor 1010 at a test speed, measuring and recording the imbalance, and installing balance weights 1080 in the balance ring 1016 to balance the rotor 1010, as described above, can be repeated for one or more additional critical speeds to achieve a sufficient level of balance. To determine if the rotor 1010 has been sufficiently balanced, the rotor 1010 can then be rotated at a target speed, the imbalance measured and recorded, and the imbalance compared to the imbalance at some other recorded rotational speed (e.g., the initial test speed).

[0165] Experimental results

[0166] Figure 19A graph depicting a three-dimensional plot 1160 (sometimes referred to as a waterfall plot) of experimentally measured vibration response of a rotor as a function of rotational speed and excitation frequency. Vibration data was generated using a SORVAL MX Plus micro-ultracentrifuge to rotate a rotor containing a balance ring according to an embodiment of the present invention. The SORVAL MX Plus micro-ultracentrifuge is available from Thermo Fisher Scientific of Waltham, Massachusetts, United States. Prior to measuring the vibration data depicted by FIG. 1160, modal balancing was performed on the critical speeds of the rotor at 5,000 RPM, 37,000 RPM, and 55,000 RPM by selectively adding balance weights to the balance orifices of the balance ring.

[0167] FIG. 1160 is commonly referred to as a Campbell plot and includes a horizontal axis 1162 corresponding to the rotational speed of the rotor, another horizontal axis 1164 corresponding to the frequency of the vibration detected by a vibration sensor, and a vertical axis 1166 corresponding to the amplitude of the detected vibration relative to a reference level in decibels (dB). FIG. 1160 includes a plurality of slices 1168, each slice corresponding to a certain rotational speed of the rotor. Each slice 1168 includes a peak 1170 corresponding to the eigenfrequency of the rotor at the rotational speed. For example, slice 1168a corresponds to a rotational speed of 5,000 RPM and has a peak 1170a that occurs at 83 Hz. Other peaks 1170 include peak 1170b corresponding to the eigenfrequency of 617 Hz at a rotational speed of 37,000 RPM on slice 1168b, and peak 1170c corresponding to the eigenfrequency of 917 Hz at a rotational speed of 55,000 RPM on slice 1168c. As can be seen, the vibration response of the modal balanced rotor performs well across the entire test range from 5,000 RPM to 55,000 RPM.

[0168] Figure 20 Depicts a 12 x 1.5 mL fixed angle rotor 1172 used to generate the above test data. The rotor 1172 includes a balance ring 1174 having 24 balance orifices 1176 and contains 12 sample containers 1178. During the modal balancing method, one balance weight 1180a was installed to compensate for the imbalance at 5,000 RPM, another balance weight 1180b was installed to compensate for the imbalance at 37,000 RPM, and a final balance weight 1180c was installed to compensate for the imbalance at 55,000 RPM.

[0169] Figures 21 - 23Graphs 1182 - 1184 depict the vibration response of a rotor measured experimentally before any balancing on the rotor (Graph 1182), after balancing the rotor on a hard bearing (Graph 1183), and after modal balancing the rotor according to an embodiment of the present invention (Graph 1184). Vibration data was generated by rotating the rotor at 37,000 RPM using a SORVAL WX+ series micro - ultracentrifuge. This centrifuge is also available from Thermo Fisher Scientific. The rotor used was an 8 x 100 mL rotor with a lid containing 24 balancing orifices.

[0170] Each of Graphs 1182 - 1184 includes a horizontal axis 1186 corresponding to time in seconds and a vertical axis 1188 corresponding to the acceleration due to vibration in units of gravitational equivalent g. Each of Graphs 1182 - 1184 includes corresponding plots 1190 - 1192 of the vibration response of the rotor. The RMS value of the vibration acceleration without balancing (i.e., the vibration of the unbalanced rotor) depicted by Plot 1190 is approximately 0.43 g, where the peak is slightly greater than 0.60 g. The RMS value of the vibration acceleration depicted by Plot 1191 is approximately 0.20 g or slightly less than half of the RMS vibration of the unbalanced rotor. In contrast, the RMS value of the vibration acceleration depicted by Plot 1192 is approximately 0.06 g. Thus, the vibration acceleration of the modally balanced rotor is only about 28% of that of the rotor balanced conventionally and only about 13% of the vibration acceleration of the unbalanced rotor.

[0171] Figure 24 Graph 1193 depicts a graph showing the vibration RMS level versus the rotational speed. Graph 1193 includes a horizontal axis 1194 corresponding to the rotational speed of the rotor in units of RPM x 1,000 and a vertical axis 1195 corresponding to the RMS value of the sensed vibration in units of g. Plot 1196 shows the vibration level of the rotor balanced conventionally that produced the data described in Figure 22 and Plot 1197 shows the vibration level of the rotor modally balanced that produced the data depicted in Figure 23 The lower threshold 1198 illustrates an exemplary 0.3 g threshold for the acceptable vibration tolerance limit of the centrifuge, and the upper threshold 1199 illustrates an exemplary 0.7 g unbalance switch trigger limit at which the centrifuge can disconnect. As can be seen, the RMS vibration of the rotor balanced conventionally climbs as the rotational speed increases. In contrast, the RMS vibration of the rotor modally balanced is lower than that of the rotor balanced conventionally at all speeds. In the specific example shown, the RMS vibration reaches a maximum between 15,000 RPM and 20,000 RPM and then decreases as the rotational speed increases. However, there may be minor variations for the same rotor model with different serial numbers at different speeds. Thus,Figure 24 Chart 1193 provides an overall view of the effectiveness of modal balancing for centrifuge rotors, particularly for rotors driven by flexible spindles. In any case, it is evident that a modal balanced rotor can operate at a higher rotational speed and with less vibration compared to a conventionally balanced rotor.

[0172] Now refer to Figure 25 , an embodiment of the present invention or a part thereof described above can be implemented using one or more computer devices or systems, such as the exemplary computer 1200. The computer 1200 can include a processor 1202, a memory 1204, an input / output (I / O) interface 1206, and a human-machine interface (HMI) 1208. The computer 1200 can also be operatively coupled to one or more external resources 1210 through the I / O interface 1206 or a network 1212. The external resources can include but are not limited to servers, databases, mass storage devices, peripheral devices, cloud-based network services, or any other resources that the computer 1200 can use.

[0173] The processor 1202 can include one or more devices selected from the following: a microprocessor, a microcontroller, a digital signal processor, a microcomputer, a central processing unit, a field programmable gate array, a programmable logic device, a state machine, a logic circuit, an analog circuit, a digital circuit, or any other device that manipulates signals (analog or digital) based on operation instructions stored in the memory 1204. The memory 1204 can include a single memory device or multiple memory devices, which include but are not limited to read-only memory (ROM), random access memory (RAM), volatile memory, non-volatile memory, static random access memory (SRAM), dynamic random access memory (DRAM), flash memory, cache memory, or data storage devices such as hard drives, optical drives, tape drives, volatile or non-volatile solid-state devices, or any other device capable of storing data.

[0174] The processor 1202 can operate under the control of an operating system 1214 resident in the memory 1204. The operating system 1214 can manage computer resources so that computer program code embodied as one or more computer software applications, such as the application 1216 resident in the memory 1204, can have instructions executed by the processor 1202. In an alternative embodiment, the processor 1202 can directly execute the application 1216, in which case the operating system 1214 can be omitted. One or more data structures 1218 can also reside in the memory 1204 and can be used by the processor 1202, the operating system 1214, or the application 1216 to store or manipulate data.

[0175] The I / O interface 1206 can provide a machine interface that operatively couples the processor 1202 to other devices and systems, such as external resources 1210 or network 1212. The application 1216 can thus cooperate with the external resources 1210 or network 1212 by communicating via the I / O interface 1206 to provide various features, functions, applications, methods, or modules including embodiments of the present invention. The application 1216 can also have program code executed by one or more external resources 1210, or otherwise rely on functions or signals provided by other systems or network components external to the computer system 1200. In fact, considering that almost infinite hardware and software configurations are possible, those of ordinary skill in the art will understand that embodiments of the present invention can include applications provided by computing resources (hardware and software) located external to the computer 1200, distributed across multiple computers or other external resources 1210, or provided as a service over the network 1212, such as cloud computing services.

[0176] The HMI 1208 can be operatively coupled to the processor 1202 of the computer 1200 to allow a user to directly interact with the computer 1200. The HMI 1208 can include a video or alphanumeric display, a touch screen, speakers, and any other suitable audio and visual indicators capable of providing data to the user. The HMI 1208 can also include input devices and controls, such as an alphanumeric keyboard, a pointing device, a keypad, buttons, control knobs, a microphone, etc., capable of receiving commands or input from the user and transmitting the input to the processor 1202.

[0177] The database 1220 can reside in the memory 1204 and can be used to collect and organize data used by the various systems and modules described herein. The database 1220 can include data and data support structures for storing and organizing the data. Specifically, the database 1220 can be arranged in any database organization or structure, including but not limited to a relational database, a hierarchical database, a network database, or a combination thereof. A database management system in the form of a computer software application executed on the processor 1202 can be used to access information or data stored in the records of the database 1220 in response to queries, which can be dynamically determined and executed by the operating system 1214, other applications 1216, or one or more modules.

[0178] Generally, routines executed for implementing embodiments of the present invention, whether implemented as part of an operating system or a specific application, component, program, object, module, or sequence of instructions or a subset thereof, may herein be referred to as "computer program code" or simply "program code". Program code typically includes computer-readable instructions that reside at various times in various memories and storage devices in a computer and, when read and executed by one or more processors in the computer, cause the computer to perform operations or elements required to perform various aspects of implementing embodiments of the present invention. The computer-readable program instructions for performing the operations of the embodiments of the present invention may be, for example, assembly language, source code, or object code written in any combination of one or more programming languages.

[0179] In particular embodiments of the present invention, the program code may be identified based on the application programs in which the embodiments are implemented as described herein. However, it should be understood that the use of any specific program nomenclature is for convenience only, and thus the present invention should not be limited to any specific application program identified or implied by such nomenclature. Additionally, considering the generally infinite number of ways in which computer programs can be organized into routines, procedures, methods, modules, objects, etc., and the various ways in which program functionality can be distributed among the various software layers residing within a typical computer (e.g., operating system, libraries, APIs, applications, applets, etc.), it should be understood that embodiments of the present invention are not limited to the specific organization and distribution of program functionality described herein.

[0180] The program code embodied in any of the application programs / modules described herein can be distributed individually or jointly in various different forms as a computer program product. Specifically, the program code can be distributed using a computer-readable storage medium having computer-readable program instructions thereon to cause a processor to perform various aspects of the embodiments of the present invention.

[0181] An inherently non-transitory computer-readable storage medium can include volatile and non-volatile, removable and non-removable tangible media implemented in any method or technology for storing data, such as computer-readable instructions, data structures, program modules, or other data. The computer-readable storage medium can further include RAM, ROM, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other solid state storage technologies, portable compact disc read-only memory (CD-ROM), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store data and can be read by a computer. A computer-readable storage medium itself should not be construed as a transient signal (e.g., radio waves or other propagating electromagnetic waves, electromagnetic waves propagating through a transmission medium such as a waveguide, or electrical signals transmitted through wires). Computer-readable program instructions can be downloaded from a computer-readable storage medium to a computer, another type of programmable data processing device, or another device, or downloaded over a network to an external computer or external storage device.

[0182] The computer-readable program instructions stored in the computer-readable medium can be used to direct a computer, other type of programmable data processing device, or other device to operate in a particular manner, such that the instructions stored in the computer-readable medium produce an article of manufacture, including instructions for implementing the functions, acts, or operations specified in the flowchart, sequence diagram, or block diagram. The computer program instructions can be provided to one or more processors of a general purpose computer, special purpose computer, or other programmable data processing device to produce a machine, such that the instructions executed by the one or more processors cause a series of computations to be performed for implementing the functions, acts, or operations specified in the specification text, flowchart, sequence diagram, or block diagram.

[0183] The flowcharts and block diagrams depicted in the figures illustrate the architecture, functionality, or operation of possible implementations of systems, methods, or computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram can represent a module, segment, or portion of instructions, which includes one or more executable instructions for implementing one or more specified logical functions.

[0184] In certain alternative embodiments, the functions, acts, or operations specified in the flowchart, sequence diagram, or block diagram can be reordered, serially processed, or parallel processed in accordance with embodiments of the present invention. Additionally, any of the flowcharts, sequence diagrams, or block diagrams can include more or fewer blocks than those shown in accordance with embodiments of the present invention. It should also be understood that each block of the block diagram or flowchart, or any combination of blocks in the block diagram or flowchart, can be implemented by a dedicated hardware-based system configured to perform the specified function or act, or by a combination of dedicated hardware and computer instructions.

[0185] The terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the embodiments of the present invention. As used herein, unless the context clearly dictates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms, and the terms "and" and "or" each are intended to include alternative and conjunctive combinations. It will be further understood that when used in this specification, the terms "comprises" or "comprising" specify the presence of the stated features, integers, acts, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, acts, steps, operations, elements, components, and / or groups thereof. Further, to the extent that the terms "includes", "having", "has", "with", "comprised of", or variations thereof are used in the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term "comprising".

[0186] While the invention has been illustrated by the description of exemplary embodiments and while these embodiments have been described in considerable detail, the applicant does not intend to restrict or in any way limit the scope of the appended claims to such details. Further advantages and modifications will be readily apparent to those skilled in the art. Thus, the invention in its broader aspects is not limited to the specific details, representative apparatus and methods, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the applicant's general inventive concept.

Claims

1. A method for balancing a rotor having a plurality of balancing orifices, each balancing orifice being configured to selectively receive a balancing mass, the method comprising: Detecting an imbalance of the rotor when rotating the rotor in a centrifuge; And In response to detecting the imbalance, selectively installing a balancing mass in a selected balancing orifice, Wherein selectively installing the balancing mass in the selected balancing orifice comprises: Measuring the imbalance of the rotor at a first test speed; Installing a test mass in a balancing orifice at a reference location; Measuring the imbalance of the rotor at the first test speed with the test mass installed at the reference location; Repeatedly moving the test mass to the next balancing orifice that is a predetermined angular distance from the current balancing orifice and measuring the imbalance of the rotor at the first test speed until the next balancing orifice will be at or beyond the reference location; and Based on the measured imbalance, determining a first target location and a first target mass to be added at the first target location to balance the rotor, Wherein the method further comprises: Determining a first balancing vector provided by the first target mass at the first target location; Selecting a first balancing orifice on one side of the first target location and a second balancing orifice on the other side of the first target location; and Determining a first balancing mass and a second balancing mass, the first balancing mass and the second balancing mass providing a second balancing vector equivalent to the first balancing vector when respectively placed in the first balancing orifice and the second balancing orifice, Installing a first mass having the first balancing mass in the first balancing orifice; Installing a second mass having the second balancing mass in the second balancing orifice; and Measuring the imbalance at the first test speed with the first mass installed in the first balancing orifice and the second mass installed in the second balancing orifice, Measuring the imbalance of the rotor at a second test speed higher than the first test speed; Installing the test mass in the balancing orifice at the reference location; Measuring the imbalance of the rotor at the second test speed with the test mass installed at the reference location; Repeatedly moving the test mass to the next balancing orifice that is the predetermined angular distance from the current balancing orifice and measuring the imbalance of the rotor at the second test speed until the next balancing orifice will be at or beyond the reference location; and Based on the measured imbalance, determining a second target location and a second target mass to be added at the second target location to balance the rotor.

2. The method according to claim 1, further comprising: Determining a third target mass and a third target location, the third target mass and the third target location providing a third balancing vector equivalent to the second balancing vector.

3. The method according to claim 2, further comprising: Select a third balance orifice located on one side of the third target position and a fourth balance orifice located on the other side of the third target position; And Determine a third balance mass and a fourth balance mass, the third balance mass and the fourth balance mass providing a fourth balance vector equivalent to the third balance vector when respectively placed in the third balance orifice and the fourth balance orifice.

4. A rotor for use in a centrifuge and used in accordance with the method of any one of claims 1 to 3, the rotor comprising: A rotor body including a rotational axis; And A plurality of balance orifices circumferentially arranged about the rotational axis, each balance orifice of the balance orifices being configured to selectively receive a heavy body, Wherein the rotor body further includes: a plurality of circumferentially spaced tubular cavities, each tubular cavity having an open end configured to receive a sample container; And A lid supported by the rotor body and configured to cover the open end of the tubular cavity when the lid is positioned on the rotor body, Wherein the balance orifices are formed in the lid, Wherein the lid includes a top surface and a bottom surface opposite the top surface, and the balance orifices are formed in one of the top surface or the bottom surface.

5. The rotor according to claim 4, further comprising: At least one heavy body received by at least one of the balance orifices.

6. The rotor according to claim 5, wherein the at least one heavy body is a screw including a threaded outer surface, and each balance orifice of the balance orifices includes a threaded inner surface configured to threadedly engage the at least one heavy body.

7. A rotor for use in a centrifuge and used in accordance with the method of any one of claims 1 to 3, the rotor comprising: A rotor body including a rotational axis; And A plurality of balance orifices circumferentially arranged about the rotational axis, each balance orifice of the balance orifices being configured to selectively receive a heavy body, Wherein the rotor body further includes an upper surface and a lower surface opposite the upper surface, the upper surface including a first annular groove, and the rotor further includes: A balance ring positioned in the first annular groove and including a balance ring upper surface, wherein the balance orifices are formed in the upper surface of the balance ring, Wherein the rotor further includes: at least one heavy body received by at least one of the balance orifices, and Wherein the at least one heavy body is selectively positioned in one or more of the balance orifices of the balance ring.

8. The rotor according to claim 7, wherein the rotor body includes an elongated bore extending along the rotational axis between the upper surface of the rotor body and the lower surface of the rotor body, and the rotor further includes: A drive hub, the drive hub being mounted within the elongated bore and including a cylindrical shaft projecting upwardly through the elongated bore, the cylindrical shaft including an upper portion having a threaded outer surface; A cap screw, the cap screw including a lower bore and a cap screw flange, the lower bore having a threaded inner surface configured to threadedly engage the threaded outer surface of the drive hub, the cap screw flange extending radially outwardly from the lower end of the cap screw; A cap, the cap including a wall portion extending radially outwardly and having a lower surface with a third annular groove; And An elastic member positioned within the third annular groove, the elastic member pressing against the upper surface of the balance ring in response to the threaded engagement of the cap screw with the drive hub.

9. The rotor according to claim 7, wherein the first annular groove includes a shoulder, and the balance ring includes a balance ring flange projecting radially inwardly to engage the shoulder.

10. The rotor according to any one of claims 4 to 9, wherein the rotor body is constructed of a polymer composite, a carbon fiber material, or both the polymer composite and the carbon fiber material.

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