An experimental device for quantitative study of rigid body rotation gyroscope and a use method thereof

Abstract

The application provides an experimental device and a use method for quantitatively studying a rigid body rotating gyroscope, which comprises a support rod vertically arranged, a connecting seat mounted on the upper end of the support rod through a precession bearing and capable of rotating horizontally around the support rod, a crossbar with a middle part mounted on the connecting seat through a pitching bearing, the crossbar being capable of oscillating up and down in the vertical direction, a rotating wheel rotatably mounted on one end of the crossbar, a weight slidably and detachably mounted on the crossbar between the other end of the crossbar and the connecting part with the pitching bearing, a first driving mechanism connected with the rotating wheel and used for driving the rotating wheel to rotate, and a second driving mechanism connected with the weight and used for driving the weight to reciprocate along the length direction of the crossbar. The method is a use method of the device for studying the gyroscopic motion of the device, the device can adjust the rotating speed of the rotating wheel, the mass of the weight and the length of the force arm, continuously adjusts the rotating angular velocity and the gravity moment, and can be well used for quantitatively studying the motion law of the rigid body rotating gyroscope.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of teaching experiment device, and particularly relates to an experimental device for quantitatively studying a rigid-body rotation gyroscope and a use method thereof. BACKGROUND

[0002] Gyroscopes are widely used in the technical fields of navigation, sensing and monitoring, and are particularly used in mobile phones, automobiles, aerospace vehicles and the like, and are closely related to modern science and technology and life. Therefore, it is necessary to introduce gyroscopes in teaching. With the advent of the electronic and information era, gyroscopes have developed into micro-sized MEMS (Micro Electro Mechanical System) gyroscopes, and various gyroscopes have been developed according to their principles, such as rigid-body rotation gyroscopes, tuning fork vibration gyroscopes, hemispherical resonator gyroscopes and optical fiber gyroscopes. Among them, the rigid-body rotation gyroscope is the most typical model of rigid-body rotation as the original mechanical gyroscope.

[0003] The rigid-body rotation gyroscope teaching device used in the current teaching process is usually a demonstration type device, and can only qualitatively demonstrate the phenomena of the fixed axis, precession and nutation of the gyroscope. The device cannot quantitatively study the changes of various physical quantities in the rigid-body rotation gyroscope model and the correlation between them. That is, the existing rigid-body rotation gyroscope teaching device cannot comprehensively display the characteristics of the rigid-body rotation gyroscope. Therefore, it is necessary to develop an experimental device that can comprehensively quantitatively study the characteristics of the rigid-body rotation gyroscope. SUMMARY

[0004] The purpose of the present application is to provide an experimental device for quantitatively studying a rigid-body rotation gyroscope and a use method thereof. The device can adjust the rotation speed of the rotating wheel, the mass of the weight and the length of the force arm, and further realize the continuous adjustment of the rotation angular velocity and the gravitational moment, and can be well used for quantitatively studying the motion law of the rigid-body rotation gyroscope.

[0005] To achieve the above purpose, the present application adopts the following technical scheme:

[0006] An experimental device for quantitatively studying a rigid-body rotation gyroscope, comprising:

[0007] A support rod vertically arranged;

[0008] A connecting seat mounted on the upper end of the support rod through a precession bearing, the connecting seat being horizontally rotatable about the support rod;

[0009] A cross rod (4) having a middle part mounted on the connecting seat through a pitching bearing, the cross rod being vertically swingable;

[0010] A rotating wheel rotatably mounted on one end of the cross rod;

[0011] A weight is slidably and detachably mounted on the crossbar, the sliding range of the weight being limited to the area between the other end of the crossbar and the pitch bearing;

[0012] A first driving mechanism and a second driving mechanism are provided. The first driving mechanism is connected to the rotating wheel and is used to drive the rotating wheel to rotate. The second driving mechanism is mounted on the crossbar and connected to the weight, and is used to drive the weight to reciprocate along the length of the crossbar.

[0013] In one embodiment of this application, a battery is also included, which is electrically connected to the first drive mechanism and the second drive mechanism.

[0014] In one embodiment of this application, it further includes:

[0015] The first sensor, mounted on the crossbar, is used to measure the rotational speed or angular velocity of the rotating wheel;

[0016] The second sensor is installed on the connecting seat or crossbar and is used to measure the rotational speed or angular velocity of the connecting seat.

[0017] The third sensor, mounted on the crossbar, is used to measure the pitch angle, pitch frequency, or pitch angular velocity of the crossbar.

[0018] In one embodiment of this application, a control terminal and a wireless communication control module wirelessly connected to the control terminal are further included. The wireless communication control module is installed inside the crossbar and electrically connected to the first sensor, the second sensor, the third sensor, the first drive mechanism, and the second drive mechanism.

[0019] In one embodiment of this application, the second driving mechanism is a lead screw motor, which is connected to a lead screw mounted on the crossbar. The lead screw is rotatably connected to the slider, wherein the weight is mounted on the slider.

[0020] In one embodiment of this application, the weights include several blocks of different masses, and any one of the weights can be detachably mounted on the slider.

[0021] In one embodiment of this application, the connecting seat has a U-shaped structure, and its bottom is coaxially rotatably connected to the upper end of the support rod via the precession bearing;

[0022] It also includes a pitch axis, which is horizontally arranged and has its two ends rotatably mounted on the upper part of the connecting seat via the pitch bearings; the crossbar passes through the U-shaped groove of the connecting seat and is connected to the pitch axis via the connecting rod.

[0023] How to use the experimental setup for quantitative research on rigid body rotating gyroscopes:

[0024] (a) When studying the angular velocity of rotation With precession angular velocity When the relationship is defined, the method includes the following steps:

[0025] S1-1. Adjust the second drive mechanism to make the weight deviate from the balance position;

[0026] S1-2. Adjust the first drive mechanism to change the rotational speed of the self-rotating wheel;

[0027] S1-3. Measure the precession angular velocity of the connecting seat. and the rotational angular velocity of the rotating wheel Obtaining precession angular velocity With rotational angular velocity The changing relationship;

[0028] or,

[0029] (ii) When studying gravitational torque and precession angular velocity When the relationship is defined, the method includes the following steps:

[0030] S2-1. Adjust the first drive mechanism to drive the rotating wheel to rotate at high speed;

[0031] S2-2, Adjusting the gravitational torque: Adjusting the second driving mechanism to drive the weight to change position, or replacing the weight with one of different masses;

[0032] S2-3. Obtain the change data of gravitational torque and measure the precession angular velocity of the connecting seat (3). Obtaining precession angular velocity The relationship between the change of gravitational torque;

[0033] or,

[0034] (III) When studying the moment of inertia I0 of a rotating wheel, the method includes the following steps:

[0035] S3-1. Perform linear fitting on the data measured in steps S1-3 and S2-3, and obtain the moment of inertia I0 of the self-rotating wheel based on the slope of the linear fitting.

[0036] or,

[0037] (iv) When studying the angular velocity of rotation When considering the relationship with the nutation frequency f, the method includes the following steps:

[0038] S4-1. Adjust the gravitational torque to cause the connecting seat to precess;

[0039] S4-2. An instantaneous torque is applied to the crossbar, causing the crossbar to nutate;

[0040] S4-3. Adjust the first drive mechanism to drive the rotating wheel and change its rotational angular velocity.

[0041] S4-4. Measure the nutation frequency f of the crossbar (4) and the rotational angular velocity of the rotating wheel (5). Obtain the nutation frequency f as a function of the rotation angular velocity The changing relationship;

[0042] or,

[0043] (v) When studying the overall moment of inertia I of an irregularly distributed gyroscope, the method includes the following steps:

[0044] S5-1. Perform linear fitting on the data measured in step S4-4, and obtain the overall moment of inertia I based on the slope of the linear fitting.

[0045] or,

[0046] (vi) When studying the damping coefficient β of a gyroscope, the method includes the following steps:

[0047] S6-1. Adjust the gravitational torque to cause the connecting seat to precess;

[0048] S6-2. An instantaneous torque is applied to the crossbar, causing the crossbar to nutate;

[0049] S6-3. Record the precession and nutation data for a period of time, perform fitting, and obtain the damping coefficient β of the gyroscope;

[0050] or,

[0051] (vii) When demonstrating the fixed-axis phenomenon of a gyroscope, the method includes the following steps:

[0052] S7-1. Adjust the gravitational torque to bring the gyroscope into a balanced state;

[0053] S7-2. Adjust the first drive mechanism to make the rotating wheel rotate at high speed;

[0054] S7-3. Rotate the support rod at will and observe the stability of the crossbar and the rotating wheel.

[0055] In one embodiment of this application, the precession angular velocity With the aforementioned rotational angular velocity The relevant formula for the relationship between gravitational torque and the moment of gravity is:

[0056]

[0057] Where Δl is the distance of the weight from its equilibrium position; m is the mass of the weight; mgΔl is the gravitational torque; and I0 is the moment of inertia of the rotating wheel.

[0058] In one embodiment of this application, the nutation frequency f and the rotation angular velocity are... The relevant formula for the relationship between the overall rotational inertia I and the following is:

[0059]

[0060] The nutation angular velocity of the crossbar The data on changes over time t can be fitted using the following formula:

[0061]

[0062] Where A, β, ω, α and C are all fitting constants;

[0063] Continuously monitored nutation angular velocity The nutation frequency f = ω / 2π can be obtained by fitting the data of the change over time t.

[0064] Based on the nutation frequency f and the rotation angular velocity By fitting the measurement data, the overall moment of inertia I of the irregularly distributed gyroscope can be obtained;

[0065] Similarly, through continuous monitoring of nutation angular velocity The damping coefficient β of the gyroscope can be obtained by fitting the data on the change over time t.

[0066] Compared with the prior art, the beneficial effects of the present invention are:

[0067] 1. The experimental apparatus for quantitatively studying rigid body rotation gyroscopes in this application can achieve continuous and stable adjustment of rotational angular velocity and gravitational torque by adjusting the rotation of the spin wheel, the mass of the weights, and the length of the lever arm (position of the weights). This facilitates quantitative research on the relationship between rotation and precession, the relationship between gravitational torque and precession, the relationship between rotation and nutation, nutation decay, and moment of inertia. The apparatus has a simple structure, reasonable setup, and can quantitatively adjust its operation, making it easier to better demonstrate the characteristics and motion laws of rigid body rotation gyroscopes.

[0068] 2. The experimental apparatus disclosed in this application is equipped with a first sensor, a second sensor, and a third sensor to measure in real time the rotational speed or angular velocity of the rotating wheel, the rotational speed or angular velocity (i.e., precession angular velocity) of the connecting seat, and the pitch angle, pitch frequency, or pitch angular velocity (i.e., nutation angle, nutation frequency, and nutation angular velocity) of the crossbar. This enables quantitative monitoring of various physical quantities during the motion of the rigid body rotating gyroscope, better demonstrating the motion law of the rigid body rotating gyroscope, and facilitating more in-depth quantitative research and teaching.

[0069] 3. The device is battery powered and uses wireless communication for control and data acquisition, effectively avoiding interference from wires in the operation and quantitative measurement of the device.

[0070] 4. This experimental setup and method for quantitatively studying rigid body rotating gyroscopes allows for qualitative and quantitative research on the relationship between spin angular velocity and precession angular velocity, the relationship between gravitational torque and precession angular velocity, the moment of inertia of the spinning wheel, the relationship between spin angular velocity and nutation frequency, the overall moment of inertia of irregularly distributed gyroscopes, the damping coefficient of the gyroscope, and the demonstration of the gyroscope's fixed-axis phenomenon. It is easy to operate and has many functions. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a three-dimensional structural diagram of the experimental setup for quantitatively studying rigid body rotating gyroscopes in this application.

[0073] Figure 2 for Figure 1 A magnified structural diagram of part A in the middle.

[0074] Figure label:

[0075] 1. Base;

[0076] 2. Support rod;

[0077] 3. Connecting seat; 31. Precessing bearing;

[0078] 4. Crossbar; 41. Pitch bearing; 42. Pitch shaft; 43. Connecting rod;

[0079] 5. Rotating wheel; 51. First drive mechanism;

[0080] 6. Weights; 60. Mounting hole; 61. Second drive mechanism; 611. Lead screw; 612. Slider. Detailed Implementation

[0081] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of this application. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0082] In the description of this invention, it should be understood that the terms "center," "length," "upper," "lower," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used to facilitate the description of this invention and to simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0083] The terms “comprising” and “having”, and any variations thereof, used in this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0084] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0085] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0086] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0087] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0088] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0089] like Figure 1 As shown in the figure, this application provides an experimental apparatus for quantitatively studying rigid body rotating gyroscopes. The experimental apparatus mainly includes the following components:

[0090] Base 1;

[0091] A support rod 2 is vertically mounted on the base 1;

[0092] Connecting seat 3 installed on the upper part of support rod 2;

[0093] The crossbar 4 is installed on the connecting seat 3;

[0094] A rotating wheel 5 installed at one end of the crossbar 4 and a weight 6 installed at the other end of the crossbar 4; as well as a first drive mechanism 51 and a second drive mechanism 61 set on the crossbar 4, etc.

[0095] The support rod 2 is vertically arranged, and the bottom of the connecting seat 3 is rotatably mounted on the upper end of the support rod 2 via the precession bearing 31. The connecting seat 3 can rotate horizontally around the support rod 2.

[0096] The middle part of the crossbar 4 is mounted on the connecting seat 3 via the pitch bearing 41, so that the crossbar 4 can swing up and down in the vertical direction.

[0097] The self-rotating wheel 5 is rotatably mounted on one end of the crossbar 4, and its axis is parallel to or coincides with the length direction of the crossbar 4.

[0098] The weight 6 is detachably mounted on the crossbar 4, specifically located between the other end of the crossbar 4 and the pitch bearing 41. The weight 6 can reciprocate along the length of the crossbar 4, that is, the weight 6 can reciprocate on the end of the crossbar 4 away from the rotating wheel 5, and its range of movement is limited to the area between the other end of the crossbar 4 and the pitch bearing 41. Figure 1 As shown, the length of the lever arm at the end of the crossbar 4 where the weight 6 is mounted is longer than the length at the end of the crossbar 4 where the rotating wheel 5 is mounted.

[0099] The first drive mechanism 51 is mounted on the crossbar 4 and located on one side of the pitch bearing 41. Its output end is connected to the rotating wheel 5 and is used to drive the rotating wheel 5 to rotate around its axis. The first drive mechanism 51 can be a speed-regulating motor, a servo motor, or a stepper motor, etc., and can stably and continuously adjust and control the rotation of the rotating wheel 5.

[0100] The second drive mechanism 61 is also mounted on the crossbar 4, located on the other side of the pitch bearing 41. The output end of the second drive mechanism 61 is connected to the weight 6, which is used to drive the weight 6 to reciprocate along its length on the crossbar 4 to adjust the lever arm length of the weight 6. The second drive mechanism 61 can be a linear drive device such as a cylinder or a lead screw.

[0101] In addition to the main structure disclosed above, the experimental device may also include a battery (not shown in the figure). This battery is installed inside the crossbar 4 and is electrically connected to the first drive mechanism 51 and the second drive mechanism 61, providing power to them. The battery can be rechargeable, fixedly installed inside the crossbar 4, and has a charging port for charging via a detachable wire. Using a wireless external power cord (wire) for battery power avoids interference from the wires on the movement of various parts of the experimental device, resulting in more accurate and precise demonstration of motion patterns.

[0102] Furthermore, in its embodiment, the experimental device may be further equipped with a first sensor, a second sensor, and a third sensor (not shown in the figure). The first sensor is mounted on the crossbar 4 and is used to measure the rotational speed or angular velocity of the rotating wheel 5. The second sensor is mounted on the connecting seat 3 and is used to measure the rotational speed or angular velocity of the connecting seat 3 when it rotates (i.e., precession) around the support rod 2. The third sensor is mounted on the crossbar 4 and is used to measure the pitch angle (i.e., the angle between the end of the crossbar 4 where the rotating wheel 5 is located and the vertical direction) when the crossbar 4 swings up and down (i.e., nutation), and / or measure the pitch frequency (i.e., the nutation frequency, the frequency of the up and down swing of the end of the crossbar 4 where the rotating wheel 5 is located), and measure the pitch angular velocity (i.e., nutation angular velocity). The first, second, and third sensors can be photogate sensors and / or Hall effect sensors, etc. The first, second, and third sensors are used to accurately measure the changes in various physical quantities during the motion of the rigid body rotating gyroscope, enabling quantitative research on the rigid body rotating gyroscope.

[0103] In another embodiment, the experimental apparatus includes a control terminal and a wireless communication control module (not shown in the figure). The wireless communication control module is installed inside the crossbar 4 and is electrically connected to the first sensor, second sensor, third sensor, first drive mechanism 51, and second drive mechanism 61. The wireless communication control module is also wirelessly connected to the control terminal, such as via Bluetooth or infrared. The control terminal can be a desktop computer, tablet computer, laptop computer, mobile phone, or other device with corresponding programs and software installed. The control terminal has functions such as instrument control, data reception, data display, data processing, data analysis, data storage, and experimental assistance.

[0104] A wireless communication control module is set up to wirelessly transmit data collected by the first, second, and third sensors to the control terminal, which then wirelessly transmits control information to the first drive mechanism 51 and the second drive mechanism 61 to control the rotation of the self-rotating wheel 5 and the movement of the weight 6. Using wireless communication for control and data acquisition effectively avoids interference from wires on the movement of various parts of the experimental device, ensuring accurate representation of the characteristics and motion laws of the rigid body rotation gyroscope.

[0105] In a specific implementation scenario, such as Figure 1 The second driving mechanism 61 is a stepper motor. The working end of the stepper motor is connected to the lead screw 611. The lead screw 611 is arranged along the length direction of the crossbar 4, and the optical axis is parallel to the lead screw 611. The slider 612 is mounted on the lead screw 611 and the optical axis. When the stepper motor is running, it can drive the lead screw 611 to rotate, driving the slider 612 to reciprocate along the lead screw 611 and the optical axis.

[0106] The weights 6 consist of several pieces of different masses, and any one of the weights 6 can be detachably mounted on the slider 612, moving back and forth along the crossbar 4 with the slider 612. By manually replacing different weights 6 to change the mass of the weights 6 on the crossbar 4, it is convenient to quantitatively study the effect of the change in the mass of the weights on the motion of the rigid body rotation gyroscope.

[0107] In a specific implementation scenario, such as Figure 1 As shown, the upper surface of the slider 612 is provided with a mounting post, and the corresponding weight 6 is provided with a mounting hole 60 that matches the mounting post. The weight 6 and the slider 612 are detachably installed by cooperating with the mounting post through the mounting hole 60. The installation and positioning are accurate, it is not easy to fall off, and the disassembly and assembly operations are convenient.

[0108] In another specific implementation scenario, one of the weights 6 and the slider 612 is made of magnet, while the other is made of iron. The weights 6 and the slider 612 are detachably connected by magnetic attraction, which is convenient to operate and not easy to fall off. It should be understood that when using magnetic attraction for detachable connection, in order to avoid the magnet generating attraction forces on other parts and affecting the motion law of the rigid body rotation gyroscope, other components should be made of non-ferrous materials.

[0109] like Figure 1 As shown, the connecting seat 3 has a U-shaped structure, and its bottom is rotatably connected to the upper end of the support rod 2 via the precession bearing 31, so that the connecting seat 3 can rotate freely horizontally about the axis of the support rod 2.

[0110] like Figure 1 and Figure 2 As shown, the upper part of the connecting seat 3 is provided with a pitch shaft 42, which is horizontally arranged. Its two ends are rotatably mounted on the upper ends of the U-shaped structure of the connecting seat 3 via pitch bearings 41. A crossbar 4 passes through the U-shaped groove of the connecting seat 3, located below the pitch shaft 42, and is connected to the middle of the pitch shaft 42 via a connecting rod 43. The crossbar 4 can swing up and down vertically about the axis of the pitch shaft 42.

[0111] The connecting seat 3 is configured as a U-shaped structure and is equipped with a pitch axis 42. A crossbar 4 is installed in the middle of the pitch axis 42 via a connecting rod 43, so that the rotation center of the crossbar 4 is located on the axial direction of the support rod 2. The structure is stable and the configuration is reasonable.

[0112] In addition, the experimental setup includes a base 1, with the lower end of the support rod 2 connected to the base 1, ensuring the support rod 2 is installed vertically. During the experiment, the base 1 is placed stably before proceeding to guarantee the accuracy of the experimental research.

[0113] Embodiments of the present invention also provide a method for using the experimental apparatus described above for quantitatively studying rigid body rotating gyroscopes.

[0114] The physical phenomena of the gyroscope experiment can be simply described as follows: when the spinning wheel 5 reaches a stable angular velocity... When the gyroscope rotates and the position of the weight 6 deviates from the equilibrium position (Δl≠0), the gyroscope (connecting seat 3 and the part above it) will precess (horizontal direction) around the precession bearing 31 and the support rod 2; when the precession is simultaneously disturbed by an external instantaneous torque (the force that instantaneously acts on the crossbar 4), the gyroscope (crossbar 4 and the part above it) will nutate (pitch direction).

[0115] The specific operation of the above-mentioned device when studying the different physical quantities of a gyroscope and their interrelationships is as follows.

[0116] (i) When used to study the angular velocity of rotation With precession angular velocity When determining the relationship, the specific operational steps include the following:

[0117] S1-1. Control the second drive mechanism 61 through the control terminal to drive the weight 6 to move, so that the position of the weight 6 deviates from the balance position.

[0118] S2-1. Control the first drive mechanism 51 through the control terminal to drive the rotating wheel 5 to change the speed, that is, drive the rotating wheel 5 to rotate at different speeds;

[0119] S3-1. The second sensor collects the horizontal rotational angular velocity of the connecting seat 3 relative to the support rod 2, that is, it collects the precession angular velocity of the connecting seat 3. At the same time, the first sensor collects the rotational angular velocity of the rotating wheel 5. Precession angular velocity and rotational angular velocity The measurement data is wirelessly transmitted to the control terminal for display. Then, the data is recorded, processed, and analyzed to obtain the precession angular velocity of connector 3. The angular velocity of the rotation of the rotating wheel 5 The changing relationship.

[0120] (ii) When used to study gravitational torque and precession angular velocity When determining the relationship, the specific operational steps include the following:

[0121] S2-1, The control terminal controls the movement of the first drive mechanism 51, driving the rotating wheel 5 to rotate at high speed. Specifically, the rotation angular velocity can be controlled. Preferred rotational angular velocity Within the range of 30–36 r / s;

[0122] S2-2, Adjusting the gravitational torque: For example, controlling the second drive mechanism 61 to drive the weight 6 to move along the crossbar 4, changing the position of the weight 6; or replacing the weight 6 with a different mass, that is, changing the mass of the weight 6;

[0123] S2-3, The precession angular velocity of the connector 3 is collected by the second sensor. Simultaneously, read the change in distance Δl between weight 6 and the equilibrium position and / or the change in mass of weight 6, i.e., the change in gravitational torque; and record the corresponding precession angular velocity. The data on gravitational torque is transmitted to the control terminal for display. Then, through the recording, processing, and analysis of the data, the precession angular velocity of the connecting seat 3 can be obtained. The relationship between the torque of weight 6 and the change of gravitational torque.

[0124] (III) When studying the moment of inertia I0 of the rotating wheel 5, the following operating steps are included:

[0125] S3-1. The measurement data obtained in steps S1-3 and S2-3 above are linearly fitted using a formula. The moment of inertia I0 of the rotating wheel 5 can be obtained based on the slope of the linear fit.

[0126] (iv) When used to study the angular velocity of rotation When determining the relationship with the nutation frequency f, the following operational steps are included:

[0127] S4-1. Adjust and change the gravitational torque (such as changing the distance Δl of the weight from the equilibrium position and / or the mass of the weight 6) to cause the connecting seat 3 to precess, that is, to undergo horizontal rotation.

[0128] S4-2. Apply an instantaneous torque to the crossbar 4 (this instantaneous torque can be an instantaneous external force acting on the crossbar 4, usually applied to the end of the crossbar 4 away from the rotating wheel 5) to cause the crossbar 4 to nutate.

[0129] S4-3, The control terminal controls the first drive mechanism 51 to drive the rotating wheel 5 and change its rotation speed.

[0130] S4-4, Nuctuation angular velocity collected by the third sensor over a period of time. The data is used to obtain the nutation frequency f through fitting by the control terminal. At the same time, the rotational angular velocity of the rotating wheel 5 is collected by the first sensor. The corresponding nutation frequency f and rotation angular velocity The data is transmitted to the control terminal, multiple sets of data are recorded, and then processed and analyzed to obtain the rotational angular velocity. The relationship between the nutation frequency f and the change.

[0131] (v) When used to study the overall moment of inertia I of an irregularly distributed gyroscope, the specific operating steps are as follows:

[0132] S5-1, The rotational angular velocity measured in step S4-4 above. The data of the nutation frequency f are linearly fitted using a formula. Based on the slope of the fitted data, the overall moment of inertia I of the irregularly distributed gyroscope can be obtained.

[0133] (vi) When studying the damping coefficient β of a gyroscope, the following steps are included:

[0134] S6-1. Adjust and change the gravitational torque (such as changing the distance Δl of the weight from the equilibrium position and / or the mass of the weight 6) to cause the connecting seat 3 to precess, that is, to undergo horizontal rotation.

[0135] S6-2. Apply an instantaneous torque to the crossbar 4 (this instantaneous torque can be an instantaneous external force acting on the crossbar 4, usually applied to the end of the crossbar 4 away from the rotating wheel 5) to cause the crossbar 4 to nutate.

[0136] S6-3, Precession data (such as precession angular velocity) is collected over a period of time by the second and third sensors. ) and nutation data (nutation angular velocity) By fitting the formula, the value of the damping coefficient β of the gyroscope can be obtained.

[0137] (vii) When demonstrating the fixed-axis phenomenon of a gyroscope, the following operating steps are included:

[0138] S7-1. Adjust and change the gravitational torque (such as changing the distance Δl of the weight from the equilibrium position and / or the mass of the weight 6) to make the gyroscope in a balanced state, that is, to make the crossbar 4 in a balanced position and not to cause nutation.

[0139] S7-2, the control terminal controls the movement of the first drive mechanism 51, driving the rotating wheel 5 to rotate at high speed, specifically, controlling the rotation angular velocity.

[0140] S7-3. Remove the support rod 2 from the base 1 and rotate it freely to observe the pointing stability of the gyroscope, specifically the stability of the crossbar 4 and the rotating wheel 5. At this time, the crossbar 4 and the rotating wheel 5 have a fixed axis.

[0141] In one embodiment, when the crossbar 4 is horizontal and there is no nutation, the precession angular velocity is... With rotational angular velocity It is inversely proportional to the gravitational torque or the distance Δl from the equilibrium position of the weight 6, where the gravitational torque is mgΔl.

[0142] Precession angular velocity With rotational angular velocity The relevant formula for the relationship between gravitational torque and gravitational moment can be written as:

[0143]

[0144] In formula (1), Δl is the distance of the weight from the equilibrium position; m is the mass of the weight; mgΔl is the gravitational torque; and I0 is the moment of inertia of the rotating wheel.

[0145] Among them, the distance Δl from the equilibrium position of the weight and the angular velocity of rotation are... The rotation angular velocity can be precisely controlled by the second drive mechanism 6 and the first drive mechanism 51, and the distance Δl of the weight deviating from the equilibrium position can be read or measured by the scale markings; and precession angular velocity Real-time and accurate data collection can be achieved through the first and second sensors.

[0146] Acquire precession angular velocity With rotational angular velocity The changing data, and the precession angular velocity By linearly fitting the data of the change in gravitational torque (or Δl) using the above formula (1), the measurement result of the rotational inertia I0 of the self-rotating wheel 5 can be obtained.

[0147] Furthermore, when the crossbar 4 nutates near its horizontal position, the nutation frequency f and the rotation angular velocity... It is directly proportional to the overall moment of inertia I of the connecting seat 3 rotating around the fulcrum of the support rod 2.

[0148] At this time, the nutation frequency f and the rotation angular velocity The relevant formula for the relationship between the overall rotational inertia I and the rotational moment of inertia can be written as:

[0149]

[0150] The change in the position of the weights will cause a change in the overall moment of inertia I, where I = I′ + mΔl 2 I′ is the overall rotational inertia of the gyroscope about the central pivot (i.e., the precession bearing) after the weights are removed.

[0151] Rotational angular velocity It can be precisely controlled by the first drive mechanism 51 and accurately measured in real time by the first sensor.

[0152] Then, by continuously monitoring nutation data That is, nutation angular velocity The data on the change over time t are fitted according to the following formula (3).

[0153]

[0154] The nutation frequency of the gyroscope can be quantitatively measured as f = ω / 2π, where A, β, α and C are all fitting constants.

[0155] Furthermore, based on the above data, the nutation frequency f and the rotation angular velocity are compared... The measurement data is linearly fitted using formula (2), and the overall rotational inertia I of the irregularly distributed gyroscope can be obtained based on the fitting slope.

[0156] Since undamped conditions do not exist in reality, continuous monitoring of nutation data is necessary. That is, nutation angular velocity The damping coefficient β can be quantitatively measured by fitting the data of the change with time t using formula (3). In this case, A, ω, α and C in formula (3) are all fitting constants.

[0157] In summary, the experimental apparatus for quantitatively studying a rigid body rotation gyroscope, as described in this application, has a connecting seat 3 rotatably mounted on a support rod 2 via a precession bearing 31, and a crossbar 4 rotatably mounted on the connecting seat 3. A spin wheel 5 is installed at one end of the crossbar 4 and is driven to rotate by a first drive mechanism 51. The middle part of the crossbar 4 is mounted on the connecting seat 3 via a pitch bearing 41, allowing the crossbar 4 to pitch up and down. A weight 6 is detachably mounted at the other end of the crossbar 4, and the weight 6 is driven by a second drive mechanism 61 to reciprocate along the length of the crossbar 4. Furthermore, the weight 6 is detachable and can be replaced with weights of different masses. This device can achieve continuous and stable adjustment of the rotational angular velocity and gravitational torque by adjusting the rotation of the spin wheel 5, the mass of the weight 6, and the length of the lever arm (position of the weight 6). This facilitates quantitative research on the relationship between rotation and precession, the relationship between gravitational torque and precession, the relationship between rotation and nutation, and nutation decay. The device has a simple structure, reasonable settings, and can quantitatively adjust its operation, making it easier to better demonstrate the characteristics and motion laws of a rigid body rotation gyroscope.

[0158] This device is equipped with a first sensor, a second sensor, and a third sensor to measure in real time the changes in the rotational speed or angular velocity of the rotating wheel, the rotational speed or angular velocity (i.e., precession angular velocity) of the connecting seat, and the pitch angle (i.e., nutation angle) of the crossbar. This enables quantitative monitoring of various physical quantities during the motion of the rigid body rotational gyroscope, allowing for a better demonstration of the motion laws of the rigid body rotational gyroscope and facilitating more in-depth quantitative research and teaching. It is battery-powered and uses wireless communication for control and data acquisition, effectively avoiding interference from wires in the device's operation and quantitative measurements.

[0159] This experimental setup and method for quantitatively studying rigid body rotating gyroscopes allows for qualitative and quantitative research on the relationship between spin angular velocity and precession angular velocity, the relationship between gravitational torque and precession angular velocity, the moment of inertia of the spinning wheel, the relationship between spin angular velocity and nutation frequency, the overall moment of inertia of irregularly distributed gyroscopes, the damping coefficient of the gyroscope, and the demonstration of the gyroscope's fixed-axis phenomenon. It is easy to use and provides comprehensive demonstrations.

[0160] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the technical solutions of the present invention. Any technical solution that can be implemented based on the above embodiments without creative effort should be considered to fall within the scope of protection of the patent of the present invention.

Claims

1. A method for using an experimental apparatus for quantitatively studying a rigid body rotating gyroscope, characterized in that, The experimental setup for quantitatively studying rigid body rotating gyroscopes includes: Support rod (2), which is set vertically; The connecting seat (3) is installed on the upper end of the support rod (2) via a precession bearing (31), and the connecting seat (3) can rotate horizontally around the support rod (2); A crossbar (4), the middle part of which is mounted on the connecting seat (3) via a pitch bearing (41), the crossbar (4) can swing up and down in the vertical direction; The self-rotating wheel (5) is rotatably mounted on one end of the crossbar (4); A weight (6) is slidably and detachably mounted on the crossbar (4), and the sliding range of the weight (6) is limited to the area between the other end of the crossbar (4) and the pitch bearing (41); The first driving mechanism (51) and the second driving mechanism (61) are connected to the rotating wheel (5) to drive the rotating wheel (5) to rotate; the second driving mechanism (61) is mounted on the crossbar (4) and connected to the weight (6) to drive the weight (6) to move back and forth along the length of the crossbar (4). The method of using the experimental apparatus for quantitatively studying rigid body rotating gyroscopes includes: When studying the angular velocity of rotation With precession angular velocity When the relationship is defined, the method includes the following steps: S1-1. Adjust the second drive mechanism (61) to make the weight (6) deviate from the balance position; S1-2. Adjust the first drive mechanism (51) to change the rotation speed of the self-rotating wheel (5); S1-3, Measure the precession angular velocity of the connecting seat (3). and the rotational angular velocity of the rotating wheel (5) Obtain the precession angular velocity With rotational angular velocity The changing relationship; When studying gravitational torque and precession angular velocity When the relationship is defined, the method includes the following steps: S2-1. Adjust the first drive mechanism (51) to drive the rotating wheel (5) to rotate at high speed; S2-2, Adjusting the gravitational torque: Adjust the second driving mechanism (61) to drive the weight (6) to change its position, or replace the weight (6) with a different mass. S2-3. Obtain the change data of gravitational torque and measure the precession angular velocity of the connecting seat (3). Obtain the precession angular velocity The relationship between the change of gravitational torque; When studying the moment of inertia I0 of a rotating wheel, the method includes the following steps: S3-1. Perform linear fitting on the data measured in steps S1-3 and S2-3, and obtain the moment of inertia I0 of the self-rotating wheel (5) based on the slope of the linear fitting. When studying the angular velocity of rotation With nutation frequency f When the relationship is defined, the method includes the following steps: S4-1. Adjust the gravitational torque to cause the connecting seat (3) to precess; S4-2, Apply an instantaneous torque to the crossbar (4), causing the crossbar (4) to nutate; S4-3, Adjust the first drive mechanism (51) to drive the rotating wheel (5) to change the rotation angular velocity. ; S4-4. Measure the nutation frequency of the crossbar (4). f and the rotational angular velocity of the rotating wheel (5) Obtain nutation frequency f With rotational angular velocity The changing relationship; When studying the overall moment of inertia I of an irregularly distributed gyroscope, the method includes the following steps: S5-1. Perform linear fitting on the data measured in step S4-4, and obtain the overall moment of inertia I based on the slope of the linear fitting. When studying the damping coefficient of a gyroscope β When the method is used, it includes the following steps: S6-1. Adjust the gravitational torque to cause the connecting seat (3) to precess; S6-2, Apply an instantaneous torque to the crossbar (4), causing the crossbar (4) to nutate; S6-3. Record the precession and nutation data for a period of time, perform fitting, and obtain the damping coefficient of the gyroscope. β ; When demonstrating the fixed-axis phenomenon of a gyroscope, the method includes the following steps: S7-1. Adjust the gravitational torque to bring the gyroscope into a balanced state; S7-2. Adjust the first drive mechanism (51) to make the rotating wheel (5) rotate at high speed; S7-3. Rotate the support rod (2) at will and observe the stability of the crossbar (4) and the rotating wheel (5).

2. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 1, characterized in that, It also includes a battery, which is electrically connected to the first drive mechanism and the second drive mechanism.

3. The method of using the experimental apparatus for quantitatively studying rigid body rotating gyroscopes according to claim 1 or 2, characterized in that, Also includes: The first sensor is mounted on the crossbar (4) and is used to measure the rotational speed or angular velocity of the self-rotating wheel (5); The second sensor is installed on the connecting seat (3) or the crossbar (4) and is used to measure the rotational speed or angular velocity of the connecting seat (3); The third sensor is installed on the crossbar (4) and is used to measure the pitch angle, pitch frequency or pitch angular velocity of the crossbar (4).

4. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 3, characterized in that, It also includes a control terminal and a wireless communication control module that is wirelessly connected to the control terminal. The wireless communication control module is installed inside the crossbar (4) and is electrically connected to the first sensor, the second sensor, the third sensor, the first drive mechanism (51), and the second drive mechanism (61).

5. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 1, characterized in that, The second drive mechanism (61) is a lead screw motor, which is connected to the lead screw (611) mounted on the crossbar (4). The lead screw (611) is rotatably connected to the slider (612), wherein the weight (6) is mounted on the slider (612).

6. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 5, characterized in that, The weights (6) include several pieces of different masses, and any one of the weights (6) can be detachably installed on the slider (612).

7. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 1, characterized in that, The connecting seat (3) has a U-shaped structure, and its bottom is coaxially rotatably connected to the upper end of the support rod (2) via the precession bearing (31); It also includes a pitch axis (42), which is horizontally arranged and has its two ends rotatably mounted on the upper part of the connecting seat (3) via the pitch bearing (41); the crossbar (4) passes through the U-shaped groove of the connecting seat (3) and is connected to the pitch axis (42) via the connecting rod (43).

8. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 1, characterized in that, The precession angular velocity With the aforementioned rotational angular velocity The relevant formula for the relationship between gravitational torque and the moment of gravity is: , in, denoted as , where is the distance the weight deviates from its equilibrium position; m is the mass of the weight. I0 is the gravitational torque; I0 is the moment of inertia of the rotating wheel.

9. The method of using the experimental apparatus for quantitatively studying a rigid body rotating gyroscope according to claim 8, characterized in that, The nutation frequency f With the aforementioned rotational angular velocity The relevant formula for the relationship between the overall rotational inertia I and the following is: , The nutation angular velocity of the crossbar The data on changes over time t can be fitted using the following formula: , Where A, β, ω, α and C are all fitting constants; Nutting angular velocity through continuous monitoring Nutting frequency can be obtained by fitting the data of changes over time t. f , ; According to nutation frequency f With rotational angular velocity By fitting the measurement data, the overall moment of inertia I of the irregularly distributed gyroscope can be obtained; Similarly, through continuous monitoring of nutation angular velocity The damping coefficient β of the gyroscope can be obtained by fitting the data on the change over time t.

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