A method and system for balancing the air jet speed of a spinning machine based on an elliptical eccentric air chamber

Abstract

The present application relates to the technical field of air jet speed balancing of spinning machines, and particularly relates to a spinning machine air jet speed balancing method and system based on an elliptical eccentric air chamber, which comprises the following steps: changing the second air chamber in the double air chamber into an elliptical air chamber, and offsetting it to the direction of the supply pipe by setting a centrifugal distance; calculating the gas mass flow at the inlet of the supply pipe, and then solving the pressure distribution of the first air chamber; mapping the ellipse to a circular domain and calculating the gauge coefficient, and obtaining the pressure distribution of the elliptical air chamber in combination with the pressure distribution of the first air chamber; establishing a jet flow speed calculation model of the air jet hole, and calculating the air jet speed of the spinning machine in combination with the pressure distribution of the elliptical air chamber; and solving the optimal elliptical semi-minor axis and centrifugal distance with the target of minimizing the air jet hole speed variance, and adjusting the shape and position of the elliptical air chamber. The present application reduces the pressure difference at the positions of the air jet holes by the design of the ellipse plus eccentricity, so as to balance the flow, reduce the air jet hole speed difference, and meet the production demand of high-quality spinning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of air jet speed balancing of spinning machines, in particular to a spinning machine air jet speed balancing method and system based on an elliptical eccentric air chamber. BACKGROUND

[0002] During the operation of a spinning machine, the air chamber, as the core component of compressed air supply and regulation, plays a crucial role. It provides stable air flow power for the spinning process, accurately controls air flow parameters such as speed, direction and intensity, and thus realizes precise regulation of key operations such as fiber transportation, condensation and twisting. Stable and uniform air flow distribution is crucial to ensure yarn quality, reducing yarn quality fluctuations and improving production efficiency and yield. Therefore, designing a reasonable and efficient air chamber structure to meet the strict requirements of the spinning machine for air flow has become a key problem in the spinning technology field that needs to be solved.

[0003] Currently, some spinning machines on the market use a single air chamber design. This design structure is relatively simple, has the advantages of compact size and fewer components, thus reducing processing and assembly costs. However, the single air chamber design has a fatal flaw. Since its only air chamber is directly connected to the main supply pipe, when the supply pipe is jetted, it will cause uneven distribution of inlet pressure. This uneven pressure distribution further causes differences in air flow speed at the outlet of each air chamber. In the spinning process, the inconsistency of air flow speed can seriously affect the transportation and condensation effect of fibers, leading to decreased yarn quality, uneven thickness, unstable strength and other problems, which cannot meet the production needs of high-quality spinning.

[0004] In order to improve the problems of single air chamber, double air chamber design emerged. The double air chamber, due to the introduction of a second air chamber, improves the pressure balance to some extent. The influence of nozzle throttling effect on the pressure of the second air chamber is small, making the overall pressure distribution more uniform than that of the single air chamber. However, the double air chamber design still has an insurmountable defect. It uses a design with only one air flow main supply pipe, resulting in asymmetric air supply. This air supply asymmetry always causes speed differences in the group of air jets opposite to the direction of the supply pipe, which in turn adversely affects the spinning quality. SUMMARY

[0005] In view of the defects in the prior art, the present application provides a spinning machine air jet speed balancing method and system based on an elliptical eccentric air chamber.

[0006] In order to achieve the above object, the first aspect of the present application provides an elliptical eccentric air chamber based spinning machine air jet speed balancing method, the method comprising the following steps: on the basis of a double air chamber design, changing the second air chamber into an elliptical air chamber, and offsetting the elliptical air chamber to the air chamber supply pipe direction by setting a centrifugal distance; calculating the gas mass flow at the air chamber supply pipe inlet, and then solving the pressure distribution of the first air chamber in the cylindrical coordinate system; mapping the ellipse to the circular domain through the elliptical coordinate system transformation and calculating the metric coefficient, and then obtaining the pressure distribution characteristics in the elliptical coordinate system by solving the Laplace equation in the elliptical coordinate; obtaining the pressure distribution of the elliptical air chamber according to the pressure distribution characteristics and the pressure distribution of the first air chamber; establishing a jet flow speed calculation model of the air jet hole, and then calculating the spinning machine air jet speed in combination with the pressure distribution of the elliptical air chamber; setting the optimization objective function to minimize the gas speed variance of all air jet holes, and then solving the optimal elliptical half minor axis and the optimal centrifugal distance based on the Lagrange function method; adjusting the shape and position of the elliptical air chamber according to the optimal elliptical half minor axis and the optimal centrifugal distance. Through the design of the ellipse plus eccentricity, the present application can reduce the pressure difference of each air jet hole position, thereby balancing the flow and reducing the speed difference of the air jet hole, and meeting the production demand of high-quality spinning.

[0007] Optionally, the calculation of the gas mass flow at the air chamber supply pipe inlet and the solving of the pressure distribution of the first air chamber in the cylindrical coordinate system comprises the following steps:

[0008] The gas mass flow at the air chamber supply pipe inlet is calculated.

[0009] The Mach number at the air chamber supply pipe inlet is solved based on the gas mass flow and the flow of the outer boundary of the first air chamber.

[0010] After the Mach number is obtained, the control equation of the fluid in the first air chamber is obtained in the cylindrical coordinate system, and then the radial momentum equation is used to gradually solve the pressure distribution of the first air chamber.

[0011] Optionally, the gas mass flow satisfies the following relationship:

[0012]

[0013] wherein, the gas mass flow is, the cross-sectional area of the air chamber supply pipe is, the stagnation pressure is, the specific heat capacity of air is, and R is the gas constant, the stagnation temperature is, the atmospheric pressure is.

[0014] Optionally, the pressure distribution of the first air chamber satisfies the following relationship:

[0015]

[0016] in, The local pressure at a radial distance r in cylindrical coordinates. To stop the pressure, The specific heat capacity of air, The radius of the air supply pipe to the air chamber. Let be the Mach number.

[0017] Optionally, the metric coefficients satisfy the following relationship:

[0018]

[0019] in, The metric coefficient is the coefficient of the metric. Let x be the x-coordinate of the circular region. The ordinate of the circular region. Radial elliptical coordinates, It is the semi-major axis of the ellipse. Let be the semi-minor axis of the ellipse. The coordinates are angular elliptical coordinates.

[0020] Optionally, the pressure distribution in the elliptical air chamber satisfies the following relationship:

[0021]

[0022] in, Radial elliptic coordinates Local pressure at the location, This refers to the local pressure at the outlet of the first air chamber. This refers to the local pressure at the jet nozzle location. The radial elliptical coordinates of the jet hole position are: The coordinates are the radial elliptical coordinates of the elliptical boundary.

[0023] Optionally, the jet velocity calculation model for the jet orifice satisfies the following relationship:

[0024]

[0025] in, Let K be the fluid velocity at the jet orifice k. The specific heat capacity of air, This represents the local pressure at the jet orifice k. , Let K be the radial elliptical coordinates at the jet hole. Let K be the fluid density at the jet orifice k. Atmospheric pressure.

[0026] Optionally, the optimal centrifugation distance satisfies the following relationship:

[0027]

[0028] wherein e is the optimal eccentric distance, is an empirical coefficient, is the diameter of the airflow passage between the first air chamber and the elliptical air chamber, is the diameter of the air injection hole, is the maximum diameter of the annular block where the air injection hole is located, is the minimum diameter of the annular block where the air injection hole is located, is the diameter of the air chamber shell, m is the diameter of the air chamber supply pipe, is the stagnation pressure, is the specific heat capacity of air, is the atmospheric pressure.

[0029] Optionally, the optimal elliptical semi-minor axis satisfies the following relationship:

[0030]

[0031] wherein b is the optimal elliptical semi-minor axis, is an empirical coefficient, is the elliptical semi-major axis, is the diameter of the airflow passage between the first air chamber and the elliptical air chamber, is the diameter of the air injection hole, is the maximum diameter of the annular block where the air injection hole is located, is the minimum diameter of the annular block where the air injection hole is located, is the stagnation pressure, is the specific heat capacity of air, is the atmospheric pressure.

[0032] In a second aspect, the present application provides an elliptical eccentric air chamber based spinning machine air injection speed balancing system, which comprises a data acquisition device, a data output device, a processor and a storage, the storage comprises a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program comprises program instructions, the program instructions enable the processor to implement an elliptical eccentric air chamber based spinning machine air injection speed balancing method provided by the present application when executed by the processor.

[0033] The present application has at least the following beneficial effects:

[0034] 1. The present application introduces an asymmetric eccentric air chamber to change the structure of the left and right cavities, thereby balancing the flow. This irregular structure can control the flow with large deviations.

[0035] 2、The method compensates for the speed difference of the near-end and far-end entrances by changing the second air chamber into an elliptical air chamber, balances the fluid speed of the air jet hole, and meets the production demand of high-quality spinning.

[0036] 3、A system suitable for the method is provided, which can improve the practicability of the method and facilitate the popularization of the method. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0038] Figure 1 A flowchart of a spinning machine air jet speed balancing method based on an elliptical eccentric air chamber according to an embodiment of the present application;

[0039] Figure 2 A structural diagram of an elliptical eccentric air chamber according to an embodiment of the present application;

[0040] Figure 3 A mathematical model of an elliptical eccentric air chamber according to an embodiment of the present application;

[0041] Figure 4 An Ansys Fluent air chamber fluid domain diagram of an elliptical eccentric air chamber according to an embodiment of the present application;

[0042] Figure 5 Analysis results of the inlet speed cross section of an air jet hole 1 according to an embodiment of the present application;

[0043] Figure 6 Analysis results of the inlet speed cross section of an air jet hole 2 according to an embodiment of the present application;

[0044] Figure 7 Analysis results of the inlet speed cross section of an air jet hole 3 according to an embodiment of the present application;

[0045] Figure 8 Analysis results of the inlet speed cross section of an air jet hole 4 according to an embodiment of the present application;

[0046] Figure 9 An XY cross section of an elliptical eccentric air chamber according to an embodiment of the present application;

[0047] Figure 10 X-direction speed on the core airflow conveying plane according to an embodiment of the present application;

[0048] Figure 11Y-direction velocity on the core airflow conveying plane of the embodiment of the present application;

[0049] Figure 12 Z-direction velocity on the core airflow conveying plane of the embodiment of the present application;

[0050] Figure 13 X-direction velocity of the airflow outlet of the vortex tube of the embodiment of the present application;

[0051] Figure 14 Y-direction velocity of the airflow outlet of the vortex tube of the embodiment of the present application;

[0052] Figure 15 Z-direction velocity of the airflow outlet of the vortex tube of the embodiment of the present application;

[0053] Figure 16 A frame schematic diagram of a spinning machine air jet velocity balancing system based on an elliptical eccentric air chamber according to an embodiment of the present application. DETAILED DESCRIPTION

[0054] The specific embodiments of the present application will be described in detail below, it should be noted that the embodiments described herein are only used for illustration and do not limit the present application. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present application. However, it is obvious to those skilled in the art that the specific details need not be used to practice the present application. In other instances, well-known circuits, software or methods have not been specifically described in order to avoid obscuring the present application.

[0055] Throughout the specification, the reference to "one embodiment", "an embodiment", "one example" or "an example" means that a particular feature, structure or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present application. Therefore, the phrases "in one embodiment", "in an embodiment", "one example" or "an example" appearing throughout the specification do not necessarily all refer to the same embodiment or example. In addition, specific features, structures or characteristics can be combined in any appropriate combination and / or subcombination in one or more embodiments or examples. In addition, those skilled in the art should understand that the diagrams provided herein are for illustrative purposes only and the diagrams are not necessarily drawn to scale.

[0056] It should be noted in advance that in an alternative embodiment, in addition to making independent descriptions, the same symbols or letters appearing in all formulas have the same meaning and value.

[0057] In an alternative embodiment, please refer to Figure 1 The present application provides a spinning machine air jet velocity balancing method based on an elliptical eccentric air chamber, the method comprising the following steps:

[0058] S1, on the basis of the double-chamber design, the second chamber is changed to an oval chamber, and the oval chamber is offset to the gas chamber supply pipe direction by setting the centrifugal distance.

[0059] Specifically, in the present embodiment, please refer to Figure 2 , the double-chamber design of the spinning machine is retained, and the second chamber is changed from a ring-shaped chamber to an oval chamber. Among them, Q1 is the first chamber, Q2 is the oval chamber (second chamber), 1, 2, 3, 4 are the numbers of the four air injection holes.

[0060] Further, please refer to Figure 3 , Figure 3 The mathematical representation of the chamber size of the spinning machine in the present embodiment is given. Among them, m is the diameter of the gas chamber supply pipe, and the gas enters the spinning machine chamber from the pipe; is the half long axis of the oval chamber; b is the half short axis of the oval chamber; is the diameter of the air flow channel between the first chamber and the oval chamber; is the diameter of the air injection hole; is the minimum diameter of the first chamber; is the outer diameter of the nozzle block; is the inner diameter of the nozzle block; is the chamber shell diameter (the maximum diameter of the first chamber); e is the centrifugal distance, that is, the distance between the center of the oval chamber and the center of the first chamber, which is also the distance by which the oval chamber is offset to the gas chamber supply pipe direction. By setting e, the "eccentric" design is realized, but before the optimal centrifugal distance is obtained, the value of e is uncertain.

[0061] The present embodiment balances the flow by introducing an asymmetric eccentric design. The eccentricity changes the structure of the left and right cavities of the chamber, so that the inlet air pressure of air injection holes 1 and 4 is reduced, and the inlet air pressure of air injection holes 2 and 3 is increased, thereby balancing the flow. This irregular structure can restrict the flow deviation between the air injection holes. The second chamber is changed to an oval chamber. Because of the existence of the half long axis of the oval chamber, the gas flow trajectory into air injection hole 1 is lengthened, and relatively, the gas flow trajectory into air injection hole 3 is shortened due to the influence of eccentricity (offset of the second chamber). This structure design suppresses the high speed of air injection hole 1 and balances the fluid speed of air injection holes 2, 3 and 4. Subsequent steps will optimize the design of "oval" + "eccentric" by finding the optimal oval half short axis and centrifugal distance, to maximize the balance of the fluid speed of each air injection hole.

[0062] S2, calculate the gas mass flow at the inlet of the gas chamber supply pipe, and then solve the pressure distribution of the first chamber in the cylindrical coordinate system.

[0063] Among them, step S2 specifically includes the following steps:

[0064] S21. Calculate the mass flow rate of the gas at the inlet of the gas chamber supply pipe.

[0065] Specifically, in this embodiment, mass flow rate The defining formula is:

[0066]

[0067] In this relation, For fluid density, V represents the cross-sectional area of ​​the pipe, and V represents the fluid velocity. In this embodiment, the fluid is air.

[0068] For compressible fluids, their density and velocity vary with pressure; therefore, we need to start with the energy equation and obtain the stagnation enthalpy through the energy conservation condition. Equal to static enthalpy Plus kinetic energy ,Right now:

[0069]

[0070] For an ideal gas, enthalpy h is linearly related to temperature, that is:

[0071]

[0072] In this relation, is the specific heat capacity at constant pressure, and T is the temperature.

[0073] Therefore, we can conclude that:

[0074]

[0075] In this relation, Stagnation temperature, which is the temperature at which a fluid decelerates to zero velocity.

[0076] The further expression for the fluid velocity V can be obtained as follows:

[0077]

[0078] For isentropic processes, the pressure ratio is related to the temperature ratio, that is:

[0079]

[0080] In this relation, The stagnation pressure is the pressure at which the fluid decelerates to zero velocity, and is referred to as the supply pressure in the following text; P is the static pressure, which will be the outlet pressure later. The specific heat capacity of air, Substituting this relationship into the expression for the fluid velocity V, we get:

[0081]

[0082] Using the thermodynamic relation , the final expression for the fluid velocity V is obtained by substituting the previous relation into the equation:

[0083]

[0084] where R is the gas constant. This relation is known as the St. Venant-Weisbach equation, which describes the isentropic expansion of a compressible fluid through a jet.

[0085] Further, the density also varies with pressure, from the isentropic relation The expression for the density is obtained by substituting the previous relation into the equation:

[0086]

[0087] In this relation, is the stagnation density, .

[0088] Substituting the expressions for the fluid velocity V and the density into the mass flow equation, we obtain:

[0089]

[0090] After simplifying this relation, we obtain the general form of the isentropic mass flow equation:

[0091]

[0092] At the inlet of the air chamber supply pipe of the air jet spinning structure, is the supply pressure, ; is the exit pressure, which is the pressure of the first air chamber or the atmospheric pressure. In the spinning process, the exit pressure is basically atmospheric pressure , so substitute . The cross-sectional area of the air chamber supply pipe . Therefore, the mass flow of the gas at the inlet of the air chamber supply pipe is:

[0093]

[0094] In this relation, is the mass flow of the gas.

[0095] S23, based on the mass flow of the gas and the flow rate of the outer boundary of the first air chamber, solving the Mach number at the inlet of the air chamber supply pipe.

[0096] Specifically, in the present embodiment, the Mach number defined as the fluid velocity at the inlet of the plenum supply pipe to the speed of sound , so the mass flow rate of the gas at the inlet of the plenum supply pipe satisfies:

[0097]

[0098] The mass flow rate of the gas passing through the outlet of the first plenum is:

[0099]

[0100] In this relationship, is the mass flow rate of the gas passing through the outlet of the first plenum, is the cross-sectional area of the gas flow passage between the first plenum and the elliptical plenum, is the fluid velocity at the outlet of the first plenum.

[0101] Since , it is solved that:

[0102]

[0103] S24, after obtaining the Mach number, the control equation of the fluid in the first plenum is obtained in the cylindrical coordinate system, and then the radial momentum equation is used to gradually solve the pressure distribution of the first plenum.

[0104] Specifically, in the present embodiment, the first plenum is a ring-shaped circular cavity, the maximum radius of which is , and the minimum radius is . After the gas flow enters the first plenum from the inlet of the plenum supply pipe, it diffuses radially. In the ring-shaped area of the first plenum, the cylindrical coordinate system is used, r is the radial distance, is the azimuth angle, and z is the height, then the continuity equation describing the conservation of fluid mass is:

[0105]

[0106] In this relationship, is the fluid velocity at the radial distance r, is the fluid velocity at the azimuth angle , and is the fluid velocity at the height z. Since the first plenum is axisymmetric in shape, all (axisymmetric flow assumption), and the vertical velocity component (mainly radial flow feature), so the continuity equation can be simplified as:

[0107]

[0108] This equation shows that In the radial direction, the constant of mass conservation (which physically means that the mass flow rate is conserved through any cylindrical surface), the integral is:

[0109]

[0110] In this relationship, is a constant determined by the inlet conditions, representing the radial mass flow rate.

[0111] Based on the above analysis, the radial momentum equation is used to gradually solve the pressure distribution of the first gas chamber in this embodiment. The radial momentum equation describes the balance between pressure gradient and convective acceleration, which is the application of Newton's second law on the fluid element. The left side is the inertial force, and the right side is the pressure gradient force, that is:

[0112]

[0113] Combined with the isentropic relationship (const is a constant) and the radial momentum equation, we can get:

[0114]

[0115] Integrating this relationship gives the energy conservation equation, which is the compressible form of the Bernoulli equation, representing the conversion relationship between kinetic energy and pressure energy, that is:

[0116]

[0117] Calculating the integral in this equation gives:

[0118]

[0119] Therefore:

[0120]

[0121] In this relationship, is the integral constant. The integral constant is determined by the boundary conditions: at the inlet of the gas chamber supply pipe, the radial distance , the pressure , the fluid velocity , substitute this relationship into , and the energy equation is obtained:

[0122]

[0123] In this relationship, is actually equal to , which embodies the energy conservation.

[0124] Combined with the continuity equation At the inlet of the plenum supply pipe, Meanwhile, where the sound speed Using the isentropic relation, the density can be expressed as Substituting these relations into the continuity equation gives

[0125]

[0126] Simplifying this relation gives

[0127]

[0128] Substituting this expression into the energy equation gives

[0129]

[0130] After rearranging this relation, the equation for P is obtained as

[0131]

[0132] It can be found that and from the ideal gas state equation Thus:

[0133]

[0134] Substituting this relation into the equation for P gives

[0135]

[0136] Simplifying the coefficients gives the expression for the pressure ratio as

[0137]

[0138] Through algebraic manipulation, the pressure distribution in the first plenum is finally obtained as

[0139]

[0140] This pressure distribution formula shows that the local pressure gradually decreases with increasing radial distance, and the rate of decrease depends on the Mach number and the geometric size ratio. Combined with the calculation relation of the Mach number in step S23, the local pressure at different positions in the first plenum can be calculated.

[0141] S3, mapping the ellipse to a circular domain through an elliptical coordinate system transformation and calculating the metric coefficients, and then obtaining the pressure distribution characteristics in the elliptical coordinate system by solving the Laplace equation in the elliptical coordinates.

[0142] Specifically, in the embodiment, the elliptical chamber is an elliptical cavity, and the eccentric distance is e, so the elliptical equation is:

[0143]

[0144] In the elliptical equation, is the coordinate on the ellipse.

[0145] For the eccentric elliptical chamber, an elliptical coordinate system transformation needs to be introduced to obtain the optimal eccentric distance and elliptical half minor axis subsequently. Specifically, the ellipse is mapped to a circular domain through a conformal transformation, that is:

[0146]

[0147] In this relationship, z is a complex number, is the radial elliptical coordinate, , is the angular elliptical coordinate, , and i is the imaginary unit. Through this relationship, the circular domain coordinates can be solved:

[0148]

[0149] In this relationship, is the horizontal coordinate of the circular domain, is the vertical coordinate of the circular domain.

[0150] After obtaining the circular domain coordinates, the embodiment introduces a metric coefficient, which determines the scale factor of the coordinate transformation. It reflects the relationship between the actual distance and the coordinate increment, and the metric coefficient satisfies:

[0151]

[0152] The metric coefficient represents the local stretching property of the coordinate system. When is larger, the physical distance corresponding to the unit coordinate increment is larger, which is crucial for subsequent processing of the expression of the differential operator.

[0153] Further, in the embodiment, the pressure distribution characteristics in the elliptical coordinate system are obtained by solving the Laplace equation under the elliptical coordinates. In the elliptical region occupied by the elliptical chamber, the Laplace equation is:

[0154]

[0155] In the elliptical coordinate system, the Laplace equation becomes:

[0156]

[0157] Its general solution is:

[0158]

[0159] In this relationship, A, B, and C are integration constants, which need to be determined through boundary conditions.

[0160] Considering the symmetry of the elliptical chamber structure and the airflow distribution characteristics, the pressure distribution mainly varies radially. This symmetry causes P to... Regardless, this simplification reduces the Laplace equation in elliptical coordinates to an ordinary differential equation, thus yielding the pressure distribution characteristics in elliptical coordinates as follows:

[0161]

[0162] The mathematical relationship implied by the solution of this linear distribution is that, in an elliptical coordinate system, pressure varies with... The coordinates change linearly.

[0163] S4. Based on the pressure distribution characteristics, and in conjunction with the pressure distribution of the first air chamber, obtain the pressure distribution of the elliptical air chamber.

[0164] Specifically, in this embodiment, at the elliptical boundary Pressure satisfy:

[0165]

[0166] At the jet hole location Pressure satisfy:

[0167]

[0168] Combining equations 1 and 2, and taking into account the pressure distribution characteristics obtained in step S3, the pressure distribution in the elliptical air chamber satisfies the following relationship:

[0169]

[0170] In this relation, Radial elliptic coordinates Local pressure at the location, The radial elliptical coordinates of the jet hole position are... Let be the radial elliptical coordinates of the elliptical boundary. This formula shows that the pressure varies uniformly in the elliptical coordinate system, and its gradient is determined by the boundary pressure difference and the coordinate distance.

[0171] Furthermore, based on the pressure distribution relationship within the elliptical air chamber, the local pressure at each jet orifice of the elliptical air chamber is obtained as follows:

[0172]

[0173] In this relationship, is the local pressure at the jet hole k in the elliptical air chamber, is the radial elliptical coordinate at the jet hole k.

[0174] S5, a jet hole jet velocity calculation model is established, and then the spinning machine jet velocity is calculated in combination with the pressure distribution of the elliptical air chamber.

[0175] Specifically, in the present embodiment, referring to the manner of obtaining the fluid velocity V in step S21, the jet hole jet velocity calculation model can be constructed as:

[0176]

[0177] In this relationship, is the fluid velocity at the jet hole k, is the local pressure at the jet hole k, is the fluid density at the jet hole k. The local pressure at the jet hole k can be calculated according to the pressure distribution calculation relationship of the elliptical air chamber obtained in step S4.

[0178] It is easy to know that due to the elliptical eccentric design, the pressure at the four jet holes is not the same, but in a strict sense, it is still different, which will cause the fluid velocity at each jet hole to be slightly different.

[0179] S6, set the optimization objective function to minimize the gas velocity variance of all jet holes, and then solve the best elliptical half minor axis and the best eccentric distance based on the Lagrange function method.

[0180] Specifically, in the present embodiment, the optimization objective function is set to minimize the gas velocity variance of all jet holes, that is:

[0181]

[0182] In this relationship, is the optimization objective function, related to e and b; is the average fluid velocity, . The optimization objective function needs to be minimized.

[0183] Let , then the optimization problem is:

[0184]

[0185] The Lagrange multiplier method is used to construct geometric constraints:

[0186]

[0187] In this relationship, L represents the Lagrange function, and is the Lagrange multiplier, is the minimum of e, is the minimum of b.

[0188] 1. Take the partial derivative .

[0189] Since the constraint term is linear, its partial derivative is . Thus, can be written as:

[0190]

[0191] The optimization objective function depends on e, so the chain rule must be applied:

[0192]

[0193] is determined by , and depends on the parameter e, so we have:

[0194]

[0195] Substitute this relationship into the calculation relationship of , we have:

[0196]

[0197] Finally, we have:

[0198]

[0199] Further, calculate in this relationship. Given by the isentropic expansion formula:

[0200]

[0201] Through the isentropic relationship associated with the pressure, for simplicity of expression, define the function:

[0202]

[0203] In this relationship, is a constant, at this time if we let , then this relationship can be written in the following form:

[0204]

[0205] For​ Differentiation yields:

[0206]

[0207] in, Therefore, we can conclude that:

[0208]

[0209] Simplifying this relation, we get:

[0210]

[0211] The expression quantifies the sensitivity of the fluid velocity at the jet orifice to local pressure. Its value is usually negative, indicating that an increase in pressure will lead to a decrease in the fluid velocity at the jet orifice.

[0212] pressure gradient It needs to be solved using the differential relations of elliptic geometry. Specifically, and The coupling is achieved directly through coordinate transformation, therefore:

[0213]

[0214] In this relation, It is a constant; It needs to be derived from the definition of elliptical coordinates. Therefore, this relation can be further written as:

[0215]

[0216] This formula reflects how changes in eccentricity e affect pressure distribution through geometric constraints.

[0217] Will and Substitute the calculation formula The calculation formula is obtained. The complete expression is:

[0218]

[0219] This formula uses eccentricity Adjusting and optimizing airflow distribution, eccentricity This directly affects the symmetry of the elliptical air chamber, thereby altering the airflow distribution efficiency at the four jet holes. When When the system reaches its optimal state, the variance of the fluid velocity at the four jet holes is minimized, ensuring the uniformity and stability of the spinning process.

[0220] 2. Find the partial derivatives .

[0221] First, since the constraint term is linear, its partial derivative is . Thus, can be written as:

[0222]

[0223] The optimization objective function depends on b, so the chain rule must be applied:

[0224]

[0225] is determined by , and depends on the parameter b, so we have:

[0226]

[0227] Substituting this relationship into the calculation relationship of , we get:

[0228]

[0229] Finally, we get:

[0230]

[0231] The pressure gradient must be solved by the differential relationship of elliptic geometry. Specifically, the coupling with b is achieved through the metric coefficient, so:

[0232]

[0233] In this relationship, is a constant; must be derived from the definition of elliptic coordinates, , . Therefore, this relationship can be further written as:

[0234]

[0235] This formula reflects how the change of the elliptic semi-minor axis b affects the pressure distribution through geometric constraints.

[0236] Substituting the calculation relationships of and into the calculation relationship of , we get the complete expression of :

[0237] ​

[0238] The formula can be solved by letting The optimal b value can be solved to minimize the nozzle speed variance and improve the spinning uniformity.

[0239] Let And Equal to 0, the following equation group can be obtained:

[0240]

[0241] By coupling analytical solution, the optimal centrifugal distance and the optimal elliptical half minor axis respectively satisfy the following relationships:

[0242]

[0243]

[0244] Wherein, And Are empirical coefficients, , .

[0245] S7, adjusting the shape and position of the elliptical air chamber according to the optimal elliptical half minor axis and the optimal centrifugal distance.

[0246] The effectiveness of the present scheme will be verified by specific experiments below.

[0247] First, set the basic structure parameters of the air chamber as follows: m = 3.93 mm, ; , , , , , . Through calculation, e = 0.43 mm, b = 7.47 mm.

[0248] Then, carry out simulation experiment. Please refer to Figure 4 , according to the above structure parameters, the air chamber is modeled by SolidWorks fluid domain, and put into Ansys Fluent for simulation, and the analysis results of the inlet velocity section of each air jet hole 1, 2, 3, 4 are shown in Figure 5 、 6 , 7, 8 respectively, Figure 5 、 6 , the longitudinal coordinate "velocity" in 7, 8 is the fluid velocity. From Figure 5 、 6As shown in Figures 7 and 8, after the speed stabilizes, the speed at jet orifice 1 is approximately 185.78 m / s, the speed at jet orifice 2 is approximately 184.05 m / s, the speed at jet orifice 3 is approximately 185.21 m / s, and the speed at jet orifice 4 is approximately 184.65 m / s. The speed variance of the four jet orifices is 0.413. It can be observed that the speed difference between the near and far ends (jet orifices 1 and 3) should have been relatively large, but at this point they are very close, indicating that the speeds at jet orifices 1 and 3 are balanced. While balancing the speeds at jet orifices 1 and 3, the speeds at jet orifices 2 and 4 also do not differ significantly, which intuitively demonstrates the significant effect of the "elliptical" + "eccentric" design. When the speed variance is particularly small, it indicates that the speeds at the inlet of the four jet orifices are very similar, which makes the airflow during spinning very symmetrical and stable.

[0249] Next, as Figure 9 As shown, an XY cross-section was created using the central axis of the eight airflow channels connecting the first air chamber and the elliptical air chamber as a reference. A horizontal plane was then established to analyze the fluid velocity in the X, Y, and Z directions on this cross-section of the elliptical air chamber. The analysis results are as follows: Figure 10 , 11 As shown in Figure 12. From Figure 10 , 11 As can be seen from Figures 1 and 12, the velocity distribution of the fluid in the X, Y, and Z directions exhibits good central and axial symmetry, indicating that the design does not significantly affect the movement of the airflow on the horizontal plane of the air chamber (if the structure is not good, it will seriously affect the central and axial symmetry of the velocity), indicating that the velocity in the fluid domain is well constrained and compensated by the elliptical eccentric design.

[0250] Furthermore, the velocities of the airflow at the outlet of the vortex tube in the X, Y, and Z directions are analyzed. The velocities of the airflow at the outlet of the vortex tube in the X, Y, and Z directions are as follows: Figure 13 , 14 As shown in Figure 15. From Figure 13 , 14 As can be seen from Figure 15, in the X and Y directions, the velocity tends to be centrally symmetrical, and the positive and negative velocity changes are very uniform (the values ​​are concentrated near the 0 line, and the difference is almost equal far from the 0 line); in the Z direction, the velocity distribution is more axially symmetrical, indicating that the elliptical eccentric design cancels out a large amount of uneven airflow, which will result in a good fiber twisting effect.

[0251] It should be noted that in some cases, the actions described in the specification can be performed in different orders and still achieve the desired results. In this embodiment, the order of steps is given only to make the embodiment clearer and easier to explain, and not to limit it.

[0252] In one optional embodiment, please refer to Figure 16, in order to improve the practicability of the method and facilitate the popularization of the method, the application also provides a spinning machine air jet speed balancing system based on an elliptical eccentric air chamber, the spinning machine air jet speed balancing system based on the elliptical eccentric air chamber comprises: a data acquisition device 1, a data output device 2, a processor 3 and a storage 4, the storage 4 comprises a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program comprises program instructions, the processor 3 comprises an encoder, and the program instructions enable the processor 3 to realize the contents of steps S1 to S7 when the processor 3 executes the program instructions.

[0253] To sum up, the method has at least the following advantages: the method balances the flow by introducing an asymmetric eccentric design, the eccentricity changes the structure of the left and right cavities of the air chamber, the optimal centrifugal distance is calculated, so that the air injection holes 1 and 4 are depressurized, and the air injection holes 2 and 3 are pressurized, thereby balancing the flow, and this irregular structure can restrict the flow with large deviations; the second air chamber is changed to an elliptical air chamber, because of the existence of the semi-major axis of the ellipse, the trajectory of the airflow entering the air injection hole 1 is lengthened, and relatively, the trajectory of the airflow entering the air injection hole 3 is shortened due to the influence of eccentricity, this structure design suppresses the high speed of the air injection hole 1, by calculating the optimal elliptical semi-minor axis and combining the optimal centrifugal distance to adjust the position of the elliptical air chamber, the gas speed of all air injection holes can be balanced to the greatest extent, and the production demand of high-quality spinning is met; a system adapted to the method is provided, which can improve the practicability of the method and facilitate the popularization of the method.

[0254] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application, and they should be covered in the scope of the claims and the specification of the application.

Claims

1. A method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber, characterized in that, Includes the following steps: Based on the dual-chamber design, the second chamber is changed to an elliptical chamber, and the elliptical chamber is offset towards the air supply pipe by setting a centrifugal distance. Calculate the gas mass flow rate at the inlet of the gas chamber supply pipe, and then solve the pressure distribution of the first gas chamber in cylindrical coordinates; By transforming the ellipse into the circular domain and calculating the metric coefficients, the pressure distribution characteristics in the ellipse coordinate system are obtained by solving the Laplace equation in the ellipse coordinate system. Based on the pressure distribution characteristics, the pressure distribution of the elliptical air chamber is obtained by combining the pressure distribution of the first air chamber; A jet velocity calculation model is established, and then the jet velocity of the spinning machine is calculated in combination with the pressure distribution of the elliptical air chamber. The objective function is set to minimize the gas velocity variance of all jet holes, and then the optimal semi-minor axis and optimal centrifugal distance of the ellipse are solved based on the Lagrange function method. Adjust the shape and position of the elliptical air chamber according to the optimal semi-minor axis of the ellipse and the optimal centrifugal distance.

2. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The calculation of the gas mass flow rate at the inlet of the gas chamber supply pipe, and then the solution of the pressure distribution in the first gas chamber in cylindrical coordinates, includes the following steps: Calculate the mass flow rate of the gas at the inlet of the gas chamber supply pipe; The Mach number at the inlet of the gas supply pipe is calculated based on the gas mass flow rate and the flow rate at the outer boundary of the first gas chamber. After obtaining the Mach number, the governing equations of the fluid in the first air chamber are obtained in cylindrical coordinates, and then the radial momentum equation is used to solve the pressure distribution in the first air chamber step by step.

3. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The gas mass flow rate satisfies the following relationship: ， in, The mass flow rate of the gas is... The cross-sectional area of ​​the gas chamber supply pipe, To stop the pressure, Let R be the specific heat capacity of air, and R be the gas constant. For stagnation temperature, Atmospheric pressure.

4. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 2, characterized in that, The pressure distribution in the first air chamber satisfies the following relationship: ， in, The local pressure at a radial distance r in cylindrical coordinates. To stop the pressure, The specific heat capacity of air, The radius of the air supply pipe to the air chamber. Let be the Mach number.

5. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The metric coefficients satisfy the following relationship: ， in, The metric coefficient is the coefficient of the metric. Let x be the x-coordinate of the circular region. The ordinate of the circular region. Radial elliptical coordinates, It is the semi-major axis of the ellipse. Let be the semi-minor axis of the ellipse. The coordinates are angular elliptical coordinates.

6. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The pressure distribution in the elliptical air chamber satisfies the following relationship: ， in, Radial elliptic coordinates Local pressure at the location, This refers to the local pressure at the outlet of the first air chamber. This refers to the local pressure at the jet nozzle location. The radial elliptical coordinates of the jet hole position are... The coordinates are the radial elliptical coordinates of the elliptical boundary.

7. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The jet velocity calculation model for the jet nozzle satisfies the following relationship: ， in, Let K be the fluid velocity at the jet orifice k. The specific heat capacity of air, This refers to the local pressure at the jet orifice k. , Let K be the radial elliptical coordinates at the jet hole. Let K be the fluid density at the jet orifice k. Atmospheric pressure.

8. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The optimal centrifugation distance satisfies the following relationship: ， Where e is the optimal centrifugation distance. This is an empirical coefficient. The diameter of the airflow channel between the first air chamber and the elliptical air chamber is [missing information]. The diameter of the jet orifice. The maximum diameter of the annular block containing the jet hole. The minimum diameter of the annular block containing the jet hole. Where m is the diameter of the air chamber shell, and m is the diameter of the air chamber supply pipe. To stop the pressure, The specific heat capacity of air, Atmospheric pressure.

9. The method for balancing the air jet velocity of a spinning machine based on an elliptical eccentric air chamber according to claim 1, characterized in that, The optimal semi-minor axis of the ellipse satisfies the following relationship: ， Where b is the semi-minor axis of the optimal ellipse, This is an empirical coefficient. It is the semi-major axis of the ellipse. The diameter of the airflow channel between the first air chamber and the elliptical air chamber is [missing information]. The diameter of the jet orifice. The maximum diameter of the annular block containing the jet hole. The minimum diameter of the annular block containing the jet hole. To stop the pressure, The specific heat capacity of air, Atmospheric pressure.

10. A jet velocity balancing system for a spinning machine based on an elliptical eccentric air chamber, characterized in that, The aforementioned air jet speed balancing system for a spinning machine based on an elliptical eccentric air chamber includes: a data acquisition device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor, cause the processor to implement the air jet speed balancing method for a spinning machine based on an elliptical eccentric air chamber as described in any one of claims 1-9.

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