Leaf spring and its swing arm shape determination method

Abstract

The present disclosure relates to a leaf spring and a method for determining the shape of its swing arm, the method comprising: obtaining an initial three-dimensional model of the swing arm, the swing arm thickness, the allowable fatigue stress of the selected material, and the maximum axial bearing capacity; based on the initial three-dimensional model, the swing arm thickness, the allowable fatigue stress, and the maximum axial bearing capacity, performing cyclic iterations to determine the equivalent point of action position, arm width distribution, and a new three-dimensional model of the swing arm for each iteration; until the distance between the equivalent point of action positions obtained in two adjacent iterations is less than a preset distance, the final arm width distribution of the swing arm is determined, and the shape of the swing arm is determined based on this. Thus, based on the fact that the maximum stress of each cross section of the swing arm is uniformly distributed and equal to the allowable stress, the arm width distribution is designed, and the equivalent point of action is used as a convergence condition. The arm width distribution is obtained through a cyclic iteration algorithm. The swing arm stress distribution of the leaf spring is relatively uniform, the allowable stroke is improved, the radial-axial stiffness is relatively large, and its comprehensive performance is improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of mechanical transmission mechanisms, and in particular to a leaf spring and a method for determining the shape of its swing arm. Background Art

[0002] Leaf springs, also known as flexible linear bearings, can play the dual role of radial support and axial spring at the same time. They can be used as key components of long-life, high-reliability space pulse tube refrigerators, free piston Stirling refrigerators and engines. They are conducive to meeting the strict gap sealing requirements between the piston and the cylinder, and can avoid friction caused by mutual contact. The main parameters that characterize the performance of leaf springs include axial stiffness, radial stiffness, and allowable stroke under rated life.

[0003] Leaf springs can be divided into scroll arm leaf springs and straight arm leaf springs. Straight arm leaf springs have a larger radial-axial stiffness ratio, but their use is limited due to their larger size, smaller stroke, and radial stiffness decaying too quickly with stroke. There is a negative correlation between the radial-axial stiffness ratio of the scroll arm leaf spring and the sweep angle of the spiral arm (i.e., the difference between the maximum and minimum polar angles of the center line of the spiral arm in polar coordinates). In order to obtain a larger radial-axial stiffness ratio, the sweep angle of the spiral arm of the scroll leaf spring is usually designed to be smaller. Although the radial-axial stiffness ratio of the scroll leaf spring is smaller than that of the straight arm leaf spring, its allowable stroke is larger and its overall dimensions are smaller, so it is more widely used.

[0004] As the involute sweep angle decreases, the radial-axial stiffness ratio of the vortex leaf spring increases, and at the same time, the stress also increases, and the allowable stroke decreases. Therefore, in order to further increase the allowable stroke of the vortex leaf spring and reduce the maximum stress value during axial deformation, a special vortex groove line design is required. The existing design method of the vortex arm leaf spring is to determine the shape of the leaf spring arm by designing the groove line. In this way, the maximum stress uniformity of each section of the leaf spring arm is poor, resulting in poor performance of the leaf spring. Summary of the invention

[0005] In order to solve the above technical problem or at least partially solve the above technical problem, the present disclosure provides a leaf spring and a method for determining the shape of a spiral arm thereof.

[0006] The present disclosure provides a method for determining a spiral arm shape of a leaf spring, the method comprising:

[0007] Obtain the initial three-dimensional model of the swing arm, the swing arm thickness, the allowable fatigue stress and the maximum axial bearing capacity of the selected material;

[0008] Based on the initial three-dimensional model, the thickness of the swing arm, the allowable fatigue stress and the maximum axial bearing force, a cyclic iteration is performed to determine the equivalent action point position of the swing arm, the arm width distribution and the new three-dimensional model of each iteration; the equivalent action point is the point where the additional couple is zero when the force acting on the end face of the swing arm is equivalently translated;

[0009] When the distance between the equivalent action point position obtained in the current iteration and the equivalent action point position obtained in the previous iteration is less than a preset distance, the arm width distribution obtained in the current iteration is determined as the arm width distribution of the spiral arm;

[0010] Based on the determined arm width distribution, a spiral arm shape is determined.

[0011] In some embodiments, obtaining an initial stereoscopic model of the spiral arm includes:

[0012] Determining the centerline sweep angle of the spiral arm and the outer diameter within the flexible region;

[0013] The initial three-dimensional model is determined based on the centerline sweep angle and the inner outer diameter of the flexible area in combination with the three-dimensional model determined by the shape factor method.

[0014] In some embodiments, based on the initial three-dimensional model, the thickness of the spiral arm, the allowable fatigue stress and the maximum axial bearing force, a cyclic iteration is performed to determine the equivalent action point position, arm width distribution and new three-dimensional model of the spiral arm in each iteration, including:

[0015] Based on the initial three-dimensional model, determining the position of the equivalent action point;

[0016] When the distance between the current equivalent action point position and the previous equivalent action point position is equal to or greater than a preset distance, determining the arm width distribution based on multiple cross sections of the initial three-dimensional model, the equivalent action point position, the maximum axial bearing force and the allowable fatigue stress;

[0017] Obtaining the center line of the initial three-dimensional model;

[0018] Based on the arm width distribution, the center line and the spiral arm thickness, a new three-dimensional model is determined, and the above steps are repeated.

[0019] In some embodiments, determining the equivalent action point position based on the initial three-dimensional model includes:

[0020] Based on the three-dimensional model, determining the force condition of the end surface of the swing arm;

[0021] Obtain the calculation formula of the end face center coordinates and the equivalent action point coordinates;

[0022] Determine the position of the equivalent action point based on the end face force condition, the end face center coordinates and the equivalent action point coordinate calculation formula;

[0023] The calculation formula of the equivalent action point coordinates is:

[0024]

[0025] In the formula, (x i ,y i ) is the coordinate of the center position of the i-th section, such as the coordinate of the center of the end face; M x 、M y are the moments about the x direction and the y direction respectively, and F is the axial force, both of which represent the force on the end surface; among which, the x direction and the y direction are two mutually perpendicular directions in the plane of the leaf spring respectively.

[0026] In some embodiments, determining a new three-dimensional model based on the arm width distribution, the center line and the spiral arm thickness includes:

[0027] Determining a planar shape of the spiral arm based on the arm width distribution and the center line;

[0028] The new three-dimensional model is determined based on the planar shape of the spiral arm and the thickness.

[0029] In some embodiments, determining the planar shape of the spiral arm based on the arm width distribution and the center line includes:

[0030] Determining edge line point coordinates based on the center line point coordinates and the arm width distribution;

[0031] Based on the edge line point coordinates, a closed continuous curve is generated using an interpolation method to determine the planar shape of the spiral arm.

[0032] The present disclosure also provides a leaf spring, wherein the width of a spiral arm of the leaf spring is determined by any of the above methods.

[0033] In some embodiments, the arm width distribution of the spiral arm satisfies:

[0034] Solving the maximum normal stress expression of any cross section of the spiral arm, the numerical solution of the arm width is the arm width distribution; the maximum normal stress expression of any cross section of the arm is:

[0035]

[0036] Where F is the axial force of the spiral arm, h is the thickness of the spiral arm, b is the cross-sectional width of the spiral arm, and R c R is the radius of curvature of the center line of the spiral arm at the cross section, ie is the radius of curvature of the inner edge of the spiral arm at the cross section (approximately equal to ); is the bending section coefficient of the rectangular section; is the torsional section coefficient of the rectangular cross section; It is the correction factor of shear stress caused by torsion of curved arm beam relative to that of straight arm beam.

[0037] In some embodiments, the spiral arm is a one-piece flexible sheet.

[0038] In some embodiments, the root of the spiral arm of the leaf spring is clamped and fixed by a clamping plate and a gasket.

[0039] Compared with the prior art, the technical solution provided by the embodiments of the present disclosure has the following advantages:

[0040] The method for determining the shape of the spiral arm of a leaf spring provided in the embodiment of the present disclosure designs the arm width distribution based on the fact that the maximum stress in each cross section of the spiral arm is uniformly distributed and equal to the allowable fatigue stress (i.e., stress demand), and uses the equivalent point of action as the convergence condition. After a cyclic iterative algorithm, the arm width distribution is obtained, so that the stress distribution of the spiral arm of the leaf spring is more uniform, the allowable stroke is improved, the radial axis stiffness is relatively large, and it is beneficial to improve the performance of the leaf spring. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0043] Figure 1 A schematic diagram of a flow chart of a method for determining a spiral arm shape according to an embodiment of the present disclosure;

[0044] Figure 2 It is an internal force analysis diagram of a cross section perpendicular to the center line of the swing arm according to an embodiment of the present disclosure;

[0045] Figure 3 A schematic diagram of a cross-sectional internal force simulation result of an embodiment of the present disclosure;

[0046] Figure 4 A schematic diagram of equivalent action points of each cross section along a spiral arm according to an embodiment of the present disclosure;

[0047] Figure 5 A schematic diagram of a trend of the equivalent action point position changing with the sweep angle of the spiral arm according to an embodiment of the present disclosure;

[0048] Figure 6 A schematic diagram of a distance from an equivalent action point to a rotation center changing with a sweep angle of a spiral arm according to an embodiment of the present disclosure;

[0049] Figure 7 is a schematic diagram of a three-dimensional model of a rotary arm according to an embodiment of the present disclosure;

[0050] Figure 8 A schematic flow chart of another method for determining the shape of a spiral arm according to an embodiment of the present disclosure;

[0051] Fig. 9 A schematic diagram of a method for obtaining a centerline of a spiral arm according to an embodiment of the present disclosure;

[0052] Fig.10 is a first round of iterative arm width distribution curve of an embodiment of the present disclosure;

[0053] Fig.11 It is a schematic diagram of constructing a spiral arm shape based on the arm width according to an embodiment of the present disclosure;

[0054] Fig.12 A schematic diagram of the process of deformation of a spiral arm and movement of the position of an equivalent action point in the iterative step of an embodiment of the present disclosure;

[0055] Fig.13 A schematic diagram of an iterative convergence indicator change according to an embodiment of the present disclosure;

[0056] Fig.14 A schematic diagram of stress distribution cloud diagram comparison according to an embodiment of the present disclosure;

[0057] Fig.15 It is a schematic diagram of a fixing method of a leaf spring according to an embodiment of the present disclosure;

[0058] Fig.16 This is a physical schematic diagram of a leaf spring according to an embodiment of the present disclosure;

[0059] Fig.17 A schematic diagram of stress distribution of a leaf spring of an embodiment of the present disclosure when the axial displacement is 5 mm;

[0060] Fig.18 It is a schematic structural diagram of a spiral leaf spring of equal arm width with a spiral arm sweep angle of 310° according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0061] In order to more clearly understand the above-mentioned objectives, features and advantages of the present disclosure, the scheme of the present disclosure will be further described below. It should be noted that the embodiments of the present disclosure and the features in the embodiments can be combined with each other without conflict.

[0062] In the following description, many specific details are set forth to facilitate a full understanding of the present disclosure, but the present disclosure may also be implemented in other ways different from those described herein; it is obvious that the embodiments in the specification are only part of the embodiments of the present disclosure, rather than all of the embodiments.

[0063] The method for determining the shape of the leaf spring arm provided in the embodiment of the present disclosure can be applied to an extended root fixed structure. The method introduces the concept of an equivalent effective point of action of the leaf spring arm (i.e., an equivalent point of action), and exemplarily derives an expression for the maximum normal stress of the arm section, which is applied to the iteration process of the arm width distribution. Finite element simulation analysis shows that for a leaf spring whose arm width distribution is determined by the arm shape iteration method, the maximum normal stress of each section is more evenly distributed along the arm, and the fluctuation compared with the stress design target does not exceed 3%, which is beneficial to improving the performance of the leaf spring.

[0064] Combine the following Figure 1-Figure 18 , the leaf spring and the method for determining the shape of the spiral arm thereof provided in the embodiment of the present disclosure are exemplarily described.

[0065] Figure 1 FIG. 1 is a flow chart of a method for determining a spiral arm shape according to an embodiment of the present disclosure. Figure 1 , the method may include:

[0066] S101. Obtain an initial three-dimensional model of the swing arm, the swing arm thickness, the allowable fatigue stress and the maximum axial bearing capacity of the selected material.

[0067] Among them, the initial three-dimensional model is the shape of the spiral arm in the three-dimensional space, which is the initial iterative model in the subsequent iterative process; the thickness of the spiral arm is the dimension of the spiral arm in the direction perpendicular to the plane in which it is located, the allowable fatigue stress of the selected material can also be called the required stress, and the maximum axial bearing capacity is equal to the product of the allowable stroke and the axial stiffness.

[0068] This step provides basic data for subsequent loop iterations.

[0069] S102. Based on the initial three-dimensional model, the thickness of the swing arm, the allowable fatigue stress and the maximum axial bearing capacity, a cyclic iteration is performed to determine the equivalent action point position, the arm width distribution and the new three-dimensional model of the swing arm in each iteration.

[0070] The equivalent action point is the point where the additional couple is zero when the force acting on the end face of the spiral arm is equivalently translated, which is described in detail below. The spiral arm thickness and allowable fatigue stress are constants during the cyclic iteration process.

[0071] In this step, based on the three-dimensional model, the thickness of the spiral arm, the allowable fatigue stress and the maximum axial bearing capacity, the position of the equivalent point of action (hereinafter referred to as "equivalent point of action") can be determined, and then the arm width distribution can be determined, and then a new three-dimensional model can be determined; based on this, the position of the equivalent point of action can be determined, and then the arm width distribution can be determined, and then a new three-dimensional model can be determined; and this cycle can be repeated.

[0072] S103, until the distance between the equivalent action point position obtained in the current iteration and the equivalent action point position obtained in the previous iteration is less than a preset distance, determining the arm width distribution obtained in the current iteration as the arm width distribution of the spiral arm.

[0073] The equivalent action point position approaches a certain point near the rotation center, and thus the equivalent action point position can be used as a convergence indicator. Based on the above steps, if the distance between the equivalent action point positions obtained by two adjacent iterations is less than the preset distance, the iteration ends; at this time, the corresponding arm width distribution is the arm width distribution of the spiral arm.

[0074] Subsequently, based on the arm width distribution, combined with the point coordinates of the center line and the thickness of the spiral arm, the three-dimensional structure of the spiral arm can be determined.

[0075] It should be noted that the preset distance may be 0.1 mm, 0.15 mm or other preset distance values, and may be set according to the convergence condition requirements, which is not limited in the embodiments of the present disclosure.

[0076] S104. Determine the spiral arm shape based on the determined arm width distribution.

[0077] This step may include determining the three-dimensional shape of the spiral arm based on the arm width distribution determined in S103 in combination with parameters such as the center line of the spiral arm and the thickness of the spiral arm.

[0078] In the method for determining the shape of the spiral arm provided in the embodiment of the present disclosure, the arm width distribution is designed based on the stress requirement and the maximum axial load, and the equivalent action point is used as the convergence condition. After a cyclic iterative algorithm, the arm width distribution is obtained, so that the stress distribution of the spiral arm of the leaf spring is more uniform, which is beneficial to improving the performance of the leaf spring.

[0079] In some embodiments, Figure 1 Based on this, S101 may include:

[0080] Determine the centerline sweep angle of the arm and the outer diameter within the flexible zone;

[0081] Based on the centerline sweep angle and the outer diameter in the flexible area, combined with the three-dimensional model determined by the shape factor method, the initial three-dimensional model of the spiral arm is determined.

[0082] Among them, the shape factor method changes the shape of the spiral arm by modifying the involute equation and adding a correction value with the first and last positions changing to 0 and a sinusoidal change in the middle. The shape factor f describes the degree of widening. The larger the f value, the smaller the narrowest width of the spiral arm. The shape factor method has only one coefficient f that needs to be adjusted, which makes the optimization simpler and can fix the starting and end points of the groove line. Therefore, the shape factor method only changes the shape of the vortex groove and does not translate the vortex groove line, but its style is close to the eccentric involute, so it is also called an eccentric vortex leaf spring. On this basis, the method of this embodiment can further optimize the arm width distribution of the spiral arm to reduce the maximum stress of the leaf spring during axial deformation, obtain a leaf spring with more uniform stress, and thus effectively increase the allowable stroke of the leaf spring.

[0083] In some embodiments, Figure 1 Based on this, S102 may include:

[0084] Step 1: Based on the initial three-dimensional model, determine the position of the equivalent action point.

[0085] Exemplarily, this step may include using Ansys software to simulate the force and moment of the end face in the xyz direction; on this basis, combined with the end face center coordinates, the equivalent action point coordinate calculation formula is used to calculate the position of the equivalent action point.

[0086] In some embodiments, this step may include:

[0087] Based on the initial three-dimensional model, determine the end force of the swing arm;

[0088] Obtain the calculation formula of the end face center coordinates and the equivalent action point coordinates;

[0089] The position of the equivalent action point is determined based on the end face force condition, the end face center coordinates and the equivalent action point coordinate calculation formula.

[0090] Among them, the calculation formula of the equivalent action point coordinates is:

[0091]

[0092] In the formula, (x i ,y i ) is the coordinate of the center position of the i-th section, such as the coordinate of the end face center; M x 、M y are the moments about the x direction and the y direction respectively, and F is the axial force, both of which represent the force on the end surface; among which, the x direction and the y direction are two mutually perpendicular directions in the plane of the leaf spring respectively.

[0093] In this way, the position of the equivalent action point can be determined based on the initial three-dimensional model.

[0094] Step 2: When the distance between the current equivalent action point position and the previous equivalent action point position is equal to or greater than the preset distance, the arm width distribution is determined based on multiple cross-sections of the initial three-dimensional model, the equivalent action point position, the maximum axial bearing capacity and the allowable fatigue stress.

[0095] In this step, it is determined whether the distance between the equivalent action point positions obtained by two adjacent iterations is less than the preset distance. If not, the surface needs to continue to iterate. At this time, multiple sections of the three-dimensional model can be selected, and the arm width of each section can be determined in combination with the equivalent action point position, maximum axial bearing force and allowable fatigue stress, that is, the arm width distribution of the spiral arm can be determined to prepare for the subsequent determination of a new three-dimensional model.

[0096] Exemplarily, this step may include using Mathematica software to obtain a numerical solution of an inverse function based on a stress distribution formula (exemplarily described below), namely, the arm width distribution.

[0097] Step 3: Get the center line of the initial three-dimensional model.

[0098] In this step, the center line of the spiral arm is determined based on the stereo model used in the current iteration, in preparation for the subsequent determination of a new stereo model.

[0099] Step 4: Determine a new three-dimensional model based on the arm width distribution, center line and spiral arm thickness, and repeat the above steps.

[0100] That is, based on the arm width distribution, center line and thickness determined in the previous steps, a new three-dimensional model is determined, and steps one to four are repeated based on the new three-dimensional model.

[0101] In some embodiments, this step may include:

[0102] Determine the planar shape of the spiral arm based on the arm width distribution and center line;

[0103] A new three-dimensional model is determined based on the plane shape and thickness of the spiral arms.

[0104] Exemplarily, it may include using Mathematica software to perform spline interpolation drawing of discrete points to obtain edge-dense discrete points; importing the edge-dense discrete points into an Excel table, and then importing them into Inventor drawing software, using spline interpolation to form a closed continuous curve, that is, generating a plane sketch, and obtaining the plane shape of the spiral arm.

[0105] Afterwards, using Inventor drawing software, the plane sketch is stretched according to the thickness to obtain a new three-dimensional model.

[0106] In some embodiments, determining the planar shape of the spiral arm based on the arm width distribution and the center line may include:

[0107] Based on the point coordinates of the center line and the arm width distribution, the point coordinates of the edge line are determined;

[0108] Based on the coordinates of the edge line points, a closed continuous curve is generated using the interpolation method to determine the plane shape of the spiral arm. Fig.11 Describe in detail.

[0109] Let's first combine Figure 2-Figure 7 , the physical principles on which the embodiments of the present disclosure are based are exemplarily described.

[0110] Figure 2 This is an internal force analysis diagram of a cross section perpendicular to the centerline of the spiral arm according to an embodiment of the present disclosure, showing the internal force of the cross section perpendicular to the centerline of the spiral arm in the three-dimensional model of the spiral arm; wherein 011 represents the internal force analysis, and 012 represents the simplified internal analysis. Figure 2 , the internal force borne by any cross section of the spiral arm during axial deformation can be decomposed into three-direction component forces and three-direction component moments. A flow coordinate system uvw is established along the centerline of the spiral arm, with the centerline direction as w and the downward direction perpendicular to the leaf spring plane as v. Then the cross-sectional force can be decomposed into the force Q perpendicular to the plane where the leaf spring is located. v , and the in-plane force Q u and Q w The section moment can be decomposed into the moment in the plane of the leaf spring (bending moment M u and torque M w ), and the moment M perpendicular to the plane of the leaf spring v .

[0111] Figure 3 This is a schematic diagram of a cross-sectional internal force simulation result of an embodiment of the present disclosure, showing the Ansys simulation analysis result of the plane internal force of the leaf spring arm cross section during axial deformation; wherein 021 represents the simulation result of the cross-sectional internal force, and 022 represents the simulation result of the cross-sectional internal moment. Figure 3 , the simulation results are given in the form of a fixed coordinate system xyz, the direction perpendicular to the leaf spring plane downward is z, and the xy plane coincides with the uw plane. Figure 2 , the internal force conversion relationship is:

[0112]

[0113] in, It is the acute angle between the x-axis and the u-axis. Figure 3 It can be seen that the plane internal force component Q u and Q w and the moment M perpendicular to the plane of the leaf spring v The component is almost 0. Among them, Q u and Q w Q v4 orders of magnitude lower, M v Also better than M u and M w Based on this, the model can be simplified, assuming that the spring arm cross-sectional force only has a component Q perpendicular to the plane of the leaf spring v The spring arm section moment only has the in-plane bending moment component M u and torque component M w , the simplified internal force components are shown as 012 in 2.

[0114] According to the principle of force translation, the force acting on an object can be equivalently translated to any point on the object, but a couple is required, and the moment vector of the couple is equal to the moment vector of the original force on the translation point. Based on this, for the spiral arm, the end face force Q v and the bending moment M on the end face u and torque M w The resultant moment of can be equivalent to a force acting on point 0, for example Figure 4 , this point can be defined as the equivalent force action point, that is, the equivalent action point, or simply the action point. The additional force couple at this point is zero. In this way, the force on the swing arm can be simplified to the equivalent force acting on this point. The calculation formula for the equivalent action point position is:

[0115]

[0116] Among them, (x i ,y i ) is the coordinate of the center position of the i-th section; M x 、M y are the moments about the x and y directions respectively, and F is the cross-sectional force, i.e. the axial force.

[0117] Figure 4 Schematic diagram of equivalent action points along each cross section of a spiral arm according to an embodiment of the present disclosure, showing the force and moment along each cross section of the spiral arm obtained by analyzing a spiral arm as an example. Figure 4 It can be seen that from No. 1 to No. 45, the equivalent action points of each section coincide with point 0, that is, (-2.51, 1.80); and the equivalent force of each section is equal in magnitude and direction. After verification, not only the section perpendicular to the center line of the spiral arm, but also any section perpendicular to the plane of the leaf spring conforms to this rule.

[0118] Exemplarily, Table 1 shows the change in the position of the equivalent force action point under different displacements. Taking section 1 as an example, when the axial displacements are 5 mm, 10 mm and 15 mm, the calculated displacement vector of the equivalent force action point remains unchanged, that is, the position of the equivalent force action point is always point 0, which shows that the position of the equivalent action point is not related to the degree of axial deformation.

[0119] Table 11 Coordinates of equivalent action points under different displacements

[0120]

[0121] Figure 5 The present invention is a schematic diagram of the change trend of the position of the equivalent effect point of the embodiment of the present invention with the sweep angle of the spiral arm (i.e., the sweep angle of the center line of the spiral arm), which shows the change trajectory of the equivalent effect point of three spiral arms of equal arm width with the sweep angle of the spiral arm. Assume that the equation of the center line of the three spiral arms is R=35-kθ. Among them, R is the center line radius (mm), θ is the spiral arm vortex angle (rad); k is the vortex coefficient (mm / rad), and the values ​​of k of the three spiral arms are 0, 5 / π and 10 / π respectively, among which the spiral arm with k of 0 is the arc arm, and the other two are vortex arms. Based on this, the change trajectory of the equivalent effect points of the three spiral arms is obtained by simulation with Ansys software. When θ is greater than 2π, it is assumed that the arc arms do not overlap and are approximately spiral column springs, and the trajectory of their action points is obtained by theoretical calculation alone; as the sweep angle θ of the spiral arm increases, the position of the equivalent effect point of action is closer to the rotation center of the center line of the spiral arm. After the sweep angle is greater than 2π, the activity trajectory of the equivalent effect point of action is nested elliptical, and finally approaches a point near the rotation center, such as Figure 5 Shown in the enlarged image on the right.

[0122] Figure 6 This is a schematic diagram of the variation trend of the distance from the equivalent action point to the rotation center with the sweep angle of the spiral arm in an embodiment of the present disclosure, showing the variation law of the distance from the equivalent action point to the rotation center with the sweep angle of the spiral arm. The horizontal axis represents the sweep angle of the spiral arm in degrees, and the vertical axis represents the function X / r of the position of the action point, where r is the distance from the outer end point of the spiral arm centerline to the rotation center, X is the distance between the action point and the rotation center, and X / r describes the function of the position of the action point. Figure 6 It can be seen that X / r changes approximately linearly in the spiral arm sweep angle θ interval [0,2π], fluctuates in a small range in the spiral arm sweep angle θ interval [2π,∞), and eventually approaches a number close to 0 in the range of (0~0.2) as the spiral arm sweep angle increases. Therefore, the equivalent force action point approaches a point near the rotation center, showing a convergent state.

[0123] Among them, any shape change, such as a change in arm width distribution, will affect the position of the equivalent force point, but the position of the equivalent force point remains almost unchanged when the arm width distribution changes proportionally. However, when designing the spiral arm, in order to obtain a uniform stress distribution, the adjustment of the spiral arm width distribution is not a proportional change, but is adjusted according to the unevenness of the stress, that is, the part with high stress becomes wider and the part with low stress becomes narrower. After the adjustment, the position of the equivalent force point will change.

[0124] Based on this, the disclosed embodiment proposes an iterative design method for the width distribution of the leaf spring swing arm to obtain a leaf spring swing arm shape with a more uniform stress distribution. Among them, when the centerline shape and axial stiffness of the swing arm are constant, the swing arm shape with uniform distribution of maximum stress in each section only exists, that is, there will not be two or more swing arm shapes that simultaneously satisfy the uniform stress distribution. If the maximum stress of each section is optimized to be uniformly distributed, that is, the maximum stress value of the swing arm is minimum when the axial displacement is constant, the allowable stroke of the swing arm can be optimized to the maximum. Based on this, when the centerline shape and axial stiffness are constant, the width of each section of the swing arm can be adjusted to achieve the purpose of uniform and minimum stress, that is, a spring swing arm shape with uniform stress distribution can be obtained through an iterative design algorithm for the width distribution of the swing arm of a curved beam arm leaf spring.

[0125] Figure 7 Schematic diagram of a three-dimensional model of a rotary arm according to an embodiment of the present disclosure. Figure 7 After the equivalent force action point is determined, the internal force distribution of the cross section can be determined, that is: the cross section bending moment M u is FLsinα, torque M w is FLcosα; where L is the length of the displacement vector at the point of action, and α is the acute angle between the displacement vector at the point of action and the cross section.

[0126] The normalized equivalent stress expression of any infinitesimal element in the flow coordinate system uvw is:

[0127]

[0128] Among them, σ u , σ v , σ w are the normal stresses in the u, v, and w directions within the microelement respectively; τ uv , τ vw , τ wu are the shear stresses in the microelement plane in the directions of v, w, and u, respectively, and are related to τ vu , τ wv , τ uw The maximum stress occurs near the inner edges of the upper and lower surfaces, where the normal stress and shear stress of the cross section reach their maximum values ​​at the same time. Substituting the bending moment M into the above formula u The maximum normal stress (σ u ) max and torque M w The maximum shear stress (τ uw ) max , ignoring other minor stress components and ignoring the warping stress caused by the fixed constraint near the root, the maximum normal stress expression of any section of the spiral arm can be obtained:

[0129]

[0130] Where F is the axial force of the spiral arm, h is the thickness of the spiral arm, b is the cross-sectional width of the spiral arm, and R c R is the radius of curvature of the center line of the spiral arm at the cross section, ie is the radius of curvature of the inner edge of the spiral arm at the cross section (approximately equal to ); is the bending section coefficient of the rectangular section; is the torsional section coefficient of the rectangular cross section; It is the correction factor of shear stress caused by torsion of curved arm beam relative to that of straight arm beam.

[0131] For a spiral arm with uneven stress, it is difficult to achieve uniform stress distribution if the arm width distribution is simply adjusted by the idea of ​​widening the area with high stress and narrowing the area with low stress; this is because the position of the point of action of the equivalent force will also change after the shape adjustment, that is, if the width is adjusted at one place, the stress at other positions of the spiral arm will also change. From the above formula, it can be seen that when the equivalent force and the position of its point of action are known, the maximum stress distribution of each section along the spiral arm can be obtained. Conversely, if the required maximum allowable fatigue stress value is known, a reasonable arm width distribution can be obtained, and the spiral arm width b can be calculated. In the above stress expression, when solving the arm width distribution, except for the cross-sectional arm width b, which is an unknown quantity, all others are known quantities. Therefore, the mathematical calculation software Mathematica can be used to obtain the numerical solution of the arm width b at each position on the center line of the spiral arm.

[0132] The spiral arm shape is constructed based on the center line and the calculated arm width distribution to form its three-dimensional model. However, after the width b is optimized, the shape of the spiral arm changes, and the actual equivalent action point position is also offset. Therefore, the arm width distribution is recalculated based on the new equivalent action point position, and a new three-dimensional model of the spiral arm is constructed. This iteration is repeated until the equivalent action point position changes by no more than a preset distance, for example, 0.1 mm. After verification, the change in the equivalent action point position becomes smaller and smaller, and finally approaches a point, which confirms the above statement that "the spiral arm shape with uniform distribution of maximum stress in each section exists uniquely".

[0133] Figure 8 FIG. 1 is a flow chart of another method for determining the shape of a spiral arm according to an embodiment of the present disclosure, showing the process from the beginning to the end of the iteration. Figure 8 , the iterative process may include:

[0134] S200, start.

[0135] In the following, the optimization design of a three-spiral curved beam leaf spring with a swing arm inner diameter of 15 mm, an outer diameter of 65 mm, and a swing arm sweep angle of 240° (the corresponding groove line sweep angle is 360°) is taken as an example to introduce the specific process of the swing arm shape iterative design algorithm.

[0136] S201. Extract the three-dimensional model of the spiral arm designed by the shape factor method, determine its center line, thickness, end face center coordinates, end face force conditions, and maximum axial bearing capacity; or iterate from an equal-arm-width arc arm model.

[0137] Among them, starting the iteration process from a starting point with a higher degree of optimization can reduce the number of iteration steps, so the shape factor method optimization result can be selected as the iteration starting point. Compared with the shape factor method, if the equal arm width arc spiral arm is used as the iteration starting point, although the final result after the iteration is completed must be the same, the number of iteration steps will increase.

[0138] For example, Fig. 9 FIG. 1 is a schematic diagram of a method for obtaining the centerline of a spiral arm according to an embodiment of the present disclosure, showing a spiral arm optimized by the shape factor method. Fig. 9 The sweep angle of the groove line is 360°, and the optimal shape factor is f=0.08. The center line of the spiral arm can be extracted by writing a program using Mathematica software.

[0139] For example, 15 points can be taken on average on the outer edge of the spiral arm to find the point closest to the corresponding inner edge. The midpoint interpolation curve between the two is the centerline of the spiral arm, and the effective spiral arm sweep angle is 240°. In the process of optimizing the arm width distribution to make the spiral arm stress uniform, the centerline will always be kept fixed.

[0140] S202: Calculate the equivalent action point position of the three-dimensional model.

[0141] For example, the result obtained by the shape factor method is used as the initial design, and the force, moment and displacement of the action point of the outer fixed end face when the axial displacement is 5 mm are calculated using Ansys finite element software. The results are shown in Table 2.

[0142] Table 2 Calculation table of displacement vector of action point

[0143]

[0144] Based on this, the equivalent action point of the spiral arm can be calculated, which is (-8.07mm, 4.68mm).

[0145] Table 3 Calculation table of equivalent action point position

[0146]

[0147] S203: Determine whether the distance between the current equivalent action point position and the previous equivalent action point position is less than a preset distance.

[0148] If (Y), the iteration ends, that is, S207.

[0149] If not (N), the arm width distribution is determined based on the equivalent action point position, a new three-dimensional model is obtained, and the process returns to S202, including executing:

[0150] S204. Select cross sections densely, calculate the arm width of each cross section based on the performance requirements such as the position of the equivalent action point, the maximum axial bearing capacity (allowable stroke × axial stiffness), allowable fatigue stress and life, and obtain the arm width distribution.

[0151] The density of cross-section selection may be set based on the requirements of the shape determination method, which is not limited in the embodiments of the present disclosure.

[0152] For example, the arm width distribution of the leaf spring spiral arm is obtained from the first wheel equivalent action point (-8.07mm, 4.68mm), such as Fig.10 As shown. For example, Fig.10 This is a first-round iterative arm width distribution curve of an embodiment of the present disclosure, where the horizontal axis represents the center angle of the interface, in degrees (°), and the vertical axis represents the arm width, in millimeters (mm).

[0153] S205. Based on the point coordinates of the center line and the arm width distribution, the edge line point coordinates are calculated and the plane sketch is constructed using the interpolation spline curve.

[0154] For example, Fig.11 FIG. 1 is a schematic diagram of constructing a spiral arm shape based on the arm width according to an embodiment of the present disclosure. Fig.11 , points can be densely taken on the center line of the spiral arm, and a series of point coordinates of the inner and outer edge lines can be obtained according to the center line coordinates and the arm width distribution; the points of the inner and outer edge lines are respectively connected by spline interpolation curves to obtain the inner and outer edge lines of the spiral arm. The specific operation steps may include:

[0155] Step 1: Draw a tangent line l1 through point A to the center line.

[0156] Step 2: Draw a perpendicular line to the tangent line l1 through point A, which is the point l2 where the cross section is located.

[0157] Step 3: Select points B and C on straight line l2 so that the lengths of AC and BC are both half the arm width.

[0158] Step 4: Use the spline interpolation curve to obtain the inner and outer edges of the spiral arm, that is, to determine the plane sketch.

[0159] S206. Based on the thickness, the plane sketch is stretched to form a new three-dimensional model.

[0160] Then, the process returns to S202 and enters a loop iteration process until the distance between the equivalent action point positions obtained by two adjacent iterations is less than a preset distance.

[0161] Based on the above steps, a new three-dimensional model is constructed, and the corresponding equivalent force action point of the newly constructed spiral arm (i.e., the actual action point, point 1) is moved compared with the design arm width action point (i.e., point 0), and the moved point is (-9.51mm, 4.32mm). Based on this, iterative calculations will be performed.

[0162] That is: take point 1 as the action point again, calculate the new arm width distribution, and construct the spiral arm action point position to get point 2 (-10.60mm, 4.01mm); then take point 2 as the action point, calculate the new arm width distribution, and construct the new spiral arm action point position; repeat this process to calculate a series of equivalent force action points, and the distance between adjacent equivalent force action points will become smaller and smaller, such as Fig.12 In combination with the above, illustratively, the action point gradually approaches point 9 (-12.40 mm, 1.55 mm).

[0163] Fig.13 This is a schematic diagram of the change of iterative convergence index of an embodiment of the present disclosure, showing the change of the iterative moving distance of the equivalent force action point before and after two times; the horizontal axis represents the point number, and the vertical axis represents the distance between the action point and the previous action point, in millimeters (mm). Fig.13 When the iteration reaches the 9th round, the distance between the action point 9 and the action point 8 is only 0.05mm, which is less than the iteration termination condition of 0.1mm. Continuing the iteration will not change the shape of the spiral arm much. Taking this point as the equivalent force action point position, the arm width distribution is calculated according to the formula, or the numerical solution of the arm width distribution is obtained through the software contact. The corresponding spiral arm has a uniform stress distribution and is equal to the design allowable fatigue stress.

[0164] For example, Fig.14 031 represents the stress distribution simulation result before optimization, and 032 represents the stress distribution simulation result after optimization. Fig.14 Under the same 5mm stroke, the maximum stress of the optimized swing arm is reduced from the initial 312MPa to 266MPa, a decrease of 14.7%; the corresponding allowable stroke is increased from 6.4mm to 7.5mm, an increase of 17.2%; and the stress distribution is more uniform, the stress variation range is 260MPa±6MPa at 5mm stroke, and the fluctuation does not exceed 3%; the axial stiffness of the swing arm before optimization is 2.1N / mm, and the radial stiffness is 582N / mm. The axial stiffness and radial stiffness after optimization are 2.0N / mm and 574N / mm respectively. The axial stiffness and radial stiffness before and after optimization are basically unchanged.

[0165] The present disclosure also provides a leaf spring, the shape of the spiral arm of the leaf spring is determined by any of the above methods. Therefore, the maximum stress of each cross section of the leaf spring is evenly distributed along the spiral arm, the stress is uniform and minimum during axial deformation, and the allowable stroke can reach the maximum value; under the same design stroke, the leaf spring has the maximum diameter-to-axis stiffness ratio and the smallest size diameter.

[0166] In some embodiments, the arm width distribution of the spiral arm satisfies:

[0167] Solving the maximum normal stress expression of any cross section of the spiral arm, the numerical solution of the arm width is the arm width distribution; the maximum normal stress expression of any cross section of the arm is:

[0168]

[0169] Where F is the axial force of the spiral arm, h is the thickness of the spiral arm, b is the cross-sectional width of the spiral arm, and R c R is the radius of curvature of the center line of the spiral arm at the cross section, ie is the radius of curvature of the inner edge of the spiral arm at the cross section (approximately equal to ); is the bending section coefficient of the rectangular section; is the torsional section coefficient of the rectangular cross section; It is the correction factor of shear stress caused by torsion of curved arm beam relative to that of straight arm beam.

[0170] In some embodiments, the spiral arm is a one-piece flexible sheet.

[0171] Such an arrangement, compared with the Oxford leaf spring (using multiple swing arms, which are disassembled and assembled separately, i.e., split swing arms), each swing arm installation of the split swing arm requires alignment adjustment, the assembly process is cumbersome, and the cumulative error is large, while the one-piece flexible sheet only needs to adjust the coaxiality of the mover and stator once, which is more convenient to assemble and can improve the coaxiality.

[0172] In some embodiments, Fig.15 A method of fixing a leaf spring is shown. Fig.15The component formed by the leaf spring may also include a protruding fixing structure at the root of the swing arm; the component may include a first clamping plate 310, a first leaf spring 320, a gasket 330, a second leaf spring 340 and a second clamping plate 350 arranged in sequence along the central axis direction, wherein the first clamping plate 310 and the second clamping plate 350 include corresponding inner clamping plates 311 and outer clamping plates 312, and the gasket 330 includes an inner gasket 331 corresponding to the inner clamping plate 311 and an outer gasket 332 corresponding to the outer clamping plate 312; based on this, the protruding fixing structure at the root 321 of the swing arm includes an inner clamping plate 311, an outer clamping plate 312, an inner gasket 331 and an outer gasket 332, and the root 321 of the swing arm is fixed by the inner clamping plate 311, the outer clamping plate 312 and the corresponding inner gasket 331 and outer gasket 332 according to a preset geometric relationship.

[0173] The transition from the root of the spiral arm to the fixed structure affects the travel and life of the leaf spring. Generally, a teardrop-shaped hole expansion is used to alleviate the problem of stress concentration at the root of the spiral arm. In this embodiment, the extended clamping plate structure is applied to the eccentric scroll arm leaf spring.

[0174] Specifically, the teardrop-shaped expansion hole or the general annular gasket does not impose special constraints on the root of the spiral arm. At this time, the intersection of the outer edge of the spiral arm and the fixed edge can easily cause stress concentration, so it is necessary to design an opening structure to unload stress.

[0175] The present embodiment adopts an extended structure to fix the roots of the inner and outer ends of the leaf spring arm; the extended fixed structure changes the extended angle of the arm (i.e., the angle of the centrifugal opening in the tangent angle between the center line of the arm and the fixed edge) and the two edge angles (i.e., the inner angle in the tangent angle between the inner and outer edges of the arm and the fixed edge); it can significantly reduce the concentration of root stress, so that the roots of the inner and outer edges of the arm can share the stress more evenly, and the maximum stress no longer appears at the root, but in the middle section of the arm. Therefore, there is almost no need to correct the transition line design at the root of the arm. Usually, the extended angle of the vortex leaf spring is small, and its angle range is generally 5° to 15°; while the extended fixed structure can allow the extended angle of the leaf spring to be increased, and the extended angle of the center line of the arm can be 60° to 80°.

[0176] By configuring in this way, the root of the spiral arm is fixed, so that the stress at the root of the spiral arm can be kept small, which is smaller than the maximum stress of the spiral arm, so the spiral arm is not likely to break at the root.

[0177] In some embodiments, the sweep angle θ of the center line of the spiral arm of the leaf spring satisfies: 60°≤θ≤240°; wherein the sweep angle of the center line of the spiral arm is the difference between the maximum polar angle and the minimum polar angle of the center line of the spiral arm in polar coordinates.

[0178] Such an arrangement can increase the radial-axial stiffness ratio, that is, the radial supporting capacity can be increased under the condition of the same axial stiffness.

[0179] In some embodiments, the relationship between the inner diameter and the outer diameter of the leaf spring satisfies: 30% D1≤D2≤90% D1; wherein D2 represents the inner diameter and D1 represents the outer diameter.

[0180] With such an arrangement, a leaf spring with a large inner hole can be obtained, which is conducive to realizing a compact arrangement of the leaf spring, thereby facilitating a compact design of the motor.

[0181] For example, Fig.16 FIG. 1 is a schematic diagram of a leaf spring according to an embodiment of the present disclosure, which is a leaf spring formed based on the above method. The sweep angle of the spiral arm is 120°, the thickness is 0.5 mm, and the stress distribution is as follows: Fig.17 As shown. Combined Fig.16 and Fig.17 The leaf spring is a large-diameter leaf spring. The large-diameter design is to facilitate the cylinder and the inner return iron to pass through during assembly to form the double-sided support of the mover assembly. Fig.17 It can be seen that when the axial displacement is full stroke 5mm, the stress distribution of the swing arm is uniform and is within the range of 400MPa±10Mpa; the leaf spring adopts a small sweep angle design to obtain a larger radial stiffness; the leaf spring root adopts an extended clamp fixing method, and the fixing direction meets the extension angle condition of 70°. The maximum stress of the root 349MPa is less than the maximum stress of the swing arm 400MPa.

[0182] Fig.18 The structural schematic diagram of a spiral leaf spring with an equal arm width and a spiral arm sweep angle of 310° according to an embodiment of the present disclosure is used as a comparative example. The leaf spring is an equal arm width spiral leaf spring with a thickness of 1 mm, a design stroke of 5 mm, and a diameter of 70 mm.

[0183] Table 4 Stress uniformity design of curved beam arm leaf spring stiffness value table

[0184]

[0185] Table 5 Spring stiffness values ​​of equal-arm-width vortex plates with a sweep angle of 310°

[0186]

[0187] Table 4 shows the stiffness values ​​of the curved beam arm leaf spring with a sweep angle of 120°, and Table 5 shows the stiffness values ​​of the equal-arm-width vortex leaf spring with a sweep angle of 310°. It can be seen from Tables 4 and 5 that the experimental values ​​are well consistent with the simulation values. The radial-axial stiffness ratio of the curved beam arm leaf spring reaches more than 400, and the radial stiffness reaches 1350N / mm at a full stroke of 5mm. The radial-axial stiffness ratio of the vortex leaf spring is only 27, and the radial stiffness is only 129N / mm at a full stroke of 5mm. Therefore, under the premise of the same stroke and design size and stress meeting the requirements, the performance of the curved beam arm leaf spring with a sweep angle of 120° is better than that of the ordinary equal-arm-width vortex spring.

[0188] The leaf spring provided in the embodiment of the present disclosure may be a leaf spring of an extended fixed structure, and its optimal extension angle is about 60°-80°. The extended structure leaf spring fixes the root, which can significantly reduce the stress concentration at the root, reducing it by 20% to 40% compared with the ordinary eccentric involute leaf spring. The embodiment of the present disclosure proposes and applies the equivalent action point of the leaf spring spiral arm, and deduces the spiral arm stress distribution formula, which can iteratively determine the spiral arm width distribution curve with uniform stress distribution, and use it to directly construct the spiral arm shape. The above optimization results show that the axial stiffness and radial stiffness of the leaf spring with the arm width distribution determined by the above method are no more than 3% different from the leaf spring designed by the shape factor method, but the uniformity of the spiral arm stress value is significantly improved, and the stress unevenness deviation does not exceed 3%, the maximum stress value is reduced by 14.7%, and the corresponding allowable stroke is increased by 17.2%, which greatly improves the performance of the leaf spring.

[0189] The disclosed embodiment further provides a leaf spring group, which includes at least two coaxially arranged leaf springs, wherein the leaf springs are any of the leaf springs described above.

[0190] The leaf spring group can achieve the following functions: providing anti-bending moment function that a single leaf spring cannot provide. In addition to the force effect, radial force (such as gravity, magnet side suction, etc.) also has a moment effect. In view of this, a single leaf spring has almost no anti-bending moment function. However, when two leaf springs form a leaf spring group, the greater the distance between the two leaves, the stronger the anti-bending moment function of the leaf spring group.

[0191] The leaf spring assembly is particularly suitable for linear motors with large moving mass and placed horizontally, such as Stirling engines, etc.; or suitable for dynamic magnet linear motors or Stirling engines with large magnet side suction in the dynamic magnet structure.

[0192] The disclosed embodiment also provides an oscillating linear motor, which can be a Stirling engine, a refrigerator or a compressor, and the linear motor can include any of the above leaf springs, thereby facilitating the improvement of its performance. The refrigerant can be a space pulse tube refrigerator or a free piston Stirling refrigerator.

[0193] The embodiment of the present disclosure also provides a vibration reduction device, which may include any of the above leaf springs. In the vibration reduction device, the leaf spring may be used to adjust the resonant frequency of the dynamic vibration reduction device to the excitation frequency to form a dynamic vibration damper; or the leaf spring may be used to achieve a flexible connection between the vibration source and the fixed platform, which is conducive to improving the vibration reduction performance.

[0194] In other implementations, the leaf spring may also be applied to other mechanical structures, which is not limited in the embodiments of the present disclosure.

[0195] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0196] The above description is only a specific embodiment of the present disclosure, so that those skilled in the art can understand or implement the present disclosure. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure will not be limited to the embodiments described herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining the shape of a leaf spring arm, characterized in that: include: Obtain the initial three-dimensional model of the swing arm, the swing arm thickness, the allowable fatigue stress and the maximum axial bearing capacity of the selected material; Based on the initial three-dimensional model, the thickness of the swing arm, the allowable fatigue stress and the maximum axial bearing force, a cyclic iteration is performed to determine the equivalent action point position of the swing arm, the arm width distribution and the new three-dimensional model of each iteration; the equivalent action point is the point where the additional couple is zero when the force acting on the end face of the swing arm is equivalently translated; When the distance between the equivalent action point position obtained in the current iteration and the equivalent action point position obtained in the previous iteration is less than a preset distance, the arm width distribution obtained in the current iteration is determined as the arm width distribution of the spiral arm; Based on the determined arm width distribution, a spiral arm shape is determined.

2. The method according to claim 1, characterized in that The step of obtaining an initial stereoscopic model of the spiral arm comprises: Determining the centerline sweep angle of the spiral arm and the outer diameter within the flexible region; The initial three-dimensional model is determined based on the centerline sweep angle and the inner outer diameter of the flexible area in combination with the three-dimensional model determined by the shape factor method.

3. The method according to claim 1, characterized in that Based on the initial three-dimensional model, the thickness of the swing arm, the allowable fatigue stress and the maximum axial bearing force, a cyclic iteration is performed to determine the equivalent action point position, arm width distribution and a new three-dimensional model of the swing arm in each iteration, including: Based on the initial three-dimensional model, determining the position of the equivalent action point; When the distance between the current equivalent action point position and the previous equivalent action point position is equal to or greater than a preset distance, determining the arm width distribution based on multiple cross sections of the initial three-dimensional model, the equivalent action point position, the maximum axial bearing force and the allowable fatigue stress; Obtaining the center line of the initial three-dimensional model; Based on the arm width distribution, the center line and the spiral arm thickness, a new three-dimensional model is determined, and the above steps are repeated.

4. The method according to claim 3, characterized in that Based on the initial three-dimensional model, determining the position of the equivalent action point includes: Based on the initial three-dimensional model, determining the force condition of the end surface of the swing arm; Obtain the calculation formula of the end face center coordinates and the equivalent action point coordinates; Determine the position of the equivalent action point based on the end face force condition, the end face center coordinates and the equivalent action point coordinate calculation formula; The calculation formula of the equivalent action point coordinates is: In the formula, (x i ,y i ) is the coordinate of the center position of the i-th section; M x 、M y are the moments about the x direction and the y direction respectively, and F is the axial force, both of which represent the force on the end surface; among which, the x direction and the y direction are two mutually perpendicular directions in the plane of the leaf spring respectively.

5. The method according to claim 3, characterized in that: Based on the arm width distribution, the center line and the spiral arm thickness, a new three-dimensional model is determined, including: Determining a planar shape of the spiral arm based on the arm width distribution and the center line; The new three-dimensional model is determined based on the planar shape of the spiral arm and the thickness of the spiral arm.

6. The method according to claim 5, characterized in that Based on the arm width distribution and the center line, determining the planar shape of the spiral arm includes: Determining edge line point coordinates based on the center line point coordinates and the arm width distribution; Based on the edge line point coordinates, a closed continuous curve is generated using an interpolation method to determine the planar shape of the spiral arm.

7. A leaf spring, characterized in that: The shape of the spiral arm of the leaf spring is determined by the method described in any one of claims 1-6.

8. The leaf spring according to claim 7, characterized in that The arm width distribution of the spiral arm satisfies: Solving the maximum normal stress expression of any cross section of the spiral arm, the numerical solution of the arm width is the arm width distribution; the maximum normal stress expression of any cross section of the arm is: Where F is the axial force of the spiral arm, h is the thickness of the spiral arm, b is the cross-sectional width of the spiral arm, and R c R is the radius of curvature of the center line of the spiral arm at the cross section, ie is the radius of curvature of the inner edge of the spiral arm at the section; FL sin α is the section bending moment; is the bending section coefficient of the rectangular section; is the torsional section coefficient of the rectangular cross section; It is the correction factor of shear stress caused by torsion of curved arm beam relative to that of straight arm beam.

9. The leaf spring according to claim 7, characterized in that The rotary arm is an integrated flexible sheet.

10. The leaf spring according to claim 7, characterized in that The root of the spiral arm of the leaf spring is clamped and fixed by a clamping plate and a gasket.

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