CN102680356A - Density measuring device and method based on electromagnetic suspension - Google Patents

Abstract

A density measurement device and method based on electromagnetic levitation, the device includes remote observation and recording equipment, a levitation chamber and a magnetic field generator; Scale scale; the magnetic field generating device includes a first magnet, a second magnet, a first bracket and a second bracket, the first magnet and the second magnet have the same name and their poles are opposite, and the suspension cavity is placed between the two magnets and is in the same position as the two magnets. On the vertical axis, the two sides of the first magnet and the second magnet are respectively fixedly connected with the first bracket and the second bracket through fixing screws; the remote observation and recording equipment includes an external camera and a computer. Methods By measuring the levitation height of the sample in the standard solution to achieve magnetic levitation, the functional relationship between the sample density and the levitation height was established, so as to obtain a more accurate value of the sample density.

Description

A density measuring device and method based on electromagnetic levitation

technical field

The invention belongs to the field of measurement technology, in particular to a density measurement device and method based on electromagnetic levitation.

Background technique

Density is one of the most basic physical parameters representing material properties, and accurate density measurement is critical to the fields of petroleum, chemical industry, metallurgy, building materials, light industry, etc. It is related to the control, testing and production of semi-finished products and product quantity and quality important aspects of process management.

Most of the existing density measuring devices can only unilaterally measure the density of specific types of solid or liquid substances. Among them, the commonly used density measurement methods for solid state are: unequal arm balance method, microwave technology measurement method, radioactive principle measurement method and so on. CN2051738U discloses " rock (ore) stone density measuring instrument " has improved measuring efficiency and precision than previous density measuring method, but because be subjected to the restriction of sensor, also exist for using the same load cell for the sample that range is bigger or range is smaller The problem of large measurement accuracy error, due to the technical conditions at that time, also has the disadvantages of small amount of stored data and inconvenient data transmission. The "hydraulic induction volume density meter and its measuring method and application" disclosed in CN1456875A can detect the volume density of human organs and irregular shapes, and it is difficult to accurately measure the sample. It is accurate and reliable to measure the volume density of human specimens. The "Solid Object Density Measuring Device" disclosed in ZL200520028675.3 adopts the method of replacing the load cell to increase the measuring range and reduce the measurement error. The above methods all have the disadvantages of relatively slow measurement speed, harsh conditions of use, complicated process, and limited to solid measurement. On the other hand, for the density measurement of liquid substances, densitometers or experimental methods are widely used in industry to measure liquid density. A density meter is a special instrument for measuring the density of a liquid. According to the balance principle of object suspension, different density meters are used to measure liquids with a density greater than or less than water, and the measurement range is small. The experimental method to measure the density of liquid, although the accuracy can be guaranteed to a certain extent, the operation is more cumbersome and the efficiency is low.

Obviously, with the development of social science and technology, these density measurement devices are gradually difficult to meet the requirements of technological diversification, and density measurement devices must continue to develop in the direction of more popularization, simplification, precision, and miniaturization. Therefore, people need a solid-liquid density measurement method with easy operation, stable performance, fast measurement, wide application range, certain accuracy and low cost.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a density measuring device and method based on magnetic levitation. By measuring the levitation height of the sample in the standard solution to achieve magnetic levitation, the functional relationship between the sample density and the levitation height is established, thereby obtaining a comparative Accurate sample density value.

The technical solution of the present invention is realized as follows: a density measurement device based on magnetic levitation, including a levitation chamber, a magnetic field generating device and remote observation and recording equipment;

The suspension cavity is placed in the magnetic field generating device;

The suspension cavity is a cylindrical measuring container, and a scale scale is arranged vertically outside the suspension cavity;

The magnetic field generating device includes a first magnet, a second magnet, a first bracket and a second bracket, the first magnet and the second magnet have the same poles of the same name, and the suspension cavity is placed between the two magnets, and is in the same vertical On the straight axis, both sides of the first magnet and the second magnet are respectively fixedly connected with the first bracket and the second bracket by screws;

Described first magnet and second magnet can select electromagnet or permanent magnet for use; In the situation of selecting electromagnet for use, need to connect the magnetic field strength adjuster through the first electromagnet wire and the second electromagnet wire to meet the regulation of electromagnet field strength According to the requirements, the magnetic induction intensity B ₀ on the surface of the magnet is required to be not less than 0.8T, and the adjustment range of the magnetic induction intensity on the surface of the electromagnet is required to be 0.2-1.0T during actual measurement, and the electromagnet is powered by 24V DC power supply; in the case of permanent magnets, it is required Its surface magnetic induction intensity B ₀ is not less than 0.4T; when using permanent magnets, use fixing screws to fix the permanent magnets at different positions on the bracket to adjust the surface distance between the two permanent magnets, thereby changing the spatial magnetic field intensity; when using electromagnets, except In addition to adjusting the distance between the magnets, the magnetic field intensity regulator can also be adjusted to change the surface magnetic induction intensity of the electromagnet to achieve the purpose of changing the spatial magnetic field intensity.

The magnetic field strength regulator includes a fixed-gear sliding rheostat and a DC power supply. After the first magnet and the second magnet are connected in parallel, the fixed-gear sliding rheostat and the DC power supply are connected in series. Different fixed gears correspond to different surface magnetic induction intensities of the electromagnets. Bit directly reads the value of the surface magnetic induction intensity to realize the continuous change of the surface magnetic induction intensity of the electromagnet within the range of 0-1.0T, thereby expanding the measurable range. The DC power supply can be replaced by an AC power supply connected in series with a transformer.

The material of the first bracket and the second bracket is a non-magnetic alloy material, and a non-magnetic connection is adopted. The bracket and the magnet are connected by screws, so that the distance between the two magnets can be adjusted in steps of 5 mm within the range of 35 to 60 mm;

The remote observation and recording equipment includes an external camera and a computer; the external camera is connected to the computer through its connecting wire, and the external camera needs to be selected according to the measurement accuracy requirements, and a high-speed camera should be selected for accurate measurement.

The method for performing density measurement using the above-mentioned density measurement device based on magnetic levitation comprises the following steps:

Step 1: Take a standard solution of a certain concentration and inject it into the suspension chamber, so that the liquid level of the solution reaches more than 4/5 of the overall height of the suspension chamber; take a granular sample with a diameter of 0.2~3mm in the substance to be tested, and put the test sample The sample is completely immersed in the standard solution, and ensure that there are no air bubbles on the surface of the sample;

Step 2: Place the suspension cavity in the space between the two magnets (that is, in the magnetic field), so that the centerline of the suspension cavity and the vertical centerline of the two magnets coincide as much as possible to ensure that the system is stable for a certain period of time;

Step 3: If the sample can be suspended stably in the magnetic field, read its suspension height h through an external camera device; if the sample cannot be suspended stably, adjust the magnetic field strength according to the actual situation, and repeat step 2 until the sample can To reach a stable suspension, read its suspension height h;

Adjusting the magnetic field intensity according to the actual situation is specifically: adjusting the magnet spacing when selecting a permanent magnet; adjusting the gear position of the fixed-range sliding rheostat when selecting an electromagnet to realize the adjustment of the magnetic field intensity.

At room temperature, take a sufficiently small sample of the substance to be tested (which can be considered to have uniform density, stable properties, and can represent the physical properties of the substance to be tested), and place it in a magnetic fluid (standard solution) under the action of a gradient magnetic field. ), when the sample is stably suspended in the standard solution, the sample is balanced under the action of four forces, namely gravity G, the buoyancy F _f of the standard solution on the sample, the force F _m of the magnetic field on the sample, The force F _s of the magnetic fluid on the sample in the inhomogeneous magnetic field is expressed as:

G+F _f +F _m +F _s =Fg+F _mag =0 (1)

In the formula: G is the gravity of the sample; F _f is the buoyancy of the standard solution on the sample; F _m is the force of the magnetic field on the sample; F _s is the force of the magnetic fluid on the sample in the non-uniform magnetic field; _g =G+F _f is the resultant force of gravity and buoyancy; F _mag =F _m +F _s is the resultant force generated by the magnetic field.

Step 4: Carry out numerical conversion of the suspension height h and the sample density ρ _s to obtain the sample density ρ _s ;

Step 4.1: Determine the local gravitational acceleration g;

Step 4.2: Calculate the density ρ _m and the magnetic susceptibility χ _m of the standard solution according to the molar concentration of the injected standard solution;

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1000</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}$

In the formula: c is the concentration of the solution, M is the relative molecular mass, and a is the mass percentage of the solute.

${\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 14350</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; cm</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mol</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}$

In the formula: ρ is the solution density, the unit is g/cm ³ ; M′ is the molar mass of the manganese chloride solution, the unit is g/mol.

Step 4.3: If the magnetic susceptibility of the substance to be measured or its calculation method is known, find out or calculate the exact value x _s of the magnetic susceptibility of the substance to be measured; if the magnetic susceptibility of the substance to be measured cannot be determined, then approximately χ _s =- 5×10 ^-6 , it has been proved by practice that the error between the density value calculated by this method and the real value is less than 5%, so it can be used for approximate calculation;

Step 4.4: Determine the magnetic induction intensity B ₀ on the surface of the magnet;

If a permanent magnet is used, find out its calibrated surface magnetic induction B ₀ ; if an electromagnet is used, determine the surface magnetic induction B ₀ of the magnet according to the resistance value and gear position of the rheostat when the sample reaches stable suspension;

Step 4.5: Calculate the magnetic induction intensity distribution on the center line of the magnet;

According to the gravitational acceleration g, the density ρ _m of the standard solution, the magnetic susceptibility χ _m , the magnetic susceptibility χ _s of the substance to be measured, and the magnetic induction intensity B ₀ of the magnet surface, combined with the relational expression of the change of the magnetic induction intensity of the magnet in space, the spatial magnetic induction intensity B _z is obtained The relationship between the levitation height h, since the position of the sample levitation is on the center line of the magnet and the distance from the surface of the magnet below is h, according to the relationship between the change of the magnetic induction intensity of the magnet in space, the h defined in the formula is related to the z here exactly the same. In the following derivation, in order to avoid confusion, replace z with h, that is, here h is completely equivalent to z and can be directly replaced.

The relationship between the change of the magnetic induction intensity of the magnet in space is as follows:

When the magnet is in the shape of a cuboid,

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; ]</span>$

When the magnet is in the shape of a cylinder,

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span>$

Calculate the functional relationship between the magnetic induction intensity B _z on the central axis and the height h by the method of vector sum, such as formula (2), (3);

In this device, two identical magnets with the same name and magnetic poles face each other with a distance of H. For a cuboid-shaped permanent magnet, within the space range of 0 to H, the magnetic induction intensity B _z on the central axis satisfies:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; ]</span>$

In the formula: B _r is the surface density of the magnetic charge of the magnet; a, b are the length and width of the horizontal plane of the permanent magnet; L _m is the thickness of the magnet; H is the distance between the two magnet surfaces; z is the distance from any point on the axis to the surface of the magnet below.

If an electromagnet is used, the distribution of magnetic induction intensity in its space is similar to the above formula, and the magnetic induction intensity B _z on the central axis within the space range of 0 to H can also be obtained:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula: R is the diameter of the electromagnet;

Step 4.6: Calculate the functional relationship between the suspension height h of the sample and the density ρ _s of the sample when the sample is balanced under the combined action of gravity, buoyancy and magnetic field force;

The sample is under the force balance under the joint action of gravity, buoyancy and magnetic field force, and the functional relationship between the sample suspension height h and the sample density ρ _s is deduced according to the definition formula of each force;

Analyzing formula (1), we can see that under a given magnetic field B, according to the force balance:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; mag</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Vg</span>}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula: ρ _s and ρ _m represent the densities of the sample and the calibration liquid respectively; V (m ³ ) represents the volume of the sample; g is the local gravity acceleration, where the buoyancy ρ _m gV of the target particle in the medium is considered Influence; χ _s and χ _m respectively represent the magnetic susceptibility of the sample and paramagnetic medium (standard solution); μ ₀ is the vacuum permeability, the size is 4π×10 ^-7 (N·A ^-2 ); is the Laplace operator, $\&dtri;=\frac{{\&PartialD;B}_x}{\&PartialD;x}+\frac{{\&PartialD;B}_{\mathrm{the\; y}}}{\&PartialD;\mathrm{the\; y}}+\frac{{\&PartialD;B}_z}{\&PartialD;z}.$

Since the gravitational acceleration g=(0,0,-g), that is, only exists in the direction of the z-axis, only the balance in the direction of the z-axis is considered. From equations (2), (3) and (4), we can know B _z , therefore, the relationship between the suspended height of the target particle and its density can be expressed as:

$\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\frac{{\mathrm{<span\; class="notranslate">\; dB</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

It can be seen from the analysis that the calculation of solving the above formula is cumbersome and the workload is heavy. Therefore, the height-density (ρ-h) conversion program provided by the present invention solves formula (5) under the premise of given basic parameters, the basic parameters include: gravitational acceleration g, vacuum permeability μ ₀ , standard The molar concentration m of the solution, the magnetic induction intensity B ₀ of the magnet surface;

Step 4.7: generate a density-height curve;

Step 4.8: Obtain the precise density value of the tested sample according to the suspension height of the sample;

In the case that the exact density value is not required, it is also possible to directly compare the readings on the ρ-h curve to achieve the calculation of the sample density ρ _s by measuring the suspension height.

Combined with formula (2) and formula (5) of magnetic induction intensity on the axis, the precise density value of the tested sample can be obtained.

Step 5: Record the obtained sample density ρ _s , and the measurement ends.

Beneficial effects: Under the conditions of determining the magnetic induction intensity, spacing and standard solution of the electromagnet, the sample can achieve magnetic levitation in a short period of time, and the measurement accuracy is high; the electromagnet device is used, and the magnetic induction intensity can be effectively controlled by the magnetic field intensity regulator , so as to obtain a wider range of density measurement; during the measurement process, the distance between the two electromagnets can be adjusted according to the needs, which greatly increases the flexibility of the device and expands the measurement range; the device of the present invention is small in size and light in weight, not only easy to carry, And it is easy to protect the internal precision container, so that it will not affect the measurement accuracy due to transportation, and the working performance is stable; it can be used to measure the density of solid materials and some liquid materials at the same time, without special adjustment devices, and the operation is simple; except for measurement In addition to the main function of material density, it can also be used for the measurement of material magnetic susceptibility after parameter modification, details and data special processing. It can measure the magnetic susceptibility of solid or immiscible fluid with water, and the measurement angle is changeable.

Description of drawings

Fig. 1 is a schematic structural diagram of a density measuring device based on magnetic levitation in an embodiment of the present invention, wherein, 1-the first magnet, 2-the first bracket, 3-the first fixing screw, 4-suspension cavity, 5-scale scale, 6- Sample, 7-standard solution, 8-second fixing screw, 9-third fixing screw, 10-fourth fixing screw, 11-fifth fixing screw, 12-second magnet, 13-second bracket, 14- Sixth fixing screw, 15-seventh fixing screw, 16-eighth fixing screw, 17-computer, 18-camera connecting wire, 19-ninth fixing screw, 20-camera, 21-second electromagnet wire i, 22 -the second electromagnet wire ⅱ, 23-magnetic field intensity regulator, 24-the first electromagnet wire ⅱ, 25-the first electromagnet wire ⅱ, 26-the tenth fixing screw;

Fig. 2 is the schematic diagram of the magnetic field intensity regulating circuit of the embodiment of the present invention;

Fig. 3 is a method flowchart of an embodiment of the present invention;

Fig. 4 is a flow chart of ρ-h data conversion according to the embodiment of the present invention.

Detailed ways

The specific implementation manners of the present invention will be described in detail below in conjunction with the accompanying drawings.

The density measurement device based on magnetic levitation in this embodiment, as shown in Figure 1, includes a levitation chamber 4, a magnetic field generator and remote observation and recording equipment;

The suspension cavity 4 is a cylindrical measuring container, and the cavity is made of colorless glass; the vertical direction outside the suspension cavity 4 is provided with a scale scale 5;

During the measurement process, inject a standard solution 7 with a certain concentration into the suspension chamber 4, so that the liquid level of the solution reaches more than 4/5 of the overall height of the suspension chamber 4; take a granular test sample with a diameter between 0.2 and 3 mm in the substance to be tested. Sample 6, completely immerse sample 6 in standard solution 7;

Described magnetic field generator comprises a first magnet 1, a second magnet 12, a first support 2 and a second support 13, the first magnet 1 and the second magnet 12 have opposite magnetic poles of the same name, the suspension cavity 4 is between the two magnets, and The center of the suspension chamber and the center of the two magnets are on the same vertical axis, the first magnet 1 is connected to the first bracket 2 through the first fixing screw 3, and the first magnet 1 is connected to the bracket II13 through the tenth fixing screw 26; the second magnet 12 Connect with the first bracket 2 through the third fixing screw 9, and connect the second magnet 12 with the second bracket 13 through the eighth fixing screw 16;

Described first magnet 1 and second magnet 12 can be selected electromagnet or permanent magnet; The electromagnet wire i21 is connected to the a node of Fig. 2, the first electromagnet wire ii 25 and the second electromagnet wire ii 22 are all connected to the b node in Fig. Power supply, the first magnet (1) and the second magnet (12) are connected in parallel and connected in series with the fixed-range sliding rheostat and the DC power supply. The switch S is responsible for the switching of the DC power supply. The gear corresponds to the different surface magnetic induction of the electromagnet. The actual measurement requires the adjustment range of the magnetic induction of the electromagnet surface to be 0.2-1.0T. The electromagnet is powered by a 24V DC power supply; the DC power supply can be replaced by an AC power supply connected in series with a transformer.

In the case of selecting a permanent magnet, its surface magnetic induction intensity B ₀ is required to be not less than 0.4T; by adjusting the second (permanent) magnet 12 to the second fixing screw 8, the ninth fixing screw 19, and the third fixing screw 9 And the eighth fixing screw 16, the fourth fixing screw 10 and the seventh fixing screw 15, the fifth fixing screw 11 and the sixth fixing screw 14 positions are fixedly connected with the first bracket 2 and the second bracket 13, so that between the two magnets The distance between the two permanent magnets can be adjusted in steps of 5mm within the range of 35-60mm, and the surface distance of the two permanent magnets can be adjusted to change the strength of the magnetic field in space;

The material of the first bracket 2 and the second bracket 13 is a non-magnetic alloy material, and a non-magnetic connection is adopted;

Described long-distance observation and recording equipment comprises external camera equipment and computer 17; External camera equipment selects Aoni ANC Core super strong edition camera 20 for use, and its configuration is: sensor: CMOS, pixel: 5,000,000, maximum frame number: 30 frames, The camera 20 is connected to the computer 17 via a camera connection line 18 . Computer 17 configuration requirements: Windows 2000 or above; Intel Pentium III processor or above CPU; memory above 256M, 512M recommended; hard disk space above 450M; 16-bit, 24-bit or 32-bit OpenGL graphics card. The external camera equipment should be selected according to the measurement accuracy requirements, and a high-speed camera should be used for accurate measurement.

Example 1

In the device in this embodiment, the magnetic field generating device is a cuboid NdFeB permanent magnet with a surface magnetic induction of 0.4T and a surface magnetic induction of 0.4T. The suspension cavity is a transparent glass cylinder with a diameter of 10mm and a height of 45mm. The container, the effect of the standard solution injected into the suspension chamber on the sample and the suspension of the sample can be observed through an external camera device. The scale measures the suspension height of granular samples.

A manganese chloride solution with known density and magnetic susceptibility is used as a paramagnetic medium, ie a standard solution, with a density of 1.24g/cm ³ and a magnetic susceptibility of 1.41*10 ^-4 . Take silica gel with a density of 1.180g/ ^cm3 as the substance to be tested.

The method for performing density measurement using the above-mentioned density measurement device based on magnetic levitation comprises the following steps:

Step 1: Take a manganese chloride solution with a concentration of 2.5mol/L and inject it into the suspension chamber, so that the liquid level of the solution reaches more than 4/5 of the overall height of the suspension chamber; For the sample, completely immerse the sample in the manganese chloride solution, and ensure that there are no air bubbles on the surface of the sample;

Step 2: Place the suspension cavity in the space between the two magnets (that is, in the magnetic field), so that the centerline of the suspension cavity and the vertical centerline of the two magnets coincide as much as possible to ensure that the system is stable for a certain period of time;

Step 3: If the sample can be suspended stably in the magnetic field, read its suspension height h through an external camera device; if the sample cannot be suspended stably, adjust the magnetic field strength according to the actual situation, and repeat step 2 until the sample can Stable suspension is reached, and the suspension height is read out; in this embodiment, the suspension height h=9.1mm of the sample is measured;

Step 4: Carry out numerical conversion of suspension height h, sample density ρ _s ;

Step 4.1: Determine the local acceleration of gravity g according to the actual situation;

Step 4.2: Calculate the density ρ _m and the magnetic susceptibility χ _m of the standard solution according to the molar concentration of the injected standard solution;

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1000</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}$

In the formula: c is the concentration of the solution, M is the relative molecular mass, and a is the mass percentage of the solute.

${\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 14350</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; cm</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mol</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}$

In the formula: ρ is the solution density, the unit is g/cm ³ ; M′ is the molar mass of the manganese chloride solution, the unit is g/mol.

Step 4.3: If the magnetic susceptibility of the substance to be measured or its calculation method is known, find out or calculate the exact value χ _s of the magnetic susceptibility of the substance to be measured; if the magnetic susceptibility of the substance to be measured cannot be determined, then approximately take χ _s =- 5×10 ^-6 , it has been proved by practice that the error between the density value calculated by this method and the real value is less than 5%, so it can be used for approximate calculation;

Step 4.4: Determine the magnetic induction intensity B ₀ on the surface of the magnet;

Step 4.5: Calculate the magnetic induction intensity distribution on the center line of the magnet;

For a cuboid-shaped permanent magnet, within the space range of 0-H, the magnetic induction intensity B _z on the central axis satisfies:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; ]</span>$

In the formula: B _r is the magnetic charge surface density of the permanent magnet; a and b are the length and width of the horizontal plane of the permanent magnet; L _m is the thickness of the permanent magnet; H is the distance between the two magnet surfaces; z is the distance from any point on the axis to the surface of the magnet below distance.

Step 4.6: Calculate the functional relationship between the suspension height h of the sample and the density ρ _s of the sample when the sample is balanced under the combined action of gravity, buoyancy and magnetic field force;

The relationship between the suspension height of the target particle and its density is expressed as:

$\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\frac{{\mathrm{<span\; class="notranslate">\; dB</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Under the premise of given basic parameters, formula (5) is solved as a function. The basic parameters include: vacuum magnetic permeability μ ₀ , molar concentration m of standard solution;

Step 4.7: Generate ρ-h (density-height) curve;

Step 4.8: Obtain the precise density value of the sample to be tested according to the suspension height of the sample;

In the case that the exact density value is not required, it is also possible to directly compare the readings on the ρ-h curve to achieve the calculation of the sample density ρ _s by measuring the suspension height.

The precise density value of the tested sample can be obtained by combining the formula (2) and formula (5) of the magnetic induction intensity on the axis. The calculated density of the sample is 1.175 g/cm ³ .

Step 5: Record the obtained sample density ρ _s , and the measurement ends.

The relative error between the measured value and the standard value is 0.42%, and the measurement accuracy is high, which can realize the measurement function and meet the measurement requirements.

Example 2

The magnetic field generating device of the device of this embodiment selects a cylindrical electromagnet with a diameter of 60 mm and a thickness of 60 mm. Because the electromagnet is selected, an external magnetic field strength regulator 23 is required, and other parts of the measuring device are the same as in Embodiment 1.

Manganese chloride solution with known density and magnetic susceptibility is used as paramagnetic medium and standard solution, its density is 1.27g/cm ³ and magnetic susceptibility is 1.45*10 ^-4 . Take silicon dioxide with a density of 2.230g/ ^cm3 as the substance to be tested.

Inject the selected manganese chloride solution as a paramagnetic medium into the suspension cavity, then place the sample particles in the paramagnetic medium (standard solution), and place the cavity between the two magnets, so that the electromagnet and the suspension cavity in the coaxial vertical direction.

The method for performing density measurement using the above-mentioned density measurement device based on magnetic levitation comprises the following steps:

Step 1: Take a manganese chloride solution with a concentration of 2.5mol/L and inject it into the suspension chamber, so that the liquid level of the solution reaches more than 4/5 of the overall height of the suspension chamber; take particles with a diameter of 0.2~3mm in the silica For the sample, immerse the sample completely in the manganese chloride solution, and ensure that there are no air bubbles on the surface of the sample;

Step 2: Place the suspension cavity in the space between the two magnets (that is, in the magnetic field), so that the centerline of the suspension cavity and the vertical centerline of the two magnets coincide as much as possible to ensure that the system is stable for a certain period of time;

Step 3: If the sample can be suspended stably in the magnetic field, read its suspension height h through an external camera device; if the sample cannot be suspended stably, adjust the magnetic field strength and the magnetic field regulator according to the actual situation so that the The surface magnetic induction intensity is 0.4T, repeat step 2 until the sample can reach a stable suspension, and read its suspension height; in this embodiment, the suspension height of the sample is h=38.0mm;

Step 4: Execute the ρ-h data conversion program to perform numerical conversion of the suspension height h and the sample density ρs;

Step 4.1: Determine the local acceleration of gravity g according to the actual situation;

Step 4.2: Calculate the density ρ _m and the magnetic susceptibility χ _m of the standard solution according to the molar concentration of the injected standard solution;

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1000</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}$

In the formula: c is the concentration of the solution, M is the relative molecular mass, and a is the mass percentage of the solute.

${\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 14350</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; cm</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mol</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}$

In the formula: ρ is the solution density, the unit is g/cm ³ ; M is the molar mass of the manganese chloride solution, the unit is g/mol.

Step 4.3: If the magnetic susceptibility of the substance to be measured or its calculation method is known, find out or calculate its exact value χ _s ; if the magnetic susceptibility of the substance to be measured cannot be determined, then approximately take χ _s =-5×10 ^{- 6.} It has been proved by practice that the error between the density value calculated by this method and the real value is less than 5%, so it can be used for approximate calculation;

Step 4.4: Determine the magnetic induction intensity B ₀ on the surface of the magnet;

Step 4.5: Calculate the magnetic induction intensity distribution on the center line of the magnet;

For a cuboid-shaped permanent magnet, within the space range of 0-H, the magnetic induction intensity B _z on the central axis satisfies:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}\frac{\mathrm{<span\; class="notranslate">\; ab</span>}}{\sqrt{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}}<span\; class="notranslate">\; ]</span>$

In the formula: B _r is the magnetic charge surface density of the permanent magnet; a and b are the length and width of the horizontal plane of the permanent magnet; L _m is the thickness of the permanent magnet; H is the distance between the two magnet surfaces; z is the distance from any point on the axis to the surface of the magnet below distance.

Step 4.6: Calculate the functional relationship between the suspension height h of the sample and the density ρ _s of the sample when the sample is balanced under the combined action of gravity, buoyancy and magnetic field force;

The relationship between the suspension height of the target particle and its density is expressed as:

$\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&chi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\frac{{\mathrm{<span\; class="notranslate">\; dB</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{\mathrm{<span\; class="notranslate">\; d\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Under the premise of given basic parameters, formula (5) is solved as a function. The basic parameters include: vacuum magnetic permeability μ ₀ , molar concentration m of standard solution;

Step 4.7: Generate ρ-h (density-height) curve;

Step 4.8: Obtain the precise density value of the tested sample according to the suspension height of the sample;

In the case that the exact density value is not required, it is also possible to directly compare the readings on the ρ-h curve to achieve the calculation of the sample density ρ _s by measuring the suspension height.

The precise density value of the tested sample can be obtained by combining the formula of magnetic induction on the axis and formula (5). The calculated density of the particle to be tested is 2.220 g/cm ³ .

Step 5: Record the obtained sample density ρ _s , and the measurement ends.

The relative error between the measured value and the standard value is 0.45%, and the measurement accuracy is high, meeting the measurement requirements.

Example 3

In this example, the density measurement device based on electromagnetic levitation is the same as that in Embodiment 2.

A manganese chloride solution with known density and magnetic susceptibility is used as a paramagnetic medium, ie a standard solution, with a density of 1.10g/cm ³ and a magnetic susceptibility of 1.25*10 ^-4 . Take polystyrene with a density of 1.050g/ ^cm3 as the particles to be tested.

The experimental conditions and experimental operation are the same as in Example 2, the current is adjusted so that the surface magnetic induction of the electromagnet is 0.4T, the suspension height of the particles to be tested is obtained by the scale scale as 8.0mm, and the density of the particles to be tested is calculated to be 1.045g/ cm ³ . The relative error between the measured value and the standard value is 0.48%, and the measurement accuracy is high, meeting the measurement requirements.

Example 4

In this example, the measuring device is the same as in Example 2, and the liquid density is measured.

A manganese chloride solution with known density and magnetic susceptibility is used as a paramagnetic medium, ie a standard solution, with a density of 1.10g/cm ³ and a magnetic susceptibility of 1.25*10 ^-4 . Take milk droplets with a density of 1.030g/ ^cm3 as the particles to be tested.

Inject the selected manganese chloride solution into the suspension chamber as a paramagnetic medium, and then use a dropper to drop the sample particles in the paramagnetic medium. The experimental conditions and experimental operations are the same as in Example 2, and the current is adjusted so that the surface of the electromagnet The magnetic induction intensity is 0.4T, the suspension height of the particles to be tested is 5.5mm obtained by the scale scale, and the density of the particles to be tested is 1.035g/cm ³ according to the calculation. The relative error between the measured value and the standard value is 0.49%, and the measurement accuracy is high, meeting the measurement requirements.

Claims (4)

1. the density measuring equipment based on electromagnetic suspension comprises the remote observation recording unit, it is characterized in that: also comprise suspension chamber and field generator for magnetic;

Said suspension chamber (4) is positioned in the field generator for magnetic;

Said suspension chamber (4) is the cylindrical measurement container, and suspension chamber (4) outside vertical direction is provided with graduated scale;

Said field generator for magnetic comprises first magnet (1), second magnet (12), first support (2) and second support (13); First magnet (1) is relative with second magnet (12) magnetic pole of the same name; Suspension chamber (4) places between two magnet; And be on the same vertical axis with two magnet, the both sides of first magnet (1) and second magnet (12) are fixedly connected with second support (13) with first support (2) through gib screw respectively;

Said remote observation recording unit comprises external picture pick-up device and computing machine (17); External picture pick-up device is connected to computing machine (17) through its output line.

2. the density measuring equipment based on electromagnetic suspension according to claim 1 is characterized in that: said first magnet (1) and second magnet (12) are selected electromagnet or permanent magnet for use;

If select electromagnet for use, then the electromagnet lead connects the magnetic field intensity regulator; The magnetic field intensity regulator comprises fixed shelves slide rheostat and direct supply, first magnet (1) connect with second magnet (12) parallel connection back grade slide rheostat and direct supply calmly.

3. the density measuring equipment based on electromagnetic suspension according to claim 1 is characterized in that: when said first magnet (1) and second magnet (12) were electromagnet, magnet surface magnetic induction density was not less than 0.8T; When said first magnet (1) and second magnet (12) were permanent magnet, magnet surface magnetic induction density was not less than 0.4T.

4. adopt that claim 1 is described carries out the method for density measure based on the density measuring equipment of electromagnetic suspension, it is characterized in that: comprise the steps:

Step 1: get certain density standard solution and inject the suspension chamber, make the liquid level of solution height reach more than 4/5 of suspension chamber overall height; The graininess sample of cut-off footpath between 0.2 ~ 3mm is immersed in sample in the standard solution fully, and guarantees that specimen surface does not have bubble in test substance;

Step 2: the suspension chamber is positioned in the space between two magnet, suspension chamber cavity center line is overlapped with two magnet vertical direction center lines as far as possible, guarantee the system stability certain hour;

Step 3:, then read its hoverheight h through external picture pick-up device if sample can reach stable suspersion in magnetic field; If sample can't stable suspersion, then according to actual conditions adjustment magnetic field intensity, repeating step 2 can reach stable suspersion until sample, reads its hoverheight h;

Adjust magnetic field intensity based on actual conditions:, then, realize magnetic field intensity is regulated through regulating the spacing of permanent magnet if select permanent magnet for use; If select electromagnet for use, then pass through the fixed shelves of an adjustment slide rheostat gear, realize the magnetic field intensity adjusting;

Step 4: carry out hoverheight h, sample density ρ _sNumerical value conversion, obtain sample density ρ _sConcrete steps are following:

Step 4.1: confirm local gravitational acceleration g;

Step 4.2: according to the density p of the volumetric molar concentration basis of calculation solution of the standard solution that injects _mWith magnetic susceptibility χ _m

Step 4.3: if test substance magnetic susceptibility exact value χ is then found or calculated to known test substance magnetic susceptibility or its computing method _sIf test substance magnetic susceptibility is not sure of, what then can be similar to gets χ _s=-5 * 10 ^-6

Step 4.4: confirm the magnet surface magnetic induction density B ₀

If what use is permanent magnet, then find the surface induction intensity B of its demarcation ₀If use electromagnet, rheostat resistance and gear when then reaching stable suspersion according to sample are confirmed the magnet surface magnetic induction density B ₀

Step 4.5: calculate magnetic induction density distribution on the magnet centerline;

Two identical magnet magnetic poles of the same name are relative, and spacing is H, then for the rectangular shape permanent magnet, and in 0～H spatial dimension, magnetic induction density B on its axis _zSize satisfies:

$B_z=\frac{B_r}{\mathrm{\&pi;}}[\arcsin \frac{\mathrm{ab}}{\sqrt{[a^2+{(H-z)}^2][b^2+{(H-z)}^2]}}-\arcsin \frac{\mathrm{ab}}{\sqrt{[a^2+{(H-z+L_m)}^2][b^2+{(H-z+L_m)}^2]}}---\left(2\right)$

$-\arcsin \frac{\mathrm{ab}}{\sqrt{(a^2+z^2)(b^2+z^2)}}+\arcsin \frac{\mathrm{ab}}{\sqrt{[a^2+{(z+L_m)}^2][b^2+{(z+L_m)}^2]}}]$

In the formula: B _rMagnetic charge surface density for magnet; A, b are permanent magnet surface level length, width; L _mBe magnet thickness; H is two magnet surface spacings; Z is any some distance of magnet surface to the below on the axis;

If use electromagnet, its space intrinsic inductance distributes similar with permanent magnet, can draw the B that concerns of its space magnetic induction density and hoverheight h equally _z:

$B_z=\frac{B_r}{2}(\frac{H-z+L_m}{\sqrt{{(H-z+L_m)}^2+R^2}}-\frac{H-z}{\sqrt{{(H-z)}^2+R^2}}-\frac{z+L_m}{\sqrt{{(z+L_m)}^2+R^2}}+\frac{z}{\sqrt{z^2+R^2}})---\left(3\right)$

In the formula: R is the electromagnet diameter;

Step 4.6: calculate sample when gravity, buoyancy, the action of a magnetic field power acting in conjunction lower stress balance, specimen suspension height h and sample density ρ _sFuntcional relationship;

Sample reaches the hoverheight h of balance and the relation of its density can be expressed as:

$\frac{({\mathrm{\&rho;}}_s-{\mathrm{\&rho;}}_m)g{\mathrm{\&mu;}}_0}{({\mathrm{\&chi;}}_s-{\mathrm{\&chi;}}_m)}=B_z\frac{{\mathrm{dB}}_z}{\mathrm{dh}}---\left(5\right)$

In the formula, χ _sBe the magnetic susceptibility of sample, μ ₀Be permeability of vacuum;

Step 4.7: generate density-altitude curve;

Step 4.8:, try to achieve the accurate density value of institute's test specimens according to the specimen suspension height;

Step 5: record gained sample density ρ _s, measure and finish.

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