Abstract: This paper comprehensively discusses the application of magnetic transmission technology in stirring devices. Through analysis and experiments on specific structures, the specific design methods and calculation formulas are obtained and verified. Keywords: Magnetic transmission, torque, magnetic circuit design Introduction Stirring devices are indispensable in chemical reactors, and stirring device technology is an important part of chemical engineering technology. Stirring technology involves multiple disciplines such as fluid mechanics, biochemistry, thermodynamics, and surface tension. In recent years, a large number of high-tech products from the polymer chemical industry, pharmaceutical industry, and especially the bioengineering industry have been put into production. The stirring and reaction of materials often take place under high temperature, high pressure, vacuum, flammable, explosive, and highly toxic conditions. This places new technical requirements on stirring equipment, prompting the design and research of stirring equipment to break through the technological boundaries. Magnetic transmission technology has therefore been increasingly widely used in stirring devices. 1 Working Principle and Device Form To ensure the stability of the reaction conditions, the stirring equipment must be shaft sealed. Mechanical seals and stuffing boxes are commonly used. Mechanical seals, in principle, still fall under the category of dynamic seals, and leakage is unavoidable. In chemical mixing production, leaks under certain special operating conditions can cause explosions, seriously endangering the safety of operators and equipment, and polluting the surrounding working environment. Magnetic drive technology is the only way to completely solve the sealing problem. Based on the structural principle of magnetic couplers, it transmits torque without contact. This is achieved by adding an isolation sleeve (also called a sealing sleeve) between the inner and outer magnetic rotors, completely isolating the medium inside the mixing vessel from the outside environment, thus obtaining an absolutely sealed magnetically driven stirred reactor. Magnetic drive technology is applied to mixing devices in three structures. 1.1 Top-entry magnetic stirring device: The traditional mixing device for reactors is a top-mounted vertical stirring system. Due to the current development of the chemical industry, more and more reactions are carried out under high temperature and high pressure conditions. Two structures are available depending on the temperature (see Figure 1); Type a has an internal bearing extending into the vessel, shortening the cantilever length of the stirring shaft for better support. Type b has an internal bearing with a bottom cooling structure, offering higher temperature resistance. 1.2 Bottom-Entry Magnetic Stirring Devices Most magnetic stirring devices currently use a top-stirring structure. The main problem with this type of device is that due to the excessively long cantilever of the stirring shaft, poor support performance, and unstable operation, varying degrees of oscillation occur during operation when working conditions change. This causes friction between the inner magnetic rotor and the inner wall of the isolation sleeve, thus shortening the service life of the equipment. In modern chemical engineering fields such as polymers and pesticides, the aforementioned transmission defects often lead to catastrophic failures. Therefore, many new technology engineering designs must adopt bottom-entry magnetic stirring devices to ensure safety. This device is particularly effective in operating conditions where materials are prone to precipitation during stirring or reaction. Bottom-entry magnetic stirring can be divided into two types of transmission: cylindrical and disc (see Figure 2). The cylindrical magnetic drive is radially coupled, with high magnet utilization and large space arrangement. Under the same magnetic parameters, it can obtain a larger transmitted torque, and is therefore widely used, especially for high-power magnetic torque. Disc-type magnetic drive is axially coupled, which simplifies the geometry of the magnets and the axial dimensions of the magnetic drive device. However, due to its low magnetic drive efficiency, it is only suitable for applications with small torque transmission. 1.3 Side-entry magnetic stirring device With the development of the chemical industry, technical equipment is becoming larger and more efficient. 500m3 reactors are common in China. The main problem is that the stirring efficiency in large-volume reactors is significantly reduced. The stirring efficiency does not simply follow the geometric amplification law. Using conventional top-entry or bottom-entry magnetic stirring devices results in unacceptable equipment costs, energy consumption, and load. Therefore, a side-entry magnetic stirring device is necessary for large containers. The stirrer is inserted at an appropriate depth of the medium in the large container, and multiple units are combined and directionally arranged to achieve the best reaction effect. This can be considered a high-efficiency stirring device. Side-entry magnetic drive devices (also known as magnetic drive side stirring) are also widely used in some special applications (see Figure 3). 2. Optimization Design of Magnetic Torque To ensure the smooth start-up and operation of the agitator under various working conditions, the inner and outer magnetic rotors must not slip and must possess sufficient magnetic torque margin. Therefore, a key issue in the application of magnetically driven agitators is the design and calculation of the magnetic circuit. According to relevant literature, there are many methods for calculating magnetic torque. Domestic researchers dedicated to magnetic transmission have successively introduced methods for high-precision calculations, such as the two-dimensional static magnetic field finite element method (FEM), two-dimensional (2D) and three-dimensional (3D) cylindrical air gap and tile-shaped magnet radial magnetization coupling analysis methods, and the equivalent magnetic charge method (i.e., magnetic charge integration method). These methods have provided valuable research results for the design of permanent magnet couplings. However, due to the complexity of the magnetic field distribution, and the need to treat the permanent magnet as a boundary current model using electromagnetic field analysis, extensive mathematical and electromagnetic derivations are required, making calculations time-consuming. Engineering applications prioritize the mechanical behavior of the calculations, seeking simple, practical, and accurate calculation procedures. This paper mainly focuses on the design of the most widely used cylindrical magnetic coupler. 2.1 Mechanical Characteristics For practical purposes, considering both technical and economic factors, we evaluate the design of magnetic couplers using the following three different indicators: (1) maximum torque per unit magnetic volume; (2) maximum torque given a total coupler volume; (3) minimum price for a given torque. Only designs that simultaneously consider the above conditions are optimal designs. The cylindrical magnetic drive device (see Figure 4) typically consists of n radially magnetized, oppositely magnetized tile-shaped magnets (n = number of poles). In the driving (outer magnet) and driven (inner magnet) cylindrical magnets, n/2 N poles and n/2 s poles are arranged in an even number alternating pattern along the circumference of the surface. The magnitude of its torque depends on the position angle Ψ of the outer magnet relative to the inner magnet (see Figure 5), which may have the following possibilities: Ψ = 0: opposite polarity magnetic poles face each other. π/n), the torque decreases, and the coupling is unstable within this range, i.e., slippage occurs. 2π/n: the inner and outer magnets of the coupler repel each other. It can be considered that the functional relationship between the displacement angle and the torque π/n changes sinusoidally (see Figure 6). The maximum magnetic torque is reached when the displacement angle Ψ = π/n. The above-mentioned static characteristics of magnetic transmission should be fully considered in practical applications, especially in stirring reactions where synchronous rotation is strictly required. The tile-shaped magnets are arranged in even numbers along the circumferential direction with different polarities and fixed on a low-carbon steel ring to form a magnetic circuit connection. The outside is surrounded by a non-ferromagnetic material to create magnetic shielding. Due to the mutual attraction between the front faces of each pair of magnetic poles of the inner and outer magnets and the mutual repulsion between adjacent opposite pole faces, it can be seen that the torque is the largest when the driven magnetic pole is located in the middle position between two adjacent magnetic poles (i.e., = π/n) (see Figure 6). The magnetic circuit formed by this magnetic pole arrangement is usually called an attraction-repulsion (or push-pull) magnetic circuit. Thus, the inner magnet is subjected to the combined action of attraction (F) and repulsion (F2), which are additive in the direction of rotation (F=F1+F2), which increases the torque transmitted to the driven magnetic pole due to the reaction effect of adjacent opposite magnetic poles, which is very beneficial to prevent slippage (see Figure 7). 2.2 Magnetic circuit design Figure 7 Dynamic analysis of the driven magnetic pole The permanent magnet, working air gap and magnetic conductor constitute the permanent magnet magnetic circuit. Here it refers to the magnetic circuit constructed using permanent magnets. The task of magnetic circuit design is, in addition to enabling the permanent magnet to provide the required magnetic field within a certain air gap, to also enable the magnetic transmission device to have the smallest size, lightest weight, lowest cost and high magnetic stability. (1) Selection of magnetic materials The magnetic materials used to transmit torque not only need high magnetic induction intensity (Br), but also high coercivity (Hc) and magnetic energy product (BH)max. Magnetic materials that meet these requirements include ferrite magnets and rare earth magnets. Neodymium iron boron (Nd-Fe-B), which was introduced in 1983 and is known as the third generation of rare earth permanent magnets, has the best magnetic energy product. Samarium cobalt alloy, a rare earth type of magnet, is expensive due to its low temperature coefficient (a[sub]t[/sub]=-0.03%/℃), but it is also the first choice under high temperature (>150℃) stirring conditions. Nd-Fe-B magnetic materials have excellent magnetic properties and low price. They can obtain satisfactory magnetic torque for cylindrical combined magnetic circuit structures. These permanent magnet couplers have unique advantages such as small size, light weight, high power and high efficiency, and are therefore widely used in magnetic stirring reactors. (2) Working air gap and ideal number of poles Usually, the absolute air gap geometry (R3-R2) or the relative air gap geometry (r=R2/R3) of a magnetic coupler is given (see Figure 8). To find the optimal size of the coupler, parameters R1 and R4 and the number of magnetic poles n are often changed, and the number of magnet poles will greatly affect the transmission efficiency of the magnetic circuit. Figure 8 shows the ideal number of poles n for different values ​​of r (relative air gap). It can be seen that the ideal number of poles increases sharply with increasing r (i.e., decreasing the air gap). Since the number of poles can only be even, the curve consists of isolated points. Figure 8 shows the possible distribution width of the ideal number of poles. Because Ψ = л/n, the maximum allowable torsional angle of the coupler can be obtained from the ideal number of poles n. Related research also indicates that once the magnetic circuit dimensions are determined, the ideal number of poles can also be determined through calculation. In the formula, Kj is the polarity coefficient, and when = 4, it is the optimal number of poles. D3 is the inner diameter of the outer magnet, and Lg is the air gap. In some cases, considering the increase in magnetic torque, a higher number of poles may be better. Considering the demagnetizing effect of the air gap, the air gap should be designed to be as small as possible within permissible limits. The reasonable number of magnet poles and the size of the air gap can only be determined through magnetic circuit calculations. 3. Magnetic Torque Calculation The purpose of magnetic circuit calculation is to accurately calculate the magnitude of the magnetic torque to match the stirring power. Based on years of practical experience in the design, calculation, experimentation, and application of magnetic couplings, our magnetic torque calculation method has certain application value in engineering. This calculation method differs from some previous methods in that it does not require the addition of correction coefficients during the calculation process. Instead, it directly uses the formula to calculate the value of the magnetic flux density (Br), a key characteristic of magnetic materials, based on different magnetic circuit parameters. 3.1 Calculation of the Static Magnetic Field of the Magnetic Coupler A cylindrical magnetic coupler consists of two magnetic rings, each composed of n tile-shaped magnets with alternating N and S poles. Therefore, the magnetic flux density at the center of the air gap is the superposition of the magnetic flux densities generated by the inner and outer magnets. The magnetic induction intensity of the inner magnet in the air gap is 3.2 The maximum magnetic torque is calculated as follows: As mentioned above, the function relationship between magnetic torque and magnet displacement angle ( ) is sinusoidal, and T[sub]max[/sub]=T(Ψ=л／n). Practice has shown that when the displacement angle is equal to Ψ, the torque generated in the attraction-repulsion magnetic circuit is the largest. According to the relationship between magnetic torque and static magnetic field, the expression of magnetic torque is: In the magnetic stirring device, the inner and outer magnets are often combined with different magnetic materials to obtain the most economical and ideal effect. At this time, in order to calculate the magnetic torque more accurately, equation (3) needs to be decomposed. Magnetic torque generated by inner magnet and magnetic torque generated by outer magnet We use equation (4) and equation (5) to calculate the magnetic torque of the MTC series magnetic drive stirring device and compare it with the measured value (see Table 1). It can be seen that its calculation accuracy is feasible in engineering applications. 3.3 Magnetic Torque and Temperature As temperature increases, the magnetic torque decreases due to the decrease in magnetic induction intensity. Neodymium iron boron magnets are quite sensitive to temperature changes, with a magnetic temperature coefficient (αt) of approximately -0.14%/℃. In calculations, it can be assumed that when the temperature is t℃, the maximum operating temperature of the stirring vessel must be considered. The magnitude of the magnetic torque at this temperature is calculated as the basis for magnetic circuit design, ensuring the reliable operation of the magnetic coupler. 4 Conclusion Through theoretical exploration and experimental research, we introduced the tedious calculation of varying parameters into computer-programmed design. Magnetic circuit parameters are input according to design requirements, compared, and the optimal values ​​are printed out, thus avoiding a large amount of unnecessary repetitive calculations. Finally, the accuracy of the calculated values ​​is checked on a torque tester, providing a reliable basis for the next input of magnetic circuit parameters. References: 1. Guan Xingfan, ed., Modern Pump Technology Handbook, Beijing: Aerospace Press, 1995. 2. [Japan] Makino Noboru, Magnet Design and Application, Beijing: Machinery Industry Press, 1982. 3. Zhao Kezhong, ed., Magnetic Drive Technology and Equipment, Beijing: Chemical Industry Press, 2004.