Giant magnetostrictive bar dynamic characteristic test system and use method thereof

Abstract

The invention discloses a giant magnetostrictive bar dynamic characteristic test system and a use method thereof, the giant magnetostrictive bar dynamic characteristic test system comprises a body structure and a support structure, and the support structure is provided with a visual detection unit; the body structure comprises a coil framework used for being inserted into a giant magnetostrictive bar, and a magnet exciting coil is wound outside the coil framework. The magnet exciting coil is sleeved with a magnetic conductive sleeve. An upper magnetic conductive circular plate is fixed to the top of the magnetic conductive sleeve, and the upper end and the lower end of the giant magnetostrictive bar make contact with the magnetic conductive blocks and extend out of the coil framework. Openings for exposing the upper end and the lower end of the giant magnetostrictive bar are formed in the magnetic conductive sleeve; an output rod is placed on the top of the upper magnetic conductive circular plate, and a pressure sensor, a base plate and a disc spring are sequentially installed between the pre-tightening end cover and the disc body from bottom to top. The method has the characteristics of high test precision, stability, safety and reliability, and can guide the engineering application of the giant magnetostrictive material.

Description

Technical Field

[0001] The invention relates to the technical field of testing systems, and in particular to a giant magnetostrictive rod dynamic characteristic testing system and a use method thereof. Background Art

[0002] Giant magnetostrictive materials have the characteristics of huge magnetic strain, good magnetic coupling coefficient, high energy density and fast response, such as Fe-Ga alloy (Galfenol) and Tb-Dy-Fe alloy (Terfenol-D), which are widely used in intelligent robots, precision sensors, underwater acoustic transducers and vibration control actuators. The accuracy, reliability and repeatability of the dynamic characteristics test of giant magnetostrictive bars are the key to fully exert their performance.

[0003] However, the research on the dynamic characteristics of magnetostrictive rods by scholars at home and abroad is still incomplete and the description is sparse, so it is impossible to accurately obtain the dynamic response parameters of giant magnetostrictive rods. The prior art tests the static parameters of giant magnetostrictive rods under different prestress and bias magnetic fields, but does not test the dynamic characteristic parameters such as magnetic field intensity, magnetic induction intensity and rod output strain under alternating magnetic fields. In addition, giant magnetostrictive rods are rare earth ferromagnetic materials and are relatively expensive. The output force in the axial direction under a strong magnetic field is very large. Long-term repeated work can easily cause the edges of both ends of the rod to wear or even partially fall off. Therefore, a dynamic characteristic measurement system for giant magnetostrictive rods based on visual detection is needed to detect defects on the edges of both ends of the rod in real time, reduce costs and ensure the reliability of the system. Summary of the invention

[0004] The purpose of the present invention is to provide a giant magnetostrictive rod dynamic characteristic testing system and a use method thereof.

[0005] To achieve the above object, the technical solution of the present invention is as follows: A giant magnetostrictive rod dynamic characteristics testing system comprises a main body structure and a support structure, wherein a visual detection unit is installed on the support structure; the main body structure comprises a coil frame for inserting the giant magnetostrictive rod, an excitation coil is wound around the coil frame; a magnetic sleeve is arranged outside the excitation coil; an upper magnetic plate is fixed on the top of the magnetic sleeve, and a lower magnetic plate is fixed on the bottom; through holes are formed at the centers of the upper and lower magnetic plates, and magnetic blocks are placed in the through holes. The upper and lower ends of the rod are in contact with the magnetic blocks respectively and extend out of the coil frame; the magnetic sleeve is provided with openings exposing the upper and lower ends of the giant magnetostrictive rod; an output rod is placed on the top of the upper magnetic plate, the output rod includes a disc body, a rod body is fixed at the center of the upper surface of the disc body, a pre-tightening end cover passes through and is slidably connected to the top of the rod body, and a pressure sensor, a pad, and a disc spring are sequentially installed between the pre-tightening end cover and the disc body from bottom to top; the pre-tightening end cover and the upper magnetic plate are fixedly connected to the upper magnetic plate by pre-tightening bolts; The visual detection unit includes a first high-speed camera, a second high-speed camera and light sources facing the upper and lower ends of the giant magnetostrictive rod; the first high-speed camera is arranged facing the top of the rod body, and the second high-speed camera is arranged facing the opening; the pressure sensor, the first high-speed camera and the second high-speed camera are all connected to the host computer through a switch communication.

[0006] As a further improvement, there are two openings which are arranged opposite to each other.

[0007] A further improvement is that the support structure includes a camera support, on which a plurality of adjustable sliders are slidably mounted, and the adjustable sliders are connected to a mounting rod; the first high-speed camera, the second high-speed camera and the light source are all mounted on the mounting rod; the camera support is fixed on a support bottom plate, and the support bottom plate is fixed on a base.

[0008] Further improvements also include a magnetic field dynamic characteristics testing unit, which includes an induction coil wrapped around the giant magnetostrictive rod and a Hall element fixed on the coil frame. The induction coil and the Hall element are electrically connected to a data acquisition card, and the data acquisition card is connected to a host computer through a switch communication.

[0009] As a further improvement, the lower magnetic conductive circular plate is fixed to the bottom plate by bolts, and the bottom plate is fixed to the base by bolts.

[0010] As a further improvement, the coil skeleton is a non-magnetic aluminum sleeve or a ceramic sleeve, the giant magnetostrictive rod is a Tb-Dy-Fe alloy round rod; and the magnetic sleeve is made of pure iron or silicon steel.

[0011] As a further improvement, the magnetic conductive block is formed by laminating silicon steel sheets, and includes a plurality of small holes formed on the silicon steel sheets for suppressing eddy current loss and providing a magnetic circuit.

[0012] As a further improvement, the pressure sensor is annular; the pressure sensor, the backing plate, the disc spring and the pre-tightening end cover are all sleeved outside the rod body.

[0013] A method for using a giant magnetostrictive rod dynamic characteristic testing system, the structure of the giant magnetostrictive rod dynamic characteristic testing system is shown above.

[0014] The steps include: Step 1: Assemble the main structure; Step 2: Install the visual inspection unit; Step 3, calibrating the light source and adjusting the resolution of the first high-speed camera and the second high-speed camera; Step 4: adjust the pre-tightening bolt and feed back the pre-stress in real time through the pressure sensor until the desired value is reached, and then pass AC current to the excitation coil to provide an AC magnetic field with a DC bias to form a preset bias magnetic field and an excitation magnetic field; the giant magnetostrictive rod produces a magnetostrictive effect and vibrates; Step 5: Use the first high-speed camera and the second high-speed camera to measure the displacement and detect the edge of the giant magnetostrictive rod; if the giant magnetostrictive rod has no defects, perform a magnetic field dynamic characteristic test; if there are defects, take it out and test the next giant magnetostrictive rod.

[0015] Further improvement, the method of detecting the dynamic characteristics of the magnetic field is as follows: The induction coil is evenly wound on the surface of the giant magnetostrictive rod to generate an induced electromotive force in an alternating magnetic field. , using formula (1) to measure the magnetic induction intensity , the formula is described as follows: (1) in, is the number of turns of the induction coil; is the cross-sectional area of ​​the induction coil, Indicates time t Derivation; The Hall element (26) measures the magnetic field strength using formula (2): , the formula is described as follows: (2) in, Output voltage for the Hall chip; is the magnetic permeability of air; is the sensitivity of the Hall chip.

[0016] The advantages of the present invention are as follows: The present invention adopts visual detection technology to test the dynamic characteristics of the rod and detect the defects on the edges of the two ends of the rod, which can accurately measure the dynamic displacement of the rod and detect the loss of the rod, improve the measurement accuracy and the service life of the rod, ensure the stability and reliability of the system, and provide guidance for the engineering application of giant magnetostrictive materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of visual detection of the present invention.

[0018] Figure 2 It is a schematic cross-sectional view of the main body structure of the present invention.

[0019] Figure 3 It is a schematic diagram of the magnetic field dynamic characteristic test of the present invention.

[0020] Figure 4It is a test flow chart of the present invention.

[0021] In the figure, 1 is a main body structure, 2 is a light source, 3 is a first high-speed camera, 31 is a second high-speed camera, 4 is an adjustable slider, 41 is a mounting rod, 5 is a camera bracket, 6 is a bracket base plate, 7 is a switch, 8 is a host computer, 9 is an output rod, 91 is a disk body, 92 is a rod body, 10 is a bolt, 11 is a pre-tightening end cover, 12 is a disc spring, 13 is a pad, 14 is a pressure sensor, 15 is an excitation coil, 16 is a coil skeleton, 17 is a giant magnetostrictive rod, 18 is a magnetic block, 19 is a positioning pin, 20 is an upper magnetic conductive circular plate, 21 is a magnetic conductive sleeve, 22 is a lower magnetic conductive circular plate, 221 is a through hole, 23 is a bottom plate, 24 is a base, 25 is an induction coil, 26 is a Hall element, and 27 is an opening. DETAILED DESCRIPTION

[0022] In order to facilitate understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification are only for describing specific implementation purposes and are not intended to limit the present invention.

[0024] See attached Figure 1, is a schematic diagram of visual inspection of the present invention, including a main body structure 1, a light source 2, a first and a second high-speed camera, an adjustable slider 4, a camera bracket 5, a bracket bottom plate 6, a switch 7 and a host computer 8, which are used to accurately measure the dynamic displacement of the giant magnetostrictive rod and detect the edge loss of the rod. The main body structure 1 is placed on a flat ground, kept horizontal and fixed; the light source 2 includes a mixed light source of two groups of LEDs and a backlight, which is placed horizontally facing the upper and lower edges of the rod to be inspected, and can slide freely through the adjustable slider 4, and is fixed with the camera bracket 5; there are two high-speed cameras 3, and the camera lenses are placed facing the output rod and the rod respectively, and are fixed and adjusted to a suitable focal length position using the camera bracket 5. The camera facing the output rod is used to collect the motion image of the rod under vibration at a frequency of hundreds or even thousands of Hz, and the camera facing the rod The camera is used to detect the loss at the edges of both ends of the bar. The two high-speed cameras 3 are integrated through the switch 7 and communicate with the host computer 8 in real time. The host computer 8 performs dynamic calibration, motion displacement measurement and bar edge loss detection on the collected images; the adjustable slider 4 is equipped with bolts, and the sliding and tightening on the camera bracket 5 are achieved by adjusting the tightness of the bolts; the camera bracket 5 is a number of aluminum smooth round rods, and the front view position of the camera and the light source can be achieved by cooperating with the adjustable slider 4; the bracket bottom plate 6 is an aluminum square plate, which is used to carry and fix the camera bracket 5. The adjustable slider 4 is closely matched with the camera bracket 5 to achieve damping positioning or is positioned by threaded connection with the positioning bolt.

[0025] See attached Figure 2, is a schematic diagram of the main structure of the present invention, which includes an output rod 9, a pre-tightening bolt 10, a pre-tightening end cover 11, a disc spring 12, a pad 13, a pressure sensor 14, an excitation coil 15, a coil skeleton 16, a giant magnetostrictive rod 17, a magnetic block 18, a positioning pin 19, an upper magnetic plate 20, a magnetic sleeve 21, a lower magnetic plate 22, a bottom plate 23 and a base 24, which are used to match the visual detection unit and the magnetic field dynamic characteristic test unit to realize the dynamic characteristic test of the giant magnetostrictive rod and the edge loss detection of the rod; the output rod 9 is directly rigidly connected with the magnetic block and the giant magnetostrictive rod, which is used to characterize the displacement output of the rod during magnetostriction; the pre-tightening bolts 10 are all hexagon socket bolts, which are used to tighten the pre-tightening end cover 11 and the magnetic sleeve 21 and apply prestress. The upper magnetic plate 20 and the magnetic sleeve 21 are also fastened by bolts, the lower magnetic plate 22 and the bottom plate 23 are fastened, and the bottom plate 23 and the base 24 are fastened. The pre-tightening end cover 11 includes 6 small through holes, 4 threaded holes and 1 large through hole. The small through holes are used to pass the pre-tightening bolts 10 and tighten the pre-tightening end cover 11 and the magnetic sleeve 21. The threaded holes are used to tighten the upper magnetic plate 20 and the pre-tightening end cover 11. The large through hole is used to pass the output rod 9. The disc spring 12 includes 2 brass disc springs, which are stacked and placed to maintain pressure and absorb the additional expansion and contraction force generated when the bar vibrates. The center of the pad 13 includes a through hole for passing the output rod and carrying the disc spring 12, solving the disc spring problem. The problem of the aperture of 12 not matching the aperture of the pressure sensor 14; the pressure sensor 14 is a ring structure, and its aperture is slightly larger than the output rod 9, which is used to pass through the output rod and test the real-time prestress value; the excitation coil 15 is wound by 880 turns of flat copper wire, which is used to connect the programmable AC power supply and provide the rod with an alternating magnetic field with a DC bias; the coil skeleton 16 is a non-magnetic ceramic sleeve, and a square through hole of appropriate size is cut on the wall of the sleeve, which is used to place the Hall element 26 and measure the magnetic induction intensity B, used for winding the excitation coil and suppressing eddy current loss; the giant magnetostrictive rod 17 is a Tb-Dy-Fe alloy round rod, which is radially cut to produce magnetostrictive effect and suppress eddy current loss; the magnetic block 18 is stacked by a number of silicon steel sheets with holes, which is used to combine giant magnetostrictive rods, provide magnetic circuits and suppress eddy current losses; the positioning pin 19 includes 4 non-magnetic aluminum positioning pins, which are used to carry the excitation coil and make it symmetrically distributed along the center of the skeleton; the upper magnetic conductive circular plate 20 is silicon steel, including 6 small through holes, 4 countersunk holes and 1 large through hole, the small through hole is used to pass bolts and tighten the pre-tightening end cover 11 and the magnetic conductive sleeve 21, the countersunk hole is used to tighten the upper magnetic conductive circular plate 20 and the pre-tightening end cover 11, and the large through hole is used to pass the output rod 9 to provide a magnetic circuit; the magnetic conductive sleeve 21 is silicon steel, including 6 threaded holes on the upper and lower sides, which are used to fasten bolts and provide a magnetic circuit; the lower magnetic conductive circular plate 22 is silicon steel, including 6 small through holes, 4 blind holes, 4 countersunk holes and 1 large through hole, the small through holes are used to pass the bolts and fasten the magnetic conductive sleeve 21, the blind holes are used to fix the positioning pins, the countersunk holes are used to fasten the lower magnetic conductive circular plate 22 and the bottom plate 23, and the large through hole is used to pass the magnetic conductive block; the bottom plate 23 is an aluminum plate, including 4 countersunk holes, 4 threaded holes and 6 through holes, the countersunk holes are used to fasten the bottom plate 23 and the base 24, the threaded holes are used to fasten the lower magnetic conductive circular plate 22 and the bottom plate 23, and the through holes are used to pass the bolts and fasten the bottom plate 23 and the magnetic conductive sleeve 21; the base 24 is a large-volume thick aluminum plate, including 4 threaded holes, which are used to fasten the bottom plate 23 and the base 24, and are used to fix the entire test system.

[0026] See attached Figure 3 , is a schematic diagram of the magnetic field dynamic characteristics test of the present invention, which includes a giant magnetostrictive rod, an induction coil 25, a data acquisition card, a Hall element 26 and a DC power supply; the induction coil 25 is evenly wound on the surface of the rod, and is used to generate an induced electromotive force in an alternating magnetic field. , using formula (1) to measure the magnetic induction intensity , the formula is described as follows: (1) in, is the number of turns of the induction coil; is the cross-sectional area.

[0027] Attached Figure 3 The data acquisition card has a built-in amplifier for amplifying the induction signal and converting it into a digital signal; the Hall element 26 includes a PCB circuit board and a Hall probe, and uses formula (2) to measure the magnetic field strength , the formula is described as follows: (2) in, Output voltage for the Hall chip; is the magnetic permeability of air; is the sensitivity of the Hall chip.

[0028] Attached Figure 3 The DC power supply includes a 5V output interface for providing a stable DC voltage for the Hall element.

[0029] See attached Figure 4 , is a test flow chart of the present invention, which includes assembling the main body structure, assembling the visual inspection unit, calibrating the light source, the lens and adjusting the resolution, establishing a magnetic field dynamic characteristics test unit, applying prestress, bias magnetic field and excitation magnetic field, rod vibration, image acquisition and preprocessing, feature extraction and displacement measurement, defect judgment, induction coil, Hall element, data acquisition and processing, condition judgment that meets the requirements, changing the working condition and replacing the rod, etc., which is used to measure the dynamic characteristics of the giant magnetostrictive rod and detect the edge loss of the rod. The prestress, bias magnetic field and excitation magnetic field are applied, and the prestress of the rod is adjusted by a number of pre-tightening bolts, and the prestress is fed back in real time through a pressure sensor to determine whether the expected value is reached, and a programmable AC power supply is used to apply the bias magnetic field and the excitation magnetic field; the rod vibrates, and the giant magnetostrictive rod produces a magnetostrictive effect and vibrates under the set prestress, bias magnetic field and excitation magnetic field; the image acquisition and preprocessing, the high-speed camera sends the acquired image data to the host computer for preprocessing, and performs feature extraction and displacement measurement through grayscale, image enhancement and edge detection technology; the defect judgment, if the rod is detected to be defective, the rod needs to be replaced to ensure the authenticity and reliability of the test data, if the rod is detected to be defect-free, the dynamic magnetic field data should be measured by the induction coil and the Hall element, and the corresponding data acquisition and processing should be performed by the data acquisition card and the host computer; the changing working condition, when a set of normal data acquisition and processing is completed, if the test has multiple working condition requirements, it is necessary to change the prestress, bias magnetic field and excitation magnetic field to repeat the test until the test requirements are met, record the corresponding test data and end the test.

[0030] In summary, the present invention is a giant magnetostrictive rod dynamic characteristics testing system based on visual inspection, which consists of three main parts: a visual inspection unit, a main body structure, and a magnetic field dynamic characteristics testing unit. Visual inspection technology is used to test the dynamic characteristics of the rod and detect defects on the edges of both ends of the rod, thereby improving the measurement accuracy and the service life of the rod, ensuring the stability and reliability of the system, and providing guidance for the engineering application of giant magnetostrictive materials.

[0031] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A giant magnetostrictive rod dynamic characteristics testing system, characterized in that: The invention comprises a main body structure (1) and a support structure, wherein a visual detection unit is installed on the support structure; the main body structure (1) comprises a coil frame (16) for inserting a giant magnetostrictive rod (17), an excitation coil (15) being wound around the coil frame (16); a magnetic conductive sleeve (21) is provided on the outer sleeve of the excitation coil (15); an upper magnetic conductive circular plate (20) is fixed on the top of the magnetic conductive sleeve (21), and a lower magnetic conductive circular plate (22) is fixed on the bottom; a through hole (221) is formed at the center of each of the upper magnetic conductive circular plate (20) and the lower magnetic conductive circular plate (22), a magnetic conductive block (18) is placed in the through hole, and the upper and lower ends of the giant magnetostrictive rod (17) are respectively in contact with the magnetic conductive block (18) and extend The coil skeleton (16) is outwardly connected to the coil skeleton (16); the magnetic sleeve (21) is provided with openings (27) for exposing the upper and lower ends of the giant magnetostrictive rod (17); an output rod (9) is placed on the top of the upper magnetic conductive circular plate (20); the output rod (9) comprises a disk (91); a rod (92) is fixed at the center of the upper surface of the disk (91); a pre-tightening end cover (11) passes through the top of the rod (92) and is slidably connected; a pressure sensor (14), a pad (13), and a disc spring (12) are installed in sequence from bottom to top between the pre-tightening end cover (11) and the disk (91); the pre-tightening end cover (11) and the upper magnetic conductive circular plate (20) are fixedly connected to the upper magnetic conductive circular plate (20) via pre-tightening bolts (10); The visual detection unit comprises a first high-speed camera (3), a second high-speed camera (31) and light sources (2) facing the upper and lower ends of the giant magnetostrictive rod (17); the first high-speed camera (3) is arranged facing the top of the rod body (92), and the second high-speed camera (31) is arranged facing the opening (27); the pressure sensor (14), the first high-speed camera (3) and the second high-speed camera (31) are all connected to a host computer (8) via a switch (7) for communication.

2. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: There are two openings (27) which are arranged opposite to each other.

3. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: The support structure comprises a camera support (5), a plurality of adjustable sliders (4) are slidably mounted on the camera support (5), and the adjustable sliders (4) are connected to a mounting rod (41); the first high-speed camera (3), the second high-speed camera (31) and the light source (2) are all mounted on the mounting rod (41).

4. The giant magnetostrictive rod dynamic characteristics testing system according to claim 3, characterized in that: The camera bracket (5) is fixed on a bracket bottom plate (6), the bracket bottom plate (6) is fixed on a base (24), the lower magnetic conductive circular plate (22) is fixed on the bottom plate (23) by means of bolts, and the bottom plate (23) is fixed on the base (24) by means of bolts.

5. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: It also includes a magnetic field dynamic characteristics testing unit, which includes an induction coil (25) wound around the giant magnetostrictive rod (17) and a Hall element (26) fixed on the coil frame (16), the induction coil (25) and the Hall element (26) being electrically connected to a data acquisition card, and the data acquisition card being communicatively connected to a host computer (8) via a switch (7).

6. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: The coil frame (16) is a non-magnetic aluminum sleeve or a ceramic sleeve, the giant magnetostrictive rod (17) is a Tb-Dy-Fe alloy round rod; and the magnetic sleeve (21) is made of pure iron or silicon steel.

7. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: The magnetic conductive block (18) is formed by laminating silicon steel sheets, and includes a plurality of small holes formed on the silicon steel sheets for suppressing eddy current loss and providing a magnetic circuit.

8. The giant magnetostrictive rod dynamic characteristics testing system according to claim 1, characterized in that: The pressure sensor (14) is annular; the pressure sensor (14), the backing plate (13), the disc spring (12) and the pre-tightening end cover (11) are all sleeved outside the rod body (92).

9. A method for using a giant magnetostrictive rod dynamic characteristics testing system, characterized in that: The structure of the giant magnetostrictive rod dynamic characteristics testing system is as shown in claim 5; The steps include: Step 1: Assemble the main structure (1); Step 2: Install the visual inspection unit; Step 3, calibrating the light source (2) and adjusting the resolution of the first high-speed camera (3) and the second high-speed camera (31); Step 4: adjusting the pre-tightening bolt (10) and providing real-time feedback of the pre-stress through the pressure sensor (14) until the desired value is reached, and then passing alternating current through the excitation coil (15) to provide an alternating magnetic field with a DC bias, thereby forming a preset bias magnetic field and an excitation magnetic field; the giant magnetostrictive rod (17) generates a magnetostrictive effect and vibrates; Step 5: Using the first high-speed camera (3) and the second high-speed camera (31), the displacement measurement and edge detection of the giant magnetostrictive rod (17) are performed; if the giant magnetostrictive rod (17) has no defects, the magnetic field dynamic characteristics detection is performed; if there are defects, the giant magnetostrictive rod (17) is removed and the next giant magnetostrictive rod (17) is tested.

10. The method for using the giant magnetostrictive rod dynamic characteristics testing system according to claim 9, characterized in that: The method for detecting the dynamic characteristics of the magnetic field is as follows: The induction coil (25) is evenly wound on the surface of the giant magnetostrictive rod (17) and is used to generate an induced electromotive force by an alternating magnetic field. , using formula (1) to measure the magnetic induction intensity , the formula is described as follows: (1) in, is the number of turns of the induction coil; is the cross-sectional area of ​​the induction coil, Indicates time Derivation; The Hall element (26) measures the magnetic field strength using formula (2): , the formula is described as follows: (2) in, Output voltage for the Hall chip; is the magnetic permeability of air; is the sensitivity of the Hall chip.

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