Damper element with flexible legs for vibration dampening apparatus for turbine blade

Abstract

To provide a damper element and a vibration dampening system including a plurality of the stacked damper elements which may be used in a body opening in a rotating blade in a turbine.SOLUTION: The damper elements (170) include a head member having an at least partially ramped surface, and a plurality of flexible legs extending from the head member. Each flexible leg includes a radially extending body section having an end section, and the end section has an outer end surface and an inner end surface. Centrifugal force caused by rotation of the rotating blade causes the head member of an adjacent damper element to force the outer end surfaces of the plurality of flexible legs into frictional engagement with an inner surface of the body opening (160) to dampen vibration. In certain embodiments, an elongated body may extend through an opening in the head member of the one or more damper elements.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present disclosure relates generally to damping vibrations in a rotating blade, and more particularly to a vibration damping system including a plurality of damper elements, each having a plurality of flexible legs. [Background technology]

[0002] One concern in turbine operation is the tendency of rotating turbine blades to undergo vibratory stresses during operation. In many installations, turbines are operated under conditions of frequent acceleration and deceleration. During turbine acceleration or deceleration, the blade airfoils are subjected to vibratory stresses, at least momentarily, at certain frequencies, often at secondary or tertiary frequencies. Nozzle airfoils are also subjected to similar vibratory stresses. For example, fluctuations in gas temperature, pressure, and / or density can excite vibrations throughout the rotor assembly, and particularly within the blade vanes. Periodic, or "pulsating," gases exiting the turbine and / or compressor sections upstream can also excite undesirable vibrations. When airfoils are subjected to vibratory stresses, the vibration amplitudes can easily accumulate to a point that can adversely affect gas turbine operation and / or component life. Solid damper elements stacked within the turbine blade have been used to dampen vibrations, but centrifugal forces can cause the damper elements to lock up, reducing or eliminating their ability to dampen vibrations. Summary of the Invention

[0003] All aspects, examples and features described below may be combined in any manner that is technically possible.

[0004] One aspect of the disclosure provides a damper element for a vibration damping system for a body opening of a rotating blade of a turbine, the damper element comprising: a head member having an at least partially inclined surface; and a plurality of flexible legs extending from the head member, each flexible leg including a radially extending body portion having an end section, the ends having outer end surfaces and inner end surfaces.

[0005] Another aspect of the present disclosure includes any of the preceding aspects, wherein the at least partially inclined surface has an angle in the range between 25° and 55° relative to an inner surface of the body opening, and inner end surfaces of the plurality of flexible legs have an angle in the range between 25° and 55° relative to an inner surface of the body opening.

[0006] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member and, collectively, the radially extending body section of the plurality of flexible legs each have a first outer diameter, and the outer end surfaces of the plurality of flexible legs collectively define a second outer diameter that is larger than the first outer diameter.

[0007] Another aspect of the present disclosure includes any of the preceding aspects, wherein the body opening has an inner surface with a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the plurality of flexible legs pass freely within the body opening.

[0008] Another aspect of the disclosure includes any of the preceding aspects, wherein inner end surfaces of the plurality of flexible legs are configured to receive at least a partially inclined surface of a head member of an adjacent damper element, and under the influence of centrifugal forces caused by rotation of the rotating blade at a rotational speed greater than a predetermined rotational speed, the head member of the adjacent damper element urges outer end surfaces of the plurality of flexible legs into frictional engagement with an inner surface of the body opening to damp vibrations.

[0009] Another aspect of the present disclosure includes any of the preceding aspects, wherein an outer end surface of each flexible leg frictionally engages an inner surface of the body opening at a line.

[0010] Another aspect of the present disclosure includes any of the preceding aspects, wherein an outer end surface of each flexible leg is parallel to an inner surface of the body opening in a relaxed state of the plurality of flexible legs.

[0011] Another aspect of the present disclosure includes any of the preceding aspects, wherein adjacent radially extending body portions of the flexible legs define a slot therebetween having a rounded radially outer extent.

[0012] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member having the at least partially angled surface has a frustoconical shape.

[0013] One aspect of the present disclosure includes a vibration damping system for a rotating blade, the vibration damping system including a plurality of stacked damper elements for positioning in a body opening defined in the rotating blade, each damper element including a head member having at least a partially inclined surface and a plurality of flexible legs extending from the head member, each flexible leg including a radially extending body portion having an end section, the end section having an outer end surface and an inner end surface.

[0014] Another aspect of the present disclosure includes any of the preceding aspects, wherein the at least partially inclined surface of each damper element has an angle in the range of 25° to 55° relative to an inner surface of the body opening, and inner end surfaces of the plurality of flexible legs have an angle in the range of 25° to 55° relative to an inner surface of the body opening.

[0015] Another aspect of the disclosure includes any of the preceding aspects, wherein the head member and collectively the radially extending body portions of the multiple flexible legs of each damper element each have a first outer diameter, and the outer end surfaces of the multiple flexible legs of each damper element collectively define a second outer diameter that is greater than the first outer diameter.

[0016] Another aspect of the present disclosure includes any of the preceding aspects, wherein the body opening has an inner surface with a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the multiple flexible legs of each damper element pass freely within the body opening.

[0017] Another aspect of the disclosure includes any of the preceding aspects, wherein an inner end surface of the plurality of flexible legs of each damper element is configured to receive an at least partially inclined surface of a head member of an adjacent damper element of the plurality of stacked damper elements, such that under influence of centrifugal forces caused by rotation of the rotating blade at a rotational speed greater than a predetermined rotational speed, the head member of the adjacent damper element urges an outer end surface of the plurality of flexible legs into frictional engagement with an inner surface of the body opening to dampen vibrations.

[0018] Another aspect of the present disclosure includes any of the preceding aspects, wherein an outer end surface of each flexible leg frictionally engages an inner surface of the body opening at a line.

[0019] Another aspect of the present disclosure includes any of the preceding aspects, wherein adjacent radially extending body portions of the plurality of flexible legs of each damper element define a slot therebetween having a rounded radially outward extent.

[0020] Another aspect of the present disclosure includes any of the preceding aspects, wherein the plurality of flexible legs further includes a radially inner end element extending radially inward from the head members of each of the plurality of damper elements, the radially inner end element having a head member having an at least partially sloped surface configured to engage an inner end surface of the plurality of flexible legs of a radially innermost one of the plurality of stacked damper elements.

[0021] Another aspect of the present disclosure includes any of the preceding aspects, wherein the plurality of flexible legs further includes a radially outer end element extending radially outward from the head member of each of the plurality of damper elements and configured to engage the plurality of flexible legs of a radially outermost one of the stacked plurality of damper elements.

[0022] Another aspect of the present disclosure includes any of the preceding aspects, wherein the plurality of damper elements have at least one of the following characteristics that differ between at least two of the damper elements: overall mass, overall radial length, radial length of the plurality of flexible legs, force required to deflect the plurality of flexible legs outward, shape of the inner end surface, shape of the outer end surface, angle of the at least partially inclined surface.

[0023] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member of each damper element has an inclined surface having an at least partially conical shape.

[0024] One aspect of the disclosure includes a damper element for a vibration damping system in a body opening of a rotating blade of a turbine, the damper element comprising: a head member having an at least partially inclined surface; an opening defined through a center of the head member; a plurality of flexible legs extending from the head member, each flexible leg including a radially extending body portion having ends, the ends having outer and inner end faces; and an elongated body portion extending through the opening in the head member.

[0025] Another aspect of the present disclosure includes any of the preceding aspects, wherein the elongated body is configured to resonate at the same frequency as the rotating blades, such that the elongated body generates a force against the damper element.

[0026] Another aspect of the present disclosure includes any of the preceding aspects, wherein the at least partially inclined surface has an angle in the range between 25° and 55° relative to an inner surface of the body opening, and inner end surfaces of the plurality of flexible legs have an angle in the range between 25° and 55° relative to an inner surface of the body opening.

[0027] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member and collectively the radially extending bodies of the plurality of flexible legs each have a first outer diameter, and the outer end surfaces of the plurality of flexible legs collectively define a second outer diameter that is greater than the first outer diameter.

[0028] Another aspect of the present disclosure includes any of the preceding aspects, wherein the body opening has an inner surface with a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the plurality of flexible legs pass freely within the body opening.

[0029] Another aspect of the disclosure includes any of the preceding aspects, wherein the inner end surfaces of the plurality of flexible legs are configured to receive at least partially inclined surfaces of head members of adjacent damper elements, such that under the influence of centrifugal forces caused by rotation of the rotating blade at a rotational speed greater than a predetermined rotational speed, the head member of the adjacent damper element forces the outer end surfaces of the plurality of flexible legs into frictional engagement with an inner surface of the body opening to dampen vibration.

[0030] Another aspect of the present disclosure includes any of the preceding aspects, wherein an outer end surface of each flexible leg frictionally engages an inner surface of the body opening at a line.

[0031] Another aspect of the present disclosure includes any of the preceding aspects, wherein adjacent radially extending body portions of the plurality of flexible legs define a slot therebetween having a rounded radially outward extent.

[0032] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member of each damper element has an at least partially sloped surface having a cone-shaped shape through which the opening extends.

[0033] One aspect of the disclosure includes a vibration damping system for a rotating blade, the vibration damping system including a plurality of stacked damper elements, each damper element for positioning in a body opening defined in the rotating blade, the plurality of stacked damper elements including: a head member having an at least partially inclined surface and an opening defined through a center of the head member; a plurality of flexible legs extending from the head member, each flexible leg including a radially extending body portion having an end, the end having an outer end surface and an inner end surface; and an elongated body portion extending through the opening in the head member of each of the plurality of damper elements.

[0034] Another aspect of the present disclosure includes any of the preceding aspects, wherein the at least partially inclined surface of each damper element has an angle in the range between 25° and 55° relative to an inner surface of the body opening, and inner end surfaces of the plurality of flexible legs have an angle in the range between 25° and 55° relative to an inner surface of the body opening.

[0035] Another aspect of the disclosure includes any of the preceding aspects, wherein the head member and collectively the radially extending body portions of the multiple flexible legs of each damper element each have a first outer diameter, and the outer end surfaces of the multiple flexible legs of each damper element collectively define a second outer diameter that is greater than the first outer diameter.

[0036] Another aspect of the present disclosure includes any of the preceding aspects, wherein the body opening has an inner surface with a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the multiple flexible legs of each damper element pass freely within the body opening.

[0037] Another aspect of the disclosure includes any of the preceding aspects, wherein an inner end surface of the plurality of flexible legs of each damper element is configured to receive an at least partially inclined surface of a head member of an adjacent damper element of the plurality of stacked damper elements, such that under influence of centrifugal forces caused by rotation of the rotating blade at a rotational speed greater than a predetermined rotational speed, the head member of the adjacent damper element urges an outer end surface of the plurality of flexible legs into frictional engagement with an inner surface of the body opening to dampen vibrations.

[0038] Another aspect of the present disclosure includes any of the preceding aspects, wherein an outer end surface of each flexible leg frictionally engages an inner surface of the body opening in a line.

[0039] Another aspect of the present disclosure includes any of the preceding aspects, wherein adjacent radially extending body portions of the plurality of flexible legs of each damper element define a slot therebetween having a rounded radially outward extent.

[0040] Another aspect of the present disclosure includes any of the preceding aspects, further including a radially outer retention element secured to the elongate body and retaining a plurality of the stacked damper elements on the elongate body.

[0041] Another aspect of the disclosure includes any of the preceding aspects, wherein the plurality of flexible legs extend radially inward from the head members of each of the plurality of damper elements, further comprising a radially inner end element having: a head member having at least a partially sloped surface configured to engage an inner end surface of the plurality of flexible legs of a radially innermost one of the plurality of stacked damper elements; and an opening through the radially inner end element and through which an elongated body extends, the radially inner end element being slidable over the elongated body.

[0042] Another aspect of the present disclosure includes any of the preceding aspects, wherein the plurality of flexible legs extend radially outward from the head members of each of the plurality of damper elements and further include a radially inner end element configured to engage the head member of a radially innermost one of the stacked plurality of damper elements, the radially inner end element including an opening through which the elongated body extends, the radially inner end element being slidable over the elongated body.

[0043] Another aspect of the present disclosure includes any of the preceding aspects, wherein the plurality of damper elements have at least one of the following characteristics that differ between at least two of the damper elements: overall mass, overall radial length, radial length of the plurality of flexible legs, force required to deflect the plurality of flexible legs outward, shape of the inner end surface, shape of the outer end surface, angle of the at least partially inclined surface.

[0044] Another aspect of the present disclosure includes any of the preceding aspects, wherein the head member of each damper element has an at least partially sloped surface having a cone-shaped shape through which the opening extends.

[0045] Two or more aspects described in this disclosure, including those described in this Summary, may be combined to form embodiments not specifically described herein, i.e., all embodiments described herein can be combined with each other.

[0046] The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will become apparent from the description and drawings, and from the claims. [Brief description of the drawings]

[0047] These and other features of the present disclosure will be more readily understood from the following detailed description of the various aspects of the disclosure taken in conjunction with the accompanying drawings illustrating various embodiments of the present disclosure. [Figure 1]1 illustrates a cross-sectional view of an exemplary turbomachine in the form of a gas turbine system including a turbine. [Diagram 2] 1 is a cross-sectional view of a portion of an exemplary turbine in accordance with an embodiment of the present disclosure. [Diagram 3] 1 is a perspective view of an exemplary turbine blade including a vibration damping system according to an embodiment of the present disclosure. [Figure 4] 1 illustrates a schematic cross-sectional view of a turbine blade having a vibration damping system including a plurality of damper elements according to an embodiment of the present disclosure. [Diagram 5] 1 is a schematic cross-sectional view of a turbine blade having a vibration damping system including a plurality of damper elements according to an embodiment of the present disclosure; [Figure 6] FIG. 2 is a side view of a damper element according to an embodiment of the present disclosure. [Figure 7A] 1 is a partial cross-sectional side view of a vibration damping system including a plurality of stacked damper elements in a first position according to an embodiment of the present disclosure. [Figure 7B] 1 is a partial cross-sectional side view of a vibration damping system including a plurality of stacked damper elements in a second position according to an embodiment of the present disclosure. [Figure 8] Figure 8A is a top view taken along line 8A-8A in Figure 7A, and Figure 8B is a top view taken along line 8B-8B in Figure 7B. [Figure 9] FIG. 13 is a side partial cross-sectional view of a radially inner end element for a vibration damping system according to any embodiment of the present disclosure. [Figure 10] FIG. 13 is a side partial cross-sectional view of a radially outer end element for a vibration damping system according to any embodiment of the present disclosure. [Figure 11] FIG. 13 is a perspective view of a damper element according to another embodiment of the present disclosure. [Figure 12] 2 shows a schematic cross-sectional view of a turbine blade having a vibration damping system including a plurality of damper elements according to another embodiment of the present disclosure; [Figure 13] 2 is a schematic cross-sectional view of a turbine blade having a vibration damping system including a plurality of damper elements according to another embodiment of the present disclosure; [Figure 14] FIG. 13 is a side view of a damper element with its top surface superimposed on a damper element according to another embodiment of the present disclosure. [Figure 15A] 1 is a partial cross-sectional side view of a vibration damping system including a plurality of stacked damper elements in a first position according to another embodiment of the present disclosure. [Figure 15B] 13 is a partial cross-sectional side view of a vibration damping system including a plurality of stacked damper elements in a second position according to another embodiment of the present disclosure. [Figure 16] Figure 16A shows a top-down view along view line 16A-16A of Figure 15A, and Figure 16B shows a top-down view along view line 16B-16B of Figure 15B.

[0048] It should be noted that the drawings of the present disclosure are not necessarily to scale. The drawings are intended to depict only typical aspects of the present disclosure and therefore should not be considered as limiting the scope of the present disclosure. In the drawings, like numbers represent like elements between the drawings. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0049] At the outset, in order to clearly explain the subject matter of this disclosure, it becomes necessary to select certain terms when referring to and describing relevant mechanical components within a turbine. Wherever possible, common industry terms are used and employed in a manner consistent with their common meaning. Unless otherwise noted, such terms should be given a broad interpretation consistent with the context of this application and the scope of the appended claims. Those skilled in the art will appreciate that certain components are often referred to using several different or overlapping terms. What is described herein as being a single part may in other contexts include and be referred to as being made up of several parts. Alternatively, what is described herein as including several components may be referred to elsewhere as being a single part.

[0050] Additionally, some descriptive terms may be used regularly herein, and it should prove useful to define these terms at the beginning of this section. It is often required to describe components that are located at different radial positions relative to the central axis. The term "radial" refers to movement or position perpendicular to the axis. For example, if a first component is located closer to the axis than a second component, the specification states that the first component is "radially inward" or "inboard" of the second component. On the other hand, if a first component is located further from the axis than the second component, the specification may state that the first component is "radially outward" or "outboard" of the second component. The term "axial" refers to movement or position parallel to the axis. Finally, the term "circumferential" refers to movement or position around the axis. It will be understood that such terms may be applied in relation to the central axis of the damper element or the central axis of the turbine.

[0051] Furthermore, certain descriptive terms may be used regularly herein, as explained below: The terms "first," "second," and "third" may be used interchangeably to distinguish one component from another, and are not intended to imply a position or importance of the individual components.

[0052] The terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the disclosure. As used herein, the singular forms "a," "an," and "the" are intended to include the plural unless the context clearly indicates otherwise. Furthermore, as used herein, it will be understood that the terms "comprises" and / or "comprising" specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. "Optional" or "optionally" means that the subsequently described event or circumstance may or may not occur, or that the subsequently described component or element may or may not be present, and that the description includes instances in which the event occurs or the component is present as well as instances in which it does not occur or is not present.

[0053] When an element or layer is referred to as "resting on," "engaging," "connecting," or "bonded" to another element or layer, it may be directly resting on, engaging, connecting, or bonding with the other element or layer, or there may be intervening elements or layers present. In contrast, when an element is referred to as "directly resting on," "directly engaging," "directly connected," or "directly bonded" to another element or layer, there are no intervening elements or layers present. Other words used to describe relationships between elements should be interpreted similarly (e.g., "directly between" vs. "between," "directly adjacent" vs. "adjacent," etc.). As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items.

[0054] An embodiment of the present disclosure provides a damper element and vibration damping system for a turbine blade. The vibration damping system includes a plurality of the stacked damper elements. One or more damper elements for the vibration damping system may be used in a body opening of a rotating blade in a turbine. The damper element includes a head member having an at least partially inclined surface and a plurality of flexible legs extending from the head member. Each flexible leg includes a radially extending body portion having an end, the end having an outer end surface and an inner end surface. Under the influence of centrifugal forces caused by rotation of the rotating blade at a rotational speed higher than a predetermined rotational speed, the head members of adjacent damper elements urge the outer end surfaces of the plurality of flexible legs of the damper element into frictional engagement with the inner surface of the body opening to damp vibrations. In certain embodiments, an elongated body may extend through the opening of the head member of the one or more damper elements.

[0055] One or more damper elements according to embodiments of the present disclosure are more likely to capture relative motion than other stacked damper pins because they are forced to expand and contact the inner surface of the body opening in the rotating blade. This arrangement is advantageous because it allows the damper elements to move instantly with the inner surface of the body opening of the rotating blade, i.e., when centrifugal forces may not expand the flexible legs, and the sliding movement from unloaded flexible legs to loaded, flexed legs creates a stick-slip motion that is effective for vibration damping. The vibration damping system reduces blade vibration with a simple arrangement and does not add much extra mass to the blade. Thus, the vibration damping system and damper elements do not increase the overall centrifugal forces on the blade tips and do not require changes to the blade configuration.

[0056] Referring to the drawings, Figure 1 is a cross-sectional view of an exemplary machine including a turbine to which the teachings of the present disclosure may be applied. In Figure 1, a turbomachine 90 in the form of a combustion turbine or gas turbine (GT) system 100 (hereinafter "GT system 100") is shown. The GT system 100 includes a compressor 102 and a combustor 104. The combustor 104 includes a combustion region 105 and a fuel nozzle section 106. The GT system 100 also includes a turbine 108 and a common compressor / turbine shaft 110 (hereinafter "rotor 110").

[0057] The GT system 100 may be, for example, a 7HA.03 engine available from General Electric Company, Greenville, SC. ​​The present disclosure is not limited to any particular GT system and may be implemented in connection with other engines, including, for example, other HA, F, B, LM, GT, TM, and E class engine models from General Electric Company, as well as engine models from other manufacturers. More importantly, the teachings of the present disclosure do not necessarily apply only to turbines in GT systems, but may be applied to virtually any type of industrial machine or other turbine, such as steam turbines, jet engines, compressors (as in FIG. 1), turbofans, turbochargers, etc. Thus, references to the turbine 108 of the GT system 100 are merely illustrative and not limiting.

[0058] FIG. 2 illustrates a cross-sectional view of an exemplary portion of the turbine 108. In the illustrated example, the turbine 108 includes four stages L0-L3 that may be used with the GT system 100 of FIG. 1. The four stages are designated L0, L1, L2, and L3. Stage L0 is the first stage and is the smallest (radially) of the four stages. Stage L1 is the second stage and is disposed axially adjacent to the first stage L0. Stage L2 is the third stage and is disposed axially adjacent to the second stage L1. Stage L3 is the fourth and final stage and is the largest (radially). It should be understood that four stages are shown by way of example only and each turbine may have more or less than four stages.

[0059] A plurality of stationary turbine vanes or nozzles 112 (hereinafter "nozzles 112" or "nozzles 112") may cooperate with a plurality of rotating turbine blades 114 (hereinafter "blades 114" or "blades 114") to form each stage L0-L3 of the turbine 108 and define a portion of a working fluid path through the turbine 108. The blades 114 of each stage are coupled to the rotor 110 (FIG. 1), for example, by a respective rotor wheel 116 that circumferentially couples them to the rotor 110 (FIG. 1). That is, the blades 114 are circumferentially spaced apart and mechanically coupled to the rotor 110, for example, by the rotor wheel 116. A static nozzle section 115 includes a plurality of nozzles 112 mounted to a casing 118 and spaced circumferentially around the rotor 110 (FIG. 1). It will be appreciated that the blades 114 rotate with the rotor 110 (FIG. 1) and thus experience centrifugal forces, while the nozzles 112 are stationary.

[0060] 1 and 2, during operation, air flows through the compressor 102 and the compressed air is delivered to the combustor 104. Specifically, the compressed air is delivered to a fuel nozzle section 106 that is integral with the combustor 104. The fuel nozzle section 106 is in flow communication with a combustion zone 105. The fuel nozzle section 106 is also in flow communication with a fuel source (not shown in FIG. 1 ) and channels fuel and air to the combustion zone 105. The combustor 104 ignites and combusts the fuel to generate combustion gases. The combustor 104 is in flow communication with a turbine 108 in which thermal energy from the combustion gas stream is converted to mechanical rotational energy by directing the combusted fuel (e.g., a working fluid) through a working fluid path to rotate blades 114. The turbine 108 is rotatably coupled to and drives a rotor 110. The compressor 102 may also be rotatably coupled to the rotor 110. At least one end of the rotor 110 may extend axially away from the compressor 102 or the turbine 108 and may be attached to a load or machine (not shown), such as, but not limited to, an electrical generator, a load compressor, and / or another turbine.

[0061] Figure 3 is a perspective view of a (rotating) blade 114 of a type in which embodiments of the vibration damping systems 120, 320 of the present disclosure may be employed. As described herein, Figures 4 and 5 show schematic cross-sectional views of a blade 114 including a vibration damping system 120, 320 according to various embodiments of the present disclosure.

[0062] 3, each blade 114 includes a body 128 having a base end 130, a tip 132, and an airfoil 134 extending between the base end 130 and the tip 132. As shown in FIG. 3, the blade 114 includes a dovetail 140 at the base end 130 by which the blade 114 is attached to a rotor wheel 116 ( FIG. 2 ) of the rotor 110 ( FIG. 1 ). The base end 130 of the blade 114 may further include a shank 142 extending between the dovetail 140 and a platform 146. The platform 146 is disposed at the junction of the airfoil 134 and the shank 142 and defines a portion of an inboard boundary of a working fluid path ( FIG. 2 ) through the turbine 108.

[0063] It will be appreciated that the airfoil 134 of the blade 114 is the active component of the blade 114 that intercepts the flow of working fluid and directs the rotor 110 (FIG. 1) to rotate. It will be appreciated that the airfoil 134 of the blade 114 includes a concave pressure side (PS) outer sidewall 150 and a circumferentially or laterally opposed convex suction side (SS) outer sidewall 152 that extend axially between opposing leading and trailing edges 154, 156, respectively. The sidewalls 150, 152 also extend radially from the base end 130 (i.e., the platform 146 of the blade 114) to the tip 132 (i.e., the tip 158 of the blade 114). However, the teachings of the present disclosure are equally applicable to blades that include a tip shroud at the tip 158. The blade 114 shown in FIG. 3 is merely exemplary, and the teachings of the present disclosure are applicable to a wide variety of blades.

[0064] During operation of the turbine, the blades 114 may be excited into vibration by a number of different forcing functions. For example, fluctuations in temperature, pressure, and / or density of the working fluid may excite vibrations throughout the rotor assembly, particularly in the airfoil portion and / or tips of the blades 114. Periodic, or "pulsating," gases exiting the turbine and / or compressor sections upstream may also excite undesirable vibrations. Embodiments of the present disclosure reduce vibrations in the rotating blades 114 without significant changes to the blade design.

[0065] 4 and 5 each show a schematic cross-sectional view of a blade 114 including a vibration damping system 120 according to an embodiment of the present disclosure. The vibration damping system 120 for the blade 114 may include a body opening 160 extending through the airfoil 134 at least partially through the body 128 between its tip 132 and base 130. The body opening 160 may extend a portion of the distance between the base 130 and the tip 132, or may extend through one or more of the base 130 or tip 132. The body opening 160 may be defined in any portion of any structure of the body 128. For example, if the body 128 includes an internal partition wall (not shown) for defining a cooling circuit therein, the body opening 160 may be defined as an internal cavity of the partition wall of the body 128. The body opening 160 generally extends in a radial direction of the body 128. However, some angling, and possibly curvature, of the body opening 160 relative to the radial extent of the body 128 is possible. The body opening 160 has an inner surface 162. The body opening can have an inner diameter ID.

[0066] The body opening 160 may originate at the proximal end 130 of the blade 114, as shown in FIG. 4, or may originate at the distal end 132 of the blade 114, as shown in FIG. 5. More specifically, the body opening 160 may open at the proximal end 130 and terminate at the distal end 132, as shown in FIG. 4, or may open at the distal end 132 and terminate at the proximal end 130, as shown in FIG. 5. Wherever the body opening 160 is located, it may aid in the assembly of the vibration damping system 120 on the blade 114 and may allow the system to be retrofitted to existing blades. If the body opening 160 extends through the proximal end 130, as shown in FIG. 4, a closure member 164 may be provided to close the body opening 160. If the body opening 160 extends through the distal end 132, as shown in FIG. 5, a closure member 166 may be provided for the body opening 160. In addition to closing the body opening 160, the closure members 164, 166 also prevent removal of the vibration damping system 120 from the body opening 160, for example during use. The body opening 160 may have a radially inner end 206 and a radially outer end 210, each of which may be provided at least in part by the closure members 164, 166 in some embodiments.

[0067] Figure 6 is a perspective view of a damper element 170 according to an embodiment of the present disclosure. Figure 7A shows a partial cross-sectional view of a vibration-damping system 120 in a first position and Figure 7B shows a partial cross-sectional view of a vibration-damping system 120 in a second position according to an embodiment of the present disclosure. Figure 8A shows a top view along line 8A-8A of Figure 7A and Figure 8B shows a top view along line 8B-8B of Figure 7B.

[0068] As shown in Figures 7A-B, a damper element 170 for vibration damping system 120 is shown within body opening 160 of a rotating blade 114 of turbine 108 (Figure 1). As shown in Figures 6 and 7A-B, damper element 170 includes a head member 172 having an at least partially inclined surface 174. Damper element 170 also includes a plurality of flexible legs 180 (hereinafter simply "flexible legs 180") extending from head member 172. Each flexible leg 180 includes a radially extending body portion 182 (relative to blade 114) having an end section 184. End section 184 has an outer end surface 186 and an inner end surface 188. As further described herein and shown in Figures 7B and 8B, the head member 172 engages with a flexible leg 180 of another adjacent damper element 170, causing the flexible leg 180 to bend outwardly and frictionally engage with the inner surface 162 of the body opening 160 under the influence of a centrifugal force CF caused by rotation of the rotating blade 114 above a predefined rotational speed to damp vibrations.

[0069] Each flexible leg 180 may have any structure that allows it to flex outwardly so that the outer end surface 186 can frictionally engage the inner surface 162 of the body opening 160 of the blade 114. In the illustrated exemplary embodiment, adjacent radially extending body portions 182 (hereinafter "body portions 182") of the flexible legs 180 define a slot 190 therebetween. The slot 190 may terminate at the head member 172. The slot 190 may have a rounded radially outer extent 192, e.g., U-shaped, although other shapes are possible, e.g., V-shaped, cathedral-shaped, etc. Any number of flexible legs 180 may be provided on each damper element 170. In certain embodiments, between three (3) and six (6) flexible legs 180 are used on each damper element 170, although other numbers are possible. In other embodiments, the body portion 182 can have alternative structures to assist and / or control its deflection, such as, but not limited to, wider or thinner sections, curvatures, voids, etc.

[0070] As previously mentioned, the head member 172 has an at least partially inclined surface 174. The at least partially inclined surface 174 (hereafter, for brevity, the "inclined surface 174") may extend around its entire circumference, for example as a solid circular surface, or may be partially around the circumference of the head member 172, i.e., have a break or open area between similarly inclined surfaces. The inclined surface 174 may have an angle α in the range of 25° to 55° with respect to the inner surface 162 of the body opening 160. As previously mentioned, the body opening 160 may extend generally radially within the body 128 of the blade 114. The inner end surfaces 188 of the plurality of flexible legs 180 are configured to receive, i.e., to engage and move under the influence of, the inclined surface 174 of the head member 172 of the adjacent damper element 170. The inner end surface 188 of the flexible leg 180 can have an angle β in the range of 25° to 55° relative to the inner surface 162 of the body opening 160. Although the angles α and β can be the same, this is not necessary in all cases as long as the head members 172 can bias the legs 180 of the adjacent damper elements 170 outwardly toward the inner surface 162 of the body opening 160. That is, the head members 172 of the adjacent damper elements 170 can frictionally engage the outer end surfaces 186 of the flexible legs 180 with the inner surface 162 of the body opening 160 to damp vibrations when a particular centrifugal force CF is applied based on a predetermined rotational speed of the blade 114.

[0071] In a particular embodiment, the head member 172 and collectively the body portion 182 of the flexible leg 180 each have a first outer diameter OD1. The outer end surface 186 of the flexible leg 180 collectively defines a second outer diameter OD2 that is greater than the first outer diameter OD1. Thus, the head member 172 and the body portion 182 have an outer diameter OD1, i.e., OD2, that is smaller than the outer end surface 186 of the flexible leg. Although illustrated and described as having the same outer diameter OD1, the body portion 182 and the head member 172 may have different outer diameters, so long as they are both smaller than the outer diameter OD2 of the outer end surface 186. As shown in FIGS. 7A and 8A, the second outer diameter OD2 of the outer end surface 186 is smaller than the inner diameter ID of the body opening 160 through which the flexible leg 180 passes freely in the relaxed state. Additionally, in some embodiments, the outer end surface 186 of each flexible leg 180 may be parallel to the inner surface 162 of the body opening 160 in the relaxed state of the plurality of flexible legs 180. In other embodiments, the outer end surface 186 of each flexible leg 180 may be non-parallel to the inner surface 162 of the body opening 160 in the relaxed state of the plurality of flexible legs 180, but within ±5°. In any case, the damper elements 170 can be easily inserted into the body opening 160, either singly or in a pre-stacked manner, without the outer end surfaces 186 of their ends 184 interfering with the insertion.

[0072] 7B and 8B, under the influence of centrifugal force CF caused by rotation of the rotating blade 114 at a rotational speed higher than a predefined rotational speed, the head member 172 of the adjacent damper element 170 urges the outer end surface 186 of the flexible leg 180 into frictional engagement with the inner surface 162 of the body opening 160 to dampen vibrations. In certain embodiments, as shown, the outer end surface 186 of each flexible leg 180 can include an edge 194 that frictionally engages the inner surface 162 of the body opening 160 at a line. The outer end surface 186 of each flexible leg 180 is parallel to the inner surface 162 of the body opening 160 in a relaxed state of the multiple flexible legs 180, but tilts as the flexible leg 180 flexes outward to meet the inner surface 162 at its edge 194.

[0073] As shown in FIGS. 7A-8B, the vibration damping system 120 for the rotating blade 114 includes a plurality of stacked damper elements 170 for positioning in the body opening 160 defined in the rotating blade 114. Any number of damper elements 170 may be used. As previously described, each damper element 170 includes a head member 172 having an at least partially inclined surface 174 and a plurality of flexible legs 180 extending from the head member 172. Each flexible leg 180 includes a radially extending body portion 182 having an end 184 having an outer end surface 186 and an inner end surface 188. The inner end surface 188 of the plurality of flexible legs 180 of each damper element 170 is configured to receive the inclined surface 174 of the head member 172 of an adjacent damper element 170 of the stacked plurality of damper elements 170. As shown in Figures 7B and 8B, under the influence of centrifugal force CF caused by rotation of the rotating blade 114 at a rotational speed higher than a predetermined rotational speed, the head member 172 of the adjacent damper element 170 frictionally engages the outer end surfaces 186 of the multiple flexible legs 180 with the inner surface 162 of the body opening 160 to damp vibrations.

[0074] If the damper elements 170 in a stack are identical, they may all react in the same manner, e.g., the flexible legs 180 spring outward, either simultaneously or sequentially in the stack. However, in other embodiments, two or more damper elements 170 may be customized to react differently. In this case, the damper elements 170 differ between at least two damper elements in at least one of the following characteristics: total mass, total radial length, radial length of the flexible legs, one or more forces required to deflect the flexible legs outward, one or more shapes of the inner end surface, one or more shapes of the outer end surface, and / or one or more angles of the at least partially inclined surface. Different damper elements 170 may be actuated for friction damping in different situations. For example, one or more damper elements 170 may be activated under a first centrifugal force CF1 at a first predetermined rotational speed ω1 of the rotating blades 114, and one or more different damper elements 170 may be activated under a second centrifugal force CF2 (different from the first centrifugal force CF1) at a second predetermined rotational speed ω2 (different from the first predetermined rotational speed ω1) of the rotating blades 114. As one skilled in the art will recognize, numerous different characteristics and different damper elements 170 can be used to provide customized vibration damping, for example, at different centrifugal forces, different radii along the blades 114, and other operating parameters, among others.

[0075] In certain embodiments, as shown in Figures 4 and 5, the vibration damping system 120 includes a plurality of stacked damper elements 170 alone, i.e., has a damper element that interacts with the radially outer end 210 of the body opening 160, i.e., the end of the body opening 160, as in Figure 4, or has a closure member 166 that provides at least a portion of the radially outer end 210, as in Figure 5.

[0076] 9 illustrates a cross-sectional view of an optional embodiment in which a plurality of flexible legs 180 extend radially inward from a respective head member 172 of a damper element 170, similar to FIG. 4. In FIG. 9, the vibration damping system 120 further includes a radially inner end element 200 having a head member 202 having an at least partially inclined surface 204 configured to engage an inner end surface 188 of a plurality of flexible legs 180 of a radially innermost one 170I of the plurality of stacked damper elements 170. The inclined surface 204 of the radially inner end element 200 can have a similar configuration as the inclined surface 174 of the head member 172 of the damper element 170. More specifically, the radially inner end element 200 may have a radially inner end 208 configured to engage a radially inner end 206 of the body opening 160 (i.e., the end of the body opening 160 with or without a closure member 164 (within the dashed lines in FIG. 9 )) in a relaxed, non-actuated state of the rotating blade 114. In an actuated state of the blade 114, the centrifugal force CF urges the radially inner end element 200 against the radially innermost damper element 170I, frictionally engaging the outer end surface 186 (i.e., edge 194) of its flexible leg 180 with the inner surface 162 of the body opening 160 to damp vibrations. The radially inner end element 200 may be weighted to increase the centrifugal force CF applied to its radially outer stacked damper element 170.

[0077] 10 illustrates a cross-sectional view of an optional embodiment in which a plurality of flexible legs 180 extend radially outward from a head member 172 of each of the plurality of stacked damper elements 170, similar to FIG. 5. In FIG. 10, the vibration damping system 120 may further include a radially outer end element 220 configured to engage a flexible leg 180 of a radially outermost one 170X of the plurality of stacked damper elements 170. More specifically, the radially outer end element 220 may have a radially outer end 222 (i.e., an end of the body opening 160 with or without a closure member 166 (dashed line in FIG. 9)) configured to engage a radially outer end 210 of the body opening 160, and a head member 224 having an at least partially inclined surface 226 configured to engage an inner end surface 188 of the plurality of flexible legs 180 of the radially outermost one 170X of the plurality of stacked damper elements 170. The angled surface 226 of the radially outer end element 220 may have a similar configuration as the angled surface 174 of the head member 172 of the damper element 170. The centrifugal force CF biases the radially outermost damper element 170X against the radially outer end element 220, causing its outer end surface 186 (i.e., edge 194) to frictionally engage the inner surface 162 of the body opening 160 to dampen vibrations.

[0078] 4 and 5, FIG. 4 shows a cross-sectional view of an embodiment in which a plurality of flexible legs 180 extend radially inward from the head member 172 of each of a plurality of damper elements 170, and a closure member 164 is at the proximal end 130 of the blade 114. FIG. 5 also shows a cross-sectional view of an embodiment in which a plurality of flexible legs 180 extend radially outward from the head member 172 of each of a plurality of stacked damper elements 170, and a closure member 166 is at the distal end 132 of the blade 114. It is emphasized that the arrangement of stacked damper elements 170 in FIG. 4 and FIG. 5 is interchangeable. That is, the arrangement of damper elements 170 shown in FIG. 5 can be used for a blade 114 in which the closure member 164 is at the proximal end 130 of the blade 114 as in FIG. 4, and the arrangement of damper elements 170 shown in FIG. 4 can be used for a blade 114 in which the closure member 166 is at the distal end 132 of the blade 114 as in FIG. 5. Any of the embodiments of end elements 200, 220 may also be used in their alternate configurations as desired.

[0079] 4-10, head member 172 of damper element 170 has a sloped surface 174 having a cone shape. Figure 11 shows a perspective view of another embodiment of damper element 170 in which head member 172 has a sloped surface 174, but has a domed end 230, i.e., a rounded end rather than a flat end.

[0080] In operation, each of the stacked damper elements 170 provides a flexible leg 180 that expands to frictionally engage the inner surface 162 of the body opening 160. As previously discussed, the damper elements 170 can be customized in many ways to expand and frictionally engage at different operating parameters. The stacked damper elements 170 tend to capture relative motion as they are forced to expand into contact with the inner surface 162 of the body opening 160 of the blade 114. This arrangement is advantageous because it not only allows the damper elements 170 to move readily with the body opening 160 of the blade 114, but the sliding between adjacent damper elements 170 creates a stick-slip motion that is also effective for vibration damping.

[0081] 12-16B show a vibration damping system 320 having a plurality of stacked damping elements 370 according to another embodiment of the present disclosure. FIG. 12-16B are similar to FIG. 4-8B in terms of layout. More specifically, FIG. 12 shows a schematic cross-sectional view of a turbine blade having a vibration damping system 320 including a damper element 370 according to another embodiment of the present disclosure, and FIG. 13 shows a schematic cross-sectional view of a turbine blade having a vibration damping system 320 including a plurality of damper elements 370 according to yet another embodiment of the present disclosure. FIG. 14 shows a side view of a damper element 370 with its upper surface 388 superimposed on the damper element. FIG. 15A shows a side, partial cross-sectional view of a vibration damping system 320 including a plurality of stacked damper elements 370 in a first position according to another embodiment of the present disclosure, and FIG. 15B shows a side, partial cross-sectional view of a vibration damping system 320 including a plurality of stacked damper elements 370 in a second position according to another embodiment of the present disclosure. 16A is a top view taken along line 16A-16A in FIG. 15A, and FIG. 16B is a top view taken along line 16B-16B in FIG. 16B.

[0082] As shown in Figures 12 and 13, the vibration damping system 320 for the blade 114 can include a body opening 160 extending through the body 128 at least partially between its tip 132 and base 130 and extending through the airfoil 134. The body opening 160 can extend a portion of the distance between the base 130 and the tip 132, or can extend through one or more of the base 130 or tip 132. The body opening 160 can be defined in any portion of any structure of the body 128. For example, if the body 128 includes an internal partition wall (not shown) for defining a cooling circuit therein, the body opening 160 can be defined as an internal cavity of the partition wall of the body 128. The body opening 160 generally extends in a radial direction of the body 128. However, some angling, and possibly curvature, of the body opening 160 relative to the radial extent of the body 128 is possible. The body opening 160 has an inner surface 162. The body opening can have an inside diameter ID.

[0083] The body opening 160 may originate at the proximal end 130 of the blade 114, as shown in FIG. 12, or may originate at the distal end 132 of the blade 114, as shown in FIG. 13. More specifically, the body opening 160 may be open at the proximal end 130 and terminate at the distal end 132, as shown in FIG. 12, or may be open at the distal end 132 and terminate at the proximal end 130, as shown in FIG. 13. The open ends may aid in the assembly of the vibration damping system 120 on the blade 114 and may allow the retrofitting of the system to existing blades. If the body opening 160 extends through the proximal end 130, as shown in FIG. 12, a closure member 164 may be provided to close the body opening 160. If the body opening 160 extends through the distal end 132, as shown in FIG. 13, a closure member 166 may be provided for the body opening 160. In addition to closing the body opening 160, the closure members 164, 166 prevent the vibration damping system 120 from being removed from the body opening 160, for example, during use. The body opening 160 may have a radially inner end 206 and a radially outer end 210, each of which may be provided at least in part by the closure members 164, 166 in some embodiments.

[0084] The vibration damping system 320 (and damper elements 370 therefor) are substantially similar in structure and function to those described in connection with other embodiments herein. For example, the damper elements 370 are substantially similar to the damper elements 170 described in connection with Figs. 4-8B. In particular, the damper elements 370 include a head member 172 having an at least partially inclined surface 174 and a plurality of flexible legs 180 extending from the head member 172. In contrast to the damper elements 170 (Figs. 4-8B), the damper elements 370 include an opening 390 defined through the center of the head member 172 and an elongated body 392 extending through the opening 390 in the head member 172. As shown in Fig. 14, the head members 172 of each damper element 370 have an inclined surface 174 having a cone shape through which the opening 390 extends. Other shapes of the head members 172 are possible.

[0085] The opening 390 and the elongated body 392 can have any mating cross-sectional shape, such as circular (e.g., as shown in FIG. 14 ), oval or elliptical, polygonal, etc. A single elongated body 392 can extend through each damper element 370 in the stack of damper elements 370 in the vibration damping system 320. The elongated body 392 is configured to resonate at the same frequency as the rotating blades 114, such that the elongated body 392 generates a force against the damper elements 370. The elongated body 392 can be configured to resonate at the same frequency as the rotating blades 114, particularly by controlling its mass, deflection, stiffness, diameter, and length. The elongated body 392 slides freely within the opening 390, but has a close clearance with the opening 390 such that movement of the elongated body 392 caused by vibration of the blades 114 physically impacts the inside of the opening 390, moving each damper element 370. In this manner, the elongated body 392 can reduce the likelihood of the damper elements 370 sticking to the inner surface 162 of the body opening 160 or to each other.

[0086] The vibration damping system 320 may include only stacked damper elements 370, similar to the arrangement shown in Figures 4 and 5 for the damper element 170. In other embodiments, as shown in Figures 12 and 13, the vibration damping system 320 may further include a radially outer retaining element 330 secured to the elongated body 392 for retaining the plurality of stacked damper elements 370 on the elongated body 392. The radially outer retaining element 330 may take a variety of forms. In one example shown in Figure 12, the radially outer retaining element 330 may include an end 332 configured to abut the radially outer end 210 of the body opening 160, i.e., the end of the body opening 160, in use, with or without the closure member 166 (Figure 13). The radially outer retaining element 330 may also include a radially inner end 334 having a shape corresponding to the head member 172 of the radially outermost damper element 370X. 12, where multiple flexible legs 180 extend radially outward from the head members 172 of each of multiple damper elements 370, the radially inner end 334 of the radially outer retaining element 330 is shaped to engage or receive the head member 172 of the radially outermost damper element 370X. For example, the radially inner end 334 of the radially outer retaining element 330 may have a flat surface that engages the head member 172 or may have a trapezoidal concave cross-section (not shown) for receiving a (complementarily) matching head member 172. If the head members 172 have a different shape, the radially inner end 334 of the radially outer retaining element 330 may have a complementary shape. 13 , where multiple flexible legs 180 extend radially outward from a respective head member 172 of each of multiple damper elements 370, radially inner end 334 of radially outer retaining element 330 has a similar shape to head member 172 of radially outermost damper element 370X, i.e., a cone shape for biasing flexible legs 180 of radially outermost damper element 370X into frictional engagement with inner surface 162 of body opening 160. Where head member 172 has a different shape, radially inner end 334 of radially outer retaining element 330 may be a complementary shape.

[0087] 12 and 13, the vibration damping system 320 may further include a radially inner end element 340 slidably coupled to the elongated body 392 for applying additional centrifugal force to the plurality of damper elements 370 stacked on the elongated body 392. As shown in FIG. 12, where the flexible legs 180 extend radially inward from the head members 172 of each of the plurality of damper elements 370, the radially inner end element 340 may include a radially outer end (head member) 342 having an at least partially sloped surface 344 configured to engage the inner end surface 188 (FIGS. 15A-B) of the plurality of damper elements 370. The stacked damper elements 370 include an inner end surface 188 (FIGS. 15A-B) of a plurality of flexible legs 180 (FIGS. 15A-B) of a radially innermost one 370I of the stacked damper elements 370 and an opening 346 through a radially inner end element 340 through which an elongated body 392 extends. The radially inner end element 340 is slidable on the elongated body 392, i.e., applies additional centrifugal force to the stacked damper elements 370. The radially inner end 348 of the radially inner end element 340 can have any shape adjacent the radially inner end 206 of the body opening 160 in the non-actuated state of the blade 114, i.e., with or without the closure member 164 (FIG. 12).

[0088] As shown in FIG. 13, when the flexible legs 180 extend radially outward from the head members 172 (FIGS. 15A-B) of each of the damper elements 370, the radially inner end element 340 may be configured to engage the head member 172 (FIG. 14) of the radially innermost one 370I of the stacked damper elements 370. For example, the radially outer end 342 of the radially inner end element 340 may have a flat surface that engages the head member 172 or may have a trapezoidal concave cross-section (not shown) that receives a (complementarily) matching head member 172. The radially inner end element 340 also includes an opening 346 through which the elongated body 392 extends. The radially inner end element 340 is slidable on the elongated body 392, i.e., applies additional centrifugal force to the stacked damper elements 370. In FIG. 13, the radially inner end 348 of the radially inner end element 340 can have any shape adjacent the radially inner end 206 of the body opening 160 in the unactuated state of the blade 114, i.e., with or without the closure member 164 (FIG. 12).

[0089] The vibration damping system 320 for the rotating blade 114 includes a plurality of stacked damper elements 370 for positioning in the body openings 160 defined in the rotating blade 114. As previously described, each damper element 370 includes a head member 172 having an at least partially inclined surface 174 and an opening 390 defined through the center of the head member 172. A plurality of flexible legs 180 extend from the head member 172 and an elongated body 392 extends through the openings 390 in the head member 172 of each damper element 370. Other embodiments of the vibration damping system 320 may be arranged as described for the vibration damping system 120 (FIGS. 4, 5, 7A-8B).

[0090] In certain embodiments, if the damper elements 370 in a stack are identical, they can all react in the same manner, e.g., the flexible legs 180 spring outwardly, either simultaneously or sequentially in the stack. However, in other embodiments, two or more damper elements 370 can be customized to react differently. In this case, the damper elements 370 differ between at least two damper elements in at least one of the following characteristics: total mass, total radial length, radial length of the flexible legs, force required to deflect the flexible legs outward, shape of the inner end surface, shape of the outer end surface, angle of at least a portion of the inclined surface. In this way, different damper elements 370 can operate for friction damping in different situations. For example, one or more damper elements 370 may be activated under a first centrifugal force CF1 (not shown in the drawings) at a first predetermined rotational speed ω1 of the rotating blades 114, and one or more different damper elements 370 may be activated under a second centrifugal force CF2 (different from the first centrifugal force CF1) at a second predetermined rotational speed ω2 (different from the first predetermined rotational speed ω1) of the rotating blades 114. As one skilled in the art will recognize, multiple (multiple) different characteristics and different damper elements 370 can be used to provide customized vibration damping, for example, at different centrifugal forces, different radii along the blades 114, and other operating parameters, among others.

[0091] In operation, the stacked damper elements 370 each provide a flexible leg 180 that expands to frictionally engage the inner surface 162 of the body opening 160. As previously mentioned, the damper elements 370 can be customized in many ways to expand and frictionally engage at different operating parameters. The stacked damper elements 370 tend to capture relative motion because they are forced to expand into contact with the inner surface 162 of the body opening 160 of the blade 114. This arrangement is advantageous because it not only allows the damper elements 370 to move readily with the body opening 160 of the blade 114, but the sliding between adjacent damper elements 370 creates a stick-slip motion that is also effective for vibration damping. The elongated body 392 reduces the possibility of the damper elements 370 sticking against the inner surface 162 of the body opening 160 or against each other.

[0092] The damper elements 170, 370 may be formed using any now known or later developed manufacturing process, such as casting. In certain preferred embodiments, the damper elements 170, 370 may be additively manufactured from any material capable of withstanding the environment in which they will be used, including, but not limited to, cobalt chrome. The damper elements 170, 370, elongated body 392, and the various end elements 200, 220, 330, 340 may be made of any material having sufficient strength, flexibility, and durability for a given function and environment within the blade 114.

[0093] The embodiments of the present disclosure provide various technical and commercial advantages, examples of which are described herein. The damper element(s) and vibration damping system having the damper elements are more likely to capture relative motion as they are forced to expand and contact the inner surface of the body opening of the rotating blade. The various arrangements described herein are advantageous because they not only allow the damper element(s) to move with the inner surface of the body opening of the rotating blade immediately, i.e., when centrifugal forces do not expand the flexible legs, but also because the sliding from unloaded flexible legs to loaded, flexed legs creates a stick-slip motion that is effective for vibration damping. The vibration damping system also reduces blade vibration with a simple arrangement and does not add much extra mass to the blade. Thus, the vibration damping system and damper elements do not need to significantly increase the overall centrifugal force on the blade tip or change the configuration of the blade.

[0094] Approximate expressions used throughout the specification and claims can be applied to modify any quantitative expression that can be permissibly changed without resulting in a change in the basic function to which it relates. Thus, values ​​modified by terms such as "about", "approximately", "substantially" and the like are not limited to the exact values ​​specified. In at least some instances, approximation expressions may correspond to the precision of the instrument for measuring the value. Throughout the specification and claims, range limitations may be combined and / or interchanged. Such ranges are specified and include all subranges contained therein, unless the context or language indicates otherwise. "Approximately" or "about" applied to a particular value in a range applies to both endpoints and may indicate ±10% of the stated value, unless dependent on the precision of the instrument for measuring the value.

[0095] Corresponding structures, materials, acts, and equivalents of all means or step-plus-function elements in the following claims are intended to include any structure, material, or act for performing a function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description, but is not intended to be exhaustive or limiting of the disclosure in the disclosed form. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the present disclosure. The embodiments have been selected and described in order to best explain the principles and practical applications of the present disclosure, and to enable those skilled in the art to understand the present disclosure in various embodiments with various modifications as suited to the particular uses contemplated. [Explanation of symbols]

[0096] 90: turbomachine 100: GT system 102: compressor 104: combustor 105: combustion region 106: fuel nozzle section 108: turbine 110: rotor 112: nozzle 114: rotating blades 115: stationary nozzle section 116: rotor wheel 118: casing 120: vibration damping system 128: body 130: base end 132: tip 134: airfoil 140: dovetail 142: shank 146: platform 150: pressure side outer sidewall 152: suction side outer sidewall 156: leading edge 158: trailing edge 160: body opening 162: inner surface 164, 166: closure member 170: damper element 170I: ​​radially innermost damper element 170X: radially outermost damper element 172: head member 174: at least partially beveled surface / beveled surface 180: flexible leg 182: body portion 84: end 186: outer end face 188: inner end face 190: slot 192: rounded radially outer extent 194: edge 200: radially inner end element 202: head member 204: beveled surface 206: radially inner end 208: radially inner end 210: radially outer end 220: radially outer end element 224: head member 226: beveled surface 230: domed end 320: vibration damping system 330: radially outer retaining element 332: end 334: radially inner end 340: radially inner end element 342: radially outer end 344: at least partially beveled surface 346: opening 348: radially inner end 370: damper element 370I: radially innermost damper element 370X: radially outermost damper element 388: upper surface 90: opening 392: elongated body α, β: angle ID: inner diameter CF: centrifugal force L0-L3: stage OD1: first outer diameter OD2: second outer diameter ω1: first rotation speed ω2: second rotation speed

Claims

1. 1. A damper element (170, 370) for a vibration damping system (120, 320) in a body opening (260) of a rotating blade (114) of a turbine (108), comprising: a head member (172, 202, 224, 342) having an at least partially inclined surface (174, 204, 226, 344) and an opening (390) defined through a center of the head member (172, 202, 224, 342); a plurality of flexible legs (180) extending from the head member (172, 202, 224, 342), each flexible leg (180) including a radially extending body portion (182) having an end portion (184), the end portion (184) having an outer end surface (186) and an inner end surface (188); an elongate body (392) extending through an opening (390) in the head member (172, 202, 224, 342); A damper element (170, 370).

2. The damper element (170, 370) of claim 1, wherein the elongated body (392) is configured to resonate at the same frequency as the rotating blades (114), whereby the elongated body (392) generates a force on the damper element (170, 370).

3. 2. The damper element (170, 370) of claim 1, wherein the at least partially inclined surface (174, 204, 226, 344) has an angle in the range between 25° and 55° relative to the inner surface (162) of the body opening (160), and the inner end surfaces (188) of the multiple flexible legs (180) have an angle in the range between 25° and 55° relative to the inner surface (162) of the body opening (160).

4. 2. The damper element (170, 370) of claim 1, wherein the head members (172, 202, 224, 342) and collectively the radially extending body portions (182) of the plurality of flexible legs (180) each have a first outer diameter, and the outer end surfaces (186) of the plurality of flexible legs (180) collectively define a second outer diameter that is greater than the first outer diameter.

5. 5. The damper element (170, 370) of claim 4, wherein the body opening (160) has an inner surface (162) having a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the plurality of flexible legs (180) pass freely within the body opening (160).

6. an inner end surface (188) of the plurality of flexible legs (180) configured to receive an at least partially inclined surface (174, 204, 226, 344) of a head member (172, 202, 224, 342) of an adjacent damper element (170, 370); 5. The damper element (170, 370) of claim 4, wherein under the influence of centrifugal forces caused by rotation of the rotating blade (114) at a rotational speed greater than a predetermined rotational speed, the head members (172, 202, 224, 342) of adjacent damper elements (170, 370) frictionally engage outer end surfaces (186) of the multiple flexible legs (180) with an inner surface (162) of the body opening (160) to damp vibrations.

7. The damper element (170, 370) of claim 6, wherein an outer end surface (186) of each flexible leg (180) frictionally engages an inner surface (162) of the body opening in a single line.

8. 2. The damper element (170, 370) of claim 1, wherein adjacent radially extending body portions (182) of the plurality of flexible legs (180) define a slot (190) therebetween having a rounded radially outer extent (192).

9. 2. The vibration damping system of claim 1, wherein the head member of each damper element has an at least partially inclined surface having a cone shape with an opening extending therethrough.

10. A vibration damping system (120, 320) for a rotating blade (114), comprising: a plurality of stacked damper elements (170, 370) for positioning in a body opening (160) defined in a rotating blade (114), each damper element (170, 370) comprising: a head member (172, 202, 224, 342) having an at least partially inclined surface (174, 204, 226, 344) and an opening (390) defined through a center of the head member (172, 202, 224, 342); a plurality of flexible legs (180) extending from the head member (172, 202, 224, 342), each flexible leg (180) including a radially extending body portion (182) having an end portion (184), the end portion (184) having an outer end surface (186) and an inner end surface (188); an elongated body (392) extending through an opening (390) in the head member (172, 202, 224, 342) of each of the plurality of damper elements (170, 370); A vibration damping system (120, 320).

11. 11. The vibration damping system (120, 320) of claim 10, wherein the at least partially inclined surface (174, 204, 226, 344) of each damper element (170, 370) has an angle in the range between 25° and 55° relative to the inner surface (162) of the body opening (160), and the inner end surfaces (188) of the multiple flexible legs (180) have an angle in the range between 25° and 55° relative to the inner surface (162) of the body opening (160).

12. 11. The vibration damping system of claim 10, wherein the head member and, collectively, the radially extending body portions of the flexible legs of each damper element each have a first outer diameter, and the outer end surfaces of the flexible legs of each damper element collectively define a second outer diameter that is greater than the first outer diameter.

13. 13. The vibration damping system (120, 320) of claim 12, wherein the body opening (160) has an inner surface (162) having a third inner diameter, and the second outer diameter is smaller than the third inner diameter, such that in a relaxed state, the multiple flexible legs (180) of each damper element (170, 370) pass freely within the body opening (160).

14. an inner end surface (188) of the plurality of flexible legs (180) of each damper element (170, 370) configured to receive at least a partially inclined surface of a head member (174, 204, 226, 344) of an adjacent damper element (172, 202, 224, 342) of the stacked plurality of damper elements (170, 370); 13. The vibration damping system (120, 320) of claim 12, wherein under the influence of centrifugal forces caused by rotation of the rotating blade (114) at a rotational speed greater than a predetermined rotational speed, the head members (172, 202, 224, 342) of adjacent damper elements (170, 370) frictionally engage outer end surfaces (186) of the multiple flexible legs (180) with an inner surface (162) of the body opening (160) to damp vibrations.

15. The vibration damping system (120, 320) of claim 14, wherein an outer end surface (186) of each flexible leg (180) frictionally engages an inner surface (162) of the body opening (160) in a single line.

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