Method for determining parameters of a vibration isolator and vibration isolator

Abstract

This application provides a method for determining vibration isolator parameters and a vibration isolator. Based on the geometric structure and physical parameters of the vibration isolator, a restoring force-displacement function of the vibration isolator is constructed. Based on the restoring force-displacement function, the parameter constraints for the vibration isolator to achieve quasi-zero stiffness characteristics are solved. Based on the restoring force-displacement function, the dynamic equation of the vibration isolator under excitation is established, and the dynamic equation is solved using the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The mass of the object to be supported is obtained. Based on the object mass, parameter constraints, and force transmissibility function and displacement transmissibility function, the parameters of the vibration isolator are solved. The parameters of the vibration isolator are designed by using the object mass, parameter constraints, and force transmissibility function and displacement transmissibility function, so that the parameters of the vibration isolator are adapted to the actual mass of the object to be supported, so that the vibration isolator can both stably support the object and effectively isolate vibrations during transportation.

Description

Technical Field

[0001] This application belongs to the field of vibration isolation technology, and in particular relates to a method for determining vibration isolator parameters and a vibration isolator. Background Technology

[0002] Currently, robots are increasingly used in industrial manufacturing and household life, with robots equipped with robotic arms or legs being gradually promoted due to their wide range of functions. However, the vibrations and shocks generated during road transportation can adversely affect the precision, reliability, and durability of robotic arms and legs.

[0003] In the existing technology, the common method for protecting products during transportation is to wrap the object with cushioning materials such as foam and airbags. The material absorbs energy through deformation to prevent the object from being damaged due to collision. This type of packaging can alleviate instantaneous impact to a certain extent to avoid damage.

[0004] However, for robots with complex structures and numerous movable joints, relying solely on wrapping methods such as foam and airbags can only prevent damage caused by collisions, but cannot avoid the impact of vibrations on the robot's joints. Summary of the Invention

[0005] This application provides a method for determining vibration isolator parameters and a vibration isolator that can isolate vibrations during transportation, fundamentally avoiding the adverse effects of vibrations on transported objects.

[0006] In a first aspect, embodiments of this application provide a method for determining vibration isolator parameters, the method comprising: Based on the geometric structure and physical parameters of the vibration isolator, the restoring force displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle. The displacement in the restoring force displacement function is the displacement change of the vibration isolator platform relative to the base. Based on the restoring force displacement function, solve the parametric constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position; Based on the restoring force displacement function, the dynamic equation of the vibration isolator under excitation is established, and the dynamic equation is solved by the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation. Obtain the mass of the object to be supported, and solve for the parameters of the vibration isolator based on the object mass, parameter constraints, force transmissibility function, and displacement transmissibility function.

[0007] In one alternative implementation of the first aspect, based on the geometry and physical parameters of the vibration isolator, the restoring force displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle, including: Based on the geometric connection relationship and physical parameters of the vibration isolator, the kinetic energy function and potential energy function of the vibration isolator are established. Based on the kinetic and potential energy functions of the vibration isolator, and by applying the Lagrange equation, the dynamic equation of the vibration isolator is constructed. Based on d'Alembert's principle, the restoring force displacement function of the vibration isolator is derived from the dynamic equation.

[0008] In an optional implementation of the first aspect, the parametric constraints for achieving quasi-zero stiffness characteristics of the vibration isolator at its static equilibrium position are solved based on the restoring force displacement function, including: Based on the geometric structure and physical parameters of the vibration isolator, the restoring force displacement function is dimensionlessly processed to obtain a dimensionless restoring force displacement function; Differentiating the dimensionless restoring force displacement function yields the stiffness displacement function; Based on the stiffness-displacement function, let the stiffness of the stiffness-displacement function at the static equilibrium position of the vibration isolator be the target value, and solve for the parameter constraints.

[0009] In an optional implementation of the first aspect, based on the restoring force displacement function, a dynamic equation for the vibration isolator under excitation is established, and the dynamic equation is solved using the harmonic balance method to obtain the force transmissibility and displacement transmissibility of the vibration isolator under excitation, including: Based on the geometric structure and physical parameters of the vibration isolator, the dynamic equation under excitation is dimensionlessly processed to obtain the dynamic equation under dimensionless excitation. The harmonic balance method is used to solve the dynamic equations under dimensionless excitation to obtain the force amplitude and displacement amplitude. The force transmissibility function and displacement transmissibility function are solved based on the amplitude of force and the amplitude of displacement.

[0010] In one alternative implementation of the first aspect, the mass of the object to be supported is obtained, and based on the object mass, parametric constraints, and force transmissibility and displacement transmissibility functions, the parameters of the vibration isolator are solved, including: Based on the mass of the object and the static equilibrium relationship between the spring force of the vertical spring and the weight of the object, the stiffness coefficient and pre-compression of the vertical spring are selected. Based on the stiffness coefficient and pre-compression of the vertical spring, and using parameter constraints, the parameters of the vibration isolator are determined. Substitute the parameters of the vibration isolator into the force transmissibility function and the displacement transmissibility function to solve for the force transmissibility and displacement transmissibility of the vibration isolator, and determine whether the force transmissibility and displacement transmissibility meet the preset force transmissibility threshold and displacement transmissibility threshold. If the conditions are not met, the parameters of the vibration isolator are re-determined based on the parameter constraints until the obtained force transmissibility and displacement transmissibility satisfy the force transmissibility threshold and displacement transmissibility threshold, respectively.

[0011] Secondly, embodiments of this application provide a vibration isolator parameter determination device, the device comprising: The module is used to construct the restoring force displacement function of the vibration isolator based on its geometry and physical parameters, using the Lagrange equation and d'Alembert's principle. The displacement is the change in displacement of the platform relative to the base. The first solution module is used to solve the parametric constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position based on the restoring force displacement function. The second solution module is used to establish the dynamic equation of the vibration isolator under excitation based on the restoring force displacement function, and to solve the dynamic equation using the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation. The acquisition module is used to obtain the mass of the object to be supported, and solve the parameters of the vibration isolator based on the object mass, parameter constraints, force transmissibility function and displacement transmissibility function.

[0012] Thirdly, embodiments of this application provide a vibration isolator, the parameters of which are determined based on any one of the methods in the first aspect, and the vibration isolator includes: Base; A support device is vertically fixed to the base to support the platform. The support device is equipped with a vertical spring perpendicular to the base, which acts between the platform and the base to provide elastic support in the vertical direction. The main support body of the support device is a support column that is vertically fixed to the platform. The support column is also used to support the guide rail. The guide rail is used to guide the movement of the support column in the vertical direction of the base so that the platform only produces vertical displacement when vibrating. Two pairs of curved surface components are fixed on the base. One pair of curved surface components and the other pair of curved surface components are arranged symmetrically about the support device. The surfaces of the two pairs of curved surface components facing the support device are curved surfaces with the same curvature. Each pair of curved components has two parallel rollers on its curved surface that can move along the curved surface. The two parallel rollers are connected by a connecting rod spring. When the two parallel rollers move along the curved surface, they cause the connecting rod spring to deform. The two ends of the connecting rod are hinged to two parallel rollers, and the middle of the connecting rod is hinged to the support device.

[0013] In an alternative embodiment of the third aspect, the vibration isolator includes: a positive stiffness provided by a vertical spring coupled with a negative stiffness generated by a curved component, a roller, a connecting rod, and a connecting rod spring, such that the vibration isolator has quasi-zero stiffness characteristics at the equilibrium position.

[0014] Fourthly, embodiments of this application provide an electronic device, the device including: a processor, and a memory storing computer program instructions; The processor reads and executes computer program instructions to implement a method for determining vibration isolator parameters, as described in any of the first aspects.

[0015] Fifthly, embodiments of this application provide a computer storage medium storing computer program instructions, which, when executed by a processor, implement a vibration isolator parameter determination method as described in any of the first aspects.

[0016] In a sixth aspect, embodiments of this application provide a computer program product in which instructions, when executed by a processor of an electronic device, cause the electronic device to perform a vibration isolator parameter determination method as described in the first aspect.

[0017] The vibration isolator parameter determination method and vibration isolator provided in this application embodiment are based on the geometric structure and physical parameters of the vibration isolator. Using the Lagrange equation and d'Alembert's principle, a restoring force-displacement function of the vibration isolator is constructed. Then, based on the restoring force-displacement function, the parameter constraints for achieving quasi-zero stiffness characteristics of the vibration isolator at the static equilibrium position are solved. Based on the restoring force-displacement function, the dynamic equation of the vibration isolator under excitation is established, and the harmonic balance method is used to solve the dynamic equation, obtaining the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. Finally, by obtaining the mass of the object to be supported, and based on the object mass, parameter constraints, and the force transmissibility function and displacement transmissibility function, the parameters of the vibration isolator are solved. Compared to existing technologies that use cushioning materials such as foam and airbags to wrap around objects to buffer damage to robots from instantaneous impacts, but cannot avoid the impact of vibration on robot joints, this application solves the parameter constraints of the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position, as well as the force transmissibility function and displacement transmissibility function. Thus, when transporting objects, the parameters of the vibration isolator are designed based on the object's mass, parameter constraints, and force and displacement transmissibility functions. This allows the vibration isolator parameters to be adapted to the actual mass of the object to be carried, achieving the goal that the vibration isolator can both stably support the object and effectively isolate vibrations during transportation. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This illustrates one application of vibration isolators; Figure 2A schematic diagram of the vibration isolator structure provided in this application is shown; Figure 3 A flowchart illustrating a method for determining vibration isolator parameters according to an embodiment of this application is shown; Figure 4 A two-dimensional structural schematic diagram of the vibration isolator provided in this application is shown; Figure 5 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown; Figure 6 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown; Figure 7 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown; Figure 8a A simplified dynamic model and force diagram of the vibration isolator under harmonic force excitation are shown; Figure 8b A simplified dynamic model and force diagram of the vibration isolator under displacement excitation are shown; Figure 9 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown; Figure 10 This paper presents a schematic diagram of the overall process for determining vibration isolator parameters according to the present application. Figure 11 A schematic diagram of a vibration isolator parameter determination device provided in this application is shown; Figure 12 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0020] Figure label: 21-Base; 22-Support device; 23-Platform; 24-Vertical spring; 25-Curved surface component; 26-Roller; 27-Linkage spring; 28-Linkage; 221-Support column; 222-Guide rail. Detailed Implementation

[0021] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0022] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0023] First, let me explain the terms used in this application: The Da Vinci system is a classic nonlinear vibration system model. Its core feature is that the relationship between restoring force and displacement is no longer a simple linear proportional relationship, but includes a cubic term of displacement.

[0024] Quasi-zero stiffness: refers to the state in which the dynamic stiffness of a system is infinitely close to zero in a region near its static equilibrium position.

[0025] High static stiffness: refers to the system's strong ability to resist deformation when static or under slow loading.

[0026] Low dynamic stiffness: refers to the system's weak ability to resist deformation under dynamic vibration environment.

[0027] Force transmission rate: The ratio of the amplitude of the force transmitted to the equipment to the amplitude of the external excitation force.

[0028] Displacement transmissibility: The ratio of the vibration displacement amplitude of the equipment to the displacement amplitude of the foundation excitation.

[0029] Currently, product protection during transportation typically involves wrapping objects with cushioning materials such as foam and airbags to prevent cosmetic damage from collisions. However, for robots, especially humanoid robots, which have numerous movable joints, simply wrapping them with foam and airbags during transportation is insufficient to isolate them from vibrations generated during transport. These vibrations can severely damage these joints, adversely affecting the precision, reliability, and durability of the robot's robotic arms and legs.

[0030] Based on this, this application provides a method for determining vibration isolator parameters and a vibration isolator. By designing a vibration isolator with quasi-zero stiffness characteristics, it is installed under the object to be transported, thereby isolating vibrations during transportation. Furthermore, after designing the vibration isolator with quasi-zero stiffness characteristics, this application provides a method for determining vibration isolator parameters. The restoring force displacement function of the vibration isolator is derived using the Lagrange equation and d'Alembert's principle, and the parameter constraints that make the vibration isolator satisfy the quasi-zero stiffness characteristics are solved. Then, the vibration isolator under excitation is solved based on the harmonic balance method. Finally, the static equilibrium relationship between the vertical spring force and the object's weight, the parameter constraints, and the force transmissibility function and displacement transmissibility function jointly guide the selection of vibration isolator parameters, enabling the vibration isolator to simultaneously meet load-bearing requirements and vibration isolation requirements, thereby effectively isolating vibrations generated during transportation and significantly improving transportation safety and the robot's service life.

[0031] To address the problems of the prior art, embodiments of this application provide a method for determining vibration isolator parameters and a vibration isolator. To clearly illustrate the method for determining vibration isolator parameters provided in this application, a vibration isolator provided in this application will first be described.

[0032] Figure 1 This paper illustrates one application of the vibration isolator, which isolates vibrations during transport by adding the vibration isolator provided in this application to the object to be transported. For example, adding the vibration isolator provided in this application to the bottom of the robot's outer packaging isolates vibrations during transport, thereby achieving vibration damping of the robot during transport.

[0033] Figure 2 A schematic diagram of the vibration isolator structure provided in this application is shown, as follows: Figure 2 As shown, the vibration isolator provided in this application includes: The base 21 and the support device 22 vertically fixed on the base 21 are used to support the platform 23. The support device 22 is provided with a vertical spring 24 perpendicular to the base 21, which acts between the platform 23 and the base 21 to provide elastic support in the vertical direction. The main support of the support device 22 is a support column 221 vertically fixed on the platform 23. The support column 221 is also used to support the guide rail 222. The guide rail 222 is used to guide the movement of the support column 221 in the vertical direction of the base 21 so that the platform 23 only produces vertical displacement when vibrating.

[0034] In this embodiment, the base 21 is fixed at the bottom of the vibration isolator and directly contacts the ground or the bottom of the transport vehicle to provide a stable installation foundation. The fixed support device 22 is used to support the platform 23. The platform 23 is located at the top of the vibration isolator, thereby forming a stable installation surface for directly placing or fixing the object to be transported.

[0035] A vertical spring 24, perpendicular to the base 21, is provided on the support device 22. This spring acts between the platform 23 and the base 21 to provide elastic support in the vertical direction, reducing the impact of vibration on the support device 22 and the base 21. In one example, the vertical spring 24 is sleeved on the support device 22.

[0036] The main support of the support device 22 is a support column 221 that is vertically fixed on the platform 23. The support column 221 is also used to support the guide rail 222, which is fixed on the base 21. The support column 221 is used to support the structural frame of the vibration isolator and provides installation and fixing points for other parts such as the platform 23, the guide rail 222, or the connecting rod 28. The guide rail 222 is vertically inserted between the platform 23 and the base 21 and is fixed by the support column 221. It is used to guide the support column 221 to achieve vertical movement so that the platform 23 only produces vertical displacement when vibrating. The vertical spring 24 and the guide rail 222 enable the platform 23 of the vibration isolator to have a large load-bearing capacity and static stiffness.

[0037] Two pairs of curved surface parts 25 are fixed on the base 21. One pair of curved surface parts and the other pair of curved surface parts are arranged symmetrically about the support device 22. The surfaces of the two pairs of curved surface parts facing the support device 22 are curved surfaces with the same curvature.

[0038] In this embodiment of the application, the curved component 25 can be directly mounted on the base 21. In one example, two side plates are fixed face to face on the base 21 of the vibration isolator. The two side plates are located on both sides of the support device 22, and a pair of curved components 25 are fixed on each side plate. The center line between the curved components 25 is perpendicular to the base 21, and the side of the curved component 25 facing the support device 22 is curved. By distributing four identical curved components around the platform 23, the horizontal stability of the vibration isolator is ensured.

[0039] Each pair of curved surface components 25 has two parallel rollers 26 that can move along the curved surface. The two parallel rollers 26 are connected by a connecting rod spring 27. When the two parallel rollers 26 move along the curved surface, they cause the connecting rod spring 27 to deform.

[0040] In this embodiment, each pair of curved surface components 25 has two parallel rollers 26 that can move along the curved surface. The two parallel rollers 26 are connected by a connecting rod spring 27. When the two parallel rollers 26 move along the curved surface, they can cause the connecting rod spring 27 to deform, thereby providing buffering and absorbing vibration energy through the elastic deformation of the connecting rod spring 27. By reasonably setting the curvature of the curved surface component 25, the movement trajectory of the connecting rod 28 can be adjusted to keep it stable under force, and the force direction of the connecting rod spring 27 can be reasonably adjusted to ensure that the compression and release of the connecting rod spring 27 always act on the optimized path. In one example, the connecting rod spring 27 is located on the inner side of the curved surface component 25.

[0041] The two ends of the connecting rod 28 are respectively hinged to the two parallel rollers 26, and the middle part of the connecting rod 28 is hinged to the support device 22.

[0042] In this embodiment, the two ends of the connecting rod 28 are hinged to two parallel rollers 26, thereby connecting the connecting rod 28 and the curved surface member 25 through the rollers 26. By converting the sliding friction between the connecting rod 28 and the curved surface member 25 into rolling friction, the frictional force between the connecting rod 28 and the curved surface member 25 is reduced, allowing the connecting rod 28 to move smoothly on the curved surface member 25 when the guide rail 222 moves. Furthermore, the middle part of the connecting rod 28 is hinged to the support device 22, which is used to convert the vertical movement of the platform 23 into the movement of the connecting rod 28, thereby driving the rollers 26 to move along the curved surface member 25 and causing the connecting rod spring 27 to deform.

[0043] Through the design of the above-mentioned vibration isolator structure and the reasonable setting of the parameters of each component in the vibration isolator, the positive stiffness provided by the vertical spring 24 in the vibration isolator is coupled with the negative stiffness generated by the curved part 25, the roller 26, the connecting rod 28 and the connecting rod spring 27, so that the vibration isolator has quasi-zero stiffness characteristics in the equilibrium position.

[0044] In this embodiment, positive stiffness is the core of the vibration isolator to achieve static load bearing. The vertical spring 24 is vertically arranged between the base 21 and the platform 23. Under the weight of the object to be supported, it is in a pre-compressed state, generating an upward elastic force and forming positive stiffness. The positive stiffness of the vertical spring 24 ensures that the vibration isolator has sufficient static load bearing capacity and can stably support the weight of the object to be supported. When the platform 23 moves downward, the connecting rod 28 drives the roller 26 to roll upward along the curved surface, and the connecting rod spring 27 is further stretched, thereby generating negative stiffness. The coupling of positive and negative stiffness achieves both static load bearing and dynamic vibration isolation.

[0045] In this embodiment, the vibration isolator includes a base 21 and a support device 22 vertically fixed to the base 21 for supporting a platform 23. The support device 22 is provided with a vertical spring 24 perpendicular to the base 21, acting between the platform 23 and the base 21 to provide elastic support in the vertical direction. The main support of the support device 22 is a support column 221 vertically fixed to the platform 23. The support column 221 also supports a guide rail 222, which guides the support column 221 to move in the vertical direction of the base 21 so that the platform 23 only produces vertical displacement when vibrating. Two side plates fixed to the base 21 are located on both sides of the support device 22. Each side plate is fixed with a pair of curved surface parts 25. The center line between the pair of curved surface parts 25 is perpendicular to the base 21. The side of the curved surface part 25 facing the support device 22 is curved. Each pair of curved surface parts 25 has two parallel rollers 26 that can move along the curved surface. The two parallel rollers 26 are connected by a connecting rod spring 27. When the two parallel rollers 26 move along the curved surface, they drive the connecting rod spring 27 to deform. The two ends of the connecting rod 28 are respectively hinged to the two parallel rollers 26. The middle part of the connecting rod 28 is hinged to the support device 22. Compared to existing technologies that use cushioning materials such as foam and airbags to wrap around objects to buffer instantaneous impacts on robots, but cannot avoid the impact of vibrations on robot joints, this application provides a vibration isolator. The vertical spring 24 provides positive stiffness and static load-bearing capacity, bearing and supporting the weight of the transported object, ensuring the stability of the vibration isolator in a static state. The guide rail 222 and the support column 221 constitute the core guiding and supporting frame. The guide rail 222 strictly restricts the platform 23 to move only in the vertical direction to avoid lateral displacement. The support column 221 provides rigid support for the entire structure and fixes the relative positions of each component. Finally, through the synergistic action of the curved part 25, roller 26, connecting rod, and connecting rod spring 27, a negative stiffness is formed, which is coupled with the positive stiffness provided by the vertical spring 24. Thus, the vibration isolator achieves quasi-zero stiffness characteristics in the static equilibrium position, effectively isolating vibrations during transportation. This avoids problems such as decreased precision and accelerated wear of robot joints due to frequent vibrations, significantly improving the safety and reliability of robot transportation.

[0046] The following describes a method for determining vibration isolator parameters provided in an embodiment of this application. This method is used to determine the parameters of the vibration isolator described above. Figure 2 The parameters of the vibration isolator provided.

[0047] Figure 3 A flowchart illustrating a method for determining vibration isolator parameters according to an embodiment of this application is shown. Figure 3 As shown, the method may include the following steps: S301: Based on the geometry and physical parameters of the vibration isolator, the restoring force displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle.

[0048] In this embodiment, based on the geometry and physical parameters of the vibration isolator, and utilizing Lagrange's equations and d'Alembert's principle, a restoring force displacement function for the vibration isolator is constructed. In one example, the displacement in the restoring force displacement function is the change in displacement of the vibration isolator's platform relative to the base.

[0049] The restoring force displacement function describes how a vibration isolator generates a restoring force to resist motion after being subjected to external forces, causing the isolator to tend towards an equilibrium state. The restoring force displacement function is one of the important characteristics of a vibration isolator, reflecting the mode and extent of its response to vibration or displacement. For the symmetrical vibration isolator in this application, the restoring force displacement function describes the reaction force generated after the isolator shifts from its equilibrium position. The restoring force determines the mechanical characteristics of the vibration isolator under different displacements. For the vibration isolator, the restoring force displacement function also reflects whether it can effectively recover to an equilibrium state under vibration disturbance. Therefore, constructing the restoring force displacement function of the vibration isolator is the foundation for vibration reduction performance analysis and helps determine the response characteristics of the vibration isolator during vibration.

[0050] S302: Based on the restoring force displacement function, solve the parametric constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position.

[0051] In this embodiment, quasi-zero stiffness is the core characteristic of the vibration isolator to achieve high static stiffness load bearing and low dynamic stiffness vibration isolation, which directly determines the vibration isolation effect. Based on the constructed restoring force displacement function, the stiffness displacement function is derived through mathematical processing, thereby obtaining the parameter constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position.

[0052] S303: Based on the restoring force displacement function, establish the dynamic equation of the vibration isolator under excitation, and use the harmonic balance method to solve the dynamic equation to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation.

[0053] In this embodiment, force transmissibility and displacement transmissibility are the core indicators for quantifying vibration isolation effect. The lower the force transmissibility and displacement transmissibility, the better the vibration isolation performance of the vibration isolator. Based on the restoring force-displacement function, the dynamic equation of the vibration isolator under harmonic force excitation and displacement excitation is established, and the dynamic equation is solved by the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function.

[0054] S304: Obtain the mass of the object to be supported, and solve for the parameters of the vibration isolator based on the object mass, parameter constraints, force transmissibility function and displacement transmissibility function.

[0055] In this embodiment, the parameter selection of the vibration isolator can be guided by parameter constraints, force transmissibility function and displacement transmissibility function, so that the vibration isolator parameters are adapted to the actual mass of the object to be carried, thereby achieving that the vibration isolator can stably carry the object and effectively isolate the vibration during transportation.

[0056] In this embodiment, based on the geometry and physical parameters of the vibration isolator, the restoring force-displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle. Then, based on the restoring force-displacement function, the parameter constraints for achieving quasi-zero stiffness characteristics of the vibration isolator at the static equilibrium position are solved. Based on the restoring force-displacement function, the dynamic equation of the vibration isolator under excitation is established, and the harmonic balance method is used to solve the dynamic equation to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. Finally, by obtaining the mass of the object to be supported, the parameters of the vibration isolator are solved based on the object mass, parameter constraints, and force transmissibility function and displacement transmissibility function. Compared to existing technologies that use cushioning materials such as foam and airbags to wrap around objects to buffer damage to robots from instantaneous impacts, but cannot avoid the impact of vibration on robot joints, this application solves the parameter constraints of the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position, as well as the force transmissibility function and displacement transmissibility function. Thus, when transporting objects, the parameters of the vibration isolator are designed based on the object's mass, parameter constraints, and force and displacement transmissibility functions. This allows the vibration isolator parameters to be adapted to the actual mass of the object to be carried, achieving the goal that the vibration isolator can both stably support the object and effectively isolate vibrations during transportation.

[0057] For ease of description, according to Figure 2 The provided vibration isolator has an equivalent two-dimensional model, such as... Figure 4 As shown, Figure 4 A two-dimensional structural schematic diagram of the vibration isolator provided in this application is shown. Figure 4 As shown, when At this time, the vibration isolator is in a static equilibrium position, and the load on the platform is the ideal load of the vibration isolator. At the same time, the connecting rod spring is in a stretched state, and the vertical spring is in a compressed state. Let the compression of the vertical spring at this time be... The symmetrically distributed forces are in equilibrium with each other. This represents the length of the connecting rod spring at any position; it is a dynamic parameter that changes with displacement. L is the length of the connecting rod. l Indicates the structural parameters of the vibration isolator. This indicates the relative displacement of the platform with respect to the base. x Indicates the absolute displacement of the platform. y This indicates the absolute displacement of the base. When external disturbances occur due to road bumps... At that time, the original static equilibrium is broken, and the platform will deviate. When the position of the platform experiences vertical displacement, the connecting rod rotates with the platform's movement, causing the roller to slide along the curved surface. This sliding of the roller causes elastic deformation of the connecting rod spring, generating an elastic force. The curvature of the curved surface affects the direction of this elastic force, while the stiffness of the connecting rod spring determines the magnitude of the force generated per unit deformation. Therefore, the geometry of the curved surface, the stiffness of the connecting rod spring, and the degree of deformation collectively determine the law governing the change of the vibration isolator's restoring force with relative displacement. First, the relationship between the connecting rod spring length and relative displacement is established: Assume the length of the linkage spring is [value missing] when the platform is in any position. ,but The expression is: (1) in, Indicates the length of the connecting rod spring; This indicates the length of the connecting rod spring when the vibration isolator is in a static equilibrium position. , is a variable that controls the shape of curved parts or the length function of connecting rods and springs.

[0058] Figure 5 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown. Figure 5 As shown above, in the above Figure 3 Based on the illustrated embodiment, a specific implementation of step S301 is as follows: S501: Based on the geometric connection relationship and physical parameters of the vibration isolator, establish the kinetic energy function and potential energy function of the vibration isolator.

[0059] In this embodiment, to eliminate the influence of the initial state geometric parameters of the vibration isolator and the mass of the connecting rod and other components on the dynamic equations, this application only considers the mass of the vibration isolator platform. This is considered as a load. Therefore, the kinetic energy function and potential energy function, expressed in terms of the relative displacement of the platform relative to the base, are established: (2) (3) in, This indicates the kinetic energy of the vibration isolator; This represents the potential energy of the vibration isolator; Indicates platform quality; This represents the derivative of relative displacement with respect to time. This represents the derivative of the absolute displacement of the base with respect to time. This indicates the stiffness coefficient of a vertical spring; This indicates the relative displacement of the platform with respect to the base; This indicates the amount of compression of the vertical spring; This indicates the stiffness coefficient of the connecting rod spring; Indicates the length of the connecting rod spring; Indicates the original length of the connecting rod spring; Indicates external disturbance force; This indicates the length of the connecting rod spring when the vibration isolator is in a static equilibrium position. g Represents the gravitational acceleration constant; y This indicates the absolute displacement of the base.

[0060] S502: Based on the kinetic energy function and potential energy function of the vibration isolator, and applying the Lagrange equation, the dynamic equation of the vibration isolator is constructed.

[0061] In this embodiment, the dynamic equation of the vibration isolator is constructed by applying the Lagrange equation based on the kinetic energy function and potential energy function of the vibration isolator.

[0062] Using the relative displacement of the platform with respect to the base as generalized coordinates, the Lagrange equation is constructed based on the kinetic energy function and the potential energy function: (4) Where Q represents the Lagrange quantity; This represents the derivative of relative displacement with respect to time. This indicates the relative displacement of the platform with respect to the base; Indicates external disturbance force; c Indicates the damping coefficient; Indicates platform quality; g Represents the gravitational acceleration constant; This indicates the kinetic energy of the vibration isolator; This represents the potential energy of the vibration isolator; S503: Based on d'Alembert's principle, the restoring force displacement function of the vibration isolator is derived from the dynamic equation.

[0063] In the embodiments of this application, the restoring force displacement function of the vibration isolator can be derived from the dynamic equation based on d'Alembert's principle.

[0064] First, substituting formulas (2) and (3) into formula (4) yields: (5) in, Indicates platform quality; This represents the second derivative of the relative displacement with respect to time. This represents the second derivative of the absolute displacement of the base with respect to time. This indicates the stiffness coefficient of a vertical spring; This indicates the relative displacement of the platform with respect to the base; Indicates the amount of compression of the vertical spring; This indicates the stiffness coefficient of the connecting rod spring; Indicates the length of the connecting rod spring; Indicates the original length of the connecting rod spring; This represents the derivative of the length of the connecting rod spring with respect to the relative displacement; This indicates the initial tension of the connecting rod spring; g Represents the gravitational acceleration constant; Indicates external disturbance force; c Indicates the damping coefficient; It represents the derivative of relative displacement with respect to time.

[0065] At the static equilibrium position, that is... At this point, the load and the restoring force of the vertical spring are balanced, and the surface mechanism is irrelevant. g Then, the above equation (5) can be written as: (6) in, Indicates platform quality; This represents the second derivative of the relative displacement with respect to time. This indicates the stiffness coefficient of a vertical spring; This indicates the amount of compression of the vertical spring; This indicates the relative displacement of the platform with respect to the base; This indicates the stiffness coefficient of the connecting rod spring; Indicates the length of the connecting rod spring; Indicates the original length of the connecting rod spring; This represents the derivative of the length of the connecting rod spring with respect to the relative displacement; This indicates the initial tension of the connecting rod spring; Indicates external disturbance force; c Indicates the damping coefficient; This represents the derivative of relative displacement with respect to time. This represents the second derivative of the absolute displacement of the base with respect to time.

[0066] According to d'Alembert's principle, the force-displacement function of the vibration isolator can be obtained from equation (6): (7) in, Indicates force; This indicates the stiffness coefficient of a vertical spring; This indicates the amount of compression of the vertical spring; This indicates the relative displacement of the platform with respect to the base; This indicates the stiffness coefficient of the connecting rod spring; Indicates the length of the connecting rod spring; Indicates the original length of the connecting rod spring; This represents the derivative of the length of the connecting rod spring with respect to the relative displacement; This indicates the initial tension of the connecting rod spring.

[0067] The restoring force displacement function of a symmetrical vibration isolator at the static equilibrium position can be expressed as follows: (8) (9) in, Indicates resilience; This indicates the stiffness coefficient of a vertical spring; This indicates the amount of compression of the vertical spring; and, g ; The coefficients in the restoring force displacement function are related to the force displacement function expressed by formula (7).

[0068] As can be seen from formula (8), the restoring force displacement function has nonlinear characteristics. This nonlinearity allows the vibration isolator to exhibit different response behaviors under different loads and vibration conditions, thereby improving the vibration isolator's adaptability to large-amplitude and complex excitations. Specifically, the restoring force displacement function reflects the vibration isolator's recovery capability under different vibration amplitudes by including linear and nonlinear terms. The higher-order nonlinear terms enhance the vibration isolator's restoring force under large displacement disturbances, while the linear terms ensure rapid recovery under small disturbances. These characteristics enable the vibration isolator to effectively recover to the equilibrium state after being subjected to vibration disturbances of different frequencies and amplitudes, thereby ensuring the stability and excellent vibration reduction performance of the vibration isolator.

[0069] In this embodiment, based on the geometric connection relationship and physical parameters of the vibration isolator, the kinetic energy function and potential energy function of the vibration isolator are established. Then, based on the kinetic energy function and potential energy function of the vibration isolator, and applying the Lagrange equation, the dynamic equation of the vibration isolator is constructed. Finally, based on d'Alembert's principle, the restoring force displacement function of the vibration isolator is derived from the dynamic equation. The derived function accurately correlates the displacement and the restoring force, providing a core basis for subsequent parameter constraints and performance analysis, and ensuring that the parameter design can match the actual vibration scenario.

[0070] Figure 6 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown. Figure 6 As shown above, in the above Figure 3 Based on the illustrated embodiment, a specific implementation of step S302 is as follows: S601: Based on the geometry and physical parameters of the vibration isolator, the force-displacement function is processed to obtain a dimensionless force-displacement function.

[0071] In this embodiment of the application, in order to obtain an accurate Da Vinci system without a principal stiffness term, the length of the connecting spring is assumed to be: (10) in, Indicates the length of the connecting rod spring; This indicates the length of the connecting rod spring when the vibration isolator is in its static equilibrium position. ;set up ,in, This represents the structural parameters of the curved surface component; in one example, it represents the curvature of the curved surface component. l Indicates the structural parameters of the vibration isolator; This indicates the relative displacement of the platform with respect to the base.

[0072] Calculate the dimensionless parameters using the geometry and physical parameters of the vibration isolator: (11) in, Represents dimensionless force; Indicates dimensionless relative displacement; Indicates force; This indicates the stiffness coefficient of a vertical spring; l Indicates the structural parameters of the vibration isolator; This indicates the stiffness ratio of the connecting rod spring and the vertical spring; This indicates the stiffness coefficient of the connecting rod spring; This indicates the stiffness coefficient of a vertical spring; This indicates the relative displacement of the platform with respect to the base; This represents the dimensionless preload of the connecting rod spring. This indicates the preload of the connecting rod spring.

[0073] By substituting formulas (10) and (11) into the force-displacement function in formula (7) obtained above, the dimensionless force-displacement function is obtained: (12) in, Represents dimensionless force; Indicates dimensionless relative displacement; This indicates the stiffness ratio of the connecting rod spring and the vertical spring; Indicates the structural parameters of the curved surface component; This represents the dimensionless preload of the connecting rod spring.

[0074] S602: Differentiate the dimensionless force-displacement function to obtain the stiffness-displacement function.

[0075] In this embodiment of the application, the dimensionless force-displacement function is differentiated to obtain the stiffness-displacement function, that is, the stiffness-displacement function is obtained by differentiating the above formula (12): (13) in, Indicates dimensionless stiffness; Indicates dimensionless relative displacement; This indicates the stiffness ratio of the connecting rod spring and the vertical spring; Indicates the structural parameters of the curved surface component; This represents the dimensionless preload of the connecting rod spring.

[0076] S603: Based on the stiffness-displacement function, set the stiffness value of the stiffness-displacement function at the static equilibrium position of the vibration isolator to the target value, and solve the parameter constraint conditions.

[0077] In this embodiment of the application, in order to obtain accurate cubic stiffness, the stiffness value at the static equilibrium position should satisfy the following condition: (14) in, This indicates the stiffness ratio of the connecting rod spring and the vertical spring; Indicates the structural parameters of the curved surface component; This represents the dimensionless preload of the connecting rod spring.

[0078] Furthermore, the corresponding dimensionless restoring force function at this time is: .

[0079] In summary, to eliminate the influence of static load, the dimensionless restoring force of the vibration isolator is approximately zero over a wide range [-0.2, 0.2], and its amplitude is much smaller than that of a typical linear vibration isolator. Since the static load of the vibration isolator depends only on the stiffness and compression of the vertical spring, theoretically, the High-static-low-dynamic Bench Vibration Isolator (HFBVI) has a large load-bearing capacity over a wide range. Furthermore, HFBVI... There is a wide and gently sloping low-stiffness region on both sides [-0.2, 0.2]. In this region, the dimensionless stiffness is almost zero, much smaller than the stiffness of a typical linear vibration isolator. Furthermore, with... With the increase of [something], the size of the static stiffness and low dynamic stiffness regions of the vibration isolator will also increase, and regardless of [something]... Regardless of the value, the dimensionless stiffness of the vibration isolator is always greater than or equal to zero, and there is no negative stiffness region overall. The vibration isolator will not become unstable due to the presence of curved components. Therefore, the vibration isolator has a wide and stable range of high static stiffness and low dynamic stiffness, and can achieve large static stiffness and very low dynamic stiffness within a large dimensionless region. Furthermore, within the design limits, the greater the pretension of the connecting rod spring, the stronger the high static stiffness and low dynamic stiffness characteristics of the vibration isolator, and the better the theoretical vibration isolation performance.

[0080] In this embodiment, based on the geometry and physical parameters of the vibration isolator, the force-displacement function is dimensionlessly processed to obtain a dimensionless force-displacement function. Then, the derivative of the dimensionless force-displacement function is obtained to obtain the stiffness-displacement function. Finally, based on the stiffness-displacement function, the stiffness value of the stiffness-displacement function at the static equilibrium position of the vibration isolator is set as the target value, and the parameter constraint conditions are solved. By transforming the abstract quasi-zero stiffness characteristic into quantifiable parameter constraint conditions, the selection of vibration isolator parameters can be guided based on the parameter constraint conditions, thereby achieving quasi-zero stiffness characteristics at the static equilibrium position.

[0081] Figure 7 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown. Figure 7 As shown above, in the above Figure 3 Based on the illustrated embodiment, a specific implementation of step S303 is as follows: S701: Based on the geometry and physical parameters of the vibration isolator, the dynamic equation under excitation is processed into a dimensionless form to obtain the dynamic equation under dimensionless excitation.

[0082] In this embodiment, the dynamic equation under excitation is first established, and then the dynamic equation under excitation is dimensionlessly processed based on the geometric structure and physical parameters of the vibration isolator to obtain the dynamic equation under dimensionless excitation.

[0083] To clearly illustrate the process of constructing the dynamic equations under excitation, Figure 8a A simplified dynamic model and force diagram of the vibration isolator under harmonic force excitation are shown; Figure 8b A simplified dynamic model and force diagram of the vibration isolator under displacement excitation are shown.

[0084] According to d'Alembert's principle, the dynamic equation of the vibration isolator is as follows: in, Indicates platform quality; This represents the second derivative of the relative displacement with respect to time. c Indicates the damping coefficient; This represents the derivative of relative displacement with respect to time. Indicative of motivation; This represents the second derivative of the platform's absolute displacement with respect to time. This represents the second derivative of the absolute displacement of the base with respect to time. This represents the first derivative of the platform's absolute displacement with respect to time. This represents the first derivative of the absolute displacement of the base with respect to time; x Indicates the absolute displacement of the platform. y Indicates the absolute displacement of the base; Y This indicates displacement excitation.

[0085] in, and It is the elastic restoring force of the vibration isolator platform, assuming the force excitation is: The displacement excitation is: Then, by introducing variables The above formula (15) can be rewritten as: (16) in, Indicates platform quality; This represents the second derivative of the relative displacement with respect to time. c Indicates the damping coefficient; This represents the derivative of relative displacement with respect to time. Indicates force; Indicates the amplitude of harmonic force; Indicates the amplitude under displacement excitation; Indicates the excitation frequency; t Indicates time.

[0086] Calculate the dimensionless parameters using the geometry and physical parameters of the vibration isolator: , , , , , , , , , in, Indicates dimensionless relative displacement; This indicates the relative displacement of the platform with respect to the base; l Indicates the structural parameters of the vibration isolator; x Indicates the absolute displacement of the platform; y Indicates the absolute displacement of the base; This represents the dimensionless damping coefficient; c Indicates the damping coefficient; This indicates the stiffness coefficient of a vertical spring; Indicates platform quality; t represents dimensionless time; t represents actual time. Indicates the dimensionless excitation frequency; Indicates the excitation frequency; Indicates the characteristic frequency of the vibration isolator; Indicates a dimensionless force excitation; Indicates the amplitude of harmonic force; This indicates dimensionless displacement excitation; Indicates the amplitude under displacement excitation; This represents the third nonlinear coefficient in the restoring force displacement function; Indicates the structural parameters of the curved surface component; This represents the dimensionless preload of the connecting rod spring.

[0087] By substituting the dimensionless parameter into the above formula (16), the dimensionless dynamic equation is obtained as follows: (17) in, This represents the dimensionless rate of change of acceleration under force excitation; This represents the dimensionless damping coefficient; , This represents the dimensionless acceleration under force excitation. This represents dimensionless relative displacement. Indicates time; This represents the third nonlinear coefficient in the restoring force displacement function; Indicates dimensionless velocity; This represents the dimensionless rate of change of acceleration under displacement excitation; , This represents the dimensionless acceleration under displacement excitation. This represents the absolute displacement of the dimensionless platform. This represents the absolute displacement of the dimensionless base. , indicating a dimensionless force excitation; , indicating dimensionless displacement excitation.

[0088] S702: The harmonic balance method is used to solve the dynamic equations under dimensionless excitation to obtain the force amplitude and displacement amplitude.

[0089] In this embodiment, the dynamic equation under excitation is a nonlinear differential equation, and an exact analytical solution cannot be obtained. Therefore, the dynamic equation under dimensionless excitation is solved using the harmonic balance method. The harmonic balance method is an effective approximation method for solving the steady-state response of a nonlinear system. It is assumed that the steady-state response of the vibration isolator under harmonic excitation is a sinusoidal function: (18) in, Indicates the steady-state response; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; Indicates time; This indicates the phase of the harmonic response.

[0090] Substituting formula (18) into formula (17) and ignoring higher harmonic terms, we get: (19) in, This represents the third nonlinear coefficient in the restoring force displacement function; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; Indicates the phase of the harmonic response; This represents the dimensionless damping coefficient; This represents dimensionless harmonic excitation, where Indicates a dimensionless force excitation. This indicates dimensionless displacement excitation.

[0091] Then the above (19) is transformed into: (20) in, This represents the third nonlinear coefficient in the restoring force displacement function; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; This represents the dimensionless damping coefficient; This represents dimensionless harmonic excitation, where Indicates a dimensionless force excitation. This indicates dimensionless displacement excitation.

[0092] Therefore, the amplitude of the force transmitted to the vibration isolator base under force excitation is: (twenty one) in, Indicates the amplitude of the force; This represents the third nonlinear coefficient in the restoring force displacement function; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; This represents the dimensionless damping coefficient.

[0093] The absolute displacement of the vibration isolator platform is: x= ， in, Let represent the steady-state solution of the dynamic equation, and y represent the absolute displacement of the base. Then, under displacement excitation, the absolute displacement amplitude of the vibration isolator platform is: (twenty two) in, x This represents the absolute displacement amplitude of the vibration isolator platform; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; Indicates the phase of the harmonic response; Indicates the dimensionless displacement amplitude; Indicates time.

[0094] S703: Solving for force transmissibility and displacement transmissibility functions based on force amplitude and displacement amplitude.

[0095] In the embodiments of this application, the force transmissibility function and the displacement transmissibility function are solved based on the obtained force amplitude and displacement amplitude.

[0096] Force transmissibility is defined as the ratio of the amplitude of the basic force to the amplitude of the excitation force. Therefore, the force transmissibility function of a vibration isolator is: (twenty three) in, Represents the force transmissibility function; Indicates the amplitude of the force; Indicates a dimensionless force excitation; This represents the amplitude of the dimensionless harmonic force; This represents the third nonlinear coefficient in the restoring force displacement function; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; This represents the dimensionless damping coefficient.

[0097] The displacement transmissibility function is the ratio of the amplitude of the displacement to the amplitude of the excitation displacement. Therefore, the displacement transmissibility function of the vibration isolator is: (twenty four) in, Represents the displacement transmissibility function; x This represents the absolute displacement amplitude of the vibration isolator platform; A Indicates the harmonic response amplitude; Indicates the dimensionless excitation frequency; Indicates the phase of the harmonic response; It represents the amplitude under dimensionless displacement excitation.

[0098] Furthermore, an equivalent linear vibration isolator was established without curved components, and its displacement transmissibility is expressed as: (25) in, This indicates the displacement transmissivity of the vibration isolator when there are no curved components. This represents the dimensionless damping coefficient; This represents the dimensionless excitation frequency.

[0099] In this embodiment, based on the geometry and physical parameters of the vibration isolator, the dynamic equation under excitation is dimensionlessly processed to obtain the dynamic equation under dimensionless excitation. Then, the harmonic balance method is applied to solve the dynamic equation under dimensionless excitation to obtain the force amplitude and displacement amplitude. Finally, the force transmissibility function and displacement transmissibility function are solved based on the force amplitude and displacement amplitude. The vibration reduction effect is evaluated by the calculated force transmissibility and displacement transmissibility. The lower the force transmissibility and displacement transmissibility, the better the vibration isolation performance of the vibration isolator. The calculated force transmissibility function and displacement transmissibility function provide a clear performance judgment standard for subsequent vibration isolator parameter optimization, which facilitates the selection of the optimal parameter combination with the lowest force transmissibility and displacement transmissibility.

[0100] Figure 9 A flowchart illustrating a method for determining vibration isolator parameters according to another embodiment of this application is shown. Figure 9 As shown above, in the above Figure 3 Based on the illustrated embodiment, a specific implementation of step S304 is as follows: S901: Based on the mass of the object and the static balance relationship between the vertical spring force and the object's gravity, select the stiffness coefficient and pre-compression of the vertical spring.

[0101] In this embodiment, based on the obtained mass of the object to be supported, and combined with the static equilibrium relationship between the vertical spring force and the object's weight, the stiffness coefficient and pre-compression of the vertical spring are selected. That is, according to the static equilibrium relationship, the vertical spring force equals the object's weight; therefore, when the stiffness coefficient of the vertical spring multiplied by the compression equals the object's weight, the stiffness coefficient and compression of the vertical spring are selectable. In one example, the object's weight can be the weight of the object to be supported plus the weight of the vibration isolator platform.

[0102] S902: Based on the stiffness coefficient and pre-compression of the vertical spring, and using parameter constraints, determine the parameters of the vibration isolator.

[0103] In the embodiments of this application, parameter constraints are the core basis for achieving quasi-zero stiffness characteristics. Other parameters need to be determined based on the selected vertical spring parameters and constraints to ensure that the parameters of each component work together.

[0104] Based on the above formula (14), the stiffness coefficient of the vertical spring can be substituted into formula (14), and the stiffness coefficient of the connecting spring, the pretension of the connecting spring, the structural parameters of the vibration isolator, and the structural parameters of the curved component can be selected to satisfy formula (14). In one example, there is more than one combination of the stiffness coefficient of the connecting spring, the pretension of the connecting spring, the structural parameters of the vibration isolator, and the structural parameters of the curved component that satisfy formula (14).

[0105] S903: Substitute the parameters of the vibration isolator into the force transmissibility function and the displacement transmissibility function to solve for the force transmissibility and displacement transmissibility of the vibration isolator, and determine whether the force transmissibility and displacement transmissibility meet the preset force transmissibility threshold and displacement transmissibility threshold.

[0106] In this embodiment, although the parameter combination selected based on the above steps meets the load-bearing requirements and quasi-zero stiffness constraints, the actual vibration isolation performance needs to be verified by the transmissibility. This is to avoid the transmissibility exceeding the standard due to improper parameter combination, which would prevent effective vibration isolation. Substituting the selected parameters into formulas (22) and (23) yields the force transmissibility and displacement transmissibility. Then, the obtained force transmissibility and displacement transmissibility are compared with the preset force transmissibility threshold and displacement transmissibility threshold. If the obtained force transmissibility is less than or equal to the preset force transmissibility threshold and the obtained displacement transmissibility is less than or equal to the preset displacement transmissibility threshold, then the parameters of this set of vibration isolators meet the load-bearing requirements and quasi-zero stiffness constraints, and can also effectively isolate vibration.

[0107] S904: If not satisfied, the parameters of the vibration isolator are re-determined based on the parameter constraints until the obtained force transmissibility and displacement transmissibility satisfy the force transmissibility threshold and displacement transmissibility threshold, respectively.

[0108] In the embodiments of this application, the parameters initially determined may result in a failure to meet the transfer rate due to the coupling relationship between the parameters. It is necessary to iteratively adjust and optimize the parameter combination to reduce the transfer rate below the threshold under the premise of satisfying the load-bearing and quasi-zero stiffness constraints. If the transfer rate does not meet the threshold requirement, the geometric structural parameters or physical parameters are readjusted within the range of parameter constraints, and the verification steps are repeated until the transfer rate meets the standard.

[0109] In this embodiment, the object's mass is used as input. Static equilibrium is used to ensure that the vertical spring parameters match the load-bearing requirements, preventing excessive compression due to insufficient stiffness or impact on buffering performance due to excessive stiffness. Then, constraints are used to correlate the vertical spring parameters with other parameters, ensuring all parameters form a synergistic system to achieve near-zero stiffness characteristics. Finally, force and displacement transmissibility are used to verify whether the parameters can adapt to real-world transportation vibration scenarios and effectively isolate vibrations during transport. Vertical spring parameter selection ensures load-bearing safety, constraints guarantee near-zero stiffness characteristics, and transmissibility verifies and quantifies the vibration isolation effect. This ensures the vibration isolator meets both load-bearing and vibration protection requirements, preventing damage to the robot from high-frequency vibrations during transport and significantly improving transportation safety and robot lifespan.

[0110] In one example, Table 1 below shows a set of parameter combinations determined according to the vibration isolator parameter determination method of this application: Table 2 shows the spring information determined based on the linkage spring and vertical spring parameters identified above. Figure 10 The diagram illustrates the overall flow of a vibration isolator parameter determination method provided in this application. S1001: Establish a theoretical model of the vibration isolator; S1002: Determine the restoring force of the vibration isolator using the Lagrange equation and d'Alembert's principle; S1003: Construct the restoring force-displacement function by introducing a cubic stiffness vibration isolator designed with a curved surface mechanism based on the restoring force; S1004: Solve the dynamic response of the vibration isolator using the harmonic balance method and derive the transmissibility expression of the vibration isolator under force and displacement excitation. The vibration isolator and the parameters determined by the method provided in this application ensure that the vibration isolator meets the load-bearing and vibration isolation requirements during transportation, enabling the vibration isolator to significantly buffer and attenuate high-frequency vibrations, effectively reducing high-frequency vibrations caused by uneven road surfaces during robot transportation.

[0111] Figure 11 A schematic diagram of a vibration isolator parameter determination device provided in this application is shown. Figure 11 As shown, the vibration isolator parameter determination device 1100 provided in this application includes: Module 1101 is used to construct the force-displacement function of the vibration isolator based on the geometry and physical parameters of the vibration isolator, using the Lagrange equation and d'Alembert's principle. The displacement is the change in displacement of the platform relative to the base. The first solution module 1102 is used to solve the parametric constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position based on the force-displacement function. The second solution module 1103 is used to establish the dynamic equation of the vibration isolator under excitation based on the force-displacement function, and solve the dynamic equation using the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation. The acquisition module 1104 is used to acquire the mass of the object to be supported, and to solve the parameters of the vibration isolator based on the object mass, parameter constraints, force transmissibility function and displacement transmissibility function.

[0112] In one example, building module 1101 includes: Based on the geometric connection relationship and physical parameters of the vibration isolator, the kinetic energy function and potential energy function of the vibration isolator are established. Based on the kinetic and potential energy functions of the vibration isolator, and by applying the Lagrange equation, the dynamic equation of the vibration isolator is constructed. Based on d'Alembert's principle, the force-displacement function of the vibration isolator is derived from the dynamic equation.

[0113] In one example, the first solver module 1102 includes: Based on the geometric structure and physical parameters of the vibration isolator, the force-displacement function is processed to obtain a dimensionless force-displacement function. Differentiating the dimensionless force-displacement function yields the stiffness-displacement function; Based on the stiffness-displacement function, let the stiffness of the stiffness-displacement function at the static equilibrium position of the vibration isolator be the target value, and solve for the parameter constraints.

[0114] In one example, the second solver module 1103 includes: Based on the geometric structure and physical parameters of the vibration isolator, the dynamic equation under excitation is dimensionlessly processed to obtain the dynamic equation under dimensionless excitation. The harmonic balance method is used to solve the dynamic equations under dimensionless excitation to obtain the force amplitude and displacement amplitude. The force transmissibility function and displacement transmissibility function are solved based on the amplitude of force and the amplitude of displacement.

[0115] In one example, module 1104 is retrieved, including: Based on the mass of the object and the static equilibrium relationship between the spring force of the vertical spring and the weight of the object, the stiffness coefficient and pre-compression of the vertical spring are selected. Based on the stiffness coefficient and pre-compression of the vertical spring, and using parameter constraints, the parameters of the vibration isolator are determined. Substitute the parameters of the vibration isolator into the force transmissibility function and the displacement transmissibility function to solve for the force transmissibility and displacement transmissibility of the vibration isolator, and determine whether the force transmissibility and displacement transmissibility meet the preset force transmissibility threshold and displacement transmissibility threshold. If the conditions are not met, the parameters of the vibration isolator are re-determined based on the parameter constraints until the obtained force transmissibility and displacement transmissibility satisfy the force transmissibility threshold and displacement transmissibility threshold, respectively.

[0116] Figure 12 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0117] An electronic device may include a processor 1201 and a memory 502 storing computer program instructions.

[0118] Specifically, the processor 1201 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0119] Memory 1202 may include mass storage for data or instructions. For example, and not limitingly, memory 1202 may include a hard disk drive (HDD), a floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. In one instance, memory 1202 may include removable or non-removable (or fixed) media, or memory 1202 may be a non-volatile solid-state memory.

[0120] In one instance, memory 1202 may be read-only memory (ROM). In one instance, the ROM may be a mask-programmed ROM, a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), an electrically rewritable ROM (EAROM), or flash memory, or a combination of two or more of these.

[0121] Memory 1202 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Therefore, generally, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this disclosure.

[0122] The processor 1201 reads and executes computer program instructions stored in the memory 1202 to implement a method for determining vibration isolator parameters in the above embodiment.

[0123] In one example, the electronic device may also include a communication interface 1203 and a bus 1204. For example, Figure 12 As shown, the processor 1201, memory 1202, and communication interface 1203 are connected through bus 1204 and complete communication with each other.

[0124] The communication interface 1203 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0125] Bus 1204 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 1204 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, this application contemplates any suitable bus or interconnect.

[0126] In addition, in conjunction with the vibration isolator parameter determination method in the above embodiments, this application embodiment can provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the vibration isolator parameter determination methods in the above embodiments.

[0127] This application also provides a computer program product, including a computer program, which, when executed, implements any of the vibration isolator parameter determination methods described in the above embodiments.

[0128] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0129] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, read-only memory (ROM), flash memory, erasable read-only memory (EROM), floppy disks, compact disc read-only memory (CD-ROM), optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0130] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0131] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0132] The above are merely specific embodiments of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for determining vibration isolator parameters, characterized in that, include: Based on the geometric structure and physical parameters of the vibration isolator, the restoring force displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle. The displacement in the restoring force displacement function is the displacement change of the vibration isolator platform relative to the base. Based on the restoring force displacement function, solve the parameter constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position; Based on the restoring force displacement function, the dynamic equation of the vibration isolator under excitation is established, and the dynamic equation is solved by the harmonic balance method to obtain the force transmissibility function and displacement transmissibility function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation. Obtain the mass of the object to be supported, and based on the object mass, the parameter constraints, the force transmissibility function, and the displacement transmissibility function, solve for the parameters of the vibration isolator.

2. The method according to claim 1, characterized in that, Based on the geometry and physical parameters of the vibration isolator, the restoring force displacement function of the vibration isolator is constructed using the Lagrange equation and d'Alembert's principle, including: Based on the geometric connection relationship and physical parameters of the vibration isolator, the kinetic energy function and potential energy function of the vibration isolator are established. Based on the kinetic energy function and potential energy function of the vibration isolator, and by applying the Lagrange equation, the dynamic equation of the vibration isolator is constructed. Based on d'Alembert's principle, the restoring force displacement function of the vibration isolator is derived from the dynamic equation.

3. The method according to claim 1, characterized in that, The parameter constraints for solving the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position based on the restoring force displacement function include: Based on the geometric structure and physical parameters of the vibration isolator, the restoring force displacement function is processed to obtain a dimensionless restoring force displacement function; Differentiating the dimensionless restoring force displacement function yields the stiffness displacement function; Based on the stiffness-displacement function, let the stiffness value of the stiffness-displacement function at the static equilibrium position of the vibration isolator be the target value, and solve the parameter constraint conditions.

4. The method according to claim 1, characterized in that, Based on the restoring force displacement function, the dynamic equation of the vibration isolator under excitation is established, and the dynamic equation is solved using the harmonic balance method to obtain the force transmissibility and displacement transmissibility of the vibration isolator under excitation, including: Based on the geometric structure and physical parameters of the vibration isolator, the dynamic equation under the excitation is processed into a dimensionless form to obtain the dynamic equation under dimensionless excitation. The harmonic balance method described above is used to solve the dynamic equations under the dimensionless excitation, and the force amplitude and displacement amplitude are obtained. The force transmissibility function and the displacement transmissibility function are solved based on the amplitude of the force and the amplitude of the displacement.

5. The method according to claim 1, characterized in that, The process of obtaining the mass of the object to be supported, and solving for the parameters of the vibration isolator based on the object mass, the parameter constraints, and the force transmissibility function and the displacement transmissibility function, includes: Based on the mass of the object, and combined with the static balance relationship between the vertical spring force and the object's weight, the stiffness coefficient and pre-compression of the vertical spring are selected. Based on the stiffness coefficient and pre-compression of the vertical spring, and using the parameter constraints, the parameters of the vibration isolator are determined. Substitute the parameters of the vibration isolator into the force transmissibility function and the displacement transmissibility function to solve for the force transmissibility and displacement transmissibility of the vibration isolator, and determine whether the force transmissibility and displacement transmissibility meet the preset force transmissibility threshold and displacement transmissibility threshold. If the conditions are not met, the parameters of the vibration isolator are re-determined based on the aforementioned parameter constraints until the obtained force transmission rate and displacement transmission rate satisfy the aforementioned force transmission rate threshold and displacement transmission rate threshold, respectively.

6. A device for determining vibration isolator parameters, characterized in that, The device includes: The module is used to construct the restoring force displacement function of the vibration isolator based on its geometric structure and physical parameters, using the Lagrange equation and d'Alembert's principle. The displacement is the amount of displacement change of the platform relative to the base. The first solution module is used to solve the parameter constraints for the vibration isolator to achieve quasi-zero stiffness characteristics at the static equilibrium position based on the restoring force displacement function. The second solution module is used to establish the dynamic equation of the vibration isolator under excitation based on the restoring force displacement function, and to solve the dynamic equation using the harmonic balance method to obtain the force transmissivity function and displacement transmissivity function of the vibration isolator under excitation. The excitation includes harmonic force excitation and displacement excitation. The acquisition module is used to acquire the mass of the object to be supported, and to solve the parameters of the vibration isolator based on the mass of the object, the parameter constraints, the force transmissibility function and the displacement transmissibility function.

7. A vibration isolator, characterized in that, The vibration isolator includes: Base; A support device is vertically fixed to the base for supporting the platform. The support device is provided with a vertical spring perpendicular to the base, which acts between the platform and the base to provide elastic support in the vertical direction. The main support body of the support device is a support column vertically fixed to the platform. The support column is also used to support a guide rail. The guide rail is used to guide the movement of the support column in the vertical direction of the base so that the platform only produces vertical displacement when vibrating. Two pairs of curved surface components are fixed on the base. One pair of curved surface components and the other pair of curved surface components are arranged symmetrically about the support device. The surfaces of the two pairs of curved surface components facing the support device are curved surfaces with the same curvature. Each pair of curved components has two parallel rollers on its curved surface that can move along the curved surface. The two parallel rollers are connected by a connecting rod spring. When the two parallel rollers move along the curved surface, they cause the connecting rod spring to deform. The two ends of the connecting rod are respectively hinged to the two parallel rollers, and the middle part of the connecting rod is hinged to the support device.

8. A vibration isolator according to claim 7, characterized in that, include: The positive stiffness provided by the vertical spring is coupled with the negative stiffness generated by the curved component, the roller, the connecting rod and the connecting rod spring, so that the vibration isolator has quasi-zero stiffness characteristics in the equilibrium position.

9. An electronic device, characterized in that, The device includes: a processor and a memory storing computer program instructions; the processor reads and executes the computer program instructions to implement a method for determining vibration isolator parameters as described in any one of claims 1-5.

10. A computer-readable storage medium, characterized in that, The computer storage medium stores computer program instructions, which, when executed by a processor, implement a method for determining vibration isolator parameters as described in any one of claims 1-5.

11. A computer program product, characterized in that, When the instructions in the computer program product are executed by the processor of the electronic device, the electronic device performs a vibration isolator parameter determination method as described in any one of claims 1-5.

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