A turbomachine rotor with improved rotor dynamics, turbomachine including the rotor, and method

Abstract

The compressor rotor comprises a rotor shaft and a plurality of impellers axi- ally positioned along the rotor shaft between a first shaft end and a second shaft end. At least one dummy element is positioned along the rotor shaft between the first shaft end and the second shaft end. The dummy element is adapted to modify at least one rotordynamic characteristic of the rotor. Disclosed herein is also a compressor includ- ing the rotor and a method for assembling the rotor.

Description

A TURBOMACHINE ROTOR WITH IMPROVED ROTOR DYNAMICS, TURBOMACHINE INCLUDING THE ROTOR, AND METHODDESCRIPTIONTECHNICAL FIELD

[0001] The present disclosure relates to turbomachines and relevant components thereof, specifically rotors. Embodiments disclosed herein concern in particular dynamic compressors, and rotors of dynamic compressors, especially centrifugal compressors.BACKGROUND ART

[0002] Dynamic compressors, such as axial and centrifugal compressors, operate at high rotary speed, often higher than the speed corresponding to the first bending mode frequency of the compressor rotor (i.e. so-called supercritical rotor). This means that during startup the rotor must cross one or more critical speeds to reach the design rotation speed. Typically, the rotor needs to cross the first rigid mode, the second rigid mode and the first bending mode frequencies. According to design rules, a sufficient separation margin shall be maintained between the design rotation speed and the closest bending mode frequency of the compressor rotor.

[0003] Similar issues may arise in other sectors of the turbomachine technology, such as axial compressors, as well as axial and radial turbines.

[0004] Magnetic actuators used as active magnetic bearings are nowadays often adopted for supporting fast-rotating machines, including axial and centrifugal compressors. Active magnetic bearings provide efficient friction reduction and vibration damping and control. They include position sensors and current sensors as well as a controller, aimed at adjusting the current flowing through the coils of the magnetic bearing, to reduce vibrations and displacement of the rotary shaft. For an active magnetic bearing to function effectively, the rotor vibrational modes must be both observable and controllable. Observability refers to the control system ability to detect displacements caused by the rotor vibrational modes through sensors positioned along the rotary shaft. Conversely, controllability is the bearing capacity to apply correctiveforces to the shaft, thereby mitigating the displacements induced by the vibrational modes.

[0005] The rotordynamic behavior of a turbomachine rotor, specifically of a compressor rotor, plays a crucial role in ensuring its proper and safe operation. Additionally, it is essential for enabling the bearings to effectively suppress vibrations. Rotordynamic behavior of the compressor rotor may change when the operating conditions change. For example, a variation in the flowrate of the process fluid, or in the pressure and pressure ratio can affect the rotordynamic behavior of the compressor. The chemical and physical characteristics of the process gas may also have an impact on the compressor rotordynamics. For example, a different density of the process gas may influence the rotordynamic behavior of the compressor.

[0006] Designing a turbomachine, such as a compressor, from scratch for a specific application is a complex, expensive, and time-consuming process. Therefore, it would be highly advantageous to adapt the rotordynamics of a compressor to varying operating conditions without requiring a complete redesign of the compressor or of components thereof, such as the impellers.SUMMARY

[0007] According to a first aspect, disclosed herein is a turbomachine rotor comprising a rotor shaft and a plurality of rotary stage components, which are axially positioned along the rotor shaft between a first shaft end and a second shaft end. At least one dummy element is positioned along the rotor shaft between the first shaft end and the second shaft end. The dummy element is adapted to modify at least one rotordynamic characteristic of the rotor.

[0008] In general terms, as understood herein a rotary stage component is a component which rotates around the rotation axis of the turbomachine and interacts with a process fluid to exchange energy therewith. If the rotor is a compressor rotor, the rotary stage component includes a rotor disk or an impeller, for example. If the turbomachine is a radial machine, such as a centrifugal compressor or a radial turbine, the rotary stage component is usually an impeller.

[0009] According to an aspect, disclosed herein is a stacked rotor for a turbomachine, the stacked rotor comprising: a first shaft portion, a second shaft portion, a plurality of impeller stacked between the first shaft portion and the second shaft portion, at least one dummy element along the stacked rotor, between the first shaft portion and the second shaft portion, and a tie rod connecting the first shaft portion and the second shaft portion, the tie rod extending through the plurality of impellers and said at least one dummy element. Disclosed herein is further a turbomachine including a casing and a stacked rotor with a dummy element as defined herein, supported for rotation in the casing.

[0010] In certain embodiments disclosed herein the turbomachine rotor comprises a rotor shaft having: a first shaft portion forming a first shaft end; a second shaft portion forming a second shaft end. A tie rod connects to one another the first shaft portion and the second shaft portion to one another. The rotor further includes a plurality of rotary stage components axially positioned along an axis of the rotor shaft, and stacked between the first shaft portion and the second shaft portion. The tie rod extends through the plurality of rotary stage components. Torsional coupling features, such as Hirth couplings, are positioned between adjacent rotary stage components, between the first shaft portion and a first rotary stage component of said plurality of rotary stage components, and between the second shaft portion and a last rotary stage component of said plurality of rotary stage components. To set or modify at least one rotordynamic characteristic of the rotor, at least one dummy element is positioned along the rotor shaft.

[0011] Specifically in one embodiment the at least one dummy element is positioned between two sequentially arranged rotary stage components, and torsional coupling features mechanically connect the at least one dummy element to the two sequentially arranged rotary stage components in a torsional fashion, such that a torque can be transmitted therebetween.

[0012] In another embodiment the at least one dummy element is positioned between the first shaft portion and the first rotary stage component, torsional coupling features mechanically coupling the at least one dummy element to the first shaft portion and the first rotary stage component.

[0013] In yet another embodiment, the at least one dummy element is positioned between the last rotary stage component and the second shaft portion, torsional coupling features mechanically coupling the at least one dummy element to the last rotary stage component and the second shaft portion.

[0014] These embodiments can be combined to one another, if more than one dummy element is provided. For example, one dummy element may be positioned between two sequentially arranged, i.e. adjacent, rotor stage components and a further dummy element may be positioned between one, the other, or both the first and second shaft portions and the adjacent rotary component. In yet further embodiments, more than one dummy element may be positioned between respective pairs of consecutive rotary stages. In other embodiments a first dummy element may be positioned between the first shaft portion and the first rotary component and a second dummy element may be positioned between the last rotary component and the second shaft portion, with or without one or more dummy elements arranged between adjacent rotary components.

[0015] The stacked rotor configuration disclosed herein is particularly advantageous in combination with one or more dummy elements added to a basic rotor structure for changing, adjusting, or modifying rotordynamic characteristics of the rotor. In the stacked rotor configuration, a dummy element may be selectively disposed at any desired position between adjacent stacked components forming the rotor, without requiring redesign of the rotor structure.

[0016] According to another aspect, disclosed herein is a turbomachine, comprising: a casing; and a turbomachine rotor as set forth above, supported for rotation in said casing by a bearing arrangement. In embodiments disclosed herein the turbomachine can be a compressor, in particular a centrifugal compressor. In advantageous embodiments, the rotor is supported by active magnetic bearings.

[0017] According to yet another aspect, the present disclosure relates to method for assembling a turbomachine rotor, such as in particular, but not exclusively, a centrifugal compressor rotor. The method may include the following steps:• positioning a plurality of rotary stage components, a first shaft portion forming a first shaft end, and a second shaft portion forming a second shaft end along an axis;• positioning at least one dummy element along the axis:• connecting the first shaft portion to the second shaft portion with a tie rod extending through the at least one dummy element and the rotary stage components; and• torsionally coupling to one the first shaft portion, the rotary stage components, the second shaft portion, and the at least one dummy element with respective torsional coupling features therebetween.

[0018] The at least one dummy element may be positioned: between two sequentially arranged rotary stage components; or between the first shaft portion and a first one of said rotary stage component; or between a last one of said rotary stage components and the second shaft portion.

[0019] According to a further aspect, disclosed herein is a turbomachine, such as a centrifugal compressor, comprising a casing and a turbomachine rotor supported for rotation in said casing by a bearing arrangement. The bearing arrangement comprises active magnetic bearings. The turbomachine rotor comprises a rotor shaft having a first shaft end and a second shaft end: The rotor further comprises a plurality of rotary stage components, such as centrifugal impeller, axially positioned along the rotor shaft between the first shaft end and the second shaft end. The turbomachine rotor further comprises at least one dummy element positioned along the rotor shaft between the first shaft end and the second shaft end. The dummy element is adapted to modify at least one rotordynamic characteristic of the rotor.

[0020] Further features and embodiments of the rotor, the turbomachine and the method of the present disclosure are set forth in the appended claims and described below with reference to the attached drawings.BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Reference is now made briefly to the accompanying drawings, in which:Fig.l illustrates a sectional view of a centrifugal compressor along a plane containing the rotation axis;Fig.2 illustrates a sectional view of the rotor of a centrifugal compressor; Fig.3 illustrates a sectional view of the rotor of Fig.2 with dummy elementsinserted along the rotor shaft;Fig.4 illustrates a schematic of a rotor;Fig.5 illustrates a Bode diagram at the active magnetic bearings of the rotor of Fig.4;Fig.6 illustrates the same rotor of Fig.4 with one dummy element added; Fig.7 illustrates a Bode diagram at the active magnetic bearings of the rotor of Fig.6;Fig.8 illustrates a rotor similar to the rotor of Fig.4 with three dummy elements added;Figs.9 and 10 illustrate the Bode diagram at the active magnetic bearings of the rotor of Fig.8 with the dummy elements removed (Fig.9) and with the dummy elements added (Fig.10);Fig.11 illustrates the same rotor of Fig.4 with two dummy elements added; Fig.12 illustrates a Bode diagram at the active magnetic bearings of the rotor of Fig.11; andFigs 13 and 14 illustrate the effect of the addition of dummy elements as on controllability and observability of the vibration modes.DETAILED DESCRIPTION

[0022] In summary, it is proposed to adapt the rotor of a turbomachine to varying operating conditions, without redesigning the rotor or parts thereof. The rotor is modified by adding one or more dummy elements along the rotor shaft. A dummy element, as understood herein, is generally an axially symmetric component that does not affect the process gas flow but changes the rotordynamics of the turbomachine to cope with an operating condition that is different from the condition for which the compressor or other turbomachine was originally designed.

[0023] The following detailed description relates to a centrifugal compressor, and more particularly to a centrifugal compressor including active magnetic bearings. However, those skilled in the art of turbomachinery will understand that aspects of the present disclosure may be applied also to other turbomachinery, where similar issues arise.

[0024] Turning now to the drawings, an exemplary embodiment of a centrifugalcompressor, in which the novel features disclosed herein can be implemented, is shown in Fig.l, in a sectional view along a plane containing a rotation axis A-A of the compressor rotor.

[0025] The compressor 1 comprises a casing 3 and a rotor 5 supported in the casing 3 by means of bearings 7, 9. The bearings 7, 9 preferably include active magnetic bearings or other active bearings, adapted to control the vibration of the rotor 5.

[0026] In the embodiment disclosed herein the compressor is a multi-stage compressor and the e rotor 5 comprises therefore a plurality of impellers 6 arranged in sequence along a compression path extending from a compressor inlet 11 to a compressor discharge 13. Each impeller 6 represents a respective rotary stage component of the turbomachine 1. The casing 3 houses a compressor bundle 17 comprising diaphragms, with diffusers 16 and return channels 18 of the several compressor stages. Reference 19 indicates a volute arranged downstream of the last, i.e. most downstream, diffuser 16 which extends around the most downstream impeller 6.

[0027] The rotor 5 is shown in a side view in Fig.l, and in a sectional view in Fig.2, where the stationary components of the compressor are omitted. As best shown in Fig.2, in some embodiments the rotor 5 comprises a rotor shaft 20 including a first shaft portion 21 and a second shaft portion 23. The first shaft portion 21 features, i.e., forms a first shaft end 21.1 and the second shaft portion 23 features, i.e. forms a second shaft end 23.1. The impellers 6 are positioned between the first shaft portion 21 and the second shaft portion 23. The first shaft portion 21, the impellers 6 and the second shaft portion 23 are axially stacked along the rotation axis A-A. Therefore, in this embodiment, the rotor is a so-called stacked rotor.

[0028] In some embodiments, the first shaft portion 21, the second shaft portion 23 and the impellers 6 therebetween can be connected to one another by a tie rod arrangement. In the embodiment of Fig.2 the tie rod arrangement comprises a single tie rod 25 coaxial with the rotation axis A-A. Opposite ends 25.1, 25.2 of the tie rod 25 are mechanically coupled to the first shaft portion 21 and to the second shaft portion 23, respectively.

[0029] Torsional coupling features are positioned between each pair of adjacentcomponents forming the rotor 5, i.e. between the first shaft portion 21 and the most upstream impeller 6, between adjacent impellers 6, and between the most downstream impeller 6 and the second shaft portion 23. The torsional coupling features may include Hirth couplings, i.e. front teeth meshing with one another, or other couplings adapted to transmit a torque between mutually adjoining components of the rotor 5.

[0030] The shaft portions 21 and 23 have outer generally cylindrical surfaces coacting with the active magnetic bearings 7, 9 and with dry gas seals or other seal arrangements 31, 33 (Fig.l) positioned inboard of the respective active magnetic bearings 7, 9. One of the first shaft portion 21 and second shaft portion 23 is adapted to be drivingly coupled to a driver, e.g. a gas turbine, an electric motor, a steam turbine or another driver, not shown. In the exemplary embodiment, the second shaft portion 23 is configured for coupling to the driver. The second shaft portion 23 is also referred to as the drive end of the rotor 5, in contrast to the first shaft portion 21, which is also referred to as non-drive end of the rotor 5. Thus, the bearing 7 is the drive-end bearing, and the bearing 9 is the non-drive end bearing. One or the other of said bearings 7, 9 can include a radial bearing and the other of said bearings 7, 9 can include a radial bearing and an axial bearing.

[0031] The rotor 5 configured as shown in Figs. 1 and 2 is characterized by some critical speeds corresponding to the frequencies of the rotor vibration modes. Since the first two rigid modes are not visible in the rotor frequency response (i.e. in Figs. 5 and 7, described below) the lower critical speed corresponds to the first bending mode frequency. Detecting rotor vibrations and, when necessary, suppressing them through the use of active magnetic bearings can be crucial under various operating conditions.

[0032] The operating conditions can vary for example depending upon the physical characteristics of the circuit in which compressor 1 is positioned, and / or based on physical or chemical features of the process gas. Changing the operating condition may result in a need to operate the compressor too near to one of the critical speeds, e.g. the first or the second critical speed. It would be advantageous to modify the structure of the rotor to enhance the rotordynamic characteristics thereof, such as by adjusting the first and / or the second critical speeds of the rotor. This improvement would help ensure safer operation at the desired operating speed.

[0033] Therefore, starting from the design shown in Figs. 1 and 2, it may be useful under certain circumstances to change the structure of rotor 5 and thereby increasing or decreasing at least the first, or at least the second, or both the first and the second critical speeds thereof and / or changing one or more modal shapes of the rotor, specifically the modal shape of the first bending mode and of the second bending mode.

[0034] According to the present disclosure, this can be achieved by introducing one or more dummy elements along the rotor 5.

[0035] The dummy element(s) shall be dimensioned and positioned correctly to achieve the desired rotordynamic features of rotor 5. The dimensions, shape, weight, and position of the dummy element(s) useful to achieve the desired final behavior of rotor 5 can be determined based on simulations and analysis.

[0036] As mentioned, in general terms a dummy element is a mechanical component which is axial symmetrical and which affects the rotordynamic of the rotor, without modifying the interaction between the rotor and the process gas flow. In general, therefore, the dummy elements do not contact the flow path and do not alter the manner in which the compressor acts on the process gas.

[0037] The stacked structure of the rotor 5 is particularly advantageous in view of this approach for changing the rotodynamic features of rotor 5, since a dummy element can be simply interposed between two sequentially arranged impellers 6, or between one of the shaft portions 21, 23 and the respective adjacent (first or last) impeller 6. The addition of a dummy element simply requires replacement of tie rod 25 with a longer tie rod and the adaptation of the stationary bundle inside the casing 3. It is usual practice in compressor designs, to configure the casing such that different bundles can be housed therein. Thus, the structure of casing 3 does not need to be changed.

[0038] In Fig.3 a schematic arrangement of rotor 5 including three additional dummy elements is shown by way of non-limiting exemplary embodiment. The dummy elements are labeled 41, 42 and 43. They are interposed between adjacent impellers 6, and specifically between the second and third impeller, between the fifth and sixth impeller and between eight and ninth impeller. In other embodiments, one or two dummy elements can be interposed between the first shaft portion 21 and the firstimpeller 6, and between the second shaft portion 23 and the last impeller 6.

[0039] Each dummy element 41, 42, 43 comprises an axially symmetrical body which can have a central through hole, through which the tie rod 25 extends. Torsional coupling features are provided on the opposite front ends of each dummy element 41, 43, 45, providing a torsional connection with the adjacent component (the shaft portion or the impeller) of rotor 5. In some embodiments, the torsional coupling features include Hirth couplings complementary to the Hirth couplings of the adjacent impeller 6 or of the adjacent shaft portion 21, 23.

[0040] As detailed below, the insertion of one or more dummy elements can produce one or both the following effects: altering the frequencies of one or more critical speeds, adjusting the bending mode shape of one or more bending modes, particularly the shape of the second bending mode and modifying the location of the relevant nodes, i.e. the points along the vibrating structure where the amplitude of the radial vibration is zero.

[0041] The first effect can be beneficial because it can increase the distance between the operational speed and the adjacent critical speed(s), thereby reducing the risk of exciting the corresponding vibrational mode of the rotor.

[0042] The second effect can be beneficial as it can enhance the controllability and observability of one or more problematic rotor modes.

[0043] Additionally, lowering the critical speed(s) can lead to more efficient vibration reduction, as actuators tend to be more effective at lower frequencies due to their higher dynamic capacity.

[0044] For a better understanding of the design approach disclosed herein, a first configuration of dummy elements and the effect thereof are described with reference to Figs. 4, 5, 6 and 7. Fig.4 illustrates a schematic representation of a rotor 5 with six impellers 6, without dummy elements there along. Fig.5 illustrates the Bode diagrams for the active magnetic bearings at the drive end and at the non-drive end of the rotor. The Bode diagram at the drive end is shown at DE and the diagram at the non-drive end is shown at NDE. The rotational speed expressed in Hz is plotted on the horizontalaxis , and the magnitude of the displacement at the bearing (absolute value) is plotted on the vertical axis. OF is a desired operational frequency range around 100 Hz. The first bending mode (i.e. the first critical speed) is at around 61 Hz and the second bending mode (i.e. the second critical speed) is at around 124 Hz.

[0045] Fig.6 illustrates the same rotor 5 of Fig. 4, with the addition of a dummy element 41 in a central position, corresponding to the node of the second bending mode. Fig.7 illustrates the resulting Bode diagram at the bearings and corresponds to the diagram of Fig.5. As can be seen by comparing Figs. 5 and 7, the effect of the dummy element 41 is a reduction of the first bending mode frequency, which drops from 61 to 40 Hz. The dynamic capacity of the actuators of the active magnetic bearings supporting the rotor 56 increases because of the frequency decrease. Moreover, the operation frequency range OF is more distant from the first critical speed. The adjustment of the first bending mode frequency thus obtained improves the rotodynamic performance of the compressor.

[0046] A similar effect is illustrated in Figs. 8, 9 and 10, wherein Fig.8 illustrates a rotor 5 with four impellers 6 and four dummy elements 40 added along the rotation axis. Figs. 9 and 10 illustrate the effect o the bode diagram, wherein Fig.9 illustrates the Bode diagram of the rotor without the dummy elements 40 and Fig. 10 illustrates the Bode diagram of the rotor with the dummy elements 40 added thereto.

[0047] Referring to Figs. 11 and 12, a different effect on the rotodynamic of compressor rotor 5 is shown, which may be beneficial in some instances. The rotor shown schematically in Fig.l 1 is the same rotor shown in Fig.4, but with the addition of two dummy elements 40 positioned at the nodes of the first bending mode. Fig.12 illustrates, similarly to Fig. 5, the Bode diagrams at the active magnetic bearings in this configuration. As an effect of the insertion of the two dummy elements 40, the first critical speed (i.e. the first bending mode frequency) drops from around 61 Hz to around 50 Hz, while the second critical speed drops from around 124 Hz to around 73 Hz. The operation frequency range OF is now above the second critical speed and distanced therefrom.

[0048] This adjustment increases the possible operational frequency range, and further enables the controller of the active magnetic bearings to manage the secondbending mode with a higher dynamic capacity, due to the reduced frequency of the second bending mode.

[0049] The addition of dummy elements along the rotor may be used not only to adjust the bending mode frequencies and to adapt them to differing operating conditions but can be beneficial also in terms of observability and controllability of the rotor vibration, specifically when active magnetic bearings are used for supporting the rotor.

[0050] Active magnetic bearings can be used to make the rotor suspend stably through an active feedback control using displacement sensors. The sensors combined with an active magnetic bearing can detect a displacement of the shaft due to vibration and can control the currents flowing in the active magnetic bearings to reduce rotor vibration. An active feedback control can only operate correctly if the sensors are positioned such as to be able to observe, i.e. detect, the shaft displacement due to the rotor modes (so-called “observability”) and if the active magnetic bearings are positioned such that their action can reduce vibration of the shaft (so-called “controllability”).

[0051] In some circumstances, if the node of the modal shape to be controlled falls near or at the position where the sensor is placed, observability is poor or can be lost. If the node is too near or at the position of the active magnetic bearing, controllability is prejudiced.

[0052] Since the rotor components and operating conditions are determined prior to the control design of the active magnetic bearings, the placement of sensors and bearings may not be sufficiently far from the expected nodes of the modal shapes of interest, typically the first and second modal shapes, to achieve optimal performance.

[0053] Properly dimensioned and positioned dummy elements can be used, in such case, to re-position the nodes of the modal shapes such as to improve observability and controllability. This effect is illustrated in Figs. 13 and 14, where the rotor of Fig.8 without and with dummy elements is illustrated. More specifically, Fig.13 illustrates the rotor without dummy elements and Fig.14 illustrates the same rotor with the insertion of four dummy elements 40. The second modal shape is shown at M and Nl, N2, N3 are the nodes thereof. Reference number 61 designates the positions of the bearingsensors, and 63 designates the positions of the bearings.

[0054] As can be seen in Fig.13, node N1 is located at the position of the left-hand sensor (61), while the node N3 is located at the position of the right-hand bearing (63). Under these circumstances, displacements of the left-hand end of the shaft cannot be properly detected by the respective sensor, and the displacements of the right-hand end of the shaft cannot be properly controlled by the respective active magnetic bearing.

[0055] The insertion of the dummy element 40 modifies the modal shape (M), as shown in Fig.14, such that the first node N1 is moved away from the position of the sensor (61) and the third node N3 is moved away from the center of the bearing (63), such that observability and controllability are restored or improved.

[0056] Exemplary embodiments have been disclosed above and illustrated in the accompanying drawings. It will be understood by those skilled in the art that various changes, omissions and additions may be made to that which is specifically disclosed herein without departing from the scope of the invention as defined in the following claims.

Claims

CLAIMS1. A turbomachine rotor, comprising:a rotor shaft having: a first shaft portion forming a first shaft end; a second shaft portion forming a second shaft end; and a tie rod interconnecting the first shaft portion and the second shaft portion to one another;;a plurality of rotary stage components axially positioned along an axis of the rotor shaft, between the first shaft end and the second shaft end;; wherein the rotary stage components are stacked between the first shaft portion and the second shaft portion, the tie rod extending through the plurality of rotary stage components;torsional coupling features between adjacent rotary stage components, between the first shaft portion and a first rotary stage component of said plurality of rotary stage components, and between the second shaft portion and a last rotary stage component of said plurality of rotary stage components; andat least one dummy element adapted to modify at least one rotordynamic characteristic of the rotor; wherein the at least one dummy element is positioned:between two sequentially arranged rotary stage components, torsional coupling features mechanically coupling the at least one dummy element to said two sequentially arranged rotary stage components: orbetween the first shaft portion and the first rotary stage component, torsional coupling features mechanically coupling the at least one dummy element to the first shaft portion and the first rotary stage component; orbetween the last rotary stage component and the second shaft portion, torsional coupling features mechanically coupling the at least one dummy element to the last rotary stage component and the second shaft portion.

2. The turbomachine rotor of claim 1, wherein the torsional coupling features comprise Hirth couplings.

3. The turbomachine rotor of claim 1 or 2, wherein the at least one dummy element comprises an axially symmetrical body.

4. The turbomachine rotor of claim 3, wherein the at least one dummy element comprises: an outer side surface of revolution; a first front surface with first torsional coupling features; a second front surface with second torsional couplingfeatures; and an axial through hole.

5. The turbomachine rotor of claim 4, wherein the first torsional coupling features and the second torsional coupling features of the at least one dummy element comprise Hirth couplings.

6. The turbomachine rotor of any preceding claim, wherein the at least one dummy element is configured to modify:a frequency of at least one bending mode of the turbomachine rotor compared to the case of the same turbomachine rotor without said dummy element; or a modal shape of at least one bending mode of the turbomachine rotor compared to the case of the same turbomachine rotor without said dummy element; or a combination thereof.

7. The turbomachine rotor of claim 6, wherein the at least one bending mode includes the first bending mode, or the second bending mode, or both the first bending mode and the second bending mode.

8. The turbomachine rotor of any one of the preceding claims, wherein the turbomachine rotor is a compressor rotor.

9. The turbomachine rotor of claim 8, wherein the compressor rotor is a centrifugal compressor rotor, and wherein the rotary stage components are centrifugal compressor impellers.

10. A turbomachine, comprising:a casing; anda turbomachine rotor according to any one of the preceding claims, supported for rotation in said casing by a bearing arrangement.

11. The turbomachine of claim 10 wherein the turbomachine is a compressor, in particular a centrifugal compressor.

12. The turbomachine of claim 10 or 11, wherein the bearing arrangement comprises active magnetic bearings.

13. A method for assembling a turbomachine rotor, comprising thefollowing steps:positioning a plurality of rotary stage components, a first shaft portion forming a first shaft end, and a second shaft portion forming a second shaft end along an axis;positioning at least one dummy element along the axis :between two sequentially arranged rotary stage components; or between the first shaft portion and a first one of said rotary stage component; orbetween a last one of said rotary stage components and the second shaft portion;connecting the first shaft portion to the second shaft portion with a tie rod extending through the at least one dummy element and the rotary stage components; andtorsionally coupling to one the first shaft portion, the rotary stage components, the second shaft portion, and the at least one dummy element with respective torsional coupling features therebetween.

14. The method of 13, wherein the at least one dummy element is configured and positioned to modify:a frequency of at least one bending mode of the turbomachine rotor compared to the case of the same turbomachine rotor without said dummy element; or a modal shape of at least one bending mode of the turbomachine rotor compared to the case of the same turbomachine rotor without said dummy element; or a combination thereof.

15. The method of claim 14, wherein the at least one bending mode includes the first bending mode, or the second bending mode, or both the first bending mode and the second bending mode.

16. The method of any one of claims 13 to 15, wherein the turbomachine is a compressor.

17. The method of claim 16, wherein the compressor is a centrifugal compressor .and the rotary stage components are centrifugal compressor impellers.

18. A stacked rotor for a turbomachine, the stacked rotor comprising: a first shaft portion, a second shaft portion, a plurality of impeller stacked between the first shaft portion and the second shaft portion, at least one dummy element along the stacked rotor, between the first shaft portion and the second shaft portion, and a tie rod connecting the first shaft portion and the second shaft portion, the tie rod extending through the plurality of impellers and said at least one dummy element.

19. A turbomachine comprising a casing and a stacked rotor according to claim 18, supported for rotation in the casing.

20. The turbomachine of claim 19, including active magnetic bearing configured to rotatingly support the stacked rotor in the casing.-17-

Images