A two-dimensional nonlinear force programmable generation method

Abstract

This invention relates to the fields of vibration control and nonlinear mechanics, and provides a programmable method for generating two-dimensional nonlinear forces. The method includes: responding to a two-dimensional nonlinear force generation request; acquiring the structure and structural parameters of a mechanical realization device; determining the trajectory of the center point of a rolling component during motion based on mechanical equilibrium relationships, and acquiring the geometric expression of the rolling component's trajectory surface; and, based on the geometric dimensions of the rolling component, performing equidistant mapping along the normal direction on the rolling component's trajectory surface, causing the rolling component to adhere to and roll along a three-dimensional guide surface, thereby generating a nonlinear force corresponding to a target nonlinear force function. This method not only generates nonlinear forces of arbitrary continuous form based on a preset target force function and supports personalized customization of nonlinear stiffness characteristics, but also generates nonlinear forces that meet target requirements in two mutually orthogonal motion directions.

Description

Technical Field

[0001] This invention relates to the fields of vibration control and nonlinear mechanics, and in particular to a method for programmable generation of two-dimensional nonlinear forces. Background Technology

[0002] With the development of vibration control technology, nonlinear forces are widely used in vibration isolation systems, nonlinear energy traps, and vibration energy harvesting. Compared with linear mechanical systems, the reasonable introduction of nonlinear forces can change the equivalent stiffness characteristics and energy distribution characteristics of the system, resulting in better performance in low-frequency vibration isolation, broadband vibration absorption, and energy harvesting efficiency. For example, in vibration isolation systems, introducing nonlinear force structures with negative stiffness or quasi-zero stiffness characteristics can effectively reduce the system's isolation initiation frequency; in nonlinear energy traps, nonlinear forces can extend the effective frequency band for targeted energy transfer; and in vibration energy harvesting systems, constructing bistable or multistable nonlinear force characteristics can improve energy harvesting efficiency and operational stability.

[0003] In existing technologies, nonlinear forces are typically achieved through specific mechanical structures or physical effects, including magnetic mechanisms, geometrically large deformation structures (such as buckling beams and buckling plates), combined spring mechanisms, nonlinear disc springs, and structures such as cylindrical cam-roller-preloaded springs. These structures rely on the geometry or material properties of the components to generate nonlinear forces that vary with displacement during motion. Some solutions utilize a preloaded spring in conjunction with a cam or slide to achieve a certain form of nonlinear force output; others utilize magnetic forces or structural buckling effects to create multi-steady-state mechanical properties, meeting specific application requirements.

[0004] However, the aforementioned existing technologies still have significant limitations in practical applications. On the one hand, the mechanical properties of existing nonlinear force structures are usually determined by the inherent parameters of the structure, and the form of nonlinear force variation with displacement is relatively fixed, making it difficult to flexibly construct the required nonlinear force characteristics according to different application scenarios, especially to achieve complex or asymmetric force-displacement relationships. On the other hand, most existing solutions only introduce nonlinear forces for a single direction of motion. When moving in two dimensions or multiple degrees of freedom, it is difficult to simultaneously achieve the coordinated construction of nonlinear force characteristics in multiple directions. In addition, some solutions rely on external control devices or constant load assumptions during implementation, resulting in complex system structures and high implementation difficulty, which limits their widespread application in engineering scenarios. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing nonlinear force implementation methods, such as the difficulty in flexibly constructing nonlinear force characteristics, the limitation of force-displacement relationships by inherent structural parameters, and the fact that they are usually only applicable to a single direction of motion. This invention proposes a programmable method and device for generating two-dimensional nonlinear forces. Utilizing a sliding track structure with continuously changing spatial curvature, in conjunction with rolling components and elastic elements, the force generated by the elastic element is decomposed and transmitted along the track normal during two-dimensional motion. This generates nonlinear force characteristics that vary with displacement in two independent motion directions, achieving the coordinated construction of two-dimensional nonlinear forces. It eliminates the need for complex external control devices or constant load assumptions, enabling the desired nonlinear force output through the mechanical structure itself. This invention is suitable for applications such as vibration isolation, nonlinear energy traps, and vibration energy harvesting. The objective of this invention can be achieved through the following technical solutions: This invention provides a two-dimensional nonlinear force programmable generation method, comprising, Step S1: Respond to the request for generating a two-dimensional nonlinear force and determine the target nonlinear force function based on the request; Step S2: Based on the functional form of the target nonlinear force function, select a structure suitable for the mechanical realization device that generates the target nonlinear force in two mutually orthogonal motion directions and obtain the corresponding structural parameters; Step S3: Based on the target nonlinear force function, establish the mechanical equilibrium relationship of the mechanical realization device during the motion process, and determine the center point trajectory of the rolling component in the mechanical realization device during the motion process by the mechanical equilibrium relationship, thereby obtaining the geometric expression of the motion trajectory surface of the rolling component; Step S4: Based on the geometric dimensions of the rolling component, the motion trajectory surface of the rolling component is equidistantly mapped along the normal direction to establish the geometric correspondence between the motion trajectory surface of the rolling component and the three-dimensional guide surface of the mechanical realization device, so that the rolling component fits and rolls along the three-dimensional guide surface during the motion, generating nonlinear forces corresponding to the target nonlinear force function in two mutually orthogonal motion directions.

[0006] Furthermore, the structure of the mechanical realization device includes a nonlinear force design platform, a three-dimensional guide surface, rolling components, several fixed bases, elastic elements, and a two-dimensional planar motion guiding mechanism. The nonlinear force design platform is connected to the first fixed base through a two-dimensional planar motion guide mechanism, and moves independently in a straight line along two mutually orthogonal motion directions, including a first motion direction and a second motion direction. The nonlinear force design platform is connected to the second fixed base along the first motion direction and the second motion direction through corresponding support springs. The three-dimensional guide surface is a spatial curvature surface, which is fixedly set on the side of the nonlinear force design platform near the rolling component; The rolling component is connected to the linear motion component moving along the third motion direction through a connecting structure. The linear motion component is connected to the third fixed base through a compression spring arranged along the third motion direction, so that the rolling component contacts the spatial curvature surface and rolls along the spatial curvature surface. The rolling component includes a rolling element and its support, wherein the third motion direction is orthogonal to the first motion direction and the second motion direction.

[0007] Furthermore, the structural parameters include the stiffness and pre-compression of the compression spring, the stiffness of the support spring in the first and second motion directions, and the geometric parameters of the rolling component.

[0008] Further, step S2 includes, The structure of the mechanical realization device is determined based on the functional form of the target nonlinear force function. When the mechanical realization device is in the initial equilibrium state, the center point of the rolling component 3 that keeps in contact with the three-dimensional guide surface 2 is the origin O of the coordinate system. A three-dimensional rectangular coordinate system is established by drawing x-axis, y-axis and z-axis along the third motion direction, the second motion direction and the first motion direction, respectively. The functional form is a polynomial or piecewise nonlinear force function.

[0009] Furthermore, in step S3, the formula for the geometric expression of the rolling component's motion trajectory surface is: ; in, Here is the geometric expression for the surface of the trajectory of the rolling component. and These are the target nonlinear force functions in the second and first motion directions, respectively. and The stiffness of the supporting springs is respectively determined in the second and first directions of motion. and Displacement in the second direction of motion and the first direction of motion, To compress the spring stiffness, This is the pre-compression amount of the compression spring.

[0010] Further, step S4 includes, Step S41: Based on the acquired rolling component motion trajectory surface Obtain the partial derivatives of the second motion direction and the first motion direction. and These are used to characterize the slope changes of the trajectory surface of the rolling component's center point in the second and first motion directions, respectively, and to determine the normal direction of the trajectory surface of the rolling component at any point. These are the displacement coordinates of the center point of the rolling component in the second and first motion directions, respectively. For partial derivatives, This is the geometric expression for the surface of the trajectory of the rolling component; Step S42: Obtain the radius of the rolling member based on its geometry. And along the normal direction of the surface of the rolling component's trajectory, according to the radius Equidistant offset is performed to obtain the spatial positional relationship between the rolling component's motion trajectory surface and the three-dimensional guide surface in the mechanical realization device.

[0011] Further, in step S42, according to the radius The formula for obtaining the spatial relationship between the rolling component's trajectory surface and the three-dimensional guide surface in the mechanical realization device by performing equidistant offset is as follows: ; in, These are the displacement coordinates of the center point of the rolling component in the second and first motion directions, respectively. For partial derivatives, Here is the geometric expression for the surface of the trajectory of the rolling component. Let the radius of the rolling component be . and These are the position coordinates of the center point of the rolling component after equidistant offset adjustment when the rolling component is in contact with the three-dimensional guide surface. is the surface function of the rolling component's motion trajectory surface after equidistant offset, and is the geometric expression of the three-dimensional guide surface.

[0012] Furthermore, step S4 also includes, Step S43: Based on the geometric expression of the three-dimensional guide surface, design and process the required contour surface to form a slide that conforms to the rolling component's fit, and complete the assembly of each component of the mechanical realization device, so that the rolling component moves along the slide and fits the three-dimensional guide surface during the movement to generate a nonlinear force corresponding to the target nonlinear force function. Step S44: Verify the mechanical realization device through simulation or physical testing to determine the degree of conformity between the nonlinear force generated by the rolling component during its rolling motion along the three-dimensional guide surface and the target nonlinear force function, as well as the contact state between the rolling component and the three-dimensional guide surface within the predetermined motion range, so as to confirm that the mechanical realization device can meet the preset mechanical performance requirements and generate the expected nonlinear force.

[0013] Compared with the prior art, the present invention has at least one of the following technical advantages: This invention establishes a correspondence between a target nonlinear force function and the structure of a mechanical realization device, enabling programmable design and precise generation of nonlinear force characteristics. This method not only generates nonlinear forces of arbitrary continuous form based on a preset target force function and supports personalized customization of nonlinear stiffness characteristics, but also generates nonlinear forces that meet target requirements in two mutually orthogonal motion directions. This overcomes the limitations of existing technologies where nonlinear forces are fixed in form, difficult to customize, and difficult to achieve multi-directional collaborative design. Attached Figure Description

[0014] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below: Figure 1 This is a flowchart illustrating the steps of the two-dimensional nonlinear force programmable generation method of the present invention; Figure 2 This is a schematic diagram of the mechanical implementation device in an embodiment of the present invention, wherein, Figure 2 (a) in the figure is the xy view of the mechanical realization device. Figure 2 (b) in the image is the xz view; Figure 3 This is a schematic diagram of the working principle of the mechanical implementation device from the xy perspective in the two-dimensional nonlinear force programmable generation method of the present invention, wherein, Figure 3 (a) in the diagram is the initial state diagram. Figure 3 (b) in the diagram represents the downward motion state. Figure 3 (c) in the diagram represents the upward motion state; Figure 4 This is a schematic diagram of the working principle of the mechanical implementation device from the xz perspective in the two-dimensional nonlinear force programmable generation method of the present invention, wherein... Figure 4 (a) in the diagram is the initial state diagram. Figure 4 (b) in the diagram represents the downward motion state. Figure 4 (c) in the diagram represents the upward motion state; Figure 5 This is a coordinate system diagram for establishing the motion trajectory surface of the rolling component in an embodiment of the present invention; Figure 6 This is a schematic diagram showing the relationship between the motion trajectory surface of the rolling component and the three-dimensional guide surface in an embodiment of the present invention.

[0015] Explanation of reference numerals in the attached figures: 1: Nonlinear force design platform; 2: Three-dimensional guide surface; 3: Rolling component; 4: Connecting structure; 5: Moving part of linear motion component; 6: Stationary part of linear motion component; 7: Compression spring; 8: First support spring; 9: Second support spring. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0018] First Embodiment This embodiment provides a two-dimensional nonlinear force programmable generation method for generating nonlinear forces of a preset form in two mutually orthogonal motion directions. The method is based on the spatial geometric constraint relationship between the rolling component 3 and the three-dimensional guide surface 2. By modeling the motion trajectory surface of the rolling component 3 and combining the mechanical properties of the elastic element, the target nonlinear force can be personalized (precisely) customized in two-dimensional space.

[0019] Specifically, in existing nonlinear force design, the introduction of nonlinear forces mainly relies on permanent magnets, geometrically nonlinear structures (such as buckling beams or buckling plates), cylindrical cam-roller-spring mechanisms, combined springs, and nonlinear disc springs. However, these methods generally suffer from the following problems: (1) In existing nonlinear force design methods, nonlinear forces are usually introduced through a pre-defined function form. This design method has certain limitations in terms of motion dimension and flexibility of function expression. Specifically, the nonlinear force is restricted in terms of the direction of action and the form of the nonlinear force function. The main problems include the following: ① The design of nonlinear forces in a single direction: the nonlinear forces introduced by the existing methods are often limited to the form of odd function polynomials (as shown in Equation (1)), and can only design nonlinear forces in a single direction, and cannot achieve nonlinear force output in multiple directions.

[0020] (1); In the formula, For the introduction of nonlinear forces; For displacement; For nonlinear stiffness coefficients, i = 1 ~ n; ② The form of nonlinear force function is limited. In the existing technology, the expression of nonlinear force is mostly based on simple polynomial model. This method can only realize the design of nonlinear force in a single direction and lacks support for complex nonlinear force forms, such as piecewise nonlinear force or asymmetric nonlinear force. In other words, it is difficult to realize asymmetric nonlinear force, with odd and even function components coexisting, as shown in equation (2); piecewise nonlinear force and other complex objective function forms cannot meet the diverse needs for nonlinear force characteristics in multiple scenarios.

[0021] (2); In this model, for Nonlinear force in direction, The coefficient of the nonlinear force. For displacement.

[0022] (2) In existing nonlinear force design methods, the nonlinear stiffness parameters of each order are usually indirectly determined by the structural geometry or material properties. It is difficult to independently and accurately set the nonlinear stiffness coefficients during the design process, and the values ​​of each order of nonlinear stiffness parameters cannot be arbitrarily specified according to the target mechanical properties. At the same time, existing solutions usually only introduce nonlinear forces in a single direction of motion, making it difficult to achieve accurate construction and coordinated control of nonlinear forces in two directions of motion at the same time, thus limiting their application in two-dimensional or multi-degree-of-freedom systems.

[0023] Based on in-depth analysis and long-term engineering practice of existing nonlinear force design methods, the inventors discovered that current technologies generally rely on forward design methods to introduce nonlinear forces. The typical design process is as follows: first, determine the specific structural device and its parameters that generate the nonlinear force; then, establish the functional relationship between the structural parameters and the generated nonlinear force through mechanical derivation; finally, locally modify the expression of the nonlinear force by adjusting some structural parameters. This method is difficult to generate arbitrary nonlinear forces, stiffness parameters are difficult to precisely customize, and it usually only allows design in a single direction, making it difficult to meet the complex requirements of refined and coordinated nonlinear force design in two-dimensional or multi-degree-of-freedom systems.

[0024] Based on the above understanding, the inventors propose a novel reverse design approach: instead of using the structural device and its parameters that introduce nonlinear forces as the starting point, they directly use the desired nonlinear force function as the design objective. This approach maps the characteristics of the target nonlinear force function in two mutually orthogonal motion directions to a spatial geometric constraint relationship with the geometric characteristics of the rolling component's trajectory surface. Furthermore, by programmably designing the curvature radius of the slide's three-dimensional contour, continuous mapping and precise control of the nonlinear force characteristics are achieved. Based on this, the inventors have constructed a "slide-rolling component-spring" mechanical realization device based on programmable design of the three-dimensional curvature radius. By establishing a functional relationship between the target nonlinear force function and the curvature radius of the slide's three-dimensional contour, the curvature of the slide is programmed, thus forming a spatial three-dimensional curved surface slide with continuously changing curvature radius. This allows the rolling component 3 to generate nonlinear forces corresponding to the target function in both motion directions, ultimately achieving precise and programmable generation of two-dimensional nonlinear forces. The specific implementation method is as follows: like Figure 1 As shown, the present invention provides a two-dimensional nonlinear force programmable generation method, including, Step S1: Respond to the request for generating a two-dimensional nonlinear force and determine the target nonlinear force function based on the request; Step S2: Based on the functional form of the target nonlinear force function, select a structure suitable for the mechanical realization device that generates the target nonlinear force in two mutually orthogonal motion directions and obtain the corresponding structural parameters; Step S3: Based on the target nonlinear force function, establish the mechanical equilibrium relationship of the mechanical realization device during the motion process, and determine the center point trajectory of the rolling component 3 in the mechanical realization device during the motion process by the mechanical equilibrium relationship, thereby obtaining the geometric expression of the motion trajectory surface of the rolling component 3; Step S4: Based on the geometric dimensions of the rolling component 3, the motion trajectory surface of the rolling component 3 is mapped equidistantly along the normal direction to establish the geometric correspondence between the motion trajectory surface of the rolling component 3 and the three-dimensional guide surface 2 of the mechanical realization device, so that the rolling component 3 fits and rolls along the three-dimensional guide surface 2 during the motion, generating nonlinear forces corresponding to the target nonlinear force function in two mutually orthogonal motion directions.

[0025] Specifically, in the implementation of this invention, firstly, in response to the request for generating two-dimensional nonlinear forces, the target nonlinear forces to be generated in two mutually orthogonal motion directions, the functional form of the corresponding target nonlinear force function, and their corresponding application requirements are clarified. Subsequently, based on the functional form of the target nonlinear force function, the structural configuration and related structural parameters of the corresponding mechanical realization device are obtained, including the arrangement relationship of the rolling component 3, the elastic element, and the three-dimensional guide surface 2. According to the target nonlinear force function, the mechanical equilibrium relationship of the mechanical realization device during the motion process is established. Through the mechanical equilibrium relationship, the force state and displacement relationship of the rolling component 3 during the motion process are derived, thereby determining the motion trajectory of the center point of the rolling component 3 in space, and further obtaining the geometric expression relationship of the motion trajectory surface of the rolling component 3. Subsequently, combining the geometric dimensions of the rolling component 3, especially the radius information of the rolling component 3, the motion trajectory surface of the rolling component 3 is equidistantly mapped along its normal direction to construct a three-dimensional guide surface 2 that fits with the rolling component 3. This enables the rolling component 3 to stably fit and roll along the three-dimensional guide surface 2 during motion, thereby generating nonlinear forces corresponding to the target nonlinear force function in two mutually orthogonal motion directions, realizing the programmable generation of two-dimensional nonlinear forces.

[0026] Furthermore, the structure of the mechanical realization device includes a nonlinear force design platform 1, a three-dimensional guide surface 2, a rolling component 3, several fixed bases, elastic elements, and a two-dimensional planar motion guiding mechanism. The nonlinear force design platform 1 is connected to the first fixed base through a two-dimensional planar motion guide mechanism, and moves independently in a straight line along two mutually orthogonal motion directions, including a first motion direction and a second motion direction. The nonlinear force design platform 1 is connected to the second fixed base along the first motion direction and the second motion direction through corresponding support springs. The three-dimensional guide surface 2 is a spatial curvature surface, which is fixedly set on the side of the nonlinear force design platform 1 near the rolling component 3; The rolling component 3 is connected to the linear motion component moving along the third motion direction through the connecting structure 4. The linear motion component is connected to the third fixed base through the compression spring 7 set along the third motion direction, so that the rolling component 3 contacts the spatial curvature surface and rolls along the spatial curvature surface. The rolling component 3 includes a rolling body and its support, wherein the third motion direction is orthogonal to the first motion direction and the second motion direction respectively.

[0027] Specifically, such as Figure 2 As shown, Figure 2 This is a schematic diagram of the mechanical implementation device in an embodiment of the present invention, wherein, Figure 2 (a) in the figure is the xy view of the mechanical realization device. Figure 2In the diagram (b), the xz view is defined as follows: for ease of explanation, in this embodiment, the x-axis corresponds to the third motion direction, the y-axis corresponds to the second motion direction, and the z-axis corresponds to the first motion direction.

[0028] In the mechanical implementation device of this embodiment, the nonlinear force design platform 1 can move in a straight line in two mutually orthogonal directions, y and z, through a two-dimensional planar motion guide mechanism. The two-dimensional planar motion guide mechanism can be implemented using existing mature linear guide technology, such as consisting of two sets of mutually orthogonal linear guide rails, linear bearings, or equivalent linear guide components. Its specific structural form does not constitute the focus of improvement of this invention, so it will not be described in detail here. The three-dimensional guide surface 2 is a three-dimensional slide with a spatial curvature radius to be designed, i.e., a spatial curvature surface. It is fixedly installed on the nonlinear force design platform 1 and moves synchronously with the nonlinear force design platform 1. The rolling component 3 is specifically a universal ball or bullseye bearing, used to contact the three-dimensional guide surface 2 and roll along the three-dimensional guide surface 2. The connecting structure 4 is a support structure, with one end fixedly connected to the rolling component 3 and the other end fixedly connected to the moving part 5 of the linear motion component. The linear motion component includes the moving part 5 and the stationary part 6 of the linear motion component, such as a linear bearing, a linear guide slider, etc. One end of the pre-compression spring 7 is fixed to the fixed base, and the other end is connected to the moving part 5 of the linear motion component. One end of the first support spring 8 in the y direction is fixed, and the other end is connected to the nonlinear force design platform 1. The second support spring 9 in the z direction is fixed at one end and connected to the nonlinear force design platform 1 at the other end.

[0029] At the same time, such as Figure 3 , 4 As shown, Figure 3 This is a schematic diagram illustrating the working principle of the mechanical realization device from the xy-angle perspective. Figure 3 (a) in the diagram is the initial state diagram. Figure 3 (b) in the diagram represents the downward motion state. Figure 3 (c) in the diagram represents the upward motion state; Figure 4 This is a schematic diagram illustrating the working principle of the mechanical realization device from the xz perspective. Figure 4 (a) in the diagram is the initial state diagram. Figure 4 (b) in the diagram represents the downward motion state. Figure 4 (c) in the diagram represents the upward motion state; exist Figure 3 In the initial state, i.e., the initial equilibrium state (such as...) Figure 3 As shown in (a), the pre-compression spring 7 is in a preset compression state, the nonlinear force design platform 1 is in an equilibrium position, and the rolling component 3 is located at the center of the three-dimensional guide surface 2. At this time, the normal force generated by the rolling component 3 on the three-dimensional guide surface 2 only acts along the x-axis, denoted as _____. When the nonlinear force design platform 1 undergoes displacement along the y-direction (e.g.) Figure 3 (b) As shown, the contact position between the rolling member 3 and the three-dimensional guide surface 2 changes, thereby generating a component force along the y-axis on the three-dimensional guide surface 2, denoted as By programming the radius of curvature of the spatial surface of the three-dimensional guide surface 2 projected onto the xoy plane, the component force along the y-axis exerted by the rolling component 3 on the three-dimensional guide surface 2 can be precisely controlled. This component force, combined with the supporting force generated by the first supporting spring 8 in the y-direction, is denoted as... These forces work together on the nonlinear force design platform 1, thereby enabling the nonlinear force design platform 1 to generate the required customized nonlinear force in the y-direction.

[0030] Similarly, in Figure 4 In the process, when the nonlinear force design platform 1 moves linearly along the z-axis, the radius of curvature of the spatial surface of the three-dimensional guide surface 2 projected onto the xoz plane is precisely programmed and designed. This allows the resultant force on the nonlinear force design platform 1 in the z-direction, including the component force along the z-axis generated by the three-dimensional guide surface 2, denoted as […]. The supporting force generated by the second supporting spring 9 in the z direction is denoted as This generates customized nonlinear forces to meet demand.

[0031] Furthermore, the structural parameters include the stiffness and pre-compression of the compression spring 7, the stiffness of the support springs in the first and second motion directions, and the geometric dimensions of the rolling member 3.

[0032] Further, step S2 includes, The structure of the mechanical implementation device is determined based on the functional form of the target nonlinear force function. When the mechanical implementation device is in its initial equilibrium state, the center point of the rolling component 3, which maintains contact with the three-dimensional guide surface 2, is taken as the origin O. A three-dimensional rectangular coordinate system is established along the x-axis, y-axis, and z-axis, respectively, along the third motion direction, the second motion direction, and the first motion direction. The function form is a polynomial or piecewise nonlinear force function. Specifically, according to user requirements, it is assumed that the target nonlinear force to be generated in the y-axis direction is... The target nonlinear force to be generated in the z-axis direction is The spatial contour of the corresponding three-dimensional guide surface 2 is determined by the function The above parameters are the parameters to be designed, among which, and Design objectives for nonlinear forces, Depend on and The functional form and the relationship between the number of adoptions are determined.

[0033] And such Figure 5As shown, based on the established three-dimensional rectangular coordinate system, it can be confirmed that during the rolling process of the rolling component 3 along the three-dimensional guide surface 2, the displacement changes of the center point of the rolling component 3 in the y-axis and z-axis directions together constitute a spatial surface. This spatial surface is used to characterize the motion trajectory of the center point of the rolling component 3, and is denoted as ; Furthermore, in step S3, it is assumed that the nonlinear force to be designed in the y-direction is... The nonlinear force to be designed in the z-direction is The geometric expression of the trajectory surface of the center point of the rolling element in rolling component 3 is shown in equation (3). (3) in, Here is the geometric expression for the surface of the motion trajectory of the rolling component 3. and These are the target nonlinear force functions in the second and first motion directions, respectively. and The stiffness of the supporting springs is respectively determined in the second and first directions of motion. and Displacement in the second direction of motion and the first direction of motion, To compress the stiffness of spring 7, This is the pre-compression amount of the compression spring 7.

[0034] Further, step S4 includes, Step S41: Based on the obtained motion trajectory surface of the rolling component 3 Obtain the partial derivatives of the second motion direction and the first motion direction. and These are used to characterize the slope changes of the trajectory surface of the center point of the rolling component 3 in the second and first motion directions, respectively, and to determine the normal direction of the trajectory surface of the rolling component 3 at any point. These are the displacement coordinates of the center point of the rolling component 3 in the second and first motion directions, respectively. For partial derivatives, Here is the geometric expression for the surface of the motion trajectory of the rolling component 3; Step S42: Obtain the radius of the rolling member 3 based on its geometric dimensions. And along the normal direction of the motion trajectory surface of the rolling member 3, according to the radius Equidistant offset is performed to obtain the spatial positional relationship between the motion trajectory surface of the rolling component 3 and the three-dimensional guide surface 2 in the mechanical realization device.

[0035] Further, in step S42, according to the radius The formula for obtaining the spatial positional relationship between the motion trajectory surface of the rolling component 3 and the three-dimensional guide surface 2 in the mechanical realization device by performing equidistant offset is as follows: (4) in, These are the displacement coordinates of the center point of the rolling component 3 in the second and first motion directions, respectively. For partial derivatives, Here is the geometric expression for the surface of the motion trajectory of the rolling component 3. Let the radius of rolling member 3 be 3. and These are the position coordinates of the center point of the rolling component 3 after equidistant offset adjustment when it contacts the three-dimensional guide surface 2. is the surface function of the trajectory surface of the rolling component 3 after equidistant offset, and is the geometric expression of the three-dimensional guide surface 2.

[0036] Furthermore, step S4 also includes, Step S43: Based on the geometric expression of the three-dimensional guide surface 2, design and process the required contour surface to form a slide that conforms to the rolling component 3, and complete the assembly of each component of the mechanical realization device so that the rolling component moves along the slide and conforms to the three-dimensional guide surface 2 during the movement to generate a nonlinear force corresponding to the target nonlinear force function. Step S44: Verify the mechanical realization device through simulation or physical testing to determine the degree of conformity between the nonlinear force generated by the rolling component 3 during its rolling motion along the three-dimensional guide surface 2 and the target nonlinear force function, as well as the contact state between the rolling component 3 and the three-dimensional guide surface 2 within the predetermined motion range, so as to confirm that the mechanical realization device can meet the preset mechanical performance requirements and generate the expected nonlinear force.

[0037] Second Embodiment In the first embodiment, the overall technical solution, mechanical implementation device structure, and construction process of the three-dimensional guide surface 2 of a programmable two-dimensional nonlinear force generation method have been described in detail. To further verify the correctness of the method in terms of mechanical mechanism and its ability to realize the target nonlinear force function, this embodiment, based on the first embodiment, mathematically derives and verifies the generation process of the two-dimensional nonlinear force by establishing the system's potential energy function and mechanical equilibrium relationship, and provides a corresponding design example.

[0038] (1) To verify the correctness and self-consistency of the two-dimensional nonlinear force programmable generation method at the mechanical mechanism level, this embodiment, based on the structure and design method given in the previous embodiment, performs mathematical modeling and derivation analysis of the mechanical behavior of the mechanical realization device during the motion process from the energy perspective. By establishing the potential energy function of the system and combining it with the mechanical equilibrium relationship, the correspondence between the motion trajectory surface of the rolling component 3 and the target nonlinear force function is derived, thereby verifying that the preset nonlinear force characteristics can be accurately generated in two mutually orthogonal motion directions through the geometric design of the three-dimensional guide surface 2.

[0039] When the nonlinear force design platform 1 generates vibration displacement At that time, the potential energy of the entire system can be expressed as: (5) In the formula, Platform 1 is designed for nonlinear forces in the initial state under gravity. The static displacement of the first support spring 8 in the y-direction caused by the action includes: ; From equation (5), it can be seen that the nonlinear force applied by the rolling member to the three-dimensional guide surface 2 is... The components of the force in each direction can be expressed as follows: (6) Integrating equation (6) yields: (7) Substituting z=0 and y=0 into equation (6) respectively, we get: (8) Integrating equation (8) yields: (9) Substituting equation (9) into equation (7), we get: (10) From equation (10), we can obtain: (11) Equation (11) and Equation (3) are exactly the same, thus proving the correctness of the nonlinear force programmable design method proposed in the previous embodiment.

[0040] Therefore, equations (4) and (11) establish the nonlinear force that needs to be designed. With 3D guide surface 2 3D contour surface The relationship between them. In other words, the contour surface of the 3D guide surface 2 is designed through programming. It can realize any nonlinear force that needs to be designed. This enables precise design of nonlinear forces in two directions.

[0041] (2) To further illustrate the specific implementation of the two-dimensional nonlinear force programmable generation method proposed in the previous embodiment, this embodiment provides two design embodiments based on the method. Without limiting the scope of protection of this invention, this design embodiment shows the specific design process of the mechanical implementation device and the three-dimensional guide surface 2 under the condition that the target nonlinear force function is known: ① Design Example 1: Designing Polynomial Nonlinear Forces (I) Determine the expression of the two-dimensional nonlinear force function to be designed based on the application scenario. Assumption: Nonlinear forces need to be designed in the y and z directions. and All of them can be expressed as polynomial functions as shown in equation (12): (12) (II) Determine the form and structural parameters of the structure. Let the initial pre-compression amount of the pre-compression spring 7 be... Its stiffness is It adopts a linear spring structure. The stiffness of the first support spring 8 in the y-direction is... It adopts a linear spring structure. The stiffness of the second support spring 9 in the z-direction is... It adopts a wire spring structure. The radius of the rolling element of the rolling component is... It adopts a omnidirectional ball structure. The linear motion components adopt a linear-guide rail structure. The nonlinear force design platform 1, by setting two layers of linear-guide rail structure, can ensure its linear motion in both the y and z directions.

[0042] (III) Establish description Three-dimensional coordinate system of curved surface Create description The Cartesian right-hand spiral coordinate system. The origin of the coordinate system is at... The center of symmetry of the curved surface.

[0043] (IV) Establishment and and Functional relationship From equation (11), it can be seen that the trajectory of the center point of the rolling component ③ is... It can be represented as and The function.

[0044] (13) (V) Establish and Functional relationship The contour surface formed by the trajectory of the center point of the rolling component By translating each coordinate point along its normal direction by a distance r, the contour surface of slide ② can be obtained. .

[0045] (14) (15) (16) (VI) Program and design the slide rail and complete its machining to finalize the design. according to The contour surface is machined into a three-dimensional guide surface 2, the various components are assembled, and the final design is completed.

[0046] ② Design Example 2: Design of Piecewise Nonlinear Force (I) Based on the application scenario, determine the target nonlinear forces to be designed in two directions. Assuming nonlinear forces need to be designed in the y and z directions and Both can be expressed as piecewise functions, as shown in equations (17) and (18): (17) (II) Determine the form and structural parameters of the structure. Let the initial pre-compression amount of the pre-compression spring 7 be... Its stiffness is It adopts a linear spring structure. The stiffness of the first support spring 8 in the y-direction is... It adopts an air spring structure. The stiffness of the second support spring 9 in the z-direction is... It adopts an air spring structure. The radius of the rolling element of the rolling component is... It adopts a bullseye bearing structure. The linear motion components adopt a linear bearing structure. The nonlinear force design platform 1①, by setting two layers of linear-guide rail structure, can ensure its linear motion in both the y and z directions. (18) (III) Establish description A three-dimensional coordinate system for a curved surface.

[0048] Create description The Cartesian right-hand spiral coordinate system. The origin of the coordinate system is at... The center of symmetry of the curved surface.

[0049] (IV) Establishment and and The functional relationship.

[0050] From equation (11), it can be seen that the trajectory of the center point of the rolling component is... It can be represented as and The function.

[0051] (19) in , , , (V) Establish and The functional relationship.

[0052] The contour surface formed by the trajectory of the center point of the rolling component By translating each coordinate point along its normal direction by a distance r, the contour surface of the three-dimensional guide surface 2 can be obtained. .

[0053] (20) (VI) Program and design the slide surface and complete the machining and assembly to complete the final design.

[0054] according to The contour surface is machined into a three-dimensional guide surface 2, the various components are assembled, and the final design is completed.

[0055] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Many modifications and personalized choices of implementation methods can be made based on the content of this specification, including but not limited to different demodulation methods, different error correction and detection coding methods, and different segment arrangements. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A programmable method for generating two-dimensional nonlinear forces, characterized in that, include, Step S1: Respond to the request for generating a two-dimensional nonlinear force, and determine the target nonlinear force function based on the request; Step S2: Based on the functional form of the target nonlinear force function, select a structure suitable for the mechanical realization device that generates the target nonlinear force in two mutually orthogonal motion directions and obtain the corresponding structural parameters; Step S3: Based on the target nonlinear force function, establish the mechanical equilibrium relationship of the mechanical realization device during the motion process, and determine the center point trajectory of the rolling component in the mechanical realization device during the motion process by the mechanical equilibrium relationship, thereby obtaining the geometric expression of the motion trajectory surface of the rolling component; Step S4: Based on the geometric dimensions of the rolling component, the motion trajectory surface of the rolling component is equidistantly mapped along the normal direction to establish a geometric correspondence between the motion trajectory surface of the rolling component and the three-dimensional guide surface of the mechanical realization device, so that the rolling component fits and rolls along the three-dimensional guide surface during the motion, generating a nonlinear force corresponding to the target nonlinear force function in the two mutually orthogonal motion directions.

2. The two-dimensional nonlinear force programmable generation method according to claim 1, characterized in that, The structure of the mechanical implementation device includes a nonlinear force design platform, the three-dimensional guide surface, the rolling component, several fixed bases, elastic elements, and a two-dimensional planar motion guiding mechanism. The nonlinear force design platform is connected to the first fixed base through the two-dimensional planar motion guide mechanism, and moves independently in a straight line along the two mutually orthogonal motion directions, including a first motion direction and a second motion direction. The nonlinear force design platform is connected to the second fixed base along the first motion direction and the second motion direction through corresponding support springs. The three-dimensional guide surface is a spatial curvature surface, which is fixedly set on the side of the nonlinear force design platform near the rolling component; The rolling component is connected to a linear motion component moving along a third motion direction via a connecting structure. The linear motion component is connected to a third fixed base via a compression spring arranged along the third motion direction, so that the rolling component contacts the spatial curvature surface and rolls along the spatial curvature surface. The rolling component includes a rolling element and a support member, wherein the third motion direction is orthogonal to the first motion direction and the second motion direction, respectively.

3. The two-dimensional nonlinear force programmable generation method according to claim 2, characterized in that, The structural parameters include the stiffness and pre-compression of the compression spring, the stiffness of the support spring in the first and second motion directions, and the geometric dimensions of the rolling member.

4. The two-dimensional nonlinear force programmable generation method according to claim 3, characterized in that, Step S2 includes, The structure of the mechanical realization device is determined based on the functional form of the target nonlinear force function. When the mechanical realization device is in the initial equilibrium state, the center point of the rolling component that keeps in contact with the three-dimensional guide surface is the origin O of the coordinate system. A three-dimensional rectangular coordinate system is established by drawing x-axis, y-axis and z-axis along the third motion direction, the second motion direction and the first motion direction, respectively. The functional form is a polynomial or piecewise nonlinear force function.

5. The two-dimensional nonlinear force programmable generation method according to claim 3, characterized in that, In step S3, the formula for the geometric expression of the motion trajectory surface of the rolling component is: ； in, The geometric expression for the surface of the motion trajectory of the rolling component. and These are the target nonlinear force functions in the second motion direction and the first motion direction, respectively. and The stiffness of the support spring in the second direction of motion and the first direction of motion are respectively. and Displacement in the second direction of motion and the first direction of motion, The stiffness of the compression spring. This is the pre-compression amount of the compression spring.

6. The two-dimensional nonlinear force programmable generation method according to claim 5, characterized in that, Step S4 includes, Step S41: Based on the obtained motion trajectory surface of the rolling component Obtain the partial derivatives of the second motion direction and the first motion direction. and These are used to characterize the slope changes of the trajectory surface of the center point of the rolling component in the second motion direction and the first motion direction, respectively, and to determine the normal direction of the trajectory surface of the rolling component at any point. These are the displacement coordinates of the center point of the rolling component in the second motion direction and the first motion direction, respectively. For partial derivatives, The geometric expression for the surface of the motion trajectory of the rolling component; Step S42: Obtain the radius of the rolling member based on its geometric dimensions. And along the normal direction of the trajectory surface of the rolling member, according to the radius The equidistant offset is performed to obtain the spatial positional relationship between the motion trajectory surface of the rolling component and the three-dimensional guide surface in the mechanical realization device.

7. The two-dimensional nonlinear force programmable generation method according to claim 6, characterized in that, In step S42, according to the radius The formula for obtaining the spatial positional relationship between the rolling component's motion trajectory surface and the three-dimensional guide surface in the mechanical realization device by performing the equidistant offset is as follows: ; in, These are the displacement coordinates of the center point of the rolling component in the second motion direction and the first motion direction, respectively. For partial derivatives, The geometric expression for the surface of the motion trajectory of the rolling component. The radius of the rolling member. and The coordinates of the center point of the rolling component after the equidistant offset adjustment are given when the rolling component is in contact with the three-dimensional guide surface. The surface function of the rolling component's motion trajectory surface after the equidistant offset is the geometric expression of the three-dimensional guide surface.

8. The two-dimensional nonlinear force programmable generation method according to claim 6, characterized in that, Step S4 also includes, Step S43: Based on the geometric expression of the three-dimensional guide surface, design and process the required contour surface to form a slide that conforms to the rolling component, and complete the assembly of each component of the mechanical realization device, so that the rolling component moves along the slide and conforms to the three-dimensional guide surface during the movement to generate the nonlinear force corresponding to the target nonlinear force function; Step S44: Verify the mechanical implementation device through simulation or physical testing to determine the degree of conformity between the nonlinear force generated by the rolling component during its movement along the three-dimensional guide surface and the target nonlinear force function, as well as the contact state between the rolling component and the three-dimensional guide surface within a predetermined range of motion, so as to confirm that the mechanical implementation device can meet the preset mechanical performance requirements and generate the expected nonlinear force.

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