GB2499621A - A damper assembly - Google Patents
A damper assembly Download PDFInfo
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- GB2499621A GB2499621A GB1203070.6A GB201203070A GB2499621A GB 2499621 A GB2499621 A GB 2499621A GB 201203070 A GB201203070 A GB 201203070A GB 2499621 A GB2499621 A GB 2499621A
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- Prior art keywords
- damper
- damper assembly
- assembly according
- impact surface
- mass
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- 238000013016 damping Methods 0.000 claims description 58
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Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect
- F16F7/104—Vibration-dampers; Shock-absorbers using inertia effect the inertia member being resiliently mounted
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect
- F16F7/104—Vibration-dampers; Shock-absorbers using inertia effect the inertia member being resiliently mounted
- F16F7/116—Vibration-dampers; Shock-absorbers using inertia effect the inertia member being resiliently mounted on metal springs
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Vibration Dampers (AREA)
- Manipulator (AREA)
- Chutes (AREA)
Abstract
A damper assembly is provided. The damper assembly includes least one damper mass D which damps the motion of a moving body B as it approaches an impact surface I by colliding with the body and bouncing back and forth between it and the impact surface I to decelerate the body in a series of collisions C1, C2, C3. Such collisions may involve multiple damper masses arranged to act in series and/or parallel. The damper assembly may comprise a one-shot or re-usable device and may be used in robotic, machining, valve-controlling or other apparatus with repetitive, controlled movements, such as reciprocating actuators. Where the impact surface is upon a freely movable second body, the damper collisions with the impact surface may achieve progressive acceleration of the second body away from the moving body.
Description
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DAMPER ASSEMBLY
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a damper assembly for 5 reducing the kinetic energy of a moving body, to apparatus including such an assembly and to a method of using such a damper assembly.
The damper assembly may be used progressively to decelerate a relatively moving body, in particular, so as to 10 lessen its impact, or the impact of a connected component, against a surface, stop or another body. Such an assembly may form part of reciprocating apparatus, such as, for example, high speed linear or rotary action actuators. The damper assembly may also be used progressively to accelerate a 15 second body via the progressive deceleration of the first body.
BACKGROUND OF THE INVENTION
In applications where actuators are configured for high speed reciprocating movement, for example, in machining or 20 valving applications, the operating stresses imparted on the components controlled by the actuators due to the rapid accelerations and decelerations as a result of initiation of movement, or arrest of movement, especially where the latter are by travel limiting stops, may reduce longevity, or, may 25 produce undesirable rebound.
It would therefore be desirable to dampen any sudden arrests or sudden initiated motion so that these may be more gradual, thereby reducing such operating stresses, and/or rebound, particularly where such starting or stopping 30 movements occur frequently. Further, in arrangements where the deceleration involves an impact against a stop, it would be desirable to dampen such an impact.
SUMMARY OF THE INVENTION
The present invention provides a damper assembly 35 comprising an impact surface, and at least one damper mass for damping the motion of a body, wherein the assembly is configured such that, in use, when a body approaches the
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impact surface it collides with the at least one damper mass in an initial position to cause the at least one damper mass to bounce back and forth between the impact surface and the body undergoing a series of collisions with the moving body 5 that decelerate the body.
The damper assembly may include as part of the mechanism a body configured to approach the impact surface.
By "series of collisions", it is meant at least two collisions with the moving body that progressively reduce its 10 k inetic energy. The collisions may involve a single damper mass bouncing back and forth between the impact surface and the approaching body, or, may involve a plurality of damper masses moving back and forth between the impact surface and the approaching body; in the latter case, one mass may only 15 travel a short distance and may only collide with other masses, for example, but the combined effect will again be successive momentum transfer between the approaching body and the impact surface. The plurality of damper masses may be configured (for example, constrained) to move in a co-20 ordinated fashion, or to move in a random fashion or to move in parallel, or, in series (i.e. colliding with one another successively so as to transfer the momentum across from the moving body to the impact surface), or any combination thereof, providing that they undergo the required series of 25 collisions.
By "configured" it is meant that the properties and arrangement of the components in the assembly inevitably result in at least two collisions occurring, thereby progressively damping the motion of the moving body. 30 Such "percussive" damping is progressive in that deceleration occurs in stages as a result of the series of collisions of the body with the at least one damper mass, rather than in one single abrupt deceleration. For this damping mechanism to occur, sufficient strain energy must be 35 imparted to the damper mass by impact with the body to result in separation of the body and the damper mass. In the case of a single damper mass, the damper mass will then travel ahead of the body towards the impact surface where strain energy
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will again be stored in the damper mass as a result of the collision with the impact surface. Some strain energy is also imparted to the impact surface and is attenuated through the supporting structure. The release of this strain energy 5 results in the damper mass reversing its direction of travel and, after separation from the impact surface, colliding again with the body when the cycle will repeat. Damping occurs as a result of the imperfect nature of each collision, ie, each collision has a restitution coefficient of less than 10 unity but greater than zero (<1 and >0). As the gap between the body and the impact surface is reduced the impact frequency will usually increase (although very low restitution coefficients may result in a constant or reducing frequency of collisions); this increase in impact frequency 15 can make the damping action particularly effective. Moreover, the present damper assembly may be implemented in mechanically simple and hence, reliable apparatus.
The damping mechanism is illustrated in a graph in Figure 5, which shows the separation distances x of a body B 20 and a damper mass D, respectively, from the impact surface (x=0) with time as they undergo the multiple collisions. Initially, in this case, damper mass D remains stationary at a fixed distance x=A from the impact surface, which distance is close enough for multiple collisions to take place based 25 on, for example, the damper mass, the expected momentum of the body B, and their respective coefficients of restitution. In this example Body B is accelerated towards the stop by an external force. Body B undergoes a first collision at point Ci, after which damper mass D moves towards the impact 30 surface faster than body B, whose momentum has now been reduced. Damper mass D collides with the impact surface at T=Ti and the stored strain energy is then released causing it to reverse its direction, moving back towards the body B where it collides again with it at point C2. The body B is 35 thus decelerated relative to the impact surface by successive momentum transfer to the damper mass D. The damper mass transfers this momentum to the impact surface and, although the total momentum of the body, the body of which the impact
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surface is a part and the damper mass is maintained, the relative momentum of the body to the impact surface is reduced by dissipation through multiple damper mass collisions with both body and impact surface.
5 The impact surface may be configured to remain stationary during the damping, and may be provided upon a second body that is stationary (e.g. static or fixed), or that is free to move (in which case it may gradually accelerate away from the moving body).
10 In one embodiment, the assembly is configured such that the series of collisions involve a single damper mass. This may be a baton, ball, puck or any suitable robust, smooth, preferably outwardly curved object likely to provide a good rebound (i.e. required dynamic hardness), and could be 15 suspended or anchored or tethered or the like; it could also be an elongate self-supporting (e.g. pivotally hung) element, e.g. a rod, cylinder or resilient cantilever.
In an alternative embodiment, the assembly is configured such that the series of collisions involve multiple damper 20 masses bouncing back and forth (e.g. partially or fully) between the impact surface and the moving body. This increases the number of collisions per unit time and dissipates energy faster. The multiple damper masses may be arranged to act in series and/or in parallel. The multiple 25 dampers may comprise a plurality of rounded damper masses
(e.g. balls or rods) or a plurality of resilient cantilevers.
For example, such multiple dampers may be a series of successively aligned, closely spaced damper masses disposed between the body and impact surface and capable of 30 transferring momentum away from the body by virtue of a series of collisions with the body and impact surface,
wherein momentum is transferred across the series of damper masses i.e. from one mass to the adjacent mass and so on. For example, the masses may comprise individual damper masses 35 arranged and constrained to move in a line or in an arc, for linear or rotary damping, respectively. The damper masses may be freely movable or may be anchored (e.g. to restrain their respective paths of movement) to respective anchor points, or
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to a common anchor point, or may be anchored to one another, and the anchoring connections may be resilient or rigid and may be single or paired connections.
The multiple dampers may comprise masses constrained for 5 movement in a line via elements such as rigid or resilient or flexible, usually elongate, elements, which may be anchored as above. The multiple dampers may also comprise masses constrained for movement in an arc via attachments to the ends of such elements (e.g. leaf springs) including being 10 suspended from such elements (e.g. inelastic cable, wires or the like).
Alternatively, the multiple dampers may comprise a series of adjacent cantilevers pivotally hinged at a common hinge point (e.g. moving in an arc like leaves of a book). 15 Such dampers may employ both percussive damping and gas damping, whereby gas is forced out of the leaves as they rotate relative to one another, providing an additional damping effect.
The damper assembly may be used in applications where a 20 moving body needs to be brought to a temporary (e.g. momentary) halt or permanent halt. Alternatively, the assembly could be arranged such that after a series of collisions the moving body continues with its reduced momentum but without any further momentum reduction from the 25 damper assembly where, for example, the impact surface and dampers are arranged to be withdrawn rapidly from the path of the partially decelerated moving body.
In one embodiment, the damper assembly is a one-shot device. For example, the damper assembly may be installed as 30 a protective one-off device in vehicles to assist in protecting passengers or vehicle components during their deceleration in a high speed collision of the vehicle. As described below, the damper assembly may also be used to accelerate a second body (via the deceleration of the first 35 moving body), and this may be as a one-off device to assist in launching a vulnerable projectile or, for example, an aircraft ejector seat.
In an alternative embodiment, the damper assembly is a
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re-usable (i.e. multi-shot) device. In this case, the damper assembly includes a reset mechanism configured to reposition the at least one damper mass in the initial position for reuse. This mechanism may or may not include additional 5 components over and above the design of the damper itself. The mechanism may enable the at least one damper to damp the same body or a further body.
The at least one damper mass may be moving or stationary when the moving body collides with it in the initial position 10 (at a selected proximity to the impact surface). In the damper assembly, the at least one damper mass may be a free body, for example, one dropped into, or launched as a projectile into, the path of the approaching body, which mass may then follow a random (e.g. zigzagging) path undergoing 15 the series of collisions.
Usually, the damper assembly is configured such that the movement of the at least one damper mass is constrained to follow a selected path, which may be a linear or rotary path. The damper mass may be constrained by virtue of one or more 20 (e.g. a matched pair of) restraints, which may be a resilient restraint or flexible restraint or a rigid but movable restraint; a resilient restraint may be capable of flexing, stretching or otherwise deforming out of its equilibrium position and subsequently returning to that position. The 25 restraint may also act as the reset mechanism.
The restraint may be anchored to a fixed or movable body, which may include, for example, another damper (that could for example be acting in a corresponding matched (e.g. symmetrical) role. For example, a damper may be supported 30 upon one end of a resilient restraint (e.g. leaf spring), or a pair of matched dampers may be attached to either end of the restraint, where the latter is, for example, confined within a channel, groove, bore, ring, or similar partly or fully encircling device.
35 The action (e.g. flexing) of the restraint needs to be sufficiently light as to allow the damper mass to undergo the required energy damping collisions, the purpose of the restraint (e.g. spring or cantilever) being primarily an
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anchoring or confining function so as to ensure the damper mass remains positioned between the body and surface.
In one embodiment, the damper assembly is configured such that the damper is reset in the initial position by 5 virtue of its motion being constrained with respect to the moving body. For example, the damper may be carried by the body and/or may at least partially or fully encircle the body or otherwise be constrained with respect to the body.
The damper assembly will usually be configured to 10 operate in air or other gaseous environment. The damper assembly will tolerate variations in gas pressure, although extremely high gas pressures may lead to some viscous damping which may lead to reduced percussive damping.
Usually, the moving body will form part of apparatus in 15 which the body is forced to undergo controlled movements, including rapid accelerations from rest, or rapid decelerations to rest, and it is desired to damp these extremes of movement.
The damper assembly may form part of robotic apparatus, 20 machining apparatus, valve-controlled apparatus or other apparatus involving repetitive (and often fast) controlled movements of controlled components, usually in combination with an actuator or similar assembly. It is especially beneficial for use in unlubricated actuated machinery (i.e. 25 where lubrication is undesirable), such as, for example,
unlubricated weaving apparatus or food production apparatus.
The present damper assembly has the advantage that this percussive mechanism can react within fast time frames, as opposed to some alternative damper mechanisms, for example, 30 certain viscose dampers, which operate in too slow a time frame for use in these applications. Furthermore, the present damper assembly is remarkably tolerant of speed variations. During tests, it was found that even when the speed of the moving body is changed quite significantly, roughly the same 35 number of collisions will still occur, but they will merely happen in a shorter or longer time frame (i.e. if the body speed is doubled, the form of the damping curve of Fig 5 above remains the same, but damping takes place in a shorter
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time frame). The present damper assembly may also be implemented in high or low temperature environments, since the apparatus can be simple mechanical in nature and since the percussive mechanism does not require any form of liquid 5 (c.f. hydraulic damping) or lubricant (pivotal damper bearings, for example, can be self-lubricating).
The damper assembly may form part of, or be operatively linked to, an actuator assembly e.g. a reciprocating linear or rotary actuator. The moving body may be part of an 10 actuator arm, where its motion requires damping, or more usually a component carried by the actuator, for example, a framework supporting an object which is the subject of the desired actuated movement (e.g. a movable valve plate), or a component carried by or connected to the object, in 15 particular, where such components are designed as abutment means for bringing the object to a halt at a far extent of its motion. The present damper assembly is of especial application where a component carried by the actuator is delicate and should be protected from rapid accelerations or 20 decelerations. For example, Applicant's earlier application W02009/074800, describes a valve including a flexible valve plate whose movement may be controlled by an actuator and in which apparatus the valve plate kick-off's and/or halts may be damped by incorporation of the present damper assembly. 25 In one embodiment, the moving body forms part of apparatus in which the body follows a linear or rotary path.
The damper assembly may be provided in apparatus as a single action damper that only damps the deceleration of a moving body when it moves in one direction i.e. at one extent 30 of its motion. For example, a door that is opened and closed may only require a single action damper to damp the closing action. A further example would be pivotally connected arms, where the pivot joint itself requires damping to slow the closing of the arms to subtend the smallest angle. Similarly, 35 the damper assembly could be used to assist in initiating the opening of such a joint, where the pivot joint is a second body gradually accelerated by the gradual deceleration of a first moving body.
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More usually, a fast moving body will be undergoing a back and forth motion that requires damping at both extents of its motion. This may be linear or rotary reciprocating movement (e.g. a valve such as a linear or rotary (slide) 5 valve or plate valve). Thus, the moving body may form part of apparatus in which the body follows a reciprocating path, and the damper assembly may be a double action damper assembly so configured as to provide damping at each end of the reciprocating stroke of the moving body (e.g. whereby the 10 damping components of the assembly (i.e. impact surface and damper(s)) are present at each end of the reciprocating stroke of the moving body).
For example, a separate respective damper and separate respective impact surface may be provided at each end of the 15 stroke, or a common damper and/or a common impact surface may be provided for both ends. Each of these might partly encircle (e.g. a "C" or claw shape) or fully encircle the moving body (as an annular ring), and the damper may be disposed inwardly of the impact surface.
20 In one embodiment, the damper assembly comprises a common damper mass. This may be carried by the moving body and so configured as to damp the motion of the moving body at each end of its reciprocating stroke. The common damper mass may be a collar loosely fitted around the moving body. The 25 collar may be held within the plane of motion of the body; it may comprise inwardly disposed (facing), forward and rear striking surfaces against which the element collides during its forward and rearward reciprocating movement,
respectively, and similarly, may comprise outwardly disposed 30 (facing), forward and rear striking surfaces which collide against the impact surfaces. The striking surfaces are preferably convex and preferably made of a material with the required rebound (or dynamic) hardness (i.e. requisite elastic stiffness).
35 In one embodiment, the damper assembly comprises a pivotally supported damper provided with two damper arms, optionally pivotally supported at, or near to (for example, hung from), its centre of percussion. The centre of
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percussion of a pin-supported object is a point on it where a perpendicular impact at a location remote from that point will produce no reaction force at the pivot point, hence causing the least wear and tear at the pivot point.
5 During any collision between the at least one damper mass and the impact surface or the moving body, strain energy is stored in the two bodies and the release of that stored energy is the source of bounce. Also, a collision between two flat surfaces will yield a poorer bounce due to local rocking 10 around the impact site than a collision between a flat and a convex surface or two convex surfaces. Thus, the damper assembly is preferably configured so that a collision of the at least one damper with the body and/or a collision of the at least one damper with the impact surface involves at least 15 one convex surface. This may conveniently be achieved using a damper mass having an outwardly curved surface or surfaces; normally, the impact surface will be flat. Preferably, none of the collisions involve the collision of two flat surfaces.
The number of collisions of the at least one damper mass 20 with the approaching body is at least 2, and may be at least 3, at least 5, or at least 10, or in the range of at least 3 to 6, or in the range of at least 7 to 10. The damper assembly may be selectively configured so that the approaching body undergoes a selected minimum number of 25 collisions so as to ensure damping is sufficiently gradual. For example, if more collisions are required, a material with a higher coefficient of restitution may be chosen, or the damper mass may be configured to store the strain energy remotely from the impact points.
30 As a separate matter, it may be desirable to restrict the total number of collisions with the moving body; for example, some damper mass arrangements might undergo thousands of tiny impacts if unchecked, which would be undesirable. Hence, additionally or alternatively, the 35 assembly may be selectively configured so that the approaching body undergoes a selected maximum number of collisions, for example, for example, no more than 3, or 5 or 10 or 50 or 100. Thus, the assembly can be adjusted to
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operate in different time frames depending on the required responsivity and may be employed to provide effective damping in very short time frames.
The number of collisions may be limited by a further 5 mechanism; this may involve the use of an intermediate stop surface. For example, the damper assembly may further comprise an intermediate stop surface positioned between the moving body and the impact surface and so arranged not to impede the initial bouncing back and forth of the at least 10 one damper mass, but to halt the motion of the moving body once it reaches the intermediate stop surface. The intermediate stop surface may be arranged outwardly of the line of movement of the at least one damper mass.
In one embodiment, the intermediate stop surface may 15 comprise a continuous flat surface with an inset cavity having an end wall at the far end of the cavity comprising the impact surface against which the damper mass impacts; in this case, the cavity may be an elongate cavity and the damper mass an elongate rod, wherein the rod is not as long 20 as the cavity. The length of the rod (and hence cavity) may be selected to secure sufficient damping; a longer rod is better at storing strain energy and will give a more vigorous bounce. In an alternative embodiment, the impact surface may comprise a continuous flat surface, while the intermediate 25 stop surface comprises one or a plurality of bodies partially or fully encircling the path of the oscillating damper mass and disposed in the path of the approaching body.
In one embodiment, the damper assembly comprises a secondary damping mechanism. This can attenuate energy within 30 the damper mass and hence reduce bounce.
Such a secondary damping mechanism may comprise a single impact damper (e.g. a ball bearing loosely mounted in a cavity) or a plurality of impact dampers, and these may be incorporated within or attached to the body of the at least 35 one damper.
Alternatively, the damping mechanism may comprise a gas damping mechanism. For example, a multiple damper arrangement may comprise a set of adjacent cantilevers capable of both
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impacting one another for percussive damping, where gas damping between the leaves attenuates the energy of the multiple damper to reduce bounce.
The properties and arrangement of the components in the 5 assembly should be selectively configured, that is, they should be intentionally selected so as to ensure that at least two collisions occur, thereby progressively damping the motion of the moving body. The factors are of course interrelated, but as a general rule the mass of the damper 10 relative to that of the moving body is not more than 1:2,
preferably, not more than 1:4, or 1:10. Providing the mass of the damper is sufficiently small relative to that of the body, then the momentum (mass x velocity) exchange during the collision will ensure the damper will move away quickly 15 enough to bounce off the impact surface and return for at least one further momentum exchanging collision.
The damper assembly may be employed in applications where the impact surface is movable e.g. provided upon a body that is free to move. In particular, the impact surface may 20 be part of a second body and the collisions of the one or more dampers with the impact surface may result, via the deceleration of the first moving body, in the progressive acceleration of the second body away from the moving body, as opposed to a single abrupt initiation. There is further 25 provided the use of the above damper assembly configured gradually to accelerate a second body, usually at rest, away from a first moving body.
This may be very useful where the undamped acceleration forces associated with initially launching/kicking-off 30 movement of a component can damage it. Hence, the assembly could comprise a first moving body in the form of a controlled striking device (i.e. just initially controlled until the first impact or fully controlled) that is configured to approach a second body and assists its initial 35 acceleration from rest via a series of collisions with an appropriately selected intermediately positioned damper mass. Such an arrangement may be re-usable, and may for example initiate movement of a second body that is, for example,
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itself undergoing reciprocating movement. More usually, such a progressive acceleration application will be in a one-off device, for example, to assist in launching a projectile or, for example, an aircraft ejector seat, where reduced ejection 5 forces can mitigate spinal column trauma.
The present invention further provides apparatus comprising a damper assembly as above, and such apparatus may comprise robotic apparatus, machining apparatus, valve-controlling apparatus or other apparatus involving singular 10 or repetitive, single action or double action, controlled movements of components, and may optionally comprise an actuator assembly.
The present invention further provides a method of decelerating a body using at least one damper mass and an 15 impact surface together configured in a damper assembly, the method comprising:-
- providing at least one damper mass in an initial position; and,
- causing the body to approach the impact surface such 20 that it collides with the at least one damper mass in the initial position, whereupon the at least one damper mass bounces back and forth between the impact surface and the approaching body undergoing a series of collisions with the body that gradually decelerate the body.
25 The present invention also provides a damper assembly comprising an impact surface, a body configured to approach the impact surface, and at least one damper mass for damping the motion of the body, wherein the assembly is configured such that as the body approaches the impact surface it 30 collides with the at least one damper mass in an initial position to cause the at least one damper mass to bounce back and forth between the impact surface and the approaching body undergoing a series of collisions with the body that decelerate the body.
35 According to the present invention, there is also provided the use of a damper assembly to damp the motion of a moving body as it approaches an impact surface, wherein the damper assembly comprises the impact surface and at least one
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damper mass, and wherein the damper assembly is configured such that as the body approaches the impact surface it collides with the at least one damper mass in an initial position to cause the at least one damper mass to bounce back 5 and forth between the impact surface and the approaching body undergoing a series of collisions with the body that decelerate the body.
There is further provided the use of the present damper assembly progressively to decelerate and/or halt a moving 10 body, or, progressively to accelerate a second body on which the impact surface is disposed. In particular, the use may be in apparatus in which the moving body is undergoing reciprocating rotary or linear strokes.
The present invention further provides any novel and 15 inventive combination of the above mentioned features which the skilled person would understand as being capable to being combined. For example, any feature disclosed in respect of a single action damper may usually also be employed for a double action or multiple action damper.
20 BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will now be described, by way of example only, with reference to the accompanying drawings in which:-
Fig.l is a schematic plan view of a single action damper 25 assembly according to the invention;
Figs. 2a and 2b are, respectively, schematic perspective and side views of a double action damper assembly according to the invention;
Fig. 3 is a schematic plan view of a double action, 30 multiple damper assembly according to the invention;
Figure 4 is a schematic perspective view of a further double action, multiple damper assembly according to the invention;
Figure 5 is a graph showing the separation distances x 35 of the body and damper mass from the impact surface of the damper assembly of Figure 1, respectively, as they undergo the multiple collisions;
Figure 6 is a perspective schematic view of a further
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double action, damper assembly according to the invention;
Figure 7 illustrates Steps 1 to 10 showing the operation of the damper assembly according to Figure 6;
Figure 8 is a schematic side view of a single action 5 damper assembly configured gradually to accelerate a second body away from a first moving body;
Figure 9 shows, as Steps 1 to 3, the operation of a single action damper in which the maximum number of collisions is limited;
10 Figure 10 is a graph similar to that of Figure 5 showing the separation distances x of the body and damper mass from the impact surface in the damper assembly of Figure 9 as they undergo the multiple collisions;
Figures 11a and lib are, respectively, a front view and 15 transverse sectional view of a double action damper assembly according to the invention with a secondary damper mechanism, while Figure 11c is a front view of a similar double action damper assembly; and,
Figures 12a to d show schematic side views of various 20 damper assemblies with different arrangements of damper masses.
DETAILED DESCRIPTION
In the embodiments of the invention described below, it should be noted that (although not explicitly stated for 25 reasons of brevity) for each of the damper assemblies to achieve progressive damping of the motion of the moving body, they have been selectively configured, that is, the properties and arrangement of the respective components in the assembly have been selected so as to ensure that at least 30 two collisions of the moving body with a damper mass take place.
For example, one factor for progressive damping to occur is that the body needs to approach the impact surface with sufficient kinetic energy to trigger the series of collisions 35 of the at least one damper back and forth between the moving body and the impact surface (i.e. too slow an approach will not result in multiple collisions), that is to say, a body of a particular mass should have a selected minimum velocity, if
16
all factors remain unchanged. Another factor which may be important for damping to occur (e.g. if friction is an issue) is that, at the moment of the initial collision, the at least one damper should be disposed in a selected position 5 sufficiently close to the impact surface, since too large a separation may also not result in the required series of collisions. Other factors will include, for example,
selection of appropriate coefficients of restitution of the respective colliding components, selection of the shapes 10 and/or textures of their respective contact surfaces during collision, how much the kinetic energy of the colliding components is affected (e.g. damped) by other factors, to name a few factors.
Figure 1
15 Referring to Figure 1, this shows a plan view of a damping mechanism according to the invention for damping the arrest of a door 3 against a wall 5. The mechanism 1 comprises a damper mass 7 in the form of a hard rubber ball 7 resiliently supported on the end of a leaf spring 15 attached 20 to the wall 5, the ball being selectively positioned across the entrance to a cavity 11 inset into the wall. The end wall of the cavity is provided with an impact surface in the form of a striker block 9, and the door 3 with a similar striker block 13.
25 In situations where the door is moved sufficiently fast towards the wall, the striker block 13 on the door will collide with rubber ball 7 leading to a build-up of strain energy which, upon release, causes it to accelerate away and ahead of the (still moving) door into the cavity where it 30 collides with the static striker block 9 on the wall 5. Upon colliding with the wall 5, the ball will reverse its direction, accelerating away from the wall towards the (still approaching) door leading to a further collision with the door, and to the sequence of events repeating. The door is 35 thus decelerated relative to the wall by successive momentum transfer to the rubber ball from the multiple collisions. Moreover, the rates of collision increase with decreasing separation distance of the door from the wall enhancing the
17
effectiveness of the damping. Thus, if the door is pushed towards the wall at high speed, this percussive damping mechanism acts to dampen the arrest of the door body in a controlled and progressive manner reducing the wear and noise 5 as compared with an uncontrolled impact.
In this single action mechanism, the anchoring allows the ball to be reset in its initial position after use.
As indicated above, for multiple collisions and hence effective percussive damping to take place, the configuration 10 of the damper mechanism and choice of components should be appropriately selected. For example, in this case, the material of the ball and the blocks should be selected to have a suitable co-efficient of restitution (i.e. springiness or stiffness), the ball should be sufficiently light in mass 15 to accelerate away and ahead of the door, the ball should be appropriately anchored in a position suitably spaced close to the wall and the leaf spring or other similar resilient anchoring member should not significantly impede the ball but rather allow it to move and collide relatively freely. 20 Where the door 3 approaches the wall 5 very slowly,
however, the leaf spring 15 and damper will merely flex to arrest the door while remaining in contact therewith.
Figures 2a and 2b
These figures show a double action damper assembly 20 25 that forms part of a linearly reciprocating actuator mechanism for a slide valve. Reciprocating arm 22 forms part of a structure that supports the slide valve (not shown) and has twin forks 26 provided with opposed striking surfaces 24 which would normally impact against objects such as static 30 stops to halt the arm's movement. In this case, however, the stops have been replaced by a double action damper mechanism to achieve a gradual deceleration.
The damper mechanism comprises a single, common damper mass in the form of a hard, solid, cylindrical puck 28. This 35 is constrained by a leaf spring 30 to travel in an arc bouncing back and forth between impact surfaces 32a-32d of fixed common curved bracket assembly 34 and the moving twin forks 26. The bracket assembly has upper arms 36 and lower
18
arms 38 and the cylindrical puck damper 28 extends beyond the upper and lower arms in length, as may be seen in Fig. 2b, so that when the damper bounces off the upper and lower arms on one side of the bracket 34, it receives balanced angular 5 forces about its centre of mass 40 (point of attachment). The reciprocating arm 22 reciprocates linearly back and forth within a plane of motion between the upper and lower arms, as may also be seen in Fig. 2b, and at each end of its stroke one of the forks 26 will move outside the curved bracket 10 assembly 34. Thus, at one end of the arm's stroke, the damper puck 28 will be bouncing back and forth between impact surfaces 32a/32b and one fork 26' reducing the kinetic energy of the arm, and at the other end of the arm's stroke between impact surfaces 32c/32d and the other fork 26.
15 Figure 3
Figure 3 shows a schematic plan view of a double action, multiple damper assembly 50 intended to damp the rotary reciprocations of a controlled actuator arm 52. In this case, damping is achieved using a separate multi-puck 20 arrangement 54 and 54'on each end of the reciprocating stroke whereby the pucks collide with each other and the impact surfaces 56 and 56', respectively, of a common "C" shaped bracket assembly.
Figure 4
25 Figure 4 is a schematic perspective view of a further double action, multiple damper assembly 60.
Arm 62 is part of an actuator frame and undergoes rapid reciprocations more or less linearly to the left and right. The end of the arm is secured to a common damper in the form 30 of a resilient cantilever 64, whose length and resilience allows the arm freely to reciprocate. At each end of the stroke, damper 64 impacts against respective multidamper arrangements 66 and 66, each comprising shorter multi-cantilevered arms 68.
35 In this example, two damping mechanisms slow the arm 62
which is particularly effective. The arm is decelerated by successive impacts of the adjacent flexing leaves of the shorter multi-cantilevered arms 68, and there is secondary
19
gas damping as gas is forced out from the adjacent leaves thereby attenuating the energy in those leaves.
Figure 6
Figure 6 is a further double action damper assembly 70 5 forming part of an actuator assembly that is supporting a slide valve (not shown).
Moving actuator frame 72 reciprocates linearly to and fro and includes arm 74 extending perpendicular to the line of motion which extends through a rectangular aperture 7 6 in 10 slideway 78. Mounted upon the arm 74 is rectangular collar 80, which acts as a common damper for both ends of the reciprocating strokes, sliding along the slideway 78 in a plane of motion perpendicular to the arm 74 and colliding with the separate impact surfaces of static abutments 82, 82' 15 and arm 74 so as to decelerate the arm, as described in more detail with respect to Figure 7 below.
Figure 7
Figure 7 illustrates the operation of the damper assembly of Figure 6.
20 The 8 respective striking surfaces involved in the decelerating collisions are as follows:
• Impact surfaces A and H of static abutments 82' and 82
• Strike surfaces D and E of Actuator Arm 74(Moving body)
• External striking surfaces B and G of Collar 80(Common 25 Damper)which impact A and H, respectively
• Internal striking surfaces C and F of Collar 80(Common Damper)which impact D and E, respectively
• Surfaces A and H and D and E are flat, while all the remaining striking surfaces of the Common Damper are
30 convex.
Steps 1 to 10 illustrate the operation as follows:-1 - Actuator Arm 74(Moving body) is pressed against Collar 80(Common Damper) which is pressed against abutment 82', both at a temporary halt;
35 2 - Arm 74 starts to move off to the left without stationary collar 80;
3 - Arm 74 collides in 1st Impact Ci at its strike
20
surface E with internal striking surface F of Collar 80;
4 - Release of strain energy in Collar 80 causes it to move in the same direction as the Arm 74 but faster so that it moves away from moving Arm 74, which has lost some
5 momentum;
5 - Collar 80 keeps moving in same direction (Arrow 1) and collides at its external striking surface G with impact surface H, where it is caused to reverse its direction (Arrow 2) ;
10 6 - Collar 80 bounces back towards moving Arm 74;
7 - Collar 80 collides in 2nd Impact C2 at its internal striking surface F with strike surface E of Arm 74 and the exchange of momentum causes Collar 80 to reverse its direction bouncing away from Arm 74, which has lost further
15 momentum;
8 - Collar 8 again collides at its external striking surface G with impact surface H, where it is caused to reverse its direction again (Arrow 2);
9 - Shortly after leaving impact surface H, Collar 8
20 collides in 3rd Impact C3 at its internal striking surface F with strike surface E of Arm 74, where it again reverses its direction to move back against the impact surface H;
10 - Both Arm 74 and Collar 80 are pressed against impact surface H at a temporary halt, which corresponds to
25 the opposite end of the reciprocation = Step 1 above.
Figure 8
Figure 8 is an example of a single action, one-shot damper assembly configured gradually to accelerate a second body away from a first moving body.
30 Assembly 90 is an ejector assembly for an aircraft ejector seat and propellant or rocket device or charge 92 acts as the moving body. A damper mass 94 is centrally suspended in a selected initial stationary position directly above the charge 92 by means of a plurality of radially
35 extending, sacrificial tethers 96 designed to snap easily upon rapid movement of the damper mass 94. The releasable ejector seat 96 is disposed directly above the damper mass 94 and includes a reinforced impact surface 100 on its
21
underside.
Activation of the charge 92 causes it to be propelled towards the damper mass 94, which immediately snaps its tethers upon the collision and accelerates towards the impact 5 surface 100. The damper mass 94 then bounces back and forth between the impact surface 100 and the still approaching charge 92 undergoing multiple collisions that result in successive momentum transfer from the charge 92 to the ejector seat 96 before the charge itself impacts the ejector 10 seat 96 in a softened impact. The progressive acceleration of the ejector seat 96 due to the damping mechanism mitigates the effect of the main impact, thereby minimising the risk of a spinal column trauma in the passenger.
Figure 9
15 Figure 9 shows Steps 1 to 3 of the operation of a single action, one-shot damper assembly in which the number of collisions is limited, or rather, the action of the damper assembly per se is restricted. The assembly comprises moving body B, damper mass comprising a metal rod D and an elongate 20 cavity C extending within and perpendicular to surface S. Cavity C is longer in length than rod D and is provided at its far end with impact surface I. Such an assembly could be part of a protective device for damping the deceleration of vehicle component B before it impacts surface S during a 25 vehicle accident.
Step 1 - Moving body B collides in collision Ci with end A of damper rod D causing momentum transfer to the rod which bounces away towards inset cavity C where its other end Z collides with the inset impact surface I.
30 Step 2 - The assembly is configured such that the rod D
bounces back out of the cavity C to undergo a second decelerating collision C2 at its end A with moving body B, whereby the body loses further momentum and the damper rod D once again bounces away towards the cavity C.
35 Step 3 - Damper rod D enters the cavity with insufficient energy and comes to rest fully within the cavity where it cannot impede the progress of the moving body B and moving body B is then brought to an abrupt halt by a third
22
collision C3 with surface S; the possibility of damage to body B having been lessened by the gradual deceleration of the damping mechanism.
Figure 10
5 Figure 10 is a graph similar to that of Figure 5 showing the separation distances x of the body B and end A of damper mass D from the impact surface as they undergo the multiple collisions of Steps 1 to 3.
Figures lla-c
10 Figure 11a depicts a further double action damper assembly according to the invention, with additional damper mechanisms to attenuate the energy within the damper mass.
Damper assembly 110 comprises a common damper 111 comprising a pivotally hung, fork shaped body 111 having two 15 respective damper arms 112 and 112'.The moving body comprises moving actuator arm 114 supported (not shown) for rotary (or linear) reciprocation back and forth between impact surfaces of stops 116 and 116'.
The fork shaped body 111 is pivotally hung at, or close 20 to, its centre of percussion 120 so as to minimise wear and tear at the pivot point. The pivot bearing is also a self-lubricating, graphite bearing, with the result that the fork shaped body 111 is tuned to swing very freely. This is ideal for longevity but can lead to an excessive number of 25 collisions (i.e. damping curve extends) so attenuation of the energy in the damper mass is desirable. Firstly, the fork shaped body 111 incorporates a single impact damper 118 offset from the pivot point, in this case, directly above the pivot point; this may be a ball bearing confined in a cavity 30 against which it strikes during reciprocation to dissipate some of the kinetic energy in the body 111. Secondly, as in the Figure 9 embodiment above, it is preferable if the ends of the damper arms 112, 112' are receivable within slightly larger cavities (Fig. lib) that curtail damping by limiting 35 the number of collisions, so that actuator arm 114 eventually collides with stops 116, 116'.
Fig. 11c shows a slightly modified arrangement, where multiple impact dampers 118 are provided above the pivot
23
point 120 for more aggressive attenuation of the kinetic energy. The stiffness (springiness) of the damper limbs may be adjusted by changing the necking 122 of the limbs, as shown in Fig. 11c, for even further fine tuning. (In this 5 way, more energy may be stored in a single collision for subsequent attenuation by the ball dampers.)
Because the above damper assembly requires no lubrication, it is suitable for use in high or low temperature environments.
10 Figures 12a~d
Figures 12a and b respectively show multiple dampers D arranged in series and parallel prior to undergoing damping collisions between moving body B and impact surface I. They could be individually tethered or tethered to each other, 15 and, if initially stationary, could be configured for simple linear movement in parallel lines of motion.
Figure 12c shows multiple dampers D arranged randomly prior to undergoing damping collisions between moving body B and impact surface I. They could be individually tethered or 20 tethered to each other (e.g. by 2D or 3D net), and, if initially stationary, could be configured for simple linear movement in parallel lines of motion.
Figure 12d shows a single damper arrangement whereby a free damper mass D is used, and is projected into the space 25 between the moving body B and impact surface I in order to provide damping, its resulting zigzagging motion after collisions being unpredictable and random.
While the invention has been described by reference to specific embodiments, it should be understand that the 30 invention is not limited to the described embodiments and numerous modifications may be made within the scope of the present invention.
24
Claims (1)
- Claims:I. A damper assembly comprising an impact surface, and at least one damper mass for damping the motion of a body, wherein the assembly is configured such that, in use, when a5 body approaches the impact surface it collides with the at least one damper mass in an initial position to cause the at least one damper mass to bounce back and forth between the impact surface and the body undergoing a series of collisions with the moving body that decelerate the body. 10 2. A damper assembly according to claim 1, wherein the impact surface is configured to remain stationary during the damping.3. A damper assembly according to claim 1 or claim 2, wherein the assembly is configured such that the series of15 collisions involve a single damper mass.4. A damper assembly according to claim 1 or claim 2, wherein the assembly is configured such that the series of collisions involve multiple damper masses bouncing back and forth between the impact surface and the moving body.20 5. A damper assembly according to claim 4, wherein the multiple damper masses are arranged to act in series and/or in parallel.6. A damper assembly according to claim 4 or claim 5, wherein the multiple dampers comprise a plurality of rounded25 damper masses or a plurality of resilient cantilevers.7. A damper assembly according to any preceding claim, wherein the damper assembly is a one-shot device.8. A damper assembly according to any of claims 1 to 6, wherein the damper assembly is a re-usable device.30 9. A damper assembly according to claim 8, wherein the damper assembly includes a reset mechanism configured to reposition the at least one damper mass in the initial position for re-use.10. A damper assembly according to any preceding claim, 35 wherein the damper assembly is configured such that the movement of the at least one damper mass is constrained to follow a selected path.II. A damper assembly according to claim 9 and claim 10,25wherein the reset mechanism is configured to constrain the at least one damper mass to follow the selected path.12. A damper assembly according to claim 10 or claim 11, wherein the at least one damper mass is constrained by one or5 more, optionally resilient, restraints.13. A damper assembly according to claim 9, wherein the damper assembly is configured such that the damper is reset in the initial position by virtue of its motion being constrained with respect to the moving body.10 14. A damper assembly according to any preceding claim,wherein the damper assembly forms part of, or is operatively linked to, an actuator assembly.15. A damper assembly according to any preceding claim, wherein the moving body forms part of apparatus in which the15 body follows a linear or rotary path.16. A damper assembly according to any preceding claim, wherein the moving body forms part of apparatus in which the body follows a reciprocating path.17. A damper assembly according to claim 16, wherein the 20 damper assembly is a double action damper assembly so configured as to provide damping at each end of the reciprocating stroke of the moving body.18. A damper assembly according to claim 17, wherein the damper assembly comprises a common damper mass, which is25 optionally carried by the moving body and so configured as to damp the motion of the moving body at each end of its reciprocating stroke.19. A damper assembly according to claim 17, wherein the damper assembly comprises a pivotally supported damper30 provided with two damper arms, optionally pivotally supported at or near its centre of percussion.20. A damper assembly according to any preceding claim, wherein the damper assembly is configured so that a collision of the at least one damper with the body and/or a collision35 of the at least one damper with the impact surface involves at least one convex surface.21. A damper assembly according to any preceding claim, wherein the damper assembly is selectively configured so that26the moving body will undergo a selected minimum number of collisions so as to ensure damping is sufficiently gradual.22. A damper assembly according to any preceding claim, wherein the assembly is selectively configured so that the5 moving body will undergo a selected maximum number of collisions.23. A damper assembly according to claim 22, wherein the number of collisions is limited by a further mechanism.24. A damper assembly according to claim 23, wherein the 10 damper assembly further comprises an intermediate stop surface positioned between the moving body and the impact surface and so arranged not to impede the initial bouncing back and forth of the at least one damper mass, but to halt the motion of the moving body once it reaches the 15 intermediate stop surface.25. A damper assembly according to claim 24, wherein the intermediate stop surface is arranged outwardly of the line of movement of the at least one damper mass.26. A damper assembly according to any preceding claim,20 wherein the damper assembly comprises at least one further damping mechanism.27. A damper assembly according to any preceding claim, wherein the mass of the damper relative to that of the moving body is not more than 1:2, and preferably not more than 1:4.25 28. A damper assembly according to claim 1, wherein the impact surface is provided upon a body that is free to move.29. A damper assembly according to claim 28, wherein the impact surface is part of a second body and the assembly is configured so that the collisions of the one or more dampers30 with the impact surface will result in the progressive acceleration of the second body away from the moving body.30. Apparatus comprising a damper assembly according to any preceding claim, wherein the apparatus comprises robotic apparatus, machining apparatus, valve-controlling apparatus35 or other apparatus involving repetitive, controlled movements of components, and optionally comprises an actuator assembly.31. The use of a damper assembly to damp the motion of a moving body as it approaches an impact surface, wherein the27damper assembly comprises the impact surface and at least one damper mass, and wherein the damper assembly is configured such that as the body approaches the impact surface it collides with the at least one damper mass in an initial 5 position to cause the at least one damper mass to bounce back and forth between the impact surface and the approaching body undergoing a series of collisions with the body that decelerate the body.32. The use of a damper assembly according to claim 110 progressively to decelerate and/or halt a moving body, or, progressively to accelerate a second body on which the impact surface is disposed.33. The use according to claim 31 or 32, wherein the use is in apparatus in which the moving body is undergoing15 reciprocating rotary or linear strokes.34. A method of decelerating a body using at least one damper mass and an impact surface together configured in a damper assembly, the method comprising:-- providing at least one damper mass in an initial 20 position; and,- causing the body to approach the impact surface such that it collides with the at least one damper mass in the initial position, whereupon the at least one damper mass bounces back and forth between the impact surface and the25 approaching body undergoing a series of collisions with the body that gradually decelerate the body.35. An apparatus, method or use substantially as hereinbefore described with reference to the accompanying drawings.
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
GB1203070.6A GB2499621A (en) | 2012-02-22 | 2012-02-22 | A damper assembly |
GB1414209.5A GB2517840A (en) | 2012-02-22 | 2013-02-05 | Multiple damper assembly |
PCT/GB2013/050264 WO2013124619A1 (en) | 2012-02-22 | 2013-02-05 | Multiple damper assembly |
PCT/GB2013/050262 WO2013124617A1 (en) | 2012-02-22 | 2013-02-05 | Damper assembly |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
GB1203070.6A GB2499621A (en) | 2012-02-22 | 2012-02-22 | A damper assembly |
Publications (2)
Publication Number | Publication Date |
---|---|
GB201203070D0 GB201203070D0 (en) | 2012-04-04 |
GB2499621A true GB2499621A (en) | 2013-08-28 |
Family
ID=45940033
Family Applications (2)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
GB1203070.6A Withdrawn GB2499621A (en) | 2012-02-22 | 2012-02-22 | A damper assembly |
GB1414209.5A Withdrawn GB2517840A (en) | 2012-02-22 | 2013-02-05 | Multiple damper assembly |
Family Applications After (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
GB1414209.5A Withdrawn GB2517840A (en) | 2012-02-22 | 2013-02-05 | Multiple damper assembly |
Country Status (2)
Country | Link |
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GB (2) | GB2499621A (en) |
WO (2) | WO2013124619A1 (en) |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2005069279A (en) * | 2003-08-20 | 2005-03-17 | Honda Motor Co Ltd | Dynamic damper |
JP2008281141A (en) * | 2007-05-11 | 2008-11-20 | Shinko Electric Co Ltd | Electromagnetic brake and electromagnetic clutch |
US20110020592A1 (en) * | 2009-07-21 | 2011-01-27 | Eurocopter | Insulating coating with mass amplification |
Family Cites Families (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2520937A (en) * | 1949-05-19 | 1950-09-05 | Jr Dwight C Kennard | Spring and vibration damper therefor |
US4612429A (en) * | 1984-08-13 | 1986-09-16 | Westinghouse Electric Corp. | Multiple-impact shock absorbing means for circuit interrupter and other apparatus |
US4698470A (en) * | 1986-05-22 | 1987-10-06 | Westinghouse Electric Corp. | Multiple-impact shock-absorbing assembly for circuit interrupter and other apparatus |
EP2220410B8 (en) | 2007-12-11 | 2012-04-11 | Isentropic Limited | Valve |
-
2012
- 2012-02-22 GB GB1203070.6A patent/GB2499621A/en not_active Withdrawn
-
2013
- 2013-02-05 WO PCT/GB2013/050264 patent/WO2013124619A1/en active Application Filing
- 2013-02-05 GB GB1414209.5A patent/GB2517840A/en not_active Withdrawn
- 2013-02-05 WO PCT/GB2013/050262 patent/WO2013124617A1/en active Application Filing
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2005069279A (en) * | 2003-08-20 | 2005-03-17 | Honda Motor Co Ltd | Dynamic damper |
JP2008281141A (en) * | 2007-05-11 | 2008-11-20 | Shinko Electric Co Ltd | Electromagnetic brake and electromagnetic clutch |
US20110020592A1 (en) * | 2009-07-21 | 2011-01-27 | Eurocopter | Insulating coating with mass amplification |
Also Published As
Publication number | Publication date |
---|---|
GB201414209D0 (en) | 2014-09-24 |
WO2013124617A1 (en) | 2013-08-29 |
GB2517840A (en) | 2015-03-04 |
GB201203070D0 (en) | 2012-04-04 |
WO2013124619A1 (en) | 2013-08-29 |
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