Device for measuring two-dimensional magnetic induction intensity on axis plane of Helmholtz coil

Abstract

The utility model discloses a device for measuring two-dimensional magnetic induction intensity on an axial plane of a Helmholtz coil, and belongs to the technical field of electronic components. The device comprises a two-dimensional Hall probe, a stepping motor guide rail moving circuit and a high-precision voltage acquisition module, wherein the two-dimensional Hall probe consists of a two-dimensional Hall probe mounting base and two linear Hall sensors which are orthogonally mounted on the two-dimensional Hall probe mounting base; the stepping motor guide rail moving circuit and the high-precision voltage acquisition module are connected with the two-dimensional Hall probe; two ends of the high-precision voltage acquisition module are respectively connected with the two-dimensional Hall probe and the computer. According to the utility model, the symmetrical distribution characteristic of the Helmholtz coil magnetic field is utilized, the two-dimensional Hall probe is designed by using the two mutually orthogonal Hall sensors, and the three-dimensional space magnetic field distribution is reflected by measuring the two-dimensional magnetic field of the 1 / 4 axis plane of the Helmholtz coil; the high-precision voltage acquisition module is designed based on the single-chip microcomputer, so that measurement errors are effectively Compared with an existing device of the same type, measurement is easier and more convenient, experimental data processing is easier and more intelligent, and the expandability of the device is higher.

Description

Technical Field

[0001] This utility model belongs to the field of electronic components technology, specifically relating to a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil. Background Technology

[0002] A Helmholtz coil is a specially designed electromagnetic coil capable of generating a relatively uniform magnetic field within a specific spatial region. This coil consists of two parallel, coaxial circular coils with current flowing in the same direction and of equal magnitude. When the distance between these two coils is equal to their radii, they work together to produce a uniform magnetic field along their axis.

[0003] Experiments measuring the magnetic field of a Helmholtz coil typically use a Hall sensor to measure the magnetic field along the one-dimensional axis of the coil, utilizing the Hall effect. However, this approach lacks a direct visual understanding of the spatial magnetic field generated by the coil, presenting significant limitations. Measuring the three-dimensional magnetic field generated by a Helmholtz coil requires considering all three dimensions, and determining the spatial coordinates and the magnitude and direction of the magnetic induction intensity is challenging, easily leading to substantial measurement errors. Furthermore, the equipment required is more complex and costly. In contrast, the magnetic field of a Helmholtz coil exhibits axisymmetric distribution characteristics. Therefore, measuring the two-dimensional magnetic field in a quarter-axis plane of the coil can reflect the magnetic field distribution across the entire axis, while being less difficult and less costly.

[0004] To overcome the limitations of traditional devices, directly measuring the three-dimensional magnetic field in space presents significant challenges for experimental instrumentation and design. Due to the spatial symmetry of the Helmholtz coil's magnetic field, measuring a quarter of the magnetic field can simulate the coil's spatial magnetic field. Literature review revealed that the magnetic field components on each cross-section of the Helmholtz coil are identical, and one of the three magnetic flux density components on each cross-section is zero. Therefore, measuring only two magnetic flux density components on a single cross-section is sufficient to reflect the overall magnetic flux density distribution of the Helmholtz coil in space. Thus, a stepper motor-guided circuit is needed to precisely move the two-dimensional Hall probe along the X and Z axes. By controlling the movement of the two-dimensional Hall probe in a two-dimensional plane, planar magnetic field measurement can be achieved. Utility Model Content

[0005] In order to overcome the shortcomings of the prior art, the purpose of this utility model is to provide a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, so as to solve the technical problem that the existing Helmholtz coil magnetic field measuring device cannot intuitively reflect the two-dimensional magnetic induction intensity on the axial plane of the Helmholtz coil. On this basis, the device measures the two-dimensional magnetic induction intensity on the 1 / 4 axial plane of the coil with a spacing of 2R.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This utility model discloses a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, comprising: a Helmholtz coil, a two-dimensional Hall probe connected to the Helmholtz coil, and a stepper motor guide rail moving circuit and a high-precision voltage acquisition module connected to the two-dimensional Hall probe; the stepper motor guide rail moving circuit is used to control the movement of the two-dimensional Hall probe; the high-precision voltage acquisition module is used to acquire the output voltage of the two-dimensional Hall probe and transmit it to a computer; one end of the high-precision voltage acquisition module is connected to the two-dimensional Hall probe, and the other end is connected to the computer.

[0008] Preferably, the two-dimensional Hall probe consists of a two-dimensional Hall probe mounting base and two linear Hall sensors orthogonally mounted on the two-dimensional Hall probe mounting base.

[0009] More preferably, the linear Hall sensor is an SS495A type linear Hall sensor.

[0010] Preferably, the stepper motor guide rail moving circuit includes: a stepper motor guide rail, a stepper motor driver electrically connected to the stepper motor guide rail, a 24V power supply, and an STM32 guide rail control circuit; the two-dimensional Hall probe is fixed on the stepper motor guide rail, and the STM32 guide rail control circuit is used to control the movement of the two-dimensional Hall probe.

[0011] More preferably, the STM32 rail control circuit includes: an STM32F103C8T6 chip, a power supply circuit, a clock circuit, a self-reset button circuit, and a decoupling circuit; the clock circuit is connected to the corresponding pin of the STM32F103C8T6 chip, the self-reset button circuit is connected to the corresponding pin of the STM32F103C8T6 chip, and the decoupling circuit is connected between the power supply circuit and the ground line.

[0012] Preferably, the high-precision voltage acquisition module includes: an analog-to-digital converter circuit, an MCU circuit electrically connected to the analog-to-digital converter circuit, a high-precision voltage source, and a 4th-order RC low-pass filter; the MCU circuit is connected to an STM32F407ZGT6J chip and the analog-to-digital converter; the high-precision voltage source is connected to the positive reference voltage input pin of the analog-to-digital converter; the 4th-order RC low-pass filter is connected in series at the analog signal input terminal of the analog-to-digital converter.

[0013] More preferably, the analog-to-digital conversion circuit includes: an analog-to-digital converter, a power supply circuit, a clock circuit, an input circuit, an SPI communication circuit, a reference voltage circuit, and a filter circuit; the power supply circuit is connected to the corresponding power supply pin of the analog-to-digital converter, the clock circuit is connected to the clock pin of the analog-to-digital converter, the voltage under test is connected to the probe connected to the input circuit, the SPI communication circuit is connected to the data input pin of the STM32F407ZGT6J chip and the data output pin of the analog-to-digital converter, the reference voltage circuit is connected to the positive voltage reference pin of the analog-to-digital converter, the decoupling capacitor is connected between the power supply circuit and the ground line, and the input circuit is connected to the filter circuit and the eight analog signal input channels of the analog-to-digital converter.

[0014] More preferably, the STM32F407ZGT6J chip is an F3 series chip or an F4 series chip.

[0015] More preferably, the analog-to-digital converter is an ADS1256 analog-to-digital converter.

[0016] More preferably, the high-precision voltage source consists of a voltage reference chip, a filter circuit, and an input voltage detection circuit. The input voltage detection circuit uses a transistor, resistor, Zener diode, and LED connected in parallel to the voltage input terminal. When the input voltage is between 6 and 12V, it illuminates green; below 2V, it remains off; between 2 and 6V, it illuminates yellow; and outside this voltage range, it displays red. The input voltage detection circuit is connected to pin 2 of the voltage reference chip. A filter circuit is connected between the input voltage detection circuit and ground, and the output voltage of the voltage reference chip is also connected to ground.

[0017] Preferably, it also includes an HLZ solenoid magnetic field experiment apparatus and a DM-A2 digital ammeter, wherein the HLZ solenoid magnetic field experiment apparatus and the DM-A2 digital ammeter are electrically connected to a two-dimensional Hall probe, respectively.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] This invention discloses a device for measuring the two-dimensional magnetic flux density on the axial plane of a Helmholtz coil. The device includes a Helmholtz coil, a two-dimensional Hall probe, a two-dimensional Hall probe mounting base, an HLZ solenoid magnetic field experimental apparatus, a DM-A2 digital ammeter, a stepper motor guide rail movement circuit, and a high-precision voltage acquisition module. This invention utilizes this device to investigate the magnetic flux density components on the axial plane of the Helmholtz coil. The movement step size of the two-dimensional Hall probe in this device can be varied. To measure as many magnetic flux density components on the axial plane of the Helmholtz coil as possible, the movement step size can be as small as possible; for simplicity of the measurement process, a 5mm movement step size is chosen. Finally, the high-precision voltage acquisition module acquires the output voltage of the two-dimensional Hall probe and converts the output voltage into magnetic flux density, displaying it on a personal computer, thus making the acquired voltage more accurate. Compared to using three Hall sensors for measurement in three-dimensional space, measurement in a two-dimensional plane has lower costs. Compared to complex three-dimensional motion mechanisms, the mechanical design and control of the two-dimensional motion platform are relatively simple, and the two-dimensional motion mechanism is also relatively simple, making maintenance and calibration more convenient. Attached Figure Description

[0020] Figure 1 This is a comparison chart of the measured magnetic field results of the Helmholtz coil along its half-axis and the theoretical curve in Embodiment 1 of this utility model;

[0021] Figure 2 In Embodiment 2 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value;

[0022] Figure 3 In Embodiment 2 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value;

[0023] Figure 4 In embodiment 4 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value;

[0024] Figure 5 In embodiment 4 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value;

[0025] Figure 6 Schematic diagram of the principle of measuring magnetic field using the Hall effect;

[0026] Figure 7 Schematic diagram of magnetic field measurement principle for a single current-carrying coil;

[0027] Figure 8 Schematic diagram of the Helmholtz coil spatial magnetic field measurement principle;

[0028] Figure 9 This is a circuit diagram for an analog-to-digital converter.

[0029] Figure 10 This is the circuit diagram for the STM32F103C8T6 chip.

[0030] Figure 11 This is a circuit diagram for the stepper motor guide rail movement.

[0031] Figure 12 This is a high-precision voltage source circuit diagram;

[0032] Figure 13 This is the MCU circuit diagram;

[0033] Figure 14 This is a schematic diagram of the device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, as disclosed in this utility model.

[0034] Figure 15 A schematic diagram of a Helmholtz coil;

[0035] Figure 16 This is a schematic diagram of a two-dimensional Hall effect sensor.

[0036] Figure 17 This is a schematic diagram of a stepper motor guide rail;

[0037] Figure 18 This is a schematic diagram of a high-precision voltage acquisition module;

[0038] Figure 19 Schematic diagram of the HLZ solenoid magnetic field experimental apparatus and the DM-A2 digital current display;

[0039] Figure 20 Schematic diagram of a mounting base for a 3D-printed two-dimensional Hall probe;

[0040] Figure 21 This is a schematic diagram of the STM32 guide rail control circuit.

[0041] The components include: 1. Helmholtz coil; 2. Two-dimensional Hall probe; 3. Two-dimensional Hall probe mounting base; 4. HLZ solenoid magnetic field experimental instrument; 5. DM-A2 digital ammeter; 6. Stepper motor guide rail; 7. Stepper motor driver; 8. 24V power supply; 9. STM32 guide rail control circuit; 10. High-precision voltage acquisition module; 11. Analog-to-digital converter circuit; 12. MCU circuit; 13. High-precision voltage source; 14. 4th-order RC low-pass filter; 15. STM32F407ZGT6J chip; 16. Analog-to-digital converter; 17. STM32F103C8T6 chip. Detailed Implementation

[0042] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0043] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this utility model are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the utility model described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0044] The present invention will now be described in further detail with reference to the accompanying drawings:

[0045] The magnetic field generated by the Helmholtz coil 1 is measured along its axis and radial direction using a two-dimensional Hall probe 2, and the magnetic induction intensity data is recorded. However, this method can only reflect the axial magnetic field or the approximately uniform magnetic induction intensity within the Helmholtz coil 1, and cannot depict the spatial distribution of the magnetic field, which has significant limitations. This invention discloses a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, comprising: a two-dimensional Hall probe mounting base 3 and a two-dimensional Hall probe 2 composed of two orthogonally mounted linear Hall sensors on the mounting base 3; a stepper motor guide rail moving circuit and a high-precision voltage acquisition module 10 connected to the two-dimensional Hall probe 2; one end of the high-precision voltage acquisition module 10 is connected to the two-dimensional Hall probe 2, and the other end is connected to a computer. This invention utilizes the symmetrical distribution characteristics of the magnetic field of the Helmholtz coil 1, and independently designs a two-dimensional Hall probe 2 using two orthogonally mounted linear Hall sensors. By measuring the two-dimensional magnetic field in the 1 / 4 axial plane of the Helmholtz coil 1, it reflects the three-dimensional spatial magnetic field distribution; the high-precision voltage acquisition module 10, designed based on a microcontroller, effectively reduces measurement errors. It is simpler to measure than existing similar devices, and the experimental data processing is simpler and more intelligent, and the device is more scalable.

[0046] This utility model discloses a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, comprising a Helmholtz coil 1, a two-dimensional Hall probe 2, a two-dimensional Hall probe mounting base 3, an HLZ solenoid magnetic field experimental instrument 4, a DM-A2 digital ammeter 5, a stepper motor guide rail moving circuit, and a high-precision voltage acquisition module 10. The two-dimensional Hall probe 2 consists of the two-dimensional Hall probe mounting base 3 and two linear Hall sensors. The stepper motor guide rail moving circuit consists of a stepper motor guide rail 6, a stepper motor driver 7, a 24V power supply 8, and an STM32 guide rail control circuit 9. The high-precision voltage acquisition module 10 consists of an analog-to-digital converter circuit 11, an MCU circuit 12, a high-precision voltage source 13, and a 4th-order RC low-pass filter 14. The analog-to-digital converter circuit 11 consists of an analog-to-digital converter 16, a power supply circuit, a clock circuit, an input circuit, an SPI communication circuit, a reference voltage circuit, and a ground wire, and also includes protection and filtering circuits. The analog power supply is connected to the corresponding power supply pin of the analog-to-digital converter (ADC) 16. The clock circuit (external crystal oscillator) is connected to the X1 and X2 pins of the ADC 16. Analog signals are connected to the eight input channels of the ADC 16. The SPI interface is connected to the MCU circuit 12. The reference voltage circuit is connected to the positive voltage reference pin of the ADC 16. The decoupling capacitor is connected between the power supply and ground. The voltage reference chip ADR2545 in the reference voltage circuit of the ADC 11 can also be replaced with other 2.5V voltage reference chips. The high-precision voltage source 13 consists of an ISL21009BFB850Z voltage reference chip, a filter circuit, and an input voltage detection circuit. The fourth-order RC low-pass filter 14 is composed of four cascaded first-order RC low-pass filters, designed to perform low-pass filtering on the input signal (i.e., retaining low-frequency components and attenuating high-frequency components). Its order (4th order) determines the frequency response characteristics of the filter, such as the attenuation rate and filtering accuracy.

[0047] This invention discloses a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil. When acquiring voltage data, the device can be connected to a personal computer for data recording and processing. Users need to be familiar with analyzing the spatial magnetic field generated by the Helmholtz coil 1 based on the Biot-Saffar law and performing magnetic field simulation using MATLAB. The user will master the principle and method of measuring the two-dimensional axial plane magnetic field of the Helmholtz coil 1 using a two-dimensional Hall probe 2 assembled from two linear Hall sensors. The user will understand how to use a microcontroller to control the movement of the two-dimensional Hall probe 2 and acquire the output voltage. Furthermore, the user will use a self-designed Hall probe and its supporting experimental setup, and perform instrument error analysis. Magnetic field simulation will be performed using Mathematica and MATLAB. The device will measure the two-dimensional axial plane magnetic field of the Helmholtz coil 1 (the distance between the two coils is equal to the coil radius R). The device will also measure the two-dimensional axial plane magnetic field when the distance between the two coils is 2R.

[0048] Figure 6A schematic diagram of the Hall effect magnetic field measurement; a Hall element sheet is placed vertically in magnetic field B, and the charge carriers in the Hall element are in the operating current. Driven by the current, these carriers will undergo directional motion. When exposed to a magnetic field, these moving carriers will experience a Lorentz force perpendicular to both the operating current and the magnetic field. The effect of the Lorentz force is that charge carriers move laterally, and the upper and lower plates of the Hall element begin to charge and accumulate charge. One plate accumulates positive charge, and the other plate accumulates negative charge, thus generating an electric field between the plates. This electric field exerts an electric force on the charge carriers in the opposite direction to the Lorentz force. When the electric force and the Lorentz force are equal in magnitude When the net force on the charge carriers is zero, the potential difference between the two plates reaches a stable value, which is called the Hall voltage U. The Hall voltage is perpendicular to the operating current. The direction of the magnetic field B can be represented as:

[0049]

[0050] Where n is the carrier concentration, q is the charge of a single carrier, and b is the thickness of the Hall element. Hall sensitivity is defined. = Then the Hall voltage is:

[0051]

[0052] in The Hall sensitivity is related to the geometric dimensions, carrier concentration, and other material properties of the Hall element. When the Hall element material is constant, Since it is a definite constant, the Hall voltage is proportional to the operating current. And the magnetic flux density B. In fact, the Hall voltage also varies with the angle of the magnetic flux density B, reaching its maximum value when the magnetic field is perpendicular to the Hall element. The advantage of using a Hall element to measure magnetic fields is that, given the Hall element and operating current, theoretically the output Hall voltage depends only on the spatial magnetic flux density and is independent of the frequency.

[0053] Figure 7 This is a schematic diagram of a single current-carrying coil measurement principle. The Biot-Saffar law is the equation describing the magnetic field generated by a constant current, relating the magnetic field to the magnitude, direction, length, and distance of the current. The magnetic field distribution of a single current-carrying circular coil in space is derived using the Biot-Saffar law and vector cross product, and then extended to the magnetic field distribution of a Helmholtz coil 1 in space. Let the distance from a point P in space to the central axis z of the current-carrying circular coil be r, and the distance o from the projection point of P on the z-axis be z. As shown in the figure, based on geometric relationships, we can obtain:

[0054] =(r-Rcos ) - Rsin +z

[0055] =Rd (cos -sin )

[0056] thus

[0057] d ×r′=Rd [zcos +zsin +(R -rcos ) ]

[0058] According to the Biot-Safar law:

[0059]

[0060] And by performing diagonal integration, we get:

[0061]

[0062]

[0063]

[0064] As can be seen from the spatial magnetic field measurement method of current-carrying circular coil, it is only necessary to measure the radius R of the current-carrying circular coil, the distance r from point P to the center of the coil, and the angle. Then the magnitude of its magnetic field can be calculated.

[0065] Figure 8 This is a schematic diagram illustrating the principle of measuring the spatial magnetic field of a Helmholtz coil. To measure the spatial magnetic field of Helmholtz coil 1, this experiment utilizes a two-dimensional Hall sensor to measure the components of the magnetic field of Helmholtz coil 1 along the x and z axes, and integrates these measurements to obtain the spatial magnetic field. The measurement of the spatial magnetic field of Helmholtz coil 1 is shown below. Figure 8 As shown. Among them and These are the axial distances from point P to the first and second coils, respectively, and r is the distance from point P to point O.

[0066]

[0067]

[0068] Diagonal integration yields:

[0069] d

[0070] d

[0071] + ]d

[0072] B=

[0073] Helmholtz coil half-axis magnetic field measurement

[0074] The magnitude of the magnetic field along the axis of the Helmholtz coil is measured as follows:

[0075]

[0076] The functional relationship between the Hall sensor output voltage and the magnetic field is as follows:

[0077] (V)

[0078] Where R is the radius of the Helmholtz coil, and U is the output voltage of the Hall sensor. This is the initial output voltage.

[0079] Helmholtz coil quarter-axis plane magnetic field measurement

[0080] The measurement of the two-dimensional magnetic field is achieved by measuring the magnetic field of the coil along the X and Z axes. The calculation is as follows:

[0081] d

[0082]

[0083] + ]d

[0084] B=

[0085] Where R is the radius of the Helmholtz coil. Let P be the axial distance from point P to the first coil. Let P be the axial distance from point P to the second coil.

[0086] According to the parity analysis of functions, we can obtain... =0, meaning the magnetic field distribution of the current-carrying circular coil in the axial plane is only distributed along the axial (z-direction) and radial directions. Therefore, we decided to use a self-assembled two-dimensional Hall probe 2 to measure the two-dimensional axial plane magnetic field of the Helmholtz coil 1. and The components are used to calculate the magnetic flux density and direction in the two-dimensional axial plane space.

[0087] The present invention discloses a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil. Taking the center of the magnetic field of the Helmholtz coil 1 as the origin, the device records the voltage value of the Hall sensor and calculates the magnetic induction intensity of the axis and axial plane of the Helmholtz coil 1 using the above formula.

[0088] The high-precision voltage acquisition module 10 includes: an analog-to-digital converter (ADC) circuit 11, an MCU circuit 12, a high-precision voltage source 13, and a 4th-order RC low-pass filter 14. After the basic peripheral circuits of the MCU circuit 12 and the ADC circuit 11 are completed, SPI communication is implemented. The reference voltage circuit in the ADC circuit 11 is connected to the corresponding positive reference voltage input pin VREFP of the ADC 16. Each chip is powered by several independent voltage sources, which can accept 6-16V power. Low-frequency filters are respectively set at the analog signal input and power supply terminals of the ADC 16. The data interface is connected to the MCU circuit 12 for convenient debugging and other communication needs. The ADC 16 is an ADS1256 ADC.

[0089] Figure 9 This is a schematic diagram of an analog-to-digital converter (ADC). The ADC circuit 11 is an electronic device that converts analog signals into digital signals; its schematic diagram is shown below. Figure 9 As shown. Its core principle is based on the sampling theorem, which states that analog signals are sampled at equal intervals within a certain time period, and the sampling frequency is kept higher than twice the highest frequency of the signal to avoid aliasing. During the sampling process, the converter converts the continuous analog signal into discrete sample points. Subsequently, the quantization process maps these sample points to a finite number of values, each value representing a specific voltage range. Finally, the encoding process converts the quantized values ​​into digital codes. The analog-to-digital converter used in this experiment is a hexadecimal 16, which resolves the 0-5.25V voltage signal into 2^24, achieving a sampling accuracy of 0.149uV, i.e., an error within 0.001%, and converts the first eight bits of the analog signal into numbers from 0 to 80000000.

[0090] Figure 10 The circuit diagram for the STM32F103C8T6 chip is shown below. The signal outputs of the STM32F103C8T6 chip 17 are the corresponding I / O inputs. Voltage conversion is performed within the STM32F103C8T6 chip 17, and data is displayed via HC340 serial communication. The circuit diagram for the STM32F103C8T6 chip 17 is shown below. Figure 10 As shown.

[0091] Figure 11This is a circuit diagram for a stepper motor guide rail movement. A stepper motor guide rail movement circuit is a device for precisely controlling the position of mechanical components. Its working principle is based on the stepping characteristics of a stepper motor. The stepper motor controls its internal electromagnetic coil by receiving pulse signals. Each pulse signal causes the motor to rotate by a fixed angle, called the step angle. By precisely controlling the number and frequency of pulses, the rotation angle and speed of the motor can be precisely controlled, thereby controlling the movement speed and time of the slider. In this experiment, the stepper motor guide rail movement circuit system consists of a stepper motor guide rail (6), a stepper motor driver (7), a 24V power supply (8), and an STM32 guide rail control circuit (9). The stepper motor guide rail (6) provides a stable linear motion path, ensuring smooth and controllable movement. In this experiment, an STM32F103C8T6 chip (17) sends pulse signals to the ENA+, DIR+, and PUL+ terminals of a stepper motor driver (7). After the stepper motor driver (7) is set up, the stepper motor rotates one revolution every 3200 pulses, and each pulse advances the slide rail by 0.0025mm. An independent button is designed to control the direction and number of movements of the stepper motor to achieve accurate measurement. The stepper motor driver (7) is a TB6600 stepper motor driver. The stepper motor guide rail movement circuit is as follows: Figure 11 As shown.

[0092] Figure 12 This is a circuit diagram for a high-precision voltage source. To ensure the SS495A Hall sensor operates at a stable 5V voltage and minimize errors caused by sensor operating conditions, this experiment independently designed and soldered a high-precision voltage source 13. This voltage source uses the ISL21009BFB850Z voltage reference chip as the main controller, and incorporates a filter circuit and an input voltage detection circuit to ensure the voltage source operates properly. The ISL21009BFB850Z used in this experiment is a high-precision, low-noise voltage reference chip manufactured by Intersil, offering multiple fixed output voltage options, excellent initial accuracy (±0.5mV to ±2.0mV), wide input voltage range (3.5V to 16.5V), low operating current (maximum 180μA), and excellent temperature stability (temperature coefficient 3ppm / °C to 10ppm / °C). This circuit uses a 9V power supply, stabilizing the output voltage within the range of 4.995~5.005V and allowing for long-term operation, meeting the high-precision requirements of this experiment. The circuit diagram of the high-precision voltage source 13 is shown below. Figure 12 As shown.

[0093] Figure 13 This is the MCU circuit diagram; MCU circuit 12 is connected to STM32F407ZGT6J chip 15 and analog-to-digital converter 16 via SPI (Serial Peripheral Interface).

[0094] Figure 14This is a schematic diagram of a device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, as disclosed in this utility model. The experimental setup includes: a Helmholtz coil 1, a two-dimensional Hall probe 2, a two-dimensional Hall probe mounting base 3, an HLZ solenoid magnetic field experimental instrument 4, a DM-A2 digital ammeter 5, a stepper motor guide rail moving circuit, and a high-precision voltage acquisition module 10. Utilizing the symmetrical distribution characteristics of the magnetic field of the Helmholtz coil 1, a two-dimensional Hall probe 2 is designed using two mutually orthogonal SS495A linear Hall sensors to measure the two-dimensional magnetic field on the quarter-axial plane of the Helmholtz coil 1.

[0095] Figure 15 A schematic diagram of a Helmholtz coil; 1. Self-designed and wound Helmholtz coil as shown. Figure 15 As shown, there is a pair of coaxial circular coils that are parallel to each other and connected. The current in the two coils is in the same direction and has the same magnitude.

[0096] Figure 16 This is a schematic diagram of a two-dimensional Hall probe; the two-dimensional Hall probe 2 is composed of two orthogonally combined linear Hall sensors, which measures the two-dimensional magnetic field along the axis of Helmholtz coil 1 and the two-dimensional magnetic field at a point approximately 1 / 4 of the distance from Helmholtz coil 1. Figure 16 As shown.

[0097] Figure 17 This is a schematic diagram of a stepper motor guide rail. Stepper motor guide rail 6 consists of two mutually orthogonal CBX1204-200MM guide rails. Precise positioning and movement are achieved by accurately controlling the number and direction of pulses. This provides smoother motion and higher resolution, reducing instrument errors and errors caused by uncertain positions.

[0098] Figure 18 This is a schematic diagram of a high-precision voltage acquisition module. The high-precision voltage acquisition module 10 is integrated with an analog-to-digital converter circuit 11, an MCU circuit 12, a high-precision voltage source 13, and a fourth-order RC low-pass filter 14. As a high-precision voltage measuring instrument, we apply it to acquire the output voltage of the two-dimensional Hall probe 2 in this experiment.

[0099] Figure 19 The HLZ solenoid experimenter 4 serves as the current source to power the coil, while the DM-A2 digital ammeter 5 is used as an ammeter to measure the current magnitude.

[0100] Figure 20 This diagram illustrates the mounting base for a 3D-printed two-dimensional Hall probe. The Hall probe firmware is 3D printed, allowing for easy modification of the firmware during experiments. The firmware is made of resin to avoid interfering with the measurement of the magnetic field of Helmholtz coil 1.

[0101] Figure 21 This is a schematic diagram of the STM32 guide rail control circuit; used to control the movement of the two-dimensional Hall probe 2 on the stepper motor guide rail 6.

[0102] The instruments and supplies required for the experiment are shown in Table 1, with a total cost of approximately 2373 yuan.

[0103] Table 1 Experimental Instruments and Supplies

[0104]

[0105] Example 1

[0106] An apparatus for measuring the two-dimensional magnetic flux density on the axial plane of a Helmholtz coil, comprising:

[0107] The system comprises: a Helmholtz coil 1; a two-dimensional Hall probe 2 consisting of Hall probe firmware and two linear Hall sensors; a stepper motor rail movement circuit consisting of a stepper motor rail 6, a stepper motor driver 7, a 24V power supply 8, and an STM32 rail control circuit 9; a high-precision voltage acquisition module 10 consisting of an analog-to-digital converter circuit 11, an MCU circuit 12, a high-precision voltage source 13, and a 4th-order RC low-pass filter 14; and a high-precision voltage source 13 consisting of an ISL21009BFB850Z voltage reference chip, a filtering circuit, and an input voltage detection circuit. The 4th-order RC low-pass filter 14 is an electronic filter composed of four cascaded first-order RC low-pass filters, designed to perform low-pass filtering on the input signal, i.e., retaining low-frequency components and attenuating high-frequency components. Its order (4th order) determines the filter's frequency response characteristics, such as attenuation rate and filtering accuracy.

[0108] The experiment was conducted with a coil current of 1A, an average coil radius of 0.08m, and a coil spacing of 0.08m. The magnetic flux density within a range of 0-100mm along the half-axis of Helmholtz coil 1 was measured. MATLAB was used to derive the theoretical magnetic flux density on the axial plane of Helmholtz coil 1. A high-precision voltage acquisition module 10 was used as a voltmeter, as conventional voltmeters lack sufficient accuracy and data recording capabilities. The high-precision voltage acquisition module 10 can transmit voltage data to a computer. Analysis using the goodness-of-fit method showed that the measured results and theoretical results were in good agreement. coefficient of determination .

[0109] Figure 1 This is a comparison chart of the measured magnetic field results of the Helmholtz coil 1 along its half-axis and the theoretical curve in Embodiment 1 of this utility model. As can be seen from the chart, the measured magnetic field results of the Helmholtz coil 1 along its half-axis are in good agreement with the theoretical results, indicating that the measurement of the one-dimensional magnetic field is effective and the measurement accuracy is high.

[0110] Example 2

[0111] An apparatus for measuring the two-dimensional magnetic flux density on the axial plane of a Helmholtz coil, comprising:

[0112] The system comprises a Helmholtz coil 1, a two-dimensional Hall probe 2 consisting of Hall probe firmware and two linear Hall sensors, a stepper motor rail movement circuit consisting of a stepper motor rail 6, a stepper motor driver 7, a 24V power supply 8 and an STM32 rail control circuit 9, a high-precision voltage acquisition module 10 consisting of an analog-to-digital conversion circuit 11, an MCU circuit 12, a high-precision voltage source 13 and a 4th-order RC low-pass filter 14, and a high-precision voltage source 13 consisting of an ISL21009BFB850Z voltage reference chip, a filtering circuit and an input voltage detection circuit.

[0113] The experiment was set with a coil current of 1A, an average coil radius of 0.08m, a coil spacing of 0.08m, and a measurement range of 100mm. Over a 100mm area, the theoretical magnetic flux density components on the 1-axis plane of a Helmholtz coil were obtained using MATLAB. A high-precision voltage acquisition module 10 was used as a voltmeter; conventional voltmeters lack sufficient accuracy and data recording capabilities. The high-precision voltage acquisition module 10 can transmit voltage data to a computer. The measurement results agree well with the theoretical results. coefficient of determination of components , .

[0114] Figure 2 In Embodiment 2 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value; as can be seen from the figure, the value obtained through this device is... The measured values ​​match the theoretical values ​​well, indicating high accuracy.

[0115] Figure 3 In Embodiment 2 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value; as can be seen from the figure, the value obtained through this device is... The measured values ​​agree well with the theoretical values, indicating high accuracy. This demonstrates that the present invention is effective in measuring two-dimensional magnetic fields.

[0116] Example 3

[0117] A device for measuring the two-dimensional magnetic induction intensity in an axial plane when the distance between two coils is 2R, comprising:

[0118] The system comprises a Helmholtz coil 1, a two-dimensional Hall probe 2 consisting of Hall probe firmware and two linear Hall sensors, a stepper motor rail movement circuit consisting of a stepper motor rail 6, a stepper motor driver 7, a 24V power supply 8 and an STM32 rail control circuit 9, a high-precision voltage acquisition module 10 consisting of an analog-to-digital conversion circuit 11, an MCU circuit 12, a high-precision voltage source 13 and a 4th-order RC low-pass filter 14, and a high-precision voltage source 13 consisting of an ISL21009BFB850Z voltage reference chip, a filtering circuit and an input voltage detection circuit.

[0119] The experiment was set with a coil current of 1A, an average coil radius of 0.08m, and a coil spacing of 0.16m. Measurements were taken between the two coils. The magnetic flux density within the 0-100mm range along the axis was measured using MATLAB. The theoretical magnetic flux density on the axial plane was calculated when the distance between the two coils was 2R. A high-precision voltage acquisition module 10 was used as a voltmeter to transmit voltage data to a computer. Analysis using the goodness-of-fit method showed that the measured results and theoretical results were in good agreement. coefficient of determination .

[0120] Example 4

[0121] A device for measuring the two-dimensional magnetic induction intensity in an axial plane when the distance between two coils is 2R, comprising:

[0122] The system comprises a Helmholtz coil 1, a two-dimensional Hall probe 2 consisting of Hall probe firmware and two linear Hall sensors, a stepper motor rail movement circuit consisting of a stepper motor rail 6, a stepper motor driver 7, a 24V power supply 8 and an STM32 rail control circuit 9, a high-precision voltage acquisition module 10 consisting of an analog-to-digital conversion circuit 11, an MCU circuit 12, a high-precision voltage source 13 and a 4th-order RC low-pass filter 14, and a high-precision voltage source 13 consisting of an ISL21009BFB850Z voltage reference chip, a filtering circuit and an input voltage detection circuit.

[0123] The experiment was set with a coil current of 1A, an average coil radius of 0.08m, a coil spacing of 0.16m, and a measurement range of 100mm. Over a 100mm area, the theoretical magnetic flux density components on the axial plane were obtained using MATLAB. The high-precision voltage acquisition module 10 was used as a voltmeter, transmitting the voltage data to a computer. The measurement results showed good agreement with the theoretical results. coefficient of determination of components , .

[0124] Figure 4In embodiment 4 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value; as can be seen from the figure, the value obtained through this device is... The measured values ​​match the theoretical values ​​well, indicating high accuracy.

[0125] Figure 5 In embodiment 4 of this utility model Comparison chart of theoretical and measured values; where (a) is The measured value, (b) is Theoretical value; as can be seen from the figure, the value obtained through this device is... The measured values ​​agree well with the theoretical values, demonstrating high accuracy. This invention also exhibits high scalability, enabling the measurement of magnetic fields from coils with varying spacing.

[0126] The experimental steps of the two-dimensional magnetic induction intensity component measuring device in the axial plane of a Helmholtz coil disclosed in this utility model are as follows:

[0127] (1) Use Mathematica and MATLAB to perform simulation to verify whether the experimental scheme is correct.

[0128] (2) Calibrate the two-dimensional Hall probe 2 to eliminate the influence of the geomagnetic field.

[0129] (3) Turn on the DM-A2 digital ammeter 5 and the HLZ solenoid magnetic field experiment instrument 4, measure the output voltage at the starting measurement point, and record it.

[0130] (4) Press the MCU processor self-reset button 9 to move the stepper motor guide rails 6 on the X and Z axes respectively, thereby driving the two-dimensional Hall probe 2 to move on the 1 / 2 axis of the Helmholtz coil 1, collecting the voltage magnitude at this time, converting it into magnetic induction intensity and recording it in the table; drive the two-dimensional Hall probe 2 to move in the 1 / 4 axis plane, collect the voltage magnitude at this time, convert it into magnetic induction intensity and record it in the table.

[0131] (5) Repeat the above steps, change the coil spacing to 2R, and measure the magnetic induction intensity of 1 / 2 axis and 1 / 4 plane when the coil spacing is 2R.

[0132] (6) After recording, use MATLAB to fit the theoretical values ​​of the data. Compare the experimental values ​​with the theoretical values ​​to obtain the experimental error.

[0133] This experimental setup has two main functions:

[0134] (1) Measure the magnetic induction intensity of the coil at 1 / 2 axis or 1 / 4 axis plane.

[0135] (2) By changing the coil spacing, the difference in magnetic induction intensity of the coil axis plane with different spacing can be compared.

[0136] The improvement of this utility model is as follows:

[0137] (1) Design of a two-dimensional Hall probe 2 for measuring two-dimensional magnetic fields: This experiment fully utilizes the symmetrical distribution characteristics of the magnetic field of the Helmholtz coil 1 and designs a two-dimensional Hall probe 2 using two linear Hall sensors. The magnetic field distribution of the axial plane is reflected by measuring the magnetic field of 1 / 4 of the two-dimensional axial plane. Furthermore, by measuring the magnetic induction intensity of the coils in the 1 / 4 axial plane with a 2R spacing, it is reflected that the spacing of the coils has a direct impact on the magnetic induction intensity. This is well-suited for use as teaching content in university physics experiments.

[0138] (2) Simulation and error analysis using software: MATLAB and Mathematica were used to simulate the magnetic fields generated by Helmholtz coil 1 and the two coils with a distance of 2R between them, respectively. The theoretical values ​​obtained by MATLAB were compared with the measured values ​​to perform error analysis. The coefficients of determination R² between the theoretical and measured values ​​of the magnetic field along the 1 / 2 axis and the magnetic field along the 1 / 4 two-dimensional axis were found to be greater than 0.985 and 0.995, respectively, indicating that the theoretical and measured values ​​have a very high degree of agreement.

[0139] (3) Effectively reduce measurement error: The output voltage of the two-dimensional Hall probe 2 is acquired by the high-precision voltage acquisition module 10; the two-dimensional Hall probe 2 is powered by the high-precision voltage source 13, which reduces the error caused by power supply aging or other reasons; the two-dimensional Hall probe 2 is moved by the stepper motor guide rail moving circuit, which significantly reduces the error caused by human operation and mechanical device return; the high-precision voltage acquisition module 10 integrates automatic calibration of geomagnetic field function, algorithm filtering function and noise filtering function, which effectively reduces measurement error.

[0140] (4) 3D printing improves the scalability of the experiment: The self-designed model and then the 3D printed coil skeleton and base can realize the adjustable distance between the two coils of 0.5R, R, 1.5R, 2R, 2.5R or 3R, which improves the scalability of the experiment; 3D printed two-dimensional Hall probe mounting base 3 improves the self-controllability of the experiment.

[0141] The above content is only for illustrating the technical concept of this utility model and should not be construed as limiting the scope of protection of this utility model. Any modifications made to the technical solution based on the technical concept proposed in this utility model shall fall within the scope of protection of the claims of this utility model.

Claims

1. A device for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil, characterized in that, include: The system includes a Helmholtz coil (1), a two-dimensional Hall probe (2) connected to the Helmholtz coil (1), a stepper motor guide rail moving circuit and a high-precision voltage acquisition module (10) connected to the two-dimensional Hall probe (2); the stepper motor guide rail moving circuit is used to control the movement of the two-dimensional Hall probe (2); the high-precision voltage acquisition module (10) is used to acquire the output voltage of the two-dimensional Hall probe (2) and transmit it to the computer; one end of the high-precision voltage acquisition module (10) is connected to the two-dimensional Hall probe (2), and the other end is connected to the computer.

2. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 1, characterized in that, The two-dimensional Hall probe (2) consists of a two-dimensional Hall probe mounting base (3) and two linear Hall sensors that are orthogonally mounted on the two-dimensional Hall probe mounting base (3).

3. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 1, characterized in that, The stepper motor guide rail moving circuit includes: a stepper motor guide rail (6), a stepper motor driver (7) electrically connected to the stepper motor guide rail (6), a 24V power supply (8), and an STM32 guide rail control circuit (9); the two-dimensional Hall probe (2) is fixed on the stepper motor guide rail (6), and the STM32 guide rail control circuit (9) is used to control the movement of the two-dimensional Hall probe (2).

4. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 3, characterized in that, The STM32 rail control circuit (9) includes: an STM32F103C8T6 chip (17), a power supply circuit, a clock circuit, a self-reset button circuit, and a decoupling circuit; the clock circuit is connected to the corresponding pin of the STM32F103C8T6 chip (17), the self-reset button circuit is connected to the corresponding pin of the STM32F103C8T6 chip (17), and the decoupling circuit is connected between the power supply circuit and the ground.

5. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 1, characterized in that, The high-precision voltage acquisition module (10) includes: an analog-to-digital converter (11), an MCU circuit (12) electrically connected to the analog-to-digital converter (11), a high-precision voltage source (13), and a fourth-order RC low-pass filter (14); the MCU circuit (12) is connected to an STM32F407ZGT6J chip (15) and an analog-to-digital converter (16); the high-precision voltage source (13) is connected to the positive reference voltage input pin of the analog-to-digital converter (16); the fourth-order RC low-pass filter (14) is connected in series at the analog signal input terminal of the analog-to-digital converter (16).

6. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 5, characterized in that, The analog-to-digital converter circuit (11) includes: an analog-to-digital converter (16), a power supply circuit, a clock circuit, an input circuit, an SPI communication circuit, a reference voltage circuit, and a filter circuit. The power supply circuit is connected to the power supply pin of the analog-to-digital converter (16), the clock circuit is connected to the clock pin of the analog-to-digital converter (16), the voltage under test is connected to the probe connected to the input circuit, the SPI communication circuit is connected to the data input pin of the STM32F407ZGT6J chip (15) and the data output pin of the analog-to-digital converter (16), the reference voltage circuit is connected to the positive voltage reference pin of the analog-to-digital converter (16), the decoupling capacitor is connected between the power supply circuit and the ground line, and the input circuit is connected to the filter circuit and the eight analog signal input channels of the analog-to-digital converter (16).

7. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 5, characterized in that, The STM32F407ZGT6J chip (15) is either an F3 series chip or an F4 series chip.

8. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 5, characterized in that, The analog-to-digital converter (16) is an ADS1256 analog-to-digital converter.

9. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 5, characterized in that, The high-precision voltage source (13) consists of a voltage reference chip, a filter circuit, and an input voltage detection circuit. The input voltage detection circuit uses a transistor, a resistor, a Zener diode, and a light-emitting diode connected in parallel to the voltage input terminal. When the input voltage detection circuit is between 6 and 12V, it lights up green; when it is below 2V, it does not light up; when it is between 2 and 6V, it lights up yellow; and when it is outside the voltage range, it displays red light. The input voltage detection circuit is connected to pin 2 of the voltage reference chip. A filter circuit is connected between the input voltage detection circuit and the ground wire. A filter circuit is also connected between the output voltage of the voltage reference chip and the ground wire.

10. The apparatus for measuring the two-dimensional magnetic induction intensity on the axial plane of a Helmholtz coil according to claim 1, characterized in that, It also includes an HLZ solenoid magnetic field experimental instrument (4) and a DM-A2 digital ammeter (5), which are electrically connected to the two-dimensional Hall probe (2).

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