Nonlinear tuned mass damper optimization design method and system

Abstract

The application provides a nonlinear tuning inertial mass damper optimization design method and system, which comprises the following steps: first, determining the target inertance coefficient and processing the ball screw inertance container, and then carrying out a dynamic test on the ball screw inertance container to obtain nonlinear response data; then, based on the physical force transmission path of two sections in series, a mechanical model containing four nonlinear effects is constructed, and the model parameters are identified based on the test data; then, the nonlinear mechanical model is converted into an equivalent linear model of three elements in parallel according to the principles of equivalent inertial force, equivalent elastic force and single cycle energy dissipation; finally, the tuning frequency and tuning damping ratio of the TMDI are optimized based on the equivalent linear model, and the tuning spring stiffness and tuning damping coefficient are obtained by deducting the equivalent stiffness and equivalent damping of the inertance container itself, and the iteration is carried out until the accuracy requirement is met through simulation or test verification, which can overcome the defect that the existing technology cannot quantify the nonlinear factors by generally regarding them as manufacturing errors.

Description

Technical Field

[0001] This application relates to the field of passive structural vibration control technology, specifically to an optimization design method and system for a nonlinear tuned inertial mass damper. Background Technology

[0002] An inertial container is an inertial element with two endpoints, where the relative acceleration between its two ends is proportional to the output force, with the proportionality coefficient being the capacitive inertial coefficient b. Compared to traditional mass elements, inertial containers can provide hundreds or even thousands of times the equivalent inertial mass without significantly increasing the physical mass, thus having broad application prospects in the field of structural vibration control. Among them, the ball-screw inertial container is the most widely used and technologically mature form. Its basic working principle is as follows: when both ends are subjected to axial force, the relative translational motion is converted into the rotational motion of the rotating body through the ball screw pair, thereby utilizing the rotational inertia of the flywheel and screw to generate an inertial effect. This type of inertial container has advantages such as high transmission efficiency (>90%), low friction loss, ease of processing, and compact structure, and has been applied in vehicle suspension systems, mechanical steering compensators, and helicopter vibration isolation systems.

[0003] Currently, the tuning parameters (stiffness and damping) of TMDI are generally designed based on ideal linear inertial container mechanical models, such as Den Hartog's fixed-point theory. optimization, Through optimization and other methods, numerous experimental studies have shown that actual ball screw inertial dampers exhibit significant nonlinear dynamic behavior under wide-bandwidth, variable-amplitude excitation. Due to nonlinear factors, tuned inertial mass dampers designed based on ideal linear models often deviate from the optimal tuning state in actual operation, resulting in a significant decrease in control efficiency. Summary of the Invention

[0004] This application provides a method and system for optimizing the design of a nonlinear tuned inertial mass damper, which overcomes the shortcomings of existing technologies that categorize nonlinear factors as manufacturing errors without quantification, and provides a physically accurate model basis for subsequent tuning design.

[0005] A first aspect of this application provides an optimization design method for a nonlinear tuned inertial mass damper, the method comprising: Obtain the key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-compression ratio; Design and manufacture the ball screw inertia container according to the target inertia coefficient; A dynamic test was conducted on the ball screw inertia container to obtain nonlinear response data; A nonlinear mechanical model of the ball screw inertia container is constructed, and the model parameters are identified based on the nonlinear response data; The nonlinear mechanical model is transformed into an equivalent linear model of three parallel elements; The tuning parameters of the tuned inertial mass damper are optimized based on the equivalent linear model. The control effect is verified by simulation or experiment. If the requirements are not met, the parameter identification step is returned for iteration.

[0006] In one possible implementation, the step of conducting a dynamic test on the ball screw inertia container to obtain nonlinear response data includes: Using a sinusoidal displacement loading method, with the modal frequency of the controlled structure as the fixed loading frequency, different loading displacement amplitudes were set to test the influence of the loading amplitude on the nonlinearity of the inertial container. Based on a fixed loading displacement amplitude, different loading frequencies were set to test the effect of loading frequency on the nonlinearity of the inertial container. Record the displacement time history and reaction time history under all loading conditions. For each loading condition, record the data results for ten or more cycles to obtain nonlinear response data.

[0007] In one possible implementation, the construction of the nonlinear mechanical model for the ball screw inertia container includes: Based on the premise that the preloaded nut eliminates the clearance, the nonlinear effects are identified as friction, screw damping, screw stiffness, and nonlinear inertial coefficient. The physical force transmission path of the ball screw inertia container is divided into two series structures: the transmission pair segment and the screw body segment. Correspondingly, the nut end node, the intermediate node where the screw and flywheel intersect, and the flywheel end node are defined. For the screw body segment between the intermediate node and the nut end node, construct the force output model of the screw body segment; For the transmission pair between the flywheel end node and the intermediate node, a force output model of the transmission pair is constructed; Based on the principle that the forces on the two connected sections are equal, the output force model of the screw body section and the output force model of the transmission pair section are combined to obtain the nonlinear mechanical model of the ball screw inertia container.

[0008] In one possible implementation, constructing the output model of the screw body segment between the intermediate node and the nut end node includes: Using the relative displacement between the intermediate node and the nut end node as input, a screw stiffness force model is constructed based on Hooke's law, where the screw stiffness force is proportional to the relative displacement between the two nodes. Using the relative velocity between the middle node and the nut end node as input, a screw damping force model is constructed based on the viscous damping law. The screw damping force is proportional to the relative velocity between the two nodes. The screw stiffness force model and the screw damping force model are arranged in parallel, and the relative motions at both ends of the two are consistent. The total output force of the screw body section is the superposition of the screw stiffness force and the screw damping force, thus obtaining the output force model of the screw body section.

[0009] In one possible implementation, constructing the output model of the transmission pair between the flywheel end node and the intermediate node includes: Using the relative acceleration between the flywheel end nodes and the intermediate nodes as input, and based on the constitutive definition that the output force of the inertial container is proportional to the relative acceleration, an equivalent inertial capacitive force model is constructed. A friction force model is constructed based on Coulomb's law of friction, where the amplitude of the friction force is constant and its direction is opposite to the relative velocity direction between the flywheel end node and the middle node. The equivalent inertial force model and the friction force model are arranged in parallel, with their two ends moving in the same direction. The total output force of the transmission pair is the superposition of the equivalent inertial force and the friction force, thus obtaining the output force model of the transmission pair.

[0010] In one possible implementation, the step of identifying model parameters based on the nonlinear response data includes: The screw stiffness, screw damping, and equivalent inertia coefficient are set to constants, and the friction coefficient is set to be a function of the loading frequency. The objective function is constructed with the goal of minimizing the cumulative relative error between the reaction force output by the nonlinear mechanical model and the experimentally measured reaction force. The objective function is optimized and solved to identify the parameters of each model. The curve of friction coefficient as a function of loading frequency is obtained by polynomial fitting.

[0011] In one possible implementation, transforming the nonlinear mechanical model into an equivalent linear model of three parallel elements includes: Based on the principles of equivalent inertial force, equivalent elastic force, and equivalent single-cycle energy consumption under simple harmonic excitation, the nonlinear mechanical model is subjected to harmonic linearization. The equivalent inertia coefficient is taken as the nonlinear inertia coefficient obtained by parameter identification; The elastic component that is in phase with the displacement is extracted from the test force signal, and the equivalent stiffness coefficient is identified. Based on the principle that the energy consumption of hysteresis in a single test cycle is equal, the equivalent damping coefficient is calculated. An equivalent linear model consisting of three parallel elements—equivalent inertial coefficient, equivalent damping coefficient, and equivalent stiffness coefficient—is used to generate external forces, which are the superposition of inertial force, damping force, and elastic force.

[0012] In one possible implementation, the optimization design of the tuning parameters of the tuned inertial mass damper based on the equivalent linear model includes: Using the ratio of the equivalent inertia coefficient to the tuning mass as the equivalent inertia ratio, and combining it with the tuning mass ratio, the optimal tuning frequency and optimal tuning damping ratio of the nonlinear TMDI are obtained by correction. The total required stiffness of the system is calculated based on the optimal tuning frequency. The equivalent stiffness coefficient of the inertial container is then deducted to obtain the design stiffness of the tuning spring. The total required damping of the system is calculated based on the optimal tuned damping ratio. The equivalent damping coefficient of the inertial container is then deducted to obtain the design damping of the tuned damper.

[0013] In one possible implementation, the step of verifying the control effect through simulation or experimentation, and if the requirements are not met, returning to the parameter identification step for iteration, includes: Simulation calculations were performed using a nonlinear mechanical model after parameter identification, and the control effects of equivalent linearization design and nonlinear simulation were compared. If the vibration reduction efficiency of the equivalent linearized design is lower than that of the nonlinear model, then return to re-identify the model parameters or adjust the equivalent linearization method until the accuracy requirements are met.

[0014] This example provides a method and system for optimizing the design of a nonlinear tuned inertial mass damper (TMDI). First, the target inertial capacity coefficient is calculated based on the controlled structural parameters, and a ball screw inertial container is manufactured. Then, dynamic tests with varying frequency and amplitude are conducted on the ball screw inertial container to obtain nonlinear response data. Next, based on the physical force transmission path of the ball screw inertial container's transmission pair and the screw body connected in series, a lumped parameter mechanical model is constructed, incorporating four nonlinear effects: friction, screw damping, screw stiffness, and nonlinear inertial capacity coefficient. The model parameters are then identified based on experimental data. Following the principles of equivalent inertial force, equivalent elastic force, and equivalent single-cycle energy consumption, the nonlinear mechanical model is transformed into an equivalent linear model with three parallel elements. Finally, the tuning frequency and tuning damping ratio of the TMDI are optimized based on the equivalent linear model. The tuning spring stiffness and tuning damping coefficient are corrected by subtracting the equivalent stiffness and damping of the inertial container itself. The process is iterated through simulation or experimentation until the accuracy requirements are met, resulting in the following beneficial effects: 1. By constructing a lumped-parameter mechanical model that includes friction, screw damping, screw stiffness, and nonlinear inertia coefficient, and identifying model parameters based on wideband, variable amplitude dynamic test data, the complex nonlinear behavior of the ball screw inertia container in the structurally sensitive frequency band is accurately characterized. This overcomes the shortcomings of existing technologies that categorize nonlinear factors as manufacturing errors and cannot quantify them, providing a physically accurate model basis for subsequent tuning design.

[0015] 2. By transforming the nonlinear mechanical model into an equivalent linear model of three parallel elements, and correcting the tuning spring stiffness and tuning damping coefficient of TMDI by deducting the equivalent stiffness and equivalent damping of the inertial container itself, engineers can directly use classical linear design formulas for parameter design. At the same time, the influence of the nonlinear additional stiffness and additional damping of the inertial container itself on the tuning state is eliminated, solving the technical problem of lack of connection between the nonlinear model and existing design theory, and making the design results accurately correspond to the actual control effect.

[0016] 3. By establishing a closed-loop design process from inertial container design and manufacturing to experimental verification, the entire design process of the inertial mass damper in this example has self-correcting capabilities. This avoids the drawbacks of traditional methods where testing, modeling, and TMDI design are separated, and designers can only rely on experience for compensation, thus improving the reliability of the design results.

[0017] A second aspect of this application provides an optimization design system for a nonlinear tuned inertial mass damper, the system comprising: The first module is used to obtain the key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-compression ratio. The second module is used to design and process the ball screw inertia container according to the target inertia coefficient. The third module is used to conduct dynamic tests on the ball screw inertial container and obtain nonlinear response data. The fourth module is used to construct a nonlinear mechanical model of the ball screw inertia container and identify model parameters based on the nonlinear response data; The fifth module is used to transform the nonlinear mechanical model into an equivalent linear model of three parallel elements; The sixth module is used to optimize the tuning parameters of the tuned inertial mass damper based on the equivalent linear model, and to verify the control effect through simulation or experiment. If the requirements are not met, the module returns to the parameter identification step for iteration.

[0018] A third aspect of this application provides a terminal including a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, wherein the memory is used to store a computer program, the computer program including program instructions, and the processor is configured to invoke the program instructions to execute the steps of the nonlinear tuned inertial mass damper optimization design method as described in the first aspect of this application.

[0019] A fourth aspect of this application provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the nonlinear tuned inertial mass damper optimization design method of the first aspect of this application.

[0020] A fifth aspect of this application provides a computer program product, comprising a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the nonlinear tuned inertial mass damper optimization design method of the first aspect of this application. The computer program product may be a software installation package. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This application provides a schematic diagram of the overall process for optimizing the design of a nonlinear tuned inertial mass damper. Figure 2 This application provides a schematic diagram of a nonlinear inertial container mechanical model for an optimized design method of a nonlinear tuned inertial mass damper, as shown in the embodiments of this application. Figure 3 This application provides an embodiment of the equivalent process of transforming the nonlinear inertial container mechanical model into an equivalent linearized model in an optimization design method for a nonlinear tuned inertial mass damper. Figure 4 This application provides a schematic diagram of the overall structure of an optimized design system for a nonlinear tuned inertial mass damper. Figure 5 This application provides a schematic diagram of the structure of a terminal. Figure label: Module 1-1, Module 2-2, Module 3-3, Module 4-4, Module 5-5, Module 6-6. Detailed Implementation

[0023] 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, and 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.

[0024] The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0025] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0026] To better understand the nonlinear tuned inertial mass damper optimization design method provided in this application embodiment, a brief introduction to the scenarios in which this method is applied is given below. The ball-screw inertial device is the most widely used and technologically mature type in engineering. Its basic working principle is as follows: when both ends are subjected to axial force, the relative translational motion is converted into the rotational motion of the rotating body through the ball screw pair, thereby utilizing the rotational inertia of the flywheel and screw to generate an inertial effect. This type of inertial device has advantages such as high transmission efficiency (>90%), low friction loss, ease of processing, and compact structure, and has been applied in vehicle suspension systems, mechanical steering compensators, and helicopter vibration isolation systems.

[0027] A tuned mass damper inerter (TMDI) couples an inertial container to a tuned mass damper, connected in parallel with a spring and damper. Compared to traditional TMDs, TMDIs can significantly increase the equivalent mass ratio without significantly increasing the tuned mass, thereby improving vibration reduction and broadening the effective frequency band. In recent years, TMDIs have shown significant advantages in bridge buffeting control, high-rise building wind vibration control, and multimodal vibration reduction of wind turbine towers. However, existing TMDI design methods are almost entirely based on an ideal linear inertial container model, assuming that the reaction forces at both ends of the inertial container strictly satisfy F=b·a (where a is the relative acceleration and b is the target inertial coefficient). This assumption ignores the complex nonlinear behavior of actual ball screw inertial containers under wide-bandwidth, variable-amplitude excitation, leading to a significant deviation between the design results and the actual control effect.

[0028] Currently, the tuning parameters (stiffness and damping) of TMDI are generally based on the ideal linear inertial container mechanical model (i.e., the reactions at both ends strictly satisfy...). ( For relative acceleration, Design for the target inertia coefficient, such as Den Hartog's fixed-point theory, optimization, Optimization and other methods.

[0029] However, numerous experimental studies have shown that actual ball screw inertia containers exhibit significant nonlinear dynamic behavior under broadband, variable amplitude excitation, mainly including: 1. Nonlinearity of mechanical friction: Contact friction between balls, nuts, and screw guides, including the Stribeck effect, Coulomb friction, viscous friction, and rolling friction. Especially under low acceleration and low frequency excitation, the friction effect may even dominate the dynamic response of the device (manifested as a horizontal band in the force-displacement curve and a sawtooth pattern in the force time history).

[0030] 2. Screw elastic effect: Under the action of inertial force, shear force and guide rail friction, the screw will undergo compression and elongation deformation, introducing elastic stiffness and damping, which is manifested as the negative stiffness characteristics and hysteresis loop of the force-displacement curve.

[0031] 3. Gap effect: There may be non-contact gaps between the balls, nuts, and screws, causing a lag in external force. Although pre-tightening can partially eliminate this, it cannot be ignored under certain operating conditions.

[0032] 4. Torque fluctuation and parasitic motion: Geometric defects in ball screws may cause additional torque fluctuations. The mechanism is complex and difficult to model accurately. Its nonlinearity is usually incorporated into the elastic effect for simulation.

[0033] The aforementioned nonlinear factors cause the tuned inertial mass damper designed based on the ideal linear model to often deviate from the optimal tuning state in actual operation, resulting in a significant decrease in control efficiency.

[0034] The optimization design method for nonlinear tuned inertial mass dampers is applied to the optimization design system of nonlinear tuned inertial mass dampers. Figure 1 A schematic diagram illustrating the overall flow of an optimization design method for a nonlinear tuned inertial mass damper is shown. Figure 1 As shown, it includes: S1. Obtain the key parameters of the controlled structure, determine the target inertia-mass ratio and mass ratio, and calculate the target inertia-capacity coefficient.

[0035] Among them, the key parameters of the controlled structure include the structural modal frequencies. Structural modal quality Structural modal damping ratio The inertia ratio of the target and mass ratio .

[0036] Specifically, inertia-mass ratio The calculation formula is:

[0037] In the formula, The ratio of the target inertia coefficient to the TMDI tuning quality. The target inertia coefficient, For TMDI tuning quality.

[0038] Furthermore, quality ratio The calculation formula is:

[0039] In the formula, For TMDI mass ratio, For TMDI tuning quality, For structural modal mass.

[0040] The formula for calculating the target inertia coefficient is as follows:

[0041] Furthermore, in this example, the design objectives of the ball screw inertia container also include constraints: Installation space (such as the internal height of the main beam) and maximum allowable static deformation of the spring, wherein the formula for calculating the static deformation of the spring is as follows:

[0042] In the formula, This is the static deformation length of the spring. This is the ratio of the inertia coefficient to the TMDI tuning quality. It is the square of the modal frequency of the vibrating bridge.

[0043] S2. Design and process the ball screw inertia container according to the target inertia coefficient.

[0044] Based on the theoretically calculated target inertia coefficient, a ball screw inertia container is designed and manufactured. The inertia container structure consists of a screw, ball nuts, bearings, flywheel, and outer frame.

[0045] Among them, the screw and flywheel provide the inertial effect.

[0046] The key design formula provides a rotational inertia component consisting of a flywheel and a screw, with a target inertia coefficient. As shown below:

[0047] In the formula, Let be the moment of inertia of a rotating object; For lead; These are the physical masses of the flywheel and the screw, respectively. These are the rotation radii of the flywheel and the screw, respectively.

[0048] S3. Conduct a dynamic test on the ball screw inertia container to obtain nonlinear response data.

[0049] Step S3 includes the following sub-steps: S301. Using a sinusoidal displacement loading method, with the modal frequency of the controlled structure as the fixed loading frequency, different loading displacement amplitudes are set to test the influence of the loading amplitude on the nonlinearity of the inertial container.

[0050] S302. Based on a fixed loading displacement amplitude, set different loading frequencies and test the effect of loading frequency on the nonlinearity of the inertial container.

[0051] S303. Record the displacement time history and reaction time history under all loading conditions. Record the data results for ten or more cycles for each loading condition to obtain nonlinear response data.

[0052] S4. Construct a nonlinear mechanical model of the ball screw inertia container and identify the model parameters based on the nonlinear response data.

[0053] In step S4, constructing the nonlinear mechanical model of the ball screw inertia container includes the following sub-steps: S401. Based on the premise that the preloaded nut eliminates the clearance, the nonlinear effects are determined as friction, screw damping, screw stiffness, and nonlinear inertial coefficient.

[0054] In this example, the basic assumption is that the effect of inertial capacity clearance is ignored (clearance is eliminated by pre-tightening the nut). The nonlinear influencing factors mainly include friction, screw damping, screw stiffness, and nonlinear inertial capacity coefficient.

[0055] S402. The physical force transmission path of the ball screw inertia container is divided into two series structures: the transmission pair segment and the screw body segment. The corresponding nodes are defined as the nut end node, the intermediate node where the screw and flywheel intersect, and the flywheel end node.

[0056] S403. For the screw body segment between the intermediate node and the nut end node, construct the output force model of the screw body segment.

[0057] The nonlinear mechanical model of the inertial container constructed in this example is as follows: Figure 2 As shown, Figure 2 A schematic diagram of the nonlinear inertial container mechanical model is shown in the figure, illustrating the optimization design method for a nonlinear tuned inertial mass damper. Indicates the coefficient of friction; Indicates the nonlinear inertia coefficient; Indicates screw stiffness; Indicates screw damping. This represents the absolute displacement of the flywheel end node (lower end point). This represents the absolute displacement of the intermediate node. This represents the absolute displacement of the nut end node (upper end point).

[0058] Step S403 includes the following sub-steps: S4031. Using the relative displacement between the intermediate node and the nut end node as input, construct a screw stiffness force model based on Hooke's law. The screw stiffness force is proportional to the relative displacement between the two nodes.

[0059] S4032. Using the relative velocity between the intermediate node and the nut end node as input, construct a screw damping force model based on the viscous damping law. The screw damping force is proportional to the relative velocity between the two nodes.

[0060] S4033. Arrange the screw stiffness force model and the screw damping force model in parallel, with the two ends moving in the same direction. The total output force of the screw body section is the superposition of the screw stiffness force and the screw damping force, thus obtaining the output force model of the screw body section.

[0061] Among them, screw stiffness The force expression is:

[0062] Among them, screw damping The force expression is:

[0063] Among them, the friction output of the inertial container The force expression is:

[0064] In the formula, , , These are equivalent screw stiffness, screw damping, and inertial container friction output, respectively. For screw stiffness; For screw damping; The coefficient of friction; This represents the absolute displacement of the intermediate node; This represents the absolute displacement of the nut end node (upper end point); The absolute velocity of the intermediate node; The absolute velocity of the nut end node (upper end point); This is the absolute speed of the flywheel end node (lower end point).

[0065] S404. Construct a force output model for the transmission pair between the flywheel end node and the intermediate node.

[0066] Step S404 includes the following sub-steps: S4041. Using the relative acceleration between the flywheel end node and the intermediate node as input, and based on the constitutive definition that the output force of the inertial container is proportional to the relative acceleration, construct an equivalent inertial container force model.

[0067] S4042. Construct a friction force model based on Coulomb's friction law. The amplitude of the friction force is constant, and its direction is opposite to the relative velocity direction between the flywheel end node and the middle node.

[0068] S4043. Arrange the equivalent inertial compressive force model and the frictional force model in parallel, with the two ends moving in the same direction. The total output force of the transmission pair is the superposition of the equivalent inertial compressive force and the frictional force, thus obtaining the output force model of the transmission pair.

[0069] S405. Based on the principle that the forces on the two connected sections are equal, the output force model of the screw body section and the output force model of the transmission pair section are combined to obtain the nonlinear mechanical model of the ball screw inertia container.

[0070] The nonlinear mechanical model expression for the ball screw inertia container is as follows:

[0071] In the formula, The coefficient of friction; The inertia coefficient is a nonlinear coefficient. For screw stiffness; For screw damping; Force is applied to the end points of the inertial container; This is the absolute acceleration at the flywheel end node (lower end point); The absolute acceleration of the intermediate node; It is a symbolic function; The absolute velocity of the flywheel end node (lower end point); The absolute velocity of the intermediate node; This represents the absolute displacement of the intermediate node; This represents the absolute displacement of the nut end node (upper end point); The absolute velocity of the intermediate node; This is the absolute velocity of the nut end node (upper end point).

[0072] In step S4, the identification of model parameters based on the nonlinear response data includes the following sub-steps: S406. Set the screw stiffness, screw damping, and equivalent inertia coefficient to constants, and set the friction coefficient to a function of the loading frequency.

[0073] S407. The objective function is constructed with the goal of minimizing the cumulative relative error between the reaction force output by the nonlinear mechanical model and the experimentally measured reaction force.

[0074] S408. Optimize and solve the objective function, identify the parameters of each model, and obtain the curve of friction coefficient changing with loading frequency through polynomial fitting.

[0075] Specifically, screw stiffness ( ) and damping ( ) is a dimensional parameter. For a ball screw inertia container, it will not change with the change of normal loading conditions, so it can be assumed to be a constant value.

[0076] Nonlinear inertia coefficient ( The inertial capacity coefficient (CCC) represents the inertial effect of the container and should be related to the ideal target inertial capacity coefficient. Since it is close to the value, it will be slightly affected by the machining precision and equipment error, so it can also be assumed to be a constant.

[0077] coefficient of friction ( The value represents the main nonlinear indices of the inertial container under different loading conditions, which change slightly with the loading frequency.

[0078] Based on the above assumptions, an objective function for the experimental data and nonlinear mechanical model in step S3 was formulated, namely the cumulative relative error between the mechanical model and the experimental data, as follows:

[0079] In the formula, and These represent the number of test conditions and the number of sampling points for each condition, respectively. and These represent the nonlinear model and the reaction force signal collected from the experiment, respectively. To test the number of working conditions, This represents the number of discrete data points measured under each test condition.

[0080] The objective function J is optimized using gradient descent or a genetic algorithm. Based on the above assumptions, , , They are constants, The frequency-dependent curve function is obtained by fitting a polynomial.

[0081] S5. Transform the nonlinear mechanical model into an equivalent linear model of three parallel elements.

[0082] Step S5 includes the following sub-steps: S501. Based on the principles of equivalent inertial force, equivalent elastic force, and equivalent single-cycle energy consumption under simple harmonic excitation, the nonlinear mechanical model is subjected to harmonic linearization.

[0083] S502, take the equivalent inertia coefficient as the nonlinear inertia coefficient obtained by parameter identification.

[0084] S503. Extract the elastic component in phase with the displacement from the test force signal and identify the equivalent stiffness coefficient.

[0085] S504. Based on the principle that the energy consumption of hysteresis in a single test cycle is equal, the equivalent damping coefficient is calculated.

[0086] S505 is an equivalent linear model consisting of three parallel elements: equivalent inertial coefficient, equivalent damping coefficient, and equivalent stiffness coefficient. The external force is the superposition of inertial force, damping force, and elastic force.

[0087] The transformation process from a nonlinear mechanical model to an equivalent linear model of three parallel elements is as follows: Figure 3 As shown, Figure 3 The diagram illustrates the equivalent process from the nonlinear inertial container mechanical model to the equivalent linearized model in an optimization design method for a nonlinear tuned inertial mass damper. The specific formulas of the equivalent linear model are shown below:

[0088] In the formula, The equivalent inertia coefficient; and These represent equivalent damping and stiffness, respectively. , , These represent equal acceleration, velocity, and displacement at both ends, respectively.

[0089] Specifically, the model conversion process requires inertia equivalence, stiffness equivalence, and damping equivalence.

[0090] In this context, inertial equivalence can be assumed to be the equivalent inertial capacity coefficient identified in the experiment. During the equivalent damping transformation process, the energy dissipation in the measured experimental data can be represented by the equivalent model damping coefficient; identifying the equivalent linear damping coefficient is sufficient. The equivalent stiffness coefficient... The equivalent stiffness coefficient is identified through experimental test results.

[0091] Specifically, the equivalent inertia coefficient is obtained directly from the parameter identification results, as shown below:

[0092] In the formula, The equivalent inertia coefficient, This is the equivalent inertia coefficient.

[0093] Furthermore, the equivalent damping coefficient is calculated by equalizing the energy dissipation of a single hysteresis loop, as shown in the following formula:

[0094] In the formula, This is the equivalent damping coefficient. The energy consumption of an inertial container for one hysteresis cycle. For a period of time, For speed, For time.

[0095] S6. Optimize the tuning parameters of the tuned inertial mass damper based on the equivalent linear model, and verify the control effect through simulation or experiment. If the requirements are not met, return to the parameter identification step for iteration.

[0096] In step S6, the optimization design of the tuning parameters of the tuned inertial mass damper based on the equivalent linear model includes the following sub-steps: S601. Using the ratio of the equivalent inertia coefficient to the tuning mass as the equivalent inertia ratio, and combining it with the tuning mass ratio, the optimal tuning frequency and optimal tuning damping ratio of the nonlinear TMDI are obtained by correction.

[0097] S602. Calculate the total required stiffness of the system based on the optimal tuning frequency, subtract the equivalent stiffness coefficient of the inertial container, and obtain the design stiffness of the tuning spring.

[0098] S603. Calculate the total required damping of the system based on the optimal tuning damping ratio, subtract the equivalent damping coefficient of the inertial container, and obtain the design damping of the tuning damper.

[0099] Specifically, in this example, the equivalent linearized ball screw inertia container is connected in parallel with a spring and a damper to form a TMDI.

[0100] Compared to TMD, the tuning principle of TMDI is that the tuning mass and inertia coefficient together replace the tuning mass and structural tuning resonance in the original TMD. Therefore, the tuning frequency and tuning damping ratio of linear TMDI can be obtained by analogy.

[0101] TMD tuning frequency ( ) and tuning damping ratio ( ) can be represented as:

[0102]

[0103] In the formula, This represents the tuning quality ratio of the TMD.

[0104] By analogy, the tuning frequency of TMDI can be obtained ( ) and tuning damping ratio ( ) can be represented as:

[0105]

[0106] In the formula, The tuning quality ratio of TMDI; The linear inertia coefficient ratio of TMDI.

[0107] After considering the nonlinearity of the inertia container, the equivalent inertia coefficient in the equivalent nonlinear model of the inertia container can be used to optimize the design of the TMDI considering the nonlinearity of the ball screw inertia container. The specific formula is as follows:

[0108]

[0109] In the formula, For the design frequency of nonlinear TMDI, The design damping ratio for nonlinear TMDI. is the equivalent inertia coefficient of the inertia container.

[0110] Considering the nonlinear stiffness in the equivalent model and nonlinear damping The optimal nonlinear TMDI tuning stiffness and damping are obtained by correction, and the specific formulas are as follows:

[0111]

[0112] In the formula, The optimal tuning stiffness for nonlinear TMDI; This is the optimal tuned damping for nonlinear TMDI.

[0113] By modifying the TMDI spring as described above ( ) and damping ( The parameters are substituted into the TMDI structural system to conduct a performance analysis of the control system.

[0114] In step S6, the control effect is verified through simulation or experiment. If the requirements are not met, the process returns to the parameter identification step for iteration. This includes the following sub-steps: S604. Simulation calculations are performed using a nonlinear mechanical model after parameter identification, and the control effect of equivalent linearization design is compared with that of nonlinear simulation.

[0115] S605. If the vibration reduction efficiency of the equivalent linearized design is lower than that of the nonlinear model, then return to re-identify the model parameters or adjust the equivalent linearization method until the accuracy requirements are met.

[0116] Specifically, a prototype is fabricated and subjected to random / harmonic excitation tests on a vibration table or a free decay structure system to measure the vibration reduction rate.

[0117] Furthermore, if the vibration reduction efficiency of the equivalent method is lower than that of the nonlinear model, then return to step S3 to re-identify the parameters or adjust the equivalent linearization method.

[0118] This example provides a method and system for optimizing the design of a nonlinear tuned inertial mass damper (TMDI). First, the target inertial capacity coefficient is calculated based on the controlled structural parameters, and a ball screw inertial container is manufactured. Then, dynamic tests with varying frequency and amplitude are conducted on the ball screw inertial container to obtain nonlinear response data. Next, based on the physical force transmission path of the ball screw inertial container's transmission pair and the screw body connected in series, a lumped parameter mechanical model is constructed, incorporating four nonlinear effects: friction, screw damping, screw stiffness, and nonlinear inertial capacity coefficient. The model parameters are then identified based on experimental data. Following the principles of equivalent inertial force, equivalent elastic force, and equivalent single-cycle energy consumption, the nonlinear mechanical model is transformed into an equivalent linear model with three parallel elements. Finally, the tuning frequency and tuning damping ratio of the TMDI are optimized based on the equivalent linear model. The tuning spring stiffness and tuning damping coefficient are corrected by subtracting the equivalent stiffness and damping of the inertial container itself. The process is iterated through simulation or experimentation until the accuracy requirements are met, resulting in the following beneficial effects: 1. By constructing a lumped-parameter mechanical model that includes friction, screw damping, screw stiffness, and nonlinear inertia coefficient, and identifying model parameters based on wideband, variable amplitude dynamic test data, the complex nonlinear behavior of the ball screw inertia container in the structurally sensitive frequency band is accurately characterized. This overcomes the shortcomings of existing technologies that categorize nonlinear factors as manufacturing errors and cannot quantify them, providing a physically accurate model basis for subsequent tuning design.

[0119] 2. By transforming the nonlinear mechanical model into an equivalent linear model of three parallel elements, and correcting the tuning spring stiffness and tuning damping coefficient of TMDI by deducting the equivalent stiffness and equivalent damping of the inertial container itself, engineers can directly use classical linear design formulas for parameter design. At the same time, the influence of the nonlinear additional stiffness and additional damping of the inertial container itself on the tuning state is eliminated, solving the technical problem of lack of connection between the nonlinear model and existing design theory, and making the design results accurately correspond to the actual control effect.

[0120] 3. By establishing a closed-loop design process from inertial container design and manufacturing to experimental verification, the entire design process of the inertial mass damper in this example has self-correcting capabilities. This avoids the drawbacks of traditional methods where testing, modeling, and TMDI design are separated, and designers can only rely on experience for compensation, thus improving the reliability of the design results.

[0121] For those consistent with the above, please refer to Figure 4 , Figure 4 This application provides a schematic diagram of the structure of an optimized design system for a nonlinear tuned inertial mass damper. For example... Figure 2 As shown, the system includes: Module 1 is used to obtain key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-capacity coefficient.

[0122] The second module 2 is used to design and process the ball screw inertia container according to the target inertia coefficient.

[0123] The third module 3 is used to conduct dynamic tests on the ball screw inertial container and obtain nonlinear response data.

[0124] Module 4 is used to construct a nonlinear mechanical model of the ball screw inertia container and identify model parameters based on the nonlinear response data.

[0125] Module 5 is used to transform the nonlinear mechanical model into an equivalent linear model of three parallel elements.

[0126] Module 6 is used to optimize the tuning parameters of the tuned inertial mass damper based on the equivalent linear model, and to verify the control effect through simulation or experiment. If the requirements are not met, the module returns to the parameter identification step for iteration.

[0127] For examples consistent with the above embodiments, please refer to... Figure 5 , Figure 5 This is a schematic diagram of the structure of a terminal provided in an embodiment of this application, such as... Figure 5 As shown, it includes a processor, an input device, an output device, and a memory, which are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions. The program includes instructions for performing the following steps. Obtain the key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-capacity coefficient.

[0128] Design and manufacture the ball screw inertia container based on the target inertia coefficient.

[0129] A dynamic test was conducted on the ball screw inertial container to obtain nonlinear response data.

[0130] A nonlinear mechanical model of the ball screw inertia container is constructed, and the model parameters are identified based on the nonlinear response data.

[0131] The nonlinear mechanical model is transformed into an equivalent linear model with three elements in parallel.

[0132] The tuning parameters of the tuned inertial mass damper are optimized based on the equivalent linear model. The control effect is verified by simulation or experiment. If the requirements are not met, the parameter identification step is returned for iteration.

[0133] The above mainly describes the solutions of the embodiments of this application from the perspective of the method execution process. It is understood that, in order to achieve the above functions, the terminal includes the corresponding hardware structure and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments provided herein, this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0134] This application embodiment can divide the terminal into functional units according to the above method example. For example, each function can be divided into a separate functional unit, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this application embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0135] This application also provides a computer storage medium storing a computer program for electronic data interchange, which causes a computer to perform some or all of the steps of any of the nonlinear tuned inertial mass damper optimization design methods described in the above method embodiments.

[0136] This application also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program that causes a computer to perform some or all of the steps of any of the nonlinear tuned inertial mass damper optimization design methods described in the above method embodiments.

[0137] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0138] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0139] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0140] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0141] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software program module.

[0142] If the integrated unit is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0143] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage device, which may include: a flash drive, a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc.

[0144] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for optimizing the design of a nonlinear tuned inertial mass damper, characterized in that, include: Obtain the key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-compression ratio; Design and manufacture the ball screw inertia container according to the target inertia coefficient; A dynamic test was conducted on the ball screw inertia container to obtain nonlinear response data; A nonlinear mechanical model of the ball screw inertia container is constructed, and the model parameters are identified based on the nonlinear response data; The nonlinear mechanical model is transformed into an equivalent linear model of three parallel elements; The tuning parameters of the tuned inertial mass damper are optimized based on the equivalent linear model. The control effect is verified by simulation or experiment. If the requirements are not met, the parameter identification step is returned for iteration.

2. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The dynamic test of the ball screw inertia container to obtain nonlinear response data includes: Using a sinusoidal displacement loading method, with the modal frequency of the controlled structure as the fixed loading frequency, different loading displacement amplitudes were set to test the influence of the loading amplitude on the nonlinearity of the inertial container. Based on a fixed loading displacement amplitude, different loading frequencies were set to test the effect of loading frequency on the nonlinearity of the inertial container. Record the displacement time history and reaction time history under all loading conditions. For each loading condition, record the data results for ten or more cycles to obtain nonlinear response data.

3. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The nonlinear mechanical model for constructing the ball screw inertia container includes: Based on the premise that the preloaded nut eliminates the clearance, the nonlinear effects are identified as friction, screw damping, screw stiffness, and nonlinear inertial coefficient. The physical force transmission path of the ball screw inertia container is divided into two series structures: the transmission pair segment and the screw body segment. Correspondingly, the nut end node, the intermediate node where the screw and flywheel intersect, and the flywheel end node are defined. For the screw body segment between the intermediate node and the nut end node, construct the force output model of the screw body segment; For the transmission pair between the flywheel end node and the intermediate node, a force output model of the transmission pair is constructed; Based on the principle that the forces on the two connected sections are equal, the output force model of the screw body section and the output force model of the transmission pair section are combined to obtain the nonlinear mechanical model of the ball screw inertia container.

4. The optimization design method for a nonlinear tuned inertial mass damper according to claim 3, characterized in that, The process of constructing a force output model for the screw body segment between the intermediate node and the nut end node includes: Using the relative displacement between the intermediate node and the nut end node as input, a screw stiffness force model is constructed based on Hooke's law, where the screw stiffness force is proportional to the relative displacement between the two nodes. Using the relative velocity between the middle node and the nut end node as input, a screw damping force model is constructed based on the viscous damping law. The screw damping force is proportional to the relative velocity between the two nodes. The screw stiffness force model and the screw damping force model are arranged in parallel, and the relative motions at both ends of the two are consistent. The total output force of the screw body section is the superposition of the screw stiffness force and the screw damping force, thus obtaining the output force model of the screw body section.

5. The optimization design method for a nonlinear tuned inertial mass damper according to claim 3, characterized in that, The aforementioned construction of a force output model for the transmission pair between the flywheel end node and the intermediate node includes: Using the relative acceleration between the flywheel end nodes and the intermediate nodes as input, and based on the constitutive definition that the output force of the inertial container is proportional to the relative acceleration, an equivalent inertial capacitive force model is constructed. A friction force model is constructed based on Coulomb's law of friction, where the amplitude of the friction force is constant and its direction is opposite to the relative velocity direction between the flywheel end node and the middle node. The equivalent inertial force model and the friction force model are arranged in parallel, with their two ends moving in the same direction. The total output force of the transmission pair is the superposition of the equivalent inertial force and the friction force, thus obtaining the output force model of the transmission pair.

6. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The method for identifying model parameters based on the nonlinear response data includes: The screw stiffness, screw damping, and equivalent inertia coefficient are set to constants, and the friction coefficient is set to be a function of the loading frequency. The objective function is constructed with the goal of minimizing the cumulative relative error between the reaction force output by the nonlinear mechanical model and the experimentally measured reaction force. The objective function is optimized and solved to identify the parameters of each model. The curve of friction coefficient as a function of loading frequency is obtained by polynomial fitting.

7. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The process of transforming the nonlinear mechanical model into an equivalent linear model with three elements in parallel includes: Based on the principles of equivalent inertial force, equivalent elastic force, and equivalent single-cycle energy consumption under simple harmonic excitation, the nonlinear mechanical model is subjected to harmonic linearization. The equivalent inertia coefficient is taken as the nonlinear inertia coefficient obtained by parameter identification; The elastic component that is in phase with the displacement is extracted from the test force signal, and the equivalent stiffness coefficient is identified. Based on the principle that the energy consumption of hysteresis in a single test cycle is equal, the equivalent damping coefficient is calculated. An equivalent linear model consisting of three parallel elements—equivalent inertial coefficient, equivalent damping coefficient, and equivalent stiffness coefficient—is used to generate external forces, which are the superposition of inertial force, damping force, and elastic force.

8. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The tuning parameters of the tuned inertial mass damper optimized based on the equivalent linear model include: Using the ratio of the equivalent inertia coefficient to the tuning mass as the equivalent inertia ratio, and combining it with the tuning mass ratio, the optimal tuning frequency and optimal tuning damping ratio of the nonlinear TMDI are obtained by correction. The total required stiffness of the system is calculated based on the optimal tuning frequency. The equivalent stiffness coefficient of the inertial container is then deducted to obtain the design stiffness of the tuning spring. The total required damping of the system is calculated based on the optimal tuned damping ratio. The equivalent damping coefficient of the inertial container is then deducted to obtain the design damping of the tuned damper.

9. The optimization design method for a nonlinear tuned inertial mass damper according to claim 1, characterized in that, The process of verifying the control effect through simulation or experimentation, and if the requirements are not met, returning to the parameter identification step for iteration, includes: Simulation calculations were performed using a nonlinear mechanical model after parameter identification, and the control effects of equivalent linearization design and nonlinear simulation were compared. If the vibration reduction efficiency of the equivalent linearized design is lower than that of the nonlinear model, then return to re-identify the model parameters or adjust the equivalent linearization method until the accuracy requirements are met.

10. A nonlinear tuned inertial mass damper optimization design system, characterized in that, include: The first module is used to obtain the key parameters of the controlled structure, determine the target inertia-to-mass ratio and mass ratio, and calculate the target inertia-to-compression ratio. The second module is used to design and process the ball screw inertia container according to the target inertia coefficient. The third module is used to conduct dynamic tests on the ball screw inertial container and obtain nonlinear response data. The fourth module is used to construct a nonlinear mechanical model of the ball screw inertia container and identify model parameters based on the nonlinear response data; The fifth module is used to transform the nonlinear mechanical model into an equivalent linear model of three parallel elements; The sixth module is used to optimize the tuning parameters of the tuned inertial mass damper based on the equivalent linear model, and to verify the control effect through simulation or experiment. If the requirements are not met, the module returns to the parameter identification step for iteration.

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