JPH04506927A - tension band centrifuge rotor - Google Patents

Abstract

The present invention relates to an applied load accepting band (12) for a centrifuge rotor (10) that is configured such that, while rotating, the applied loads on the band (12) are balanced by the tension in the band (12), so that during rotation the band (12) is subjected only to a tensile force.

Description

[Detailed description of the invention] name of invention tension band centrifuge rotor Background of the invention field of invention The present invention relates to a band for a centrifuge rotor, and in particular to a band that is only under tension during operation. It's about a band that receives a lot of attention.

Description of prior art The manufacture of rotating equipment such as centrifuge rotors and energy storage flywheels is The use of homogeneous materials such as aluminum and titanium has evolved to the use of composite materials. . Using such materials increases the ability to support centrifugal loads. This is considered to be advantageous in that it can be done. Improved load-bearing capacity is achieved through composite rows. The weight of the motor is reduced, allowing faster rotation for a given driving force, and a larger This is achieved because relative centrifugal force can be obtained.

Prior art rotating devices considered relevant to the present invention include several types of The band has an arbitrary predetermined shape when at rest. However, this A band such as Due to its tendency to be exposed to loads during operation. This phenomenon can be explained from the following simplified example. I can understand it.

Here, we consider a bias for a centrifuge rotor that is circular in its resting (i.e., non-rotating) state. Consider a load receiving band. In addition, samples in which this band is separated by three equal angles ・Assuming that the carrier receives three applied loads corresponding to the When the centrifugal force is applied to the sample carrier, the effect of the centrifugal force on the sample carrier It tends to add weight and pull the band to form "corners." subjected to added load The band periphery approximately midway through the section will be deflected radially inward from its original circular shape. Ru. The band has a certain degree of rigidity, so when it rotates it changes from its resting shape to its flat shape. Deflection of the band into a balanced configuration creates bending stresses. this bend Stress does not contribute to the load carrying capacity of the band and may actually reduce rotor life. This is harmful to the band.

From the above point of view, when the band is rotating it is exposed to stress due to shape change It would be advantageous to have a centrifuge rotor that avoids harmful effects. Conceivable.

Summary of the invention The present invention balances the applied load on the band with the tension of the band during rotation. This invention relates to a load-receiving band for a centrifuge rotor in which the band receives only tension.

Brief description of the drawing The present invention will be better understood from the following detailed description taken in conjunction with the accompanying drawings, which form a part of this application. I hope you understand. In the attached drawings: FIG. 1 is a schematic plan view of a centrifuge rotor with a load receiving band according to the invention ( The sample carrier is omitted), and Figure 2 is a perspective view of the rotor in Figure 1. It is a diagram.

Figure 1A is an enlarged view of a portion of Figure 1, showing how the struts are attached to the band. FIG.

FIG. 3A is a free body diagram of a portion of a band for a centrifuge rotor according to the present invention. ram, and a constant thickness dimension from which an equation can be derived to describe the shape of the band. This paper describes the state in which a load-receiving band is realized using a wound band made of a composite material with Figures 3B to 3D show the mathematical relationships used in the derivation of the appendix. FIG.

FIGS. 4 and 5 each show a constant load-bearing band according to the invention. FIG. 4 is a plan view and a sectional view taken along line 5-5 in FIG. 4 for explaining a square centrifuge rotor. .

6 and 7 respectively show a vertical FIG. 6 is a plan view and a sectional view taken along line 7-7 in FIG. 6 for explaining a type centrifuge rotor. .

Figure 6A is an enlarged view of a portion of Figure 6 showing the sample carrier loading into the band. FIG. 3 is a diagram showing the state and structure of the load transfer pad.

8 and 9 respectively show a rocking device with a load receiving band according to the invention FIG. 1 is a plan view and a perspective view of a basket-type centrifuge rotor.

FIG. 10 shows a first load-bearing band with variable cross-sectional area according to the invention; It is a top view similar to the figure.

The derivation of the formula discussed here is described in the additional explanation (pages 17 to 27), but this forms part of this application.

Detailed description of the invention Throughout the following detailed description, like reference numbers refer to like reference numbers in all figures of the drawings. The components of

1 and 2 each have a circumferential load receiving band 12 according to the invention. 1 is a plan view and a perspective view of a centrifuge rotor 10. FIG. The band 12 has a predetermined thickness. It has an inner surface 12I and an outer surface 12E.

The rotor IO includes a central hub 14, which is shown schematically in FIG. so that the rotor 10 can be connected to a suitable motive force source M, such that the rotor 10 It can rotate around the rotation axis 10A. The central hub 14 has a plurality of radially outwardly It has an extending strut 16. The central hub and struts can be made of metal. Yes, but it may be preferable to use composite or reinforced plastic materials. do not have.

A circumferential band 12 is attached to the struts 16 and surrounds the hub 14. band 12 can be connected to struts 16 by any suitable means, as described below. . The band 12 has a predetermined thickness and has an inner surface 12I and an outer surface 12E.

Band 12 has a plurality of angularly spaced load receiving areas 18. these In region 18, the sample carrier (FIGS. 4 to 7), which will be explained below, is in band I2. or the rocking basket type sample carrier 2 described later. 0 (FIG. 8.9) is the portion that abuts against the inner surface 121 of the band 12. Purpose of analysis For a single point on the band where it can be said that the load applied to the band acts However, in reality, the applied load receiving area 18 is around the circumference of the band 12. extends a given finite distance consisting of .

The adjacent load-receiving region 18 is located in a plane perpendicular to the axis 10A (i.e., in the first In the plane of the figure), depending on the number of sample carriers 20 on the rotor 10, They are separated by a predetermined angular distance (2θ). This angle (2θ) is (2θ) (degrees) is 360 divided by N. is equal to the quotient.

As will be described later, the load-receiving band 12 according to the present invention is capable of receiving only tension during centrifugal action. Therefore, it is possible to eliminate areas with high stress concentration that shorten the band life.

The load receiving band 12 is made of composite material or aluminum or titanium. It can be made from metal. First, a band formed from a composite material will be explained. composite material When considering the economics of fabrication using materials, it was found that the formed band was constant. It is necessary to have a cross-sectional area of .

Therefore, in the following description, a band of composite material has a constant transverse line along its entire circumference. It has an area.

According to the present invention, in a plane perpendicular to the rotational axis 10A of the rotor 10, The load-receiving band 12 is configured between adjacent load-receiving regions 18, indicated by broken lines. has a predetermined equilibrium curve 22. This equilibrium curve 22 defines the shape of the band. is used here. Preferably, the equilibrium curve runs through the middle of the thickness of the band 12. , that is, it is assumed that it extends through the middle between the inner surface 121 and the outer surface 12E. . However, if the equilibrium curve 22 has any radial position within the thickness of the band 12, It should be understood that it can also be defined as extending through. equilibrium curve 2 2 has a predetermined center point 22C. Preferably, the struts 16 have an equilibrium curve. Attach it to the band 12 at the center point 22C of 22.

As can be seen in the enlarged view of Figure 1A, the desired attachment of the inner surface 12I of the band is not possible. Extending radially inwardly to the radially outer surface of the struts 16 is an elastic sheet 1. 7 and a layer 19 of composite material. A suitable adhesive layer 21 is attached to the inner surface 12r of the band 12. between the elastic sheets 1.7, between the elastic sheet 17 and the layer of composite material 19; It is provided between the layer 19 and the strut 16. The elastic sheet 17 is attached to the adhesive layer 21. provided to adjust the shear forces to limit the strain in the composite material layer. 19 is provided to remove stress in the lateral direction. trying to glue Any suitable adhesive compatible with the material can be used.

Each point on the equilibrium curve 22 lies in the plane of FIG. 1 and in the free-body diaphragm of FIG. and is located at a predetermined radial short distance MR from the axis 10A. Axis line 1. OA The distance from the axis 10A to the intermediate point 22C is indicated by reference symbol The distance to the load-receiving area is indicated by the reference RL. Adjacent load receiving areas Since areas 18L-1 and 18L-2 are separated by an angular distance (2θ), the radius R8 and half The angular distance of the radius RL is indicated by the angle θ. Band 12 attaches it to hub 14 When the band 12 is removed from the strut 16 and the band 12 is stationary, the intermediate point 2 2C adjacent to either one of the load receiving areas 18L-1 and 18L-2. The equilibrium curve 22 up to the point is defined by the following relationship. That is, d(R/Ro)/ dθ-(R/RO)"RAD(1-(K/2[(R/RO)2-1]1)"-( R/R,) (1) K=CCr (IJ"ROsu(1/g)(1/σ,)] (2) Here, Ro is two adjacent loads from the axis 10A on the equilibrium curve 22. It is the distance to the midpoint 22C between the heavy receptor areas 18L-1 and 18L-2, and K is: is the curvature multiplier (shape factor) of the band with a value greater than zero and less than 1, That is, 0<K<1.

Here, the symbol r RADJ is used throughout this application (including the appendix) to calculate the square root. Please understand that it is used as a radical sign indicating calculation.

The derivation of formulas (1) and (2) is described in the appendix attached to this application and forming a part thereof. .

The constant is the shape factor K for each equation group that satisfies the differential equation (1). stipulate. Since we are only going to expose the band to tension during rotation, the shape factor is 0. must be limited to within a range of 1. If K is outside this limit It is impossible to obtain an equilibrium state. The physical explanation of the limit for K is It will be understood if we consider the range of loads that can be achieved with the band according to the invention. can.

As can be seen in Figure 3D, differential equation (1) defines a family of equilibrium curves. shape person If the number = 1, the equilibrium curve takes the shape of a circle. However, for the equilibrium curve A circle with such an equilibrium curve supports a load applied to it. This means that there is no band tension component that contributes to the Tension when rotating A band subjected to only This is the result. Therefore, a circular band must be bent to support the load. Must be.

When the shape factor = 0, the equilibrium curve takes the form of a straight line.

In this case, a band with such an equilibrium curve will have a centrifugal force added to the mass of the band. It has no band tension component that can contribute to supporting forces. death Therefore, a band that has an equilibrium curve in the form of a straight line and is only subjected to tension during rotation has a high quality. The quantity must be zero, which is clearly unreasonable.

Therefore, the band according to the present invention subjected only to tension during rotation necessarily has a shape factor of It must have an equilibrium curve where K is in the range O<K<1.

Equilibrium curve for any band according to the invention (i.e., a band subjected only to tension during rotation) ) is the midpoint of the band segment and the equilibrium curve defined by Eq. with a point on the band adjacent to the load-receiving area that closely corresponds to one of the groups. There will be an equilibrium curve in between. Here again, the species of which the load receiving area 18 is made Since the band has a limited range, the actual shape of the band is determined by its flatness in the load receiving area 18. It is possible to deviate from the equilibrium curve but still remain within the intended scope of the invention. I want to be understood.

Furthermore, the band portion between the intermediate point and the point adjacent to the applied load receiving area is expressed by the formula (1), Although it also deviates from the mathematical definition of the equilibrium curve given by (2), it is still , while remaining within the intended scope of the invention. For this purpose, flat The equilibrium curve 22 defines a neutral or reference radial distance R, for each value of θ. It can be seen as a reference curve. The actual radial distance R of the band is the equilibrium curve 2 As long as this approximates the neutral radial distance R, defined by the expression for should be construed as falling within the contemplation of the present invention. However, Therefore, the actual radial distance in the band must match the equilibrium curve of Eq. This is not necessary, and as long as the band as a whole is only subjected to tension during rotation, it is within the scope of the present invention. It should be interpreted as within the range.

Optimal performance is achieved when the shape of the band matches the equilibrium curve and therefore the bending moment obtained when the bending stress is equal to zero, but some stress resulting from the bending moment force is acceptable when designing a centrifuge rotor to have performance that falls below optimal performance. It is recognized that it can be done. As a result, if the band approximates the equilibrium curve, the present invention should be construed as within the intended scope.

To determine the band equilibrium curve for an actual rotor, first the band is Remove it from the The actual band contours are then plotted. of tension when the band rotates. When exposed to will match closely. i.e. the band equilibrium song from the real rotor The line will be one of a family of curves in the range between R, and Ro, or the line will be in equilibrium It will be within a predetermined range of the equilibrium curve of one of the curves.

To make sure that such a band is only subjected to tension, apply a brittle lacquer tape. Strapping the rotor (preferably as described above) before disassembling from the kit). Brittle lacquer test Richard C,D ove, Paul H. Adams, “Expertmental Str. Ess Analysis and Motion Measurement’ (Charles E, Merrill Book, Columbus, Ohio) s, Inc., published in 1964). The band only receives tension Other tests may also be performed to confirm that In this test, the radial direction of the band Attach strain gauges to the inner and outer surfaces.

When the band 12 has a shape that satisfies the equilibrium curve 22 of equations (1) and (2), Receives only tension. The shape of band 12 changes when it is accelerating or becomes When it is rotating at speed, it does not change. However, the centrifugal effect As a result, the band 12 bulges outward, and the sample key attached to the band 12 bulges outward. The carrier 20 will be displaced radially outward. However, in band 12 The applied load (its own weight plus the weight of the sample carrier) is the tension in the band. It will be balanced by. The band is thus subjected to no bending stress. There will be no.

If band 12 is made of a composite material, the preferred material is polyester ketone. A tissue consisting of multiple uniaxial fibers surrounded by a matrix of ketones (PEKK). It is a loop.

This fiber preferably has the registered trademark RKEVLARJ. DuPa Manufactured and sold by Ne1ours and Company. It is an aramid fiber. Band 12 has a predetermined shape corresponding to equilibrium curve 22. Wind the filament using either tow or tape onto the mandrel It is formed. When the tape was wound onto a mandrel, it formed The band is given the shape of an equilibrium curve. The band 12 thus formed is approximately having a constant radial or thickness dimension. Again, with a constant cross section The band can also be formed from homogeneous materials, for example titanium or aluminum I hope you understand that.

The strut (.16) is preferably located at an intermediate point 22C along the equilibrium curve 22. and is attached to the inner surface 121 of the band 12. In reality, strut 16 is A slight preload is applied to the strut to absorb changes in the radial stiffness of the band 12 and strut 16. It may also be possible to This preload is applied to the strut-mounted form of the band. The shape may be deformed from the shape corresponding to the equilibrium curve. However, the change due to preload The shape is an elastic deformation. So obviously, if you remove it from the Bandura strut As mentioned above, the shape at rest matches the relationship shown in equations (1) and (2), Therefore, it should be understood that it is within the scope of the present invention. The preload allows the strut to When assembled into a strut and at rest, the band is attached to the strut at an initial predetermined compression (all i.e., applying a radially inward) force. However, when the band rotates, The strut expands due to centrifugal force and exerts a predetermined smaller compressive force on the strut.

Here, the equilibrium curve 22 can be obtained only when the bending stress is equal to zero. I hope you understand. When in use, apply a preload to the strut to form a band. , to compensate for the difference in radial stiffness and the resulting difference in deformation when the rotor rotates. is advantageous. According to the design, in this case the rotor reaches the design speed and carries the design load. An equilibrium shape will be obtained only when the At zero speed, due to preload Bending stress is maximum. As the rotor increases speed, the preload causes The bending stress decreases and the stress caused by the load increases. rotor reaches design speed Then, the bending stress caused by the preload becomes zero, and the band is fully stretched by the load. You will receive power. At this point the band obtains an equilibrium curve.

Said band 12 has a substantially uniform cross-sectional area along the equilibrium curve. However However, from the point of view of material usage efficiency, it is important that the band has a constant stress along its circumference. It may be desirable to have a specific cross-section).

According to another embodiment shown in FIG. 10, it falls within the scope of the invention and the barrier 12 has a variable cross-sectional area along the equilibrium curve but a constant stress. Can be done.

In this example, the equilibrium curve corresponds to the following equation, as will be clear from the additional explanation.

d(R/L)dθ=(R/Ro)RAD[(R/Ro)''](expf-KE( R/Ro)2-Ill-1) (1 person) K=r(γω2R,') (1,/gX 1/σ, )] (2A) (A/A0)-exp-(-(K/2) [(R/R6) ”(]l　(3A)where AO is the cross-sectional area of the band at radius Ro.Equation I The band corresponding to the relationship A, 2A can be formed by any suitable method such as numerically controlled milling. made from a homogeneous material such as titanium or aluminum by a method Can be done. 2 Here, the band according to this alternative embodiment of the invention can be made from a composite material. Please understand that.

The band 12 according to the invention is made according to whether it is made of composite or homogeneous material. As can be seen from Figures 4 to 9, the Can be used.

FIG. 4.5 shows a top view, vertical section, of a rotor 10 with a bandeye 2 according to the invention. 2, where the sample carrier 30 constitutes a constant angle centrifuge rotor. It is configured to do so. In this example, each of the sample carriers 30 is It is attached directly to the band at the load receiving area 18, thereby providing support. has been done. The sample carrier 30 is attached to the band at the load receiving area 18. It is attached to a load transfer pad 32 attached to 12. As can be seen in Figure 4.5 The sample carrier 30 has a sample container receiving cavity 6 . this Although two such cavities 36 are shown, any convenient number of cavities 36 may be included in the carrier 30. Please understand that it can be formed as In the embodiment of FIG. 4.5, each void 36 Axis 36A is inclined with respect to rotation axis 10A. Or, in Figure 6 , the axis 36A of each cavity 36 is parallel to the axis of rotation 10A, and the axis 36A of each cavity 36 is parallel to the axis of rotation 10A, This is how the data is structured.

In Figures 4 to 7, the sample carrier 30 is a molded plastic material. It's made. In these figures (as well as in Figure 8.9), the load transfer pad 32 is made of a molded elastic material such as polyurethane. You can see it in Figure 6A. The pad 32 is attached to the inner surface 12I of the band 12 using the adhesive layer 35. It is. The composite member 33 is secured radially to the pad 32 by another adhesive layer 35. It's a burning feeling inside. The radially inner surface of the composite member 33 is flat; The radially outer surface of the pad 32 has a load receiving area 18 to which the pad is attached. The shape corresponds to the inner surface 121 of the band 12 in FIG. Sample carrier 3 ° can be attached to the member 33 using the adhesive layer 35 of 811, or The sample carrier 30 can also be nested between the hub 16 and the S material 33. Wear.

In yet another embodiment, as can be seen in Figure 8.9, the sample carrier 30 may be of a swinging type. For this purpose, the sample carrier 30 is During centrifugation, the axis 36A of the cavity 36 is in a first substantially vertical position. from one position to a second position. In the second position, the axis 36A of each cavity 36 is It is located in a plane substantially perpendicular to the rotation axis 10A. Furthermore, means 38 are provided. so that the end of the sample carrier 30 is within the load receiving area 18 on the band 12. Move radially outward to a supporting position relative to the installed pad 32.

Pivoting the sample carrier 30 to the hub 14 can be done in a variety of ways. . In the embodiment shown in Figure 8.9, the hub 14 has angularly spaced radial arcs. 38A and 38B. Each arm 38A, 38B has a sample carrier. A slot adapted to receive a trunnion bin 42 located in the rear 30. 40. Of course, the arms 38A and 38B are connected to the carrier 30, respectively. may support a trunnion bin housed within.

Numerous modifications will occur to those skilled in the art having the benefit of the teachings of the invention as described above. It can be done. However, such modifications are defined by the appended claims. It is within the intended scope of the present invention.

Additional explanation Referring to the 31st ff free-body diagram, the equilibrium curve of band 12, Therefore, the set of equations 1.2.1. A, 2A and 3A I can understand the derivation. In FIG. 3A, there is shown an equilibrium curve 22 of band I2. The portion between the intermediate point 22C and the predetermined end point 22L-2 is shown. Here is a big The reference axes of the root coordinate system and the polar coordinate system are also shown. In this derivation, the end point 22L -2 is on the band 12 in the applied load receiving area 18-2 (FIG. 1), and The regions are shown as points on which applied loads can act. in the actual band , the load-receiving region extends over a finite distance on the band. that At each point, the radius of the band is denoted R,,R,, respectively. any The angular distance between radius R and radius R8 is indicated by angle θ. Not shown in Figure 3A, The portion of the equilibrium curve 22 between the midpoint 22C and the end point 22L-1 of the equilibrium curve 22 is It is symmetrical to the part of the equilibrium curve shown in Figure 3A.

The free body diagram acts on band 12 as it rotates. It shows power. According to the invention, the band 12 has the same shape both when stationary and when rotating. be. The shape of the band is such that it only experiences tension when it is rotating It becomes. Alternatively, when rotating, the tension in the band is determined by the mass of the band as well as the applied load. The centrifugal force acting on the band is balanced by the load acting on the band in the weight receiving area.

As seen in a free-body diadem, each end of a segment of the band is under tension. ing. These tensions are each labeled T. , denoted by T. this is intermediate It represents the tension within the band at point 22C1 and end point 22L-1.

The magnitude of the tension shown here acting on the band is originally ・Includes the load on the band due to the weight of the carrier. Acting on the center of mass of the band The centrifugal force caused by this is indicated by the symbol F.

Adding up the force in the X direction and then differentiating it gives the following.

dF, =-dT, (^) Similarly, by summing the forces in the y direction and then differentiating them, we get:

d F, = d T, (B) As can be seen from Figures 3B and 30, the mass of the differential segment ds of the band is dIl , its cross-sectional area is 8, its angular velocity is ω, and its density is γ, then the band The differential centrifugal force dF acting on the differential segment of Ru.

dF=Rω! 6 meals (C) Substituting the formula (γ　＾ds)(1/g) for the differential mass d■, the formula (C) becomes dF=(y^ωs(1/g)(Rds)(D).

From Figure 3C, a similar triangle arises.

dF/dF, =R/x; dF/dF, =R/.

and (E) dF, = dF(x/R): dF, = dF(y/R) From formulas (D) and (E), d The component of F is dF, = (7A (IJ”) (1/g) - ds (F) dFy = (7＾ω”) (1/g), ds (G) From formulas (A) and (F) dT, /ds=-(7A (IJS(1/g), (IT) and formula (B), From (G) dTy/ds = (γA ω”) (1/g)y (I) Free-body die in Figure 3A from agram "r" = Ty" + T% Differentiating and dividing by 2 gives us T dT=T, dT, +T, dT.

TdT=Tyo[(T, /Twork)dT, + dT,] (IJ vector ds, T both have the same direction (perpendicular to the end face of the band segment) Therefore, a similar triangle occurs in FIG. 3A.

(T, /T,)=-(dy/dx); T,=T(dx/ds) (K) Formula (K ) into equation (J), we get TdT=T(dx/ds) [-(dy/dx)dT, +dT,] (L) Formula (L ), we get dT=-(dT,/ds)dy+(dT,/ds)dx (1) Formula (H ), from (I) dT=-[(y^(JJ")(1/g)y]dy+-[(y^(IJ") (1/g)x]dx(N) and, dt = - (r ^ (IJ)”) (1/g) (y dy + x dx) (0) Assuming that the field is of constant cross section, the limit T. - Integrate equation (0) over T Then, T-To=-(7A ω") (1/2g) (y"-Ro"+x") (P)th From Figure 3C, noting that (y!+xri=R2), formula (P) is TTo=−(7＾ω”)(1/2g)(R2−Ro2)(Q), and the formula Factorizing and rearranging Ro” from (Q), T=To−[:(γA　ω”) (1/2g)IRo"[(R/R0)"-11(R) Divide the formula (R) by T, Recalling that we assumed a band of constant cross-section, we can calculate that the stress is the tension per unit area. (i.e., σ.=T0/^0), equation (R) becomes T/To= 1-[(7ω”Ro”) (1/2g) (1/σo)] [(R/Ro)” -11(S) and, T/T, = 1-(K/2[(ll/R,)2-111 (T) where, K=[(γω2Ro”)(1/g)(1,/σo)] (2).

From the free-body diagram in Figure 3A, if we add up the moments around the origin, we get T, Ro = T, R(U) To / 1', = L, , / R (V) In Figure 3A, the crab angle of T to be taken The shape is TR2+Tn2=T” Rearrange T. Dividing by 2 gives us (TIl/T,)’ = (T/TO) 2- (T#/T,))” (W )2(J), (T) into equation (1), (TR/T,)”=(1-[K /2 [(R/R,)2-111　)”-(Ro/R)2 and, (T*/To)=　RAD(1-fK/2[(R/Ll)2-1]1　)”-( Ro/R)2(X) R/l on the right side of equation (X)? Multiply by o and add (T, /T#) to the left side [from formula (y) to R /Ro] multiplied by +j, (T,,t/T,)=(R/Ro)RAD (1-(K/2 [(R/R,,) 2-111) 2- (17,/R) ”(Y) Vector Rdθ and vector dR are in the same direction as vectors T# and TR, respectively. As it extends, similar triangles result.

TIl/T, = dR/Rde (Z) Multiplying the numerator and denominator of formula (Z) by (1/Ro) yields T, /T, : d(R/R o) / [(R/R,)dθ] (^^) Simplifying, (R/l?o) (TR/T#) = d(R/RO)/d e (BB) Therefore, in the case of a band with a constant area, substituting equation (Y) into equation (8B), we get d(R/R,)/dθ=　(R/Ro)”RAD(1-!Ni/2[(R/Ro) "-111)"-(R/R,)2(1) here, K = [(y (IJ” I?o”) (1/g) (1/σo)], 0<K<1 The constant is the shape factor K for each equation group that satisfies the differential equation (1). stipulate. Since we are only going to expose the band to tension during rotation, the shape factor is 0. Must be limited to <K<1. If K is outside this limit It is impossible to obtain an equilibrium state. The physical explanation of the limit for K is It will be understood if we consider the range of loads that can be achieved with the band according to the invention. can.

As can be seen in Figure 3D, differential equation (1) defines a family of equilibrium curves. shape person If the number = 1, the equilibrium curve takes the shape of a circle. However, for the equilibrium curve The circular shape represents the band tension component that contributes to overcoming the load applied to the band. It means not wanting. A band that receives only tension during rotation will have zero load. It would be possible to adapt, but this is an impractical outcome. Therefore, it supports the load. To achieve this, the circular band must be bent.

When the shape factor = 0, the equilibrium curve takes the form of a straight line.

In this case, the mass of the band can contribute to supporting the centrifugal force applied to it. The band tension component is not fixed (therefore, it has a linear equilibrium curve) , the band subject to only tension during rotation must have zero mass, which is clearly It's unreasonable.

Therefore, the band according to the present invention that is subjected only to tension during rotation always has 0<K< It must have a shape factor K within the range of 1.

Equilibrium curve for any band according to the invention (i.e., a band subjected only to tension during rotation) ) is the midpoint of the band segment and the equilibrium curve defined by Eq. endpoints that closely match one of the groups (these points remain defined here) ) will have an equilibrium curve between

To determine the band equilibrium curve as used in an actual rotor, first the band from the strut that attaches it to the hub. actual band outline may be plotted. The equilibrium curve extends through the center of the band. actual rotor , the angle θ (degrees) of the radius (RL) passing through the load point from the axis of rotation has the following relationship: Kararekaru.

θ=360/(2N) Here, N is the number of positions on the rotor. Thus, the equilibrium curve of the actual rotor One endpoint is the point on the band immediately adjacent to the load receiving area of the actual rotor. Ru.

The midpoint of the band (radius RO) is usually (though not always) , the point is that the struts are attached to the band. If the band is under tension when rotating If accepted, the band's equilibrium curve will be one of the equilibrium curves shown in Figure 3D. It almost matches the equilibrium curve of That is, the equilibrium curve of the band from the actual rotor is , R, and R1, or an equilibrium curve. It will fall within a predetermined range of the equilibrium curve of one of the lines.

To make sure that such a band is only subjected to tension, apply a brittle lacquer tape. Strapping the rotor (preferably as described above) before disassembling from the kit). Brittle lacquer test Richard C,D ove, co-authored by Paul H. Adams, “Experi+*mentalSt Ress Analysis and Motion Measurement ” (Charl, es ElMerri Boo, Columbus, Ohio) KS, Inc., published in 1964). The band only receives tension Other tests may also be performed to confirm that the In this test, the radius of the band Attach strain gauges to the inner and outer surfaces.

Band I2, which has a shape that satisfies the equilibrium curve 22 of equations (1) and (2), is Receives only tension. The shape of band 12 changes when it is accelerating or becomes When it is rotating at speed, it does not change. However, the centrifugal effect The band 12 bulges outward and the sample key attached to the band bulges outward. The carrier 20 will be displaced radially outward. However, in band 12 The applied load (its own weight plus the weight of the sample carrier) is the tension in the band. It will be balanced by. The band is thus subjected to no bending stress. There will be no.

In the previous derived equations (1) and (2), the cross-sectional area A of the band (Figure 3B) is constant. In order to , bands where the stress is constant and, conversely, the cross-sectional area varies are also contemplated.

For a band with variable cross-sectional area and constant stress, dT=−(γ〼^ω2)( 1/g) (Y dy + x dx) (0) Multiply the numerator and denominator by 2, and again, Noting that stress is tension per unit area (i.e., σ = T/A), , dT=-(7T　ωsu(1/2g)(1/cro)(2ydy+2xdx)( CC) divided by T, and in formula (CC) y2. Recognizing the derivative of xZ, dT/T=-(yω”)(1/2g)(1/cro)(dy2+dx”)(D D) From Figure 3C, if we recognize that (dy”+dx’)=d(R2), dT/T=-(γω”) (1/2g) (1/σ.) (dl?’) (EE) Limit T. - over T (for variable T) and from R9 to R (for variable R) Integrating the equation (DD) and factorizing Ro, we get in (T/To) = - (γ ω”!?,”) (1/2g) (1/σo) [(1 ? /RO) 2-1 (FF) However, if we recognize K from equation (2), equation (FF) becomes 1, n (T/T o)=-/2 [(R/Ro)2-1] (GG) If we adopt the natural logarithm, (T/To)=exp　f-に/2　[(R/l?.)”-111(r(H) also Adding up the noodles, from formulas (W) and (J), (TI/To) = RAD (T/ T,)”-(R/R,)2(II) From the formula (Hl’!) (T, l/To)=RAD exp t-K[(R/Ro)2-1]1 (R/ Multiply the right side of the formula (JJ) by R/R, and the left side by T./T. Then, [equal to R/R, from formula (v)], (TR/Tl) = (R/RO)R AD exp (-K[(R/Ro)" January -(R/Ro)2(KK) This formula is (Tll/Ta)=RAD[(R/Ro)"](exp!-K[(R/Ro)" -1111) (LL) From similar triangles, equations (Z) and (8A) become (T,/T,)=d(R)/R dθ=d(R/Ro)/(R/Ro)dθd(R/I?,)/dθ=(R/R 0) (TR/T, ) (BB) Therefore, it is exposed to constant stress but with variable transverse For a band with a cross-sectional area, d(R/Ro)/dθ=(R/R,)RAD[(R/R,)''](expf-K [(R/R,)”-11]-1) (1 person) K=[(γω”Rori(1/g)(1/σo)] (2^)(^/Ao)=ex p(-(K/2) [(R/Ro)2-111 (3^) Submission of translation of written amendment (Article 184-8 of the Patent Law) January 31, 1992

Claims (35)

[Claims] 1. A continuous band for use as a load receiving band in the centrifuge rotor. and has a central axis extending therethrough, and first and second load receiving regions. In the band made up of It has an equilibrium curve constructed between the load-receiving regions, and the equilibrium curve is a point between this axis and the midpoint in a plane perpendicular to the central axis; within a plane perpendicular to the axis, with the distance between , at any angular position ■ from the reference line Ro, the midpoint and the applied load receiving area. Each point on the equilibrium curve is at a predetermined distance R from the axis to a point adjacent to one of the and the distance R at the corresponding angular position ■ has the following relationship, that is, d(R/Ro)/d■=(R/Ro)2RAD(1-{K/2[(R/Ro)2 -1]})2-(R/Ro)2(1), where: K = [(γω2Ro2) (1/g) (1/σo)] (2) 0<K<1 A band characterized by 2. In the band according to claim 1, the radially inner surface and the radially outer surface are characterized in that the equilibrium curve is constructed approximately midway between these radially inner and outer surfaces. A band that does. 3. The band according to claim 2, characterized in that it is made of a composite material. band. 4. The band according to claim 3, wherein the composite material is formed by a matrix. A band characterized in that it is a tape made of a plurality of surrounded uniaxial fibers. 5. In the band according to claim 1, the band has a cross-sectional area between the load receiving areas. Furthermore, the bar is characterized in that the cross-sectional area between the applied load receiving regions is approximately constant. nd. 6. The band according to claim 5, characterized in that it is made of a composite material. band. 7. The band according to claim 6, wherein the composite material is formed by a matrix. A band characterized in that it is a tape made of a plurality of surrounded uniaxial fibers. 8. A continuous band for use as a load receiving band in centrifuge rotors. a central axis extending therethrough; and first and second load-receiving regions. In a band consisting of It has an equilibrium curve constructed between the load-receiving regions, and the equilibrium curve is an intermediate point between this axis and said central axis in a plane perpendicular to said central axis; The distance between is defined by a predetermined reference line Ro, and the plane is perpendicular to the axis. At an arbitrary angular position ■ from the reference line Ro within, the midpoint and the applied load receiving area Each point on the equilibrium curve has a predetermined distance R from the axis to a point adjacent to one of the regions. , and the distance R at the corresponding angular position ■ has the following relationship, that is, d(R/Ro)d■=(R/Ro)RAD[(R/Ro)2](exp{-K[ (R/Ro)2-1]}-1) (1A)K=[(γω2Ro2)(1/g)(1 /σo)](2A)(A/Ao)=exp-{-(K/2)[(R/Ro)2- 1]} (3A), where 0<K<1. band. 9. In the band according to claim 8, the radially inner surface and the radially outer surface are characterized in that the equilibrium curve is constructed approximately midway between these radially inner and outer surfaces. A band that does. 10. The band according to claim 9, characterized in that it is made of a homogeneous material. A band to do. 11. The band according to claim 10, characterized in that it is made of metal. A band that does. 12. A continuous band for use as a load receiving band in a centrifuge rotor. a central axis extending therethrough; and first and second load-receiving regions. In a band consisting of It has an equilibrium curve constructed between the load-receiving regions, and the equilibrium curve is an intermediate point between this axis and said central axis in a plane perpendicular to said central axis; The distance between is defined by a predetermined reference line Ro, and the plane perpendicular to the axis At an arbitrary angular position ■ from the reference line Ro within, the midpoint and the applied load receiving area Each point on the equilibrium curve has a predetermined distance R from the axis to a point adjacent to one of the regions. , each distance R approximates some neutral distance RN, where the corresponding angular position ■ The distance RN at the point has the following relationship, that is, d(R/Ro)/d■=(R/Ro)2RAD(1-{K/2[(R/Ro)2 -1]})2-(R/Ro)2(1), where: K = [(γω2Ro2) (1/g) (1/σo)] (2) 0<K<1 A band characterized by 13. A continuous band for use as a load receiving band in centrifuge rotors. having a central axis extending therethrough, and having first and second load receiving areas therein. area is configured, and the load receiving area is at a predetermined angle in a plane perpendicular to the axis. degree distance (2■) apart, and each point in the middle of the applied load receiving area of the band is an axis. In a continuous band with cross-sectional area measured in a plane extending radially from the line, the bar The cross-sectional area of the band is constant at each point in the middle of the load-receiving area, and the band is rotated. , when a load is applied to the band at the load-receiving area, the band pulls. A continuous band characterized in that it is subjected only to stress due to stress. 14. A continuous band for use as a load receiving band in centrifuge rotors. having a central axis extending therethrough, and having first and second load receiving areas therein. area is configured, and the load receiving area is at a predetermined angle in a plane perpendicular to the axis. degree distance (2■) apart, and each point in the middle of the applied load receiving area of the band is an axis. In a continuous band with cross-sectional area measured in a plane extending radially from the line, the bar The cross-sectional area of the band is variable at each point in the middle of the load-receiving area, and the band is rotated. , when a load is applied to the band at the load-receiving area, the band pulls. A continuous band characterized in that it is subjected only to stress due to stress. 15. a hub having at least a first strut and attached to the strut; A continuous band used as a load-receiving band; a band having a central axis extending therethrough and first and second load-receiving regions; In a centrifuge rotor containing Remove the band from the struts that attach it to the hub and make sure this band is when at rest, the band has an equilibrium curve configured between the load-receiving regions; In a plane perpendicular to the axis, along which this equilibrium curve has a midpoint, The distance between the axis and the intermediate point is determined by a predetermined reference line Ro, At an arbitrary angular position ■ from the reference line Ro in a plane perpendicular to the axis, each point on the equilibrium curve between the midpoint of and a point adjacent to one of the load-receiving areas. If a point is located at a predetermined distance R from the axis, and the distance R at the corresponding angular position ■ is less than or equal to The relationship is d(R/Ro)/d■=(R/Ro)2RAD(1-{K/ 2[(R/Ro)2-1]})2-(R/Ro)2(1), and this Here, K = [(γω2Ro2) (1/g) (1/σo)] (2) 0<K<1 A centrifuge rotor characterized by: 16. In the centrifuge rotor according to claim 15, the radial inner surface and the radial direction and an equilibrium curve approximately midway between these radially inner and outer surfaces. A centrifuge rotor characterized by: 17. In the centrifuge rotor according to claim 15, the composite material is a matrix rotor. A centrifugal tape made of a plurality of uniaxial fibers surrounded by a machine rotor. 18. In the centrifuge rotor according to claim 17, the composite material is a matrix rotor. A centrifugal tape made of a plurality of uniaxial fibers surrounded by a machine rotor. 19. In the centrifuge rotor according to claim 16, the horizontal It has a cross-sectional area, and is further characterized in that the cross-sectional area between the applied load receiving regions is approximately constant. A typical centrifuge rotor. 20. In the centrifuge rotor according to claim 19, the rotor is made of a composite material. A centrifuge rotor featuring: 21. In the centrifuge rotor according to claim 20, the composite material is a matrix rotor. A centrifugal tape made of a plurality of uniaxial fibers surrounded by a machine rotor. 22. The centrifuge rotor according to claim 15, wherein the struts have an equilibrium curve. A centrifuge rotor characterized in that it is attached to a band at an intermediate point. 23. a hub having at least a first strut and attached to the strut; A continuous band used as a load-receiving band; a band having a central axis extending therethrough and first and second load-receiving regions; In a centrifuge rotor containing Remove the band from the struts that attach it to the hub and make sure this band is when at rest, the band has an equilibrium curve configured between the load-receiving regions; In a plane perpendicular to the axis, along which this equilibrium curve has a midpoint, The distance between the axis and the intermediate point is determined by a predetermined reference line Ro, At an arbitrary angular position ■ from the reference line Ro in a plane perpendicular to the axis, each point on the equilibrium curve between the midpoint of and a point adjacent to one of the load-receiving areas. If a point is located at a predetermined distance R from the axis, and the distance R at the corresponding angular position ■ is less than or equal to The relationship is d(R/Ro)d■=(R/Ro)RAD[(R/Ro)2 ](exp{-K[(R/Ro)2-1]}-1)(1A)K=[(γω2Ro 2) (1/g) (1/σo)] (2A) (A/Ao) = exp-{-(K/2) [(R/Ro)2-1]} (3A), where 0<K<1. A centrifuge rotor characterized by: 24. In the centrifuge rotor according to claim 23, the semi-longitudinal inner surface and the radial inner surface and an equilibrium curve approximately midway between these radially inner and outer surfaces. A centrifuge rotor characterized by: 25. The centrifuge rotor according to claim 24, which is made of a homogeneous material. A band featuring. 26. The centrifuge rotor according to claim 25, which is made of metal. A band featuring. 27. The centrifuge rotor according to claim 23, wherein the struts have an equilibrium curve. A centrifuge rotor characterized in that it is attached to a band at an intermediate point. 28. a hub having at least a first strut and attached to the strut; A continuous band used as a load-receiving band; a band having a central axis extending therethrough and first and second load-receiving regions; In a centrifuge rotor containing Remove the band from the struts that attach it to the hub and make sure this band is When at rest, the van K has an equilibrium curve configured between the load receiving areas; In a plane perpendicular to the axis, along which this equilibrium curve has a midpoint, The distance between the axis and the intermediate point is defined by a predetermined reference line R0, At an arbitrary angular position ■ from the reference line Ro in a plane perpendicular to the axis, each point on the equilibrium curve between the midpoint of and a point adjacent to one of the load-receiving areas. The point is located at the neutral distance RN consisting of the axis and the distance R at the corresponding angular position ■ N is the following relationship: d(R/Ro)/d■=(R/Ro)2RAD(1 -{K/2[(R/Ro)2-1]})2-(R/Ro)2(1)K=[(γω 2Ro2) (1/g) (1/σo)] (2) 0<K<1 A centrifuge rotor characterized by: 29. The centrifuge rotor according to claim 28, wherein the struts have an equilibrium curve. A centrifuge rotor characterized in that it is attached to a band at an intermediate point. 30. a hub having at least a first strut and attached to the strut; A continuous band used as a load-receiving band; a central axis extending through the load receiving area; The applied load receiving areas are separated by a predetermined angular distance (2■) in a plane perpendicular to the axis. , each point on the band midway through the load-receiving area is a plane extending radially from the axis. In a centrifuge rotor with a measured cross-sectional area, the cross-sectional area of the band is constant at each point in the middle of the area, and the band rotates to When a certain load is applied to the band by a roller, the band produces only tensile stress. A centrifuge rotor that is characterized by 31. The centrifuge rotor according to claim 30, wherein the struts have an equilibrium curve. A centrifuge rotor characterized in that it is attached to a band at an intermediate point. 32. a hub having at least a first strut and attached to the strut; A continuous band used as a load-receiving band; a central axis extending through the load receiving area; The applied load receiving areas are separated by a predetermined angular distance (2■) in a plane perpendicular to the axis. , each point on the band midway through the load-receiving area is a plane extending radially from the axis. In a centrifuge rotor with a measured cross-sectional area, the cross-sectional area of the band is variable at each point in the middle of the area, and the band rotates to When a certain load is applied to the band by a roller, the band produces only tensile stress. Jiru A centrifuge rotor characterized by: 33. The centrifuge rotor according to claim 32, wherein the struts have an equilibrium curve. A centrifuge rotor characterized in that it is attached to a band at an intermediate point. 34. 1. A method of manufacturing a centrifuge rotor having a hub provided with struts, the method comprising: (a) forming a mandrel with an outer surface having a predetermined shape; (b) Wrap a tape made of composite material onto a mandrel to determine the shape of the mandrel. form a continuous band with a shape corresponding to the center through which this band passes having an axis and first and second load receiving regions; In a method that includes The band has an equilibrium curve configured between the load-receiving areas, and this equilibrium curve is located there. with a midpoint along said central axis and in a plane perpendicular to said central axis; The distance between the intermediate points is determined by a predetermined reference line Ro, and the distance between At an arbitrary angular position ■ from the reference line Ro in an angular plane, the midpoint and the load Each point on the equilibrium curve between a point adjacent to one of the heavy receptor areas is located from the axis. Located at a constant distance R, the distance R at the corresponding angular position ■ has the following relationship: Therefore, d(R/Ro)/d■=(R/Ro)2RAD(1-{K/2[(R/Ro )2-1]})2-(R/Ro)2(1), where: K = [(γω2Ro2) (1/g) (1/σo)] (2) 0<K<1 and (c) attaching the band formed in step (b) to the strut on the hub; A method characterized by comprising: 35. A method of manufacturing a centrifuge rotor, the method comprising: a) adding a load receiving bar to a centrifuge rotor; machining a continuous band from a homogeneous material that is intended to be used as a , the central axis through which the band extends, and the first and second load-receiving regions. The method includes the step of having: The band has an equilibrium curve configured between the load-receiving areas, and this equilibrium curve is located there. with a midpoint along said central axis and in a plane perpendicular to said central axis; The distance between the intermediate points is determined by a predetermined reference line Ro, and the distance between At an arbitrary angular position ■ from the reference line Ro in an angular plane, the midpoint and the load Each point on the equilibrium curve between a point adjacent to one of the heavy receptor areas is located from the axis. Located at a constant distance R, the distance R at the corresponding angular position ■ has the following relationship: Therefore, d(R/Ro)d■=(R/Ro)RAD[(R/Ro)2](exp{- K[(R/Ro)2-1]}-1) (1A)K=[(γω2Ro2)(1/g) (1/σo)](2A)(A/Ao)=exp-{-(K/2)[(R/Ro) 2-1]} (3A), where 0<K<1, and b) on the hub. attaching the band formed in step a) to the strut of A method characterized by comprising: