Quasi-zero stiffness vibration isolation device and track trajectory determination method and system

Abstract

The invention provides a quasi-zero stiffness vibration isolation device and a track trajectory determination method and system, and relates to the technical field of precise supporting and vibration isolation. By adopting the horizontal telescopic guide rod, the linear spring and the nonlinear track, the sliding end of the telescopic guide rod is propped against the track to slide under the thrust of the linear spring. In the moving process of the mass block, the sliding track of the sliding end is a nonlinear similar parabola. The linear spring is pushed by the track due to the change of the parabola-like track during sliding, and the compression degree of the linear spring is changed, so that the magnitude of the acting force applied to the track by the sliding end is changed. The change of the track changes the direction of the counter-acting force of the track to the sliding end. Based on the synergistic effect of the horizontal telescopic guide rods, the linear springs and the quasi-parabola non-linear orbits, non-linear restoring force is generated through the non-linear shape of the orbits, quasi-zero-stiffness vibration isolation is achieved, negative-stiffness springs are prevented from being adopted, and the structure of the vibration isolation device is simplified in the mode that the orbits with the simple structure are adopted.

Description

Technical Field

[0001] The present invention relates to the technical field of precision support and vibration isolation, and particularly to a quasi-zero stiffness vibration isolation device, an orbit trajectory determination method and a system. Background Art

[0002] The quasi-zero stiffness technology has important applications in vibration isolation and high-precision support systems. It can achieve extremely low dynamic stiffness while maintaining the stability of the system, thereby significantly reducing the sensitivity of the system to external vibrations.

[0003] Currently, the realization of quasi-zero stiffness usually relies on a negative stiffness spring system. The core of this design is to offset the stiffness of the system through the dynamic balance of positive and negative stiffness, so as to obtain an approximately zero stiffness effect under specific working conditions. For example, the stiffness of a traditional spring is positive (the restoring force increases as the displacement increases). In contrast, the characteristic of a negative stiffness spring is that when the spring is compressed (or stretched), its restoring force decreases as the displacement increases. Thus, by superimposing positive and negative stiffness springs, the total stiffness can be offset near a specific working point.

[0004] In the prior art, negative stiffness springs usually use pre-compressed beams, magnetic levitation forces or special geometric structures to generate non-linear restoring forces. However, the existing negative stiffness springs generally have the drawback of complex structures. For example, the pre-compressed beam method includes cantilever beams, folded beams or bow-shaped beams, and the folded beam requires complex geometric designs (such as sinusoidal, serpentine) to enhance non-linearity. Another example is that the magnetic levitation force system is vulnerable to vibration interference and requires the introduction of dampers or active control, resulting in a complex structure. In addition, negative stiffness springs usually require precise adjustment of the initial pre-tightening force and installation position, increasing the complexity of design and manufacturing. Summary of the Invention

[0005] Embodiments of the present invention provide a quasi-zero stiffness vibration isolation device, an orbit trajectory determination method and a system to solve the problem of the complex structure of the existing quasi-zero stiffness vibration isolation method due to the use of negative stiffness springs.

[0006] In a first aspect, embodiments of the present invention provide a quasi-zero stiffness vibration isolation device, including: a mass block to be vibration-isolated; horizontal telescopic guide rods, linear springs and tracks are arranged on both the left and right sides of the mass block;

[0007] For any one side, the mass block is slidably connected to the horizontal telescopic guide rod;

[0008] The first end of the linear spring is fixedly connected to the mass block, and the second end is fixedly connected to the sliding end of the horizontal telescopic guide rod away from the mass block, and pushes the sliding end against the track;

[0009] The mass block can only move up and down, and drives the horizontal telescopic guide rod to move up and down; when the horizontal telescopic guide rod moves up and down, the sliding end slides along the track;

[0010] The vertical trajectory of the track is a non-linear parabola-like shape, and the opening faces the mass block;

[0011] During the movement of the mass block, the trajectory is used to change the compression degree of the linear spring, change the magnitude of the force exerted by the sliding end on the track, and also used to change the direction of the reaction force of the track on the sliding end, thereby generating a non-linear restoring force on the mass block in the vertical direction. Among them, the greater the distance of the mass block from the equilibrium point, the greater the non-linear restoring force.

[0012] In a possible implementation, it further includes: a frame, and a vertical guide rod fixed to the frame;

[0013] The track is fixed to the frame;

[0014] The mass block realizes the up and down movement relative to the track through the limitation and guidance of the vertical guide rod.

[0015] In a possible implementation, the sliding end includes a bearing;

[0016] The inner ring of the bearing is fixedly connected to the horizontal telescopic guide rod, and the outer ring abuts against the track;

[0017] The bearing is used to roll on the track through the outer ring to realize the sliding of the sliding end along the track.

[0018] In a possible implementation, the trajectory of the track is determined according to the target non-linear restoring force, the gravity of the mass block, the stiffness coefficient of the linear spring, and the deformation of the linear spring at the equilibrium point; among them, the target non-linear restoring force is the relationship between the magnitude of the non-linear restoring force in the vertical direction and the displacement from the equilibrium point.

[0019] In a possible implementation, the trajectory of the track is determined based on the following formula:

[0020]

[0021] Among them, h(y) represents the target non-linear restoring force; G represents the gravity of the mass block; k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the trajectory; y represents the ordinate of the trajectory.

[0022] In a possible implementation, the target non-linear restoring force includes a cubic non-linear restoring force or a one-third power non-linear restoring force.

[0023] In a second aspect, an embodiment of the present invention provides a method for determining the track trajectory of a quasi-zero stiffness vibration isolation device, which is applied to the quasi-zero stiffness vibration isolation device described in any item of the first aspect; the method includes:

[0024] Obtain the stiffness coefficient of the linear spring and the target non - linear restoring force;

[0025] Determine the elastic force of the linear spring based on the stiffness coefficient of the linear spring and the offset in the horizontal direction;

[0026] Determine the elastic force of the linear spring in the horizontal direction as the sine component of the track reaction force, and determine the target non - linear restoring force in the vertical direction as the cosine component of the track reaction force;

[0027] Divide the sine component by the cosine component to obtain the slope, which is used as the differential equation of the trajectory;

[0028] Integrate the differential equation to obtain the trajectory.

[0029] In a possible implementation, the step of determining the elastic force of the linear spring in the horizontal direction as the sine component of the track reaction force includes: determining the sine component of the track reaction force based on the following formula:

[0030] F N sin(θ) = k1(x + x0)

[0031] where, F N sin(θ) represents the sine component of the track reaction force, k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the trajectory;

[0032] The step of determining the target non - linear restoring force in the vertical direction as the cosine component of the track reaction force includes: determining the cosine component of the track reaction force based on the following formula:

[0033]

[0034] where, F N cos(θ) represents the cosine component of the track reaction force, h(y) represents the target non - linear restoring force; G represents the gravity of the mass block; y represents the ordinate of the trajectory.

[0035] In a possible implementation, the step of dividing the sine component by the cosine component to obtain the slope, which is used as the differential equation of the trajectory includes:

[0036] Obtain the differential equation of the trajectory based on the following:

[0037]

[0038] where, tan(θ) represents the slope of the trajectory; represents the differential of the trajectory.

[0039] In a third aspect, an embodiment of the present invention provides a quasi-zero stiffness vibration isolation system, including the quasi-zero stiffness vibration isolation device described in any one of the first aspects.

[0040] In the embodiment of the present invention, by adopting a horizontal telescopic guide rod, a linear spring, and a non-linear track in the shape of a quasi-parabola, the sliding end of the telescopic guide rod slides on the track under the thrust of the linear spring. During the movement of the mass block, the sliding trajectory of the sliding end is a non-linear quasi-parabola. The change of the quasi-parabola trajectory during sliding causes the track to push the linear spring, resulting in a change in the compression degree of the linear spring, and further causing a change in the magnitude of the force exerted by the sliding end on the track. The change of the track trajectory also changes the direction of the reaction force of the track on the sliding end.

[0041] For example, when the mass block moves upward, the track compresses the linear spring, the force exerted by the sliding end on the track becomes larger, and the direction of the normal reaction force of the track gradually deviates towards the vertical direction, and the non-linear restoring force on the mass block in the vertical direction becomes larger.

[0042] Also, due to the non-linear shape of the track, the larger the distance of the mass block from the equilibrium point, the greater the non-linear restoring force; and the smaller the distance of the mass block from the equilibrium point, the smaller the non-linear restoring force. Thus, the stiffness approaches zero at small displacements near the equilibrium point, while the stiffness increases at large displacements far from the equilibrium point, thereby achieving quasi-zero stiffness vibration isolation while taking into account the buffering and load-bearing capabilities.

[0043] Based on the synergistic effect of the horizontal telescopic guide rod, the linear spring, and the non-linear track in the shape of a quasi-parabola, the embodiment of the present invention generates a non-linear restoring force through the non-linear shape of the track, realizes quasi-zero stiffness vibration isolation, avoids using a negative stiffness spring, and simplifies the structure of the vibration isolation device by adopting a simple track structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic structural diagram of the quasi-zero stiffness vibration isolation device provided by the embodiment of the present invention;

[0045] Figure 2 is a schematic diagram of the force analysis of the sliding end provided by the embodiment of the present invention;

[0046] Figure 3 is a flowchart of the implementation of the method for determining the track trajectory of a quasi-zero stiffness vibration isolation device provided by the embodiment of the present invention;

[0047] Figure 4 is the track shape and force-displacement curve of two different cubic non-linear stiffness coefficients provided by the embodiment of the present invention;

[0048] Figure 5 is the track shape and force-displacement curve of two different one-third power non-linear stiffness coefficients provided by the embodiment of the present invention. Detailed implementation manners

[0049] The embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0050] The method of the present invention is applicable to a variety of engineering application scenarios, including but not limited to high-precision vibration isolation systems, support structures for precision instruments, and ultra-low frequency vibration isolation platforms. Taking the vibration isolation of precision instruments as an example, the vibration isolation system can isolate the micro-vibrations of the foundation (such as the low-frequency vibrations generated by air-conditioning units and human walking). The quasi-zero stiffness system is particularly suitable for low-frequency vibration isolation: under small-amplitude vibrations, the system stiffness is extremely low, effectively isolating external disturbances; when the amplitude is large, the stiffness increases rapidly to prevent structural damage. Thus, the quasi-zero stiffness system can achieve an extremely low dynamic stiffness while maintaining system stability.

[0051] Quasi-zero stiffness is a basic physical concept. Stiffness refers to the ability of an object to resist deformation. A force acting on an object causes the object to displace under the action of the force. Stiffness can be expressed as the ratio of the force to the displacement.

[0052] When a quasi-zero stiffness system is subjected to an external force, within a certain range, it hardly generates a force to resist deformation. Usually, under small displacement conditions, the system exhibits extremely small stiffness characteristics. Or rather, under small-amplitude vibrations, the system stiffness is extremely low and is very insensitive to low-frequency micro-disturbances from the outside world, effectively isolating these disturbances so that the system hardly generates obvious displacement or vibration response due to external micro-vibrations; when the vibration amplitude increases to a certain extent, the stiffness of the system will increase rapidly to prevent the system from being damaged or losing stability due to excessive displacement, ensuring that the system can still maintain a certain load-bearing capacity and stability under large-amplitude conditions.

[0053] The existing methods generally use negative stiffness springs. For example, usually, a positive stiffness spring (such as a common spring) is combined with a negative stiffness spring (such as a negative stiffness spring with a specific structure or a device that generates negative stiffness using the principle of magnetic levitation, etc.). When the positive stiffness and negative stiffness cancel each other out or balance under certain conditions, the system can exhibit quasi-zero stiffness characteristics.

[0054] In addition to the disadvantage of complex structure, negative stiffness springs generally have the following deficiencies:

[0055] 1. Large energy loss: During the operation of the negative stiffness spring, the system is prone to generate additional energy loss, reducing the overall vibration isolation performance.

[0056] 2. Difficult to adjust: The negative stiffness characteristics highly depend on material and structural parameters and are difficult to flexibly adjust to adapt to different application scenarios.

[0057] 3. Poor reliability: The negative stiffness characteristics are prone to degradation due to wear of materials and structures, and the reliability during long-term use is insufficient.

[0058] In the embodiments of the present invention, a non-linear restoring force is generated through a non-linear track, and quasi-zero stiffness is achieved with different technical concepts, which can avoid the use of a negative stiffness spring, thereby simplifying the system structure.

[0059] Figure 1 It is a schematic structural diagram of the quasi-zero stiffness vibration isolation device provided by the embodiments of the present invention. As Figure 1 shown, the embodiments of the present invention provide a quasi-zero stiffness vibration isolation device, including: a mass block to be vibration-isolated; horizontal telescopic guide rods, linear springs and tracks are arranged on both the left and right sides of the mass block; for any one side, the mass block is slidably connected to the horizontal telescopic guide rod; the first end of the linear spring is fixedly connected to the mass block, and the second end is fixedly connected to the sliding end of the horizontal telescopic guide rod far away from the mass block, and pushes the sliding end against the track; the mass block can only move up and down, and drives the horizontal telescopic guide rod to move up and down; when the horizontal telescopic guide rod moves up and down, the sliding end slides along the track; the vertical trajectory of the track is a non-linear parabola-like shape, and the opening faces the mass block; during the movement of the mass block, the trajectory is used to change the compression degree of the linear spring, change the magnitude of the force exerted by the sliding end on the track, and also used to change the direction of the reaction force of the track on the sliding end, thereby generating a non-linear restoring force on the mass block in the vertical direction, wherein the greater the distance of the mass block deviating from the equilibrium point, the greater the non-linear restoring force.

[0060] In some embodiments, a quasi-zero stiffness vibration isolation device includes: a mass block to be vibration-isolated.

[0061] It should be noted here that the mass block is only an abstraction of the vibration-isolated object, which is used to abstract the vibration-isolated object to more clearly describe the present application, and does not mean that it must be a block-shaped object in the figure. Generally, the object to be vibration-isolated has a certain mass and can be abstracted as a mass block. The vibration isolation device is arranged between the vibration-isolated object and the vibration source.

[0062] In some embodiments, horizontal telescopic guide rods, linear springs and tracks are arranged on both the left and right sides of the mass block;

[0063] Exemplarily, horizontal telescopic guide rods, linear springs and tracks are symmetrically arranged on both the left and right sides of the mass block.

[0064] Exemplarily, a horizontal telescopic guide rod, a linear spring and a track are arranged on the left side of the mass block, and a horizontal telescopic guide rod, a linear spring and a track are also arranged on the right side of the mass block.

[0065] Exemplarily, the horizontal telescopic guide rods, linear springs and tracks on both the left and right sides of the mass block are in the same vertical plane.

[0066] The composition of the device has been described above. Taking one side as an example below, the shapes and connection relationships of each part will be specifically described.

[0067] In some embodiments, for any side, the mass block is slidably connected to the horizontal telescopic guide rod.

[0068] Exemplarily, the horizontal telescopic guide rod is horizontally arranged, can be telescoped in the horizontal direction, and is a rod-shaped structure that plays roles such as guiding and supporting.

[0069] Furthermore, the mass block being slidably connected to the horizontal telescopic guide rod means that the horizontal telescopic guide rod can slide relative to the mass block. Here, the sliding connection method is not limited, and it can be direct contact sliding or connected through an intermediate sliding element. Taking the mass block as the reference system, after the mass block is slidably connected to the horizontal telescopic guide rod, the horizontal telescopic guide rod obtains the translational freedom in the horizontal direction and adjusts its position in the horizontal plane.

[0070] The horizontal telescopic guide rod also cooperates with the linear spring, as described below.

[0071] In some embodiments, the first end of the linear spring is fixedly connected to the mass block, and the second end is fixedly connected to the sliding end of the horizontal telescopic guide rod away from the mass block, and pushes the sliding end against the track.

[0072] Exemplarily, the elastic force of the linear spring is proportional to the deformation amount of the spring and follows Hooke's law. The linear spring is usually made of metal materials with good elasticity, such as spring steel, stainless steel, etc., and can also be made of polymer materials or composite materials. The common shape of the linear spring is spiral, including cylindrical spiral springs, conical spiral springs, etc.

[0073] Exemplarily, the first end of the linear spring is fixedly connected to the mass block, and the second end is fixedly connected to the sliding end of the horizontal telescopic guide rod away from the mass block. This means that the movement of the horizontal telescopic guide rod is restricted by the elastic force of the linear spring. For example, when the spring is stretched, it drives the sliding end of the horizontal telescopic guide rod to extend; when the spring is compressed, it drives the sliding end of the horizontal telescopic guide rod to retract. Here, the end of the horizontal telescopic guide rod away from the mass block is defined as the sliding end.

[0074] Regarding the state of the spring, exemplarily, the linear spring is always in a compressed state. Furthermore, the compressed linear spring pushes the sliding end against the track.

[0075] The shapes and connection relationships of each part have been described above. The following describes the movement cooperation relationship.

[0076] In some embodiments, the mass block can only move up and down and drives the horizontal telescopic guide rod to move up and down; when the horizontal telescopic guide rod moves up and down, the sliding end slides along the track;

[0077] Exemplarily, guide rods can be arranged in the vertical direction. The mass block moves up and down through the limitation and guidance of the guide rods. There are many ways to limit the mass block to only move up and down. Here, using the guide rod method is just an example. In addition, the movement direction of the mass block can also be limited by a linear slide rail in the vertical direction, which will not be elaborated here.

[0078] Exemplarily, when the mass block moves up and down, it drives the horizontal telescopic guide rod to move up and down, indicating that in the vertical direction, the relative position between the mass block and the telescopic guide rod is fixed. For example, a horizontal hole is arranged inside the mass block, and the horizontal telescopic guide rod telescopically moves horizontally inside the hole. When the mass block moves up and down, the side wall of the hole generates a vertical force on the telescopic guide rod, thereby driving the horizontal telescopic guide rod to move up and down.

[0079] Exemplarily, since it is limited that the horizontal telescopic guide rod continuously abuts against the track under the push of the linear spring, when the horizontal telescopic guide rod moves up and down, the sliding end of the telescopic guide rod can always slide along the track.

[0080] Based on the structure in the above text, no matter how the mass block moves, the sliding end can always slide along the track. Taking the sliding end as the object for force analysis, the sliding end exerts a force on the track, and the track will also generate a reaction force on the sliding end at the same time. The shape change of the track will also affect the force relationship of the sliding end.

[0081] Here, it is assumed that the track is a vertical linear track. The force exerted by the sliding end on the track and the reaction force of the track are equal in magnitude and opposite in direction. This method cannot achieve quasi-zero stiffness.

[0082] In some embodiments, the vertical trajectory of the track is a non-linear parabola-like shape, and the opening faces the mass block;

[0083] Exemplarily, the mass block drives the sliding end to move in the vertical direction, and the movement trajectory of the sliding end is restricted by the track. Generally, the movement trajectory of the sliding end is in the same vertical plane, that is, referring to Figure 1 the vertical plane shown in, the optimal way for the sliding end is to only be able to move up and down and left and right, and cannot move forward and backward.

[0084] Exemplarily, here the vertical trajectory of the track and the sliding trajectory of the sliding end are the same trajectory, hereinafter referred to as the trajectory for short.

[0085] Exemplarily, the trajectory is a non-linear parabola-like shape, and the opening faces the mass block.

[0086] A parabola is a common curve. In a plane rectangular coordinate system, it has specific shapes and properties, such as having a vertex, an opening direction, etc.

[0087] Exemplarily, a parabola-like representation indicates that the motion trajectory of an object is similar to the characteristics of a parabola, roughly presenting a curved shape of a parabola. For example, it can be divided by the vertex into two curves bending in the same direction, similar to a C shape, and does not exactly conform to the mathematical expression of a standard parabola.

[0088] Exemplarily, a non-linear trajectory indicates that the relationship between the lateral displacement and the longitudinal displacement is non-linear.

[0089] It should be noted that the trajectory design of the track is also one of the key points. The telescopic guide rod, the linear spring, and the track interact with each other to jointly achieve quasi-zero stiffness. The following specifically describes the motion modes of the interaction of each part.

[0090] First, the equilibrium state is described. If the influence of gravity is not considered, the sliding end stops at the equilibrium point under the push of the linear spring, that is, it stops at the vertex of the trajectory. The vertex of the trajectory is also the point where the trajectory is farthest from the mass block here. At the equilibrium point, the elastic potential energy of the linear spring is the smallest. If the influence of gravity is considered, the equilibrium point should be at a position below the vertex.

[0091] It should be noted that when the device is not affected by other external forces, it can maintain an equilibrium state at the equilibrium point. However, due to the influence of external vibrations, relative motion will occur between the mass block and the track.

[0092] Secondly, the motion state is described. For the convenience of describing the relative motion, the track is used as the reference system. When the mass block deviates from the equilibrium point, the distance between the parabola-like track and the mass block decreases, the sliding end contracts under the compression of the track, and the linear spring is further compressed. The elastic force of the linear spring increases, the force exerted by the sliding end on the track increases, and the reaction force of the track on the sliding end increases.

[0093] In the horizontal and vertical coordinate system, the reaction force in the normal direction of the track (hereinafter referred to as the normal force) compresses the linear spring in the horizontal direction and exerts a restoring force on the sliding end in the vertical direction to make the sliding end return to the equilibrium point.

[0094] In the horizontal direction, since the sliding end continuously presses against the track, the action force and the reaction force are balanced. In the vertical direction, the magnitude of the force continuously changes with the vertical displacement. The changing factors include both the change in the compression degree of the linear spring and the change in the normal direction of the track. For example, when the deviation from the equilibrium point is small and the vertical displacement is small, the compression degree of the linear spring is small, and at this time, the resultant force of the force in the vertical direction is small (that is, the restoring force is small), so the ratio of the restoring force to the unit deformation is small, and the stiffness of the device near the equilibrium point is small. Another example is that as the vertical offset increases, the non-linear track causes the compression degree of the linear spring to change non-linearly, and thus the restoring force also changes non-linearly, and the stiffness of the device increases non-linearly, generating a large stiffness at positions far from the equilibrium point. In summary, the device realizes the quasi-zero stiffness characteristic.

[0095] In some embodiments, during the movement of the mass block, the trajectory is used to change the compression degree of the linear spring, change the magnitude of the force exerted by the sliding end on the track, and also used to change the direction of the reaction force of the track on the sliding end, thereby generating a non-linear restoring force on the mass block in the vertical direction. Wherein, the greater the distance that the mass block deviates from the equilibrium point, the greater the non-linear restoring force.

[0096] Exemplarily, when the mass block deviates from the equilibrium point during movement, the non-linear parabolic trajectory causes the compression degree of the linear spring to change non-linearly, and the magnitude of the force exerted by the sliding end on the track to change non-linearly.

[0097] Furthermore, the non-linear parabolic trajectory causes the direction of the reaction force of the track on the sliding end to change non-linearly. For example, the farther away from the equilibrium point, the greater the angle between the normal reaction force direction of the track on the sliding end and the horizontal plane, and the greater the vertical component of the normal reaction force. Thus, the force (non-linear restoring force) generated on the mass block in the vertical direction also changes non-linearly. For example, the greater the distance that the mass block deviates from the equilibrium point, the greater the non-linear restoring force. For another example, the smaller the distance that the mass block deviates from the equilibrium point, the smaller the non-linear restoring force.

[0098] In the embodiments of the present invention, by adopting a horizontally telescopic guide rod, a linear spring, and a non-linear track of a parabolic shape, the sliding end of the telescopic guide rod is pushed against the track by the thrust of the linear spring and slides on the track. During the movement of the mass block, the sliding trajectory of the sliding end is a non-linear parabola. The change of the parabola trajectory during sliding causes the track to push the linear spring, the compression degree of the linear spring changes, and further the magnitude of the force exerted by the sliding end on the track changes. The change of the track trajectory also changes the direction of the reaction force of the track on the sliding end.

[0099] For example, when the mass block moves upward, the track compresses the linear spring, the force exerted by the sliding end on the track becomes larger, and the direction of the normal reaction force of the track gradually shifts towards the vertical direction, and the non-linear restoring force on the mass block in the vertical direction becomes larger.

[0100] Also, because the shape of the track is non-linear, the greater the distance that the mass block deviates from the equilibrium point, the greater the non-linear restoring force; and the smaller the distance that the mass block deviates from the equilibrium point, the smaller the non-linear restoring force. Thus, the stiffness approaches zero at small displacements near the equilibrium point, and increases at large displacements far from the equilibrium point, thereby achieving quasi-zero stiffness vibration isolation while taking into account the buffering and load-bearing capabilities.

[0101] Based on the synergistic effect of a horizontally telescopic guide rod, a linear spring, and a non - linear track in the shape of a quasi - parabola, the embodiments of the present invention generate a non - linear restoring force through the non - linear shape of the track, achieving quasi - zero - stiffness vibration isolation. By avoiding the use of negative - stiffness springs and adopting a simple - structured track method, the structure of the vibration isolation device is simplified.

[0102] The embodiments of the present invention provide a solution for vibration isolation technology that is simple in structure, easy to adjust, and stable in performance. The present invention proposes a quasi - zero - stiffness achieved based on a track. Different from the prior art, through the design of a specific track curve, the mass block is subjected to a non - linear restoring force within a certain motion range and can offset the influence of gravity, so that the quasi - zero - stiffness characteristic can be achieved without constructing a complex negative - stiffness spring system. This design not only simplifies the system structure, reduces energy loss, but also improves the adjustment flexibility and engineering practicability of the system. The innovation of the present invention lies in the shape design of the track. Through the synergistic effect of a clever geometric curve and a linear spring, the system exhibits quasi - zero - stiffness characteristics near a specific position, providing a solution for vibration isolation technology that is simple in structure, easy to adjust, and stable in performance.

[0103] As described above, the mass block moves relatively up and down with respect to the track. The following describes the specific implementation structure.

[0104] In a possible implementation, it further includes: a frame, and a vertical guide rod fixed on the frame; the track is fixed on the frame; the mass block realizes up - and - down movement relative to the track through the limitation and guidance of the vertical guide rod.

[0105] Refer to Figure 1 , the frame serves as the fixed basis of the entire device. The vertical guide rod and the track are both fixed on the frame. When the frame is subjected to an external vibration excitation, it will vibrate, thus generating relative movement with the mass block. The mass block is limited by the vertical guide rod to move only up and down relative to the frame.

[0106] All components can be installed inside the frame, and the frame is subjected to vibration excitation from the foundation. When the mass block moves up and down along the vertical guide rod, the mass block is subjected to the action of a non - linear restoring force, which is provided by the designed track. In addition, when the mass block moves, due to the presence of the track and the linear spring, the gravity factor of the mass block is also offset.

[0107] The horizontally telescopic guide rod, the linear spring, and the track structure provided by the embodiments of the present invention cooperate with each other to achieve quasi - zero - stiffness vibration isolation, such that the movement of the mass block exhibits low stiffness near the equilibrium point and high stiffness when far from the equilibrium point.

[0108] The following describes the structure of the sliding end and the way of sliding implementation.

[0109] In a possible implementation, the sliding end includes a bearing; the inner ring of the bearing is fixedly connected to the horizontal telescopic guide rod, and the outer ring abuts against the track; the bearing is used to roll on the track through the outer ring to realize the sliding of the sliding end along the track.

[0110] In the embodiment of the present invention, a bearing is used to realize the sliding of the sliding end. Compared with the sliding friction method, the friction loss of the rolling bearing is greatly reduced, reducing the driving energy consumption, waste heat generation and mechanical wear, and at the same time prolonging the service life of the device.

[0111] The following describes the method for determining the track of the track. In practical applications, it may be required that the vibration isolation device can realize a restoring force with a certain specific relationship. For example, as the vertical displacement changes, the magnitude of the restoring force changes according to a certain specific non-linear relationship.

[0112] In a possible implementation, the track of the track is determined according to the target non-linear restoring force, the gravity of the mass block, the stiffness coefficient of the linear spring, and the deformation of the linear spring at the equilibrium point; wherein, the target non-linear restoring force is the relationship between the magnitude of the non-linear restoring force in the vertical direction and the displacement from the equilibrium point.

[0113] Figure 2 is a schematic diagram of the force analysis of the sliding end provided by the embodiment of the present invention; referring to Figure 2 , the device considers the influence of the gravity of the mass block to determine the track. The sliding end is subjected to the gravity of the mass block and the normal reaction force of the track. The target non-linear restoring force represents the restoring force to be realized.

[0114] It should be noted that at the equilibrium point, affected by the gravity of the mass block, the sliding end will compress the linear spring to a certain extent to maintain the equilibrium state. Therefore, at the equilibrium point, the linear spring also has a certain amount of deformation.

[0115] Exemplarily, based on the stiffness coefficient of the linear spring and the deformation of the linear spring at the equilibrium point, the magnitude of the elastic force of the linear spring at the initial equilibrium state can be determined.

[0116] As the sliding end slides along the track, the horizontal displacement of the track relative to the equilibrium point determines the change in the elastic force of the linear spring and is equal to the horizontal component of the normal reaction force of the track. When considering gravity, the vertical component of the normal reaction force of the track plus the gravity is the target non-linear restoring force at the current displacement. From the above relationships, the track can be determined according to the target non-linear restoring force, the gravity of the mass block, the stiffness coefficient of the linear spring, and the deformation of the linear spring at the equilibrium point. The following gives a specific formula.

[0117] In a possible implementation, the track of the track is determined based on the following formula:

[0118]

[0119] Among them, h(t) represents the target non-linear restoring force; G represents the gravity of the mass block; k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the trajectory; y represents the ordinate of the trajectory.

[0120] Exemplarily, the origin of the xy coordinate system is set at the equilibrium point.

[0121] In a possible implementation manner, the target non-linear restoring force includes a cubic non-linear restoring force or a one-third power non-linear restoring force.

[0122] Exemplarily, the cubic non-linear restoring force refers to the non-linear characteristic that the relationship between the restoring force and the vertical displacement of the mass block presents a cubic function form.

[0123] Exemplarily, the one-third power non-linear restoring force refers to the non-linear relationship that presents a one-third power between the restoring force and the vertical displacement of the mass block.

[0124] Figure 3 It is a flowchart of the implementation of a method for determining the track trajectory of a quasi-zero stiffness vibration isolation device provided by an embodiment of the present invention. Refer to Figure 3 , an embodiment of the present invention provides a method for determining the track trajectory of a quasi-zero stiffness vibration isolation device, which is applied to the quasi-zero stiffness vibration isolation device described in any one of the above; the method includes:

[0125] Step 301, obtain the stiffness coefficient of the linear spring and the target non-linear restoring force;

[0126] Exemplarily, the target non-linear restoring force represents the change of the vertical non-linear restoring force with the vertical displacement.

[0127] Step 302, determine the linear spring elastic force based on the stiffness coefficient of the linear spring and the offset in the horizontal direction;

[0128] Exemplarily, the linear spring elastic force is: k1(x + x0), where k1 represents the stiffness coefficient of the linear spring, x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the trajectory, that is, the offset in the horizontal direction relative to the equilibrium point.

[0129] Step 303, determine the sine component of the track reaction force as the linear spring elastic force in the horizontal direction, and determine the cosine component of the track reaction force as the target non-linear restoring force in the vertical direction;

[0130] When the non - linear restoring force acting on the mass block is zero, the position of the sliding end is set as the initial position, i.e., the position of the equilibrium point. At this time, the compression of the single - side linear spring is x0. Taking the sliding end as the origin, an xOy coordinate system is established in the horizontal and vertical directions. When the sliding end deviates from the initial equilibrium position and the coordinates are (x, y), the force analysis of the bearing is carried out. The track reaction force can be decomposed into a sine component and a cosine component. F N represents the normal force provided by the track, and θ represents the angle between F N and the vertical direction.

[0131] In some embodiments, determining the sine component of the linear spring force in the horizontal direction as the track reaction force includes: determining the sine component of the track reaction force based on the following formula:

[0132] F N sin(θ) = k1(x + x0)

[0133] where, F N sin(θ) represents the sine component of the track reaction force, k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the track, i.e., the horizontal displacement relative to the initial equilibrium position;

[0134] Determining the target non - linear restoring force in the vertical direction as the cosine component of the track reaction force includes: determining the cosine component of the track reaction force based on the following formula:

[0135]

[0136] where, F N cos(θ) represents the cosine component of the track reaction force, h(y) represents the target non - linear restoring force, i.e., the non - linear restoring force to be achieved; G represents the gravity of the mass block; y represents the ordinate of the track.

[0137] Step 304: Divide the sine component by the cosine component to obtain the slope, which is used as the differential equation of the track;

[0138] In some embodiments, divide the sine component by the cosine component to obtain the slope based on the following formula:

[0139]

[0140] where, tan(θ) represents the slope, i.e., the slope of the track;

[0141] In some embodiments, dividing the sine component by the cosine component to obtain the slope and using it as the differential equation of the track includes:

[0142] Obtain the differential equation of the track based on the following:

[0143]

[0144] Among them, tan(θ) represents the slope of the trajectory; represents the differential of the trajectory.

[0145] Step 305: Integrate the differential equation to obtain the trajectory.

[0146] In some embodiments, cross-multiplying both sides of the differential equation gives:

[0147]

[0148] Furthermore, integrating the above equation gives the trajectory:

[0149]

[0150] It should be noted that this trajectory can enable the mass block to be subjected to a pure cubic nonlinear restoring force in the vertical direction considering gravity, for example, it can be a pure cubic nonlinear restoring force. Gravity becomes part of the restoring force, and at the equilibrium position, the sum of the gravitational potential energy and the elastic potential energy of the mass block reaches a minimum value.

[0151] In actual calculations, considering that the implementation methods of the sliding end selected for different working conditions are different, and the types or sizes will vary, so we ignore the influence brought by the size of the sliding end. However, assuming that there is no relative sliding during the movement of the sliding end, based on a certain relationship, the shape of the track can be obtained finally.

[0152] The embodiment of the present invention provides a method for achieving quasi-zero stiffness through track design, and this method can be widely applied to engineering fields such as vibration isolation, precision instrument support, and other fields that require ultra-low stiffness characteristics.

[0153] The method provided by the embodiment of the present invention is different from traditional quasi-zero stiffness mechanisms, such as structures based on spring combinations or flexible hinges. Instead, it utilizes the shape characteristics of the track to achieve a similar effect, thereby reducing additional energy losses and improving the stability and applicability of the system. In addition, the track can be used in combination with a linear spring to enable the system to have low stiffness characteristics within a specific working range, while ensuring the necessary restoring force to maintain the stability of the system. Through the optimized design of the track shape, it can be adapted to different masses, sizes, and working environments, thus meeting diverse engineering requirements. Compared with existing quasi-zero stiffness technologies, the structure of the present invention is more compact, the manufacturing process is simpler, and it is easy to adjust, making it have stronger applicability and promotion value in practical applications.

[0154] The following gives two comprehensive embodiments to illustrate the present application.

[0155] 1. When the mass block is subjected to a cubic nonlinear restoring force in the vertical direction, the expression for the track shape is:

[0156]

[0157] where k N is the cubic nonlinear stiffness coefficient.

[0158] Figure 4 are the track shapes and force-displacement curves of two different cubic nonlinear stiffness coefficients provided by the embodiments of the present invention. Among them, the design parameters are: the mass of the mass block is 0.7 kg, the stiffness coefficient of the linear spring 2 is 49014 N / m, the initial compression of the linear spring is 0.001 m, and the nonlinear stiffness coefficients are 5×10 7 N / m 3 and 5×10 9 N / m 3 .

[0159] 2. When the mass block is subjected to a one-third power nonlinear restoring force in the vertical direction, the expression for the track shape is:

[0160]

[0161] where k N is the one-third power nonlinear stiffness coefficient.

[0162] Figure 5 are the track shapes and force-displacement curves of two different one-third power nonlinear stiffness coefficients provided by the embodiments of the present invention. Among them, the design parameters are: the mass of the mass block 3 is 0.7 kg, the stiffness coefficient of the linear spring 2 is 49014 N / m, the initial compression of the linear spring 2 is 0.001 m, and the nonlinear stiffness coefficients are 100 N / m 1 / 3 and 1000 N / m 1 / 3 .

[0163] The core innovation of the present invention lies in the geometric design of the track. By reasonably constructing the curve of the track, the resultant force acting on the mass block during movement exhibits specific nonlinear characteristics, and a very small equivalent stiffness is generated near a specific position, thereby achieving the quasi-zero stiffness effect. The shape of the track can be described by a mathematical model, which can be derived through force balance equations or energy analysis to ensure that the system has the required mechanical properties in the target area.

[0164] The present invention uses the methods of mathematical modeling and optimization design to reasonably determine the shape of the track, so that the stiffness of the system presents a non-linear characteristic within the working range and approaches zero stiffness in a specific region. Compared with the traditional quasi-zero stiffness mechanism, this method does not require a complex combination of multi-stiffness elements to form negative stiffness. Only relying on the geometric characteristics of the track itself can achieve a stable quasi-zero stiffness effect, thereby reducing the complexity of the system and improving the reliability and manufacturability of the structure. In addition, the design of the track can be combined with a linear spring, enabling the overall system to have a wider range of applicability while ensuring the quasi-zero stiffness characteristics.

[0165] The present invention provides a general method for track design, which can be applied to a variety of different application scenarios, such as high-precision vibration isolation systems, precision instrument supports, ultra-low frequency vibration isolation devices, etc. By optimizing the track parameters, the working range of the system can be further expanded to make it applicable to target objects with different masses and sizes. The present invention provides a new idea for the development of quasi-zero stiffness technology and has important engineering application value.

[0166] In summary, the present invention realizes a new type of quasi-zero stiffness method by reasonably designing the geometric shape of the track 1, which has the advantages of simple structure, easy manufacturing, and wide application range, and can be widely applied to fields such as high-precision vibration isolation and precision support.

[0167] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean the order of execution. The order of execution of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0168] The embodiment of the present invention provides a quasi-zero stiffness vibration isolation system, including the quasi-zero stiffness vibration isolation device described in any one of the above.

[0169] In the above embodiments, the descriptions of each embodiment have their own emphases. For the parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments. Without special instructions and logical conflicts, the terms and / or descriptions between different embodiments are consistent and can be mutually referred to. The technical features in different embodiments can be combined to form new embodiments according to their internal logical relationships.

[0170] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A quasi-zero stiffness vibration isolation device, characterized in that, Comprising: A vibration-isolated mass block; horizontal telescopic guide rods, linear springs and tracks are arranged on both the left and right sides of the mass block; For any one side, the mass block is slidably connected to the horizontal telescopic guide rod; The first end of the linear spring is fixedly connected to the mass block, and the second end is fixedly connected to the sliding end of the horizontal telescopic guide rod away from the mass block, and pushes the sliding end against the track; The mass block can only move up and down, and drives the horizontal telescopic guide rod to move up and down; when the horizontal telescopic guide rod moves up and down, the sliding end slides along the track; The vertical direction trajectory of the track is a non-linear parabola-like shape, and the opening faces the mass block; During the movement of the mass block, the trajectory is used to change the compression degree of the linear spring, change the magnitude of the acting force of the sliding end on the track, and also used to change the direction of the reaction force of the track on the sliding end, thereby generating a non-linear restoring force on the mass block in the vertical direction. Among them, the greater the distance that the mass block deviates from the equilibrium point, the greater the non-linear restoring force.

2. The quasi-zero stiffness vibration isolation device according to claim 1, wherein Also comprising: A frame, and a vertical guide rod fixed on the frame; The track is fixed on the frame; The mass block realizes the up and down movement relative to the track through the limitation and guidance of the vertical guide rod.

3. The quasi-zero stiffness vibration isolation device according to claim 1, characterized in that, The sliding end includes a bearing; The inner ring of the bearing is fixedly connected to the horizontal telescopic guide rod, and the outer ring abuts against the track; The bearing is used to roll on the track through the outer ring to realize the sliding of the sliding end along the track.

4. The quasi-zero stiffness vibration isolation device according to claim 1, characterized in that, The trajectory of the track is determined according to the target non-linear restoring force, the gravity of the mass block, the stiffness coefficient of the linear spring and the deformation amount of the linear spring at the equilibrium point; wherein, the target non-linear restoring force is the relationship between the magnitude of the non-linear restoring force in the vertical direction and the displacement amount deviating from the equilibrium point.

5. The quasi-zero stiffness vibration isolation device according to claim 4, characterized in that, The trajectory of the track is determined based on the following formula: Wherein, h(y) represents the target non-linear restoring force; G represents the gravity of the mass block; k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation amount of the linear spring at the equilibrium point; x represents the abscissa of the trajectory; y represents the ordinate of the trajectory.

6. The quasi-zero stiffness vibration isolation device according to claim 4, characterized in that, The target non-linear restoring force includes a cubic non-linear restoring force or a one-third non-linear restoring force.

7. A method for determining the track trajectory of a quasi-zero stiffness vibration isolation device, characterized in that, Applied to the quasi-zero stiffness vibration isolation device according to any one of claims 1 to 6; the method includes: Obtaining the stiffness coefficient of the linear spring and the target non-linear restoring force; Determining the elastic force of the linear spring based on the stiffness coefficient of the linear spring and the offset in the horizontal direction; Determining the sine component of the elastic force of the linear spring in the horizontal direction as the reaction force of the track, and determining the cosine component of the target non-linear restoring force in the vertical direction as the reaction force of the track; Dividing the sine component by the cosine component to obtain the slope, which is used as the differential equation of the trajectory; Integrating the differential equation to obtain the trajectory.

8. The method for determining the track trajectory of the quasi-zero stiffness vibration isolation device according to claim 7, characterized in that, The determining the sine component of the elastic force of the linear spring in the horizontal direction as the reaction force of the track includes: determining the sine component of the reaction force of the track based on the following formula: F N sin(θ) = k1(x + x0) Among them, F N sin(θ) represents the sine component of the orbital reaction force, k1 represents the stiffness coefficient of the linear spring; x0 represents the deformation of the linear spring at the equilibrium point; x represents the abscissa of the trajectory; The determining the cosine component of the target non-linear restoring force in the vertical direction as the reaction force of the track includes: determining the cosine component of the reaction force of the track based on the following formula: Among them, F N cos(θ) represents the cosine component of the orbital reaction force, h(y) represents the target nonlinear restoring force; G represents the gravity of the mass block; y represents the ordinate of the trajectory.

9. The method for determining the track trajectory of the quasi-zero stiffness vibration isolation device according to claim 7, characterized in that, Dividing the sine component by the cosine component to obtain the slope, which is used as the differential equation of the trajectory includes: Obtaining the differential equation of the trajectory based on the following: where tan(θ) represents the slope of the trajectory; represents the differential of the trajectory.

10. A quasi-zero stiffness vibration isolation system, characterized in that, Comprising the quasi-zero stiffness vibration isolation device according to any one of claims 1 to 6.

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