V-spring shunt programmable excitation device and method based on reference frame transformation

Abstract

The present application relates to the technical field of nonlinear dynamics experimental equipment, in particular to a V-shaped spring oscillator programmable excitation device and method based on reference frame transformation. The device comprises a V-shaped spring structure, a driving module, a control module and a measurement module. The V-shaped spring structure comprises two springs, one end of each spring is connected to a movable suspension point, and the other end is connected to a mass. The driving module is used to drive the two movable suspension points to move synchronously. The control module is used to generate a control signal according to a target external force waveform to control the motion trajectory of the movable suspension points. The measurement module is used to collect the motion data of the mass. By transforming the reference frame to a non-inertial reference frame with the movable suspension point as the origin, the mass is subjected to an equivalent inertial force in the non-inertial reference frame, which is the programmable external force applied to the mass.

Description

Technical Field

[0001] This invention relates to the field of nonlinear dynamics experimental equipment technology, and more specifically, to a programmable excitation device and method for a V-shaped spring oscillator based on reference frame transformation. Background Technology

[0002] In experimental research on nonlinear dynamics (especially hysteresis and chaotic phenomena), how to apply controllable periodic external forces to mechanical oscillator systems has always been the key to achieving quantitative research.

[0003] At the microscopic scale, various schemes have been proposed, such as holographic optical tweezers and optohydrodynamics, magnetic tweezers and acoustic radiation forces in the optical field. Although these schemes have played a significant role in specific fields, they lack feasibility in macroscopic, easily demonstrable, and quantitative research areas, and due to their complexity, they are not suitable for fundamental physics research on a certain type of dynamic system.

[0004] From a macro perspective, existing solutions mainly fall into two categories:

[0005] The first type is direct contact excitation. Examples include electromagnetic vibrators and electric vibration tables, which connect directly to the object being measured via a push rod or connecting rod, applying pushing or pulling forces. However, due to the rigidity of the connecting rod, what is actually applied to the object is not a programmable external force, but rather a programmable displacement. This is unsuitable for tasks where displacement is the primary feedback of the system after excitation. While replacing the rigid rod with a spring or rope could be an alternative, the theoretical computational complexity would increase significantly.

[0006] The second category is non-contact excitation, including electromagnetic and wind-powered methods. Electromagnetic excitation involves installing a current-carrying wire on the object and placing it in a magnetic field to apply force. However, it has significant drawbacks: it requires adding wires and circuits to the object, altering its mass and structure, and the wires themselves introduce additional forces, making it difficult to accurately calibrate the force magnitude. Wind-powered methods, such as using fans or nozzles to apply airflow, suffer from the disadvantage that the airflow is difficult to distribute uniformly on the object's surface, and there is a complex coupling relationship between the wind force and the object's speed and position, making it almost impossible to convert the wind force into a pure, time-dependent function.

[0007] Therefore, the existing technology lacks an external force application device and method that can achieve no additional interference, can realize arbitrary waveforms through programming, and is simple in theoretical calculation and easy to build experimentally, which restricts the quantitative experimental research on strongly nonlinear systems such as V-shaped springs. Summary of the Invention

[0008] In view of this, the present invention aims to provide a programmable excitation device and method for a V-shaped spring oscillator based on reference frame transformation, so as to solve the technical problem in the prior art that it is difficult to apply a pure, programmable external force without additional interference to a mechanical oscillator system.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: This application provides a programmable excitation device for a V-shaped spring oscillator based on reference frame transformation, comprising: The V-shaped spring structure includes two springs. One end of the first spring is connected to a first movable suspension point, and one end of the second spring is connected to a second movable suspension point. The other ends of the first spring and the second spring are connected to a block. A drive module, set on a preset research platform, is used to drive the first movable suspension point and the second movable suspension point to move synchronously. The control module, electrically connected to the drive module, is used to generate control signals based on the target external force waveform to control the movement trajectory of the movable suspension point. In this process, by transforming the reference frame to a non-inertial reference frame with the first movable suspension point as the stationary reference, the movement of the first movable suspension point and the second movable suspension point causes the block to be subjected to an equivalent inertial force in the non-inertial reference frame. The equivalent inertial force is a programmable external force applied to the block. The measurement module, set on a preset research platform, is used to collect motion videos of the block in order to perform mechanical analysis on the block.

[0010] Optionally, it further includes: a guide rail, fixed to the research platform and located between the first movable suspension point and the second movable suspension point, for supporting the block and restricting the movement of the block in a preset direction; The preset direction is parallel to the movement direction of the first movable suspension point and the second movable suspension point.

[0011] Optionally, the guide rail is an air cushion guide rail, which reduces the frictional resistance between the block and the guide rail by forming an air film through compressed air between the block and the guide rail.

[0012] Optionally, the driving module includes: Two parallel and oppositely arranged linear motion modules; Two sliders are respectively set on the linear motion module, serving as the first movable suspension point and the second movable suspension point; The motor is connected to the linear motion module and is used to drive the slider to move synchronously.

[0013] Optionally, the control module includes: The host computer is used to input the target external force waveform; The controller, which is connected to the host computer, is used to calculate the target displacement trajectory of the slider based on the target external force waveform and output the corresponding control signal. The driver, electrically connected to the controller and the motor, is used to convert the control signal into drive current to drive the motor.

[0014] Optionally, the controller is a microcontroller or a programmable logic controller, and the control signal includes a pulse signal and a direction signal.

[0015] Optionally, the measurement module includes: A camera device is mounted above the research platform to capture video of the movement of the object. An image processing unit, communicatively connected to the camera device, is used to extract the displacement time-series data of the block from the motion video.

[0016] Optionally, the measurement module further includes a data processing unit for interpolating, smoothing, and numerically differentiating the displacement time series data to calculate the acceleration of the block and inversely calculating the restoring force by combining the motion equation of the block, thereby identifying the nonlinear dynamic characteristics of the block.

[0017] This application also provides a programmable excitation method based on the above-described device, comprising the following steps: Calculate the acceleration of the movable suspension point based on the target external force waveform; Integrating the acceleration yields the target displacement trajectory of the movable suspension point; The control and drive module drives the movable suspension point to move synchronously according to the target displacement trajectory; The movement of the movable suspension point causes the block to be subjected to an equivalent inertial force in a non-inertial frame. This equivalent inertial force is a programmable external force applied to the block.

[0018] Optionally, the target external force waveform is one of a sine wave, square wave, triangular wave, frequency sweep wave, or random wave.

[0019] Compared with the prior art, the solution provided in this application has the following advantages: This invention innovatively utilizes inertial force to indirectly apply force to the block, achieving pure, interference-free programmable external force application. There are no additional connecting parts or sensors on the block, completely eliminating the additional mass, stiffness, and damping interference caused by wiring, push rods, etc., in traditional excitation methods, ensuring the purity of the measured system and providing the possibility for high-precision nonlinear parameter identification.

[0020] Furthermore, this invention, based on a programmable logic controller (PLC) and a servo drive system, achieves a high degree of controllability of external force waveforms. By writing corresponding control programs in the host computer, external forces of arbitrary waveforms can be generated, such as sinusoidal forces, square wave forces, frequency-sweeping forces, and even random forces, greatly expanding the scope and depth of research. The invention strictly confines the research object to a one-dimensional motion space using guide rails, avoiding interference from motion in other dimensions, and facilitating a purer analysis of the system's motion behavior in a single dimension. Through hardware and software co-design, i.e., selecting a suitable microcontroller and customizing and optimizing the control program according to requirements, this invention not only achieves rich and complex functions to meet diverse application needs but also continuously improves system accuracy. This invention can simulate scenarios where parts are mainly subjected to inertial forces in practical applications, thereby improving the effectiveness of test or analysis results. The device structure of this invention is intuitive, with main components being general-purpose industrial components, and the cost is controllable (approximately 2400 RMB per set), making it very suitable as a university physics experimental teaching instrument, filling a gap in nonlinear dynamics experiments. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the structure of a programmable excitation device for a V-shaped spring oscillator based on reference frame transformation according to the present invention. Figure 2 These are six views of the spring connection in this invention; Figure 3 This is a block diagram of the control module structure in this invention; Figure 4 This is a flowchart of the data processing in this invention; Figure 5 This is a flowchart of the programmable excitation method in this invention.

[0023] Figure label: 1-Linear motion module; 2-Slider; 3-Screw; 4-Spring; 5-Spring fixing point; 6-Block; 7-V-shaped spring structure; 8-Clamp; 9-Guide rail; 10-Air pump; 11-Air pipe; 12-Motor; 13-Driver; 14-Controller; 15-Host computer; 16-Control module; 17-Power supply; 18-Camera device; 19-Horizontal bar; 20-Tripod. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0025] Figure 1 This is a schematic diagram of a programmable excitation device for a V-shaped spring oscillator based on reference frame transformation according to the present invention; please refer to [link / reference]. Figure 1 This embodiment may include: The V-shaped spring structure 7 includes two springs 4. One end of the first spring is connected to the first movable suspension point, and one end of the second spring is connected to the second movable suspension point. The other ends of the first spring and the second spring are connected to a block 5. Specifically, the two springs and the block together form a V-shaped structure. This V-shaped structure is the core component that generates geometric nonlinearity. When the block deviates from the equilibrium position, the direction of the spring force is not collinear with the direction of the block's motion, and the restoring force and displacement exhibit a nonlinear relationship.

[0026] The spring end and the movable suspension point are connected using a flexible connection. As a specific implementation, a thin rigid wire with a diameter of 0.3 mm to 0.5 mm and a length of approximately 30 mm to 50 mm can be used. One end of the thin rigid wire is passed through the last loop of the spring end and then tied using a double loop knot or figure-eight knot to form a reliable mechanical locking structure. This connection method ensures that the spring will not come loose during movement while allowing the spring end to rotate freely.

[0027] A drive module, set on a preset research platform, is used to drive the first movable suspension point and the second movable suspension point to move synchronously. Specifically, the drive module includes two linear motion modules 1, two sliders 2, and a motor.

[0028] Two linear motion modules are fixed parallel to each other on the research platform. Two sliders are respectively mounted on the two linear motion modules, serving as the first and second movable suspension points. A motor is connected to the two linear motion modules to drive the two sliders to move synchronously.

[0029] The linear motion module can be a synchronous belt module, a ball screw module, or a linear motor module. In this embodiment, a synchronous belt module is preferred because it has the advantages of low cost, smooth transmission, and easy control.

[0030] The motor is preferably a two-phase hybrid stepper motor or a three-phase stepper motor. It receives electrical energy signals from the driver, including pulse signals and direction signals, and converts them into mechanical energy output to precisely control the displacement of the slider.

[0031] The control module 16, electrically connected to the drive module, is used to generate a control signal based on the target external force waveform to control the motion trajectory of the movable suspension point; wherein, by transforming the reference frame to a non-inertial reference frame with the first movable suspension point as the stationary reference, the motion of the first movable suspension point and the second movable suspension point causes the block to be subjected to an equivalent inertial force in the non-inertial reference frame, and the equivalent inertial force is a programmable external force applied to the block; Specifically, the controller calculates the slider's acceleration using the inertial force formula based on the target external force waveform, then integrates the acceleration to obtain the velocity, and finally integrates again to obtain the slider's target displacement trajectory. The controller converts the displacement trajectory into pulse signals and direction signals: the frequency of the pulse signals determines the motor's speed, the number of pulse signals determines the slider's displacement, and the high or low level of the direction signal determines the motor's forward or reverse rotation.

[0032] The measurement module, set on a preset research platform, is used to collect motion videos of the block in order to perform mechanical analysis on the block.

[0033] The working principle of this invention is based on the physical principle of reference frame transformation. In the ground reference frame, the motion of the block is subject to the spring force and damping force. When the movable suspension point moves, relative motion occurs between the block and the suspension point. The reference frame is transformed to a non-inertial reference frame with the movable suspension point as the origin. In this non-inertial reference frame, in addition to the spring force and damping force, the block is also subject to an equivalent inertial force. The magnitude of this equivalent inertial force is equal to the mass of the block multiplied by the acceleration of the suspension point, and its direction is opposite to the direction of the acceleration of the suspension point. This design cleverly transforms the complex problem of "force programming" into the mature problem of "displacement programming": by precisely controlling the synchronous displacement of the two sliders, the required periodic external force can be equivalently generated. Since displacement control is already very mature in industry, this invention achieves low-cost, high-precision, and arbitrary waveform programmable external force application.

[0034] Furthermore, the research platform can be a plane, a vertical plane, or an inclined plane, or an inclined stage with an adjustable tilt angle, to adapt to the study of dynamic response under different gravitational components.

[0035] When the research platform is set as an inclined surface or uses an incline table, its tilt direction can be selected according to research needs. Specifically, when the tilt direction is parallel to the preset direction, gravity generates a component along the direction of motion, which can be used to study the motion characteristics or damping effects under gravity-driven conditions. By adjusting the tilt angle, the components of gravity in each direction can be continuously changed, thereby simulating the system response under different tilt conditions. For the case of using an incline table, flexible switching or combination of tilt directions can also be achieved to meet more complex multi-condition experimental requirements. This design makes the device suitable not only for conventional tests on horizontal surfaces but also for dynamic studies on inclined surfaces, vertical surfaces, and even variable gravity environments, significantly improving the applicability and research scope of the experimental device.

[0036] The slider on the module moves under the drive of a motor-driven conveyor belt, which in turn moves a block connected by springs and located on an air cushion guide rail. According to theoretical derivation, after changing the reference frame, in the reference frame with the slider as the stationary reference (denoted as the "slider frame"), the external force to be quantitatively applied to the block is the block's mass multiplied by the slider's acceleration. In other words, in the ground frame, a method of applying programmable external force through inertial force is realized.

[0037] In some embodiments, the device further includes: a guide rail 9, fixed to the research platform and located between the first movable suspension point and the second movable suspension point, for supporting the block and restricting the movement of the block in a preset direction; the preset direction is parallel to the movement directions of the first movable suspension point and the second movable suspension point. This configuration ensures that the block and the suspension points maintain consistent movement directions, preventing the block from swaying or shifting laterally during movement.

[0038] The guide rail is an air cushion guide rail. Compressed air is introduced between the block and the guide rail to form an air film, thereby reducing the frictional resistance between the block and the guide rail. In this way, the block is almost unaffected by friction during movement, which can more realistically reflect the dynamic characteristics of the suspension system itself and reduce the additional damping or nonlinear factors introduced by contact friction. It is particularly suitable for high-precision dynamic response studies or motion testing under small forces.

[0039] Specifically, the air track can be a triangular structure, with the block fitting snugly against it; small holes are provided on the air track. Air tracks are commonly used instruments in mechanics experiments. Compressed air is introduced into the inner cavity of the track and ejected from the small holes on the track surface, forming a thin air layer between the slider and the track. This lifts the slider, transforming the sliding friction between the slider and the track into internal friction between air molecules, reducing frictional resistance to near zero. At this point, the block is only affected by the spring tension and non-negligible air resistance, making the block's motion closer to the force model in actual engineering.

[0040] Furthermore, the air track serves to confine the motion of the block to a one-dimensional track, facilitating the study of pure one-dimensional motion. To extend to two dimensions, the air track can be replaced with a smooth plane; an air platform is recommended.

[0041] The air cushion guide rail needs to be used in conjunction with the air pump 10 and the air delivery pipe 11. After the air pump is powered on, it generates a strong airflow, which is used to deliver compressed air to the air chamber of the guide rail through the air delivery pipe.

[0042] In some embodiments, the drive module includes: two parallel and oppositely arranged linear motion modules (a first synchronous belt module and a second synchronous belt module); two sliders, respectively disposed on the linear motion modules, serving as the first movable suspension point and the second movable suspension point; and a motor 12, which is connected to the linear motion modules for driving the sliders to move synchronously.

[0043] Specifically, the first and second synchronous belt modules are fixed parallel to each other on the research platform. Each synchronous belt module is equipped with a slider; the slider on the module moves under the drive of the conveyor belt driven by motor 12, thereby moving the block connected by springs and located on the air cushion guide rail. According to theoretical derivation, after changing the reference frame, in the reference frame with the first movable suspension point as the stationary reference (also denoted as the "slider frame"), the external force to be quantitatively applied to the block is the block mass multiplied by the slider acceleration, that is, the method of applying programmable external force through inertial force is realized in the ground frame.

[0044] First, take a fixed point O as the origin in the one-dimensional direction of the block's motion. The two sliders move synchronously, and the radial vector of their centers of mass relative to the origin O is: (1) Similarly, the positional vector of the block relative to the origin O: (2) Hooker spring force: (3) Considering the equation (3) It is a variable that is independent of the frame of reference; These are preset coefficients; in this application, the damping force is considered negligible, that is, in the ground reference frame, for a block of mass m, the following is satisfied: (4) In the one-dimensional case, the relative displacement between the mass and the slider is: (5) Equation (5) is also the position vector of the block in the slider system. Substituting it into equation (4) above, we get: (6) It can be immediately seen from equation (6) that the desired programmable external force That is, the last term on the right side of the equation, i.e.: (7) Therefore, we only need to design based on the above formula and the form of the target variable force. That's all.

[0045] Furthermore, in some embodiments, the first movable suspension point and the second movable suspension point can adopt a screw 3 structure. With this configuration, the horizontal height of the spring suspension point can be adjusted by rotating the screw 3, thereby achieving precise adjustment of the spring suspension height to meet experimental requirements under different working conditions or different object masses.

[0046] To prevent the spring from sliding up and down along the screw during operation, which could affect the stability of the experimental results, a long screw and nut can be used for locking and positioning, confining the spring to a specific height on the screw. Alternatively, a smooth rod with a locking sleeve or set screw can be used to fix the height, reliably locking the spring's suspension position. Both of these structures ensure that the spring maintains a stable suspension height during the experiment, avoiding additional vibrations or nonlinear factors introduced by spring movement, thereby improving experimental repeatability and data reliability.

[0047] Specifically, for modules with a total length of approximately 60cm to 80cm, it is recommended that the spring stiffness coefficient be between 40N / m and 200N / m. If it is too large, it will be difficult for the spring to extend and retract, while if it is too small, the material will be easily worn out.

[0048] The spring diameter should not be too small; a diameter of 20mm or more is recommended. Otherwise, it is prone to bending during dynamic compression. Only under linear expansion and contraction conditions can the spring force be described using a linear model.

[0049] In summary, the feasible spring parameters are shown in Table 1.

[0050] Table 1 Spring Parameter Table

[0051] Furthermore, in this device, reference Figure 2 The connection between the spring end and the long screw adopts a flexible hinge method, which ensures that the spring will not come out during the movement, while allowing the spring end to rotate freely, so as to avoid additional bending moment due to excessive constraint, which would affect the purity of the system's dynamic characteristics.

[0052] The specific implementation method is as follows: the connection between the spring end and the long screw is achieved through the following steps: Take a piece of thin, rigid wire (such as spring steel wire or piano wire with a diameter of 0.3mm to 0.5mm), about 30mm to 50mm in length, and adjust it according to the actual spring size.

[0053] Thread one end of the thin, rigid wire through the last turn of the spring, then follow... Figure 2 The knots are tied as shown to form a reliable mechanical locking structure. A "double loop knot" or a "figure-eight knot" can be used to ensure that the knot will not loosen during long-term repeated stretching.

[0054] Furthermore, two semi-cylindrical wooden blocks are fixed to both sides of the block with hot melt adhesive, which are used to fix a smooth thin rod at the protrusion. This thin rod serves the same purpose as the long screw.

[0055] To study the nonlinear dynamic response of a system under different mass parameters, specialized counterweights can be used: many air-cushioned guide sliders have pins at both ends or specific positions for fixing counterweights with circular holes. During the experiment, weights of different masses are simply inserted directly onto the slider to smoothly increase its total mass.

[0056] Specifically, the entire device can be secured to the research platform using screws or strong adhesive to ensure stability during experiments. Even without external interference, the motor's torque is often too high, and this securing method prevents relative movement between modules.

[0057] In some embodiments, the device further includes a two-phase hybrid stepper motor. This stepper motor receives electrical signals from the driver 13, including pulse signals and direction signals, and converts them into mechanical energy output, thereby precisely adjusting the rotational speed and direction of the coupling, and thus controlling the displacement of the conveyor belt, i.e., the displacement of the slider. By adjusting the frequency and number of pulse signals, high-precision control of the slider's speed, displacement, and direction of motion can be achieved, meeting the motion requirements under different working conditions.

[0058] To ensure the system's control accuracy and response performance, it is recommended to use a high-precision two-phase or three-phase or higher stepper motor with a step angle within 1.2°. Within this step angle range, the positioning accuracy and motion smoothness required for general research can be achieved. As an example, a stepper motor of model 57J1880EC-1000-LS-SCG can be used. This model of motor has good torque output characteristics and high position resolution, which can meet the precise control requirements of displacement law in nonlinear dynamics experiments.

[0059] In some embodiments, the control module 16 includes: a host computer 15 for inputting a target external force waveform; a controller 14, communicatively connected to the host computer 15, for calculating the target displacement trajectory of the slider based on the target external force waveform and outputting a corresponding control signal; and a driver 13, electrically connected to the controller 14 and the motor, for converting the control signal into a drive current to drive the motor.

[0060] Drivers are categorized into stepper, servo, and hybrid types. Considering factors such as overall positioning accuracy, maximum speed, and heat generation, a hybrid stepper-servo driver, also known as a closed-loop stepper driver, is currently the most recommended choice. The driver connects directly to the microcontroller, converting control signals into electrical signals and sending them to the motor. The connection method between the driver and the motor can be determined according to the product's specifications, as follows: Figure 3 .

[0061] Specifically, the host computer 15 serves as a human-computer interaction and program development terminal. It connects to the microcontroller via a USB interface and is used to write, compile, and burn control programs to the microcontroller, enabling programmable control of external force waveforms. The host computer 15 can be a laptop or desktop computer, as long as it has a standard USB communication interface and supports the corresponding integrated development environment (such as Arduino IDE, Keil, etc.).

[0062] The controller 14 is a microcontroller or a programmable logic controller, and the control signals include pulse signals and direction signals.

[0063] Specifically, a microcontroller is like a miniature computer that can automatically run programs and "command" hardware with electrical signals. In detail, the microcontroller reads instructions from the program memory, processes input signals through calculations, and outputs high / low level or pulse signals to interfaces such as GPIO and PWM to achieve precise control of peripherals such as motors, sensors, and displays.

[0064] The connection methods of the motor, driver, and microcontroller are as follows: Figure 3 As shown.

[0065] Figure 3 All connections can be manually laid out; however, the connections for pulse signals, direction signals, and enable signals require additional DuPont wires. Pin 1 of the microcontroller is defined as the PLS pulse signal terminal, and pin 2 is defined as the DIR direction signal terminal. The functional interfaces corresponding to the above signals must be declared and configured in advance in the integrated development environment (IDE).

[0066] The control module 16 consists of a host computer, a microcontroller, and a driver, and is connected to the motor. Taking the Arduino microcontroller as an example, the host computer compiles and downloads the program through the Arduino development environment, and runs the host computer software responsible for building the human-computer interaction interface, implementing complex algorithms, and storing data. A communication link is established via a USB virtual serial port to download the program code to the Arduino microcontroller, which serves as the real-time control core. Under program control, the Arduino outputs control signals, which are converted into pulse and direction electrical signals by the driver, thereby driving the motor to rotate, ultimately realizing the "application of programmable external force." See the flowchart below. Figure 4 .

[0067] The host computer acts as the control core, running control programs written in Python or C++, responsible for human-computer interaction, complex algorithm calculations, and data storage. It establishes virtual serial communication via a USB interface to send commands to the lower-level computer. The microcontroller, using an Arduino UNO or Nano development board, serves as the real-time control unit. After receiving commands from the host computer, it outputs PWM control signals through its GPIO ports. The driver uses a driver module such as L298N or DRV8825 to amplify the logic level signals output by the microcontroller, converting them into the drive current required by the motor. The motor, which can be a stepper motor or a servo motor, receives the electrical signals output by the driver to achieve mechanical motion and output mechanical energy.

[0068] Furthermore, it also includes a power supply module to power the driver, which generally uses a DC regulated power supply of about 35V to ensure stable current output; its power needs to match the peak load of the motor to avoid damaging the driver.

[0069] In some embodiments, the measurement module includes: a camera device 18, disposed above the research platform, for acquiring motion video of the block; and an image processing unit, communicatively connected to the camera device 18, for extracting displacement time-series data of the block from the motion video.

[0070] The camera device 18 can be any camera device that meets the requirements of 120fps or higher. The camera is placed parallel to the plane of the device and at a distance of more than 1m directly above the center of the air cushion guide rail to collect the displacement data of the block at a high frame rate.

[0071] The purpose of keeping the camera device away from the device during shooting is to minimize parallax. Alternatively, a lens can be used. Select a plano-convex lens with a suitable focal length based on the focal length of the camera device and place it parallel to the front of the camera device to ensure that the incident light rays are parallel beams.

[0072] Specifically, it also includes a support arm for connecting and fixing the camera device. This support arm has a rigid rod-like structure, with one end detachably connected to the vertical column of the tripod 20 via a clamping mechanism, and the other end supporting the camera device 18. The clamping mechanism can be a laboratory four-jaw clamp or a similar adjustable clamping device, enabling coarse adjustment and fixation of the horizontal position and vertical height of the extension arm. The extension arm is made of aluminum alloy or stainless steel to ensure sufficient rigidity and reduce weight. By adjusting the fixed position of the clamping mechanism on the column, the vertical height of the camera device 18 can be changed; by adjusting the horizontal extension length of the extension arm, the camera device can be ensured to be directly above the center of the air cushion guide rail.

[0073] Tripod 20 serves as a support structure for the entire camera system, providing an adjustable-height vertical column. The base of tripod 20 utilizes a triangular support structure to ensure stability, while the top is equipped with a height adjustment mechanism for precise adjustment of the camera's vertical height. The column features height markings or positioning holes for easy repositioning. Tripod 20 is connected to the crossbar 19 via a rotating joint or clamp 8, allowing adjustment of the horizontal angle of the crossbar 19 to ensure the camera is aligned with the center of the guide rail. Furthermore, video data is acquired through the camera, and then Tracker software is used to plot the video frame by frame (manually or automatically) to extract the centroid coordinates of the extraction blocks and sliders in a temporal sequence.

[0074] Next, data processing is performed using an image processing unit (which can be built using Python). First, Akima cubic interpolation is used to minimize errors introduced during the data point marking process, effectively avoiding excessive oscillations near data points and increasing the sampling rate to improve the accuracy of subsequent differentiation and FFT. Then, the relative displacement is calculated by subtracting the data from the block and slider. Next, the instantaneous velocity and acceleration are calculated using Python's built-in differentiation functions; the second derivative of the relative displacement at this point represents the desired external force. Finally, the phase diagram of the block in the slider system is plotted, and FFT analysis is performed to further investigate the nonlinear dynamic characteristics of the V-shaped spring oscillator system.

[0075] It should be noted that the specific configuration of the above-mentioned drive module is merely exemplary and not limiting. The core of this invention lies in applying inertial force by moving the spring suspension point (slider). Any mechanism that can achieve "precise control of the linear displacement of the fixed end of the spring" can be considered as an alternative: for example: (1) Screw drive type: such as ball screw module or sliding screw module with servo / stepper motor. It has high precision and can realize precise control of the slider position.

[0076] (2) Linear motors: such as voice coil motors or flat linear motors. They have fast dynamic response, no transmission backlash, and are suitable for high-frequency excitation and complex waveform tracking.

[0077] (3) Mechanical transmission type: such as crank-slider mechanism or cam mechanism combined with ordinary motor. Its structure is simple and low cost, and it is suitable for repeatable experiments of specific waveforms (such as sine waves).

[0078] (4) Fluid-driven type: such as electro-hydraulic servo actuators or cylinders. They have large output force and are suitable for nonlinear testing of large or heavy structures.

[0079] Furthermore, regarding the programmable controller, the Arduino microcontroller used in this invention is merely one specific implementation. Its core function is to generate programmable control signals to drive the slider's movement. Any controller capable of achieving this function can be used as an alternative, including but not limited to: (1) Other types of microcontrollers: such as STM32, ESP32, PIC and other industrial or consumer-grade microcontrollers.

[0080] (2) Industrial controllers: such as programmable logic controllers and dedicated motion control cards.

[0081] (3) Embedded systems: such as Raspberry Pi, FPGA, etc., can realize more complex control logic or onboard data processing.

[0082] (4) Virtual instrument platform: such as LabVIEW with data acquisition card, using computer to realize waveform generation and control.

[0083] The above classification is only a typical example of the implementation path that can be adopted by the present invention. There may be technical overlap between the paths. Those skilled in the art can flexibly combine or replace them with equivalents according to actual needs.

[0084] Furthermore, the embodiment employs a "single camera device + post-image processing". An alternative could be "two laser displacement sensors," one aligned with the slider and the other with the object, directly outputting displacement data in real time, enabling higher sampling rates and real-time feedback. Combined with a Kalman filter algorithm, even higher precision displacement and acceleration detection can be achieved.

[0085] Furthermore, the guide rail can also be a "magnetic levitation guide rail" or an "air bearing guide rail".

[0086] This application also provides a programmable excitation method based on the above-described device, referring to... Figure 5 This includes the following steps: Step S101: Calculate the acceleration of the movable suspension point based on the target external force waveform; The user first inputs the desired target external force waveform via a host computer. This waveform can be any of the following: sine wave, square wave, triangular wave, frequency sweep wave, or random wave. After receiving the target external force waveform, the controller calculates it according to a modified formula of Newton's second law. Specifically, since the equivalent inertial force on the block in a non-inertial reference frame is equal to the block's mass multiplied by the acceleration of the movable suspension point, and in opposite directions, the acceleration of the movable suspension point is equal to the target external force divided by the negative of the block's mass. Through this calculation, the waveform of the user's desired "force" is converted into a directly controllable "acceleration" parameter.

[0087] Step S102: Integrate the acceleration to obtain the target displacement trajectory of the movable suspension point; The controller performs numerical integration on the calculated acceleration data. First, it performs one integration to obtain the velocity of the movable suspension point as a function of time; then, it performs a second integration to obtain the displacement of the movable suspension point as a function of time, i.e., the target displacement trajectory. This process further transforms the abstract acceleration parameters into specific displacement commands, providing a clear execution target for subsequent mechanical motion. Since displacement control technology is already very mature in industry, converting force into displacement through integration cleverly reduces the control difficulty.

[0088] Step S103: Control the drive module to drive the movable suspension point to move synchronously according to the target displacement trajectory; The controller converts the target displacement trajectory into control signals recognizable by the drive module. For stepper motor or servo motor systems, the control signals mainly include pulse signals and direction signals: the frequency of the pulse signals determines the motor speed, the number of pulse signals determines the angle of motor rotation, and thus the displacement of the slider; the high and low levels of the direction signals determine the forward and reverse rotation of the motor, and thus the direction of movement of the slider. After receiving these signals, the driver amplifies them and converts them into current to drive the motor. The motor drives the linear motion module to operate, driving the two sliders to move synchronously, so that the movable suspension point moves strictly according to the preset target displacement trajectory. The synchronous movement of the two sliders ensures the symmetry of the V-shaped spring structure, ensuring that the block is subjected to uniform force during movement.

[0089] Step S104: Through the movement of the movable suspension point, the block is subjected to an equivalent inertial force in a non-inertial frame. The equivalent inertial force is the programmable external force applied to the block.

[0090] When the movable suspension point accelerates along a preset trajectory, the reference frame with the movable suspension point as its origin becomes a non-inertial reference frame. Observed within this non-inertial reference frame, the block, in addition to being acted upon by the spring force and damping force, is also subjected to an equivalent inertial force. The magnitude of this inertial force is equal to the mass of the block multiplied by the acceleration of the movable suspension point, and its direction is opposite to the direction of acceleration. This inertial force is precisely the concrete realization of the target external force waveform in step S101. Since this inertial force is naturally generated through reference frame transformation, without the need for any contact connectors or additional devices, a pure, uninterrupted programmable external force application is achieved. Under the excitation of this external force, the block produces a corresponding dynamic response, providing ideal experimental conditions for subsequent studies of nonlinear dynamic characteristics.

[0091] The target external force waveform is one of the following: sine wave, square wave, triangular wave, frequency sweep wave, or random wave.

[0092] It should be noted that the core technology of this application is to apply programmable external forces in the form of inertial forces by changing the reference frame: that is, a structure with synchronous movement of two sliders and movement of the spring suspension point, which "applies" force to the block by moving the fixed point of the spring, rather than directly pushing the block. Applying contact or non-contact forces directly to a target is very difficult and complex, often involving a large number of signal transformations. However, for the external force applied by this invention based on the "reference frame change method," the external force can be programmed in one step simply by programming the slider displacement information. The method for generating and controlling the equivalent inertial force is as follows: In the slider system, the external force is completely equivalent to the slider acceleration, that is, by precisely controlling the synchronous displacement of the two sliders. To equivalently generate the required periodic external force By writing appropriate code in the IDE, one can generate slider displacements of arbitrary waveforms, that is, realize external forces of arbitrary waveforms, which is the key to achieving quantitative research.

[0093] When writing code, pay attention to two types of signals: direction signals and pulse signals. Direction signals, i.e., high and low levels, determine the forward and reverse rotation of the motor, while pulse signals, i.e., each pulse corresponds to one step of the motor, and the pulse frequency determines the speed.

[0094] 1. Taking a sinusoidal external force as an example, the corresponding... The target displacement is calculated as follows: (8) (9) Regarding physical displacement amplitude First, these mechanical parameters need to be determined: motor step angle. (e.g., 1.8° / step), driver microstepping (e.g., 16 subdivisions), conveyor pulley diameter or lead screw pitch (e.g., 20mm / revolution), and calculate the transmission coefficient. (pulse / mm).

[0095] Pulses per revolution: (10) Pulses per millimeter: (11) Next, we will perform amplitude pulse number conversion: (12) The displacement amplitude in equation (8) Convert to the corresponding amplitude in the pulse domain, denoted as Then the pulse sequence during programming is: (13) For hybrid motors, the calculation of that moment... And you can send it directly to the driver.

[0096] 2. Taking a triangular wave external force as an example, the corresponding force is: (14) Two integrations are needed to obtain the displacement function. The first integration of equation (14) ,have to: (15) Integrating equation (15) again, we get: (16) Equation (16) is the target displacement.

[0097] In actual code, numerical methods can be used directly for encoding; there is no need to calculate specific formulas.

[0098]

[0099]

[0100]

[0101]

[0102] It should be noted that any other waveform can be processed using this method.

[0103] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0104] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A programmable excitation device for a V-shaped spring oscillator based on reference frame transformation, characterized in that, include: The V-shaped spring structure includes two springs. One end of the first spring is connected to a first movable suspension point, and one end of the second spring is connected to a second movable suspension point. The other ends of the first spring and the second spring are connected to a block. A drive module, set on a preset research platform, is used to drive the first movable suspension point and the second movable suspension point to move synchronously. The control module, electrically connected to the drive module, is used to generate control signals based on the target external force waveform to control the movement trajectory of the movable suspension point. In this process, by transforming the reference frame to a non-inertial reference frame with the first movable suspension point as the stationary reference, the movement of the first movable suspension point and the second movable suspension point causes the block to be subjected to an equivalent inertial force in the non-inertial reference frame. The equivalent inertial force is a programmable external force applied to the block. The measurement module, set on a preset research platform, is used to collect motion videos of the block in order to perform mechanical analysis on the block.

2. The apparatus according to claim 1, characterized in that, Also includes: A guide rail, fixed to the research platform and located between the first movable suspension point and the second movable suspension point, is used to support the block and restrict the movement of the block in a preset direction; The preset direction is parallel to the movement direction of the first movable suspension point and the second movable suspension point.

3. The apparatus according to claim 2, characterized in that, The guide rail is an air cushion guide rail. Compressed air is introduced between the block and the guide rail to form an air film, thereby reducing the frictional resistance between the block and the guide rail.

4. The apparatus according to claim 1, characterized in that, The driving module includes: Two parallel and oppositely arranged linear motion modules; Two sliders are respectively set on the linear motion module, serving as the first movable suspension point and the second movable suspension point; The motor is connected to the linear motion module and is used to drive the slider to move synchronously.

5. The apparatus according to claim 4, characterized in that, The control module includes: The host computer is used to input the target external force waveform; The controller, which is connected to the host computer, is used to calculate the target displacement trajectory of the slider based on the target external force waveform and output the corresponding control signal. The driver, electrically connected to the controller and the motor, is used to convert the control signal into drive current to drive the motor.

6. The apparatus according to claim 5, characterized in that, The controller is a microcontroller or a programmable logic controller, and the control signals include pulse signals and direction signals.

7. The apparatus according to claim 1, characterized in that, The measurement module includes: A camera device is mounted above the research platform to capture video of the movement of the object. An image processing unit, communicatively connected to the camera device, is used to extract the displacement time-series data of the block from the motion video.

8. The apparatus according to claim 7, characterized in that, The measurement module also includes a data processing unit for interpolating, smoothing, and numerically differentiating the displacement time series data to calculate the acceleration of the block and, in conjunction with the motion equation of the block, back-calculate the restoring force to identify the nonlinear dynamic characteristics of the block.

9. The apparatus according to claim 1, characterized in that, The research platform can be a plane, a vertical plane, or an inclined plane.

10. A programmable excitation method based on the device according to any one of claims 1 to 9, characterized in that, Includes the following steps: Calculate the acceleration of the movable suspension point based on the target external force waveform; Integrating the acceleration yields the target displacement trajectory of the movable suspension point; The control and drive module drives the movable suspension point to move synchronously according to the target displacement trajectory; The movement of the movable suspension point causes the block to be subjected to an equivalent inertial force in a non-inertial frame. The equivalent inertial force is a programmable external force applied to the block. The target external force waveform is one of the following: sine wave, square wave, triangular wave, frequency sweep wave, or random wave.

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