WO2015113541A1

WO2015113541A1 - Bodies fixedly restrained at one end for parts of a system that rotate into the supercritical speed range and method for producing the bodies

Info

Publication number: WO2015113541A1
Application number: PCT/DE2015/000019
Authority: WO
Inventors: Bertram Hentschel; Rezo Aliyev; Rafig HUSEYNOV; Thomas GEIPEL
Original assignee: Technische Universität Bergakademie Freiberg
Priority date: 2014-01-30
Filing date: 2015-01-22
Publication date: 2015-08-06
Also published as: DE112015000602B4; DE112015000602A5

Abstract

The invention relates to bodies fixedly restrained at one end while mounted so as to resist movement and tilting for parts of a system (22) that rotate into the supercritical speed range and to a method for producing the bodies, wherein the body (2) represents a hollow body of a tubular form comprising a specified substance, the flexural vibrations of which that occur during rotation are caused by unbalance U resulting from production and mounting inaccuracies and owing to a local difference between the geometrical axis of symmetry (75) of the hollow body (2) and the axis of rotation (76) of the hollow body (2), and which has a closed-off hollow space (7), which is symmetrical with respect to the geometrical axis of symmetry (75) of the hollow body (2) and is also closed towards its end faces (8, 9). In the hollow space (7) of the hollow body (2) that is fixed and mounted at one end and is formed as at least one balancing chamber (70, 71), at least one free-flowing formless substance (4) with a defined mass ms has been introduced into the balancing chamber (71), partially filling the balancing chamber (71), and the mass ms of the free-flowing formless substance (4) introduced is defined in such a way that a vibrational damping with respect to the hollow body can be achieved in the subcritical and critical speed ranges and a damage-free resonance penetration can be achieved in the critical speed range and that the distribution of the substance (4) in the supercritical speed range that is caused by the effect of the unbalance U of the hollow body (2) compensates in a self-stabilizing manner for the effect of the unbalance U while allowing for a specified ratio between the mass ms of the substance (4) and the unbalance U in accordance with the equation (V).

Description

BODY WITH ONE-SIDED FIXED TENSION FOR PARTS OF A SYSTEM AND METHOD FOR THE PRODUCTION OF BODIES THROUGH TURNING UPTO THE OVERCRITICAL SPEED RANGE

description

The invention relates to a body with one-sided fixed clamping in displacement and tilting stability for up to the supercritical speed range rotating parts of a system with at least one drive spindle and a chuck and a method for producing the body, wherein the body is a hollow body in a tubular shape with predetermined material represents, which results in a rotation bending vibration excitation on manufacturing and storage inaccuracies resulting imbalance U due to a local difference between the axis of symmetry of the hollow body and the axis of rotation are based on the hollow body and has a related to the geometric axis of symmetry of the hollow body, symmetrical and closed cavity, which is also closed to its front sides. A fast rotating body 2 shown in Fig. 1, which is formed as a long cantilevered part of a dynamic system 22 comprising at least one drive spindle 5, a chuck 1 and said body 2, whose main drive spindle 5 is more rigid Rotor is designed, can be used in various branches of mechanical engineering. As an example of such rigid rotors, the high-frequency motor spindles 5 can be specified, which have a first critical bending natural frequency, the much higher, at about 1.5 times to 2 times their maximum usable rotational frequency, according to the documents [1, 2, 3]. The motor spindles 5 are also provided with very stiff radial bearings. The designated long cantilevered bodies 2 may preferably be shanks of high-speed cutting tools (HSCs) and also high-speed stirring shafts, drums, etc., which require more performance and smoothness. The prerequisites for this primarily include weight reduction and high operating speeds.

In order to meet the requirements, the rapidly rotating bodies 2 according to the prior art are usually made hollow in the form of a hollow shaft. However, due to various excitation mechanisms, large vibrations or bending deformations occur during operation of long, slender, tubular hollow bodies mounted on one side firmly clamped and tilted and displaced stiff, especially in the vicinity of critical rotational speeds. Since for various manufacturing reasons (eg dimensional deviations, material inhomogeneities and center of gravity eccentricities) can not be produced with absolute accuracy or with symmetrical mass distribution to the axis of rotation, always arises in dynamic operation, ie in the specified speed ranges an imbalance U. Also affects one-sided clamped and stored long, slender shanks, similar to the Focus eccentricity, even a static deflection on the smoothness on the bearing displacement and thus resulting vibration excitation negative. The resulting concentricity error is called radial stroke. Radial impact of a studied long slender hollow shaft (LD> 15, where L represents the overhang length and D is the outside diameter of the hollow shaft) for HSC machining tools, which is used in the case of high-speed machining of components with deep cavities of metallic and non-metallic materials can result not only due to the shape and dimensional deviations, but also by bearing deviation or radial and angular misalignment when clamping in the tool holder.

Due to the aforementioned deviations arise during operation centrifugal forces that increase quadratically with the increasing speed of the spindle 5 and ultimately lead to the above-mentioned excitation mechanism to large vibrations. The vibrations cause poor surface qualities, critical stresses and failure of shank tools and often lead to breakage of tool shanks and damage to the spindle 5 according to document [4].

Another problem is that large aspect ratios (UD> 20) cause the significant decrease in both the flexural stiffness and the first internal bending frequency (<200 Hz). Regardless of the shaft materials available on the market, such as carbide, steel, aluminum and CFRP, both effects result in such long cantilevered shank tools not being able to conventionally be used with HSC-capable speeds of 20,000 rpm and more. The application speeds of the long-protruding HSC tools according to the prior art are designed like "rigid rotor" according to reference [5] always in the speed range below the first critical bending natural frequency of the tool-chuck system.That means that their maximum operating speed through the first bending-critical natural frequency of the tool-chuck system is determined according to the documents [2, 3]. The problems explained force to work with lower speeds and thus lower feed rates. Thus, the advantages of HSC machining and the performance potential of modern CNC machines (eg spindle speeds of 60000-80000 rpm) remain unused. Similar problems occur in high-speed mixers.

The problem field description results in the objective of the invention, which comprises two closely linked main objectives, which are central to the design of long low-vibration hollow shafts (L D> 20). The first goal is to avoid the negative effect of the first critical bending natural frequencies of long slender hollow shafts.

The second goal is to reduce or even eliminate the dynamic influence of the existing system imbalance.

Decisive for the choice of means is the mechanism of dynamic deformation, ie. H. the ratio of the stiffness of the spindle to the rigidity of the bearing. Two types are distinguished: the "rigid" (very stiff) and the "soft" (very flexible) bearing.

The term "rigid" bearing of spindles means a significantly higher radial rigidity of the bearing of a spindle than its flexural rigidity, which means that, given a corresponding dynamic load, the movements (oscillation) of the projecting part 2 of the spindle 5 assume like a firmly clamped bending beam are:

first eigenform / eigenfrequency - bending beam;

second eigenform / natural frequency - deflection;

third eigenform / natural frequency - "sine wave".

A "soft" bearing of spindles 5 is understood to mean a significantly lower radial stiffness of the bearing of a spindle 5 with respect to its flexural rigidity, which means that, given a corresponding dynamic load, the movements (oscillation) of the projecting part 2 of the spindle 5 of the spindle movement, as in FIG Fig. 2 is shown, follow:

A: first eigenform / eigenfrequency - paraxial oscillation; B: second eigenform / natural frequency - tilting movement of the spindle about the longitudinal axis;

C: third eigenform / natural frequency - bending of the shaft and bending of the cantilever body of the shaft.

The third eigenform C of the projecting part of the shaft in "soft" storage corresponds to the first eigenmode in "rigid" storage. In general, the natural frequencies for "soft" storage are lower than for "rigid" storage. In practice, the movements of both cases, as shown in Fig. 3 is influenced by the documents [6, 7].

"Soft" bearings are used when a) wants to get into the supercritical operating range (above the first and partly second natural frequency) quickly, and when b) corresponding external damping forces act on the vibration system, as in agitators, marine propulsion and turbines after the Pamphlets [8, 9].

One way of achieving the two objectives in the case of "rigid" mounting to ensure a quiet and stable tool life is to increase the operating speed up to the supercritical speed range, thus overrunning / passing through the critical speed is necessary and operated in conjunction with low critical speeds, it comes in the driving over / transition of the resonance speed in the supercritical region to resonant vibrations, the risk of self-oscillation failure of the tool is unavoidable.

In order to pass through the critical speed range easily, it is expedient that the shafts are hollow, which allows integration of self-balancing and vibration damping. In this case, the hollow shaft should have only a minimal imbalance U. Although the imbalance U can be minimized by increasing the manufacturing accuracy of the shank, but when clamping the hollow profile into standard clamping fixtures, additional positional and fastening inaccuracies result according to document [8], with long shafts (L D> 20) with shaft length L and diameter D lead to a large radial impact at the shaft tip.

Therefore, for a more accurate description of the movement of rotationally symmetric metric, one-sided fastened and tilting and verschiebesteif stored long slender hollow bodies in a dynamic calculation model, the unbalance effect due to the geometric deviations, such as non-rectity e _g and ungleichwandigkeit e _w as well the position deviations, such as radial and angular displacement, resulting total eccentricity e _sp to take into account.

The tubular hollow shafts with diameters of about 3 mm to about 20 mm and wall thicknesses of 0.2 mm to 2 mm can be precisely produced by means of various manufacturing processes, such as cold drawing or extrusion. Nevertheless, an eccentricity of the wall thickness e _{w occur} in the range between 0 mm and 0.1 mm (0-10%), which can be determined as follows according to document [10] according to FIG. 4:

k ax 'k mm

The entire position errors e _sp lead to runout. This results in a radial impact a at the top of the hollow shaft 2, even at low speeds and can be determined by measurement. In order to calculate the total imbalance U of a hollow shaft 2 clamped in the shank holder 1, the shank cross section is regarded as a hollow disk with a mass m and the imbalance U can be calculated as follows according to document [6] according to FIG.

D ² - d ² (II)

= "+" (III)

(IV) in which

m - the mass of the hollow shaft;

D - the outside diameter;

d - the inner diameter;

k _min - the minimum wall thickness;

ax ~ the maximum wall thickness;

o - the origin of the coordinates;

M _DA - the center of the outer diameter;

w - the geometric center of the shaft;

s - the center of gravity of the clamped hollow shaft;

- the entire concentricity error or radial impact;

s - the center of gravity eccentricity;

<? _w - the relative eccentricity of the wall thickness;

egss ~ the total eccentricity of the clamped hollow shaft

are.

4 shows a section through a hollow body 2 for a calculation scheme of the total unbalance U according to equations (I) to (IV) from the shape errors and bearing errors.

Some methods and devices for reducing the residual imbalance in rotating rotationally symmetrical hollow bodies by means of balancing mass are in the publications Kaufeld: Inprocess balancing increases the efficiency in HSC milling, x-technology, I. quarter 2004, 6th edition, p. 10 and 1 1, 2004, and Kaufeld: Using in-process balancing the full speed, workshop and Betreib 137 (2004) 1 - 2, pp 47 - 53, 2004 described. Therein, a Ringauswuchtsystem for long projecting tools is preferably presented. The balancing system makes it possible to balance the tools in two levels during startup. The balancing is done by means of two special rolling bearings freely rotatable unbalanced discs that represent the balancing system. The balancing system is attached to the spindle nose and the tool tip and controlled by sensors. The discs are electromagnetically very quickly adjusted to a calculated position and thereby the vibrations generated by imbalance U are minimized. With the balancing system, the tool can be accelerated to the supercritical speed range. The integration of the illustrated balancing system in the tool greatly increases its outer dimensions or the diameter and the weight (about 5 kg). Therefore, the application in the application described above for HSC tools is almost impossible.

The tool construction shown in the publication SU 1 771 893 A1, in particular a milling tool, has the same disadvantages as the previously described design. To the milling tool, a disc is mounted with an annular channel, which are filled with a ferromagnetic liquid solidifiable by means of an applied magnetic field. For a uniform magnetic field distributed over the circumference of the disc distributed, aligned in the radial direction electromagnets.

Before rotation, the ferromagnetic fluid is in the liquid state without the magnetic field switched on and the ferromagnetic fluid can be uniformly distributed over the lower surface of the horizontal annular channel. After starting the rotation, the ferromagnetic fluid moves under the action of centrifugal force from the axis of rotation of the cutter to the wall of the annular channel. Under the influence of the imbalance, the equalizing fluid is distributed unevenly and tries to compensate for the vibrations of the imbalance. After setting a stable run, the surrounding magnetic field is activated. As a result, the ferromagnetic fluid solidifies. The milling tool is ready for operation. It has the task of eliminating small imbalances, for example caused by a missing tooth on the milling tool. The realization of the tool design is not possible with small tool diameters D (for example D = 10 mm), because the diameter is significantly increased by the annular channel.

A further disadvantage is that the milling tool is not at all suitable for HSC machining when the rotational speed of 24000 to 36000 rpm is reached. The publication DE 3 248 085 A1 describes a similar method for eliminating the imbalance U of rotationally symmetrical annular parts during operation. It is used as a compensation medium, a magnetic fluid. The change in a magnetic field controls the apparent density or mass distribution of the magnetic fluid and compensates for the imbalance U.

The fundamental disadvantage of the method for balancing is that a magnetic field is required for the implementation and the supercritical rotational speed range must be reached.

The document DE 103 20 974 B4 describes a similar method for reducing the imbalance U by means of electromagnetic fluid in a device with circumferential annular channel. In the annular channel, a certain amount of an electro-rheological fluid is introduced from a reservoir, the solidification of which can be achieved by means of a magnetic field that varies along the annular channel. The field can also be generated by separately acted upon by voltage electrodes, which preferably lie flat against the annular channel.

The disadvantage of the method is that implementation at small diameters (e.g., D = 10 mm) is virtually impossible by design.

In the document DE 103 42 096 A1, a method for balancing a rotationally symmetrical hollow body, in particular a horizontally running roller body of a conveyor is shown. The balancing is achieved by filling the cavity of the roller with a plastic material which, at a higher peripheral speed, spreads over the full axial length of the hollow body as a result of the centrifugal forces and accumulates and hardens on the inner wall. This results in a balancing of the role automatically. The method has only the task of balancing the imbalance U of the body mounted on both sides.

From the document DE PS 719 582 a device is known which allows an automatic balancing a supercritical machine running. The device has the disadvantage that the balancing mass can be brought into the balancing position only in the supercritical speed range, because the balancing mass is not only useless below the critical speed, but also leads to harmful vibration stresses. This means that the balancing mass can not be used to achieve a safe, damage-free resonance passage of the machine. A resonance passage for the presented machine is realized by the soft storage.

The publications RU 2 257 558 C1, RU 2 256 892 C1 and RU 2 265 814 C1 describes devices for automatically balancing supercritically operated rotors. The devices have hollow balancing chambers which are partially filled with meltable balancing medium. During the balancing process, the balancing mass is melted by means of an additional energy source that can be produced by various methods, and under the effect of centrifugal force, the mass assumes a position relative to the imbalance in the supercritical rotational speed range. To fix the balancing mass in the required position, the energy source is switched off. Thereafter, the compensation medium hardens and thus the balancing process is completed. The devices are used for the active balancing of rotors mounted on both sides and have similar disadvantages of previously described devices and methods, namely a large, complicated and therefore expensive construction and a low balancing quality.

The publication DE 26 32 586 C2 describes a simplified method for resonant passage for elongated rotors, which can be realized by various design solutions of passive and active resonance conveyor aids. The illustrated embodiments are referred to in the document [5] as a fishing camp. A safety bearing is additionally introduced in the rotor system bearing, which has a radial gap with the rotor shaft. Basically, it serves to limit the rotor deflection relative to the stator in order to prevent inadmissible oscillation amplitudes. A retainer bearing as Resonanzdurchlaufhilfe is ineffective in the normal operating condition of the rotor, since the radial deflections of the rotor shaft smaller than that radial gap play to the fishing camp are. If the radial rotor deflections become larger than the backup bearing clearance when approaching the critical speeds, the rotor shaft attaches to the backup bearing and the backup bearing contributes. The forces arising in the contact points change abruptly the vibration-technical properties of the overall system. After driving through the resonant speeds of the coupled system with limited deflections, the rotor shaft detaches from the backup bearing and continues to run without mutual contact. The outflow process of the rotor system from over- to the subcritical speeds is effected by the same effect.

In the document DE 26 32 586 C2 described constructive embodiments can be realized for the one-sided stiff mounted, tubular hollow body to ensure a resonant passage. The fundamental disadvantage of the method is that there is a need for a large space and wear due to abrasion in the contact point between the backup bearing and the rotor.

Another disadvantage is that no self-balancing effect, but only a Selbstzentrierungseffekt can be realized by the described catch camp in supercritical speeds. At this point, however, it must be expressly pointed out that the vibration amplitudes with realizing the self-weighting effect at supercritical speeds are considerably smaller (for example, 2 times) than the self-centering effect.

The document US 2012/0252591 A1 describes a method for reducing vibration by self-balancing a one-sidedly mounted and mounted, supercritically running, tubular hollow body. The vibration damping is achieved in that in the cavity of the hollow body is partially filled with a thixotropic material, which liquefies due to the action of the unbalanced vibrations excited and thereby increases its fluidity. After passing through the critical speeds or in the supercritical rotational speeds, the thixotropic substance is distributed eccentrically in the cavity of the hollow body about the axis of rotation of the hollow body, whereby an automatic compensation of the imbalance U takes place. The designated thixotropic substance has thereby The only task is to achieve a self-balancing effect in the supercritical rotational speed range and the associated reduction in oscillation amplitude. But the absorption of vibration energy in the critical speed range to achieve a safe passage through resonance points is hardly realized by the stated thixotropic substance, but by the soft bearing system present in the system, in particular elastic couplings, since the illustrated hollow body, as described in the publication, a propeller shaft a watercraft or a propeller shaft of the ship propulsion system. And it can be deduced, according to document [11, p. 377], that the designated rotors are typically connected by an elastic coupling to the drive train or to the motor shaft. The elastic couplings used in the system have due to their spring and damping behavior (eg in rubber-elastic couplings can be calculated with a damping constant of 0.8 to 2 according to document [12, p 420]), the function of a soft storage and change the case dynamic properties of the drive system such that resonant frequencies in the drive train are shifted towards uncritical operating ranges according to document [13, SG 64]. This means that in the case of torsional vibrations near the resonance, a natural frequency change or a lowering of the natural frequency takes place and the system falls out of resonance under slight centrifugal force according to the publication [11, p. 348]. The document [14, p. 95] describes that the elasticity of the bearing reduces the critical rotational speed of an elastic rotor, the percentage reduction being greater the softer the rotor is mounted.

The shift of the critical speed of the boat propeller shaft in the range below the operating speed can be realized simultaneously in addition by the external damping of the surrounding medium or water. Since the fluid forces occurring during operation cause a change or a reduction in the oscillation amplitude of the cantilevered shaft and a shift of the critical rotational speed to smaller values according to document [8, p. 6]. A safe resonance passage through the illustrated special feature of the dynamic system (soft storage and existing in the environment external damping) is not transferable to the case considered. The overlong cantilevered shafts (eg HSC chuck tool systems) have a low bearing damping (eg roller bearing according to document [15, p. 304]), and the influence of the existing, significantly low external damping in the environment or in the air can be neglected.

Another disadvantage of the method is the low balancing efficiency. Since, as shown in Fig. 6 of the document US 2012/0252591 A1, the thixotropic fluid at the beginning of the time in which the cavity is partially filled is evenly distributed even at the inner circumference of the cavity. Due to the initial unbalance of the hollow body, the center of gravity axis does not coincide with the axis of rotation of the body. For this purpose, it is determined that the unbalance does not result from the position errors but from the manufacturing errors or material inhomogeneities. This means that in retirement or at the beginning of the movement of the dynamic system, the geometric center axis of the hollow body coincides with its axis of rotation, since otherwise the illustrated uniform material distribution around the designated axis of rotation can not be done. However, according to the state of the art, it can be shown that, when clamping the overlong projecting shafts, a positional deviation results, which becomes larger as the projection length L increases due to the angular offset. Therefore, the imbalance resulting from this positional deviation can not be compensated with the thixotropic compensatory material proposed in US 2012/0252591 A1.

A suitable eccentric attachment of the center of gravity of the thixotropic compensating substance about the axis of rotation or against the imbalance U of the hollow body as shown in Fig. 7 of the document US 2012/0252591 A1, occurs only after a long movement time, in by the soft storage of the system supercritical operation and then an automatic bringing the center of gravity axis is achieved with the axis of rotation. Such soft storage is detrimental to the application under consideration. Therefore, the illustrated method with a thixotropic stabilizer is not suitable. Another disadvantage of the method described is the fluid-specific property of the thixotropic compensating substance, such as time-dependent flowability. The document US 2012/0252591 A1 states that the thixotropic precipitate is in the solid state of matter in the rest state of the system in which no vibrations exist. As the spin of the system commences, the centrifugal forces due to imbalance give rise to vibrations which cause the thixotropic fluid to liquefy or to lower the viscosity of the substance. Subsequently, the flowability of the thixotropic stabilizer increases. As a result, the substance begins to flow on the inner periphery of the cavity about the axis of rotation and to superimpose in the supercritical speed range against the imbalance such that a vibration reduction is achieved. The time required for this is as great as shown in FIG. 17 with approximately 22-23 seconds according to the document WO2012 / 168416 A1 that this is the case of application (L / D> 20) due to their relatively low first natural frequencies (eg about 100 Hz) and short run-up time are not suitable. Fig. 17 shows a waveform in which the vibration acceleration over the acceleration time is shown.

The section on the prior art devices and methods includes the following bibliography:

Kaufeld, M. et al .: Rationalization by high-speed machining - A way to the factory 2000 ?. Volume 424, Expert Verlag, 1994, p. 287, ISBN: 3-8169-0892-6,

[2] Huerkamp, W .: Limits of use of long cantilevered rotating tools under special aspects of process and work safety. TU Darmstadt, Diss., Shaker Verlag, 2001, p. 208, ISBN: 978-3-8265-8649-1,

[3] Abele, E .; Tian, J .; Turan, E .: Limiting speeds long overhanging

Tool systems - Influence of the tool-chuck combination on the first bending-critical natural frequency. In: Workshop Technology, wt- online Issue 1/2 (2014), pp 60-65, Springer VDI Verlag, Dusseldorf, ISSN 1436-4980,

[4] Würz, T .: Safety of high-speed milling tools. TU Darmstadt, Diss., Shaker Verlag, 1999, p. 192, ISBN: 978-3-8265-6358-4,

[5] Gasch, R .; Nordmann, R .; Pfützner, H .: Rotor Dynamics. 2nd, completely, new. u. ext. Edition., Springer Verlag, Berlin, Heidelberg, New York, 2006, p. 705, ISBN: 978-3-540-33884-0,

[6] Schneider, H .: Balancing Technique. 7. re-cultivation. Edition, Springer Verlag, Berlin, Heidelberg, New York, 2007, p. 362, ISBN: 978-3-540- 49091-3,

[7] Neugebauer, R .: Machine Tools. Springer-Verlag Berlin Heidelberg, 2012, ISBN 978-3-642-30077-6,

[8] T. Berger: Development of a numerical calculation method for

Rührwerksschwingungen. TU Munich, Mechanical Engineering, Diss. 2005,

[9] K.-H. Grote and J. Feldhusen: Dubbel Taschenbuch für die Maschinenbau. 23., newly edited and expanded edition, Springer-Verlag Berlin Heidelberg, 201 1, ISBN 978-3-642-17305-9,

[10] Vrubl, R .; Gloor, R .: Method for extruding pipe profiles.

Patent EP 1 203 623 B1, 2005, Alcan Technology & Management AG,

[1 1] Bernd Künne: Introduction to Machine Elements, Design - Calculation - Construction. 2nd, revised edition, Springer Fachmedien Wiesbaden, 2001. ISBN 978-3-519-16335-0,

[12] Herbert Wittel; Dieter Muhs; Dieter Jannasch; Joachim Voßiek: Rooff / Matek Machine Elements - Standardization, Calculation, Design. 20th, revised and expanded edition, Vieweg + Teubner Verlag, Springer Fachmedien Wiesbaden GmbH, 2011, ISBN 978-3-8348-1454-8,

[13] K.-H. Grote; J. Feldhusen: Dubbel - Paperback for Mechanical Engineering. 23, newly edited and expanded edition, ISBN 978-3-642- 17305-9, Springer-Verlag Berlin Heidelberg, 2011, S. G.64,

[14] Kellenberger W .: Elastic balancing. Springer Verlag, Berlin, Heidelberg, New York, et al., 1987, p. 512. ISBN: 978-3-642-82931-4,

[15] Reimund Neugebauer: Machine tools - structure, function and

Application of cutting and removing machine tools, Springer-Verlag Berlin Heidelberg, 2012, ISBN 978-3-642-30077-6. In summary, the known from the prior art methods and devices for damping unbalanced vibrations in rotationally symmetric bodies to realize a safe, damage-free resonance passage / resonance passage and the use of Selbstwuchtef- fect in supercritical rotational speeds in soft storage on high-speed one-sided fastened and sliding and tilt-rigidly clamped long slender hollow tool shanks not or only partially transferable. The specified methods are for active balancing and devices for resonance passage in soft storage, which require a larger space. For the implementation of additional measures such as the generation of a magnetic field, the installation of heat sources or injectors for controlling a compensation medium or a measurement technique for unbalance detection, etc. is necessary. Thus, these are technically and economically very complex.

The active balancing methods are used not only for economic reasons, but also for technical reasons (space, mass) so far only for larger tool dimensions. The implementation of the active balancing method in the slender, overlong HSC tool shanks (l_ / D> 20) is due solely to the geometric boundary conditions or due to small outer diameter of the shafts, e.g. D = 10mm, excluded.

But other possible balancing methods, as well as passive self-balancing, which could allow a safe, damage-free resonance passage and thus achieve a self-stabilization against dynamic imbalance in the supercritical speed range, have been previously implemented for one-sided and sliding and tilting mounted, long, slender, tubular Hollow body not realized.

The invention is therefore based on the object to provide body with one-sided fixed clamping in verschiebesteifer and tilting stability for up to the supercritical speed range rotating parts of a system and method for producing the body, which are designed so suitable that by passive self-damping and stabilizing better dynamic Characteristics of a safe damage-free passage of the first critical bending speeds generated and thus a self-stabilizing operation of a rotating hollow body is made possible up to the supercritical speed range.

This object is achieved with features according to claims 1 and 20.

The body with one-sided fixed restraint during displacement-resistant and tilt-stable mounting for parts of a system rotating up to a supercritical rotational speed range represents a hollow body in tubular form with a predefined material whose unbalance U resulting from manufacturing inaccuracies and bearing inaccuracies U occurring during a rotation as a result of a local difference between the geometrical axis of symmetry of the hollow body and a rotational axis of the hollow body and having a symmetrical, closed cavity related to the geometric axis of symmetry of the hollow body, which is also closed towards its front sides,

wherein according to the characterizing part of patent claim 1

at least one free-flowing shapeless material having a defined mass ms is introduced into the balancing chamber and the balancing chamber in a partially filling manner into the hollow body of the hollow body fastened and supported on one side as at least one balancing chamber

wherein the mass ms of the introduced flowable shapeless substance is defined such that a hollow body-related vibration damping in the critical and critical speed range and a resonance passage in the critical speed range can be achieved and that caused by the effect of the imbalance U of the hollow body distribution of the material in the supercritical speed range the effect of the unbalance U taking into account a predetermined ratio between the mass ms of the substance and the unbalance U relative to the associated balancing chamber according to the equation

self-stabilizing compensates, wherein

U - the imbalance,

m _s - the mass (filling material) of the flowable substance;

h ₀ - the height of the filling material of the flowable substance;

h _K - the height / length of the balancing chamber;

Ri - the inner radius of the balancing chamber and

s - a safety factor

are. The hollow body is essentially a slender, long body whose ratio between cantilever length L and mean outer diameter D is greater than "fifteen" with UD> 15.

The state of aggregation of the flowable substance in the balancing chambers remains in retirement as well as under pressure and vibration in all speed ranges.

The flowable shapeless material may optionally be fine-grained sand having a grain size of less than 1 mm.

The flowable formless fabric may have a higher density than the density of the shaft material of the hollow body.

The balancing flowable substance introduced into the balancing chambers can be a substance mixture.

The symmetrical cavity, which is related to the axis of symmetry, can be located at least on the side opposite the one-sided attachment. The axis of symmetry symmetrical cavity in the axial and radial directions may be divided into several balancing chambers to achieve a higher damping and Auswuchtwirkung with the flowable material. The symmetrical cavity, which is related to the axis of symmetry, can be designed to be multi-symmetrical.

The cavity in the form of a hollow shaft may have an annular symmetric or multi-symmetrical cross-section, wherein the cross section of the hollow shaft is formed mehrsymmetrisch.

The predetermined material of the hollow body may be tough-elastic. The predetermined material of the hollow body may be brittle-elastic.

As a result of the mass ms of at least one flowable substance introduced into at least one of the balancing chambers of the cavity, the amplitude of the oscillation as the rotational speed approaches the critical rotational speed of the hollow body representing the resonant frequency of the first bending natural oscillation remains so limited that a damage-free passage of the resonance point becomes possible, with increasing speed in the supercritical speed range, the vibration behavior of the hollow body is stabilized in that the balancing mass reverses its direction of action in the opposite direction to the unbalance U, wherein the displacement of the center of gravity of the common mass m + m _s is set so that the focus is on the axis of rotation, wherein a self-balancing effect occurs and increases the smoothness and consequently the stability of the hollow body. The hollow body can be dynamically balanced during operation in several levels.

The self-stabilizing hollow shaft can be made of solid material.

The self-stabilizing hollow shaft can be made of lightweight material. The hollow body can be designed as a hollow shaft for a clamping tool fastened to the free end of the hollow body and can be used for high-speed machining of deep and filigree contours. The associated with a drive spindle, inserted into a cutting part of a chipping tool hollow body can represent a hollow shaft, which is formed by the self-balancing, fast-running unilaterally stretched long slender hollow body with the ratio UD> 15, wherein the cutting part is designed freely depending on the purpose and the connection of the cutting part and the hollow shaft is made detachable or non-detachable.

The method for producing a body with a one-sided fixed restraint in non-displaceable and tilt-resistant storage for up to a supercritical rotational speed range rotating parts of a system,

wherein the body is a hollow body in a tubular shape with predetermined material whose bending vibration excitation resulting from inaccuracies U resulting from manufacturing inaccuracies and bearing inaccuracies U is based and has a related to the geometric axis of symmetry, symmetrical closed cavity, which also closed to its front sides is

comprises according to the characterizing part of claim 20

following steps:

- Formation of a one-sided and tilt-rigid and verschiebesteif mounted rotationally symmetric, long, slender, tubular hollow body,

Forming at least one balancing chamber in the cavity of the hollow body,

Determining the imbalance U of the hollow body having at least one balancing chamber by measuring with a balancing machine,

Determination of the mass ms of the flowable shapeless substance to be introduced by means of the equation

in at least one of the balancing chambers such that a vibration damping in the subcritical rotational speed range and in the critical rotational speed range is achieved to ensure a resonance passage and after the passage of the resonance speed range, the imbalance U in the supercritical rotational speed range is automatically compensated and vibration damping occurs in supercritical operation,

Introducing the free-flowing, shapeless substance into at least one of the balancing chambers of the hollow body corresponding to the defined mass ms of the flowable shapeless substance,

in which

U - imbalance;

m _s - the mass (filling material) of the flowable substance;

h ₀ - the height of the filling material of the flowable substance;

h _K - the height / length of the balancing chamber;

/ ?, - the inner radius of the balancing chamber and

s - a safety factor

are.

The balancing chambers can be formed by inserting one or more closures into the hollow shaft.

The first balancing chamber selectively associated further balancing chambers can be created by each after filling the flowable material in the first balancing chamber, the first balancing chamber is closed by a closure within the cavity, and in the resulting second balancing chamber a further defined mass m _{s of} the flowable material is filled, the second balancing chamber by means of another closure is closed, wherein the process of creating the predetermined number of balancing chambers is repeated with other closures.

In symmetrical hollow bodies formed with at least one balancing chamber, the flowable shapeless material is introduced, which is distributed in the balancing chamber of the stationary hollow body.

When the hollow body is rotationally accelerated, the flowable shapeless material introduced is deposited under the effect of centrifugal force on the inner wall of the hollow body in accordance with the effect of the imbalance U of the hollow body as distributing substance.

With the onset of the rotational acceleration, a speed-dependent oscillation excitation of the substance with simultaneous formation of a pressure resulting from the centrifugal force against the inner wall of the balancing chambers can be effected by applying the substance to the inner wall.

Under the training pressure, the compensation of the imbalance U takes place automatically, the time that is needed for at least on the mass ms of the introduced flowable substance, its density, its viscosity and the spin depends.

Due to an internal friction of the flowable substance, vibration damping during the rotational acceleration can act from the subcritical speed range up to the critical speed range.

The one-sided fixed and verschiebesteif and tilting rigid mounted hollow body can thus rotate when passing through the subcritical and critical speed range and in the supercritical speed range without catch storage.

The system / dynamic system may consist of at least one drive spindle, a chuck with a clamping shank and adapter and the hollow body according to the invention. Further developments and further advantageous embodiments of the invention are specified in further subclaims. The invention will be explained in more detail by means of exemplary embodiments by means of several drawings.

Show it:

1 is a schematic representation of the main rotating components of the prior art dynamic system with a high-frequency spindle, a chuck, and a long-necked body (shaft) as a system / dynamic system;

Representations of a swing mold in "soft" storage according to the document [2, p. 52],

Representations of vibration modes according to the document [7, p.

299], a section through a hollow body for a calculation scheme of the total imbalance U from form errors and bearing defects according to the prior art,

5 shows a schematic longitudinal sectional view of an adapter connected to a drive spindle and an adapter between the clamping shaft and drive spindle with the slender, tubular and shaft-shaped hollow body firmly clamped on the clamping shaft with a cavity in the form of a hollow balancing chamber closed at both ends the clamping shaft is fixed in the adapter and while the position of the hollow body is vertically suspended,

Fig. 5a is a schematic longitudinal sectional view of a clamped in a drive spindle directly by means of a clamping shaft, slender tubular and designed as a shaft hollow body with a Hollow space in the form of a hollow balancing chamber closed at both ends, wherein the position of the hollow body is vertically suspended, according to Fig. 5, Fig. 6 is a schematic longitudinal sectional view of an adapter connected to a drive spindle and between an adapter shaft and drive spindle with the clamped on the clamping shaft, slender, tubular and designed as a shank hollow body with a cavity in the form of two closed at both ends hollow balancing chambers, wherein the position of the hollow body is vertically suspended,

6a is a schematic longitudinal sectional view of a in a drive spindle directly by means of a clamping shank clamped, slender, tubular and designed as a shaft hollow body with a

Cavity in the form of two hollow balancing chambers closed at both ends, wherein the position of the hollow body is vertically suspended, according to Fig. 6, Fig. 7 is a schematic longitudinal sectional view of an adapter connected to a drive spindle and between an adapter shaft and drive spindle with the clamped on the clamping shaft , slender, tubular and designed as a shank hollow body with a cavity in the form of two closed at both ends hollow balancing chambers, wherein the position of the hollow body is vertical,

8 shows a schematic longitudinal sectional illustration of an adapter connected to a drive spindle and in an adapter connected between the clamping shaft and drive spindle with the slender, tubular and hollow shaft body clamped to the clamping shaft with a cavity in the form of two hollowed ends closed at both ends Balancing chambers, wherein the position of the hollow body is horizontal, wherein

8a shows a cross-section A-A of FIG. 8 through a hollow balancing chamber of the shaft of the stationary hollow body (static state) with the filled flowable material and through a balancing chamber without flowable material and

8b through the hollow balancing chamber of the shaft of the rotating hollow body with the filled, flowable and distributed on the inner wall fabric (dynamic state)

show a schematic longitudinal sectional view of a on a drive spindle directly by means of a clamping shaft clamped, slender, tubular and designed as a shaft hollow body with a cavity in the form of two closed at both ends hollow balancing chambers, the position of the hollow body are horizontal, wherein

Fig. 9a is a cross-section A-A of Fig. 9 through one of the hollow

Balancing chambers of the shaft with the filled flowable material in the static state and a balancing chamber without flowable material and

Fig. 9b shows a cross-section A-A of FIG. 9 through the hollow balancing chambers of the shaft with the filled, distributed on the inner wall and flowable material in the dynamic state

demonstrate,

10 shows a schematic longitudinal sectional view of an adapter connected to a drive spindle and in an adapter connected between the clamping shaft and drive spindle with the clamped, slender, tubular and shaft-shaped hollow body with a cavity in the form of several, in particular Re three mutually closed hollow balancing chambers, the position of the hollow body is vertically suspended, and two of the balancing chambers are partially filled with flowable material, Fig. 10a is a schematic longitudinal sectional view of a on a drive spindle directly by means of a clamping shank clamped, slender, tubular and as Shank-shaped hollow body having a cavity in the form of three hollow balancing chambers each closed at both ends, wherein the position of the hollow body is suspended vertically, as shown in FIG. 10,

1 is a schematic longitudinal sectional view of an adapter connected to a drive spindle and between a clamping shaft and drive spindle with a clamped on the clamping shank, slender, tubular and formed as a shaft hollow body with a cavity in the form of three each closed at both ends hollow balancing chambers with flowable material are partially filled, wherein the position of the hollow body is vertically suspended in the static state, and wherein two radial hollow balancing chambers of the shaft of the stationary hollow body are partially filled with flowable material,

11a is a schematic longitudinal sectional view of a on a drive spindle directly by means of a clamping shank clamped, slender, tubular and designed as a shaft hollow body with a

Cavity in the form of three each closed at both ends hollow balancing chambers, wherein the position of the hollow body is vertically suspended and wherein two radial hollow balancing chambers of the shaft of the stationary hollow body are partially filled with flowable material, in the static state, said

Fig. 11 b is a cross-section B-B of Fig. 11, 11 a by radial hollow

Balancing chambers of the shaft with the filled, at the FIG. 12 is a schematic longitudinal sectional view of an adapter connected to a drive spindle and an adapter shaft and drive spindle with the slender, tubular and hollow body clamped on the clamping shaft. FIG with a hollow space in the form of three hollow balancing chambers closed at both ends with two radially formed hollow balancing chambers partially filled with material, the position of the hollow body being vertical,

12a is a schematic longitudinal sectional view of a on a drive spindle directly by means of a clamping shank clamped, slender, tubular and designed as a shaft hollow body with a cavity in the form of three closed at both ends hollow chambers with two radially formed hollow balancing chambers, wherein the position of the hollow body is vertical, wherein the two radial hollow balancing chambers of the shaft of the stationary hollow body (static state) are partially filled with the flowable material, wherein

12b shows a cross-section B-B according to FIG. 12, 12a through the two radial hollow balancing chambers of the shaft of the rotating hollow body with the filled, flowable substance distributed on the inner wall (dynamic state), FIG.

13 shows a schematic longitudinal section illustration of an adapter connected to a drive spindle and in an adapter connected between the clamping shaft and the drive spindle with the slender, tubular and shaft-shaped hollow body clamped on the clamping shaft and having a nem cavity in the form of three closed at both ends hollow balancing chambers with two radially formed hollow balancing chambers, the position of the hollow body is horizontal and the radial hollow balancing chambers of the shaft of the stationary hollow body are partially filled with the flowable material, in the static

State, being

13a shows a schematic longitudinal section illustration according to FIG. 13 of a slender, tubular and shaft-shaped hollow body clamped on a drive spindle directly by means of a clamping shaft,

13b shows a cross section A-A according to FIG. 13 through the two radial hollow balancing chambers of the shaft of the stationary hollow body (static state) with the filled substance and

Fig. 13c shows a cross section A-A of Fig. 13 through the two radial hollow balancing chambers of the shaft of the rotating hollow body (dynamic state) with the filled material distributed on the inner wall

demonstrate,

14 shows a schematic longitudinal sectional illustration of an adapter connected to a drive spindle and in an adapter connected between the clamping shaft and drive spindle with the slender, tubular and shaft-shaped hollow body clamped on the clamping shaft and having a hollow space and one according to FIGS. 8, 8a and Fig. 8b section shortened shown, closed axial hollow balancing chamber, wherein the position of the hollow body is horizontal and a part of the clamping shaft is inserted for improved retention of the hollow shaft in the hollow shaft of the hollow body, wherein

Fig. 14a shows a cross section A-A of Fig. 14 by the abbreviated

shown hollow balancing chamber of the shaft with the filled in the second balancing chamber, distributed on the inner wall fabric in the dynamic state, wherein the sheath of the shank has a square shape in cross section,

Fig. 14b shows a cross-section A-A of Fig. 14 by the hollow balancing chamber of the shaft shown in abbreviated with the filled in the second balancing chamber, on the inner

Wall distributed fabric, in the dynamic state, wherein the sheath of the shaft in cross-section has a hexagonal shape,

14c shows a cross-section A-A of FIG. 14 through the hollow balancing chamber of the shank, shown in abbreviated form, with the material distributed in the second balancing chamber distributed on the inner wall, in the dynamic state, wherein the sheath of the shank has an octagonal shape. Fig. 15 shows several schematic cross-sectional views, based on the

14, by multiply on the symmetry axis related symmetric separate balancing chambers, similar to Figs. 14a, 14b, 14c, wherein Fig. 15a is a cross section AA according to FIG. 14 by the second hollow balancing chamber of the shaft of the rotating hollow body (dynamic State) with the filled, distributed on the inner wall fabric, wherein the shaft has an outer wall in the cross section of a circle and an inner wall in the cross section of a square shape,

15b shows a cross section AA according to FIG. 14 through the second hollow balancing chamber of the shaft of the rotating hollow body (dynamic state) with the filled material distributed on the inner wall, wherein the shaft has an outer wall in cross section of a square shape and an inner wall in cross section of a circle,

15c shows a cross-section AA according to FIG. 14 through the second hollow balancing chamber of the shaft of the rotating hollow shaft. Body (dynamic state) with the filled, distributed on the inner wall fabric, wherein the shaft has an outer wall in the cross section of a circle and an inner wall in the cross section of a hexagonal shape,

15d shows a cross section AA according to FIG. 14 through the second hollow balancing chamber of the shaft of the rotating hollow body (dynamic state) with the filled material distributed on the inner wall, wherein the shaft has an outer wall in cross section of a hexagonal shape and an inner wall in cross section of a circle,

FIG. 15e shows a cross section AA according to FIG. 14 through the second hollow balancing chamber of the shaft of the rotating hollow body (dynamic state) with the filled material distributed on the inner wall, the shaft having an outer wall in a circular cross-section and an inner wall in FIG Having a cross-section of an octagonal shape,

FIG. 15f shows a cross section AA according to FIG. 14 through the second hollow balancing chamber of the shaft of the rotating hollow body (dynamic state) with the filled material distributed on the inner wall, the shaft having an outer wall in cross-section of an octagonal shape and an inner wall in FIG Has a cross section of a circular shape,

demonstrate,

16 shows representations of a balancing chamber for calculating the ratio of the filling mass ms to the imbalance U, by way of example

16a is a representation of the vertically formed balancing chamber with partially filled flowable material (filling compound) in the static state, 16b shows a cross section AA of FIG. 16a through the balancing chamber with the filling material of the flowable substance in the static state, FIG.

16c shows a representation of the vertically formed balance chamber with partially filled flowable substance (filling compound) in the dynamic state,

16d shows a cross section A-A to FIG. 16c through the balancing chamber with the distributed and applied substance (filling compound) in the dynamic state, FIG.

2, a curve in which the vibration acceleration is given over the ramp-up time of a system, according to the prior art (WO2012 / 168416 A1) and an amplitude (A) / time (t) curve for starting up a high frequency spindle of a dynamic system with a hollow body according to the invention with at least one balancing chamber, which partially with at least one flowable formless material as

Fill mass is filled.

In the following, FIGS. 5 to 14 are considered together.

For example, in FIG. 5, FIG. 5a and in FIGS. 6, 6a, a body 2 with one-sided fixed clamping in displacement and tilt-rigid mounting for parts of a system 22 with at least one drive spindle 5 and rotating up to a supercritical rotational speed range a chuck 1, wherein the body 2 is a hollow body in tubular form with a predetermined material whose unbalance U resulting from manufacturing inaccuracies and storage inaccuracies resulting from a rotation due to a local difference between the geometric axis of symmetry 75 of the hollow body 2 and Rotation axis 76 of the hollow body 2 are based and one on the geometric axis of symmetry 75 of Hollow body 2 related symmetrical, closed cavity 7 has, which is also closed to its end faces 8, 9 out.

According to the invention is in the formed as at least one balancing chamber 70, 71, 72, 73, 74 cavity 7 of the cantilevered and mounted hollow body 2 at least one flowable formless material 4, 40, with the balancing chamber 70, 71, 72, 73, 74 with a certain, defined mass m _{s is} partially filled, introduced,

wherein the mass ms of the introduced flowable shapeless substance 4, 40 is defined such that a hollow body related vibration damping in the subcritical rotational speed range and in the critical speed range and a resonance passage in the critical speed range can be achieved and that caused by the effect of imbalance U of the hollow body 2 distribution of Substance 4, 40 in the supercritical speed range, the effect of imbalance U taking into account a predetermined ratio between the mass ms of the substance 4, 40 and the imbalance U

according to equation (IV)

self-stabilizing compensates,

in which

U - the imbalance,

m _s - the mass of the flowable substance 4, 40,

h ₀ - the height of the filling material of the flowable substance 4, 40,

h _K - the height or the length of the balancing chamber 70, 71, 72, 73, 74,

/ ?, - the inner radius of the balancing chamber 70, 71, 72, 73, 74 and

s - a safety factor

are.

The hollow body 2 is a slender, long body whose ratio between the cantilever length L and the mean outer diameter D is greater than "fifteen" with UD> 15. The state of aggregation of the flowable substance 4, 40 in the Wuchtkamrnerh 70, 71, 72, 73, 74 remains both in retirement and in all speed ranges under pressure and oscillations. The flowable under pressure informal fabric 4, 40 thus remains flowable.

The flowable formless fabric 4, 40, 14 may optionally be fine-grained sand with a grain size of less than 1 mm. The flowable shapeless material 4, 40 may have a higher density than the density of the given shaft material of the hollow body 2.

The balancing flowable substance 4, 40, 14 introduced into the balancing chambers 70, 71, 72, 73, 74 may be a mixture of substances.

The symmetrical cavity 7, which is related to the axis of symmetry 75, can be located at least on the side opposite the one-sided fastening. The relative to the axis of symmetry 75 symmetrical cavity 7 can in the axial and radial directions in several balancing chambers 70, 71, 72; 73, 74 be divided in order to achieve a higher damping and Auswuchtwirkung with the flowable material. The symmetrical cavity 7, which is related to the axis of symmetry 75, can be of multiple symmetrical design.

The cavity 7 in the form of a hollow shaft 2 may have an annular symmetrical or multi-symmetrical cross-section, wherein the cross-section of the hollow shaft 2 is formed multiple symmetrical.

The self-stabilizing hollow shaft 2 may be made of solid material. The self-stabilizing hollow shaft 2 may be made of lightweight material. The predetermined material of the hollow body 2 may be tough-elastic.

The predetermined material of the hollow body 2 may be brittle-elastic.

As a result of the mass m _{s of} at least one flowable substance 4, 40, 14 introduced into at least one of the balancing chambers 70, 71, 72, 73, 74 of the hollow space 7, the amplitude of the oscillation can approach the critical velocity, the resonance frequency of the oscillation Speed of the hollow body 2 representing the first bending inherent vibration so that a passage of the resonance point is possible, with increasing speed in the supercritical speed range, the vibration behavior of the hollow body 2 stabilized by the fact that the balancing mass reverses its direction of action in the opposite direction to the unbalance U, where the displacement of the center of gravity of the common mass m + m _s is adjusted so that the center of gravity lies on the axis of rotation 76, wherein a self-balancing effect occurs and the smoothness and consequently the stability of the hollow body 2 increases.

The hollow body 2 can be dynamically balanced during operation in several levels. The hollow body 2 can be designed as a hollow shaft for a clamping tool fastened to the free end 9 of the hollow body 2 and can be used for high-speed machining of deep and filigree contours.

The hollow body 2, which is connected to a drive spindle 5 and inserted into a cutting part of a tensioning tool, can constitute a hollow shaft which is formed by the self-balancing, high-speed, long-slender hollow body 2 with the ratio UD> 15 is, wherein the cutting part is designed freely depending on the purpose and the connection of the cutting part and the hollow shaft 2 detachable or

For balancing the imbalance of the mass m of the hollow body 2 without flowable substance 4, 40 which is predetermined by a measurement with a conventional balancing machine, the mass m _{s of} the flowable shapeless substance 4, 40 serving as a compensating substance is to be determined.

For this, FIG. 16 with the detailed FIGS. 16a, 16b, 16c and 16d are included.

16a shows a representation of a vertically formed balancing chamber 71 with partially filled flowable substance 4 in the static state, the balancing chamber 71 having the height h _K and the level height h _{0 of} the flowable substance 4 located therein. The axis of symmetry 75 is shown spaced apart from the rotation / rotation axis 76. The balancing chamber 71 is limited by the lower-side closure 3 and the opposite upper-side closure 10.

FIG. 16b shows a cross-section A-A to FIG. 16a through the balancing chamber 17 with the filling compound ms of the substance 4 in the static state.

16c shows a representation of the vertically formed balance chamber 71 with partially filled flowable substance 14 in the dynamic state, wherein the applied substance 14 is distributed to the inner wall of the balancing chamber 71. FIG. 16d shows a cross section A-A to FIG. 16c through the balancing chamber 17 with the applied material 14 in the dynamic state.

According to the imbalance u can have the following relationship

U = mx. (VI) are formulated, wherein x _{F is} the distance of the center of gravity F of the balance mass 4 m _s to the rotation / rotation axis 76 of the hollow body 2. The mass m _{s of} the compensating substance 4 is determined by equation (VI):

(VII)

Ϊ8] For determining the distance x _F , the equation of the mass moment of the compensating substance 4 (filling material) about the axis of rotation 76 (of FIG. 16c and 16d), the distribution of the flowable shapeless substance 4 in the balancing chamber 71 during self-balancing in the supercritical rotational speed range of the hollow body. 2 causes: x _F np _s h _K (R - R _f ) = x _w np h _K Rf (VI ")

From this follows the equation (IX)

where x _{w is} the deflection of the rotating hollow body 2, R _{s is} the inner radius of the balancing chamber 71 and R _{f is} the radius of the free surface of the applied compensation material 14. In ensuring the self-weighting effect, the following relationship can be found, which results from the geometric condition of the applied balance material 14 distributed in the balance chamber 71

Thus, for the greatest deflection of the rotating hollow body 2, the following applies:

x _w = R _t - R _f (XI) By substituting equation (XI) into equation (IX), for x _P

receive.

From equation (XI) it can be seen that to determine the distance value x _F, the radius R _{f of} the free surface of the compensating substance 14 should be known. For the determination of the mass. _{s of} the applied compensating substance 14 according to FIG. 16c and FIG. 16d is s = np _s h _K {Rf-Rf), (XIII) where p _{s is} the density of the flowable substance 4 (balancing medium) and h _{x is} the height of the balancing chamber 71 ,

For the mass m _{s of} the compensating substance 4 in the resting state of the dynamic system according to FIGS. 16a and 16b, m _s = np _s k _Q R, (XIV) where fco is the height of the compensating substance 4 filled in the hollow shaft or in the balancing chamber 71 in the state of rest of the system, consisting at least of drive spindle 5, clamping shank / chuck 1, 6 and hollow body 2 according to the invention is. To determine the mass m _s is still the condition of mass constancy, whether added at rest or movement, since the designed balancing chamber 71 is closed and thus in the dynamic system, no loss of mass m _{s of} the compensating 4 occur. Thus:

After simplifying, equation (XV) takes the following form:

KM (XVI)

From equation (XVI), the radius R _{f of} the free surface of the compensating substance 14 can be determined

By substituting the equation (XVII) into the equation (XII), the following becomes

(XVIII)

receive.

Substituting Equation (XVIII) into Equation (VII), the mass m _{s of} the equalizer 14 is determined as follows:

U \ 1 + 1

u (XIX) m _s = -

1 + ίι - ·

Equation (XIX) can be used to calculate the theoretical value of the mass m _{s of} the compensating substance 4, 14, which assumes a cylindrical shape during the distribution of the flowable, shapeless substance 4 in the cavity of the hollow body 2. But in reality, the designated ideal cylindrical shape of the compensating material 14 does not fully exist due to some factors that significantly affect the vibration behavior of the system, such B. vibrations of the drive spindle 5, fluctuations in the rotational angular velocity, positional deviations and production-related shape and roundness deviations of the cantilevered and rigidly clamped hollow body 2. Therefore, a safety factor s should be taken into account in the determination of the actual filling mass _{s of} the compensating substance. According to experiments carried out, the safety factor s can be assumed numerically from "two" to "four". Thus, for the mass m _{s to be} filled in the compensating substance 4, the equation (V) applies:

in which

U - the imbalance,

m _s - the mass of the flowable substance,

h ₀ - the height of the filling material of the flowable substance,

h _K - the height or the length of the respective balancing chamber,

R, - the inner radius of the balancing chamber and

s - a safety factor

are.

It should also be noted that for self-balancing with flowable formless material 4, the cavity 7 of the hollow body 2 is partially filled, preferably to about 50% of its cavity with the balancing mass m _s . This means that the height / length h _{K of} the cavity 7 or the balancing chamber 71 should be twice as large as the height / length k _{0 of} the filled substance 4 in retirement of the system. The largest value of s = 4 is assumed if the first bending natural frequency remains below 100 Hz. The smaller the first critical bending speed of the shaft 2 is, the faster a resonance passage can be achieved with less effect of centrifugal forces.

5 is a longitudinal sectional view of an adapter 6 located on a drive spindle 5 and in an intermediate clamping shaft 1 and drive spindle 5 with the slender, tubular and shank-shaped hollow body 2 clamped on the clamping shaft 1 with a cavity 7 in the form of a closed end on both sides hollow balance chamber 70, wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the hollow body 2 is vertically suspended, wherein the one end 8 at the first end side of the hollow body 2 of the clamping shaft 1 and the other opposite free end 9 at the second end face are closed by means of the first closure 3. Therein is the flowable substance 4 with the determined calculated mass

>. ,

Within the hollow body 2, the axis of symmetry 75 and the axis of rotation 76 are shown at a distance. The hollow body 2 has the length L and the outer diameter D.

FIG. 5a shows a schematic longitudinal section of a slender tube-shaped hollow body 2 formed as a shank and clamped in a drive spindle 5 with a cavity 7 in the form of a hollow balancing chamber 70 closed at both ends, the clamping shaft 1 being directly in the drive spindle 5 is fastened and the position of the hollow body 2 is similar to that in FIG. 5 hanging vertically, wherein the one end 8 of the hollow body 2 closed by means of the clamping shaft 1 and the other opposite free end 9 of the hollow body 2 by means of the first closure 3 are.

6 shows a schematic longitudinal section of an adapter 6 located on the drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender, tubular and shaft-shaped hollow body 2 clamped on the clamping shaft 1 with a cavity 7 in the form of two closed at both ends hollow balancing chambers 70 and 71, wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the hollow body 2 is vertically suspended. The two adjacent balancing chambers 70 and 71 are separated from each other by a second closure 10 and one end 8 of the hollow body 2 is closed by means of the clamping shank 1 and the other opposite free end 9 is closed by means of the first closure 3 according to FIG. In the first balancing chamber 70 is no flowable substance 4, 40 included, but can also be filled optionally. FIG. 6 a shows a schematic longitudinal section of a hollow tubular body 2 clamped in the drive spindle 5 directly by means of a clamping shank 1, with a hollow space 7 in the form of two hollow balancing chambers 70 and 71 closed at both ends, wherein the clamping shaft 1 is fixed in the drive spindle 5 and while the position of the hollow body 2 is vertically suspended, wherein the two adjacent balancing chambers 70 and 71 are separated by a second closure 10 and the one end 8 of the hollow body 2 by means of the clamping shank 1 and the other opposite free end 9 are closed by means of the first closure 3 of FIG. 5. No flowable substance 4, 40 is contained in the first balancing chamber 70, the second balancing chamber 71 being partially filled with the defined mass m _{s of} the flowable substance 4, 40. 7 shows the schematic longitudinal section of an adapter 6 located on a drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender, tubular and shaft-shaped hollow body 2 with a cavity 7 in the form of two sides clamped on the clamping shaft 1 closed hollow balancing chambers 70 and 71 indicated, wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the hollow body 2 is vertical, wherein the two adjacent balancing chambers 70 and 71 are separated by a second closure 10 and wherein the one end of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 are closed by means of the first closure 3 of FIG. The flowable substance 4 is located in balancing chamber 71, wherein the substance 4 only partially fills the balancing chamber 71. The hollow body 2 is vertically upright with the clamping shaft 1 in the adapter 6 attached. 8 shows a schematic longitudinal section of an adapter 6 located on a drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender, tubular and shaft-shaped hollow body 2 with a cavity 7 in the form of two sides clamped on the clamping shaft 1 closed hollow balancing chambers 70 and 71 are shown, wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the drive spindle 5 and the position of the hollow body 2 but are horizontal, the two adjacent balancing chambers 70 and 71 are separated from each other by the second closure 10 and one end 8 of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 are closed by means of the first closure 3 of FIG. 6, wherein the flowable substance 4 is located in balancing chamber 71, which only partially fills the balancing chamber 71, wherein

8a shows a cross section A-A according to FIG. 8 through the second balancing chamber 71 of the shaft 2 with the filled substance 4 of the stationary hollow body 2 (static state) and

8b show a cross-section A-A according to FIG. 8 through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled substance 14 distributed on the inner wall in the dynamic state.

9 shows a schematic longitudinal section of a on a drive spindle 5 directly by means of a clamping shank 1 clamped, slender, tubular and designed as a shaft hollow body 2 with a cavity 7 in the form of two closed at both ends hollow balancing chambers 70 and 71, wherein the clamping shaft 1 is fixed in the drive spindle 5 and the position of the drive spindle 5 and the position of the hollow body 2 are horizontal, wherein the two adjacent balancing chambers 70 and 71 are separated by the second closure 10 and the one end 8 of the hollow body 2 by means of the clamping shank 1 and the other opposite free end 9 are closed by means of the first closure 3 of FIG. 9, wherein the flowable substance 4 is located in the balancing chamber 71, which only partially fills the balancing chamber 71, wherein

9a shows a cross section A-A according to FIG. 9 through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled substance 4 in the static state and

9b show a cross section A-A according to FIG. 9 through the second balancing chamber 71 of the shaft 2 of the rotating hollow body 2 with the filled substance 14 distributed on the inner wall in the dynamic state.

Furthermore, FIG. 10 shows a longitudinal section illustration of an adapter 6 located on a drive spindle 5 and in an intermediate between the power shaft 1 and the drive spindle 5, with the slender, tubular clamped on the power shaft 1. shaped and designed as a shaft hollow body 2 with a cavity 7 in the form of three closed at both ends hollow axial balancing chambers 70, 71 and 72, wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the hollow body 2 is vertically suspended, the two adjacent balancing chambers 71 and 72 are separated from each other by a third closure 11 and the one end 8 of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 are closed by means of the first closure 3 of FIG. 6a. 10 a shows a schematic longitudinal section of a hollow tubular body 2, which is clamped on a drive spindle 5 directly by means of a clamping shaft 1 and has a cavity 7 in the form of several hollow cavities 70, 71 and 72 which are closed at both ends; wherein the clamping shaft 1 is fixed in the drive spindle 5 and while the position of the hollow body 2 is vertically suspended, wherein the two adjacent balancing chambers 71 and 72 are separated by a third closure 1 1 and the one end 8 of the hollow body 2 by means of the clamping shank. 1 and the other opposite free end 9 are closed by means of the first closure 3 according to FIG. 6.

In FIGS. 10 and 10a, the flowable material 4 is in the axial balance chamber 71 and the second flowable material 40 is in the axial balance chamber 72, with the axially disposed balance chambers 71 and 72 being only partially filled. The flowable web 40 in the balancing chamber 72 may extend from the flowable web 4, e.g. differ in density and viscosity.

FIG. 11 shows a schematic longitudinal section of an adapter 6 located on a drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender tubular body 2 clamped on the clamping shaft 1 and having a cavity 7 in the form of three hollow balancing chambers 70 and 73, 74 closed at both ends, wherein the balancing chamber 70 is an axial balancing chamber in the cavity 7 and the balancing chambers 73, 74 are located radially out of the cavity 7 as two wherein the two radial balancing chambers 73, 74 are arranged downstream of the axial balancing chamber 70 in the direction of the end 9, wherein the first radial balancing chamber 73 is arranged in the same alignment within the second radial balancing chamber 74, the adjacent balancing chambers 70 and 73, 74 are separated by a fourth closure 12 and wherein the clamping shaft 1 is fixed in the adapter 6 and while the position of the hollow body 2 is vertically suspended, said one end 8 of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 means the first shutter 3 is closed, wherein the two radial chambers 73, 74 of the shaft 2 with the fabric 4 of the stationary hollow body 2 (static state) are partially filled and wherein the two radial balancing chambers 73 and 74 are separated by an intermediate chamber casing 20 , One of the balancing chambers 73, 74 may partially be filled instead of the first material 4 with another second material 40. The shutters 3 and 12 are designed such that they lock the chamber jacket 20 to form the radial balancing chambers 73 and 74.

The required mass for carrying out the process is to be determined taking into account a safety factor in the size "two" to "four" with equation (XXI). Another filling of the balancing chamber 70, 71, 72, 73, 74 with a molar mass m _s , which is greater than the determined value, can lead to the following disadvantages:

1) an enlargement of the imbalance U of the hollow body 2 such that thereby resulting greater vibration amplitudes is caused even at subcritical and critical speeds to damage the hollow body 2 by kinking or breakage,

2) no complete distribution of the compensating substance 4, 40 or no arrangement of the substance 4, 40 in a cylindrical shape on the balancing chamber wall until the occurrence of resonance speeds (about 1-3 seconds after starting) and thus there is no possibility of resonant passage, 3) this no longer has any significant influence on the change or decrease in the first bending-critical natural frequency of the hollow body,

4) no further increase of the damping and self-weighting effect in the hyper-critical speed range, since due to the concentric mounting of the additional mass about the axis of rotation of the system 22 their

Focus axis coincides with the axis of rotation 76, that is, this part of the mass m _{s of} the substance 4, 40 compensates itself.

To avoid the disadvantages described, the balancing chamber 70 of the hollow body 2 can be designed radially with a plurality of concentric balancing chambers due to geometry, or the balancing chamber can be repeated several times axially to the hollow body, or the radially executed, multi-chamber structures can be constructed several times in the axial direction.

A schematic longitudinal section of a hollow tubular body 2, which is clamped on a drive spindle 5 directly by means of a clamping shank 1 and has a cavity 7 in the form of three hollow chambers 70 and 73, 74 closed at both ends, is shown in FIG. wherein the balancing chamber 70 is an axial balancing chamber in the cavity 7 and the balancing chambers 73, 74 as two located in the cavity 7, radially ausgebil- ended balancing chambers, the two radial balancing chambers 73, 74 of the axial balancing chamber 70 are arranged downstream towards the end 9 , wherein the first radial chamber 73 is disposed within the second radial chamber 74 in alignment, the adjacent balancing chambers 70 and 73, 74 are separated by a fourth closure 12 and wherein the clamping shaft 1 is fixed in the drive spindle 5 and thereby the position of Hollow body 2 is suspended vertically, wherein the one end 8 of the hollow body 2 by means of the Sp 1 and the other opposite free end 9 is closed by means of the first closure 3, wherein the two chambers 73, 74 of the shaft 2 of the rotating hollow body 2 with the fabric 4 (static state) are partially filled, wherein the Fig. 11b is a cross section BB shown in FIG. 11 through the two chambers 73, 74 of the shaft 2 of the rotating hollow body 2 with the filled, distributed on the inner wall fabric 14th (dynamic state) shows. The shutters 3 and 12 are designed such that they lock the chamber casing 20 to form the radial balancing chambers 73 and 74. In Fig. 12 is a schematic longitudinal sectional view of a connected to a drive spindle 5 and in between 1 and drive spindle drive shaft 5 adapter 6 with the clamped on the clamping shaft 1, slender, tubular and designed as a shaft hollow body 2 with a cavity 7 in the form of three balanced at both ends hollow balancing chambers 70 and 73, 74, wherein the balancing chamber 70 is an axial balancing chamber in the cavity 7 and the balancing chambers 73, 74 as two located in the cavity 7, radially formed balancing chambers, wherein the two radial balancing chambers 73, 74 of axial balancing chamber 70 are arranged downstream of the end 9, wherein the first radial balancing chamber 73 within the second radial balancing chamber 74 is aligned, wherein the adjacent balancing chambers 70 and 73, 74 in the axial direction by a fourth closure 12 are separated from each other and wherein the clamping shaft 1 is fixed in the adapter 6 and thereby the Position of the hollow body 2 is vertical, wherein the one end 8 of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 are closed by the first shutter 3, wherein the two radial balancing chambers 73, 74 of the shaft 2 of the stationary hollow body. 2 (Static state) are partially filled with the substance 4 and wherein the two radial with the flowable substance 4 partially filled balancing chambers 73 and 74 are separated by a chamber jacket 20 from each other.

A schematic longitudinal section of a hollow tubular body 2, which is clamped on a drive spindle 5 directly by means of a clamping shaft 1 and has a cavity 7 in the form of three hollow balancing chambers 70 and 73, 74 sealed on both ends, is shown in FIG. 12a, wherein the balancing chamber 70 is an axial balancing chamber in the cavity 7 and the balancing chambers 73, 74 as two located in the cavity 7, radially formed chambers, wherein the two radial balancing chambers 73, 74 the axial balancing chamber 70 are arranged downstream of the end 9, wherein the first radial balancing chamber 73 is aligned within the second radial balancing chamber 74, wherein the adjacent balancing chambers 70 and 73, 74 are separated by a fourth shutter 12 and wherein the clamping shaft is fixed in the drive spindle 5 and while the position of the hollow body 2 is vertical, wherein the one end 8 of the hollow body 2 by means of the clamping shaft 1 and the other opposite free end 9 are closed by means of the first shutter 3, wherein the two balancing chambers 73, 74 of the shaft of the stationary hollow body 2 (static state) are partially filled with the fabric 4, wherein

12b shows a cross section C-C according to FIG. 12, 12a through the two balancing chambers 73, 74 of the shaft 2 of the rotating hollow body 2 (dynamic state) with the filled substance 14 distributed in each case on the inner wall.

A schematic longitudinal section shown in FIG. 13 has an adapter 6 located on a drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender, tubular and shaft-shaped hollow body 2 with a cavity 7 clamped on the clamping shaft 1 of three closed at both ends hollow balancing chambers 70 and 73, 74, wherein the balancing chamber 70 is an axial chamber in the cavity 7 and the balancing chambers 73, 74 as two located in the cavity 7, radially formed chambers, wherein the two radial balancing chambers 73, 74 the axial balancing chamber 70 are arranged downstream of the end 9, wherein the first radial balancing chamber 73 is aligned within the second radial balancing chamber 74, wherein the adjacent balancing chambers 70 and 73, 74 are separated by a fourth shutter 12 and wherein the clamping shaft is fixed in the adapter 6 and while the position of the hollow body 2 is horizontal wherein the one end 8 of the hollow body 2 is closed by means of the clamping shaft 1 and the other opposite free end 9 by means of the first closure 3, wherein the two balancing chambers 73, 74 of the shaft with the substance 4 of the resting hollow body 2 (static state) are partially filled and wherein the two radial balancing chambers 73 and 74 are radially separated from each other by a chamber jacket 20, wherein

13a is a schematic longitudinal section of a in a drive spindle 5 directly by means of a clamping shank 1 clamped, slender, tubular and designed as a shaft hollow body 2,

13b shows a cross section AA according to FIG. 13 through the two radial balancing chambers 73, 74 of the shaft of the resting hollow body 2 with the filled substance 4 in the static state and FIG. 13c shows a cross section AA according to FIG. 13 through the two radial balancing chambers 73 , 74 of the shaft of the rotating hollow body 2 in the dynamic state with the filled material 14 distributed on the inner wall.

In summary, the following can apply in advance:

The symmetrical cavity 7 may be located on the side opposite the one-sided fixed bearing.

The symmetrical cavity 7 can in the axial and radial directions in at least two balancing chambers 70, 71, 72; 73, 74 be shared. The symmetrical cavity 7 may be formed with respect to the axis of symmetry 75 with respect to multiple symmetry.

The cavity 7 in the form of a hollow shaft 2 may have an annular symmetrical or multi-symmetrical cross-section, wherein the cross-section of the hollow shaft 2 with respect to the axis of symmetry 75 is formed with multiple symmetry.

In FIG. 14, a schematic longitudinal section of an adapter 6 located on a drive spindle 5 and in a clamping shaft 1 and drive spindle 5 with the slender, tubular and shaft-shaped hollow body 2 with a cavity 7 and a clamped on the clamping shaft 1 shown in section shortened, closed hollow axial balancing chamber 71 shown in FIG. 14 and FIG. 14b, wherein the position of the hollow body 2 is horizontal and a part 15 of the clamping shaft 1 is inserted for improved support in the shaft 2 of the hollow body, optionally

14a shows a cross-section AA according to FIG. 14 through the second balancing chamber 71 of the shaft of the rotating hollow body 2 (dynamic state) with the filled material 40 distributed on the inner wall, the shell 13 of the shaft 2 having a square shape in cross-section having,

14b shows a cross-section AA according to FIG. 14 through the second balancing chamber 71 of the shaft of the rotating hollow body 2 (dynamic state) with the filled substance 40 distributed on the inner wall, the shell 13 of the shaft 2 having a hexagonal shape in cross-section has, and

14c shows a cross-section AA according to FIG. 14 through the second balancing chamber 71 of the shaft of the rotating hollow body 2 (dynamic state) with the filled material 14 distributed on the inner wall (dynamic state), wherein the jacket 13 of the shaft 2 is a has octagonal shape.

Finally, FIG. 15 shows a plurality of cross-sectional representations according to FIG. 14 by symmetrical separate balancing chambers, which are referenced multiple times to the axis of symmetry 75, similar to the cross-sectional representations in FIGS. 14 a, 14 b, 14 c

15a shows a cross section AA through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled material 14 (dynamic state) distributed on the inner wall, wherein the shaft 2 has an outer wall 16 in the cross section of a circle and an inner wall 17 in FIG Having a cross-section of a square shape,

15b shows a cross section AA through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled material 14 (dynamic state) distributed in each case on the inner wall, wherein the shaft 2 has an outer wall 16 in the cross section of a square shape and an inner wall 17 in cross-section of a circle,

Fig. 15c shows a cross section AA through the second balancing chamber 71 of the shaft 2 of the rotating hollow body 2 with the filled, each distributed on the inner wall fabric 14 (dynamic state), the shaft 2 a Outer wall 16 in cross-section of a circle and an inner wall in cross-section of a hexagonal shape,

Fig. 15d shows a cross section AA through the second balancing chamber 71 of the shaft 2 of the rotating hollow body 2 with the filled, each distributed on the inner wall fabric 14 (dynamic state), wherein the shaft 2 has an outer wall 16 in cross-section of a hexagonal shape and an inner wall 17 in cross-section of a circle,

15e shows a cross section AA through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled substance 14 (dynamic state) distributed in each case on the inner wall, wherein the shaft 2 has an outer wall 16 in a circular cross section and an inner wall 17 in FIG Has cross section of an octagonal shape, and

15f shows a cross section AA through the second balancing chamber 71 of the shaft of the rotating hollow body 2 with the filled substance 14 (dynamic state) distributed in each case on the inner wall, wherein the shaft 2 has an outer wall 16 in cross section of an octagonal shape and an inner wall 17 in cross-section of a circular shape, show.

The predetermined material of the hollow body 2 may be tough-elastic.

The predetermined material of the hollow body 2 may be brittle-elastic.

The balancing flowable material 4, 40 and the each applying in the dynamic state to the inner wall fabric 14 may be a mixture (solid / solid, solid liquid, liquid / liquid) to achieve a higher Auswuchtwirkung.

The hollow body 2 can be balanced in several levels. The hollow body 2 may be operable in all spatial positions. The hollow body 2 may be formed as a hollow shaft for a cutting tool and be used for high-speed machining of deep and filigree contours. The example, with the drive spindle 5 related, preferably used in a cutting part of the clamping tool hollow body 2 represents a hollow shaft, which is formed by the self-balancing, high-speed one-sided tightened hollow body 2, wherein the cutting part is designed freely depending on the purpose and the connection of the Blade part and the hollow shaft 2 is made detachable or insoluble.

The method for producing a body 2 with a one-sided fixed clamping in verschiebesteifer and tilt-stable storage for rotating into a supercritical speed range parts of a system 22, the at least one drive spindle 5, a chuck 1, 6 and the body 2 according to the invention taking into account Fig. 5 to 16 is,

wherein the body 2 is a hollow body in tubular form with a predetermined material whose bending vibration stimulation occurring during rotation is based on inaccuracies U resulting from manufacturing inaccuracies and storage inaccuracies and which has a symmetrical closed cavity 7 related to the geometric axis of symmetry 75, which also is completed towards its end faces 8, 9,

comprises the following steps according to the invention:

- Forming a one-sided and tilt-resistant and verschiebesteif mounted, related to the axis of symmetry 75 symmetrical, long, slender, tubular hollow body 2,

- Forming at least one balancing chamber 70, 71, 72, 73, 74 in the cavity 7 of the hollow body 2 by inserting one or more closures 3, 10, 11,

Determining the imbalance U of the hollow body 2 having at least one balancing chamber 70, 71, 72, 73, 74 by measuring with a balancing machine, Determination of a defined mass m _{s of} the flowable shapeless substance 4, 40, 14 to be introduced into a balancing chamber 70, 71, 72, 73, 74 by means of the equation

in at least one of the balancing chambers 70, 71, 72, 73, 74 such that a vibration damping in the subcritical rotational speed range and in the critical rotational speed range to ensure a damage-free fast resonance passage is achieved and after the passage of the resonance speed range, the unbalance U in the subsequent supercritical rotational speed range automatically is balanced and one

Vibration damping occurs in supercritical operation,

Introducing the defined mass ms of the flowable shapeless substance 4, 40, 14 into at least one of the balancing chambers 70, 71, 72, 73, 74 of the hollow body 2,

in which

U - the imbalance of the hollow body 2 without flowable material 4, 40,

m _s - the mass of the flowable substance 4, 40,

h ₀ - the height of the filling material of the flowable substance 4, 40,

h _K - the height or the length of the corresponding balancing chamber 70, 71, 72, 73, 74,

/ ?, - the inner radius of the balancing chamber 70, 71, 72, 73, 74 and

s - a safety factor

are. The balancing chambers 71, 72, 73, 74 associated with the first balancing chamber 70 are created by respectively closing the second balancing chamber 71 within the cavity 7 by means of a closure 10 after filling the flowable substance 4, 40 into the second balancing chamber 71, and into the resulting third balance chamber 72 a further defined mass m _{s of} the flowable material fes 4, 40 is filled, wherein the third balancing chamber 72 is closed by means of a further closure 11, wherein the process of creating the predetermined number of further balancing chambers 73, 74 is repeated with other closures 12.

In symmetrical, with at least one balancing chamber 70; 71, 72; 73, 74 formed hollow body 2, the respective filling mass m _{s of} the flowable shapeless substance 4, 40 is introduced, which during the speed acceleration in the balancing chambers 70; 71, 72; 73, 74 of the hollow body 2 distribute.

The formation of at least one balancing chamber 70 by closing with at least one closure 3 can be combined with the introduction of the calculated filling mass ms of the flowable substance 4, 40 at the same time.

The introduction of the filling material m _{s of} the flowable material 4, 40 can also be performed after closing the balancing chamber 70 by closable lateral wall openings (not shown) in the shaft 2 and / or in the closure 3, wherein the passage openings (not shown) to the introduction / filling are designed to be closed. When rotationally accelerating the hollow body 2, the introduced flowable shapeless substance 4, 40 can be deposited under the action of centrifugal force on the inner wall 17 of the hollow body 2 according to the effect of the imbalance U of the hollow body 2 as distributing substance 14. With the onset of the spin, a speed-dependent vibration excitation of the substance 4, 40 with simultaneous formation of a centrifugal force resulting pressure on the inner wall 17 of the balancing chambers 70, 71, 72, 73, 74, an application of the substance 14 to the inner wall 17. Under the training pressure, the compensation of imbalance U takes place automatically, the time that is used for this depends at least on the mass ms of the introduced flowable substance 4, 40, 14, its density, its viscosity and the rotational acceleration. By an internal friction of the flowable substance 4, 40, 14 a vibration damping acts during the rotational acceleration of the subcritical speed range up to the critical speed range.

The hollow body 2 mounted on one side and displaceable and tilt-rigidly rotates when passing through the subcritical and critical rotational speed range and in the supercritical rotational speed range without catching bearings.

In this case, the mass ms to be introduced of the flowable substance 4, 40 constitutes at least one function of the imbalance U of the hollow body 2, which is at least to be reduced and, in particular, eliminated. For the mass m _{s of} the flowable substance 4, 40 to be predetermined and to be determined it should be at least a mass value in the range between a minimum mass m _Sm , n and a maximum mass msmax- Mi a minimum mass msmin at least the imbalance U can be eliminated, the minimum mass m _{Sm / n} much smaller than that in the respective balancing chamber 70, 71, 72, 73 and / or 74 is completely to be filled mass ms. With a maximum mass msmax just the unbalance U should be able to be eliminated, wherein the maximum mass msmax of the flowable substance 4, 40 in each case is smaller than the mass ms to be completely filled into the respective balancing chamber chamber.

In the symmetrical, with at least one balancing chamber 71, 72; 73, 74 formed hollow bodies 2, the flowable formless material 4, 40 is introduced, in the balancing chamber 71, 72; 73, 74 of the stationary hollow body 2 stands / stores.

With the onset of the rotational acceleration, a speed-dependent oscillation excitation of the substance 4, 40 to the shape-changed substance 14 with simultaneous formation of a pressure / pressing when applying the substance 4, 40 to the applied material 14 to the inner wall 17 of the hollow body 2 can take place. Upon further rotational acceleration of the hollow body 2, the introduced informal flowable material 4, 40 can attach to applied material 14 under the action of centrifugal force on the inner wall 17 corresponding to the imbalance U of the hollow body 2.

Under the training, caused by the centrifugal force pressure inside a balance of imbalance U takes place automatically, the time that is needed, on the mass ms of the substance 4, 40, 14, its density and viscosity and the changing spin depends , The inventive, cantilevered and mounted hollow body 2 can rotate during passage / passage of the subcritical and critical speed range and in the supercritical speed range without catch storage at least in the free-side end portion 9 of the hollow body 2. As a result of the calculated mass m _{s of} at least one flowable substance 4, 40 introduced into at least one of the balancing chambers 70 of the cavity 7, the amplitude A of the oscillation (as shown in FIG. 18) remains at the critical, the resonance frequency of the first bending natural vibration as the rotational speed approaches representing rotational speed of the hollow body 2 so within limits that a damage-free passage of the resonance point is possible, with increasing speed in the supercritical speed range, the vibration behavior of the hollow body 2 stabilized by the fact that the balancing mass reverses its direction of action in the opposite direction to the unbalance U, where the displacement of the center of gravity of the common mass m + m _s is adjusted so that the center of gravity lies on the axis of rotation 76, wherein a self-balancing effect occurs and the smoothness and consequently the stability of the hollow body 2 increases.

In an application, the run-up of a high-frequency spindle 5 of the system is shown in FIG. 18 as an amplitude (A) / time (t) curve, with the use of the hollow body 2 according to the invention having at least one balancing chamber 70, 71, 72 The flowable shapeless material 4, 40, which is in flow, can run up to the supercritical rotational speed range in two to three seconds is realized. For this purpose, the time range 18 for the subcritical speed range, the time range 19 for the critical speed range and the time range 21 for the supercritical speed range are indicated. In the time domain 19, a deflection of the hollow body 2 is achieved with a double amplitude of 1, 2 mm, without causing damage to the hollow body 2.

As a result of the internal friction of the substance 4, 40, 14, it can be established that, as shown in FIG. 18, a continuous vibration damping from the subcritical rotational speed range (about 100 rpm) up to the supercritical rotational speed range (at about 18000 rpm and further) can be achieved by means of the calculated and at least in a balancing chamber 70 filled mass ms of the flowable substance 4.

Without the inventively filled in at least one of the balancing chambers 70, 71, 72, 73, 74 flow-like substance 4, 40 takes according to FIG. 18, the hollow body 2 on passage of the critical speed range (resonance point) damage and is likely close to the chuck / of the clamping shaft 1 cancel.

With the construction of the hollow body 2 according to the invention, a system or dynamic system 22 for self-stabilizing rapidly rotating symmetrical hollow bodies 2 mounted on one side up into the supercritical rotational speed range and its run-up is provided.

LIST OF REFERENCE NUMBERS

1 clamping shank / chuck

2 hollow body / shaft / hollow shaft

3 first closure

4 first flowable substance in the static state / compensation substance

40 second flowable material in the static state / compensation substance

5 drive spindle

6 adapters

7 cavity

70 first axial balancing chamber

71 second axial balancing chamber

72 third axial balancing chamber

73 first radial balancing chamber

74 second radial balancing chamber

75 geometric axis of symmetry of the hollow body

76 axis of rotation of the hollow body

8 first end, first end face

9 second end, second end face

10 second shutter

1 1 third closure

12 fourth lock

13 coat

14 flowable substance distributed on the wall in the dynamic state, whereby the material remains flowable

15 part of the clamping shaft

16 outer wall

17 inner wall

18 Time range for the subcritical speed range

19 Time range for the critical speed range

20 chamber jacket

21 Time range for the supercritical speed range

22 system / dynamic system L overhang length

D outer diameter / average outer diameter

m mass of the hollow shaft

m _s mass of the flowable substance / compensating substance / filling compound

U imbalance

AU residual imbalance

m - the mass of the hollow shaft

D - outer diameter

ά - inside diameter

k-kin ~ minimum wall thickness

k « ₅ as ^~ maximum wall thickness

O - coordinate origin

^M DA ~ Center of the outside diameter

W - geometric center of the shaft

5 - Center of gravity of the clamped hollow shaft

F - center of gravity applied to rotation in supercritical speed range

^■ a - total concentricity error or radial impact

ε - center of gravity eccentricity

e _w - relative eccentricity of the wall thickness

e ₃ it ~ the total eccentricity of the clamped hollow shaft

m _s mass (filling material) of the flowable substance

h ₀ height / length of the filling material of the flowable substance

h _K height / length of the balancing chamber

R, inner radius of the balancing chamber

s safety factor

Claims

claims

1. body with one-sided fixed restraint in verschiebesteifer and tilt-stable storage for up to a supercritical speed range rotating parts of a system (22), wherein the body is a hollow body (2) in tubular form with a predetermined material, which occurs during rotation bending vibration excitation Production inaccuracies and storage inaccuracies resulting imbalance U due to a local difference between the geometric axis of symmetry (75) of the hollow body (2) and a rotation axis (76) of the hollow body (2) based and one related to the geometric axis of symmetry (75) of the hollow body (2) symmetrical, closed cavity (7) has, which is also closed to its end faces (8, 9),

characterized,

in that formed as at least one balancing chamber (70, 71, 72, 73, 74) cavity (7) of the one-sided mounted and mounted hollow body (2) at least one flowable formless material (4, 40) having a defined mass ms in the balancing chamber (70, 71, 72, 73, 74) and the balancing chamber (70, 71, 72, 73, 74) is introduced partially filling,

wherein the mass m _{s of} the introduced flowable shapeless substance (4, 40) is defined such that a hollow body-related vibration damping in the subcritical and critical speed range and a resonance passage in the critical speed range can be achieved and that by the effect of the imbalance U of the hollow body (2) caused distribution of the substance (4, 40, 14) in the supercritical speed range, the effect of imbalance U taking into account a predetermined ratio between the mass ms of the substance (4, 40, 14) and the imbalance U

according to equation (V)

self-stabilizing compensates, in which

U - the imbalance of the hollow body (2) without flowable material (4, 40), m _s - the mass of the flowable substance (4, 40),

h ₀ - the height of the filling material of the flowable substance (4, 40),

h _K - the height / length of the balancing chamber (70, 71, 72, 73, 74),

Ri - the inner radius of the balancing chamber (70, 71, 72, 73, 74) and s - a safety factor

are.

Body according to claim 1,

characterized,

in that the hollow body (2) is a slender long body whose ratio between cantilever length L and mean outer diameter D is greater than "fifteen" with UD> 15.

Body according to claims 1 and 2,

characterized,

in that the state of aggregation of the flowable substance (4, 40, 14) in the balancing chambers (70, 71, 72, 73, 74) remains both at rest and in all speed ranges under pressure and vibration.

Body according to claim 1,

characterized,

that the flowable under pressure informal fabric (4, 40, 14) remains fluid.

Body according to claims 3 and 4,

characterized,

that the flowable shapeless material (4, 40, 14) is optionally fine-grained sand with a grain size of less than 1 mm.

Body according to claim 1,

characterized, the flowable shapeless material (4, 40, 14) has a higher density than the density of the shaft material of the hollow body (2).

7. body according to claim 1,

characterized,

in that the balancing flowable substance (4, 40, 14) introduced into the balancing chambers (70, 71, 72, 73, 74) is a substance mixture.

8. Body according to claim 1,

characterized,

the symmetrical cavity (7), which is related to the axis of symmetry (75), is located at least on the side opposite the one-sided fastening. 9. body according to claim 1,

characterized,

in that the symmetrical cavity (7), which is related to the axis of symmetry (75), is divided in axial and radial directions into a plurality of balancing chambers (70, 71, 72, 73, 74) in order to achieve a higher damping and balancing effect with the flowable substance.

10. body according to claim 1,

characterized,

that the symmetrical cavity (7), which is related to the axis of symmetry (75), is of multiple symmetrical design.

11. body according to claim 1,

characterized,

that the cavity (7) in the form of a hollow shaft (2) has an annular symmetrical or multi-symmetrical cross section, wherein the cross section of the hollow shaft (2) is designed to be multi-symmetrical.

12. body according to claim 1, characterized,

that the material of the hollow body (2) is viscoelastic.

13. body according to claim 1,

characterized,

that the material of the hollow body (2) is brittle-elastic.

14. body according to claims 1 to 13,

characterized,

that the mass ms of at least one flowable substance (4, 40, 14) introduced into at least one of the balancing chambers (70, 71, 72, 73, 74) of the cavity (7) determines the amplitude of the oscillation as the rotational speed approaches the critical one, The resonant frequency of the first bending natural vibration representing speed of the hollow body (2) remains limited so that a passage of the resonance point is possible, with increasing speed in the supercritical speed range, the oscillatory behavior of the hollow body (2) stabilized by the fact that the balancing mass their direction of effect Opposite direction to the unbalance U reverses, wherein the shift of the center of gravity of the common mass m + ms is set so that the focus is on the axis of rotation (76), wherein a self-balancing effect occurs and the smoothness and thus the stability of the hollow body (2) elevated.

15. body according to claim 1,

characterized,

the hollow body (2) can be dynamically balanced during operation in several planes.

16. body according to claim 1,

characterized,

that the self-stabilizing hollow shaft (2) is made of solid material.

17. body according to claim 1,

characterized,

that the self-stabilizing hollow shaft (2) is made of lightweight material.

18. Body according to at least one of claims 1 to 17,

characterized,

that the hollow body (2) is designed as a hollow shaft for a clamping tool fastened to the free end (9) of the hollow body (2) and can be used for high-speed machining of deep and filigree contours.

19. Body according to claim 18,

characterized,

in that the hollow body (2), which is connected to a drive spindle (5) and inserted into a cutting part of a cutting tool, forms a hollow shaft which is formed by the self-balancing, high-speed, one-sidedly stretched long slim hollow body (2) with the ratio UD> 15, the cutting part is designed freely depending on the purpose and the connection of the cutting part and the hollow shaft (2) is made detachable or non-detachable.

20. A method for producing a body with a one-sided fixed restraint in non-displaceable and tilt-resistant storage for up to a supercritical rotational speed range rotating parts of a system (22),

wherein the body according to claims 1 to 19

represents a hollow body (2) in a tubular shape with predetermined material whose occurring during a rotation bending vibration excitation based on manufacturing inaccuracies and storage inaccuracies resulting imbalance U and one on the geometrical axis of symmetry (75) related, symmetrical enclosed cavity (7), which also its end faces (8, 9) is completed out,

characterized by the following steps: - Forming a one-sided and tilt-resistant and verschiebesteif mounted on the symmetry axis (5) related symmetrical, long, slender, tubular hollow body (2),

- forming at least one balancing chamber (70, 71, 72, 73, 74) in the cavity (7) of the hollow body (2),

Determining the imbalance U of the hollow body (2) having at least one balancing chamber (70, 71, 72, 73, 74) by measuring with a balancing machine,

Determination of a defined mass ms of the flowable shapeless substance (4, 40, 14) to be introduced by means of the equation

in at least one of the balancing chambers (70, 71, 72, 73, 74) such that a vibration damping in the subcritical rotational speed range and in the critical rotational speed range is achieved to ensure a resonance passage and after the passage of the resonance speed range the unbalance U in the supercritical rotational speed range is compensated automatically and vibration damping occurs in supercritical operation,

- Introducing the flowable, shapeless substance (4, 40, 14) in at least one of the balancing chambers (70, 71, 72, 73, 74) of the hollow body (2) corresponding to the defined mass m _s of flowable formless material (4, 40, 14)

in which

h ₀ - the height of the filling material of the flowable substance (4, 40),

h _K - the height / length of the balancing chamber (70, 71, 72, 73, 74),

Rj - the inner radius of the balancing chamber (70, 71, 72, 73, 74) and

s - a safety factor are.

21. The method according to claim 20,

characterized,

in that at least one balancing chamber (71, 72, 73, 74) assigned to the balancing chamber (70) is created by the first balancing chamber (71) being filled by filling the flowable substance (4) into the first balancing chamber (71) by means of a closure (10 ) is sealed within the cavity (7), and in the resulting second balancing chamber (72) a further defined mass m _{s of} the flowable material (4, 40) is filled, said second balancing chamber (72) by means of a further closure (11) is closed, wherein the process of creating the predetermined number of balancing chambers (73, 74) is repeated with other closures (12). 22. The method according to claim 21,

characterized,

in that the flowable shapeless material (4, 40) is introduced into symmetrical hollow body (2) formed with at least one balancing chamber (70; 71, 72; 73, 74), which is located in the balancing chamber (70; 71, 72; 74) of the stationary hollow body (2) distributed.

23. Method according to claims 20 to 22,

characterized,

that during the rotational acceleration of the hollow body (2) the introduced flowable shapeless material (4, 40) under the action of centrifugal force on the inner wall (17) of the hollow body (2) according to the effect of imbalance U of the hollow body (2) as distributing Material (14) is deposited.

24. The method according to claim 20,

characterized,

that with the onset of the rotational acceleration a speed-dependent vibration excitation of the substance (4, 40, 14) with simultaneous formation of a centrifugal force generated by the pressure on the inner wall (17) the balancing chambers (70, 71, 72, 73, 74) an application of the substance (14) to the inner wall (17).

25. The method according to claim 24,

characterized,

that under the pressure forming the compensation of imbalance U takes place automatically, the time that is needed, at least on the mass ms of the introduced flowable substance (4, 40, 14), its density, its viscosity and the spin depends.

26. Method according to claims 20 to 25,

characterized,

that by an internal friction of the flowable material (4, 40, 14) a vibration damping during the spin from the sub-critical speed range up to the critical speed range acts.

27. Method according to claims 20 to 26,

characterized,

that the hollow body (2) fastened on one side and displaceably stiff as well as tilting rigidly rotates when traversing the subcritical and critical rotational speed range and in the supercritical rotational speed range without catching bearing.