A distributed flexible load simulation system and a load simulation method

Abstract

A distributed flexible load simulation system and a load simulation method are provided, which are suitable for space vehicle flexible structure ground test, on-orbit service and space robot operation verification, and the distributed flexible load simulation system and the load simulation method are based on a modular ring guide rail and replaceable flexible slide rails. Through splicing of multiple arc guide rails, parameterized design of the flexible slide rails and distributed driving control, real simulation of a flexible load with large diameter, high bearing and reconfiguration is realized.

Description

Technical Field

[0001] This invention relates to a distributed flexible load simulation system and load simulation method, belonging to the field of space structure dynamics and ground test verification technology. Background Technology

[0002] With the widespread application of flexible structures such as large-size solar panels, deployable antennas, and space trusses, their lightweight, high aspect ratio, and deployability have significantly improved system power density and utilization efficiency. However, they have also brought about complex problems such as strong flexibility, strong coupling, nonlinearity, and time-varying dynamics. In order to verify the control algorithms, the reliability of the deployment mechanism, and the on-orbit operation strategy on the ground, there is an urgent need for a ground simulation platform that can realistically reflect the deformation and vibration characteristics of flexible structures.

[0003] In existing technologies, rigid equivalent models, simplified models with lumped mass and spring damping, or single-degree-of-freedom vibration tables are often used to replace real flexible structures. These methods have the following shortcomings: First, the model lacks realism. Rigid replacement models cannot reproduce the spatial deformation and energy transfer process of continuous flexible structures under distributed loads, resulting in significant deviations between the dynamic response and actual on-orbit conditions. Second, the structure lacks scalability. Most existing simulation devices have fixed structural forms, making it difficult to quickly adjust the equivalent stiffness, boundary conditions, and load distribution according to different flexible targets, lacking reconfigurability and scalability. Finally, the multi-objective distributed simulation capability is insufficient. Traditional platforms generally only support single targets or a small number of degrees of freedom, lacking the ability to simulate distributed flexible structures with multi-point and multi-unit coordinated motion, making it difficult to meet the research needs of complex on-orbit service missions.

[0004] Therefore, it is necessary to propose a distributed flexible load simulation system and method with scalable structure, configurable flexibility, support for multi-vehicle cooperative control, and high-precision measurement capabilities to solve the above problems. Summary of the Invention

[0005] The technical problem solved by this invention is to address the shortcomings of existing ground test devices in terms of insufficient realism, poor scalability, and difficulty in simulating multi-objective distributed flexible loads. This invention proposes a distributed flexible load simulation system and load simulation method.

[0006] The present invention solves the above-mentioned technical problem through the following technical solution: A distributed flexible load simulation system and load simulation method, comprising: Select the flexible target to be simulated, extract the target parameter information, and use it to design the diameter of the annular guide rail, the length of the flexible slide rail, and the number of distributed load trolleys corresponding to the flexible target to be simulated; The equivalent flexible slide rail is treated as a uniform beam. The maximum deflection and first natural frequency are calculated based on the target parameter information. The initial range of values ​​for the material elastic modulus, interface moment of inertia and support spacing of the flexible target to be simulated is determined based on the calculated information. Select standard arc-shaped guide rails and splice them end to end on a rigid base to form a ring guide rail according to the requirements of the experimental site. Install the flexible guide rails according to the length of the flexible guide rails. Independently driven load trolleys are arranged on the circular guide rail according to the number of distributed load trolleys, and displacement loads are applied to the flexible slide rails installed on the circular guide rail. Based on the actual working conditions of the flexible target to be simulated, the ideal trajectory of each load trolley is constructed, and the objective function for trajectory optimization of each load trolley is established to optimize the trajectory of the load trolley. The distributed load action of each load trolley after trajectory optimization is achieved on the simulated flexible target, and the response parameters are collected by displacement sensors and acceleration sensors deployed on the flexible slide rail. Adjust the design parameters of the current flexible guide rail according to the response parameters until the expected equivalent effect of the flexible target to be simulated is met, and complete the distributed load simulation and verification task of the flexible target to be simulated.

[0007] The flexible target to be simulated can be a solar panel or a deployable antenna support beam, and the target parameter information includes its equivalent length. Linear density Maximum allowable deflection Lowest natural frequency and uniformly distributed load The equivalent processing method is to treat the flexible guide rail as having a length of... A uniform beam under a uniformly distributed load Calculate the maximum deflection under action and first-order natural frequency The calculation method is as follows:

[0008]

[0009] In the formula, when the maximum deflection and first-order natural frequency Simultaneously satisfy At that time, the calculated maximum deflection is used. and first-order natural frequency Planning material elastic modulus Interface inertia moment And the initial range of values ​​for the support spacing.

[0010] The standard arc-shaped guide rails are spliced ​​end to end on a rigid base to form a circular guide rail. The posture of each segment of the standard arc-shaped guide rail is adjusted by positioning and laser collimation to reduce the overall roundness error of the circular guide rail. and track gauge error The preset error constraints are met.

[0011] The preset error constraint condition is: : In the formula, and These are the preset maximum limits for roundness error and track gauge error, respectively. Based on the design results of the flexible slide rail length and the information after the equivalent treatment of the flexible slide rail, install the flexible slide rail on the inner or outer side of the spliced ​​annular guide rail so that the overall stiffness of the annular guide rail and the flexible slide rail assembly is equivalent to the flexible target to be simulated, and reserve standardized interfaces.

[0012] The load trolley is connected to the flexible slide rail by means of roller clamping, clamping or hinge, and is used to apply displacement load to the flexible slide rail; any adjacent load trolleys meet the minimum safety distance constraint; The minimum safety clearance constraint is: Definition of the first The position of the load trolley along the arc length of the guide rail is... During the entire operation, for any two adjacent cars Apply minimum safety clearance constraints ; Real-time monitoring of the first through the controller The position of the load trolley along the arc length of the guide rail In approach It can automatically limit speed or adjust the local trajectory of the following vehicle to prevent collisions between vehicles with small loads.

[0013] The ideal trajectory of each load trolley is set as follows The objective function is optimized as follows:

[0014] In the formula, For the reference trajectory to be determined, The total test time, The weighting coefficients are obtained by optimizing the objective function. The cooperative reference trajectory of each load trolley is obtained by solving the problem, and the load trolley is driven to move by feedforward control.

[0015] The feedforward control uses the following feedforward control law:

[0016] In the formula, For the feedforward term calculated based on the reference trajectory, For actual position and velocity, The feedback gain is used to form the desired spatiotemporal load field on the flexible guide rail.

[0017] The response parameters include deflection response. And vibration response, deflection response Modal decomposition is performed to obtain modal coordinates. Frequency domain or time-frequency analysis is performed on the modal coordinates to obtain the natural frequencies and damping ratios of each order. These are then compared with the design parameters of the flexible target to be simulated. The simulation effect of the distributed load is verified based on the comparison results.

[0018] Deflection response The method for obtaining modal coordinates through modal decomposition is as follows:

[0019] In the formula, It is the modal order of the intercepted mode. For the first The first mode shape describes the vibration mode of the first mode. Spatial distribution pattern under first-order vibration mode For the first Modal coordinates, describing the first modal coordinates. The amplitude of the first mode change over time; The modal coordinates are determined by the following single-degree-of-freedom dynamic equations.

[0020] in, The second derivative of the modal coordinates (acceleration term). This is the first derivative of the modal coordinates (velocity term). For the first The first modal natural frequency determines the natural vibration frequency of that mode. For the first The first-order modal damping ratio describes the energy dissipation characteristics of that mode. For the first The first modal force is determined by the projection of the external load onto that mode. When the maximum deflection First-order natural frequency If the key modal parameters deviate from the allowable range, the parameters are corrected by adjusting the cross-sectional parameters of the flexible slide rail, the support spacing, or by replacing the local flexible slide rail, until the expected equivalent effect of the flexible target to be simulated is met. The flexible slide rail adopts a multi-segment replaceable structure. Each segment of the flexible slide rail is equipped with a uniform end interface and positioning structure. Different flexible slide rail segments are equipped with different equivalent stiffness and mass distribution. When it is necessary to change the simulated object or correct the equivalent parameters, the overall equivalent stiffness and modal distribution can be adjusted by replacing some flexible slide rail segments or adjusting the support spacing to avoid disassembling the ring guide rail.

[0021] The advantages of this invention compared to the prior art are: (1) The distributed flexible load simulation system and load simulation method provided by the present invention can flexibly configure the cross-sectional size, material and support arrangement according to different flexible targets through parametric design and modular processing of flexible slide rail, and quickly realize equivalent simulation of different stiffness and different modal characteristics, thus overcoming the problem of insufficient realism of traditional rigid replacement models. (2) The present invention uses segmented arc-shaped guide rail splicing to form a ring guide rail with a diameter of not less than 14 m, combined with high-strength support and precision base, which can not only meet the load bearing capacity of not less than 100 kg, but also adjust the number and layout of guide rail segments according to experimental needs, so as to realize the equivalent simulation of large-scale flexible structure ground in the test space. (3) The present invention arranges multiple load trolleys on a ring guide rail and realizes multi-car cooperative motion through multi-axis motion control and anti-collision constraints. Distributed load conditions can be flexibly configured in time and space, supporting multi-point and multi-unit cooperative flexible structure dynamics simulation, which significantly expands the complexity of the test scenario. Attached Figure Description

[0022] Figure 1 The load simulation flowchart provided by this invention; Figure 2 This is a structural schematic diagram of the load trolley provided by the present invention; Figure 3 This is a schematic diagram of the structure of the annular guide rail provided by the present invention. Detailed Implementation

[0023] A distributed flexible load simulation system and method are proposed, applicable to technical aspects such as ground testing of spacecraft flexible structures, on-orbit servicing, and space robot operation verification. The system and method are based on modular ring guide rails and replaceable flexible slide rails. Through the splicing of multiple arc-shaped guide rails, parametric design of flexible slide rails, and distributed drive control, the system can achieve realistic simulation of large-diameter, high-load-bearing, and reconfigurable flexible loads.

[0024] Distributed flexible load simulation system and load simulation method, the specific simulation method flow is as follows: Select the flexible target to be simulated, extract the target parameter information, and use it to design the diameter of the annular guide rail, the length of the flexible slide rail, and the number of distributed load trolleys corresponding to the flexible target to be simulated; The equivalent flexible slide rail is treated as a uniform beam. The maximum deflection and first natural frequency are calculated based on the target parameter information. The initial range of values ​​for the material elastic modulus, interface moment of inertia and support spacing of the flexible target to be simulated is determined based on the calculated information. Select standard arc-shaped guide rails and splice them end to end on a rigid base to form a ring guide rail according to the requirements of the experimental site. Install the flexible guide rails according to the length of the flexible guide rails. Independently driven load trolleys are arranged on the circular guide rail according to the number of distributed load trolleys, and displacement loads are applied to the flexible slide rails installed on the circular guide rail. Based on the actual working conditions of the flexible target to be simulated, the ideal trajectory of each load trolley is constructed, and the objective function for trajectory optimization of each load trolley is established to optimize the trajectory of the load trolley. The distributed load action of each load trolley after trajectory optimization is achieved on the simulated flexible target, and the response parameters are collected by displacement sensors and acceleration sensors deployed on the flexible slide rail. Adjust the design parameters of the current flexible guide rail according to the response parameters until the expected equivalent effect of the flexible target to be simulated is met, and complete the distributed load simulation and verification task of the flexible target to be simulated.

[0025] The flexible target to be simulated can be a solar panel or a deployable antenna support beam. Target parameter information includes its equivalent length. Linear density Maximum allowable deflection Lowest natural frequency and uniformly distributed load The equivalent processing method is to treat the flexible guide rail as having a length of... A uniform beam under a uniformly distributed load Calculate the maximum deflection under action and first-order natural frequency The calculation method is as follows:

[0026]

[0027] In the formula, when the maximum deflection and first-order natural frequency Simultaneously satisfy At that time, the calculated maximum deflection is used. and first-order natural frequency Planning material elastic modulus Interface inertia moment And the initial range of values ​​for the support spacing.

[0028] Standard curved guide rails are spliced ​​end to end on a rigid base to form a circular guide rail. The posture of each segment of the standard curved guide rail is adjusted by positioning and laser collimation to minimize the overall roundness error of the circular guide rail. and track gauge error The preset error constraints are met.

[0029] The preset error constraint is: : In the formula, and These are the preset maximum limits for roundness error and track gauge error, respectively. Based on the design results of the flexible slide rail length and the information after the equivalent treatment of the flexible slide rail, install the flexible slide rail on the inner or outer side of the spliced ​​annular guide rail so that the overall stiffness of the annular guide rail and the flexible slide rail assembly is equivalent to the flexible target to be simulated, and reserve standardized interfaces.

[0030] The load trolley is connected to the flexible slide rail by means of roller clamping, clamping or hinge, and is used to apply displacement load to the flexible slide rail; any adjacent load trolleys must meet the minimum safety distance constraint; The minimum safety clearance constraint is: Definition of the first The position of the load trolley along the arc length of the guide rail is... During the entire operation, for any two adjacent cars Apply minimum safety clearance constraints ; Real-time monitoring of the first through the controller The position of the load trolley along the arc length of the guide rail In approach It can automatically limit speed or adjust the local trajectory of the following vehicle to prevent collisions between vehicles with small loads.

[0031] The ideal trajectory of each load trolley is set as follows The objective function is optimized as follows:

[0032] In the formula, For the reference trajectory to be determined, The total test time, The weighting coefficients are obtained by optimizing the objective function. The cooperative reference trajectory of each load trolley is obtained by solving the problem, and the load trolley is driven to move by feedforward control.

[0033] The feedforward control law used is:

[0034] In the formula, For the feedforward term calculated based on the reference trajectory, For actual position and velocity, The feedback gain is used to form the desired spatiotemporal load field on the flexible guide rail.

[0035] Response parameters include deflection response And vibration response, deflection response Modal decomposition is performed to obtain modal coordinates. Frequency domain or time-frequency analysis is performed on the modal coordinates to obtain the natural frequencies and damping ratios of each order. These are then compared with the design parameters of the flexible target to be simulated. The simulation effect of the distributed load is verified based on the comparison results.

[0036] Deflection response The method for obtaining modal coordinates through modal decomposition is as follows:

[0037] In the formula, It is the modal order of the intercepted mode. For the first The first mode shape describes the vibration mode of the first mode. Spatial distribution pattern under first-order vibration mode For the first Modal coordinates, describing the first modal coordinates. The amplitude of the first mode change over time; The modal coordinates are determined by the following single-degree-of-freedom dynamic equations.

[0038] in, The second derivative of the modal coordinates (acceleration term). This is the first derivative of the modal coordinates (velocity term). For the first The first modal natural frequency determines the natural vibration frequency of that mode. For the first The first-order modal damping ratio describes the energy dissipation characteristics of that mode. For the first The first modal force is determined by the projection of the external load onto that mode. When the maximum deflection First-order natural frequency Or key modal parameters (including modal natural frequencies) Modal damping ratio Mode shape When the deviation deviates from the allowable range, the parameters are corrected by adjusting the cross-sectional parameters of the flexible slide rail, the support spacing, or by replacing the local flexible slide rail, until the expected equivalent effect of the flexible target to be simulated is met.

[0039] The flexible slide rail adopts a multi-segment replaceable structure. Each segment of the flexible slide rail is equipped with a unified end interface and positioning structure. Different flexible slide rail segments are set with different equivalent stiffness and mass distribution. When it is necessary to change the simulated object or correct the equivalent parameters, the overall equivalent stiffness and modal distribution can be adjusted by replacing some flexible slide rail segments or adjusting the support spacing to avoid disassembling the ring guide rail.

[0040] The following description, in conjunction with the accompanying drawings and preferred embodiments, provides further details: In the current embodiment, such as Figure 1 As shown, the distributed flexible load simulation system and load simulation process include: Step 1: Based on the equivalent length of the flexible structure to be simulated Linear density Maximum allowable deflection Lowest natural frequency and typical loads These parameters, along with the equivalent length of the flexible guide rail, determine its compatibility with other parameters. For a uniform beam under a uniformly distributed load, its maximum deflection approximately satisfies the following relationship with its first natural frequency: (1) (2) Through constraints The material elastic modulus of the flexible guide rail is calculated by back-calculation. Moment of inertia of cross section The range of values ​​for the support spacing is determined, and the specific cross-sectional shape and support layout are selected in conjunction with finite element analysis.

[0041] Step Two: Based on the site and accuracy requirements, Standard arc-shaped guide rail units are spliced ​​end-to-end on the base to form a ring-shaped guide rail, such as... Figure 3 As shown, the guide rail radius and gauge are adjusted by geometric positioning and laser collimation to ensure that the roundness error and gauge error meet the requirements. (3) The flexible slide rail module designed in step one is installed on the inner or outer side of the guide rail to form a continuous flexible ring structure with the target flexible characteristics.

[0042] Step 3: Arrange on the circular guide rail An independently controllable load trolley, such as Figure 2 As shown, each trolley is connected to the flexible slide rail via roller clamping or other methods to apply distributed force displacement loads; the first is defined as follows: The arc length of the small car is During operation, for any two adjacent cars Apply safety clearance constraints to avoid mechanical interference and collisions between vehicles.

[0043] Step 4: Based on the target flexible load conditions, construct an ideal trajectory for each load trolley. Furthermore, at the cost of trajectory tracking error and acceleration smoothness, a multi-vehicle cooperative trajectory optimization objective function is established. Solve the reference trajectory while satisfying the safety distance, velocity, and acceleration constraints. Subsequently, a control law is used to drive each load trolley to move in coordination along the circular guide rail, thereby forming the expected spatiotemporal load distribution on the flexible slide rail.

[0044] Step 5: Install displacement and acceleration sensors on the flexible guide rail to collect the deflection response under distributed load. Based on the vibration response, modal decomposition is performed, and frequency domain analysis is conducted on the modal coordinates to obtain the natural frequencies and damping ratios of each order. The obtained modal parameters are compared with the target flexible structure design parameters. When the deviation exceeds the allowable range, the system is corrected by adjusting the flexible slide rail section parameters, support spacing, or replacing the flexible section until the desired result is achieved. , The key modal characteristics meet the design requirements, thereby completing the equivalent load simulation of the target flexible structure.

[0045] Example 1: Based on the above, this embodiment applies operating condition design, feedforward control, and iterative optimization for simulation improvement. Specific design methods include: Step 1: Based on the equivalent length of the flexible structure to be simulated Linear density Maximum allowable deflection Lowest natural frequency and typical loads These parameters determine the diameter of the ring guide rail, the length of the flexible slide rail, and the number of distributed load trolleys. The flexible guide rail is equivalent to a length of A uniform beam under a uniformly distributed load Calculate the maximum deflection under action and first-order natural frequency To satisfy: (4) (5) And order This allows us to determine the elastic modulus of the material. Interface inertia moment And the initial range of values ​​for the support spacing.

[0046] Step Two: Based on the results obtained in Step One , , , Parameters such as these are selected, and specific cross-sectional forms (circular tube, square tube, etc.) are chosen. By combining the back calculation of formulas (4) and (5) with finite element static and modal analysis, the outer diameter, wall thickness and support point spacing of the flexible slide rail are optimized to obtain the target cross-sectional parameters and support layout that meet the strength requirements and modal constraints. At the same time, the segment length and mechanical connection method of the flexible slide rail are determined so that the flexible slide rail works in the elastic stage under the design load and the main natural frequency avoids the test equipment and environmental excitation frequency.

[0047] Step 3: Based on the experimental site dimensions and guide rail accuracy requirements, splice N standard arc-shaped guide rail units end-to-end on a marble or steel structure base to form a circular guide rail. Each arc-shaped guide rail segment is initially positioned using dovetail grooves and positioning pins. The guide rail radius and gauge are adjusted using a laser collimator and roundness testing device to minimize roundness errors. and track gauge error satisfy (6) in and The preset upper limit for roundness and gauge error is set; then the flexible slide rail and its support structure designed in step two are installed on the inner or outer side of the annular guide rail to form a continuous flexible annular structure.

[0048] Step 4: Arrange on the circular guide rail Each load trolley is equipped with a drive motor, reduction mechanism, guide wheel assembly, position encoder, and force / displacement sensor, and is connected to a flexible slide rail via roller clamping, gripping, or hinge. The first load trolley is defined as... The arc length position of the load trolley moving along the circular guide rail is During system operation, for any two adjacent load trolleys , Apply a minimum safety clearance constraint, i.e. (7) in The preset safety distance is used to avoid mechanical interference and collisions between load trolleys.

[0049] Step 5: Based on the target flexible load conditions, construct the ideal trajectory for each load trolley. A trajectory optimization objective function is constructed with trajectory tracking error and acceleration smoothness as the cost terms. Its form is (8) Where T is the total test time. and These are the weighting coefficients. The reference trajectory to be determined. The acceleration smoothing term is used to suppress abrupt trajectory changes and ensure smooth motion. Under the conditions of satisfying the safety distance constraint given by formula (7) and the maximum speed and maximum acceleration limits, the following is applied: Constraint optimization is performed to obtain the reference trajectory of each load vehicle. .

[0050] Step Six: Drive the system using a control law that combines feedforward and proportional-derivative feedback. The first load trolley moves in coordination along the circular guide rail, for the first... The control input of the load trolley is set to (9) in For the first The control input for the load trolley For based on , The calculated feedforward term, , The actual position and speed of the load trolley , The position and speed feedback gain is achieved by executing formula (9) in real time through the multi-axis motion controller and combining it with formula (7) to limit the speed or fine-tune the trajectory of the following vehicle, so as to realize the coordinated application of loads with predetermined spatiotemporal distribution by multiple vehicles.

[0051] Step 7: Under distributed load, the deflection response of the flexible structure is collected using displacement sensors and acceleration sensors installed on the flexible guide rail. and vibration response, for Perform mode decomposition, represented as (10) in For the first First-order mode shape, For the first First modal coordinates; by using Frequency domain analysis was performed to obtain the natural frequencies and damping ratios of each mode, and these were compared with the values ​​set in step one. , Compare indicators such as these.

[0052] Step 8: Based on the deviation between the modal parameters obtained in Step 7 and the design parameters of the target flexible structure, correct the cross-sectional parameters of the flexible slide rail, the support spacing, or the load trolley trajectory. When it is necessary to correct the flexible slide rail parameters, return to Step 1 or Step 2 for redesign; [The last sentence appears to be incomplete and requires further context.] After ensuring that the key modes closely approximate the target structure, repeat steps five through seven to achieve distributed flexible load simulation of the target flexible structure.

[0053] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0054] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A distributed flexible load simulation system and load simulation method, characterized in that... include: Select the flexible target to be simulated, extract the target parameter information, and use it to design the diameter of the annular guide rail, the length of the flexible slide rail, and the number of distributed load trolleys corresponding to the flexible target to be simulated; The flexible slide rail is equivalent to a uniform beam. The maximum deflection and first natural frequency are calculated based on the target parameter information. The initial range of values ​​for the material elastic modulus, interface moment of inertia and support spacing of the flexible target to be simulated is determined based on the calculated information. Select standard arc-shaped guide rails and splice them end to end on a rigid base to form a ring guide rail according to the requirements of the experimental site. Install the flexible guide rails according to the length of the flexible guide rails. Independently driven load trolleys are arranged on the circular guide rail according to the number of distributed load trolleys, and displacement loads are applied to the flexible slide rails installed on the circular guide rail. Based on the actual working conditions of the flexible target to be simulated, the ideal trajectory of each load trolley is constructed, and the objective function for trajectory optimization of each load trolley is established to optimize the trajectory of the load trolley. The distributed load action of each load trolley after trajectory optimization is achieved on the simulated flexible target, and the response parameters are collected by displacement sensors and acceleration sensors deployed on the flexible slide rail. Adjust the design parameters of the current flexible guide rail according to the response parameters until the expected equivalent effect of the flexible target to be simulated is met, and complete the distributed load simulation and verification task of the flexible target to be simulated.

2. The distributed flexible load simulation system and load simulation method according to claim 1, characterized in that: The flexible target to be simulated is a solar panel or a deployable antenna support beam, and the target parameter information includes its equivalent length. Linear density Maximum allowable deflection Lowest natural frequency and uniformly distributed load The equivalent processing method is to treat the flexible guide rail as having a length of... A uniform beam under a uniformly distributed load Calculate the maximum deflection under action and first-order natural frequency The calculation method is as follows: In the formula, when the maximum deflection and first-order natural frequency Simultaneously satisfy At that time, the calculated maximum deflection is used. and first-order natural frequency Planning material elastic modulus Interface inertia moment And the initial range of values ​​for the support spacing.

3. The distributed flexible load simulation system and load simulation method according to claim 2, characterized in that: The standard arc-shaped guide rails are spliced ​​end to end on a rigid base to form a circular guide rail. The posture of each segment of the standard arc-shaped guide rail is adjusted by positioning and laser collimation to reduce the overall roundness error of the circular guide rail. and track gauge error The preset error constraints are met.

4. The distributed flexible load simulation system and load simulation method according to claim 3, characterized in that: The preset error constraint condition is: : In the formula, and These are the preset maximum limits for roundness error and track gauge error, respectively. Based on the design results of the flexible slide rail length and the information after the equivalent treatment of the flexible slide rail, install the flexible slide rail on the inner or outer side of the spliced ​​annular guide rail so that the overall stiffness of the annular guide rail and the flexible slide rail assembly is equivalent to the flexible target to be simulated, and reserve standardized interfaces.

5. The distributed flexible load simulation system and load simulation method according to claim 3, characterized in that: The load trolley is connected to the flexible slide rail by means of roller clamping, clamping or hinge, and is used to apply displacement load to the flexible slide rail; any adjacent load trolleys meet the minimum safety distance constraint; The minimum safety clearance constraint is: Definition of the first The position of the load trolley along the arc length of the guide rail is... During the entire operation, for any two adjacent cars Apply minimum safety clearance constraints ; Real-time monitoring of the first through the controller The position of the load trolley along the arc length of the guide rail In approach It can automatically limit speed or adjust the local trajectory of the following vehicle to prevent collisions between vehicles with small loads.

6. The distributed flexible load simulation system and load simulation method according to claim 5, characterized in that: The ideal trajectory of each load trolley is set as follows The objective function is optimized as follows: In the formula, For the reference trajectory to be determined, The total test time, The weighting coefficients are obtained by optimizing the objective function. The cooperative reference trajectory of each load trolley is obtained by solving the problem, and the load trolley is driven to move by feedforward control.

7. The distributed flexible load simulation system and load simulation method according to claim 6, characterized in that: The feedforward control uses the following feedforward control law: In the formula, For the feedforward term calculated based on the reference trajectory, For actual position and velocity, The feedback gain is used to form the desired spatiotemporal load field on the flexible guide rail.

8. The distributed flexible load simulation system and load simulation method according to claim 5, characterized in that: The response parameters include deflection response. And vibration response, deflection response Modal decomposition is performed to obtain modal coordinates. Frequency domain or time-frequency analysis is performed on the modal coordinates to obtain the natural frequencies and damping ratios of each order. These are then compared with the design parameters of the flexible target to be simulated. The simulation effect of the distributed load is verified based on the comparison results.

9. The distributed flexible load simulation system and load simulation method according to claim 8, characterized in that: Deflection response The method for obtaining modal coordinates through modal decomposition is as follows: In the formula, It is the modal order of the intercepted mode. For the first The first mode shape describes the vibration mode of the first mode. Spatial distribution pattern under first-order vibration mode For the first Modal coordinates, describing the first modal coordinates. The amplitude of the first mode change over time; The modal coordinates are determined by the following single-degree-of-freedom dynamic equations. in, The second derivative of the modal coordinates, The first derivative of the modal coordinates, For the first The first modal natural frequency determines the natural vibration frequency of that mode. For the first The first-order modal damping ratio describes the energy dissipation characteristics of that mode. For the first The first modal force is determined by the projection of the external load onto that mode. When the maximum deflection First-order natural frequency If the key modal parameters deviate from the allowable range, the parameters are corrected by adjusting the cross-sectional parameters of the flexible guide rail, the support spacing, or by replacing the local flexible guide rail, until the expected equivalent effect of the flexible target to be simulated is met; key modal parameters include the modal natural frequencies. Modal damping ratio Mode shape .

10. A distributed flexible load simulation system and load simulation method according to claim 9, characterized in that: The flexible slide rail adopts a multi-segment replaceable structure. Each segment of the flexible slide rail is equipped with a uniform end interface and positioning structure. Different flexible slide rail segments are equipped with different equivalent stiffness and mass distribution. When it is necessary to change the simulated object or correct the equivalent parameters, the overall equivalent stiffness and modal distribution can be adjusted by replacing some flexible slide rail segments or adjusting the support spacing to avoid disassembling the ring guide rail.

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