A method of damping a vibration in a rotatable member and a damping system for a rotatable machine are provided. The damping system includes one or more damping stages. The rotatable machine further comprising a casing at least partially surrounding the rotor. The casing includes inwardly extending vanes that include a radially outer root, a radially inner distal end, and a stationary body extending therebetween. The one or more damping stages includes a damper supportively coupled between one or more roots of the plurality of vanes and the casing, an air bearing fixedly coupled to one or more distal ends of the plurality of vanes and configured to bear against the rotatable body wherein the damping stage is configured to receive vibratory forces from the rotatable body through the air bearing and the vane and ground the received forces to the casing through the damper.

A damper seal received in a cavity of a turbine blade includes a central body with two ends and a two sides. A portion extends from each end, one side has a faceted edge, and a projection extends from the other side to receive a lug of the turbine blade to align the damper seal relative to the turbine blade.

A damper seal received in a cavity of a turbine blade includes a central body with two ends and a two sides. A portion extends from each end, one side has a faceted edge, and a projection extends from the other side to receive a lug of the turbine blade to align the damper seal relative to the turbine blade.

A blisk assembly for vibration dampening includes a disk portion extending circumferentially about a central axis of the blisk, a plurality of blades integrally coupled to the disk, and a piezoelectric damping ring that includes a damping ring and a plurality of piezoelectric elements coupled to the damping ring. The disk portion includes a groove configured to receive the piezoelectric damping ring. As a result of centrifugal forces applied to the piezoelectric damping ring during rotation of the blisk assembly, mechanical energy may be generated at one or more of the plurality of piezoelectric elements, which is converted to electrical energy and transmitted to another one or more of the plurality of piezoelectric elements. Accordingly, the one or more of the piezoelectric elements having received the electricity can convert the electricity to mechanical energy to provide vibration damping.

A blisk assembly for vibration dampening includes a disk portion extending circumferentially about a central axis of the blisk, a plurality of blades integrally coupled to the disk, and a piezoelectric damping ring that includes a damping ring and a plurality of piezoelectric elements coupled to the damping ring. The disk portion includes a groove configured to receive the piezoelectric damping ring. As a result of centrifugal forces applied to the piezoelectric damping ring during rotation of the blisk assembly, mechanical energy may be generated at one or more of the plurality of piezoelectric elements, which is converted to electrical energy and transmitted to another one or more of the plurality of piezoelectric elements. Accordingly, the one or more of the piezoelectric elements having received the electricity can convert the electricity to mechanical energy to provide vibration damping.

A modal analysis is performed on a blade and disk assembly of a turbomachine, including creating a finite element model of the blade and disk assembly made up of a plurality of nodes corresponding to points on the blade and disk assembly and characterized by a simplifying assumption of a rigidly attached connection between the blade and disk. The modal analysis also includes selecting a target vibration frequency at which a target amplitude of vibration has been one of measured or estimated for a target node during operation, and deriving modal velocity vectors from the target amplitude at the target node. A transient analysis is then performed in a time domain on a numerical model of the blade and disk assembly, including modeling the connection between the blade and disk such that the connection is characterized by a first degree of flexibility representative of a first set of actual operating conditions at the connection, and introducing a perturbation to the transient analysis at an initial steady state condition by applying the modal velocity vectors suddenly to a plurality of nodes of the numerical model of the blade and disk assembly while maintaining the initial steady state condition.

An exemplary gas turbine includes a rotor unit, a tie-bolt, a cooling air pipe, and a clamping member. The rotor unit includes rotor blades and rotor disks. The rotor blades are arranged on outer circumferential surfaces of the rotor blades. The tie-bolt extends along the central axis of the rotor unit through the rotor disks and fastens the rotor disks. The cooling air pipe has the tie-bolt arranged therethrough and forms a ring-shaped cooling air flow path in an internal space thereof with the tie-bolt through which a cooling air is passed. The clamping member is arranged in the ring-shaped cooling air flow path so as to support the tie-bolt with respect to the cooling air pipe.

An exemplary gas turbine includes a rotor unit, a tie-bolt, a cooling air pipe, and a clamping member. The rotor unit includes rotor blades and rotor disks. The rotor blades are arranged on outer circumferential surfaces of the rotor blades. The tie-bolt extends along the central axis of the rotor unit through the rotor disks and fastens the rotor disks. The cooling air pipe has the tie-bolt arranged therethrough and forms a ring-shaped cooling air flow path in an internal space thereof with the tie-bolt through which a cooling air is passed. The clamping member is arranged in the ring-shaped cooling air flow path so as to support the tie-bolt with respect to the cooling air pipe.

A rotor blade vibration damper for a gas turbine engine includes an elongated damper body including a top portion extending longitudinally between a front end and a rear end. The top portion has a width defined between spaced apart lateral sides and is substantially flat between the front and rear ends and between the lateral sides such as to define a longitudinal plane within which the top portion lies. A front tab extends downwardly from the front end of the top portion relative to the longitudinal plane. The rear end of the top portion is flat and generally contained in the longitudinal plane. A pair of lateral tabs extends downwardly from each of said lateral sides of the top portion relative to the longitudinal plane.

A rotor blade vibration damper for a gas turbine engine includes an elongated damper body including a top portion extending longitudinally between a front end and a rear end. The top portion has a width defined between spaced apart lateral sides and is substantially flat between the front and rear ends and between the lateral sides such as to define a longitudinal plane within which the top portion lies. A front tab extends downwardly from the front end of the top portion relative to the longitudinal plane. The rear end of the top portion is flat and generally contained in the longitudinal plane. A pair of lateral tabs extends downwardly from each of said lateral sides of the top portion relative to the longitudinal plane.