Vibration absorber permanent magnet electromagnetic performance analysis and optimization method based on simulation

Abstract

The invention belongs to the technical field of electromagnetic vibration absorber performance analysis and optimization, and particularly relates to a simulation-based vibration absorber permanent magnet electromagnetic performance analysis and optimization method. Comprising the following steps: S1, establishing a vibration absorber permanent magnet equivalent magnetic circuit before and after chamfering based on an equivalent magnetic circuit method, and in equivalent magnetic circuit modeling, centrally equalizing a distribution parameter effect before chamfering into a corner magnetic resistance for processing; s2, vibration absorber permanent magnet equivalent magnetic circuit simplification processing is carried out, geometric features of corner areas are simplified into equivalent arcs for approximation, and permanent magnet equivalent magnetic circuit parameters before and after chamfering are obtained; s3, establishing a vibration absorber magnetic field space distribution rule and an electromagnetic force influence mathematical model thereof by adopting a vector field mode; S4, establishing a unified vibration absorber permanent magnet electromagnetic performance analysis model; the method provided by the invention can better carry out high-efficiency analysis and judgment on the internal structure and the characteristic relation of the permanent magnet, and is convenient to more directly confirm the influence of parameters such as the permanent magnet structure on the internal magnetic field environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of performance analysis and optimization of electromagnetic vibration absorbers, and particularly relates to a simulation-based electromagnetic performance analysis and optimization method for permanent magnets of vibration absorbers. BACKGROUND

[0002] An electromagnetic vibration absorber is a new type of noise reduction and vibration reduction device. It absorbs vibration energy through active or passive methods, thereby reducing the collision and friction between moving structures, reducing and shortening the vibration period, and can be widely applied to various equipment such as ships and large machinery. At present, the optimization of electromagnetic vibration absorbers mainly focuses on the active control method of electromagnets, the vibration reduction implementation method, and the optimization and improvement of electrical parameters in the electric control system. Since accurate control needs to be realized through relatively complex algorithms and control circuits, the control module structure is complex, and the optimization and use cost is high. However, in addition to factors such as electromagnetic control methods, the electromagnetic characteristics of the electromagnetic vibration absorber, especially the electromagnetic effect between the permanent magnet and the moving stator, and the structure parameters of the permanent magnet, also directly affect the performance of the electromagnetic vibration absorber. There are few optimization and analysis methods for these aspects, and the analysis is mainly from the influence of the internal and external environment on the overall permanent magnet vibration absorber, and the internal characteristic analysis is shallow. SUMMARY

[0003] The purpose of the present application is to meet the demand for further optimization and upgrading of permanent magnet vibration absorbers, and to provide a simulation-based electromagnetic performance analysis and optimization method for permanent magnets of vibration absorbers, which can better analyze and judge the internal structure and characteristic relationship of permanent magnets, and directly confirm the influence of permanent magnet structure parameters on the internal magnetic field environment.

[0004] Based on the actual optimization demand, in order to meet the analysis of the permanent magnet structure in the permanent magnet vibration absorber, especially the optimization parameters of the chamfer, the following technical scheme is adopted.

[0005] A simulation-based electromagnetic performance analysis method for permanent magnets of vibration absorbers, comprising the following steps:

[0006] S1, establishing the equivalent magnetic circuit of the permanent magnet of the vibration absorber before and after chamfering based on the equivalent magnetic circuit method, and in the equivalent magnetic circuit modeling, concentrating the distributed parameter effect before chamfering into a corner reluctance. processing;

[0007] The equivalent magnetic circuit after chamfering includes: the magnetic potential of the permanent magnet after chamfering , the magnetic resistance of the moving silicon steel part , the working air gap , and the magnetic resistance of the stator silicon steel part The equivalent magnetic circuit before chamfering includes: the magnetic potential of the permanent magnet before chamfering , the magnetic resistance of the moving silicon steel part , working air gap , reluctance of stator silicon steel part , corner magnetic reluctance caused by chamfered front corner ;

[0008] The proportion of magnetic potential consumed by corner magnetic reluctance is defined as , wherein 0 <0.3, the effective magnetic motive force proportion of the corner is established, wherein the effective magnetic motive force of the shunt path is , and the effective magnetic motive force of the main magnetic circuit is ;

[0009] The equivalent magnetic reluctance correction after chamfering is defined as ; is the relative permeability of the stator; is the chamfer depth of the permanent magnet, is the length in the Y direction, is the thickness of the permanent magnet in the X direction, is the length of the stator and mover in the Z direction;

[0010] S2, absorber permanent magnet equivalent magnetic circuit simplification processing

[0011] The geometric characteristics of the corner area are simplified as an equivalent circular arc for approximation, and the permanent magnet equivalent magnetic circuit parameters before and after chamfering are obtained, including:

[0012] Equivalent corner magnetic reluctance ;

[0013] Total magnetic reluctance of the main magnetic circuit before chamfering ;

[0014] Magnetic flux of the main magnetic circuit before chamfering ;

[0015] Magnetic flux in the corner shunt path ;

[0016] Total magnetic reluctance of the main magnetic circuit after chamfering ;

[0017] Main magnetic flux after chamfering ;

[0018] Change amount of the main magnetic flux caused after chamfering ;

[0019] , wherein is the relative permeability of the mover, is the equivalent action area of the magnetic flux in the permanent magnet; is the equivalent action area of the magnetic flux in the silicon steel;

[0020] ; is the air-gap reluctance, C (C is the above calculation sum, not described, can be understood as the sum of the reluctance) is the equivalent reluctance of the original permanent magnet, is the equivalent magnetomotive force of the permanent magnet.

[0021] Substitute the parameters and simplify to get the change of the main magnetic flux ;

[0022] The above formula reflects the quantitative influence of the boundary geometry optimization of the permanent magnet on the main magnetic circuit magnetic flux, and the basic physical process of magnetic field redistribution is realized by changing the geometric shape of the contact boundary of the permanent magnet and the ferromagnetic material;

[0023] The net change of the magnetic flux is determined by the relative size of the two competing effects, according to the classical Maxwell magnetic field theory, the electromagnetic force ;

[0024] is the effective air gap cross-sectional area of the stator and the mover; B is the magnetic induction intensity vector; is the vacuum permeability constant;

[0025] It can be clearly seen from the formula that the electromagnetic force is proportional to the square of the air-gap magnetic flux, that is, Therefore, the net gain of the magnetic flux will directly contribute to the improvement of the electromagnetic force, and the relative change of the electromagnetic force before and after optimization is ;

[0026] S3, the vector field is used to establish the magnetic field space distribution law and the electromagnetic force influence mathematical model of the vibration absorber, including the following steps:

[0027] Establish the electromagnetic stress state expression of any point in the space in the magnetic static or low-frequency magnetic field environment without electric field, including:

[0028] Maxwell stress tensor ;

[0029] The square of the magnetic induction intensity vector module ;

[0030] The body force density vector of any point in space is ;

[0031] Where, represents the force density of the magnetic field in the direction of on the direction of ; is the component of the magnetic induction intensity vector B in the direction of , ; is the Kronecker symbol, which takes the value 1 when , otherwise it takes the value 0;

[0032] Based on the two-dimensional profile analysis model, simplification is carried out, and the Z direction component is ignored because the magnetic field is mainly distributed in the X-Y plane, so that According to the definition of stress tensor, the surface force density component of the permanent magnet is obtained as:

[0033] ;

[0034] ;

[0035] The complete force density vector acting on the surface of the air gap is obtained as ;

[0036] Wherein is the amplitude of the magnetic field, is the deflection angle of the magnetic field;

[0037] The direction consistency coefficient is defined as , which represents the consistency degree of the electromagnetic force vector and the target direction. The physical meaning is the ratio of the Y direction electromagnetic force component to the total electromagnetic force amplitude, and the direction consistency coefficient is obtained as

[0038] ;

[0039] Fx is the x direction force, Fy is the y direction force, Fz is the z direction force, is the integral;

[0040] Wherein represents the total area of the air gap concerned; the modulus of the force density vector ;

[0041] S4, a unified electromagnetic performance analysis model of the permanent magnet of the vibration absorber is established

[0042] Based on the actual situation of the magnetic field distribution, there is a part of the total effective action area The magnetic field direction deviates, and the deflection angle is , and the remaining area maintains the ideal magnetic field distribution state. Based on this condition, the direction consistency coefficient of the electromagnetic force is calculated:

[0043] ;

[0044] S represents the total area of the air gap concerned is the distortion area; the direction consistency of the electromagnetic force, the closer to 1, the better the consistency, which means that the direction of the force is more consistent, and the output performance is improved.

[0045] Mathematical arrangement and simplification can be carried out to obtain ;​

[0046] is the area of the distortion region, k is the geometric correlation coefficient;

[0047] Based on the foregoing magnetic flux change analysis and force direction consistency change analysis, the electromagnetic force size is mainly determined by the square of the magnetic flux, and the actual effective output degree of the force is reflected by the force direction consistency coefficient. A comprehensive electromagnetic performance index is established to define ;

[0048] Further, a performance change rate is established to represent the linear superposition of the magnetic flux change effect and the force direction consistency change effect ;

[0049] wherein the relative change of the electromagnetic force size ;

[0050] The absolute change amount of the force direction consistency coefficient is:

[0051]

[0052] Substitute the electromagnetic force size change and the force direction consistency coefficient change amount into the comprehensive performance expression,

[0053] A performance model is established to represent the geometric optimization effect of the vibration absorber permanent magnet ;

[0054] wherein the first term represents the contribution of the magnetic flux enhancement effect, and the second term represents the contribution of the direction consistency improvement effect; the performance model provides an analysis basis for quantitative analysis and prediction of the optimization effect of the permanent magnet chamfer;

[0055] Further improvement or preferred embodiment of the foregoing simulation-based electromagnetic performance analysis method of the vibration absorber permanent magnet, the equivalent magnetomotive force of the permanent magnet is determined by the residual magnetic induction intensity and the effective length in the magnetization direction , wherein is the relative permeability of the permanent magnet material, and is represented as ;

[0056] Since the magnetomotive force of the permanent magnet is mainly related to the inherent properties of the material and the overall length in the magnetization direction, and the chamfering process only changes the magnetization length of the local area at the end, the influence on the overall magnetization length is negligible, i.e. the magnetomotive force before and after chamfering remains basically unchanged, and .

[0057] Further improvement or preferred embodiment of the foregoing simulation-based electromagnetic performance analysis method of the vibration absorber permanent magnet,

[0058] The application also provides a simulation-based electromagnetic performance optimization method for a vibration absorber permanent magnet. The performance model of the geometric optimization effect of the vibration absorber permanent magnet is used to perform systematic quantitative analysis and optimization on the chamfer optimization effect of the vibration absorber. Specifically, the method comprises the following steps:

[0059] A. Establishing a parameterized analysis model, including setting the structure parameters of the vibration absorber permanent magnet, including thickness, chamfer continuous variation range, magnetic flux shunt coefficient, and geometric correlation coefficient;

[0060] B. Establishing a two-dimensional simulation model of the vibration absorber permanent magnet based on a finite element program. Based on the established simulation model, parameterized simulation is performed to determine the influence law of the chamfer parameter on the key electromagnetic performance indicators. Specifically, the method comprises the following steps:

[0061] B1. Based on the integral method of Maxwell stress tensor, an integral path is set along the center line position of the working air gap to obtain the magnetic flux through the unit depth section of the path;

[0062] B2. Adjusting the chamfer depth, determining the magnetic flux through the unit depth section of the path in different depth ranges, drawing a magnetic field gradient distribution map according to the change of the magnetic flux, calculating the electromagnetic force vector, and selecting the most appropriate chamfer depth range;

[0063] B2. Based on B1, adjusting the chamfer angle, determining the magnetic flux through the unit depth section of the path in different angle ranges, drawing a magnetic field gradient distribution map according to the change of the magnetic flux, calculating the electromagnetic force vector, and selecting the most appropriate chamfer depth;

[0064] B3. Based on the depth and angle range determined in steps B1 and B2, analyzing the key electromagnetic performance indicators and optimizing the best scheme.

[0065] Further improvement or preferred embodiments of the aforementioned simulation-based electromagnetic performance optimization method for a vibration absorber permanent magnet, in step B3, the key electromagnetic performance indicators include the direction consistency coefficient of the electromagnetic force, the comprehensive electromagnetic performance indicator, the geometric optimization performance of the vibration absorber permanent magnet, the magnetic flux enhancement effect contribution, and the magnetic flux improvement effect contribution. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 is a schematic diagram of a default electromagnetic vibration absorber structure;

[0067] Figure 2 is a schematic diagram of an electromagnetic vibration absorber structure with chamfering;

[0068] Figure 3 is an equivalent magnetic circuit analysis model of a default electromagnetic vibration absorber structure;

[0069] Figure 4 is an equivalent magnetic circuit analysis model of an electromagnetic vibration absorber with chamfering.

[0070] Figure 5 Chamfer optimization effect prediction based on theoretical model;

[0071] Figure 6 Finite element simulation two-dimensional modeling;

[0072] Figure 7 Chamfer depth on the key performance parameters (a. Air gap magnetic flux density change; b. Electromagnetic force change);

[0073] Figure 8 Magnetic field gradient distribution comparative analysis (a. Gradient distribution before chamfering; b. Gradient distribution after chamfering; c. Absolute difference; d. Relative difference);

[0074] Figure 9 Magnetic flux density distribution comparative analysis (a. Magnetic field distribution before chamfering; b. Magnetic field distribution after chamfering; c. Absolute difference; d. Relative difference);

[0075] Figure 10 Electromagnetic force vector characteristic analysis (a. Comparison of force components in each direction; b. Change of resultant force vector);

[0076] Figure 11 Comparison of electromagnetic force characteristics under different current conditions. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0078] As Figure 1 shown, the present application is directed to an electromagnetic vibration absorber structure with (up-down-left-right) complete symmetrical layout, defining the up-down motion direction of the mover as Y axis, the Y axis length of the permanent magnet as , the thickness of the response horizontal X axis direction as , and the working air gap width of the mover and the stator as , on the basis of Figure 1 , the present application optimizes the outer peripheral geometric chamfer of the permanent magnet to obtain Figure 2 the electromagnetic vibration absorber structure as shown, and on this basis, an electromagnetic performance analysis model is established, and optimization is carried out based on the analysis model. The specific steps are described below.

[0079] S1, based on the equivalent magnetic circuit method, the equivalent magnetic circuit of the vibration absorber permanent magnet before and after chamfering is established,

[0080] asFigure 2 As shown in the figure, the electromagnetic vibration absorber includes a fixed stator, a mover symmetrically distributed on both sides of the stator, and an electromagnetic coil wrapped on the stator;

[0081] First, the geometric symmetry characteristics of the structure are fully utilized to establish an equivalent magnetic circuit analysis model of a quarter structure, as shown in Figure 3 , Figure 4 As shown in Figure 3 , before chamfering, at the geometric corner, due to the sharp change of the structure, the magnetic field distribution will inevitably be significantly distorted, resulting in the bending of the magnetic induction line, and the equivalent reluctance of this area is significantly higher than that of the straight magnetic conductive segment; in order to facilitate subsequent theoretical analysis, in the equivalent magnetic circuit modeling, this complex distributed parameter effect is concentrated and equivalent to a corner reluctance for processing; after chamfering, the equivalent magnetic circuit includes: the permanent magnet magnetic potential of the permanent magnet after chamfering, the magnetic reluctance of the mover silicon steel part, the working air gap , and the magnetic reluctance of the stator silicon steel part;

[0082] Before chamfering, the equivalent magnetic circuit includes: the permanent magnet magnetic potential of the permanent magnet before chamfering, the magnetic reluctance of the mover silicon steel part, the working air gap , the magnetic reluctance of the stator silicon steel part, and the corner reluctance caused by the corner before chamfering;

[0083] According to the classical magnetic potential balance theorem

[30] , under the condition of ignoring other secondary factors, the total magnetic motive force generated by the permanent magnet will be distributed to two paths: part of it is used to establish the effective working main magnetic flux, and the other part is consumed by the equivalent reluctance at the corner; in actual electromagnetic structure design, the extra magnetic potential consumption caused by the magnetic flux concentration in the corner area should be strictly controlled at a low level; assuming that the proportion of the magnetic potential consumed by the corner reluctance is , wherein 0 <0.3, the value range refers to the design experience of typical motors and transformers

[31] , then the effective magnetic motive force of the corner shunt path is , and the effective magnetic motive force of the main magnetic circuit is ;

[0084] The equivalent magnetic motive force of the permanent magnet is determined by the residual magnetic induction and the effective length in the magnetization direction together, wherein is the relative permeability of the permanent magnet material, which is represented as ;

[0085] Magnetomotive force of permanent magnet The chamfering process only changes the magnetization length of the local area at the end, so the influence on the overall magnetization length is negligible, i.e. the magnetomotive force remains basically unchanged before and after chamfering, and ;

[0086] According to the basic definition of magnetic reluctance, the equivalent magnetic reluctance of the original permanent magnet is ;

[0087] After chamfering, the effective cross-sectional area of the permanent magnet perpendicular to the magnetization direction will decrease accordingly, and the equivalent magnetic reluctance after chamfering is modified to ;

[0088] S2, equivalent magnetic circuit simplification of the vibration absorber permanent magnet

[0089] For the equivalent magnetic reluctance representing the corner geometric effect, the magnetic flux conduction path is composed of two parts in series, i.e. the permanent magnet material segment and the mover silicon steel material segment; based on the geometric characteristics of the corner region, this complex path can be simplified as an equivalent circular arc model for approximate processing; let be the relative permeability of the mover silicon steel material, and be the equivalent action area of the magnetic flux in the permanent magnet and silicon steel respectively, then the equivalent corner magnetic reluctance is ;

[0090] The core focus of the present application is to effectively suppress the above-mentioned magnetic field distortion phenomenon through the geometric chamfering process of the permanent magnet, so when establishing the system equivalent magnetic circuit model, it is reasonably assumed that the magnetic reluctance of other magnetic circuit components (including the magnetic yoke and the mover silicon steel part) except the permanent magnet remains basically unchanged, which is represented as

[0091] ;

[0092] The total magnetic reluctance of the main magnetic circuit before chamfering ; the corresponding main magnetic circuit magnetic flux ; the magnetic flux in the corner shunt path ;

[0093] The fundamental mechanism of chamfering is to effectively suppress the magnetic flux shunt effect at the corner by eliminating the geometric discontinuity; in the ideal case, when the chamfering depth is large enough, the equivalent magnetic reluctance at the corner will tend to infinity, so that the influence of this shunt path can be ignored; at this time, the magnetic flux of the shunt path after chamfering can be approximated as: ;

[0094] In this ideal state, the shunt coefficient Approaching 0, the magnetomotive force of the permanent magnet can almost completely act on the main magnetic circuit; the total magnetic resistance of the main magnetic circuit after chamfering is: ;

[0095] The main magnetic flux after chamfering , the change amount of the main magnetic flux caused by chamfering

[0096] ;

[0097] Substitute the parameters and simplify to obtain the change amount of the main magnetic flux ;

[0098] Formula (14) reflects the quantitative influence of the boundary geometry optimization of the permanent magnet on the main magnetic circuit, and reveals the basic physical process of realizing magnetic field redistribution by changing the geometric shape of the contact boundary between the permanent magnet and the ferromagnetic material;

[0099] The net change of the magnetic flux is determined by the relative size of the two competing effects. According to the classical Maxwell magnetic field theory, the electromagnetic force ;

[0100] is the effective air gap cross-sectional area of the stator and the mover; it can be clearly seen from the formula that the electromagnetic force is proportional to the square of the air gap magnetic flux, that is , so the net gain of the magnetic flux will directly contribute to the improvement of the electromagnetic force, and the relative change of the electromagnetic force before and after optimization is ;

[0101] The traditional magnetic circuit analysis method simplifies the complex magnetic field into a scalar for processing, although it can effectively predict the overall trend of the magnetic flux, but it cannot accurately characterize the directional characteristics of the magnetic field vector and its complex spatial distribution law, so it is difficult to deeply evaluate the specific influence of local magnetic field distortion on the electromagnetic force distribution and directional characteristics; in the ideal design state, all electromagnetic forces should strictly follow the predetermined motion direction of the mover; however, the unevenness and directional distortion of the actual magnetic field distribution will inevitably introduce force components in other non-desired directions, and the traditional magnetic circuit analysis method cannot effectively explain the influence mechanism of local magnetic field distortion on the consistency of force direction;

[0102] In order to overcome the inherent limitations of the traditional magnetic circuit analysis method, the optimized Maxwell stress tensor analysis method is adopted in this application to comprehensively describe the spatial distribution of the magnetic field and its influence on the electromagnetic force in the form of a vector field; this analysis method not only can accurately reflect the size of the electromagnetic force, but also can deeply analyze the directionality and spatial distribution characteristics of the force, providing a solid theoretical basis for electromagnetic force analysis under complex structures. The specific content is as follows:

[0103] S3, the vector field is used to establish the space distribution of the magnetic field of the vibration absorber and the mathematical model of the electromagnetic force, including the following steps:

[0104] In the magnetic static or low frequency magnetic field environment without electric field, the electromagnetic stress state of any point in space can be described by Maxwell stress tensor , and the mathematical definition of its component form is:

[0105] ;

[0106] Where is the stress tensor component, representing the force density of the magnetic field in the direction on the direction; is the component of the magnetic induction intensity vector B in the , direction; is the Kronecker symbol, which is 1 when , otherwise it is 0; is the vacuum permeability constant;

[0107] The square of the modulus of the magnetic induction intensity vector is defined as: ;

[0108] According to the divergence theorem in vector analysis, the body force density vector at any point in space is:

[0109] ;

[0110] In actual electromagnetic devices, the magnetic field distribution in the air gap area is affected by the structure geometry and material properties, showing obvious non-uniformity and direction distortion characteristics; in order to facilitate theoretical analysis, based on the two-dimensional section analysis model, the following reasonable simplifying assumptions are made: the magnetic field is mainly distributed in the X-Y plane, ignoring the Z direction component, i.e. ; the angle between the magnetic field direction and the y-axis is defined as ; the magnetic induction intensity vector can be represented as: ;

[0111] Correspondingly, the square of the modulus of the magnetic induction intensity is: ;

[0112] Where is the modulus of the magnetic field vector in the X-Y plane; this application mainly focuses on the electromagnetic force on the surface of the gap between the mover and the stator, and the normal vector of the key interface is along the Y-axis direction, i.e. , then the force density vector on the surface is ;

[0113] According to the definition of stress tensor, the components of surface force density are:

[0114] ;

[0115] ;

[0116] Therefore, the complete force density vector acting on the air gap surface is:

[0117] ;

[0118] Equation (25) shows that when the magnetic field direction deviates from the ideal Y-axis direction, an undesirable tangential force component will be generated , while the effective force component in the Y direction will be reduced accordingly. This physical phenomenon is the fundamental reason for the decline in the consistency of the electromagnetic force direction;

[0119] To quantitatively evaluate the degree of consistency of the electromagnetic force vector with the target direction, the present application defines the direction consistency coefficient , which has the physical meaning of the ratio of the electromagnetic force component in the Y direction to the total electromagnetic force amplitude:

[0120] ;

[0121] where represents the total area of interest of the air gap; the modulus of the force density vector is:

[0122] ;

[0123] Mathematical simplification of the above equation gives ;

[0124] The above equation reveals an important physical law: at any given point in space, the modulus of the force density vector is determined only by the magnetic field amplitude at that point, and is independent of the magnetic field deviation angle ; the change in the magnetic field direction only redistributes the components of the force density in various spatial directions at that point, without changing the total force density;

[0125] There is a deep internal physical correlation between the magnetic flux variation obtained from magnetic circuit analysis and the magnetic field direction analysis based on Maxwell's stress tensor; the abnormality of the local magnetic field distribution not only causes part of the magnetic flux to deviate from the ideal main magnetic path, but also forms a magnetic field component that is inconsistent with the direction of the main magnetic field in that area; this inconsistency in direction is the main physical factor causing the decline in the consistency of the electromagnetic force direction;

[0126] According to the magnetic field continuity condition and Ampere's law in electromagnetic field theory, the magnetic induction lines of the abnormal magnetic field region must be connected with the magnetic induction lines of the main magnetic field region to form a closed loop; at the interface between the two regions, the direction of the magnetic induction lines changes significantly, forming a local transition region with a high directional gradient, which corresponds to the distortion area in the force direction consistency analysis ; the distortion area and the shunt coefficient in the magnetic circuit analysis have the following quantitative relationship ; ;

[0127] Where is the geometric correlation coefficient, which quantitatively reflects the inherent relationship between the spatial distribution characteristics of the abnormal magnetic field region and the overall geometric structure;

[0128] Based on the actual situation of the magnetic field distribution, it is assumed that there is a part of the total effective area where the magnetic field direction deviates, and the deflection angle is , and the remaining area maintains the ideal magnetic field distribution state; based on this assumption, the electromagnetic force direction consistency coefficient is calculated:

[0129] ;

[0130] Mathematical arrangement and simplification of formula (30) can be obtained:

[0131] ;

[0132] Based on the foregoing magnetic flux variation analysis and force direction consistency variation analysis, the application establishes a comprehensive electromagnetic performance evaluation index; since the size of the electromagnetic force is mainly determined by the square of the magnetic flux, and the actual effective output degree of the force is reflected by the force direction consistency coefficient, the comprehensive electromagnetic performance index is defined as:

[0133] ;

[0134] Correspondingly, the performance change rate can be expressed as the linear superposition of the magnetic flux variation effect and the force direction consistency variation effect ;

[0135] The relative change of the electromagnetic force size is

[0136] ;

[0137] The absolute change of the force direction consistency coefficient is ;

[0138] ​The electromagnetic force size variation and the force direction consistency coefficient variation are substituted into the comprehensive performance expression to obtain a unified theoretical expression of the permanent magnet geometry optimization effect:

[0139] ;

[0140] The above formula completely represents the comprehensive performance variation as an algebraic sum of two independent contribution terms: the first term represents the contribution of the magnetic flux enhancement effect, and the second term represents the contribution of the direction consistency improvement effect; this unified expression provides an important theoretical basis for quantitatively analyzing and predicting the permanent magnet chamfer optimization effect;

[0141] The first term represents the contribution of the magnetic flux enhancement effect, and the second term represents the contribution of the direction consistency improvement effect; the performance model provides an analysis basis for quantitatively analyzing and predicting the permanent magnet chamfer optimization effect;

[0142] The performance model of the permanent magnet geometry optimization effect of the vibration absorber is used to systematically quantitatively analyze and optimize the chamfer optimization effect of the vibration absorber

[0143] A. Establish a parameterized analysis model, including setting the structure parameters of the vibration absorber permanent magnet, including thickness, chamfer continuous variation range, magnetic flux shunt coefficient, and geometry correlation coefficient;

[0144] In order to strictly maintain consistency with subsequent simulation analysis and experimental verification conditions, the thickness parameter of the permanent magnet is set to , the chamfer depth is continuously varied in the range of 0-8mm; according to the optimization parameters of typical electromagnetic structures and engineering experience, the magnetic flux shunt coefficient is set to , and the geometry correlation coefficient is set to Considering that the accurate calculation of magnetic resistance involves complex three-dimensional boundary conditions and nonlinear magnetic field distribution effects, this application uses an approximate value of magnetic resistance based on engineering experience data for trend analysis, focusing on the relative change relationship and physical law between key parameters, rather than the accurate calculation of absolute values;

[0145] B. Based on the finite element program, a two-dimensional vibration absorber permanent magnet simulation model is established, and on the basis of the established simulation model, parameterized simulation is performed to determine the influence law of the chamfer parameter on the key electromagnetic performance indicators; specifically:

[0146] B1 Based on the integral method of Maxwell stress tensor, an integral path is set along the center line position of the working air gap to obtain the magnetic flux passing through the unit depth section of the path;

[0147] B2 Adjust the chamfer depth to determine the magnetic flux passing through the unit depth section of the path in different depth ranges, draw the magnetic field gradient distribution map according to the magnetic flux variation, calculate the electromagnetic force vector, and select the most appropriate chamfer depth range;

[0148] B2 on the basis of B1, adjust the chamfer angle, determine the magnetic flux through the path unit depth section in different angle range, draw the magnetic field gradient distribution map according to the magnetic flux change, calculate the electromagnetic force vector, select the most suitable fall angle angle range;

[0149] B3 based on the depth and angle range determined in steps B1 and B2, analyze the key electromagnetic performance indicators, and optimize the best scheme; the key electromagnetic performance indicators include the direction consistency coefficient of electromagnetic force , comprehensive electromagnetic performance index , vibration absorber permanent magnet geometry optimization performance , magnetic flux enhancement effect contribution , sex improvement effect contribution ;

[0150] The following will be described in detail in combination with examples. Based on the unified performance evaluation theoretical model established in the foregoing steps, the effect of permanent magnet chamfer optimization is systematically and quantitatively predicted and analyzed.

[0151] In order to maintain strict consistency with subsequent simulation analysis and experimental verification conditions, the thickness parameter of the permanent magnet is set to , the chamfer depth is continuously changed in the range of 0-8mm; according to the design parameters of typical electromagnetic structure and engineering experience, the magnetic flux shunt coefficient , the geometric correlation coefficient , considering that the accurate calculation of magnetic resistance involves complex three-dimensional boundary conditions and nonlinear magnetic field distribution effect, the magnetic resistance approximation value based on engineering experience data is used for trend analysis in the application, and the relative change relationship and physical law between various key parameters are focused on, rather than the accurate calculation of absolute value;

[0152] Figure 5 The quantitative prediction results based on the theoretical model are shown, which will serve as an important theoretical benchmark for subsequent numerical simulation and experimental verification work; from the overall change trend, the three characteristic curves show obviously different change characteristics, which deeply reflect the complex action mechanism of various competitive physical effects in the process of permanent magnet chamfer processing;

[0153] The blue curve shows the detailed calculation results of the first item of the comprehensive performance expression, i.e. the contribution degree of the magnetic flux variation effect to the overall performance; the magnetic flux contribution shows a gradually increasing trend in the range of 0-4mm chamfer depth, reaches the peak value at the chamfer depth of 4mm, and then shows a clear downward trend in the range of larger chamfer depth; this change law clearly shows that when the chamfer depth is relatively small (0-4mm), the geometric modification mainly plays an active role in effectively suppressing the corner magnetic flux shunt, and moderate chamfer processing helps to significantly improve the overall magnetic flux distribution; however, when the chamfer depth continues to increase (4-8mm), the magnetic resistance increasing effect caused by the decrease of the effective cross-sectional area of the permanent magnet gradually becomes the dominant factor, so that the magnetic flux contribution begins to show a downward trend;

[0154] The red curve shows the detailed calculation results of the second item of the comprehensive performance expression, i.e. the contribution degree of the force direction consistency improvement effect to the overall performance; the direction consistency contribution curve shows an approximately monotonically increasing change trend, continuously rising from 0% to about 8.0% at 8mm; this approximately linear growth characteristic clearly shows that the continuous increase of the chamfer depth can continuously improve the consistency degree of the magnetic field direction; the systematic improvement of the direction consistency is mainly due to the gradual reduction of the effective area of the geometric discontinuous region and the continuous reduction of the local magnetic field deflection angle; compared with the magnetic flux contribution effect, the improvement of the direction consistency is more significant, which fully shows that the main mechanism of the chamfer optimization technology is focused on improving the spatial uniformity of the magnetic field vector distribution, rather than simply increasing the magnetic flux value;

[0155] The green curve, as the algebraic superposition of the aforementioned two contribution effects, completely represents the comprehensive performance calculation results; the comprehensive performance curve shows a typical first-increasing and then-decreasing change characteristic, the comprehensive performance steadily improves in the range of 0-6mm, the peak value appears at the chamfer depth of 6mm, reaching the maximum improvement amplitude of about 10.4%; then it shows a slight downward trend in the range of 6-8mm, and the value at 8mm is about 9.7%; this characteristic change law shows that there is a theoretically optimal chamfer depth design interval, in which the positive effects of the magnetic flux enhancement effect and the direction consistency improvement effect can be effectively superimposed, while the adverse effects of excessive geometric modification are successfully avoided;

[0156] In order to systematically verify the accuracy of the foregoing theoretical analysis framework and deeply analyze the electromagnetic field characteristic changes before and after the geometric chamfering of the permanent magnet, the present application establishes a two-dimensional finite element analysis model of the core structure of the electromagnetic vibration absorber based on the finite element software ANSYS Maxwell; on the basis of the established simulation model, a detailed parametric scanning analysis is carried out, and the influence law of the chamfer depth parameter on the key electromagnetic performance indicators is systematically studied;

[0157] In simulation analysis, the chamfer depth parameter The value range is set to 0-8mm, and the scanning step size is set to 1mm to ensure sufficient analysis accuracy; the geometric angle of the chamfer is uniformly fixed at 45°, maintaining strict consistency with the assumptions in the theoretical analysis; the geometric structures corresponding to different chamfer depths are... Figure 6 The diagram provides a clear illustration;

[0158] Through high-precision steady-state electromagnetic field simulation calculations, the system extracted key field quantity information such as magnetic flux distribution, magnetic field vector, and local magnetic field distribution under different chamfer depth conditions. The numerical calculation of electromagnetic force adopted an integration method based on Maxwell's stress tensor, with the integration path precisely set at the centerline of the working air gap. Simulation results of the influence of different chamfer depths on key performance parameters are shown below. Figure 7 As shown;

[0159] Figure 7 Simulation results demonstrate the detailed variation of the magnetic flux density line integral at the air gap center with chamfer depth. This integration path is located at the geometric center of the working air gap, and its integration result physically corresponds directly to the total magnetic flux per unit depth cross-section passing through this path, serving as a reliable quantitative indicator of the effective working magnetic flux. The simulation results clearly show that the effective working magnetic flux reaches a significant peak at a chamfer depth of 4 mm, and then decreases with increasing chamfer depth. The trend is downward as it further increases;

[0160] The trend observed in this simulation corresponds to the theoretically predicted pattern of change in magnetic flux contribution. Figure 3 The blue curves in the diagram show a high degree of consistency, strongly validating the accurate prediction of the dual effects of chamfering in the theoretical analysis; specifically, in Within this range, geometric modifications primarily play a positive role in suppressing corner flux shunting, resulting in a significant increase in effective working flux; while... Within the range, the increase in magnetic reluctance caused by the reduction in the effective cross-sectional area of ​​the permanent magnet gradually becomes the dominant factor, and the integral value of magnetic flux density begins to show a downward trend; the magnetic flux peak position at 4mm in the simulation results is completely consistent with the theoretically predicted magnetic flux contribution peak position, which fully verifies the accuracy and reliability of the established theoretical model.

[0161] Figure 7 b shows the detailed characteristics of the electromagnetic force as a function of chamfer depth; as the chamfer depth gradually increases, the electromagnetic force shows a continuous increasing trend, reaching a maximum value of 87.6N when the chamfer depth is 7mm, which is a significant increase of 23.2% compared to 71.1N without chamfering; when the chamfer depth is further increased to 8mm, the electromagnetic force begins to decrease.

[0162] By comparative analysis Figure 7 a and Figure 7 b, a very important physical phenomenon can be observed: within the 4-7mm chamfer depth interval, the magnetic flux density integral value has begun to decline, while the electromagnetic force continues to maintain a growing trend, and a clear separation phenomenon appears between the two key performance indicators; this seemingly contradictory change trend actually indicates that, within the critical 4-7mm interval, the improvement effect of magnetic field direction consistency has significantly surpassed the negative impact of magnetic flux reduction, becoming the dominant factor driving overall performance improvement; this important finding is fully consistent with the in-depth analysis in the theoretical prediction (corresponding to the intersection behavior of the medium red curve and the blue curve); Figure 3

[0163] It is worth noting that there is a slight difference between the peak of the optimal comprehensive performance and the chamfer depth corresponding to the electromagnetic force peak, mainly because the theoretical analysis is based on a simplified two-dimensional magnetic circuit model, while the numerical simulation uses a more complex geometry structure closer to the actual situation; factors such as end leakage effect, three-dimensional magnetic field distribution characteristics, etc. may cause the optimal working point to shift slightly to a larger chamfer depth; despite this slight difference in peak position, the simulation results still strongly verify the basic correctness of the theoretical analysis;

[0164] To better understand the specific impact of chamfering on magnetic field distribution, a detailed comparative analysis of the electromagnetic field distribution before and after 4mm chamfering is conducted; the basis for choosing 4mm includes that this chamfer depth corresponds to the peak point of magnetic flux contribution in the theoretical prediction, which is beneficial to verify the prediction of the magnetic flux enhancement effect in the theoretical model; secondly, the simulation results show that the slope of the magnetic flux density curve near this parameter point is close to zero, indicating that the system's sensitivity to chamfer depth changes is relatively low near this parameter point, which provides better process tolerance for actual processing and manufacturing, effectively reducing the adverse effects of manufacturing precision requirements on the final performance;

[0165] By extracting key physical quantities such as magnetic field gradient, magnetic flux density distribution, and electromagnetic force vector, the actual effect of geometric optimization is comprehensively evaluated;

[0166] Figure 8 It shows the significant impact of chamfering on local magnetic field gradient distribution; the size of the magnetic field gradient directly reflects the degree of spatial change of the magnetic field, and is an important quantitative indicator for evaluating the uniformity of the magnetic field distribution

[0167] Figure 8 a clearly shows that before chamfering, the magnetic field gradient presents a clear local concentration phenomenon at the geometric edge, with high gradient regions mainly concentrated in the sharp corners of the structure, showing a typical point-like concentration feature; this highly concentrated distribution pattern indicates that the magnetic field has undergone sharp spatial changes in these key areas; Figure 8 ​b shows that the magnetic field gradient distribution changes from the original point-like high concentration to a relatively dispersed distribution mode after chamfering, the spatial range of the high gradient region expands, but the peak intensity decreases significantly; Figure 8 c's absolute difference analysis clearly shows that the impact of chamfering is mainly concentrated in the direct vicinity of the geometric modification, the impact range is relatively limited but the effect is significant; Figure 8 d's relative difference analysis further reveals that chamfering effectively reduces the gradient concentration in certain key areas while also causing a redistribution of gradients in the surrounding adjacent areas, achieving significant uniformization of the magnetic field gradient distribution as a whole;

[0168] Figure 9 It deeply reflects the important influence of chamfering on the spatial distribution of magnetic flux density; Figure 9 a shows that before chamfering, the magnetic induction lines near the sharp edge of the permanent magnet show a relatively sharp directional change and obvious local concentration; Figure 9 b shows that after chamfering, the magnetic induction lines in the geometric modification area show a more smooth and gradual transition feature; the spatial distribution of magnetic flux density is more uniform, and the original local high-density concentration phenomenon is effectively alleviated; Figure 9 c and Figure 9 d's difference comparison analysis shows that chamfering mainly changes the local magnetic flux distribution pattern, successfully achieving the spatial redistribution of magnetic flux while maintaining the overall magnetic flux level basically stable; this beneficial redistribution helps to significantly improve the overall uniformity and effectiveness of magnetic field utilization;

[0169] Figure 10 It systematically demonstrates the important influence of chamfering on the characteristics of electromagnetic force vectors; Figure 10 a's force component analysis results show that after chamfering, the undesired force component in the X direction decreases by 1.6%, while the desired force component in the Y direction increases by 11.9%, and the overall force amplitude increases by 1.5%; this beneficial redistribution of force components shows that chamfering effectively improves the directional characteristics of electromagnetic force; Figure 10 b's polar coordinate analysis shows that the direction of the resultant force changes by 3.2°, and the amplitude changes by 1.5%; although the absolute value of the angle change is relatively small, this systematic improvement in direction has important engineering significance for the effective use of electromagnetic force;

[0170] In order to comprehensively evaluate the applicability and effectiveness of the chamfer optimization scheme in actual engineering applications, this application conducts comparative analysis of electromagnetic force characteristics under different current conditions; the coil excitation current is systematically parameterized from 1A to 5A, and the variation law of electromagnetic force at different operating points is deeply studied; detailed analysis results are shown in Figure 11 ;

[0171] Figure 11 The electromagnetic force contrast results before and after chamfering in the current range of 1-5A are shown; from the analysis of the current-force characteristic curve, it can be observed that under all test current conditions, the optimized structure after chamfering produces a significant positive force improvement effect, and the absolute increment increases steadily from 7.6N at 1A to 29.8N at 5A; the relative improvement rate changes in the range of 8.8%-11.0%, and the average improvement rate is about 10.3%; this result shows that the effect of chamfering optimization presents a positive correlation with the working strength of the system, and shows more significant improvement potential under high current working conditions; in addition, the electromagnetic forces under the two structure configurations present a good linear relationship with the excitation current, indicating that chamfering optimization does not change the basic electromagnetic characteristics of the system;

[0172] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not a limitation on the protection scope of the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the essence and scope of the technical solutions of the present application.

Claims

1. A method for analyzing electromagnetic performance of a permanent magnet of a simulated vibration absorber, characterized by, Comprising the following steps: S1, based on the equivalent magnetic circuit method, the equivalent magnetic circuit of the permanent magnet of the chamfered vibration absorber is established, in the equivalent magnetic circuit modeling, the distributed parameter effect before the chamfer is equivalent to a corner magnetic resistance processing; Wherein the equivalent magnetic circuit after chamfering includes: the magnetic potential of the permanent magnet after chamfering , the reluctance of the mover silicon steel part , the working air gap , the reluctance of the stator silicon steel part ; the equivalent magnetic circuit before chamfering includes: the magnetic potential of the permanent magnet before chamfering , the reluctance of the mover silicon steel part , the working air gap , the reluctance of the stator silicon steel part , the corner reluctance caused by the corner before chamfering ; The magnetic potential ratio of the corner magnetic reluctance consumption is defined as , wherein 0 <0.3, the effective magnetic potential ratio of the corner is established, wherein the effective magnetic potential of the shunt path is , and the effective magnetic potential of the main magnetic circuit is ; Definition of the equivalent reluctance correction after chamfering ; is the relative permeability of the stator; is the chamfer depth of the permanent magnet, is the Y-direction length, is the thickness of the permanent magnet in the X-direction, is the z-direction length of the stator-rotor. S2, Simplification of the equivalent magnetic circuit of the absorber permanent magnet The geometry of the corner region is simplified to an equivalent circular arc for approximation, and equivalent magnetic circuit parameters of the permanent magnet before and after chamfering are obtained, and the variation of the main magnetic flux is obtained ; According to the classical Maxwell's theory of magnetic fields, electromagnetic forces ; is the effective air gap cross-sectional area of the stator and rotor; B is the magnetic induction vector; is the vacuum permeability constant; the relative change of electromagnetic force before and after optimization is ; S3, Establishing the spatial distribution law of the magnetic field of the absorber and the mathematical model of the electromagnetic force influence by using the vector field method, comprising the following steps: The electromagnetic stress state expression of any point in the space in the magnetic static or low-frequency magnetic field environment without electric field is established, which is simplified based on a two-dimensional profile analysis model, the Z direction component is ignored in the main distribution plane X-Y of the magnetic field, and According to the definition of the stress tensor, the surface force density components of the permanent magnet are obtained as follows: ； ； obtaining the complete force density vector acting on the air gap surface ; wherein denotes the magnetic field amplitude, denotes the magnetic field inclination; denotes the force density of the magnetic field in direction on direction; is the component of the magnetic induction vector B in , direction. Definition of the direction consistency coefficient , which represents the degree of consistency of the electromagnetic force vector with the target direction. The physical meaning is the ratio of the electromagnetic force component in the Y direction to the total electromagnetic force amplitude, resulting in ； Fx refers to the force in the x direction, Fy refers to the force in the y direction, and Fz refers to the force in the z direction, is the integral symbol; wherein represents the total area of the air gap effect of interest; represents the modulus of the force density vector; S4, Establishing a unified electromagnetic performance analysis model of the absorber permanent magnet The direction consistency coefficient of electromagnetic force based on the actual situation of magnetic field distribution The calculation is performed: ； S denotes the total area of the air gap effect of interest denotes the area of the distortion region; After mathematical arrangement and simplification, we can get ; is the area of the distortion region (simulation), k is the geometry correlation coefficient (empirical), how to get Based on the foregoing magnetic flux variation analysis and force direction consistency variation analysis, the electromagnetic force size is mainly determined by the square of the magnetic flux, and the actual effective output degree of the force is reflected by the force direction consistency coefficient, to establish a definition of comprehensive electromagnetic performance index ; means the direction consistency of electromagnetic force (the above-mentioned formula symbols are related, not suddenly appear here) Further, the performance change rate is established in a linear superposition expression of the magnetic flux change effect and the force direction consistency change effect ; wherein the relative change in the electromagnetic force size ; The absolute change of the force direction consistency coefficient is: Substitute the electromagnetic force size change and the force direction consistency coefficient change into the comprehensive performance expression, Establishing a performance model for representing the geometric optimization effect of a vibration absorber permanent magnet ; Where the first term represents the contribution of the magnetic flux enhancement effect, and the second term represents the contribution of the direction consistency improvement effect; the performance model provides an analysis basis for quantitative analysis and prediction of the optimization effect of the permanent magnet chamfer.

2. The method for analyzing electromagnetic performance of a simulated vibration absorber permanent magnet according to claim 1, wherein, Equivalent magnetomotive force of permanent magnets by its residual magnetic induction and the effective length in the direction of magnetization together determine, wherein is the relative permeability of the permanent magnet material, expressed as ; Due to the magnetomotive force of the permanent magnet The main relationship is the inherent properties of the material and the overall length in the magnetization direction, and the chamfering only changes the magnetization length of the local area at the end, so the influence on the overall magnetization length is negligible, that is, the magnetomotive force before and after chamfering is basically unchanged, and ; According to the basic definition of magnetic reluctance, the equivalent magnetic reluctance of the original permanent magnet .

3. The method for analyzing electromagnetic performance of a simulated vibration absorber permanent magnet according to claim 1, wherein, The equivalent magnetic circuit parameters of the permanent magnet before and after chamfering include: Equivalent corner magnetoresistance ; chamfered front main magnetic circuit total magnetic reluctance ; chamfered front main magnetic circuit magnetic flux ; Magnetic flux in corner split flow path ; total magnetic resistance of the main magnetic circuit after chamfering ; chamfered main magnetic flux ; Change in main magnetic flux caused by chamfering ; wherein is the relative permeability of the mover, is the equivalent area of the magnetic flux in the permanent magnet; is the equivalent area of the magnetic flux in the silicon steel; then the magnetic reluctance and ; is the air gap reluctance, is the equivalent reluctance of the original permanent magnets, is the equivalent magnetomotive force of the permanent magnets.

4. The method for analyzing electromagnetic performance of a simulated vibration absorber permanent magnet according to claim 1, wherein, The electromagnetic stress state expression of any point in the space in a magnetic static or low-frequency magnetic field environment without electric field includes: Maxwell stress tensor ; Square of the magnetic induction vector module ; The body force density vector at any point in space is ; wherein is the Kronecker delta, which takes the value 1 when and 0 otherwise.

5. A method for optimizing the electromagnetic performance of a simulated vibration absorber permanent magnet, characterized by, The performance model of the geometric optimization effect of the absorber permanent magnet is used to systematically quantitatively analyze and optimize the effect of the absorber chamfering, specifically including: A, Establishing a parameterized analysis model, including setting the structure parameters of the absorber permanent magnet, including thickness, chamfer continuous change range, magnetic flux shunt coefficient, and geometric correlation coefficient; B, Based on the finite element program, a two-dimensional absorber permanent magnet simulation model is established, and on the basis of the established simulation model, parameterized simulation is performed to determine the influence law of the chamfer parameter on the key electromagnetic performance indicators; specifically: B1 Based on the integration method of Maxwell stress tensor, set the integral path along the center line position of the working air gap to obtain the magnetic flux passing through the unit depth section of the path; B2 Adjust the chamfer depth to determine the magnetic flux passing through the unit depth section of the path in different depth ranges, draw the magnetic field gradient distribution map according to the magnetic flux change, calculate the electromagnetic force vector, and select the most suitable chamfer depth range; B2 Based on B1, adjust the chamfer angle to determine the magnetic flux passing through the unit depth section of the path in different angle ranges, draw the magnetic field gradient distribution map according to the magnetic flux change, calculate the electromagnetic force vector, and select the most suitable chamfer depth; B3 Based on the depth and angle range determined in steps B1 and B2, analyze the key electromagnetic performance indicators to optimize the best scheme.

6. The method for simulating-based electromagnetic performance optimization of a vibration absorber permanent magnet according to claim 5, characterized in that, The key electromagnetic performance indicators in step B3 include the direction consistency coefficient of electromagnetic force , the comprehensive electromagnetic performance indicator, the geometric optimization performance of the vibration absorber permanent magnet, the magnetic flux enhancement effect contribution, and the sex improvement effect contribution.

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