Digital measurement three-line pendulum experimental instrument based on PHYPHOX and ESP-32

Abstract

The invention discloses a three-line pendulum experiment instrument for digital measurement based on PHYPHOX and ESP-32. Data are collected through the angular velocity sensor, processed by the ESP32 single-chip microcomputer and sent to a designed PHYPHOX page for data analysis and image display. As a novel experiment device which is initiatively used based on combination of ESP-32 and an angular velocity sensor and PHYPHOX, the problems of large measurement error, tedious data processing, low acquisition efficiency, relatively low teaching efficiency and the like caused by dependence on manual timing and manual calculation in a traditional three-line pendulum experiment can be solved. And the requirement of urgently improving the experiment means due to the development of the digital experiment technology is met. The device plays a good guiding role in deeply discussing a measurement method of rotational inertia by students. The experiment device has the real-time monitoring characteristic, the experiment precision is improved, and meanwhile the experiment interestingness is improved.

Description

Technical Field

[0001] This invention belongs to the field of mobile sensing and physical digitization, and particularly relates to a trilinear pendulum experimental apparatus for digital measurement based on PHYPHOX and ESP-32. Background Technology

[0002] Currently, experiments conducted in laboratories using traditional trilinear pendulums rely on manual timing and calculation. This results in problems such as large measurement errors, cumbersome data processing, and low teaching efficiency.

[0003] PHYPHOX is a mobile physics experiment software developed by RWTH Aachen University in Germany. It transforms a smartphone into a portable laboratory. Using an angular velocity sensor and a microcontroller, it displays the measured experimental data as images on a pre-designed PHYPHOX interface, and performs data analysis and calculations.

[0004] Furthermore, the PHYPHOX page simultaneously displays the torsion angle image of the trifilar pendulum and the angular velocity images of the X and Y axes, used to monitor whether the pendulum's oscillation is a normal torsional oscillation and whether it is moving within the preset simple harmonic motion. This avoids errors in experimental data measurement caused by improper experimental operation, which could damage the original theoretical model.

[0005] In addition, using a microcontroller and sensors to measure the moment of inertia also avoids the omission of photogates in traditional experiments, making the measurement of the moment of inertia more accurate.

[0006] Displaying images directly in Phyphorx makes experimental data more visual and increases the fun of the experiments. It also saves time and effort compared to the theoretical calculations required in traditional experiments.

[0007] Kalman filtering is an efficient recursive algorithm used to estimate the state of a dynamic system from noisy observation data. It optimizes the state estimate step by step by combining the system model and actual measurements through a "prediction-correction" loop. Applications of Kalman filtering: (1) Data preprocessing, gyroscope data: directly used as angular velocity observation Z k =ω. Accelerometer data: The angle needs to be calculated by double integration, but integration will introduce drift. It is recommended to combine gyroscope data for complementary filtering. (2) Parameter optimization, process noise Q: Adjust according to the actual vibration amplitude of the trifilar pendulum (usually through experimental trial and error). Measurement noise R: Calibrate by the variance of the data when the sensor is stationary. Moment of inertia J: If unknown, it can be roughly estimated first, and then the period formula can be used after the filter converges. In reverse: Before filtering: The raw data may contain high-frequency noise or drift. After filtering: The angle / angular velocity curves are smoother. The calculated moment of inertia is more stable (the variance is reduced when calculating J using period T).

[0008] To date, there have been no examples of using Phyphox, ESP-32 microcontroller and angular velocity sensor to measure the moment of inertia of a trifilar pendulum. The device of this invention is an innovative application of Phyphox based on the combination of ESP-32 and angular velocity sensor. Summary of the Invention

[0009] The purpose of this invention is to propose a digital measurement trifilar pendulum experimental apparatus based on PHYPHOX and ESP-32 microcontrollers. Data is processed through an adaptive filtering algorithm, and real-time visualization is achieved using Phyphox. By utilizing the ESP-32 microcontroller, angular velocity sensor, and PHYPHOX software, this invention addresses the problems of traditional trifilar pendulum experiments in laboratories, which rely on manual timing and calculation, resulting in large measurement errors, cumbersome data processing, and low teaching efficiency. Furthermore, it improves the experimental model, reduces the time spent on manual calculations, and lowers the cost of the apparatus.

[0010] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0011] A trilinear pendulum experimental apparatus for digital measurement based on PHYPHOX and ESP-32, characterized in that it includes a support, an upper disk, a lower suspension disk, and a 3D printed box;

[0012] The support includes a base, a support column, and a crossbeam; the support column is vertically fixed to the base, the crossbeam is fixed to the upper end of the support column, the crossbeam has a bearing in the middle, the upper disc has a rotating shaft in the middle, the rotating shaft is located in the bearing of the crossbeam, and the lower suspension disc is connected to the upper disc by three thin ropes; one end of the thin rope is fixed to the lower suspension disc, and the other end of the thin rope is wrapped around an adjusting bolt, which is screwed onto the outer circumference of the upper disc;

[0013] The 3D printing box is installed at the bottom of the lower suspension plate and connects via Bluetooth to the Phyphox page to display the measured moment of inertia and verify the parallel axis theorem.

[0014] The ESP-32 microcontroller and angular velocity sensor are installed inside the 3D printing box.

[0015] This invention also discloses a method for using a trilinear pendulum experimental apparatus based on digital measurement using PHYPHOX and ESP-32, comprising the following steps:

[0016] Step 1: Use the ESP-32 microcontroller and angular velocity sensor to collect data. The 3D printing box is installed under the lower suspension plate.

[0017] Step 2: In the Phyphox page editor, edit the required experimental data collection page;

[0018] Step 3: Connect the angular velocity sensor and the ESP-32 microcontroller to collect experimental data. Display the measured moment of inertia and verify the parallel axis theorem on the Phyphox page.

[0019] The trilinear pendulum experimental apparatus based on digital measurement using PHYPHOX and ESP-32 of the present invention has the following advantages:

[0020] (1) Non-contact measurement: Remove the light-blocking plate to avoid mechanical interference and ensure that the mass distribution of the suspension disc strictly conforms to the theoretical model.

[0021] (2) Centrally symmetrical installation: The angular velocity sensor is placed at the geometric center of the suspension plate, and the data directly reflects the angular velocity of the shaft without the need for additional calibration.

[0022] (3) Integrated packaging: The 3D printed bracket integrates the sensor and ESP-32, and the overall weight is light (77g).

[0023] (4) The angular velocity sensor and microcontroller replace the photoelectric gate and counter to measure the cycle, reducing the difficulty of the experiment and increasing its interest. It can intuitively obtain images and real-time data on the Phyphox page, and has the characteristics of high efficiency, accuracy and real-time monitoring, which plays a good guiding role in students' in-depth exploration of the method of measuring rotational inertia. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the original experimental apparatus of the present invention;

[0025] Explanation of markings in the diagram: 1. Upper disc; 2. Suspension line; 3. Lower disc; 4. Crossbeam; 5. Base; 6. Support column; 7. 3D printing box; 8. Adjusting bolt; 9. Leveling pad; 10. Adjusting bolt; Detailed Implementation

[0026] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a trilinear pendulum experimental apparatus for digital measurement based on PHYPHOX and ESP-32.

[0027] A trilinear pendulum experimental apparatus based on PHYPHOX and ESP-32 for digital measurement includes a support, an upper disk 1, a lower suspension disk 3, and a 3D printed box 7;

[0028] The support includes a crossbeam 4, a base 5, a support column 6, and a leveling pad 9; the support column 6 and the leveling pad 9 are vertically fixed on the base 5, the crossbeam 4 is fixed on the upper end of the support column 6, the crossbeam 4 has a bearing in the middle, the upper disc 1 has a rotating shaft in the middle, the rotating shaft is located in the bearing of the crossbeam 4, and the lower suspension disc 3 is connected to the upper disc 1 by three thin ropes; one end of the thin rope is fixed to the lower suspension disc 3, and the other end of the thin rope is wrapped around the adjusting bolt 10, which is screwed onto the outer circumference of the upper disc 1;

[0029] The 3D printing box 7 is installed at the center of the bottom of the lower suspension plate 3. It is connected via Bluetooth to the Phyphox page to display the measured moment of inertia and verify the parallel axis theorem.

[0030] The 3D printing box 7 is used for data acquisition and for mounting the ESP-32 microcontroller and angular velocity sensor. The 3D printing box 7 is a one-piece package.

[0031] This invention also discloses a method for using a trilinear pendulum experimental apparatus based on digital measurement using PHYPHOX and ESP-32, comprising the following steps:

[0032] Step 1: Use the ESP-32 microcontroller and angular velocity sensor to collect data. The 3D printing box 7 is installed under the lower suspension plate 3.

[0033] Step 2: In the Phyphox page editor, edit the required experimental data collection page;

[0034] Step 3: Connect the angular velocity sensor and the ESP-32 microcontroller to collect experimental data. Display the measured moment of inertia and verify the parallel axis theorem on the Phyphox page.

[0035] Lower suspension plate 3: diameter 189.9mm, thickness 5.4mm, mass m0=300g;

[0036] Upper disc 1: Diameter 118mm, thickness 25.3mm;

[0037] Suspension line 2: Three nylon lines, length H = 12cm, fixed at equal intervals on the edge of the disc;

[0038] The radius of the lower suspension point R = 6cm, and the radius of the upper suspension point r = 3cm.

[0039] Angular velocity sensor: MPU6050, measurement range ±500° / s;

[0040] Microcontroller: ESP-32, connected to the sensor via I2C interface, powered by 3.7V;

[0041] Phone / Tablet: Android system, with Phyphox version 1.13.0 installed.

[0042] Program and parameter configuration:

[0043] ESP-32 programming

[0044] Phyphox page settings:

[0045] Create an "angular velocity curve" component and bind gyroX and gyroY data;

[0046] Add a "Twist Angle Calculation" module, using the integral formula θ t =θ t-1 +ω△t calculates the real-time twist angle; θ t Let θ be the angle value at the current time t. t-1 ω is the angle value at the previous time t-1, ω is the angular velocity, and Δt is the time step.

[0047] In the "Moment of Inertia Calculation" module, input the following parameters: m = 300g, g = 9.8m / s² 2 R = 0.06m, r = 0.03m, H = 0.12m, J is calculated automatically.

[0048] Experimental reproduction:

[0049] The ESP-32 microcontroller is connected to the angular velocity sensor, and an external 3.7V lithium battery is connected. The ESP-32 microcontroller and the angular velocity sensor are installed on the lower suspension plate 3 to replace the photoelectric gate and the light blocking rod to receive and process data.

[0050] Base leveling adjustment: Use a level to adjust the leveling screws of the pendulum base to make the pendulum base level and the column vertical.

[0051] Horizontal adjustment of the lower suspension plate 3: Place the level between any two suspension lines on the suspension plate, adjust the length of the suspension lines to make the suspension plate horizontal, and fix the three adjustment knobs.

[0052] Drive the instrument to work: Gently twist the upper disc 1 until the small angle limiter of the upper disc 1 makes a clicking sound (the maximum rotation angle is controlled at about 5°), causing the lower suspension disc 3 to swing. The angular velocity sensor installed under the three-line pendulum detects the rotation and generates initial data.

[0053] Data is transmitted via ESP-32 to a Phyphor, generating real-time and overall data images. Correct experimental data can be filtered using the real-time data and images.

[0054] According to J0 = mgRrT 2 / 4π 2First, measure the distance H between the upper and lower disks, the mass m of the lower suspended disk, the mass m of the object to be measured, the distance r from the point on the upper disk 1 (the guide line) to the center, and the distance R from the point on the lower suspended disk 3 (the guide line) to the center. J0 is the moment of inertia of the empty disk, and g is the acceleration due to gravity (9.8 m / s²). 2 (This is a fixed period), where T is the experimental period (which needs to be measured).

[0055] Phyphox automatically records 10 cycles and calculates the average cycle T0 = 1.5s;

[0056] Calculate the moment of inertia:

[0057] J0=(0.3×9.8×0.06×0.03) / (4π 2 (×0.12)×1.5 2 ≈0.0009kg·m²

[0058] Theoretical value (homogeneous disk J) 理论 =1 / 2mR 2 ): J 理论 = 1 / 2 × 0.3 × 0.075 2 = 0.00084 kg·m², with an error of approximately 7%.

[0059] To verify the parallel axis theorem

[0060] 1. Hardware and parameter adjustments

[0061] Add the object to be tested:

[0062] A rectangular metal block: mass m1 = 0.15 kg, dimensions 8 cm × 5 cm × 2 cm;

[0063] The distance d = 4 cm between the center of mass of the metal block and the center of the disk.

[0064] 2. Program and page modifications

[0065] Phyphox Calculation Module:

[0066] Add a "Total Mass" input box (m = m0 + m1 = 0.45 kg); m0 is the mass of the empty disk (the mass of the lower disk without any object to be measured), and m1 is the mass of the object to be measured (i.e., the cuboid metal block).

[0067] Add a "Parallel Axis Theorem Verification" module to compare the theoretical value J. 理论 =J0+m1d 2 The measured value is d, which is the distance between the center of mass of the object to be measured (a rectangular metal block) and the center of mass of the object (the metal block has a uniform mass and the center of mass is its center position) and the center of the lower suspension plate 3 (that is, the straight-line distance between the two centers, which are the center of mass of the object to be measured and the center point of the lower suspension plate, respectively).

[0068] 3. Experiment Reproduction

[0069] The experiment was started after the metal block was placed eccentrically, and the measurement period T1 = 1.8s;

[0070] Calculate the total moment of inertia:

[0071] J1=(0.45×9.8×0.06×0.03) / (4π2×0.12)×1.8 2 ≈0.0015kg·m²

[0072] Theoretical value:

[0073] J 理论 =0.0009 + 0.15 × 0.04 2 =0.00114 kg·m²

[0074] Error analysis: The actual value deviated from the theoretical value by about 31%. Upon inspection, it was found that the measurement error of the suspension length (actual H = 12.5 cm) was found. After correction, the error was reduced to 5%, verifying the parallel axis theorem.

[0075] Key reproduction conditions

[0076] 1. Hardware consistency: The angular velocity sensor model (e.g., MPU6050), microcontroller (ESP-32), and Bluetooth communication module must be consistent;

[0077] 2. Program parameters: Sampling frequency (100Hz), data transmission protocol, and Phyphox calculation formula must be strictly set as described above;

[0078] 3. Experimental environment: Ensure the pendulum is horizontal and the swing angle θ < 5° to reduce interference from air resistance and other factors.

[0079] The above examples demonstrate how the core functionality of this invention can be fully replicated, enabling high-precision measurement and theoretical verification of rotational inertia.

[0080] Improved measurement accuracy: Photogates typically calculate angular velocity by recording the time it takes for the pendulum to pass a specific position, which is easily affected by momentary judgment errors caused by the pendulum obstructing the photogate. Angular velocity sensors, on the other hand, can directly acquire angular velocity data in real time, more accurately capturing changes in the angular velocity of the oscillating object, reducing errors caused by time measurements, and improving the accuracy of experimental data.

[0081] Data acquisition method optimization: The photoelectric gate requires manual setting of the trigger position and can only acquire discrete data from a limited number of positions. The angular velocity sensor can achieve continuous dynamic data acquisition, and can completely record the continuous change curve of angular velocity throughout the entire swing process, providing more comprehensive data support for analyzing the swing process and facilitating the study of the detailed characteristics and laws of the swing.

[0082] Improved experimental efficiency: When using photogates, it may be necessary to repeat the experiment multiple times to obtain sufficient data points, which is cumbersome and time-consuming. Angular velocity sensors, in conjunction with a data acquisition system, can quickly and automatically collect large amounts of data, reducing manual operation steps, shortening experimental time, improving experimental efficiency, and also reducing errors caused by manual operation.

[0083] With expanded functionality and diverse application scenarios, angular velocity sensors can provide more dimensions of motion information. In addition to basic angular velocity measurement, they can be combined with other sensors or data processing methods to conduct more in-depth research, such as analyzing acceleration changes and energy loss during oscillation. This provides more possibilities for experimental expansion and innovative research, enabling experiments to go beyond traditional rotational inertia measurement and be applied to a wider range of dynamic research scenarios.

[0084] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A trilinear pendulum experimental apparatus for digital measurement based on PHYPHOX and ESP-32, characterized in that, Includes a support, an upper disc (1), a lower suspension disc (3), and a 3D printing box (7); The support includes a crossbeam (4), a base (5), and a support column (6). The support column (6) is vertically fixed on the base (5), and the crossbeam (4) is fixed on the upper end of the support column (6). The crossbeam (4) has a bearing in the middle, and the upper disc (1) has a rotating shaft in the middle. The rotating shaft is located in the bearing of the crossbeam (4). The lower suspension disc (3) is connected to the upper disc (1) by three thin ropes. One end of the thin rope is fixed to the lower suspension disc (3), and the other end of the thin rope is wrapped around the adjusting bolt (10). The adjusting bolt (10) is screwed onto the outer periphery of the upper disc (1). The 3D printing box (7) is installed at the center of the bottom of the lower suspension plate (3). It is connected via Bluetooth to the Phyphox page to display the measured moment of inertia and verify the parallel axis theorem. The ESP-32 microcontroller and angular velocity sensor are installed inside the 3D printing box (7).

2. A method for using a trifilar pendulum experimental apparatus based on digital measurement using PHYPHOX and ESP-32, for use with the trifilar pendulum experimental apparatus based on digital measurement using PHYPHOX and ESP-32 as described in claim 1, characterized in that, Includes the following steps: Step 1: Use the ESP-32 microcontroller and angular velocity sensor to collect data, and install the 3D printing box (7) at the bottom of the lower suspension plate (3); Step 2: In the Phyphox page editor, edit the required experimental data collection page; Step 3: Display the measured moment of inertia and verify the parallel axis theorem on the Phyphox page.

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