A Design Method for the Folding Spring of a One-Way Coupling

Abstract

The present invention relates to a design method for a one-way coupling folding spring. By adopting this method, the directivity of the selection of spring structure parameters can be improved, and the overall design speed of the one-way coupling folding spring can be accelerated. In order to design the one-way coupling folding spring, the present invention calculates the stiffness of the folding spring by using the energy method, then conducts the selection calculation of the folding spring based on dimensional constraints, and combines theoretical calculation and simulation calculation to improve the directivity of the selection of spring structure parameters.

Description

Technical Field

[0001] The present invention relates to a spring design method, specifically to a design method for a folding spring of a one-way coupling, and belongs to the technical field of industrial machinery. Background Art

[0002] A one-way coupling is an important component in a comprehensive hydrodynamic torque converter, which is composed of an outer ring, rollers, a compression spring, and an inner ring. A certain type of existing one-way coupling uses a helical spring as the compression spring, which results in a complex overall structure and difficult installation and maintenance. Using a folding spring as the compression spring of the one-way coupling is beneficial to simplify the structure of the outer ring, reduce the weight, and simplify the assembly process. The existing folding spring structures of one-way couplings vary, and there is a lack of a general stiffness design method; therefore, it is particularly important to study how to design a folding spring according to the working load and working length of the folding spring.

[0003] The folding spring of the one-way coupling disclosed in Patent CN 110561623A is composed of a serpentine spring portion and a linear spring portion. The front part of the serpentine spring is provided with pushing pieces with V-shaped and C-shaped cross-sections to fit the rollers. An elastic frame is installed behind the folding spring to increase the locking force of the spring. This compression spring has a complex structure and is not easy to install and maintain. The postponing pieces at the front end of the serpentine spring portion have two cross-sections and are also difficult to manufacture.

[0004] The one-way coupling disclosed in Patent US 5669476A uses a folding spring with a cage as a compression mechanism. The head end of the spring is arc-shaped, which can better fit the rollers. The tail end is a rectangular folded section for installation on the cage, and elastic locking teeth are made at the tip of the tail end to assist in locking the spring. This spring has a complex structure and it is not easy to directly calculate its compression stiffness from the theoretical analysis perspective.

[0005] The folding spring structures disclosed in Patents US5078243A and US10274026B2 are simple and have strong symmetry. The contact ends with the rollers are both bent to improve the fitting effect. However, the stiffness characteristics and stiffness calculation method of the spring during compression are not given.

[0006] In the literature "Research on the Influence of the Structure of U-shaped Leaf Springs on Stiffness and Mechanical Properties", a finite element analysis was carried out on the compression stiffness characteristics of U-shaped leaf springs, and the influence law of the structural parameters of the spring on its stiffness was studied. The research is mainly based on simulation calculations, and the mathematical relationship between the spring stiffness and the structural parameters is not deduced. At the same time, the spring structure is simple, and the conclusions obtained are not applicable to multi-section folding springs.

[0007] In the literature "Research on the Influence of the Shape of Leaf Springs on Stiffness and Mechanical Properties" and "Research on the Stiffness Characteristics of Planar W-Type Microsprings Based on MEMS Technology", in-depth research was conducted on the S-type and W-type folded springs used in microelectromechanical systems. The calculation formulas for the tensile stiffness of the two types of springs were derived using the energy method, and the tensile process was simulated and calculated by the finite element method to verify the correctness of the theoretical formulas. The folded springs studied are very similar in shape to the springs in the one-way coupling, but the springs in the microelectromechanical system are mainly in tension, and the sections of the spring do not collide with each other. Therefore, the stiffness characteristics are linear during the tensile process; while the folded spring in the one-way coupling is mainly in compression during operation. As the compression amount increases, the sections of the spring come into contact with each other, resulting in its non-linear stiffness characteristics. At the same time, the boundary conditions of the springs in the microelectromechanical system are also different from those of the folded spring in the one-way coupling. Therefore, the research conclusions cannot be directly extended to the folded spring in the one-way coupling.

[0008] From this, it can be seen that the above-mentioned methods in the prior art all have the following problems that are difficult to solve:

[0009] The shape of the folded spring in the one-way coupling was designed, but the mathematical expression between the compression stiffness of the folded spring and the structural parameters was not derived, and a general design method for the folded spring could not be formed;

[0010] The tensile stiffness of the folded spring in the microelectromechanical system was studied, and linear stiffness characteristics were obtained, but the characteristics of the sections contacting each other during compression of the folded spring were ignored, which would cause the folded spring not to have linear stiffness characteristics during compression;

[0011] The finite element analysis of the performance of the U-shaped leaf spring was carried out. Since the number of segments of the U-shaped spring is small, the research conclusions are difficult to extend to the multi-segment folded spring. Summary of the Invention

[0012] In view of this, the present invention provides a design method for a folded spring of a one-way coupling. Using this method can improve the directionality of the selection of spring structural parameters and accelerate the overall design speed of the folded spring of the one-way coupling.

[0013] The technical solution of the present invention is: a design method for a folded spring of a one-way coupling, the folded spring includes I-shaped springs at both the head and the tail and II-shaped springs located between the two I-shaped springs after being connected in sequence; the I-shaped spring has a straight segment and an arc segment at the top of the straight segment; the II-shaped spring has an inclined segment and arc segments arranged at both ends of the inclined segment;

[0014] The specific steps of this design method are as follows:

[0015] Step 1: Given the working load Fw and the working length Lw of the folded spring;

[0016] Specify its width h and number of segments n according to the installation space requirements of the folding spring;

[0017] Select the material of the folding spring, thereby obtaining the cross-sectional thickness b of the folding spring and the Young's modulus E of the folding spring material;

[0018] At this time, the structural parameters to be designed include: the straight section length of the type-I spring is L1, the inner diameter r of each arc segment in the type-I spring and the type-II spring, and the central angle α of the arc segment in the type-II spring;

[0019] Step 2: Select L1 and r as the traversal objects;

[0020] According to the installation space requirements, give the value ranges of the current traversal objects L1 and r respectively, and determine the value of α according to the installation space or empirical value of the folding spring; then traverse all combinations of L1 and r within the value ranges of the current traversal objects L1 and r at a set step size, calculate the longitudinal compression Δ generated by the contact point of the folding spring and the roller of the one-way coupling along the force direction and the stiffness coefficient k1 during free compression, and further obtain the length L0 of the folding spring in the free state;

[0021] Step 3: Determine whether the longitudinal compression Δ calculated under each combination and the length L0 of the folding spring in the free state obtained by design meet the set dimensional constraints, save the combination of the current traversal objects that meet the dimensional constraints and enter the next step. If all combinations do not meet the dimensional constraints, return to Step 2 to change the traversal object or modify the value range of the current traversal object;

[0022] Step 4: Each combination of the current traversal objects that meet the dimensional constraints, combined with the structural parameters given in Step 1, can obtain a set of feasible solutions for the folding spring structural parameters, and establish a finite element model for each set of feasible solutions; through simulation analysis, obtain the stiffness curve of the folding spring corresponding to each set of feasible solutions;

[0023] Step 5: Determine whether the stiffness curve of the folding spring corresponding to each set of feasible solutions obtained in Step 4 passes through the point (U w , Fw), where U w is the actual compression during the operation of the folding spring; if it passes through, it indicates that this set of feasible solutions meets the usage requirements of the one-way coupling; if the stiffness curves of the folding springs corresponding to all feasible solutions do not pass through the point (U w , Fw), then return to Step 2 to change the traversal object or modify the value range of the current traversal object.

[0024] As a preferred embodiment of the present invention: in the second step, L1 and α are selected as the traversal objects; the value ranges of the current traversal objects L1 and α are respectively given according to the installation space requirements, and the value of r is determined according to the installation space of the spring or empirical values; then all combinations of L1 and α are traversed within the value range at a set step size, and the longitudinal compression Δ generated by the contact point of the folding spring and the roller of the one-way coupling along the force direction and the stiffness coefficient k1 in the free compression state are calculated, and further the length L0 of the folding spring in the free state is obtained.

[0025] As a preferred embodiment of the present invention: in the second step, the following method is used to calculate the longitudinal compression Δ generated by the contact point of the folding spring and the roller of the one-way coupling along the force direction and the stiffness coefficient k1 in the free compression state:

[0026] First, make the force exerted by the roller of the one-way coupling on the first-end I-shaped spring act at the middle position of the end face, and the magnitude of the acting force is F, and F = Fw;

[0027] Then calculate the strain energy of each section of the folding spring and add them up to obtain the total strain energy V of the folding spring; then the displacement generated along the F direction at the contact point of the folding spring and the roller of the one-way coupling, that is, the longitudinal compression Δ, is:

[0028]

[0029] Furthermore, the stiffness coefficient k1 of the folding spring in the free compression state in the direction of the pressure F is:

[0030]

[0031] As a preferred embodiment of the present invention: in the second step, the following method is used to calculate the longitudinal compression Δ generated by the contact point of the folding spring and the roller of the one-way coupling along the force direction and the stiffness coefficient k1 in the free compression state:

[0032] First, make the force exerted by the roller of the one-way coupling on the first-end I-shaped spring act at the middle position of the end face, and the magnitude of the acting force is F, and F = Fw;

[0033] Then calculate the strain energy of each section of the folding spring and obtain the deformation amount of each section of the folding spring along the force direction from this, that is:

[0034]

[0035] Where: i = 1, 2, 3... n; n is the total number of sections of the folding spring, and n is a natural number greater than or equal to 3; Δ i is the longitudinal compression of the i-th section of the folding spring; V i is the strain energy of the i-th section of the folding spring, F i is the force on the i-th section of the folding spring, and the F of each sectioni The size and direction are the same as F;

[0036] Then: the longitudinal compression Δ generated at the contact point between the entire folding spring and the one-way coupling roller along the force direction is:

[0037]

[0038] The stiffness coefficient k1 of the folding spring when freely compressed in the direction of the pressure F is:

[0039]

[0040] As a preferred embodiment of the present invention: in the second step, the following method is used to calculate the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 of each section when freely compressed:

[0041] First, let the force exerted by the one-way coupling roller on the first-end I-shaped spring act at the middle position of the end face, and the magnitude of the acting force is F, F = Fw;

[0042] Then calculate the strain energy of each section in the folding spring, and thus obtain the deformation amount of each section of the folding spring along the force direction, that is:

[0043]

[0044] Where: i = 1, 2, 3... n; n is the total number of sections of the folding spring, and n is a natural number greater than or equal to 3; Δ i is the longitudinal compression of the i-th section of the folding spring; V i is the strain energy of the i-th section of the folding spring, F i is the force on the i-th section of the folding spring, and the F of each section i The size and direction are the same as F;

[0045] Then calculate the stiffness coefficient of each section of the folding spring when freely compressed in the force direction, that is:

[0046]

[0047] Where: is the stiffness coefficient of the i-th section of the folding spring when freely compressed in the direction of the pressure F;

[0048] Then: the stiffness coefficient k1 of the folding spring when freely compressed in the force direction is:

[0049]

[0050] The longitudinal compression Δ generated at the contact point between the entire folding spring and the one-way coupling roller along the force direction is:

[0051]

[0052] As a preferred embodiment of the present invention: Let the type I spring in contact with the roller of the one-way coupling be the first-section type I spring, and the total number of sections of the folding spring be n;

[0053] The strain energy V1 of the first-section type I spring is:

[0054]

[0055] Where

[0056]

[0057] In formulas (1) and (2): is the bending moment at the cross-section at a length of x on the straight section of the first-section type I spring, and the value range of x is is the bending moment at the cross-section at a central angle of θ in the arc section of the first-section type I spring, and the value range of θ is I is the cross-sectional moment of inertia of the first-section type I spring;

[0058] The strain energy of the middle n - 2 section II type springs is:

[0059] Number the folding spring sequentially from the first end to the last end, and let the strain energy of the II type spring located in the i-th section be:

[0060]

[0061] Wherein:

[0062] In formulas (3) and (4): i = 2, 3,..., n - 1; the value range of γ is [0, α];

[0063] When i is odd, the "±" takes the plus sign, is the bending moment at the cross-section at a central angle of γ in the lower arc section of the II type spring 3 located in the i-th section, is the bending moment at the cross-section at a central angle of γ in the upper arc section of the II type spring located in the i-th section;

[0064] When i is even, the "±" takes the minus sign, is the bending moment at the cross-section at a central angle of γ in the upper arc section of the II type spring located in the i-th section, is the bending moment at the cross-section at a central angle of γ in the lower arc section of the II type spring located in the i-th section;

[0065] is the bending moment at a length of y on the inclined section of the II type spring located in the i-th section, and the value range of y is [0, L2];

[0066] T i-1 The reaction force of the type-II spring located in the (i-1)-th segment on the type-II spring located in the i-th segment;

[0067] The strain energy V3 of the tail-end type-I spring is:

[0068]

[0069] Wherein:

[0070] Wherein: is the bending moment on the cross-section at the central angle α of the upper arc segment of the type-II spring located in the (n-1)-th segment.

[0071] As a preferred embodiment of the present invention: the dimensional constraints set in the step three include:

[0072] Compression length constraint:

[0073] The relative error between the longitudinally compressed amount Δ obtained by theoretical calculation and the actual compressed amount U during the operation of the folding spring w is within the set requirement range; wherein: U w = L0 - L w ;

[0074] Working section ratio constraint:

[0075] The actual compressed amount Δ' during the operation of the spring is 0.3 to 0.6 of the length of the folding spring in its free state, that is:

[0076]

[0077] Length-thickness ratio constraint:

[0078] Define the length-thickness ratio of the spring as the ratio of the length L0 of the folding spring in its free state and the cross-sectional thickness b, and the length-thickness ratio constraint is

[0079] Beneficial effects:

[0080] (1) The method for selecting and calculating the folding spring based on dimensional constraints of the present invention combines theoretical calculation and simulation calculation, improves the directionality of the selection of spring structure parameters, speeds up the overall design speed, and thus quickly screens out suitable combinations of structure parameters.

[0081] (2) The present invention uses the energy method to deduce the relationship between the spring structure parameters and the compression stiffness, and can quickly calculate the stiffness of the free compression section through theoretical methods.

[0082] (3) In the design method of the present invention, three dimensional constraint bars can ensure that the set folding spring operates within the OA and AB segments, avoiding plastic deformation and enabling it to have a linear stiffness characteristic.

[0083] (4) In dimensional constraint, the aspect ratio of length to thickness is used to preliminarily judge the accuracy of the theoretical method, and it can preliminarily evaluate the influence degree of the lateral stiffness on the compression stiffness during the spring compression process. Brief Description of the Drawings

[0084] Figure 1 and Figure 2 is a schematic structural diagram of the folding spring of the present invention;

[0085] Figure 3 is a simplified installation diagram of the folding spring in a roller type one-way coupling;

[0086] Figure 4 is a structural diagram of a type I spring;

[0087] Figure 5 is a structural diagram of a type II spring;

[0088] Figure 6 is a graph of spring compression amount - force relationship;

[0089] Figure 7 is a simplified mechanical model diagram of the spring during compression;

[0090] Figure 8 is a simplified force analysis diagram of the type I spring;

[0091] Figure 9 is a simplified force analysis diagram of the type II spring;

[0092] Figure 10 is a flow chart of the design method of the folding spring for a one-way coupling based on dimensional constraint.

[0093] Wherein: 2 - type I spring, 3 - type II spring, 21 - the end of the straight segment of the type I spring, 22 - the arc segment of the type I spring, 32 - the arc segment of the type II spring, 4 - roller type one-way coupling, 41 - inner ring, 42 - outer ring, 43 - folding spring, 44 - roller. Detailed Embodiments

[0094] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0095] Embodiment 1:

[0096] This embodiment provides a design method for the folding spring of a one-way coupling, which combines theoretical calculation and simulation calculation, improves the directionality of the selection of the structural parameters of the folding spring, and speeds up the overall design speed of the folding spring of the one-way coupling.

[0097] The structure of the folding spring in this embodiment is as Figure 1 and Figure 2 shown, and it is composed of two basic elastic units, namely the type-I spring 2 and the type-II spring 3; among them, two type-I springs 2 with the same structural dimensions are respectively located at the head and tail ends of the spring (in this example, as Figure 7 shown, the right end of the folding spring is taken as the head end, the left end is taken as the tail end, and the right end is in contact with the roller of the one-way coupling), and are respectively in contact with the outer ring surface and the roller of the one-way coupling, and a plurality of type-II springs 3 are sequentially connected and located between the two type-I springs 2. Let the number of segments of the basic elastic unit in the folding spring be n, and in this example, n = 10; then it includes eight segments of type-II springs 3, and the head and tail of the eight segments of type-II springs 3 are respectively connected to the type-I springs 2 at both ends after being sequentially connected. The eight segments of type-II springs 3 have the same structural dimensions and are the main part providing elasticity.

[0098] The type-I springs 2 at both ends of the folding spring have a straight segment and an arc segment located at the top of the straight segment (that is, the type-I spring arc segment 22 as shown in Figure 4 ); the type-II spring 3 has an oblique segment and arc segments arranged at both ends of the oblique segment, that is, the type-II spring arc segment 32 as shown in Figure 5 , and the arc segments at both ends of the type-II spring 3 extend in two opposite directions.

[0099] As shown in Figure 1 and Figure 2 , the arc segment at the top of the type-I spring 2 on the left is docked with the arc segment extending to the left at the top of the first type-II spring 3, and the arc segment extending to the right at the bottom of the first type-II spring 3 is docked with the arc segment extending to the left at the top of the second type-II spring 3; and so on, the eight segments of type-II springs 3 are sequentially connected end to end until the arc segment extending to the right at the top of the eighth type-II spring 3 is docked with the arc segment at the top of the type-I spring 2 on the right, thereby forming the entire folding spring.

[0100] Among them, the endpoints of the straight segments of the two type-I springs 2 (that is, the end 21 of the type-I spring straight segment as shown in Figure 2 ) are flush with the centers of the respective arcs formed by the docking at the bottom in the folding spring. Let the free length of the folding spring in the free state be L0, and the length of the straight segment of the type-I spring 2 be L1 (that is, Figure 1 and Figure 2In the height direction shown, the central angle of the arc segment in the type-I spring 2 is 90°; the length of the inclined line segment of the type-II spring 3 is L2, the central angles of the two arc segments 32 in the type-II spring 3 are α, the inner diameters of all arc segments are equal, denoted as r, the cross-sectional thickness of the type-I spring 2 and the type-II spring 3 is b, and the width of the overall folding spring is h; the Young's modulus of the folding spring material is denoted as E. Let the length direction of the folding spring be the longitudinal direction, i.e., parallel to Figure 2 the X-axis direction shown; the vertical direction (i.e., the length direction of the straight line segment of the type-I spring) is the transverse direction, i.e., parallel to Figure 2 the Y-axis direction shown. The design of the folding spring is to design the above parameters under the dimensional constraints of the one-way coupling, so that the stiffness of the designed folding spring meets the usage requirements of the one-way coupling.

[0101] The installation method of the folding spring 43 in the roller type one-way coupling 4 is as Figure 3 shown. There is a roller 44 between the inner ring 41 and the outer ring 42 of the roller type one-way coupling 4. One end (designated as the head end) of the folding spring 43 abuts against the roller 44, and the other end (designated as the tail end) abuts against the end face of the installation groove on the outer ring 42 for installing the roller 44.

[0102] First, the process of the compression deformation of the folding spring is introduced:

[0103] As Figure 6 shown, the compression process of the folding spring consists of three segments: OA, AB, and BE; the OA segment is the free compression segment of the spring. At this time, due to the small compression amount, there is no contact between the basic elastic units, and the linear relationship between force and displacement is obvious, and the stiffness is j1; at point A, the ends 21 of the head and tail type-I springs 2 contact the adjacent type-II spring 3, and at this time the spring stiffness increases to k2. As the longitudinal compression amount increases, when compressed to point B, the adjacent arc segments 32 of the type-II spring contact each other; at point E, the spring is completely compressed. During the transition from the OA segment to the AB segment, only the head and tail type-I springs 1 contact the type-II spring 3, so k1 and k2 are relatively close, and the range of the spring stiffness can be quickly determined by calculating k1.

[0104] To design the folding spring of the one-way coupling, first, a method for calculating the stiffness k1 of the free compression segment OA is given. In this embodiment, the energy method is used to calculate the stiffness k1 of the free compression segment OA, and the specific method is as follows:

[0105] S1: Simplify the mechanical model of the folding spring compression process:

[0106] The spring compression process can be simplified into a planar mechanics problem, so the force analysis can be carried out on any cross-section parallel to the XOY plane. When the folded spring is installed inside the coupling, the tail end is in close contact with the inner wall of the profile of the outer ring of the one-way coupling. Ignoring the relative sliding between the two is equivalent to applying a fixed-end constraint at the arc of the tail end. At the same time, it is considered that the force exerted by the roller on the first-end type-I spring acts at the middle point O4 of the end face, and the magnitude of the acting force is F, as Figure 7 shown. The self-weight of the spring, the friction between the roller and the first-end face are ignored. The rotation angle at the interface of the two basic elastic units is very small and can be ignored. Then the force analysis of the type-I spring 2 and the type-II spring 3 is as Figure 8 and Figure 9 shown.

[0107] S2: Calculate the strain energy of each basic elastic unit respectively:

[0108] S201: Calculate the strain energy of the first-end type-I spring 2:

[0109] When calculating, only consider the bending moment component of the first-end type-I spring 2 (that is, only consider the bending moment when calculating the strain energy, and do not consider the shear force and axial force). Its strain energy V1 is:

[0110]

[0111] Where:

[0112] In formula (1) and formula (2): is the bending moment at the cross-section with length x on the straight-line segment of the first-end type-I spring 2 (where the superscript (1) represents the first segment of the folded spring), as Figure 8 shown. Taking the midpoint of the length of the straight-line segment of the first-end type-I spring 2 as the origin position of x, and upward as positive, then the value range of x is is the bending moment at the cross-section with central angle θ in the arc segment of the first-end type-I spring 2. The corresponding polar coordinate definition method is: taking the ray obtained by connecting the center O1 of the arc segment 22 of the first-end type-I spring and the tangent point of this arc segment and the straight-line segment as the polar axis, and the polar angle is positive in the counterclockwise direction. Therefore, the value range of θ is I is the cross-sectional moment of inertia of the first-end type-I spring 2. For a rectangular cross-section, I = hb 3 / 12.

[0113] S202: Calculate the strain energy of the middle (n - 2) segments of type-II springs 3:

[0114] The middle (n - 2) segments of type-II springs 3 are successively located in the 2nd to (n - 1)th segments of the whole folded spring (numbered sequentially from the first end to the tail end of the folded spring). Let the strain energy of the type-II spring 3 located in the i-th (i = 2, 3,..., n - 1) segment be:

[0115]

[0116] Wherein:

[0117] In formulas (3) and (4): is the bending moment on the cross-section at the position where the central angle is γ in the lower circular arc section of the type-II spring 3 in the i-th segment. The definition method of the polar coordinates is as Figure 9 shown. Taking the ray obtained by connecting the center O3 of the lower circular arc section of this segment of the type-II spring 3 and the tangent point at the end of this circular arc section as the polar axis, the polar angle is positive in the clockwise direction, and the value range of γ is [0, α]; is the bending moment at the position with a length of y on the inclined line segment of the type-II spring 3 in the i-th segment. Taking the tangent point between the inclined line segment of the type-II spring 3 and the lower circular arc section as the origin position of y, and upward as positive, then the value range of y is [0, L2]; is the bending moment on the cross-section at the position where the central angle is γ in the upper circular arc section of the type-II spring 3 in the y-th segment. The definition method of the polar coordinates is as Figure 9 shown. Taking the ray obtained by connecting the center O2 of the upper circular arc section of this segment of the type-II spring 3 and the tangent point between this circular arc section and the inclined line segment as the polar axis, the polar angle is positive in the counterclockwise direction, and the value range of γ is [0, α], as Figure 9 shown.

[0118] It should be noted that and Specifically, the bending moment equations of the upper / lower circular arc sections of the type-II spring are related to the inclination direction of the type-II spring. In this example, specifically, when i is odd, "±" takes the plus sign, is the bending moment on the cross-section at the position where the central angle is γ in the lower circular arc section of the type-II spring 3 in the i-th segment, is the bending moment on the cross-section at the position where the central angle is γ in the upper circular arc section of the type-II spring 3 in the i-th segment; when i is even, "±" takes the minus sign, is the bending moment on the cross-section at the position where the central angle is γ in the upper circular arc section of the type-II spring 3 in the i-th segment, is the bending moment on the cross-section at the position where the central angle is γ in the lower circular arc section of the type-II spring 3 in the i-th segment.

[0119] T i-1 is the reaction force exerted by the type-II spring 3 in the (i - 1)-th segment on the type-II spring 3 in the i-th segment; In particular, that is, the reaction force on the type-II spring 3 in the second segment is provided by the first segment, i.e., the first type-I spring 2.

[0120] S203: Calculate the strain energy of the end type-I spring:

[0121] According to the assumed conditions, only the upper arc section of the tail-end type I spring 2 actually participates in deformation, and its strain energy V3 is:

[0122]

[0123] Where:

[0124] Where: is the bending moment at the cross-section where the upper arc section of the type II spring 3 in the (n - 1)-th segment is at the central angle α.

[0125] S3: Calculate the total strain energy and the deformation amount at point O4, that is, the longitudinal compression amount:

[0126] The total strain energy V of the entire folding spring is:

[0127]

[0128] According to Castigliano's second theorem, the displacement generated along the F direction at point O4 (this point is the contact point between the folding spring and the roller of the one-way coupling, that is, the directly stressed point), namely the longitudinal compression amount Δ, is:

[0129]

[0130] Therefore, according to Hooke's law, the stiffness coefficient k1 of the n-segment folding spring when freely compressed in the direction of the pressure F can be obtained as:

[0131]

[0132] Based on the above stiffness calculation, combining the folding spring stiffness calculation method with the application scenario of the one-way coupling, a design method for the folding spring of the one-way coupling based on dimensional constraints is proposed, so as to quickly screen out the appropriate combination of structural parameters of the folding spring.

[0133] When designing the folding spring of the one-way coupling, on the premise that the usage environment of the folding spring, that is, the one-way coupling, is determined, its working load Fw and working length Lw are known values; however, it is difficult to judge whether the spring works in the OA section or the AB section. Since k1 and k2 are not very different, it can be assumed that the folding spring has an equal stiffness k1 = F w / (L0 - L w ), and then combined with the compression length, the proportion of the working section, and the length-thickness ratio as dimensional constraint conditions, quickly screen out the appropriate combination of structural parameters. On this basis, design several groups of springs near k1, and further determine its complete stiffness characteristics through simulation calculation; combining theoretical calculation and simulation calculation can improve the directionality of the selection of the structural parameters of the folding spring and speed up the overall design speed.

[0134] Such asFigure 10 As shown in the figure, the specific steps of the design method of the folding spring of the one-way coupling based on dimensional constraints are as follows:

[0135] Step 1: Given the working load Fw (i.e., F = Fw at this time) and the working length Lw; then, according to the installation space requirements of the folding spring, its width h and the number of segments n are given; where the number of segments n is the number of basic elastic units (when the number of segments is n, the folding spring includes n - 2 type II springs 3); select the material of the folding spring, and thus obtain the cross-sectional thickness b of the folding spring and the Young's modulus of the folding spring material, denoted as E; at this time, the structural parameters to be designed include: the straight section length of the type I spring 2 is L1, the inner diameter r of each arc segment in the type I spring 2 and the type II spring 3, and the central angle α of the arc segment 32 in the type II spring 3.

[0136] Step 2: Select the traversal objects as the straight section length L1 of the type I spring 2 and the inner diameter r of each arc segment in the type I spring 2 and the type II spring 3; then, according to the installation space size and empirical values, give the value ranges of L1 and r, that is, L1 shall not exceed Figure 3 the radial depth Le of the outer ring surface of the one-way coupling 4 shown in the figure. At this time, further combine the installation space and experience to give the value of the central angle α of the arc segment 32 in the type II spring 3; then traverse all combinations of L1 and r at a set step size (that is, take values of L1 and r within the given value ranges at a set step size, and then traverse all combinations of L1 and r), and calculate the longitudinal compression amount Δ generated along the F direction at point O4 and the stiffness coefficient k1 of each segment during free compression according to formulas (1) to (9) in the above-mentioned stiffness calculation method of the free compression section OA segment; at the same time, the length L0 of the folding spring in the free state can be calculated according to the values of b, n, L1, r, and α.

[0137] Step 3: Judge whether the longitudinal compression amount Δ calculated under each combination and the free length L0 of the folding spring designed in the free state satisfy the following dimensional constraints. Save the combinations of L1 and r that meet the dimensional constraints and enter the next step. If all combinations do not meet the dimensional constraints, change the traversal object (change the traversal object to L1 and α) or modify the value ranges of L1 and r, and then return to Step 2.

[0138] (1) Compression length constraint

[0139] The longitudinally calculated compression amount Δ must match the actual compression amount U during work w = L0 - L w It is considered that the relative error e r is within 3%, that is:

[0140]

[0141] where \(L_0\) is the length of the folding spring in the free state; \(U\) w is the compression amount of the folding spring during operation.

[0142] (2) Ratio constraint of the working section

[0143] The actual compression amount \(\Delta'\) of the spring during operation should be appropriate. It can be taken as 0.3 - 0.6 of the free length according to the situation, that is

[0144]

[0145] (3) Aspect ratio constraint

[0146] Define the aspect ratio of the spring as the ratio of its free length \(L_0\) and the cross-sectional thickness \(b\). The larger the aspect ratio, the longer and thinner the spring as a whole, and vice versa, it is shorter and thicker. The aspect ratio significantly affects the theoretical calculation accuracy of the spring compression stiffness. To improve the service life and prediction accuracy, it is recommended that the designed aspect ratio does not exceed 240, that is, the aspect ratio constraint is

[0147] Step 4: For each combination of \(L_1\) and \(r\) that satisfies the dimensional constraints, combined with the structural parameters given in Step 1, a set of feasible solutions for the folding spring structural parameters can be obtained, and a finite element model of each set of feasible solutions is established; and the stiffness curve of the folding spring corresponding to each set of feasible solutions is obtained through simulation analysis.

[0148] Step 5: Determine whether the stiffness curve of the folding spring corresponding to each set of feasible solutions obtained in Step 4 passes through the point \((U\) w , \(F_w\)). If it passes through, it indicates that this set of feasible solutions meets the usage requirements of the single - direction coupling; if the stiffness curves of the folding springs corresponding to all feasible solutions do not pass through the point \((U\) w , \(F_w\)), then change the traversal object (change the traversal object to \(L_1\) and \(\alpha\)) or modify the value ranges of \(L_1\) and \(r\), and then return to Step 2.

[0149] Example 2:

[0150] The difference from the above Example 1 is that in Step 2, the traversal object is selected as the straight - section length \(L_1\) of the I - type spring 2 and the central angle \(\alpha\) of the arc section 32 in the II - type spring 3; that is, the value ranges of \(L_1\) and \(\alpha\) are given based on empirical values. At this time, the inner diameter \(r\) values of each arc section in the I - type spring 2 and the II - type spring 3 are further given in combination with the installation space and experience; then all combinations of \(L_1\) and \(\alpha\) are traversed, and the longitudinal compression amount \(\Delta\) generated along the \(F\) direction at point \(O\) and the stiffness coefficient \(k_1\) during free compression of each section are calculated according to formulas (1) to (9) in the above free - compression section OA stiffness calculation method.

[0151] Correspondingly, when it is necessary to change the traversal object in Step 3 or Step 5, change the traversal object to \(L_1\) and \(r\).

[0152] Embodiment 3:

[0153] The difference from Embodiment 1 above lies in that when calculating the deformation amount, after calculating the strain energy in segments, first calculate the deformation amount in segments, and then add the deformation amounts of each segment to obtain the total deformation amount. That is, after calculating the strain energy of each basic elastic unit respectively by using the steps of S2 above, directly use to calculate the deformation amount of each segment (i.e., the longitudinal compression amount of each segment), and then add the deformation amounts of each segment to obtain the displacement generated along the F direction at point O4, that is, the longitudinal compression amount Δ, that is:

[0154]

[0155] Where: Δ i is the longitudinal compression amount of the i-th segment of the folding spring, V i is the strain energy of the i-th segment of the folding spring, F i is the force on the i-th segment of the folding spring, and the F i of each segment is the same in magnitude and direction as F; that is At this time, the stiffness coefficient k1 when the n-segment folding spring is freely compressed in the direction of the pressure F is:

[0156]

[0157] Embodiment 4:

[0158] The difference from Embodiment 1 above lies in that when calculating the stiffness coefficient, first solve the stiffness of each basic elastic unit, and then use the series spring stiffness formula to calculate.

[0159] The stiffness coefficient when the i-th segment of the folding spring is freely compressed in the direction of the pressure F is:

[0160]

[0161] Then the stiffness coefficient k1 when each segment of the n-segment folding spring is freely compressed in the direction of the pressure F is:

[0162]

[0163] The above content is a further detailed description of the present invention in combination with specific implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A design method for a one-way coupling folding spring, characterized in that: The folding spring includes I-shaped springs at both the head and the tail, and multiple II-shaped springs located between the two I-shaped springs after being connected in sequence; the I-shaped spring has a straight section and an arc section at the top of the straight section; the II-shaped spring has an inclined section and arc sections at both ends of the inclined section; Step 1: Given the working load Fw and working length Lw of the folding spring; According to the installation space of the folding spring, its width h and the number of segments n are given; Select the material of the folding spring, thereby obtaining the cross-sectional thickness b of the folding spring and the Young's modulus E of the folding spring material; At this time, the structural parameters to be designed include: the straight section length of the I-shaped spring is L1, the inner diameter r of each arc section in the I-shaped spring and the II-shaped spring, and the central angle α of the arc section in the II-shaped spring; Step 2: Select L1 and r as the traversal objects; According to the installation space, the value ranges of the current traversal objects L1 and r are given respectively, and the value of α is determined according to the installation space of the folding spring or empirical values; then, within the value ranges of the current traversal objects L1 and r, all combinations of L1 and r are traversed at a set step size, and the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 during free compression are calculated, and further the length L0 of the folding spring in the free state is obtained; Step 3: Determine whether the longitudinal compression Δ calculated under each combination and the length L0 of the folding spring in the free state designed satisfy the set dimensional constraints, save the combinations of the current traversal objects that satisfy the dimensional constraints and enter the next step. If all combinations do not satisfy the dimensional constraints, return to Step 2 to change the traversal object or modify the value range of the current traversal object; Step 4: Each combination of the current traversal objects that satisfy the dimensional constraints, combined with the structural parameters given in Step 1, can obtain a set of feasible solutions for the folding spring structural parameters, and a finite element model of each set of feasible solutions is established; through simulation analysis, the stiffness curve of the folding spring corresponding to each set of feasible solutions is obtained; Step Five: Determine whether the stiffness curve of the folding spring corresponding to each group of feasible solutions obtained in Step Four passes through the point (U w , Fw), where U w is the actual compression amount during the operation of the folding spring; If it passes through, it indicates that this set of feasible solutions meets the usage requirements of the single - direction coupling; if the stiffness curves of the folding springs corresponding to all feasible solutions do not pass through the point (U w , Fw), then return to Step 2 to change the traversal object or modify the value range of the current traversal object.

2. The design method of the one-way coupling folding spring according to claim 1, characterized in that, In the said Step 2, Select L1 and α as the traversal objects; according to the installation space, the value ranges of the current traversal objects L1 and α are given respectively, and the value of r is determined according to the installation space of the spring or empirical values; then, within this value range, all combinations of L1 and α are traversed at a set step size, and the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 during free compression are calculated, and further the length L0 of the folding spring in the free state is obtained.

3. The design method of the one-way coupling folding spring according to claim 1, characterized in that In the said Step 2, the following method is used to calculate the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 during free compression: First, make the force applied by the one-way coupling roller on the head I-shaped spring act at the middle position of the end face, and the magnitude of the acting force is F, F = Fw; Then calculate the strain energy of each section of the folding spring and add them up to obtain the total strain energy V of the folding spring; then the displacement generated along the F direction at the contact point between the folding spring and the one-way coupling roller, that is, the longitudinal compression Δ, is: The stiffness coefficient k1 of the further folding spring when freely compressed in the direction of the pressure F is:

4. The design method of the one-way coupling folding spring according to claim 1, characterized in that In the second step, the following method is used to calculate the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 during free compression: First, let the force exerted by the one-way coupling roller on the first-end type-I spring act at the middle position of the end face, and the magnitude of the acting force is F, where F = Fw; Then, calculate the strain energy of each section of the folding spring, and thereby obtain the deformation amount of each section of the folding spring along the force direction, that is: Where: i = 1, 2, 3... n; n is the total number of segments of the folding spring, and n is a natural number greater than or equal to 3; Δ i is the longitudinal compression of the i-th segment of the folding spring; V i is the strain energy of the i-th segment of the folding spring, F i is the force on the i-th segment of the folding spring, and the F of each segment i has the same magnitude and direction as F; Then: The longitudinal compression Δ generated at the contact point between the entire folding spring and the one-way coupling roller along the force direction is: The stiffness coefficient k1 of the folding spring when freely compressed in the direction of the pressure F is:

5. The design method of the one-way coupling folding spring according to claim 1, characterized in that, In the second step, the following method is used to calculate the longitudinal compression Δ generated at the contact point between the folding spring and the one-way coupling roller along the force direction and the stiffness coefficient k1 of each section during free compression: First, let the force exerted by the one-way coupling roller on the first-end type-I spring act at the middle position of the end face, and the magnitude of the acting force is F, where F = Fw; Then, calculate the strain energy of each section of the folding spring, and thereby obtain the deformation amount of each section of the folding spring along the force direction, that is: Where: i = 1, 2, 3... n; n is the total number of segments of the folding spring, and n is a natural number greater than or equal to 3; Δ i is the longitudinal compression of the i-th segment of the folding spring; V i is the strain energy of the i-th segment of the folding spring, F i is the force on the i-th segment of the folding spring, and the magnitude and direction of F for each segment i are the same as F; Then, calculate the stiffness coefficient of each section of the folding spring when freely compressed in the force direction, that is: Wherein: is the stiffness coefficient of the i-th section of the folding spring when freely compressed in the direction of the pressure F; Then: The stiffness coefficient k1 of the folding spring when freely compressed in the force direction is: The longitudinal compression Δ generated at the contact point between the entire folding spring and the one-way coupling roller along the force direction is:

6. The design method of the one-way coupling folding spring according to claim 3 or 4 or 5, characterized in that Let the type-I spring in contact with the one-way coupling roller be the first-end type-I spring, and the total number of sections of the folding spring be n; The strain energy V1 of the first-end type-I spring is: Where In Formulas (1) and (2): is the bending moment at the cross-section at a length of x on the straight-line segment of the first-stage Type I spring, and the value range of x is is the bending moment at the cross-section at a central angle of θ in the circular arc segment of the first-stage Type I spring, and the value range of θ is I is the cross-sectional moment of inertia of the first-stage Type I spring; The strain energy of the middle n - 2 type-II springs is: Number the folding springs sequentially from the head end to the tail end, and let the strain energy of the type-II spring in the i-th segment be as follows: Wherein: In formulas (3) and (4): i = 2, 3,..., n - 1; the value range of γ is [0, α]; When i is odd, "±" takes the plus sign, is the bending moment at the cross-section at the position of the circular arc section at the lower end of the Type II spring 3 in the i-th segment, where the central angle is γ, is the bending moment at the cross-section at the position of the circular arc section at the upper end of the Type II spring in the i-th segment, where the central angle is γ; When i is an even number, "±" takes the minus sign, is the bending moment at the cross-section where the central angle is γ on the upper arc section of the type-II spring located in the i-th segment, is the bending moment at the cross-section where the central angle is γ on the lower arc section of the type-II spring located in the i-th segment; is the bending moment at a length of y on the Type-II spring oblique line segment in the i-th segment, where the value range of y is [0, L2]; T i-1 The reaction force of the type-II spring located in the (i-1)-th segment on the type-II spring located in the i-th segment; The strain energy V3 of the tail-end type-I spring is: Where Wherein: is the bending moment at the section where the upper arc section of the Type II spring located in the (n - 1)th segment has a central angle of α at the center of the circle.

7. The design method of the folding spring of the one-way coupling according to claim 1 or 2, characterized in that The dimensional constraints set in the third step include: Compression length constraint: The longitudinally calculated compression Δ and the actual compression U w during the operation of the folding spring have a relative error within the set requirements; where: U w = L0 - L w ; Working section ratio constraint: The actual compression amount Δ′ during spring operation is 0.3 to 0.6 of the length of the folding spring in its free state, that is: Length-to-thickness ratio constraint: Define the spring length-thickness ratio as the ratio of the length L0 of the folding spring in the free state to the cross-sectional thickness b, and the length-thickness ratio is constrained to be

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