Rotational inerter and method for damping an actuator

An apparatus for damping an actuator includes an inerter. The inerter includes a first terminal and a second terminal movable relative to one another along an inerter axis and configured to be mutually exclusively coupled to a support structure and a movable device actuated by an actuator. The inerter further includes a rod coupled to and movable with the first terminal and a threaded shaft coupled to and movable with the second terminal. The inerter further includes a flywheel having a flywheel annulus coupled to one of the rod and the threaded shaft. The flywheel is configured to rotate in proportion to axial acceleration of the rod relative to the threaded shaft in correspondence with actuation of the movable device by the actuator.

FIELD

The present disclosure relates to actuators and, more particularly, to a rotational inerter and method for damping an actuator.

BACKGROUND

Aircraft typically include a flight control system for directional and attitude control of the aircraft in response to commands from a flight crew or an autopilot. A flight control system may include a plurality of movable flight control surfaces such as ailerons on the wings for roll control, elevators on the horizontal tail of the empennage for pitch control, a rudder on the vertical tail of the empennage for yaw control, and other movable control surfaces. Movement of a flight control surface is typically effected by one or more actuators mechanically coupled between a support structure (e.g., a wing spar) and the flight control surface (e.g., an aileron). In many aircraft, the actuators for flight control surfaces are linear hydraulic actuators driven by one or more hydraulic systems which typically operate at a fixed working pressure.

One of the challenges facing aircraft designers is preventing the occurrence of flutter of the flight control surfaces during flight. Control surface flutter may be described as unstable aerodynamically-induced oscillations of the flight control surface, and may occur in flight control systems where the operating bandwidth of the flight control system overlaps the resonant frequency of the flight control surface. Unless damped, the oscillations may rapidly increase in amplitude with the potential for undesirable results, including exceeding the strength capability of the mounting system of the flight control surface and the actuator. Contributing to the potential for control surface flutter is elasticity in the flight control system. For example, hydraulic actuators may exhibit a linear spring response under load due to compressibility of the hydraulic fluid. The compressibility of the hydraulic fluid may be characterized by the cross-sectional area of the actuator piston, the volume of the hydraulic fluid, and the effective bulk modulus of elasticity of the hydraulic fluid.

One method of addressing control surface flutter involves designing the flight control system such that the operating bandwidth does not overlap the resonant frequency of the flight control surface, and may include limiting the inertia of the load on the actuator and/or increasing the piston cross-sectional area as a means to react the inertia load. Unfortunately, the above known methods result in an actuator system that is sized not to provide the actuator with static load-carrying capability, but rather to provide the actuator with the ability to react larger inertia as a means to avoid resonance in the operating bandwidth. As may be appreciated, limiting control surface inertia corresponds to a decrease in control surface area. A decrease in the surface area of higher inertia control surfaces of an aircraft empennage may reduce the attitude controllability of the aircraft. As may be appreciated, an increase in the piston cross-sectional area of an actuator corresponds to an increase in the size and weight of the hydraulic system components including the size and weight of the actuators, tubing, reservoirs, and other components. The increased size of the actuators may protrude further outside of the outer mold line of the aerodynamic surfaces resulting in an increase in aerodynamic drag of an aircraft. The reduced attitude controllability, increased weight of the hydraulic system, and increased aerodynamic drag may reduce safety, fuel efficiency, range, and/or payload capacity of the aircraft.

As can be seen, there exists a need in the art for a system and method for allowing the operating bandwidth of an actuator to match or encompass the resonant frequency of a movable device without oscillatory response.

SUMMARY

The above-noted needs associated with actuators are specifically addressed and alleviated by the present disclosure which provides an apparatus including an inerter for damping an actuator. The inerter includes a first terminal and a second terminal movable relative to one another along an inerter axis and configured to be mutually exclusively coupled to a support structure and a movable device actuated by an actuator. In one example, the inerter further includes a rod coupled to and movable with the first terminal. The inerter also includes a threaded shaft coupled to and movable with the second terminal. The inerter additionally includes a flywheel having a flywheel annulus coupled to the rod. The flywheel is configured to rotate in proportion to axial acceleration of the rod relative to the threaded shaft in correspondence with actuation of the movable device by the actuator.

Also disclosed is aircraft having a flight control surface pivotably coupled to a support structure of the aircraft. The aircraft further includes a hydraulic actuator configured to actuate the flight control surface. In addition, the aircraft includes an inerter having a first terminal and a second terminal mutually exclusively coupled to the support structure and the flight control surface. The inerter additionally includes a rod movable with the first terminal, and a threaded shaft movable with the second terminal. The inerter also includes a flywheel coupled to the rod and the threaded shaft. The flywheel is configured to rotate in proportion to axial acceleration of the rod relative to the threaded shaft in correspondence with actuation of the flight control surface by the actuator.

In addition, disclosed is a method of damping an actuator. The method includes actuating, using an actuator, a movable device. In addition, the method includes axially accelerating, using an inerter coupled to the movable device, a first terminal relative to a second terminal of the inerter simultaneous with and in proportion to actuation of the movable device. Furthermore, the method includes rotationally accelerating a flywheel of the inerter in proportion to and simultaneous with the axial acceleration of the first terminal relative to the second terminal. Additionally, the method includes reducing actuator load oscillatory amplitude of the movable device and actuator in response to rotationally accelerating the flywheel.

The features, functions and advantages that have been discussed can be achieved independently in various examples of the present disclosure or may be combined in yet other examples, further details of which can be seen with reference to the following description and drawings below.

DETAILED DESCRIPTION

Referring now to the drawings wherein the showings are for purposes of illustrating various examples of the present disclosure, shown inFIG. 1is a block diagram of a hydraulic actuator204coupled between a support structure116and a movable device124and configured to move or actuate the movable device124. The block diagram advantageously includes a rotational inerter300for damping the actuator202. The inerter300is shown coupled between the support structure116and the movable device124and is configured to improve the dynamic response of the movable device124during actuation by the actuator202, as described in greater detail below. In the example shown inFIGS. 1 and 4-9, the inerter300is provided as a separate component from the actuator202. However, in other examples (e.g.,FIGS. 2 and 10-21) described below, the inerter300is integrated into the actuator202.

The actuator202includes a piston216coupled to a piston rod224. The piston216is slidable within an actuator housing228(e.g., a cylinder). The actuator202further includes a rod end214and a cap end212axially movable relative to one another in response to pressurized hydraulic fluid acting in an unbalanced manner on one or both sides of the piston216inside the actuator housing228. In the example shown, the rod end214is coupled to the movable device124and the cap end212is coupled to the support structure116. However, the actuator202may be mounted such that the rod end214is coupled to the support structure116and the cap end212is coupled to the movable device124.

Referring still toFIG. 1, the inerter300includes a first terminal302and a second terminal304axially movable or translatable relative to one another along an inerter axis306(FIG. 8) in correspondence with actuation of the movable device124by the actuator202. In the example shown, the first terminal302is coupled to the movable device124and the second terminal304is coupled to the support structure116. However, the inerter300may be mounted such that the first terminal302is coupled to the support structure116and the second terminal304is coupled to the movable device124. In an example not shown, the support structure to which the inerter300is coupled may be a different support structure than the support structure116to which the actuator202is coupled.

The inerter300includes an inerter rod308coupled to and axially movable (e.g., translatable) with the first terminal302. The inerter rod308may be aligned with or parallel to the inerter axis306. The inerter rod308may be hollow to define a rod bore310. The threaded shaft322is coupled to and axially movable (e.g., translatable) with the second terminal304. The threaded shaft322may be aligned with or parallel to the inerter axis306. The threaded shaft322has a free end324that may be receivable within the rod bore310. The threaded shaft322may be hollow or may include a shaft bore323open on the free end324of the threaded shaft322. The threaded shaft322may include radial passages325extending radially from the shaft bore323to the exterior side of the threaded shaft322to allow fluid flow between the exterior side of the threaded shaft322and the shaft bore323. The shaft bore323may allow fluid hydraulic fluid—not shown) to flow from the fluid cavity at a second terminal304(for non-integrated inerters—FIG. 1) or cap end212(for integrated inerters—FIG. 2), through the shaft bore323, and into the fluid cavity at the free end324(FIG. 8) of the threaded shaft322to allow the fluid to lubricate moving parts of the bearing328and/or at the flywheel annulus318. The size (e.g., diameter) of the shaft bore323and the size (e.g., diameter) and quantity of the radial passages325may be configured to apportion fluid flow to the bearing328and the flywheel annulus318.

As shown inFIG. 1, the inerter300includes a flywheel314(e.g., a spinning mass). In some examples (e.g.,FIGS. 6 and 8-16), the flywheel314is threadably coupled to the threaded shaft322which converts linear motion of the threaded shaft322into rotational motion of the flywheel314. The flywheel314is configured to rotate in proportion to axial movement of the inerter rod308relative to the threaded shaft322in correspondence with actuation of the movable device124by the actuator202. In this regard, the flywheel314is configured to rotationally accelerate and decelerate in proportion to axial acceleration and deceleration of the inerter rod308(e.g., coupled to the first terminal302) relative to the threaded shaft322(e.g., coupled to the second terminal304).

Advantageously, the flywheel314is coupled to the inerter rod308at a flywheel annulus318and is threadably engaged to the threaded shaft322, as shown inFIGS. 1, 8-9, and 14and described in greater detail below. However, in other examples, the flywheel annulus318may be coupled to the piston216as shown inFIGS. 10-13 and 15-16and described below. In still further examples, the flywheel annulus318may be coupled to the actuator housing228as shown inFIGS. 17-20and described below.

Regardless of the component to which the flywheel314is coupled, the flywheel314may include at least one bearing328(e.g., a thrust bearing328) at the flywheel annulus318to rotatably couple the flywheel314to the inerter rod308(FIGS. 1, 8-9, and 14), the piston216(FIGS. 10-13 and 15-16), or the actuator housing228(FIGS. 17-20). The bearing328allows the flywheel314to axially translate with the inerter rod308as the flywheel314rotates on the threads of the threaded shaft322in response to axial movement of the inerter rod308relative to the threaded shaft322. Advantageously, by coupling the flywheel314to the component (i.e., the inerter rod308, the piston216, or the actuator housing228) at the flywheel annulus318instead of at the flywheel perimeter316, the flywheel314exhibits limited flexure in the axial direction during high-frequency, oscillatory, axial acceleration of the first terminal302relative to the second terminal304. Such axial flexure of the flywheel mass would otherwise reduce flywheel rotational motion during high-frequency, oscillatory, axial acceleration.

Referring still to the example ofFIG. 1, the support structure116is shown configured as a spar118of a wing114of an aircraft100. The movable device124is shown as a flight control surface122of a flight control system120of the aircraft100. The flight control surface122may be hingedly coupled to the rigid support structure116such as a wing spar118or other structure. The flight control surface122may be pivotably about a hinge axis126. The flight control surface122may comprise any one of a variety of different configurations including, but not limited to, a spoiler, an aileron, an elevator112, an elevon, a flaperon, a rudder108, a high-lift device such as a leading edge slat, a trailing edge flap, or any other type of movable device124.

The actuator202provides positive force to move the flight control surface122to a commanded position in response to a command input from the flight crew or an autopilot. The inerter300provides for control and damping of displacements of the flight control surface122. One or more inerters300may be included in a flight control system120. In one example, the one or more inerters300may be configured to suppress or prevent control surface flutter as may be aerodynamically-induced at a resonant frequency of the flight control surface122. For example, the presently-disclosed inerter300may be configured to reduce actuator load oscillatory amplitude at resonance (e.g., at a resonant frequency) of up to approximately 20 Hz (e.g., ±5 Hz) which may correspond to the flutter frequency of a flight control surface122of an aircraft100. Additionally or alternatively, the inerter300may provide additional functionality for improving the dynamic response of a movable device124, such as increasing the actuation rate of the movable device124and/or preventing position overshoot of a commanded position of the movable device124, as described in greater detail below.

In one example, the inerter300may be configured such that rotation of the flywheel314reduces actuator load oscillatory amplitude at resonance of the coupled actuator202and movable device124by at least approximately 10 percent relative to the actuator load oscillatory amplitude that would otherwise occur using the same actuator202without an inerter300. Advantageously, the presently-disclosed inerter300permits the operating bandwidth of the actuator202to encompass or match the resonant frequency of the coupled movable device124and actuator202without the potential for oscillatory response, without the potential for exceeding the strength capability of the mounting system (not shown) of the flight control surface122and actuator202, and/or without the potential for flight control surface122deflections that could aerodynamically destabilize the aircraft100.

The presently-disclosed examples of the inerter300allow for a reduction in the overall size and weight of an actuator202system without the potential for oscillatory response. More specifically, the inerter300allows for a reduction in the inertial load on the actuator202which, in turn, allows for a reduction in piston cross-sectional area of the actuator202and a decrease in the size and weight of other hydraulic system components including reservoirs, tubing diameter, accumulators, pumps, and other components. In this regard, the inerter300increases the power density for a hydraulic actuator system in any application where dynamic response is limited by piston cross-sectional area or load inertia. The presently-disclosed inerter300examples may be implemented with hydraulic actuators204configured to be operated at a working pressure of at least 5000 psi. For example, the inerter300examples may be implemented with hydraulic actuators204operated at a working pressure of approximately 3000 psi and, in some examples, the hydraulic actuators204may be operated at a working pressure of approximately 8000 psi. A relatively high working pressure of a hydraulic actuator204may facilitate a reduction in total flow of hydraulic fluid through the hydraulic system (e.g., flight control system120) which may enable a reduction in the volumetric requirement for hydraulic fluid reservoirs and accumulators.

In the case of an aircraft100, the reduced size of the actuators202may reduce the amount by which such actuators202protrude outside of the outer mold line (not shown) of the aircraft100with a resulting decrease in aerodynamic drag. Even further, the presently-disclosed inerter examples may allow for a reduction in the amount of off-take power from the aircraft propulsion units (e.g., gas-turbine engines) which may provide the potential for using higher bypass ratio gas turbine engines such as in commercial aircraft applications. The decrease in the size of the hydraulic system, the reduction in aerodynamic drag, and/or the reduction in off-take power may translate to an increase in aircraft performance including, but not limited to, increased fuel efficiency, range, and/or payload capacity.

Although the presently-disclosed inerter examples are described in the context of a linear hydraulic actuator204, the inerter300may be implemented in other types of actuators202including, but not limited to, a rotary hydraulic actuator, an electro-hydraulic actuator (e.g., rotary or linear), a mechanical actuator, an electro-mechanical actuator, and other types of actuators. In one example (seeFIG. 21), the electro-mechanical actuator242may be a linear electro-mechanical actuator having a threaded shaft322coupled to a movable device124. As described in greater detail below with reference toFIG. 21, the linear electro-mechanical actuator242may include an electric actuator motor244for causing axial motion of a threaded shaft322. A flywheel314may be threadably engaged to the threaded shaft322and may be configured to rotationally accelerate and decelerate in proportion to axial acceleration and deceleration of the threaded shaft322during actuation of the movable device124by the linear electro-mechanical actuator242.

It should also be noted that although the presently-disclosed inerter examples are described in the context of an aircraft flight control system120, any one of the inerters300may be implemented in any type of open-loop or closed-loop control system for use in any one of a variety of different applications in any industry, without limitation. In this regard, the presently-disclosed inerters300may be implemented in any vehicular application or non-vehicular application. For example, an inerter300may be implemented in any marine, ground, air, and/or space application, and in any vehicular or non-vehicular system, subsystem, assembly, subassembly, structure, building, machine, and application that uses an actuator to actuate a movable device.

In some examples, an inerter300may be implemented for damping movement of a movable device configured to control the direction of travel of a vehicle. For example, an inerter may be implemented for damping movement of aerodynamic control surfaces of an air vehicle, hydrodynamic control surfaces of a marine vessel, thrust directors including thrust-vectoring nozzles of an aircraft or a launch vehicle (e.g., a rocket), or any other type of mechanical device that influences the direction of travel of a vehicle and which may be susceptible to external vibratory forces. In a specific example of a wheeled vehicle configured to move over land, any one of the presently-disclosed inerter examples may be implemented in a steering system to control or avoid wheel shimmy, such as may occur in a steerable wheel of an aircraft landing gear such as a nose landing gear.

FIG. 2is a block diagram of an example of an inerter300integrated into a hydraulic actuator204coupled between a support structure116and a flight control surface122of a flight control system120of an aircraft100. In the example shown, the actuator202is a linear hydraulic actuator204having a piston216coupled to a rod (e.g., piston rod224) and axially slidable within a housing (not shown). In the example shown, the flywheel314of the inerter300is rotatably coupled to the piston216at the flywheel annulus318. The flywheel314is threadably coupled to the threaded shaft322and configured to rotationally accelerate in proportion to axial acceleration of the piston216and rod relative to the threaded shaft322. However, as mentioned above, the flywheel314may be rotatably coupled to the piston216(e.g.,FIGS. 10-16) or the flywheel314may be rotatably coupled to the cap end212(e.g.,FIGS. 17-20) or rod end214of the actuator housing228.

As mentioned above, the threaded shaft322may include a shaft bore323open on the free end324and having radial passages325to allow fluid (e.g., hydraulic fluid) to flow from the cap end chamber236at the cap end212), through the shaft bore323, and out of the free end324of the threaded shaft322to allow the fluid to lubricate moving parts of the bearing328and/or the flywheel annulus318. The shaft bore323and radial passages325may be included in any one of the inerter300examples disclosed herein.

In the present disclosure, for examples wherein the inerter300is integrated into the actuator202, the rod end214or cap end212of the actuator202functions as the first terminal302of the inerter300, and the remaining rod end214or cap end212of the actuator202functions as the second terminal304of the inerter300. In this regard, the terms “first terminal” and “second terminal” are non-respectively used interchangeably with the terms “rod end” and “cap end.” In addition, for examples where the inerter300is integrated into the actuator202, the term “rod” is used interchangeably with the terms “piston rod” and “inerter rod.” Similarly, for examples where the inerter300is integrated into the actuator202, the term “housing” is used interchangeably with the terms “actuator housing” and “inerter housing.”

FIG. 3is a perspective view of an aircraft100having one or more inerters300for control and/or damping of one or more actuators202. The aircraft100may include a fuselage102and a pair of wings114extending outwardly from the fuselage102. The aircraft100may include a pair of propulsion units (e.g., gas turbine engines). As mentioned above, each wing114may include one or more movable devices124configured as flight control surfaces122which may be actuated by an actuator202damped and/or assisted by an inerter300. Such flight control surfaces122on the wings114may include, but are not limited to, spoilers, ailerons, and one or more high-lift devices such as a leading edge slats and/or trailing edge flaps. At the aft end of the fuselage102, the empennage104may include one or more horizontal tails110and a vertical tail106, any one or more of which may include flight control surfaces122such as an elevator112, a rudder108, or other types of movable devices124that may be actuated by an actuator202damped and/or assisted by an inerter300.

FIG. 4is a top view of a portion of the wing114ofFIG. 3illustrating an aileron actuated by a hydraulic actuator204located on one end of the aileron and having an inerter300located on an opposite and the aileron130. The aileron130may be hingedly coupled to a fixed support structure116of the wing114such as a spar118. InFIG. 4, the hydraulic actuator204and the inerter300are provided as separate components and may each be coupled between the support structure116(e.g., the spar118) and the aileron130.

FIG. 5is a sectional view of the wing114ofFIG. 4showing an example of a linear hydraulic actuator204mechanically coupled between the wing spar118and one end of the aileron130. In the example shown, the rod end214of the hydraulic actuator204is coupled to a bellcrank128. The bellcrank128is hingedly coupled to the aileron in a manner such that linear actuation of the hydraulic actuator204causes pivoting of the aileron about the hinge axis126. The cap end212of the hydraulic actuator204is coupled to the wing spar118.

FIG. 6is a sectional view of the wing114ofFIG. 4and showing an example of an inerter300coupled between the wing spar118and the aileron130. As mentioned above, the inerter300is located on an end of the aileron opposite the hydraulic actuator204. The first terminal302of the inerter300is coupled to a bellcrank128. The second terminal304of the inerter300is coupled to the wing spar118. Due to the hydraulic actuator204and the inerter300being coupled to the same movable device124(i.e., the aileron130), relative axial acceleration of the cap end212and rod end214of the actuator202causes proportional axial acceleration of the first terminal302and second terminal304of the inerter300resulting in rotational acceleration of the flywheel314.

FIG. 7is a partially cutaway sectional view of an example of a double-acting hydraulic actuator204having a cap end212and a rod end214axially movable relative to one another during actuation of the movable device124. As mentioned above, the rod end214and the cap end212may be mutually exclusively coupled to the support structure116and the movable device124. For example, the rod end214may be coupled to the support structure116and the cap end212may be coupled to the movable device124, or the rod end214may be coupled to the movable device124and the cap end212may be coupled to the support structure116.

InFIG. 7, the piston216is coupled to a free end324of the piston rod224and is axially slidable within the actuator housing228. The piston216divides the actuator housing228into a cap end chamber236and a rod end chamber238. The actuator housing228of the double-acting hydraulic actuator204includes a pair of fluid ports234through which pressurized hydraulic fluid enters and leaves the cap end chamber236and the rod end chamber238chambers for moving the piston216within the actuator housing228. In any of the presently-disclosed examples, the hydraulic actuator204may also be configured as a single-acting actuator (not shown) wherein the actuator housing228contains a single fluid port234for receiving pressurized hydraulic fluid in the actuator housing228as a means to move the piston216along one direction within the actuator housing228, and optionally include a biasing member (e.g., a spring—not shown) for moving the piston216in an opposite direction.

FIG. 8is a partially cutaway sectional view of an example of an inerter300having an inerter housing330containing the flywheel314and having an inerter side wall334and opposing inerter end walls332. One inerter end wall332may include a housing bore through which the inerter rod308extends and terminates at the first terminal302. The inerter300includes a threaded shaft322coupled to the inerter end wall332located at the second terminal304. In the example ofFIG. 8, the flywheel314is coupled to an end of the inerter rod308and threadably engaged to the threaded shaft322. The flywheel314rotates in proportion to axial acceleration of the inerter rod308and first terminal302relative to the threaded shaft322and second terminal304.

FIG. 9is a magnified sectional view ofFIG. 8showing the flywheel314coupled to the inerter rod308at the flywheel annulus318. The flywheel annulus318is also threadably engaged to the threaded shaft322. In the example shown, the threaded shaft322is configured as a ball screw326having helical grooves for receiving ball bearings which couple similarly-configured helical grooves in the flywheel annulus318to the ball screw326with minimal friction. Although not shown, the flywheel annulus318may include a ball nut for circulating the ball bearings coupling the flywheel314to the ball screw326. In another example not shown, the threaded shaft322may comprise a lead screw having threads to which the flywheel annulus318are directly engaged. As may be appreciated, the flywheel314may be configured for engagement to any one of a variety of different types of configurations of threaded shafts, and is not limited to the ball screw326example illustrated inFIG. 9.

Also shown inFIG. 9is an example of a bearing328for coupling the flywheel annulus318to the inerter rod308such that the inerter rod308and flywheel314may translate in unison as the flywheel314rotates due to threadable engagement with the threaded shaft322. Although the bearing328is shown as a ball bearing, the bearing328may be provided in any one a variety of different configurations capable of axially coupling the flywheel314to the inerter rod308with a minimal amount of axial free play. For example, the bearing328may be configured as a roller bearing (not shown). In still further examples, the flywheel314may be coupled to the inerter rod308without a bearing while still allowing the flywheel314to rotate during translation of the inerter rod308and flywheel314relative to the threaded shaft322.

FIG. 10is a sectional view of an example of an inerter300integrated into a hydraulic actuator204having a housing containing a piston216. The actuator202is a double-acting actuator including a pair of fluid ports234for receiving pressurized hydraulic fluid in a cap end chamber236and a rod end chamber238located on opposite sides of the piston216. The actuator202is an unbalanced actuator206wherein one of the piston sides218has a greater cross-sectional area than the opposite piston side218. The piston216may include a piston216seal (e.g., an O-ring seal—not shown) extending around the piston perimeter220for sealing the piston perimeter220to the actuator side wall232.

As mentioned above, for examples where the inerter300is integrated into an actuator202, the rod end214or the cap end212of the actuator202functions as the first terminal302of the inerter300, and the remaining rod end214or the cap end212of the actuator202functions as the second terminal304of the inerter300. In the example shown, the flywheel314is mounted in the cap end chamber236and is rotatably coupled to the piston216at the flywheel annulus318. The flywheel314is threadably engaged to the threaded shaft322which passes through the piston216and extends into the rod bore310. The flywheel314is configured to rotationally accelerate in proportion to axial acceleration of the piston216and piston rod224relative to the threaded shaft322.

FIG. 11shows an example of an inerter300having flywheel protrusions320for generating viscous damping during rotation of the flywheel314when the flywheel314is immersed in hydraulic fluid. The flywheel protrusions320generate or increase the viscous damping capability of the inerter300during rotation of the flywheel314, and thereby increase the damping capability of the inerter300.

FIG. 12is a perspective view of an example of an inerter300having a plurality of radially extending flywheel blades circumferentially spaced around the flywheel perimeter316. During rotation of the flywheel314, the flywheel blades may generate viscous damping capability and add to the inerting capability of the inerter300. AlthoughFIG. 12illustrates the flywheel protrusions320as radially-extending flywheel blades, the flywheel314may be provided with flywheel protrusions320extending from any portion of the flywheel314including one or both of the opposing sides of the flywheel314. In addition, the flywheel protrusions320may be provided in any geometric size, shape or configuration, without limitation, and are not limited to flywheel blades.

FIG. 13is a sectional view of an example of an inerter300integrated into a hydraulic actuator204configured as a partially-balanced actuator208. The partially-balanced actuator208includes an interior piston226coupled to a free end324of the threaded shaft322. The interior piston226may be axially slidable within the rod bore310and may be rotatably coupled to the end of the threaded shaft322such that the interior piston226is non-rotatable relative to the rod bore310during axial movement of the piston rod224relative to the threaded shaft322. Although not shown, the perimeter of the interior piston226may be sealed (e.g., via an O-ring) to the rod wall312of the rod bore310. The inclusion of the interior piston226may reduce the total volume of hydraulic fluid required to fill the cap end chamber236during extension of the piston rod224relative to the increased volume of hydraulic fluid required to fill the cap end chamber236for examples (e.g.,FIG. 8) lacking an interior piston226.

FIG. 14is a partially cutaway sectional view of an example of an inerter300integrated into a hydraulic actuator204configured as a balanced actuator210having opposing piston sides218with substantially equivalent cross-sectional areas. The housing may include a separator wall240separating the portion of the housing containing the flywheel314from the portion of the housing containing the piston216. A cap end chamber236is located on one of the piston sides218and the rod end chamber238is located on the opposite piston side218. The piston216may be mounted on the piston rod224. InFIG. 14, one end of the piston rod224extends through the actuator end wall230and terminates at the rod end214(e.g., the first terminal302). An opposite end of the piston rod224extends through the separator wall240. The flywheel314is rotatably coupled to the piston rod224in a manner as described above.

FIG. 15is a partially cutaway sectional view of an example of an inerter300having an electric flywheel motor350integrated into a hydraulic actuator204. The flywheel motor350may facilitate active control of flywheel314rotation using electromotive force from the integrated flywheel motor350. Active control may include using the flywheel motor350to apply a torque to the flywheel314to resist or aid the torque that is generated by the flywheel314due to axial acceleration of the first terminal302relative to the second terminal304. The flywheel motor350may be configured to provide active damping and/or active braking of the actuator202and the load inertia.

FIG. 16is a magnified sectional view ofFIG. 15showing the flywheel314rotatably coupled to and contained within a generally hollow piston216which is actually slidable within the actuator housing230. Also shown in the flywheel motor350incorporated into the flywheel314and the piston216and configured to actively control rotation of the flywheel314in correspondence with relative axial movement of the rod and threaded shaft322. The flywheel motor350may be operated in a manner to accelerate and/or decelerate the flywheel314by applying a torque to the flywheel314either in correspondence with (e.g., the same direction as) or in opposition to the direction of rotation of the flywheel314. In this manner, the flywheel motor350may apply a torque to the flywheel314to resist or aid the flywheel torque generated due to axial acceleration of the first terminal302relative to the second terminal304

In the example ofFIG. 16, the flywheel motor350is a permanent magnet direct-current (DC) motor having one or more permanent magnets354mounted to the flywheel314. For example, a plurality of permanent magnets354may be circumferentially spaced around the flywheel perimeter316. In addition, the flywheel motor350may include a plurality of windings352mounted to the piston216. In one example, a plurality of windings352may be circumferentially spaced around the piston inner wall222(e.g.,FIGS. 15-16). In another example, a plurality of windings352may be circumferentially spaced around the side wall232of the housing (e.g.,FIGS. 19-20) as described below. In other examples, the flywheel motor350may be a brushless DC motor or some other motor configuration, and is not limited to a permanent magnet DC motor configuration as shown inFIGS. 15-16 and 19-20. In an example not shown, a linear position sensor may be included with the actuator202to sense the linear position of the piston216and generate a signal representative of the linear piston position for commutating the flywheel motor350in correspondence with the piston position.

As mentioned above, the flywheel motor350inFIGS. 15-16may be configured to assist or aid in rotating the flywheel314for a commanded direction of motion of the movable device124. For example, the flywheel motor350may provide a torque to accelerate the flywheel314at the start of motion of the movable device124toward a commanded position. The torque applied to the flywheel314by the flywheel motor350may be approximately equal in magnitude to the torque required to rotationally accelerate the flywheel314due to axial acceleration of the threaded shaft322relative to the rod. By using the flywheel motor350to remove the torque required to rotationally accelerate the flywheel314, the piston216may move more quickly to a commanded position than if the flywheel motor350did not accelerate the flywheel314. In this manner, the flywheel motor350may allow faster responsiveness of a movable device124than a conventional actuator202. The level of damping provided by an inerter300having active control of the flywheel314may be greater than the damping that is feasible in a closed-loop control system without active control due to the risk of control system instability. AlthoughFIGS. 15-16illustrate a flywheel motor350incorporated into an inerter300integrated with an actuator202, a flywheel motor350may be incorporated into an inerter300that is a separate component from the actuator202(e.g.,FIGS. 4-8).

In a further example of active control, the flywheel motor350may be operated in a manner to provide a torque to decelerate the flywheel314as the movable device124approaches a commanded position. In this regard, the flywheel motor350may be operated as a brake to oppose the flywheel torque generated by the axial deceleration of the threaded shaft322relative to the piston rod224. Actively controlling flywheel314rotation in this manner may prevent or limit position overshoot of the movable device124and thereby increase the stability of the movable device124. In such an arrangement, the actuator202and inerter300may be configured with a failure mode that ensures that without active motor control, the actuator202is capable of exhibiting a desired damped response in a manner preventing underdamping of the movable device124. An inerter300having a flywheel motor350for active control may be connected to the movable device124without being part of the actuator202such that in the event of a disconnect of the actuator202from the movable device124or in the event of a failure of the actuator202to hold the load of the movable device124, the flywheel motor350may be operated in a manner preventing underdamped movement of the movable device124for the given failure mode.

Referring still toFIG. 16, in another example of active control, the flywheel motor350may include a brake360configured to provide dynamic braking of the flywheel314. In this regard, the brake360may be operated in a manner to decelerate the flywheel314or to increase existing deceleration of the flywheel314. For examples that include a flywheel motor350, the brake360may be operated in a manner to increase existing deceleration of the flywheel314caused by rotational drag of the flywheel motor350. In addition, the flywheel motor350may be operated in a manner to oppose disturbances (e.g., undesirable motion) of the actuator202.

In the example ofFIG. 16, the brake360may be configured as a disc brake having brake pads364. The flywheel314may function as a brake rotor against which the brake pads364may be frictionally engaged during braking. In other examples not shown, a separate brake rotor may be provided which may be directly or indirectly coupled to the flywheel314. In the example shown, a hydraulic brake cylinder (not shown) may be included to actuate the brake pads364into frictional engagement with one or both of the opposing axial faces362(e.g., planar faces) of the flywheel314for decelerating the flywheel314. Preferably, the brake360may include at least two pairs of opposing brake pads364located on diametrically opposing sides of the brake rotor. Each pair of brake pads364may be held in position by a bracket366. Although the brake360is described and illustrated as a disc brake, the inerter300may incorporate any one or more different types of brakes such as a drum brake or any other type of brake capable of decelerating the flywheel314.

Referring toFIG. 17, shown is a partially cutaway sectional view of another example of an inerter300integrated into a hydraulic actuator204. The flywheel314is rotatably coupled or attached to the actuator end wall230which may be coupled to the second terminal304. The piston216is fixedly coupled or attached to the piston rod224which extends from the piston216through the actuator end wall230and is coupled to the first terminal302. In an alternative example not shown, the flywheel314may be rotatably coupled to the actuator end wall230which is attached to the first terminal302, and the piston rod224may be coupled to the second terminal304.

FIG. 18is a magnified sectional view ofFIG. 17illustrating the flywheel annulus318rotatably coupled by a bearing328to the actuator end wall230. The threaded shaft322is fixedly coupled to the flywheel314and is rotatable in unison with the flywheel314. As mentioned above, the piston216is fixedly coupled to the piston rod224and threadably engaged to the threaded shaft322in a manner such that linear translation of the piston rod224relative to the threaded shaft322causes rotation of the flywheel314and threaded shaft322in unison. As indicated above, axial movement of the threaded shaft322relative to the piston rod224may be in correspondence with actuation of the movable device124by the actuator202.

FIG. 19illustrates an example of a flywheel314rotatably coupled to the actuator end wall230and incorporating a flywheel motor350for active control of the rotation of the flywheel314in a manner as described above. The flywheel motor350may include permanent magnets354mounted to the flywheel perimeter316. For example, as described above with regard toFIG. 16, a plurality of permanent magnets354may be circumferentially spaced around the flywheel perimeter316.FIG. 19also shows a plurality of windings352circumferentially spaced around the actuator side wall232of the actuator housing228.

FIG. 20illustrates an example of a flywheel314including a brake360configured to provide dynamic braking of the flywheel314. In the example shown, the brake360is configured as a disc brake having one or more pairs of brake pads364for frictionally engaging opposing axial faces362of the flywheel314. The brake360inFIG. 20may be configured and operated similar to the arrangement illustrated inFIG. 16and described above.

FIG. 21illustrates an example of an inerter300integrated into a linear electro-mechanical actuator242. The electro-mechanical actuator242may extend between a support structure116(FIG. 2) and a movable device124(FIG. 2). The electro-mechanical actuator242may include an electric actuator motor244supported by the actuator housing228. The first terminal302may be coupled to a movable device124. The electro-mechanical actuator242may include a second terminal304which may be coupled to a support structure116. Alternatively, the first terminal302may be coupled to the support structure116and the second terminal304may be coupled to the movable device124.

The electro-mechanical actuator242may include a threaded shaft322(e.g., an Acme-threaded shaft, a ball screw, etc.) extending through the actuator motor244and terminating at the first terminal302. The actuator motor244may be operably coupled to the threaded shaft322by a motor-shaft coupler246which may be threadably engaged to the threaded shaft322. Operation of the actuator motor244may cause axial motion of the threaded shaft322for actuating the movable device124. In this regard, the threaded shaft322may axially move in proportion (e.g., in magnitude and direction) to angular displacement of the actuator motor244. A flywheel314may be threadably engaged to the threaded shaft322. In addition, the flywheel annulus318may be rotatably coupled to the actuator motor244via a bearing328such that axial acceleration of the threaded shaft322causes rotational acceleration of the flywheel314. The flywheel314may be configured to rotationally accelerate and decelerate in proportion to axial acceleration and deceleration of the threaded shaft322(e.g., relative to the actuator motor244) during actuation of the movable device124.

In this regard, rotation of the flywheel314during actuation of the electro-mechanical actuator242ofFIG. 21may provide any one or more of the advantages described herein for improving the dynamic response of the movable device124during actuation by the electro-mechanical actuator242. For example, the flywheel314may reduce actuator load oscillatory amplitude at resonance of the coupled electro-mechanical actuator242/movable device124. In addition, although not shown inFIG. 21, a flywheel motor350(e.g.,FIG. 16) and/or a dynamic brake360(FIG. 16) may optionally be included with the flywheel314to allow for active control of the rotation of the flywheel314using any one or more of the flywheel control techniques described herein.

FIG. 22is a sectional view of an example of an inerter300integrated into a hydraulic actuator204as described above and illustrated inFIG. 10.FIG. 22includes the notations x, x0, x1, and x2respectively denoting reference points for translation of the rod end214, the cap end212, the piston216, and the flywheel314. The notations x, x0, x1, and x2are parameters that are used in a below-described derivation of a transfer function

X⁡(s)F⁡(s)
(Equation 220) mathematically characterizing the response of the apparatus ofFIG. 22. Table 1 includes a listing of the parameters used in the derivation of the transfer function. Included with each listed parameter is an indication of the physical type of the parameter and a brief description of the parameter.

Equations 100 to 210 inclusive are the assumptions behind the derivation of the transfer function of Equation 220. Referring to the example apparatus ofFIG. 22, the total reacted force F (e.g., at the rod end214) may be computed as the sum of the piston216reacted force F1and the flywheel314reacted force F2as shown in Equation 100, wherein the sign of F1and F2are the same from a disturbance rejection sense:
F=F1+F2(Equation 100)

The torque T2developed by the flywheel314may be determined using Equation 110 as the sum of the product of the flywheel rotational inertia J and flywheel rotational acceleration {umlaut over (θ)} and the product of a flywheel damping coefficient B and the flywheel rotational velocity {dot over (θ)}:
T2=J{umlaut over (θ)}+B{dot over (θ)}(Equation 110)

The flywheel reacted force F2may be computed using equation 120 as the product of the flywheel torque T2and the thread rate r (e.g., thread pitch) of the threaded shaft322. The thread rate may be described as the linear distance of travel of the flywheel314per revolution:
F2=r(J{umlaut over (θ)}+B{dot over (θ)})  (Equation 120)

The rotation of the flywheel314may be characterized by the flywheel angular displacement or rotational angle θ, rotational velocity {dot over (θ)}, and rotational acceleration {umlaut over (θ)}, as respectively represented by Equations 130, 140, and 150. The flywheel rotational angle θ is the product of the thread rate r and the linear distance of flywheel translation x2as represented by Equation 130. The parameter c is a constant representing a linear offset relative to a common reference. The flywheel rotational velocity {dot over (θ)} is the product of the thread rate r and the linear velocity {dot over (x)}2of the flywheel314as represented by Equation 140. The flywheel rotational acceleration {umlaut over (θ)} is the product of the thread rate r and the linear acceleration {umlaut over (x)}2of the flywheel314as represented by Equation 150.
θ+c=rx2(Equation 130)
{dot over (θ)}=r{dot over (x)}2(Equation 140)
{umlaut over (θ)}=r{umlaut over (x)}2(Equation 150)

A flywheel314to piston216compliance force F3may be computed using Equation 160 as the product of the flywheel rotational stiffness Z and the difference between flywheel translation x2and piston translation x1. For the example apparatus ofFIG. 22wherein the inerter (e.g., the flywheel314) is integrated into the actuator202, the flywheel314moves with the piston216such that the flywheel translation x2and the piston translation x1are the same, as indicated below in Equation 190. In this regard, the piston compliance force F3is zero (0) due to the assumption that x2=x1as indicated below in Equation 190.
F3=Z(x2−x1)  (Equation 160)

Substituting Equations 140 and 150 for flywheel velocity {dot over (θ)} and flywheel acceleration {umlaut over (θ)} into Equation 120, the flywheel reacted force F2may be expressed as follows:
F2=r2(J{umlaut over (x)}2+B{dot over (x)}2)  (Equation 170)

The piston reacted force F1may be computed as the sum of the product of the actuator (e.g., the piston) reacted inertia M at the rod end214and the piston acceleration {umlaut over (x)}1, the product of the actuator (e.g., the piston) resisting force C and the piston velocity {dot over (x)}, and the product of the actuator stiffness K and the piston displacement x1, as shown in Equation 180:
F1=M{umlaut over (x)}i+C{dot over (x)}1+Kx1(Equation 180)

As mentioned above, for the example shown inFIG. 22wherein the inerter (e.g., the flywheel314and threaded shaft322) is integrated into the actuator202such that the flywheel314and the piston216move in unison, the flywheel translation x2and the piston translation x1are the same as represented by Equation 190. In addition the rod end214and the piston216move in unison as represented by Equation 200. The cap end212at x0is assumed to be fixed (e.g., non-translating) as represented by Equation 210.
xz=1(Equation 190)
{dot over (x)}1={dot over (x)}(Equation 200)
{umlaut over (x)}0={dot over (x)}0=x0=0  (Equation 210)

Performing a Laplace transform on a differential equation (not shown) representing the natural frequency of the example apparatus shown inFIG. 22, the resulting transfer function

X⁡(s)F⁡(s)
is expressed as shown in Equation 220 wherein X(s) represent the response of the apparatus ofFIG. 22and F(s) represents the input to the apparatus:

The natural frequency ωnof oscillation of the example apparatus ofFIG. 22may be expressed as shown in Equation 230 wherein K is the actuator stiffness, r is the thread rate, and J is the flywheel rotational inertia, as described above.

Equation 240 represents the damping factor ζ of the example apparatus ofFIG. 22which characterizes the decay in oscillatory response to the input (e.g., flutter of a flight control surface).

FIG. 23is a graph plotting frequency380vs. magnitude382(amplitude) of the oscillatory response to a dynamic load for an actuator202operating under three (3) different working pressures (3000 psi, 5000 psi, and 8000 psi). The vertical centerline represents a flutter frequency of 20 Hz corresponding to the dynamic load. The plots ofFIG. 23illustrate the reduction in response amplitude 384 provided by the actuator202with integrated inerter300ofFIG. 22, relative to the response amplitude for the same actuator operating without an inerter. The reduction in response amplitude represents an optimization based on setting the response amplitude at the flutter frequency for the actuator202operating at 8000 psi with an inerter300equal to the response amplitude at the flutter frequency for the actuator202operating at 3000 psi without the inerter300, and optimizing the thread pitch r of the threaded shaft322, the flywheel rotational inertia J, and the damping factor ζ (Equation 240). For the actuator202operating at 8000 psi, the inerter300facilitates a reduction in response amplitude 384 of almost 5 dB at the flutter frequency of 20 Hz.

FIG. 24is a flowchart having one or more operations that may be included in a method400of damping an actuator202using an inerter300. As mentioned above, the damping of the actuator202may comprise reducing actuator load oscillatory amplitude using inerter300. As indicated above, in some examples, the inerter300may be a separate component from the actuator202and coupled to the same movable device124as the actuator202(e.g.,FIGS. 1 and 4-9). In other examples, the inerter300may be integrated into the actuator202(e.g.,FIGS. 2 and 10-22).

Step402of the method400includes actuating the movable device124using an actuator202. In the example of a flight control system120of an aircraft100, the method may include using a linear actuator such as a linear hydraulic actuator204or a linear electro-mechanical actuator242. For example,FIGS. 4-6illustrate a linear hydraulic actuator204configured to actuate an aileron130pivotably mounted to a wing114of an aircraft100. However, as mentioned above, the movable device124may be any type of movable device that may be actuated by an actuator202.

Step404of the method400includes axially accelerating, using an inerter300coupled to the movable device124, the first terminal302of the inerter300relative to the second terminal304of the inerter300. As indicated above, the inerter300may be coupled between the support structure116and the movable device124(e.g.,FIGS. 4 and 6). For example, the first terminal302may be coupled to the movable device124and the second terminal304may be coupled to the support structure116, or the first terminal302may be coupled to the support structure116and the second terminal304may be coupled to the movable device124. Alternatively, the inerter300may be integrated into the actuator202(e.g.,FIGS. 10-21) which may be coupled between the support structure116and the movable device124. In such examples, as mentioned above, the rod end214or the cap end212of the actuator202functions as (e.g., is one and the same as) the first terminal302of the inerter300, and the remaining rod end214or cap end212of the actuator202functions as (e.g., is one and the same as) the second terminal304of the inerter300.

Step406of the method400includes rotationally accelerating the flywheel314simultaneous with the axial acceleration of the first terminal302relative to the second terminal304. Because the inerter300and the actuator202are coupled to the same movable device124(e.g.,FIGS. 1 and 4-9) or because the inerter300is integrated into the actuator202(e.g.,FIGS. 2 and 10-21), the axial acceleration of the first terminal302relative to the second terminal304is simultaneous with and in proportion to the actuation of the movable device124by the actuator202. In this regard, the flywheel314rotationally accelerates and decelerates in proportion to the axial acceleration and deceleration of the first terminal302relative to the second terminal304in correspondence with the actuation of the movable device124by the actuator202.

Step408of the method400includes damping the movement of the actuator202in response to rotating the flywheel314. In one example, the method may include reducing actuator load oscillatory amplitude of the movable device124in response to rotationally accelerating the flywheel314. Regardless of whether the inerter300is a separate component from the actuator202or the inerter300is integrated into the actuator202, the method may include rotationally accelerating the flywheel314in a manner reducing actuator load oscillatory amplitude at resonance of the movable device124coupled to the actuator202. In one example, the method may include reducing actuator load oscillatory amplitude by at least 50% relative to the oscillatory amplitude for the movable device124actuated by the same actuator but without the inerter, as mentioned above. The inerter300may be configured to reduce actuator load oscillatory amplitude at a resonant frequency of up to approximately 20 Hz (e.g., ±5 Hz). The movable device124may be a flight control surface122(e.g., a hydraulically-actuated aileron130) of an aircraft100and the resonance (e.g., the resonant frequency) may correspond to flutter of the flight control surface122as induced by aerodynamic forces acting on the flight control surface122.

As mentioned above, in examples where the inerter300is integrated into the actuator202, the flywheel314may include a plurality of flywheel protrusions320(e.g., flywheel blades—seeFIGS. 11-12) extending outwardly from the flywheel314. The flywheel314and the flywheel protrusions320may be immersed in hydraulic fluid contained within the cap end chamber236. In such examples, the method may include rotating the flywheel314within the hydraulic fluid and generating or increasing viscous damping of the actuator202movement in response to rotating the flywheel314in correspondence with the actuation of the movable device124. The viscous damping may contribute toward the damping provided by the rotational inertia of the flywheel314.

In still other examples, the method may include actively controlling the rotation of the flywheel314in correspondence with relative axial movement of the piston rod224and threaded shaft322. For example, the inerter300may include or incorporate an electric flywheel motor350as described above in the examples illustrated inFIGS. 15-16 and 19-20. In some examples, as mentioned above, the actuator202may include a linear position sensor (not shown) configured to sense the linear position of the piston216within the actuator202and generate a signal representative of the piston position. The method may include commutating the flywheel motor350in correspondence with the linear position of the piston216as represented by the signal generated by the position sensor.

Active control of the flywheel314rotation may include accelerating and/or decelerating the flywheel314using the flywheel motor350. For example, the flywheel motor350may be operated in a manner to apply a torque to the flywheel314in correspondence with or in the direction of rotation of the flywheel314. In this regard, the flywheel motor350may assist a commanded direction of motion of the actuator202. In some examples, active control of flywheel rotation may include accelerating the flywheel314during initiation of actuation by the actuator202of the movable device124toward a commanded position. In this regard, the flywheel motor350may rotationally accelerate the flywheel314at the start of axial acceleration of the first terminal302relative to second terminal304by an amount at least partially or completely eliminating the force generated at the first terminal302and second terminal304due to actuation of the movable device124by the actuator202. By using the flywheel motor350to rotationally accelerate the flywheel314at the start of axial acceleration, the force required to axially move the first terminal302relative to the second terminal304may be reduced or eliminated which may increase the speed at which the actuator202moves the movable device124toward a commanded position.

Alternatively, the flywheel motor350may be operated in a manner to apply a torque to the flywheel314in a direction opposite the rotation of the flywheel314. In this regard, the application of motor-generated torque in a direction opposite the rotation of the flywheel314may resist the torque generated by the relative axial acceleration of the first terminal302and second terminal304. In this regard, active control by the flywheel motor350may oppose the terminal-developed torque at the end of actuator202motion when the commanded position is reached. In this manner, the step of actively controlling rotation of the flywheel314may include using the flywheel motor350to dynamically brake or decelerate the flywheel314as the actuator202approaches a commanded position to prevent position overshoot.

In a further example, active control of flywheel314rotation may include using a brake360(e.g.,FIGS. 16 and 20) to decelerate the flywheel314as the actuator202approaches a commanded position of the movable device124to prevent position overshoot of the commanded position. The method may additionally include dynamically braking the rotation of the flywheel314such as to oppose disturbances (e.g., undesirable motion) of the actuator202. The step of dynamically braking (e.g., decelerating or reducing rotational speed) of the flywheel314may be performed using a brake360operatively engageable to the flywheel314(e.g.,FIGS. 16 and 20) or operatively engageable to a brake rotor (not shown) that may be fixedly coupled to the flywheel314. Alternatively or additionally, the step of dynamically braking the flywheel314may be performed using rotational drag generated by the flywheel motor350as described above.

Additional modifications and improvements of the present disclosure may be apparent to those of ordinary skill in the art. Thus, the particular combination of parts described and illustrated herein is intended to represent only certain examples of the present disclosure and is not intended to serve as limitations of alternative examples or devices within the spirit and scope of the disclosure.