Push-up Hall magnetic floater rigid body rotational inertia measurement teaching aid

Abstract

The utility model relates to the technical field of rotational inertia measurement, in particular to a push-up type Hall magnetic floater rigid body rotational inertia measurement teaching aid, which comprises a rigid body rotational inertia measurement experiment instrument, a floater starting device and a floater body, a base is arranged on the surface of the bottom end of the floater starting device, and photoelectric doors are arranged at two ends of the surface of the top end of the base. A horizontal adjusting bolt is arranged on the surface of the top end of the base, a magnetic suspension device is arranged in the middle of the surface of the top end of the base, a load-bearing magnet block is arranged on the inner side of the middle of the surface of the top end of the PCB bottom plate, and a Hall sensor is arranged on the inner side of the middle of the surface of the top end of the load-bearing magnet block. By combining magnetic suspension and rigid body rotational inertia measurement, the influence of rotating shaft friction on rigid body rotational inertia measurement is avoided, the rotational inertia of a light irregular object can be obtained more simply and accurately compared with the prior art by improving precision through industrial production, and the performance of the device is effectively improved.

Description

Technical Field

[0001] The utility model relates to the technical field of moment of inertia measurement, in particular to an upward push-up Hall magnetic float rigid body moment of inertia measurement teaching aid. Background Art

[0002] After searching the Chinese patent document with the existing announcement number CN216621603U, a rigid body rotational inertia measuring device is disclosed, including a bracket, an industrial camera, a light source, an object to be measured, a stage, a bearing, a torsion spring, a base, a host computer and a power supply; the industrial camera is fixedly installed on the bracket; the industrial camera is connected to the host computer to transmit the collected image of the torsional vibration motion process; the light source is installed directly below the lens of the industrial camera; the object to be measured is placed on the stage; the stage is connected to the bearing and the torsion spring; the bearing is used to generate damping; the base is fixedly connected to the bracket, and the device solves the problems of high hardware cost, complex operation and low precision of the rotational inertia measuring device in the prior art.

[0003] The rigid body moment of inertia tester can not only measure the moment of inertia of a rigid body with uniform mass distribution and regular cross-sectional shape, but also measure the moment of inertia of a rigid body with uneven mass distribution and irregular cross-sectional shape, and can verify the laws of rotation in physics. Its rotation system consists of a cross-shaped support platform and a tower wheel, which can rotate smoothly around its vertical symmetry axis. Two symmetrically placed light-shielding thin rods rotate with the rigid body system, and continuously block light through the photoelectric gate in turn. The photoelectric gate consists of a light-emitting device and a photosensitive device. The power supply of the light-emitting device is provided by a millisecond meter. They constitute The photoelectric gate converts the shading signal of each time the thin rod passes into an electrical pulse signal and sends it to a universal computer-type millisecond meter. The millisecond meter records and stores the number of shading times and the moment of each shading. There are five winding wheels with different radii on the tower wheel to provide different force arms, which are divided into five gears from bottom to top: 15mm, 20mm, 25mm, 30mm, and 35mm. Different numbers of weights can be placed on the weight hook to change the pulling force on the rotating system. On each arm of the cross-shaped support platform of the experimental instrument, there are three small holes at equal distances along the radial direction, such as Figure 2 As shown, small steel columns can be placed on these small holes. The small steel columns change their moment of inertia with respect to the rotating shaft at different hole positions, thereby changing the moment of inertia of the entire system. Although the prior art takes the friction torque into consideration and treats the friction torque as a constant, the friction torque is not a constant in actual situations, so there is a systematic error in the prior art solution. Utility Model Content

[0004] The technical problem to be solved by the utility model is to overcome the defects of the prior art and provide a push-up type Hall magnetic float rigid body rotational inertia measurement teaching aid, aiming to solve the technical problem that although the prior art takes the friction torque into consideration and treats the friction torque as a constant, the friction torque is not a constant in actual situations, so the prior art solution has a systematic error.

[0005] In order to solve the above technical problems, the utility model provides the following technical solutions:

[0006] The utility model discloses a push-up Hall magnetic float rigid body rotational inertia measurement teaching aid, comprising a rigid body rotational inertia measurement experimental instrument, a float starting device and a float body, wherein a base is arranged on the bottom surface of the float starting device, photoelectric gates are arranged at both ends of the top surface of the base, a connector is arranged on one side surface of the photoelectric gate, a horizontal adjustment bolt is arranged on the top surface of the base, a magnetic suspension device is arranged on the middle part of the top surface of the base, a PCB bottom plate is arranged on the bottom end of the magnetic suspension device, a load-bearing magnet block is arranged on the inner side of the middle part of the top surface of the PCB bottom plate, a Hall sensor is arranged on the inner side of the middle part of the top surface of the load-bearing magnet block, a first coil, a second coil, a third coil and a fourth coil are arranged on one side of the Hall sensor respectively, a float body is arranged on the top of the magnetic suspension device, a float magnet block is arranged on the middle part of the top surface of the float body, and a light-shielding thin rod is arranged on the end of the top surface of the float body.

[0007] As a further description of the above technical solution:

[0008] The rigid body moment of inertia measuring experimental instrument is used by connecting to an external power supply, the base and the float starting device are fixedly connected, and the float starting device includes a connecting rod and a spring member.

[0009] As a further description of the above technical solution:

[0010] The base and the photoelectric gate are fixedly connected, the photoelectric gate is arranged in two groups, the top surface is arranged with concave convex blocks, and the height is adjustable. The rigid body rotational inertia measurement experiment instrument and the photoelectric gate are connected through a connector circuit and are fixedly powered for use.

[0011] As a further description of the above technical solution:

[0012] The base and the horizontal adjustment bolts are threadedly connected, and the horizontal adjustment bolts are arranged in three groups and arranged in sequence in a triangle shape. The base and the magnetic suspension device are fixedly connected, and the top of the magnetic suspension device is a cylindrical PCB bottom plate.

[0013] As a further description of the above technical solution:

[0014] The bottom surface of the PCB bottom plate is provided with pillars on both sides thereof and connected and fixed to the base. The PCB bottom plate and the load-bearing magnet block are fixedly connected. The PCB bottom plate and the Hall sensor are fixedly connected. The Hall sensor is arranged in a cross shape.

[0015] As a further description of the above technical solution:

[0016] The PCB bottom plate is fixedly connected to the first coil, the second coil, the third coil and the fourth coil, and the first coil, the second coil, the third coil and the fourth coil are arranged in a square.

[0017] As a further description of the above technical solution:

[0018] The magnetic levitation device and the float body are movably connected, the float body is a 3D printed shell, the middle part is cylindrical, and the two sides are rectangular support rods. The float body and the float magnet block are fixedly connected, the float body and the shading rod are fixedly connected, and the shading rod is a cylindrical rod.

[0019] The utility model has the following beneficial effects:

[0020] In the utility model, the influence of shaft friction on the measurement of rigid body moment of inertia is avoided by combining magnetic levitation and rigid body moment of inertia measurement. By improving the accuracy through industrialized production, the moment of inertia of light irregular objects can be obtained more simply and accurately compared with the existing technology, thereby effectively improving the performance of the device. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0022] Figure 1 It is a schematic plan view of the overall structure of the magnetic suspension device of the utility model;

[0023] Figure 2 This is a schematic diagram of the magnetic suspension structure from a top view of the utility model;

[0024] Figure 3 This is a schematic diagram of the structure of the float body of the utility model;

[0025] In the figure: 1. Rigid body moment of inertia measurement experiment instrument; 2. Float starting device; 3. Float body; 4. Base; 5. Photoelectric gate; 6. Connector; 7. Horizontal adjustment bolt; 8. Magnetic levitation device; 9. PCB bottom plate; 10. Load-bearing magnet block; 11. Hall sensor; 12. First coil; 13. Second coil; 14. Third coil; 15. Fourth coil; 16. Float magnet block; 17. Light-shielding thin rod. DETAILED DESCRIPTION

[0026] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0027] In the drawings, the same reference numerals all refer to the same components.

[0028] Example 1

[0029] Reference Figure 1-3 The utility model provides an embodiment: a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, comprising a rigid body moment of inertia measurement experimental instrument 1, a float starting device 2 and a float body 3, the bottom surface of the float starting device 2 is provided with a base 4, both ends of the top surface of the base 4 are provided with photoelectric gates 5, a connector 6 is provided on one side of the photoelectric gate 5, a horizontal adjustment bolt 7 is provided on the top surface of the base 4, a magnetic suspension device 8 is provided in the middle of the top surface of the base 4, a PCB bottom plate 9 is provided at the bottom of the magnetic suspension device 8, a load-bearing magnet block 10 is provided on the inner side of the middle of the top surface of the PCB bottom plate 9, a Hall sensor 11 is provided on the inner side of the middle of the top surface of the load-bearing magnet block 10, a first coil 12, a second coil 13, a third coil 14 and a fourth coil 15 are respectively provided on one side of the Hall sensor 11, a float body 3 is provided on the top of the magnetic suspension device 8, a float magnet block 16 is provided in the middle of the top surface of the float body 3, and a light-shielding thin rod 17 is provided at the end of the top surface of the float body 3.

[0030] The rigid body moment of inertia measuring experimental instrument 1 is used by connecting to an external power supply, and the base 4 and the float starting device 2 are fixedly connected, and the float starting device 2 includes a connecting rod and a spring member.

[0031] The base 4 and the photoelectric gate 5 are fixedly connected. The photoelectric gate 5 is arranged in two groups. The top surface is a concave convex block, and the height is adjustable. The rigid body rotational inertia measurement experiment instrument 1 and the photoelectric gate 5 are connected by a connector 6 and are fixedly powered for use.

[0032] The base 4 and the horizontal adjustment bolts 7 are threadedly connected, and the horizontal adjustment bolts 7 are arranged in three groups and arranged in sequence in a triangular shape. The base 4 and the magnetic suspension device 8 are fixedly connected, and the top of the magnetic suspension device 8 is a cylindrical PCB bottom plate 9.

[0033] Pillars are provided on both sides of the bottom surface of the PCB bottom plate 9 to connect and fix with the base 4, the PCB bottom plate 9 and the load-bearing magnet block 10 are fixedly connected, and the PCB bottom plate 9 and the Hall sensor 11 are fixedly connected, and the Hall sensor 11 is arranged in a cross shape.

[0034] The PCB bottom plate 9 is fixedly connected to the first coil 12 , the second coil 13 , the third coil 14 and the fourth coil 15 , and the first coil 12 , the second coil 13 , the third coil 14 and the fourth coil 15 are arranged in a square shape.

[0035] The magnetic suspension device 8 and the float body 3 are movably connected. The float body 3 is a 3D printed shell with a cylindrical middle part and rectangular support rods on both sides. The float body 3 and the float magnet block 16 are fixedly connected. The float body 3 and the shading rod 17 are fixedly connected, and the shading rod 17 is a cylindrical rod.

[0036] Specifically, the device is formed into an upward push-up Hall magnetic float rigid body moment of inertia measurement teaching aid through a rigid body moment of inertia measurement experiment instrument 1, a float starting device 2, a float body 3, a base 4, a photoelectric gate 5, a connector 6, a horizontal adjustment bolt 7, a magnetic suspension device 8, a PCB bottom plate 9, a load-bearing magnet block 10, a Hall sensor 11, a first coil 12, a second coil 13, a third coil 14, a fourth coil 15, a float magnet block 16 and a light-shielding thin rod 17. The rigid body moment of inertia measurement experiment instrument 1 is used to detect the number of times the float rotates and display the average acceleration of the rotation. The device for auxiliary tensioning the spring is pulled through the float starting device 2, and a horizontal bar of the float shell is close to the spring. After releasing it, the float can rotate stably. The float body 3 is a 3D printed shell. When the float body 3 rotates, the left light-shielding thin rod 17 can pass through the middle of the concave block at the top of the photoelectric gate 5, and the photoelectric gate 5 and the magnetic suspension device 8 can be supported as a whole through the base 4. At the same time, the level can be adjusted through three horizontal adjustment bolts 7. The height of the photoelectric gate 5 is adjustable, thereby ensuring that the relative position of the shading rod 17 and the photoelectric gate 5 is appropriate. The bottom support of the magnetic suspension device 8 is obtained by 3D printing, and the height is adjustable, thereby ensuring that the shading rod 17 can pass through the photoelectric gate 5 perfectly. The photoelectric gate 5 is used to detect whether the rotation of the float body 3 is uniform. The connector 6 is used to match the circuit to connect the photoelectric gate 5 to the rigid body moment of inertia measurement experiment instrument 1 and power it on. The magnetic suspension device 8 is a group of coils through the first coil 12 and the third coil 14, but the winding directions are opposite. Assuming that the first coil 12 is wound clockwise, the third coil 14 is wound counterclockwise, and the first coil 12 and the third coil 14 provide opposite corrective forces. To enhance the correction effect in the Y-axis direction, when the float body 3 deviates in the positive direction of the Y-axis, the first coil 12 will provide a pulling force, and the third coil 14 will provide a thrust. One push and one pull can correct the float body 3 to the equilibrium position more quickly. The second coil 13 and the fourth coil 15 are the same. The equilibrium position is determined by the magnetic field strength detected by the Hall sensor 11. When the float body 3 is in the equilibrium position, the voltage value of the Hall sensor 11 is read as the target setting value. Because this system requires control and detection of three degrees of freedom, three Hall sensors 11 are required. A Hall sensor 11 is placed on each axis, that is, the X-axis Hall sensor 11 detects the displacement of the float body 3 on the X-axis, the Y-axis Hall sensor 11 detects the displacement of the float body 3 on the Y-axis, and the Z-axis Hall sensor 11 detects whether the float body 3 is placed on the Z-axis. When the float body 3 deviates from the target position, the deviation can be decomposed into separate displacement components on three axes. The voltage value of the Hall detection magnetic field feedback is used for regulation by the controller. The corrective force provided by the coil makes the float body 3 return to the target position. Through closed-loop control, this process is repeated to achieve stable suspension of the float.

[0037] Usage process: the magnetic suspension device 8 is powered on, the photoelectric gate device 5 is powered on, and the number of rotations n detected by the photoelectric gate 5 is set; the spring of the float starting device 2 is tightened, and the 3D printed light-shielding thin rod 17 extending from the outside of the float body 3 is close to the spring of the float starting device 2; the float starting device is released, and the photoelectric gate rigid body moment of inertia measurement experiment instrument 1 is turned on at the same time, and the detector number is read when the detection is completed. If the acceleration displayed is very small and close to 0, it means that the float body 3 is rotating at a constant speed at this time, and its moment of inertia can be calculated; an object weighing less than 200g is placed in the middle of the float body 3, and the above operation is repeated. The difference in the moment of inertia between the two is equal to the moment of inertia value of the object.

[0038] Design principle of the push-up Hall magnetic float rigid body moment of inertia measurement teaching aid: Push-type magnetic levitation requires three-degree-of-freedom control. Two groups of four coils provide corrective forces in the x-axis and y-axis directions and thrust in the z-axis direction. When the gravity of the magnetic float and the z-axis reasoning provided by the coil are equal in size and opposite in direction, the system is balanced and the magnetic float is suspended. When the gravity direction of the magnetic float and the z-axis thrust direction are not on the same straight line, the correction force in the x-axis and y-axis directions provides correction of the magnetic float position. There is a Hall sensor 11 under the magnetic float to detect the position of the float and feed it back to the controller to achieve closed-loop control. The control algorithm is as follows:

[0039] PID algorithm:

[0040]

[0041] In the formula, Y(s) is the regulator output; E(s) is the pull-type transformation of the input deviation signal; P, TI, and TD are the proportionality, integral time, and differential time constants, respectively. Its time domain expression is:

[0042]

[0043]

[0044] In the formula, y(t) is the regulation output; e(t) is the input deviation signal in the time domain. In digital control, the input signal is a discrete signal obtained by sampling, so the above formula must be discretized, and the PID output after the nth sampling is obtained as:

[0045]

[0046] In the formula, ei is the deviation signal at the i-th sampling, T is the sampling period, this formula is called the position formula, which is the basic formula of PID. In practical applications, when using position PID calculation, the computer task is heavy, because each calculation result y(t) needs to calculate the deviation signal of each input in the past, and as the deviation accumulates, the integral unit may be saturated, which will cause large fluctuations and oscillations in the controller output value. In order to reduce the computer's calculation tasks, an incremental PID algorithm is proposed to avoid the occurrence of full calculation.

[0047] Incremental formula:

[0048]

[0049] The incremental PID algorithm greatly reduces the workload of the computer. At the same time, there is no accumulation of deviations during the calculation process, and there will be no integral saturation. In order to avoid the amplification of high-frequency interference by ideal differentials, the third ideal differential part of the above formula is changed to actual differential in actual application. The transfer function of the actual differential is:

[0050]

[0051] In the formula, KD is the differential gain. After the reverse Laplace transform of the above formula, it is rewritten into the differential expression of the actual differential as follows:

[0052]

[0053] Substituting the third ideal differential part on the right side of the above equation, the practical PID formula is obtained:

[0054]

[0055] Push-up Hall Magnetic Float Rigid Body Inertia Measurement Teaching Aids Experiment Principle: The rotating system consists of a float and a cylinder to be measured. The moment of inertia of the float about the rotating shaft when idling is recorded as J0, and the moment of inertia of the system composed of the float and the cylinder to be measured about the rotating shaft is recorded as J1, J1-J0=J, and the theoretical calculated moment of inertia of the cylinder to be measured is recorded as J * The constant energy released by the spring is The angular velocity of the float when idling is recorded as ω0, the time is recorded as t0, and the number of rotations is n0. The angular velocity of the system composed of the float and the cylinder to be measured is recorded as ω1, the time is recorded as t1, and the number of rotations is n1.

[0056] From the device structure, it can be concluded that The system rotates through the photogate to record the time interval t of the light-shielding stick passing through the photogate and the number of times 2n passing through the photogate, thus obtaining By measuring t0 and n0 when the float is idling, the formula Derived Thus, J0 is calculated by measuring t1 and n1 when the system composed of the float and the cylinder to be measured rotates. Calculate J1, and then calculate the moment of inertia J=J1-J0 of the cylinder to be measured with respect to the rotation axis.

[0057] The formula for calculating the moment of inertia of a cylindrical rigid body is Calculate the theoretical value of the moment of inertia of the known mass cylinder to be tested, and repeat the experiment with different values ​​of m and r.

[0058] First, adjust the screws on the bottom tray to make the experimental device level as a whole, then turn on the magnetic suspension device and the photoelectric gate, place the float, compress the spring to the limit position and then release it, and record the time interval t when the light shielding rod passes through the photoelectric gate and the number of times the light shielding rod passes through the photoelectric gate 2n through the photoelectric gate. According to the formula and The moment of inertia J0 of the float relative to the rotating shaft when it is idling is calculated. The elastic potential energy E of the spring used in the experiment when it is compressed to the limit position is 1×10 -4 J, The experiment was repeated 3 times.

[0059] Place cylinders of different weights on the float, ensure that the center of mass of the cylinder is at the axis of rotation, compress the spring to position x and release it, repeat the above experimental steps, and repeat the measurement 3 times. The standard cylindrical cylinders used in the experiment have masses of 50g, 100g, and 200g respectively. Repeat the measurement 3 times, and according to the formula and The moment of inertia J1 of the system composed of the float and the cylinder to be measured about the rotating shaft is calculated and is Calculate the theoretical value of the moment of inertia of the cylinder to be tested and compare it.

[0060] Finally, it should be noted that the above description is only a preferred embodiment of the utility model and is not intended to limit the utility model. Although the utility model is described in detail with reference to the above embodiments, those skilled in the art can still modify the technical solutions recorded in the above embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the utility model shall be included in the protection scope of the utility model.

Claims

1. A push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, comprising a rigid body moment of inertia measurement experimental instrument (1), a float starting device (2) and a float body (3), It is characterized in that The bottom surface of the float starter device (2) is provided with a base (4), both ends of the top surface of the base (4) are provided with photoelectric gates (5), one side surface of the photoelectric gate (5) is provided with a connector (6), the top surface of the base (4) is provided with a horizontal adjustment bolt (7), the middle part of the top surface of the base (4) is provided with a magnetic suspension device (8), the bottom end of the magnetic suspension device (8) is provided with a PCB bottom plate (9), the inner side of the middle part of the top surface of the PCB bottom plate (9) is provided with a load magnet block (10), the inner side of the middle part of the top surface of the load magnet block (10) is provided with a Hall sensor (11), the first coil (12), the second coil (13), the third coil (14) and the fourth coil (15) are respectively provided on one side of the Hall sensor (11), the top of the magnetic suspension device (8) is provided with a float body (3), the middle part of the top surface of the float body (3) is provided with a float magnet block (16), and the end of the top surface of the float body (3) is provided with a light shielding thin rod (17).

2. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that The rigid body moment of inertia measuring experimental instrument (1) is used by connecting to an external power source, the base (4) and the float starting device (2) are fixedly connected, and the float starting device (2) comprises a connecting rod and a spring member.

3. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that The base (4) and the photoelectric gate (5) are fixedly connected. The photoelectric gate (5) is provided in two groups. The top surface is provided with a concave convex block. The height is adjustable. The rigid body moment of inertia measurement experimental instrument (1) and the photoelectric gate (5) are connected by a connector (6) and are fixedly powered for use.

4. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that The base (4) and the horizontal adjustment bolts (7) are threadedly connected, and the horizontal adjustment bolts (7) are arranged in three groups and arranged in sequence in a triangular shape. The base (4) and the magnetic suspension device (8) are fixedly connected, and the top of the magnetic suspension device (8) is provided with a cylindrical PCB bottom plate (9).

5. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that Support pillars are provided on both sides of the bottom surface of the PCB bottom plate (9) and are connected and fixed to the base (4); the PCB bottom plate (9) and the load-bearing magnet block (10) are fixedly connected; the PCB bottom plate (9) and the Hall sensor (11) are fixedly connected; and the Hall sensor (11) is arranged in a cross shape.

6. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that The PCB bottom plate (9) is fixedly connected to the first coil (12), the second coil (13), the third coil (14) and the fourth coil (15); the first coil (12), the second coil (13), the third coil (14) and the fourth coil (15) are arranged in a square.

7. According to claim 1, a push-up Hall magnetic float rigid body moment of inertia measurement teaching aid, It is characterized in that The magnetic suspension device (8) and the float body (3) are movably connected, the float body (3) is a 3D printed shell, the middle part is cylindrical, and the two sides are rectangular support rods. The float body (3) and the float magnet block (16) are fixedly connected, and the float body (3) and the light-shielding thin rod (17) are fixedly connected, and the light-shielding thin rod (17) is a cylindrical rod.

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