METHOD FOR BALANCING TURBINE WHEELS OF EXHAUST GAS TURBINES, AND BALANCED TURBINE WHEELS

Description

TECHNICAL FIELD

[0001] The present invention relates to a method for balancing turbine wheels of exhaust gas turbines by introducing a mass removal region defined in terms of shape and position into the hub rear wall of a turbine wheel of exhaust gas turbines, as well as to a balanced turbine wheel for exhaust gas turbines. TECHNICAL BACKGROUND

[0002] Exhaust gas turbines are used to harness the energy contained in the exhaust gas. Turbine wheels are used to extract energy from the exhaust gas stream. These wheels are located in the exhaust stream and feature a fluid-mechanically optimized design. The turbine wheel is mounted on a shaft and supported by the shaft so that it can rotate around a rotational axis.

[0003] Due to the high speeds of exhaust turbine wheels and their position in the exhaust duct, turbine wheels are components of exhaust turbines subject to high thermal and mechanical stress. The mechanical stress within an exhaust turbine wheel is particularly enormous and stems largely from the high speeds and associated centrifugal forces. Deviations in the mass distribution around the circumference of a turbine wheel, which can disrupt the true running of the turbine wheel and potentially generate additional loads, play a significant role. The unevenly distributed mass around the circumference, also known as imbalance, is therefore actively counteracted through both design measures and remachining of an exhaust turbine wheel.

[0004] In the prior art, a balancing rim is typically provided on the hub back wall to reduce the imbalance of an exhaust turbine wheel. This balancing rim is a convex, circumferentially extending bulge on the hub back wall. During a balancing process, the balancing rim can be removed in a defined manner, thus creating a uniform mass distribution in the circumferential direction of the exhaust turbine wheel. For this purpose, it is known to remove the balancing rim using a flat grinding process.

[0005] However, the balancing rim required for the balancing process has several disadvantages. These include, but are not limited to, the provision, design, and calculation of additional components (and thus masses) in an exhaust turbine wheel, additional machining steps required in the manufacturing process, and negative effects on the internal load distribution and stress of an exhaust turbine wheel. The additional attachment of masses in an exhaust turbine wheel rotating at high speed, which causes additional centrifugal forces, as well as the unfavorable characteristics of a balancing rim on the mechanical stresses within an exhaust turbine wheel, are disadvantageous. Based on this, a balancing rim also has a negative effect on cycle life, and in particular on cycle life with regard to low-cycle fatigue, also known as low-cyclecalled cyclic capability.

[0006] In view of the above, there is a need for a method for balancing a turbine wheel of an exhaust gas turbine, which can at least partially mitigate the aforementioned disadvantages, as well as for a correspondingly balanced turbine wheel. US 2020 / 392848 A1 describes an exhaust gas turbocharger wheel with a hub comprising a nose, a rear disc with a shaft connecting portion and a rotational axis, and blades extending from the hub to define the exhaust gas flow channel. US 8 936 439 B3 describes a turbine wheel arranged around an axis and having a rear side with a separator arranged thereon, an inner undercut arranged between the separator and the axis, and an outer undercut arranged between the separator and an outer periphery of the rear side. BRIEF DESCRIPTION OF THE INVENTION

[0007] This object is achieved by a method for balancing a turbine wheel according to claim 1. Furthermore, the object is achieved by a turbine wheel according to claim 8 and an exhaust gas turbine according to claim 12. Further embodiments, modifications and improvements will become apparent from the following description and the appended claims.

[0008] According to one aspect of the invention, a method for balancing a turbine wheel for an exhaust gas turbine is provided. The turbine wheel is rotatable about its axis of rotation and has a hub and a plurality of turbine blades attached to the hub and arranged in a fluid flow region. The hub has a hub rear wall facing away from the fluid flow region with a marking bead extending concentrically around the axis of rotation. The method comprises: Moving an ellipsoidal cutting tool relative to the turbine wheel to a mass removal position adjacent the marking bead; introducing a mass removal indentation into the hub back wall that is asymmetrical with respect to the rotation axis for balancing the turbine wheel by removing, by means of the cutting tool, hub material from the hub back wall, adjacent to the marking bead and leaving the marking bead standing.

[0009] According to one aspect of the invention, a turbine wheel for an exhaust gas turbine is provided, wherein the turbine wheel is rotatable about its axis of rotation and comprises: a hub; and a plurality of turbine blades fastened to the hub and arranged in a fluid flow region, wherein the hub has a hub rear wall facing away from the fluid flow region. Located in the hub rear wall is a mass removal indentation that is asymmetrical with respect to the axis of rotation for balancing the turbine wheel. The mass removal indentation is designed as a concave depression in the hub rear wall with a cross-sectional contour in the form of an ellipse segment, wherein the cross-sectional contour is defined in a cross-sectional plane ZZ containing the axis of rotation. The hub rear wall further has a marking bead running concentrically to the axis of rotation, wherein the marking bead and the mass removal indentation are adjacent to one another without radially overlapping.

[0010] By designing the mass removal recess as a concave depression in the hub rear wall, a preferred aspect of the invention eliminates the need for a balancing rim on the hub rear wall. In particular, the hub rear wall can be designed free of non-rotationally symmetric convex elevations after balancing. This allows the rotating mass and inertia of the hub to be reduced. Reduced inertia can contribute to improved acceleration behavior of the rotor. The cross-sectional contour of the mass removal recess in the shape of an elliptical segment can further reduce the stress on the hub and avoid additional load. BRIEF DESCRIPTION OF THE CHARACTERS

[0011] The invention is explained in more detail below using embodiments, without these being intended to limit the scope of protection defined by the claims.

[0012] The accompanying drawings illustrate embodiments and, together with the description, serve to explain the principles of the invention. The elements of the drawings are relative to one another and are not necessarily to scale. Like reference numerals designate similar parts.

[0013] The figures show: Figure 1 : Top view of the hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine according to an embodiment; Figure 2 : Radial cross-section along the cross-sectional plane ZZ of the turbine wheel (10) of the Figure 1 ; Figure 3 : Radial cross section as in Figure 2 , with geometric dimensions of the individual (sub-)components; Figure 4 : a detailed view of the cross section of the Figure 2 ; and Figure 5 : Radial cross-section along the cross-sectional plane ZZ of the turbine wheel (10) during the implementation of the method according to an embodiment of the invention. DETAILED DESCRIPTION OF THE FIGURES

[0014] With reference to Figures 1 to 4 A turbine wheel (10) of an exhaust gas turbine according to one embodiment will now be described. The turbine wheel (10) is rotatable about its rotational axis (11).

[0015] Figure 1 shows a schematic plan view of the hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine according to one embodiment. The turbine wheel (10) was balanced using the method described herein. A design of the hub rear wall (15) with a scallop (wave-shaped edge) of a turbine wheel (10) of an exhaust gas turbine can be seen on the radially outer edge of the hub rear wall (15). The design with a scallop is not mandatory, and alternatively, the hub rear wall can also be circular, for example.

[0016] Radially outside the hub (12), a plurality of turbine blades can be seen schematically, which are fastened to the hub (12) and arranged in a fluid flow region (14).

[0017] The hub rear wall (15) further comprises a marking bead (16) arranged rotationally symmetrically around the rotation axis (11) and concentrically to the rotation axis (11). The marking bead (16) can be arranged at any radial position on the hub rear wall (15), preferably in the radially outer half of the hub rear wall (15), particularly preferably in the radially outer third. The marking bead can be formed as an elevation above the base surface of the hub rear wall (15) and thus protrude beyond it in the axial direction.

[0018] Furthermore, the hub rear wall (15) has a mass removal indentation (13). The mass removal indentation (13) is designed as a circular arc running around the rotation axis (11). The mass removal indentation (13) thus runs concentrically to the marking bead (16), which serves as a visual reference. The mass removal indentation (13) is not rotationally symmetrical, but rather covers only part of the hub rear wall in the circumferential direction, a maximum angular range of 180°, i.e., a maximum of half of the hub rear wall (15). The mass removal indentation (13) serves to balance the turbine wheel (10), and its dimensions were designed depending on the determined imbalance.

[0019] The mass removal indentation (13) runs directly adjacent to the marking bead (16), specifically radially outside the marking bead (16). The mass removal indentation (13) extends in the radially outer half of the hub rear wall (15), preferably in the radially outer third. The marking bead (16) can be radially spaced from the mass removal indentation (13).

[0020] Figures 2 and 3 show a cross-sectional view of the turbine wheel (10) of the Figure 1, wherein the cross-sectional plane ZZ contains the rotation axis (11). The turbine wheel (10) with the hub (12) can be seen, which can be rotated about the rotation axis (11). A fluid flow region (14) of the turbine wheel (10) is located at the front of the hub (12), although the turbine blades mounted on the hub (12) in the fluid flow region (14) are not shown. The cross-sectional contour of the mass removal indentation (13) and the cross-sectional contour of a marking bead (16) can be seen in the hub rear wall (15).

[0021] Figure 3 shows the same cross-sectional view as Fig. 2, with some geometric dimensions drawn therein. F indicates the diameter of the rear wall of the turbine wheel (10). The diameter F of a turbine wheel (10) of an exhaust gas turbine is defined as the smallest diameter passing through the axis, i.e., with respect to the radially innermost dimension of the hub rear wall, in the case of a non-circular rear wall. Therefore, if a scallop is present, as in Figure 1 As illustrated, the diameter F refers to the radially innermost (smallest) diameter of the hub (12). In the embodiment of the Fig. 1 This is the radius in the cross-sectional plane ZZ. In an alternative embodiment (not shown), there is no scallop and the hub back wall is circular with a constant diameter F.

[0022] Furthermore, Figure 3the geometric dimensions and relationships of parts of the hub rear wall (15) and in particular of the mass removal indentation (13) provided therein are evident. The mass removal indentation (13) is designed in cross-section as an ellipse segment of an ellipse, where H represents the major semi-axis of the ellipse and B the minor semi-axis of the ellipse. The penetration depth C of the mass removal indentation (13) represents the depth of penetration of the ellipse into the hub rear wall (15). Here, C is more precisely defined as the deepest penetration depth compared to the contour of the hub rear wall (15) without the mass removal indentation (13). This contour without the mass removal indentation (13) is evident from a cross-section of a part of the hub rear wall that is free of the mass removal indentation, for example from a cross-section on the side of the hub rear wall (15) opposite to the cross-section ZZ, i.e. mirrored about the axis (11). Figure 1 .

[0023] Furthermore, Figure 3the marking bead (16) can be seen. Unless otherwise stated, all position information relating to the marking bead (16) refers to the apex of the marking bead (16). The marking bead apex diameter G is therefore defined, for example, as the diameter of the apex of the marking bead (16). The marking bead (16) - or more precisely its apex - is radially spaced from the mass removal indentation (13), with D indicating the radial distance between the apex of the marking bead (16) and the adjacent (here: radially inner) boundary of the mass removal indentation (13). The radial distance between the apex of the marking bead (16) and the distant (here: radially outer) boundary of the mass removal indentation (13) is marked E. The mass removal indentation (13) has a radial extension, from radially inner to radially outer boundary, of A.The ellipsoidally shaped mass removal recess (13) is defined by an ellipse, with the ellipse having a major semi-axis H and a minor semi-axis B. The penetration depth of the mass removal recess (13) is indicated by C. Furthermore, F indicates the diameter of the rear wall of the turbine wheel (10) of an exhaust gas turbine.

[0024] Figure 4 shows a detailed view of Figure 2 and Figure 3and contains an enlarged view of the marking bead (16) and the adjacent (radially inner) boundary of the mass removal indentation (13), with a distance D therebetween. The radii of curvature K, L, M define the marking bead (16) geometrically. K indicates the concave radius of curvature of the transition between the apex of the marking bead (16) and the radially inner boundary of the mass removal indentation (13), L the convex radius of curvature at the apex of the marking bead (16), and M the concave radius of curvature of the transition from the apex of the marking bead (16) to the region of the hub rear wall (15) which lies radially inside the marking bead (16). The radius of curvature L can also be L=0, which corresponds to a sharp edge.

[0025] Furthermore, Figure 4It can be seen that the marking bead (16) is formed as a convex elevation in and relative to the hub rear wall (15), the marking bead (16) being geometrically defined by the radii of curvature K, L and M.

[0026] In the figures, as in Figure 1 visible, all in the Figures 2 and 3 illustrated elements of the hub rear wall, with the exception of the mass removal recess (13), circulate around the axis of rotation (11).

[0027] Figure 5 illustrates a method for balancing a turbine wheel (10) for an exhaust gas turbine or an exhaust gas turbine. The starting point of the method is the turbine wheel (10) of the Figures 1 to 4 , but still without a mass removal indentation (13). According to the method, the unbalance is first determined in a known manner, for example by measuring the unbalance on the rotating turbine wheel (10).

[0028] Depending on the determined imbalance of the turbine wheel (10), a material removal profile is determined for the mass removal indentation (13). This material removal profile specifies how the material removal should be performed and can be parameterized, for example, by the angular extent (starting and ending angles) and the penetration depth of a mass removal indentation (13) to be created. The material removal profile and the resulting mass removal indentation (13) are asymmetrical with respect to the rotation axis (11) to enable unbalance compensation.

[0029] Subsequently, the mass removal recess (13) is removed by means of a Figure 5The ellipsoidal cutting tool (20) shown is introduced into the hub rear wall according to the material removal profile. The introduction of mass removal at mass removal positions occurs through a relative movement of the tool (20) and the hub rear wall (15) to one another, for example, through movement of the tool (20) relative to a stationary hub rear wall (15). The shape and movement of the ellipsoidal cutting tool (20) determine the shape of the mass removal recess (13).

[0030] The movement of the tool (20) and, resulting therefrom, the position of the mass removal indentation (13) is aligned relative to the marking bead (16), namely next to and along the marking bead (16), whereby the marking bead (16) is left standing. The marking bead (16) thus enables precise orientation for the introduction of the mass removal indentation (13) at a defined location in the hub back wall (15). This ensures during the process that the radially inner region of the hub back wall (15) (radially within the marking bead (16)), which is subject to high mechanical stress or has mechanical stress maxima, is not affected. Furthermore, a visual inspection after balancing is possible. Balancing in the area radially smaller than the marking bead (16) could lead to mechanical limitations with regard to fatigue at low cycles ( low-cycle fatigue)of the turbine wheel (10). Preferably, the radial distance of the tool (20) from the marking bead (16) remains unchanged during the movement.

[0031] A grinding device with an ellipsoidal grinding head is schematically depicted here as an ellipsoidal cutting tool (20). The ellipsoidal grinding head rotates, for example, around a radial axis. Another, approximately inclined, rotation axis is also possible in alternative embodiments. In the case of a spherical cutting tool, such as a spherical grinding head, the rotation axis is freely variable.

[0032] The method may optionally comprise at least one further determination of the (remaining) unbalance and adjustment or supplementation of the mass removal indentation (13) according to the steps described above. DESCRIPTION OF FURTHER DETAILS, POSSIBLE VARIANTS AND GENERAL ASPECTS

[0033] Possible variants and general optional aspects of the invention are described below. Unless otherwise agreed, each aspect can be combined with any other aspect of the invention. These aspects are also referred to as embodiments and are partially illustrated by reference numerals that refer to the elements shown in the previously described figures, but are not limited in any further respect to the embodiments shown therein.

[0034] In the following, aspects relating to a method for balancing a turbine wheel (10) for an exhaust gas turbine or an exhaust gas turbine are first described. The turbine wheel (10) of the exhaust gas turbine is rotatably mounted and rotates about its axis of rotation (11). The turbine wheel (10) has a hub (12) and a plurality of turbine blades fastened to the hub (12) and arranged in a fluid flow region (14). The fluid flow region (14) is the region in which the fluid, in particular exhaust gas, flows against the turbine blades and performs work in the process. Furthermore, the hub (12) has a hub rear wall (15) facing away from the fluid flow region (14). The hub rear wall (15) is therefore arranged on a side of the hub (12) facing away from the fluid flow region (14), approximately opposite it. However, this does not exclude the possibility that the hub rear wall (15) may also be wetted by the fluid.The hub rear wall (15) is preferably free of turbine blades and / or can extend in a preferably radial direction (e.g., with an angular deviation of a maximum of 40° relative to the radial plane). The hub rear wall (15) has a marking bead (16) extending concentrically around the rotation axis (11).

[0035] According to a general aspect, it is provided that mass removal takes place at mass removal positions next to the marking bead (16) in the hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine by means of an ellipsoidal cutting tool.

[0036] The introduction of mass removal at mass removal positions occurs through a relative movement of an ellipsoidal cutting tool and the hub rear wall (15) to one another. The ellipsoidal cutting tool can be moved while the hub rear wall (15) remains stationary, the hub rear wall (15) can be moved while the ellipsoidal cutting tool remains stationary, and a simultaneous movement of the ellipsoidal cutting tool and the hub rear wall (15), as well as any combination thereof, can occur. Preferably, the ellipsoidal cutting tool is moved at least in the depth direction. The marking bead (16) is particularly advantageous when the ellipsoidal cutting tool is a freely movable tool and is held and guided, for example, by a human hand.

[0037] For any type and combination of relative movement of the ellipsoidal cutting tool and the hub back wall (15) to each other, the (relative) movement of the cutting tool is aligned with the marking bead (16) formed in the hub back wall (15) of the turbine wheel (10).

[0038] The introduction of mass removal at mass removal positions in the hub rear wall (15) for balancing a turbine wheel (10) of an exhaust gas turbine is carried out by removing a mass removal indentation (13) that is asymmetrical with respect to the rotational axis (11) using the ellipsoidal cutting tool. The position(s) of the mass removal indentation(s) (13) is / are aligned relative to the marking bead (16), with the marking bead (16) being left standing. The most protruding part of the marking bead (16), which contains the apex of the marking bead, thus remains untouched and unmachined.

[0039] The ellipsoidal cutting tool has a machining geometry in the form of an ellipsoid. The tool thus has an ellipsoidally shaped cutting tool head for removing material from an ellipsoid segment from the hub rear wall. The ellipsoid describing the machining geometry is defined by the three semi-axes H, B, and Y. H and B correspond to the Figure 3 shown semi-axes of the resulting cross-sectional contour of the mass removal indentation (13), and Y is the axis perpendicular to these two semi-axes (and thus to the plane of the drawing of the Figure 5 ) perpendicular semi-axis of the ellipsoid describing the tool machining geometry. For a rotating tool head, the two semi-axes perpendicular to the rotation axis are preferably equal, i.e., for an axially rotating tool head, Y=H; for a radially rotating tool head, Y=B.

[0040] In one embodiment of the ellipsoidal cutting tool, the ellipsoid describing the tool machining geometry has a configuration in which at least two of the three semi-axes H, B, and Y have the same longitudinal extent. In a further embodiment of the ellipsoidal cutting tool, the ellipsoid describing the tool machining geometry has a configuration in which all three semi-axes H, B, and Y have the same longitudinal extent. According to one aspect, the tool can have a rotating tool head with an elliptical shape corresponding to the tool machining geometry. If the tool head rotates, the axis of rotation is preferably one of the semi-axes, and at least the other two semi-axes are the same.

[0041] If all three semi-axes H, B, and Y have the same length, the resulting tool machining geometry is a sphere, i.e., a spherical cutting tool (e.g., a tool with a ball head). Such a spherical cutting tool has the advantage that the angular orientation of the tool relative to the hub back wall is irrelevant, at least within a certain angular range, which facilitates handling of the tool—especially when the tool is freely movable.

[0042] An ellipsoidal cutting tool can be any tool capable of machining. Typically, but not limited to, turning tools, drilling tools, countersinking tools, reaming tools, milling tools, planing tools, slotting tools, broaching tools, sawing tools, filing tools, rasping tools, brushing tools, scraping tools, chiseling tools, grinding tools (with and without rotating tools), belt sanders, honing tools, lapping tools, or sliding cutting tools.

[0043] In one embodiment, the ellipsoidal cutting tool is a grinding tool with an ellipsoidal grinding head, for example a spherical grinding tool with a spherical grinding head.

[0044] According to one aspect, the mass removal indentation (13) is introduced into the hub rear wall (15) of a turbine wheel of an exhaust gas turbine by an ellipsoidal cutting tool. According to one aspect, the introduction takes place along a circular sector of the hub rear wall (15) and in the circumferential direction along a circular arc around the axis (11). Preferably, the introduction takes place within a ring segment or circular segment along a circular arc. According to another aspect, introduction can also take place along any one-dimensional profile on the hub rear wall (15) of a turbine wheel (10).

[0045] According to one aspect, the mass removal indentation (13) may be provided as a continuous circular segment, as in Figure 1shown by way of example. More generally, the mass removal indentation (13) can be provided as a continuous, segmented, interrupted, or discretely punctuated indentation along a circular arc. The circular arc, along which the relative movement of the ellipsoidal cutting tool and the hub rear wall (15) occurs, is aligned with the marking bead (16) in the hub rear wall (15) such that the circular arc runs adjacent to the marking bead (16) in the hub rear wall (15).

[0046] According to one aspect, the method first comprises determining an imbalance of the turbine wheel (10). Depending on the determined imbalance of the turbine wheel (10), a material removal profile for the mass removal indentation (13) is then generated. This material removal profile can be, for example, a one-dimensional profile along a circular segment of the hub rear wall (15) and run along a circular arc next to the marking bead (16) in the hub rear wall (15). The material removal profile specifies how the material removal is to be carried out. Possible embodiments include a continuous, segment-like, interrupted, and / or discretely punctiform material removal profile. Any profiles with a (continuous or discrete) angle-dependent penetration depth can be used. According to one aspect, the profile is limited by a maximum angular range and / or a maximum penetration depth.According to a further aspect, the introduction of a material removal profile for the mass removal indentation (13) can also be carried out without a prior determination of an imbalance of the turbine wheel (10).

[0047] According to one embodiment, the material removal profile can, for example, comprise a (angular) center position on the hub rear wall (15), an angular range along the circular arc, a length along the circular arc of the mass removal indentation (13), and / or the (constant or angle-dependent) material removal depth C. In particular, a material removal depth C that can be varied over the respective angular range can be defined for the mass removal indentation (13), thus creating, for example, runouts. In this way, one material removal profile can also be provided for multiple mass removal indentations (13).

[0048] Using the provided material removal profile, the mass removal indentation (13) is introduced into the hub rear wall (15) of a turbine wheel of an exhaust gas turbine. According to one aspect, the introduction of the mass removal indentation (13) reduces the imbalance of the turbine wheel.

[0049] In order to optimize the mass removal indentation (13), according to one aspect, a removal-free hub test geometry is defined. This removal-free hub test geometry represents a design of the hub (12), in particular of the hub rear wall (15), without any material removal in the hub rear wall (15).

[0050] According to a further aspect, a maximum removed hub test geometry is defined (for example, as a further hub test geometry) as the hub test geometry with the maximum permissible material removal in the hub back wall (15). The maximum permissible material removal in the hub back wall (15) is specified, for example, based on conditions such as typically required removal, minimum permissible hub residual wall thickness at the positions of the material removal, manufacturing processes and manufacturing possibilities at the positions of the material removal, and / or structural mechanical requirements at the positions of the material removal.

[0051] According to one aspect, a first hub quality parameter is calculated based on the maximum removed hub test geometry, i.e., taking into account the maximum permissible material removal in the hub rear wall (15). Preferably, the hub geometry is optimized by optimizing a hub optimization variable determined using the first hub quality parameter.

[0052] According to one aspect, a second hub quality parameter can also be calculated based on the removal-free hub test geometry, i.e., without taking into account the maximum permissible material removal in the hub rear wall (15). Preferably, the hub optimization variable is then also determined using the second hub quality parameter, for example, by summing the respective summands determined using the first or second hub quality parameter.

[0053] The (first or second) hub quality parameter can, for example, contain at least one parameter selected from the following list: mechanical stress, mechanical principal stress, mechanical normal stress, mechanical shear stress, a mechanical cycle optimization parameter, in particular a Cyclefatigue specification (e.g., the simulated cycle capability regarding fatigue at low cycles), a notch coefficient, a shape factor, a support coefficient, a force flow, a geometric configuration of the mass removal indentation (13), a deviation from a specified target total removal. The hub optimization variable can, for example, contain a norm (e.g., L2 norm, i.e., square) of such a parameter, or the optionally weighted sum of such norms for several parameters. In particular, the hub optimization variable can thus penalize an increase in the simulated cycle capability regarding fatigue at low cycles for the wear-free and / or the maximum wear-free hub test geometry.

[0054] The optimization is preferably performed iteratively. Parameters defining the hub test geometry are preferably changed iteratively to achieve an optimum for the hub optimization size.

[0055] According to one aspect, the shape of the maximum allowable material removal can also be optimized by iteratively changing parameters that define the maximum allowable material removal. In this case, the hub optimization variable can also include a term that ensures a sufficiently large maximum allowable material removal, such as a term that penalizes deviations from a specified target total removal.

[0056] The optimization of the hub back wall geometry is carried out using at least one parameter called the hub quality parameter.

[0057] Preferably, the hub geometry is optimized as a multifactorial optimization in which more than one hub quality parameter is used. Preferably, the hub geometry is optimized by optimizing a hub optimization variable determined using multiple hub quality parameters. The optimization is preferably performed iteratively. Preferably, the material removals subtracted from the hub test geometry are iteratively changed, and subsequently, multiple hub quality parameters are calculated and compared with the existing, similar hub quality parameters. The comparison of the hub quality parameters and the optimization can be performed using any suitable mathematical optimization method.The iterative change of the subtracted material removal from the hub test geometry is limited by a hub test geometry without any material removal and by a hub test geometry with maximum permissible material removal.

[0058] Aspects relating to a turbine wheel (10) for an exhaust gas turbine or an exhaust gas turbine, for example one produced by the described method, are described below. The turbine wheel (10) is rotatably mounted and rotates about its axis of rotation (11). The turbine wheel (10) has a hub (12) and a plurality of turbine blades fastened to the hub (12) and arranged in a fluid flow region (14). Furthermore, the hub (12) has a hub rear wall (15) facing away from the fluid flow region (14). Located in the hub rear wall (15) is a mass removal indentation (13) which is asymmetrical with respect to the axis of rotation (11) and is used to balance the turbine wheel (10). The mass removal indentation (13) is designed as a concave depression in the hub rear wall (15) with a cross-sectional contour of the mass removal indentation (13) in the form of an ellipse segment.The cross-sectional contour of the mass removal indentation (13) is defined in a cross-sectional plane ZZ containing the rotation axis (11). Furthermore, the hub rear wall (15) has a marking bead (16) extending concentrically around the rotation axis (11), wherein the marking bead (16) and the mass removal indentation (13) are adjacent to one another without radially overlapping. In other words, the mass removal indentation (13) does not overlap the apex of the marking bead (16), and the apex therefore extends continuously in the circumferential direction of the hub rear wall.

[0059] According to one aspect, the mass removal indentation (13) has a cross-sectional contour in a cross-sectional plane ZZ containing the rotation axis (11). The cross-sectional contour is ellipsoidal in shape, i.e., represented by an ellipse segment. The ellipse describing this ellipse segment is defined by a first (e.g., major) semi-axis H and a second (e.g., minor) semi-axis B of the ellipse. The first semi-axis H can extend in the radial direction, and the second semi-axis B of the ellipse can extend in the axial direction. Preferably, the first semi-axis H and the second semi-axis B of the ellipse have the same longitudinal extent, resulting in a cross-sectional contour in the geometric shape of a circular segment in a cross-sectional plane ZZ containing the rotation axis (11).

[0060] Preferably, a definition of the cross-sectional contour made herein applies to a plurality of cross-sectional planes ZZ containing the rotation axis (11) and a portion of the mass removal indentation (13), particularly preferably for each such cross-sectional plane at least in a continuous angular range that covers at least half or even at least 80% of the entire angular range of the mass removal indentation (13). In the case of multiple mass removal indentations (13), a definition made herein preferably applies to all mass removal indentations (13).

[0061] According to one aspect, the cross-sectional contour of the mass removal indentation (13) has a minimum radius of curvature Kr min. The minimum radius of curvature of the underlying ellipse can be estimated by the ratio Ke min = ((B*B) / H), where H indicates the major (here: first) semi-axis of the ellipse, B the minor (here: second) semi-axis of the ellipse. The radius of curvature should typically satisfy a ratio of Kr min / F ≥ 0.03 and / or Ke min / F ≥ 0.03, where F and F indicate the diameter of the turbine wheel (10). If the major semi-axis H and minor semi-axis B of the ellipse are of equal length, and thus a circular (i.e., circular segment-shaped) cross-sectional contour, the result is R / F ≥ 0.03, where R indicates the radius of the circular cross-sectional contour.In the case of equal lengths of the major semi-axis H and the minor semi-axis B, the major semi-axis H and the minor semi-axis B correspond to each other and at the same time the major semi-axis H and the minor semi-axis B correspond to the radius R of the circular cross-sectional contour.

[0062] According to one aspect, the mass removal indentation (13) has a penetration depth C of C > 0 and / or C < 0.6*B, preferably C < 0.5*B, and particularly preferably C < 0.4*B, where B is the second (axial and / or small) ellipse semi-axis.

[0063] The mass removal indentation (13) is located in the hub rear wall (15) of the turbine wheel (10) and adjacent to the marking bead (16) also present in the hub rear wall (15). According to one aspect, the mass removal indentation (13) and / or the marking bead (16) can be introduced at any circumferential and radial position in the hub rear wall (15), with both being located adjacent to one another, i.e., without any further functional surface features in between.

[0064] The mass removal indentation (13) and / or the marking bead (16) are preferably introduced in the radially outer half of the hub rear wall (15) (relative to the diameter F), preferably at least partially in the radially outer third. The mass removal indentation (13) is preferably positioned (completely) radially outside the marking bead (16). According to one aspect, the region of the hub rear wall (15) within the marking bead (16) is free of the mass removal indentation (13) and / or is completely rotationally symmetrical. According to one aspect, the marking bead (16) allows an area to be marked for the mass removal indentation (13) (namely, for example, radially outside the marking bead (16)) and / or to ensure the marking of an area not intended for the mass removal indentation (13) (namely, for example, radially inside the marking bead (16)).The marking bead (16) ensures and easily verifies that the mass removal recess (13) is only introduced in the intended area and not outside of this area. This is particularly useful if the hub back wall geometry has been optimized for the mass removal recess (13) provided therein.

[0065] According to one aspect, any tool capable of machining can be used to create the mass removal indentation (13). Typically, but not limited to, turning tools, drilling tools, countersinking tools, reaming tools, milling tools, planing tools, shaping tools, broaching tools, sawing tools, filing tools, rasping tools, brushing tools, scraping tools, chiseling tools, grinding tools with and without rotating tools, belt grinding tools, honing tools, lapping tools, or sliding cutting tools are mentioned.

[0066] Preferably, the cutting tool is a grinding tool with an ellipsoidal grinding head. Typically, this grinding tool has a spherical grinding head and is therefore a spherical grinding tool with a spherical grinding head. The cutting tool with an ellipsoidal grinding head can also be shaped such that only the part of the cutting tool that is in contact with the turbine wheel (10) during the introduction of mass removal indentations (13) has an ellipsoidal shape.

[0067] According to one aspect, the introduction of a mass removal indentation (13) for balancing a turbine wheel (10) of an exhaust-gas turbine takes place within a circular sector of the hub rear wall (15) of a turbine wheel (10) of an exhaust-gas turbine and in the circumferential direction along a circular arc. Preferably, the introduction takes place within a ring segment or circular segment along a circular arc. By way of example, but not limited to, a continuous, segment-like, interrupted, or discrete point-like introduction along the circular arc is mentioned.

[0068] The hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine has a marking bead (16), said marking bead (16) being rotationally symmetrical with respect to the rotation axis (11) and extending concentrically around the rotation axis (11).

[0069] According to one aspect, the marking bead (16) in the hub rear wall (15) has a cross-sectional contour located in a cross-sectional plane ZZ containing the rotation axis (11). The cross-sectional contour of the marking bead (16) is convexly raised relative to the hub rear wall (15).

[0070] According to one aspect, the marking bead (16) is radially spaced by a distance D from the mass removal indentation (13) also contained in the hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine.Preferably, E = A + D and E ≤ (F - G) / 2 and G / F > 0.5, where A is the radial extent of the mass removal indentation (13) (radial distance between the radially inner boundary of the mass removal indentation (13) and the radially outer boundary of the mass removal indentation (13)), D is the radial distance between the marking bead (16) and the radially closer (here radially inner) boundary of the mass removal indentation (13), E is the radial extent between the marking bead (16) and the radially further (here radially outer) boundary of the mass removal indentation (13), F is the diameter of the rear wall of a turbine wheel (10) of an exhaust gas turbine and G is the diameter of the marking bead (16), i.e. the diameter of the circle defined by the circumferential marking bead (16) on the hub rear wall (15). Herein, unless otherwise stated, the radial position of the marking bead is always defined by its apex.If there are multiple mass removal indentations (13), an individual radial spacing D from the marking bead (16) can be determined and applied for each mass removal indentation (13). Typically, the same radial spacing D is selected and applied for all mass removal indentations (13). The minimum radial distance D between the mass removal indentation (13) and the marking bead (16) is preferably 0 < D < 0.05*F, particularly preferably 0 < D < 0.025*F.

[0071] According to one aspect, the (preferably rotationally symmetrical) cross-sectional contour of the marking bead (16) has a vertex, a radially inner flank opposite the vertex, and a radially outer flank opposite the vertex. The radially inner flank has a concave radius of curvature M, the radially outer flank has a concave radius of curvature K, and the vertex has a convex radius of curvature L. If the radius of curvature is not constant, these variables describe the smallest radius of curvature in each case. In other words, K indicates the (smallest) radius of curvature of the transition between the apex of the marking bead (16) and the radially inner boundary of the mass removal indentation (13), L the (smallest) radius of curvature at the apex of the marking bead (16) and M the (smallest) radius of curvature of the transition from the apex of the marking bead (16) to the area of ​​the hub rear wall (15) which lies radially inside the marking bead (16).According to one aspect, K > 0, L ≥ 0 and / or M > 0 applies. Furthermore, K / F < 0.07, M / F < 0.07, L / K < 0.15 and / or L / M < 0.1 preferably apply.

[0072] According to one aspect, the surface of the hub rear wall (15) is a reworked surface in the entire radial region at least from the radius of the marking bead (16) to the outermost radius of the mass removal indentation (13), thus having a higher smoothness and precision than, for example, a surface obtained directly by casting.

[0073] The marking bead (16) in the hub rear wall (15) of a turbine wheel (10) of an exhaust gas turbine can be mounted at any radial position. Preferably, the marking bead (16) is located radially within the mass removal recess (13).

[0074] According to one aspect, the imbalance of the turbine wheel is lower than the imbalance of a corresponding (imaginary) turbine wheel with a rotationally symmetric hub without a mass removal indentation (13). According to one aspect, the fatigue cycle capability of the turbine wheel at low cycles is not lower, or at most by 2% lower, than the cycle capability of a corresponding (imaginary) turbine wheel with a rotationally symmetric hub without a mass removal indentation (13).

[0075] All of the aforementioned aspects for a turbine wheel (10) of an exhaust gas turbine relate to exhaust gas turbines of any design, preferably to radial exhaust gas turbines or mixed-flow exhaust gas turbines (also referred to as diagonal exhaust gas turbines). In radial exhaust gas turbines, the turbine wheel (10) is designed as a radial turbine wheel. In mixed-flow exhaust gas turbines, the turbine wheel (10) is designed as a mixed-flow (diagonal) exhaust gas turbine wheel, i.e., with a hub front wall whose inlet tangent runs in a diagonal direction with both axial and radial components.

[0076] According to one aspect, the exhaust turbine is designed to be driven by exhaust gas from an internal combustion engine. According to one aspect, the exhaust turbine is provided for a turbocharger. In the turbocharger, the exhaust turbine drives a compressor wheel arranged on a common shaft in order to increase the pressure, density, and enthalpy of an intake fluid and thus increase the boost pressure and generally the efficiency of internal combustion engines. Alternatively or additionally, the exhaust turbine can also drive other energy converters, such as an electric generator and / or a drive shaft. According to one aspect, an internal combustion engine with the exhaust turbine driven by exhaust gas from the internal combustion engine and a turbocharger with the exhaust turbine are provided.

[0077] In a further aspect of the invention, an exhaust gas turbine with a turbine wheel (10) is provided, which has every feature of the second aspect of the invention. The exhaust gas turbine can be operated with any type of exhaust gas. Furthermore, all types of exhaust gas turbines, such as radial exhaust gas turbines or mixed-flow exhaust gas turbines, are considered. All possible consumers on the exhaust gas turbine shaft, such as compressor wheels, electric generators, or drive shafts, are also considered. The exhaust gas turbine is preferably an exhaust gas turbocharger. LIST OF REFERENCE SYMBOLS

[0078] 10Turbine wheel of an exhaust gas turbine. 11Axis of rotation of a turbine wheel of an exhaust gas turbine. 12Hub of a turbine wheel of an exhaust gas turbine. 13Mass removal indentation. 14Fluid flow area of ​​a turbine wheel of an exhaust gas turbine. 15Hub rear wall of a turbine wheel of an exhaust gas turbine. 16Marking bead. 20Ellipsoidal cutting tool. ARadial extension of the ellipsoidally shaped mass removal indentation from the radially inner boundary of the ellipsoidally shaped mass removal indentation to the radially outer boundary of the ellipsoidally shaped mass removal indentation. BSecond (minor) semi-axis of the ellipsoidally shaped mass removal indentation. CMaterial removal depth. DRadial distance from the marking bead to the radially inner boundary of the ellipsoidally shaped mass removal indentation. ERadial distance from the marking bead to the radially outer boundary of the ellipsoidally shaped mass removal indentation.FDiameter of the rear wall of an exhaust turbine wheel. GDiameter of the marking bead. HFirst (major) semi-axis of the ellipsoidal mass removal indentation. KKradius of curvature of the transition between the apex of the marking bead and the radially inner boundary of the mass removal indentation. LKradius of curvature at the apex of the marking bead. MCradius of curvature of the transition from the apex of the marking bead to the hub rear wall radially inside the marking bead. XDetail view of . Figure 2 With an enlarged view of the marking bead. Y: Third semi-axis of the ellipsoid defining the tool machining head. Z-Z: Cutting guide in a turbine wheel of an exhaust gas turbine, which contains the rotation axis.

Claims

1. A method for balancing a turbine wheel (10) for an exhaust gas turbine, wherein the turbine wheel (10) is rotatable about its rotational axis (11) and has a hub (12) and a plurality of turbine blades attached to the hub (12) and arranged in a fluid flow region (14), wherein the hub has a hub rear wall (15) facing away from the fluid flow region (14) with a marking bead (16) running concentrically about the rotational axis (11), the method comprising: - movement of an ellipsoidal material-removal tool relative to the turbine wheel (10) at a mass-removal position next to the marking bead (16); - creation of a mass-removal indentation (13), asymmetric relative to the rotational axis (11), in the hub rear wall (15) for balancing the turbine wheel (10) by removal, by means of the material-removal tool, of hub material of the hub rear wall (15), next to the marking bead (16) and leaving the marking bead (16) intact.

2. The method for production of a turbine wheel (10) for an exhaust gas turbine as claimed in claim 1, wherein the material-removal tool is a grinding tool with ellipsoidal grinding head, preferably a spherical grinding tool with spherical grinding head.

3. The method as claimed in any of the preceding claims, wherein the mass-removal indentation (13) is made along a ring segment in the circumferential direction about the rotational axis (11).

4. The method as claimed in any of the preceding claims, furthermore comprising: - determination of an imbalance of the turbine wheel; - depending on the determined imbalance, setting of a material-removal profile for the mass-removal indentation (13); and - creation of the mass-removal indentation (13) with the set material-removal profile.

5. The method as claimed in any of the preceding claims, furthermore comprising: - definition of a removal-free hub test geometry; and - calculation of a first hub quality parameter using a maximally removed hub test geometry as the defined removal-free hub test geometry, minus a maximum removal quantity from the hub rear wall of the removal-free hub test geometry; - preferably optimization of the hub geometry by optimization of a hub optimization variable, calculated using the first hub quality parameter, by iterative changing of a hub test geometry between removal-free and maximally removed hub test geometry, wherein the removal of hub material at the hub rear wall (15) is limited by the maximum removal quantity.

6. The method as claimed in claim 5, wherein the hub quality parameter comprises at least one parameter selected from the following list: a mechanical stress, a mechanical cycle optimization variable, a cycle fatigue indicator.

7. The method as claimed in claim 5 or 6, furthermore comprising: - calculation of a second hub quality parameter using the defined hub test geometry without removal of hub rear wall material from the hub test geometry; - preferably, optimization of the hub geometry by optimization of a hub optimization variable, calculated using the first and second hub quality parameters, by iterative changing of a hub test geometry between removal-free and maximally removed hub test geometry.

8. A turbine wheel (10) for an exhaust gas turbine, wherein the turbine wheel (10) is rotatable about its rotational axis (11) and has - a hub (12); and - a plurality of turbine blades attached to the hub (12) and arranged in a fluid flow region (14), wherein the hub has a hub rear wall (15) facing away from the fluid flow region (14), wherein a mass-removal indentation (13), asymmetric relative to the rotational axis (11), is provided in the hub rear wall (15) for balancing the turbine wheel (10), wherein the mass-removal indentation (13) is configured as a concave depression in the hub rear wall (15) with a cross-sectional contour in the form of an ellipse segment, wherein the cross-sectional contour of the mass-removal indentation (13) is defined in a cross-sectional plane (Z-Z) containing the rotational axis (11), wherein the hub rear wall (15) furthermore has a marking bead (16) running concentrically to the rotational axis (11), wherein the marking bead (16) and the mass-removal indentation (13) are adjacent to one another without radially overlapping.

9. The turbine wheel (10) as claimed in claim 8, wherein the mass-removal indentation (13) has at least one of the following properties (a) to (g): (a) the cross-sectional contour of the mass-removal indentation (13) has the form of a circle segment; (b) the cross-sectional contour of the mass-removal indentation (13) has a minimum curvature radius of more than 0.03*F, wherein F is the diameter of the rear wall of the turbine wheel (10); (c) the cross-sectional contour of the mass-removal indentation (13) fulfils the condition ((B*B) / H) / F ≥ 0.03, wherein H is the large semi-axis of the elliptical cross-sectional contour of the mass-removal indentation (13), B is the small semi-axis of the elliptical cross-sectional contour of the mass-removal indentation (13), and F is the diameter of the rear wall of the turbine wheel (10); (d) the mass-removal indentation (13) is arranged at least partially in the radially outer half of the hub rear wall (15); (e) the mass-removal indentation (13) is produced by means of a material-removal tool, preferably a grinding tool; (f) the mass-removal indentation (13) extends along a ring segment running circumferentially around the axis; (g) the mass-removal indentation (13) extends as a continuous line, as a sequence of portions of continuous lines, or as a sequence of discrete spot indentations.

10. The turbine wheel (10) as claimed in claim 8 or 9, wherein the marking bead (16) has at least one of the following properties (i) to (iv): (i) the marking bead (16) is raised and convex in the cross-sectional plane; (ii) the marking bead (16) is rotationally symmetrical relative to the rotational axis (11); (iii) the marking bead (16) is arranged according to the inequation E ≤ (F - G) / 2 and / or G / F > 0.5, wherein A is the radial extent of the mass-removal indentation (13) from a radially inner end of the mass-removal indentation (13) to a radially outer end of the mass-removal indentation (13), D is the radial distance of the apex of the marking bead (16) from the mass-removal indentation (13), E = A + D is the radial distance of the apex of the marking bead (16) from the radially outer limit of the mass-removal indentation (13), F is the diameter of the turbine wheel (10), and G is the diameter of the circle defined by the apex of the marking bead (16); (iv) the marking bead (16) is arranged radially inside the mass-removal indentation (13).

11. The turbine wheel (10) as claimed in any of claims 8 to 10, wherein the turbine wheel is a radial turbine wheel for a radial exhaust gas turbine, or a mixed-flow turbine wheel for a mixed-flow exhaust gas turbine.

12. An exhaust gas turbine, preferably an exhaust gas turbocharger, with a turbine wheel (10) as claimed in any of claims 8 to 11.