Design method for non-equal pitch screw connection pairs

Abstract

This invention relates to a method for designing non-unequal pitch screw connection pairs and belongs to the field of non-standard fastening members. The design method for non-unequal pitch screw connection pairs includes: determining the basic thread type, material properties, and axial load N applied to the male and female threads; and determining the length adjustment amount (l) of the gradually changing pitch screw. To obtain JPEG2026521941000114.jpg3085, (l) is an equation containing F(n'). Trial selection of the F(n') equation yields the curve equation for F(n') corresponding to good stress uniformity. Determine the ΔP equation for the pitch adjustment amount of the gradually changing pitch screw, and based on the already selected F(n') equation, the ΔP equation has only one unknown, K, where K is the overall reference coefficient, and the value of K should be determined. This invention takes into account the basic thread type of the female and male screws, material performance, and the axial load N applied to the male screw, and analysis and verification show that the design method of this invention can be used to design unequal pitch screw connection pairs with better stress uniformity.

Description

Technical Field

[0001] The present invention relates to a design method for non-uniform pitch screw connection pairs and belongs to the field of non-standard fastening members.

Background Art

[0002] The bolt connection structure (including bolts and nuts) is a relatively commonly used connection method and is widely applied in the fields of machinery and architecture. Currently, for traditional screw connection pairs, the pitches of the female and male threads are equal and are a constant value P. When a load is applied to the screw connection pair, the male thread is subjected to tensile force and elongates, and the female thread is subjected to pressure and compresses. For the male thread closer to the support surface (taking the bolt and nut as an example, the support surface is the end surface for pressing the connected member of the nut, that is, the support surface is the end surface at the end position of the screwing region of the female and male threads, and the opposite other end surface is the end surface at the starting position), the elongation amount is large, and for the male thread farther from the support surface, the elongation amount is small. As a result, the axial load of the screw connection pair is mainly applied to the first three threads closer to the support surface, and a significant stress concentration phenomenon appears at the bottom of the first three thread ridges closer to the support surface.

[0003] Currently, the conventional technical aspect adopts that the pitch of the female thread is larger than the pitch of the male thread (that is, the female thread is a tapered pitch thread). When the female and male threads act, the thread farther from the support surface is first contacted, and then the subsequent threads are sequentially contacted, thereby increasing the support force of the thread ridge farther from the support surface and reducing the support force of the thread ridge closer to the support surface, thereby reducing the stress concentration phenomenon at the bottom of the first three thread ridges closer to the support surface. For example, in the case of a screw connection having a variable gap disclosed in Patent Document 1, this aspect improves the stress uniformity of each turn of the thread to a certain extent. However, it is found through simulation according to the change trend that the pitch difference ΔP between the female and male threads gradually decreases from the starting position to the ending position of the screwing region, and its stress uniformity is not perfect and there is a large room for improvement.

[0004] Research and analysis have shown that the above-described embodiment fails to consider the load conditions and the performance of the female and male thread materials, and does not clearly provide specific formulas for calculating the length adjustment and pitch adjustment amounts of the variable-pitch thread, thus failing to produce a screw connection pair with better stress uniformity. Based on these problems, this application proposes a new design method for unequal-pitch screw connection pairs. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Chinese Patent Application Publication No. 101796312 Specification [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] The object of the present invention is to provide a method for designing non-equal pitch screw connection pairs in order to solve the problem of needing to improve the stress uniformity of conventional screw connection pairs. [Means for solving the problem]

[0007] To achieve the above objective, the design method for unequal-pitch screw connection pairs in the present invention employs the following technical aspects.

[0008] A method for designing non-equal pitch screw connection pairs, comprising the following: Determine the basic thread type, material properties, and axial load N applied to the male thread for both the female and male threads. We determine the length adjustment amount l for a gradually changing pitch screw. l is an expression that includes F(n'). Here, F(n') is the axial force acting from the female thread to the male thread at any n' turn position, starting from the starting position of the threading region of the female and male threads.

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[0009] The beneficial effects of the above-described technical embodiment are as follows. The present invention proposes a pioneering design method for unequal pitch screw connection pairs. This design method considers the basic thread types of the female and male threads, material properties, and the axial load N applied to the male thread, and provides a foundation for obtaining better stress uniformity. By calculating the length adjustment amount l of the gradually changing pitch screw, the length difference between the female and male threads can be determined, and l is an equation containing F(n'), which is related to the axial load N. By tentatively selecting the F(n') equation, a curve equation of F(n') corresponding to good stress uniformity can be obtained. Finally, the pitch adjustment amount ΔP equation of the gradually changing pitch screw is determined, and the only unknown variable in the ΔP equation is K (i.e., the overall reference coefficient), which only needs to be determined. Analysis and verification show that unequal pitch screw connection pairs with better stress uniformity can be designed using the design method of the present invention.

[0010] Furthermore, the length adjustment amount of the gradually changing pitch screw

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[0011] The beneficial effects of the above-described technology are as follows: By providing a specific calculation formula for the length adjustment amount l of a variable-pitch screw and relating it to F(n'), a constant relationship exists between the length adjustment amount l and the axial load N applied to the male screw, thereby facilitating the design of variable-pitch screws.

[0012] Furthermore, the process of finding the solution for the length adjustment amount l of a gradually changing pitch screw includes the following:

[0013] (1) Simplifying the male thread in the threaded region of the female and male threads into an equivalent force-bearing cylinder, and based on Hooke's Law and the fact that the elongation of the outer cylindrical surface of the equivalent force-bearing cylinder is less than the average elongation of the equivalent force-bearing cylinder, the total elongation of the male thread of any n' turns, starting from the starting position.

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[0014] (ii) Simplifying the female thread in the threaded region of the female and male threads into an equivalent load-bearing hollow cylinder, and based on Hooke's Law and the fact that the amount of compression of the inner cylindrical surface of the equivalent load-bearing hollow cylinder is greater than the average amount of compression of the equivalent load-bearing hollow cylinder, the total amount of compression of the female thread of any n' turns, starting from the starting position.

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[0015] (3) A simplified method for equivalent force cylinders and equivalent force hollow cylinders, i.e., from the mechanical relationship, F(n')=f1(n')=f2(n'). Therefore,

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[0016] The beneficial effect of the above technical solution lies in determining the theoretical research basis by providing the specific calculation process of the length adjustment amount l of the tapered pitch screw.

[0017] Furthermore, for the equivalent force-bearing cylindrical body with the male screw simplified, f1(n') is the resultant force of the loads on the micro outer cylindrical surface at any n' turn number position of the equivalent force-bearing cylindrical body, and the resultant force of all micro outer cylindrical surfaces is equal to the axial load N. Cut a micro cylindrical body at an arbitrary height h = n'P position of the equivalent force-bearing cylindrical body. The thickness of the micro cylindrical body is dh = Pdn', and the axial force applied to the lower cross-section of the micro cylindrical body is

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[0018] The beneficial effect of the above-described technical embodiment is the total elongation of a male screw with any n' turns l w The purpose is to provide a specific derivation process, utilize Hooke's Law, and consider the relationship between the elongation amount near the axial position of the equivalent force-bearing cylinder and the elongation amount near the cylindrical surface, thereby ensuring that the calculation results are more accurate.

[0019] Furthermore, for an equivalent load hollow cylindrical body with a simplified internal thread, f2(n') is the resultant force of the loads on the minute inner cylindrical surface at any n' turn position of the equivalent load hollow cylindrical body, and the resultant force of all minute inner cylindrical surfaces is the axial load F N It is equal to. An equivalent force is applied to a hollow cylinder, and a small hollow cylinder is cut out at an arbitrary height h=n′P. The thickness of this small hollow cylinder is dh=Pdn′, and the axial force acting on the lower cross-section of the small hollow cylinder is:

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[0020] The beneficial effect of the above technical solution is that the total compression amount l of the female thread with any number of n' turns n provides a specific derivation process, utilizes Hooke's law, and takes into account the relationship between the inner cylinder surface compression amount and the average compression amount of the equivalent stressed hollow cylinder, thus ensuring that the calculation result is more accurate.

[0021] Furthermore, the corresponding curve of F(n') is a decreasing function within the interval 0 ≦ n' ≦ n.

[0022] The beneficial effect of the above technical solution is that the stress uniformity in the case of satisfying this condition is better.

[0023] Furthermore, the pitch adjustment amount ΔP of the tapered pitch thread is the sum of the thread change amounts Δl within one turn of the thread length, that is, ΔP = ΣΔl. When 1 < n' ≦ n, the following formula holds.

[0024]

Equation

[0025]

Equation

[0026] When the materials of the female and male threads and the outer dimensions of the nut are determined, E n and A2 are both constant values. Therefore, E w A1 and E n The ratio k3 of A2 is a constant. When the elastic modulus and area in the above formula are unified as E w and A1,

Equation

[0027]

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[0028]

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[0029] The beneficial effects of the above-described technical embodiment include providing a specific derivation process for ΔP and simplifying the equations, thereby facilitating the implementation of the design method. Furthermore, because it considers cases where the value is greater than or less than one full turn, the design results are more comprehensive and accurate.

[0030] Furthermore, according to the derivation process of ΔP, the length adjustment amount of the gradually changing pitch screw

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[0031] The beneficial effect of the above-described technical embodiment is that it simplifies the formula for the length adjustment amount l of a gradually changing pitch screw and provides an upper limit for l, thereby facilitating the implementation of the design method.

[0032] Furthermore, the method for determining the overall reference coefficient K includes both test methods and finite element calculation methods.

[0033] The beneficial effect of the above-described technical configuration is that it facilitates the determination of the overall reference coefficient K.

[0034] Furthermore, when determining the overall reference coefficient K using the finite element calculation method, first, a trial value of K is taken to establish a finite element model, the stress distribution of the screw thread under the rated load is calculated, and until a K value that satisfies the requirements is obtained, the K value is decreased and recalculated if stress is concentrated at the starting position, and the K value is increased if stress is concentrated at the ending position.

[0035] The beneficial effect of the above-described technical configuration is that it facilitates the determination of the overall reference coefficient K. [Brief explanation of the drawing]

[0036] [Figure 1] Figure 1 is a schematic diagram of the basic male thread type according to the present invention. [Figure 2] Figure 2 is a schematic diagram of the basic female thread type according to the present invention. [Figure 3] Figure 3 is a schematic diagram of the female screw thread shape after pitch adjustment in the present invention. [Figure 4] Figure 4 is a schematic diagram showing the basic screw thread type before and after deformation according to the present invention. [Figure 5] Figure 5 is a schematic diagram of the pitch adjustment amount ΔP of the gradually changing pitch screw according to the present invention. [Figure 6]Figure 6 is a schematic diagram showing the start and end positions of the non-equal pitch screw connection pair under load in the present invention. [Figure 7] Figure 7 shows the length relationship between the female and male threads of the non-equal pitch screw connection pair in the present invention when there is no load. [Figure 8] Figure 8 is a schematic diagram illustrating the simplified representation of the equivalent force-receiving cylindrical body of the male screw according to the present invention. [Figure 9] Figure 9 is a schematic diagram showing the average elongation and elongation on the cylindrical surface of the small cylindrical body shown in Figure 8. [Figure 10] Figure 10 is a schematic diagram illustrating the simplified representation of the equivalent force-receiving mechanism of the female screw in a hollow cylindrical body according to the present invention. [Figure 11] Figure 11 is a schematic diagram showing the average compression amount and the compression amount on the inner cylindrical surface of the small hollow cylindrical body shown in Figure 10. [Figure 12] Figure 12 is a schematic diagram showing the force-receiving properties of the male screw in the threaded region of the female and male screws of the present invention. [Figure 13] Figure 13 shows three typical scenarios illustrating the changing trends of the axial force F(n′) acting on the male screw threads. [Figure 14(a)] Figure 14(a) is a stress cloud map corresponding to curve a in Figure 13. [Figure 14(b)] Figure 14(b) is a stress cloud map corresponding to curve b in Figure 13. [Figure 14(c)] Figure 14(c) is a stress cloud map corresponding to curve c in Figure 13. [Figure 15] Figure 15 is a schematic diagram of the change curve of the screw thread change amount Δl. [Figure 16] Figure 16 is a schematic diagram showing the thread numbers and average position of the male threads according to Embodiment 1. [Figure 17] Figure 17 is a schematic diagram of the average stress on each thread of the male screw in Figure 16. [Modes for carrying out the invention]

[0037] To further clarify the object, technical aspects and advantages of the present invention, the invention will be described in more detail below with reference to the drawings and examples. The specific examples described herein are used solely to illustrate the invention and are not intended to limit it. That is, the described examples represent only some, and not all, embodiments of the invention. Typically, the components of the embodiments of the invention described and illustrated herein may be arranged and designed in a variety of different configurations.

[0038] Accordingly, the following detailed description of embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the present invention to which protection is needed, but rather to illustrate only selected embodiments of the present invention. All other embodiments that can be obtained by those skilled in the art without any creative work based on embodiments of the present invention are all within the scope of protection of the present invention.

[0039] Furthermore, relational terms such as "first" and "second" are used solely to distinguish one entity or operation from another, and do not necessarily require or imply that there is an actual relationship or order between these entities or operations. In addition, the terms "includes," "contains," and all variations thereof are intended to cover non-exclusive inclusion, thereby including not only those elements but also other elements not explicitly listed, or elements specific to such process, method, article, or device. Unless otherwise specified, elements defined by "...includes one," etc., do not preclude the presence of another identical element in a process, method, article, or device that contains that element.

[0040] The features and performance of the present invention will be described in more detail below in relation to the examples.

[0041] Example 1 of the design method for unequal pitch screw connection pairs according to the present invention:

[0042] A method for designing non-equal pitch screw connection pairs, comprising the following: Determine the basic thread type, material properties, and axial load N applied to the male thread of the female and male threads. Determine the length adjustment amount l of the gradually changing pitch thread. l is an expression that includes F(n'). Here, F(n') is the axial force acting from the female thread to the male thread at any n' turn position, starting from the starting position of the threading region of the female and male threads.

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[0043] The design method of the present invention provides a foundation for obtaining better stress uniformity by considering the basic thread type of the female and male threads, material properties, and the axial load N applied to the male thread. In the process of calculating the length adjustment amount l of a gradually changing pitch screw, the axial load N is associated with F(n'), and by experimentally selecting the F(n') equation, the curve equation of F(n') corresponding to the case of good stress uniformity is obtained, and finally the pitch adjustment amount ΔP equation of the gradually changing pitch screw is determined, and the only unknown variable in the ΔP equation is K (i.e., the overall reference coefficient), and it is only this coefficient that needs to be determined. Using the design method of the present invention, it is possible to design unequal pitch screw connection pairs with better stress uniformity.

[0044] Example 2 of the design method for unequal pitch screw connection pairs according to the present invention:

[0045] A method for designing a non-equal pitch screw connection pair, comprising: determining the basic thread type, material properties, and axial load N applied to the male thread of the female and male threads; determining the length adjustment amount l of the gradually changing pitch screw, where l is an expression containing F(n'), where F(n') is the axial force acting from the female thread to the male thread at any n' turn position, starting from the starting position of the threading region of the female and male threads.

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[0046] The specific design procedure is as follows:

[0047] Step 1: Determine the basic thread type, material properties, and rated load of the female and male threads.

[0048] The basic thread type is a standard thread such as a metric thread, MJ thread, trapezoidal thread, or arc thread, but non-standard threads may also be used. The basic thread type is a standard pitch with a width of one along the axial direction.

[0049] The specific basic male thread type is shown in Figure 1. The male thread type is a basic male thread type, where the pitch P1 of the male thread is equal to the basic male thread pitch P (i.e., the distance between AA'), the large diameter is d, the medium diameter is d2, the small diameter is d1, the yield strength of the male thread material is σ, and the elastic modulus of the male thread material is E w The axial load applied to the male screw thread is N.

[0050] The specific basic female thread pattern is shown in Figure 2. The pitch of the basic female thread pattern is P (i.e., the distance between BB'), the large diameter is D, the medium diameter is D2, the small diameter is D1, the number of turns of the female thread is n, and the elastic modulus of the female thread material is E.n That is the case.

[0051] Up to this point, in Step 1, we have determined all parameters except for the pitch of the female and male threads.

[0052] Step 2: Determine the length adjustment amount l for the gradually changing pitch screw.

[0053] When designing a non-unequal pitch screw connection pair, the pitch of one of the female or male threads is maintained while the other is adjusted. For the sake of explanation, in this design method, the pitch of the male thread is kept constant while the female thread is adjusted; that is, the male thread is a constant-pitch thread and the female thread is a gradually changing-pitch thread. In this invention, the male thread is connected by multiple basic male threads, and the pitch of the male thread is the same as the pitch of the basic male threads, i.e., P1 = P.

[0054] The female thread in this invention is obtained by adjusting the pitch based on a basic thread profile, maintaining the basic thread profile during adjustment and adding a transition structure to the base of the female thread. As shown in Figure 3, the female thread with adjusted pitch is formed by sequentially connecting and joining multiple basic female thread profiles and transition structures G as a crest line on a plane passing through the axis, and the longitudinal cross-section of the transition structure G is a straight segment. The pitch P2 of the female thread is the distance between two adjacent basic female thread profiles on the female thread profile line and any pair of corresponding points MM′ on the threading region of the male thread. The pitch P2 of the female thread is non-deterministic. The pitch of the female thread is greater than or equal to the pitch of the basic male thread profile, i.e., P2 ≥ P. The pitch adjustment amount ΔP = P2 - P for the gradually changing pitch thread. Since the pitch P1 = P of the male thread, the pitch adjustment amount ΔP for the gradually changing pitch thread is the pitch difference between the female thread and the male thread, and at the same time is the width of the transition structure G.

[0055] In the case of a conventional equal-pitch screw, when a load is applied and they mesh, the male screw is pulled and elongated, and the female screw is compressed and shortened. The sum of the two is the total change amount of the female and male screws. At any position within the screwing region, the male and female screws are elongated or compressed to different degrees (for example, the dashed line in FIG. 4 is before the basic thread form is deformed, and the solid line is after the deformation). Therefore, as shown in FIG. 5, the pitch adjustment amount of the tapered pitch screw is calculated by obtaining the sum ΣΔl of the total elongation amount of the male screw and the total compression amount of the female screw within one turn of the screw based on the basic thread form. When adjusting the tapered pitch screw, the basic thread form is maintained, and a transition structure G is added to the bottom of the female thread. The width of the transition structure G is the tapered pitch screw adjustment amount ΔP, and ΔP = ΣΔl.

[0056] For the sake of convenience of explanation, the present invention provides a starting position and an ending position. As shown in FIGS. 6 and 7, taking the bolt 1 and the nut 2 as an example, within the screwing region of the female and male screws, the present invention uses one end face perpendicular to the axis of the female screw as the starting position section Q, and the other end face of the female screw as the ending position section Z (the conventionally considered support surface, that is, the end face for pressing the connected member of the nut 2). The direction from the starting position to the ending position is the same as the direction of the rated axial load N applied to the male screw.

[0057] Since the number of screw turns of the female screw is n, when the female and male screws are used in combination, the n turns of the female screw must be used in combination with the n turns of the male screw. When no load deformation occurs, starting from the starting position, any female screw with n′ turns (0 < n′ ≤ n) is larger than the length of the male screw. As shown in FIG. 7, for the non-equal pitch screw connection pair, starting from the starting position, the length L1 of any n′ turns of the male screw is L1 = n′P1 = n′P, and the length L2 of any n′ turns of the female screw is L2 = n′P1 + l = n′P + l. Then, L2 - L1 = l. Here, l is the length difference between the female and male screws for any n′ turns starting from the starting position, that is, the length adjustment amount of the tapered pitch screw.

[0058] As shown in Figure 8, for the sake of analysis, the male thread in the threaded region of the female and male threads is simplified to an equivalent load-bearing cylinder. The two circular cross-sections of the equivalent load-bearing cylinder are the starting position cross-section Q and the ending position cross-section Z, respectively. The cross-sectional area A1 of the equivalent load-bearing cylinder is the stress cross-sectional area of ​​the male thread. The magnitude of the axial load received by the equivalent load-bearing cylinder at the ending position cross-section Z is N, and the direction of the axial load N is directed from the starting position cross-section Q to the ending position cross-section Z. The forces acting between the female and male threads are simplified to surface loads applied to the outer cylindrical surface of the equivalent load-bearing cylinder. The surface loads are in the opposite direction to the axial load N, and the resultant force of the surface loads is the same as the magnitude of the axial load N. Starting from the starting position, the resultant force of the loads on the minute outer cylindrical surface at any n' turn position is f1(n'), and the resultant force of the loads on all minute outer cylindrical surfaces is equal to the axial load N, i.e.

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[0059] An infinitesimal cylinder is cut off from an equivalent force-bearing cylinder at an arbitrary height h=n′P, the thickness of the infinitesimal cylinder is dh=Pdn′, and the axial force acting on the lower cross-section of the infinitesimal cylinder is:

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[0060] As is clear from Figure 9, the direction of the surface load on the outer cylindrical surface of the minute cylinder is opposite to the direction of the load N1 on the lower cross section of the minute cylinder. Therefore, the amount of elongation on the outer cylindrical surface of the minute cylinder is the average elongation dl. w1 For smaller, equivalent force-bearing cylindrical bodies, the outer cylindrical surface is a simplified male thread region, and therefore the elongation of the outer cylindrical surface is equal to the elongation of the male thread dl.w should be, that is, dl w =k1·dl w1 , 0 < k1 < 1. For the convenience of analysis, assuming k1 is a constant value, starting from the starting position, the total elongation of the male thread for any number of n' turns

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[0061] As shown in Fig. 10, for the convenience of analysis, the female thread in the threaded engagement region of the female and male threads is simplified to an equivalent force-bearing hollow cylinder. The two circular-arc annular cross-sections of the equivalent force-bearing hollow cylinder are the starting position cross-section Q and the ending position cross-section Z respectively. The cross-sectional area of the equivalent force-bearing hollow cylinder is A2, and the axial load at the ending position cross-section Z of the equivalent force-bearing hollow cylinder is F N (According to the force balance, F N and N are equal), and the direction is from the ending position to the starting position. The acting force between the female and male threads is simplified to the surface load being applied to the inner cylindrical surface of the equivalent force-bearing hollow cylinder. The surface load is opposite to the direction of the axial force F N , and the resultant force of the surface load is the same as the magnitude of the axial force F N . Starting from the starting position cross-section, the resultant force of the load on the micro-inner cylindrical surface at any number of n' turns position is f2(n'), and the resultant force of the load on all the micro-inner cylindrical surfaces is equal to the axial load F N , that is

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[0062] Cut out a micro-hollow cylinder at an arbitrary height h = n'P position of the equivalent force-bearing hollow cylinder. The thickness of the micro-hollow cylinder is dh = Pdn', and the axial force applied to the lower cross-section of the micro-hollow cylinder is

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Equation

[0063] As can be seen from FIG. 11, since the surface load direction of the inner cylindrical surface of the micro hollow cylinder is opposite to the acting direction of the lower cross-section load F N of the micro hollow cylinder, the compression amount on the inner cylindrical surface of the micro hollow cylinder is larger than the average compression amount dl n1 . Since the inner cylindrical surface of the equivalent hollow cylinder is a simplified area of the female thread, the compression amount of the inner cylindrical surface is the compression amount dl n of the female thread. Therefore, dl n = k2·dl n1 , 1 < k2. For the convenience of analysis, assuming k2 is a constant value, starting from the starting position, the total compression amount of the female thread at an arbitrary number of n' turns is

Equation

[0064] As shown in FIG. 12, the axial force acting on the male thread from the female thread at the position of an arbitrary number of n' turns starting from the starting position is F(n'), and from the simplified method of the equivalent force-bearing cylinder and the equivalent force-bearing hollow cylinder, that is, the mechanical relationship, F(n') = f1(n') = f2(n'). Therefore, the following equation holds.

[0065]

Equation

[0066] Furthermore, starting from the starting position, the length adjustment amount l of the tapered pitch thread with n´ turns is the sum of the total elongation amount l w of the male thread and the total compression amount l n of the female thread, that is, the following equation holds.

[0067]

Equation

[0068] Up to this point, in Step 2, we determined the elongation amount of the male thread and the compression amount of the female thread, and then added them together to find the length adjustment amount l of the gradually changing pitch screw.

[0069] Step 3: Try selecting an equation for the axial force F(n') in the male screw thread.

[0070] In the formula for the length adjustment amount l of the gradually changing pitch screw obtained in Step 2, only F(n') and n' are variables, and there are three cases for the tendency of the axial force F(n') acting on the male thread to change according to n'. As shown in Figure 13, in curve a, F(n') increases as n' increases, in curve b, F(n') is constant, and in curve c, F(n') decreases as n' increases. From the mechanical relationship, the integrated value of the axial force F(n') on the male thread from the start position to the end position is the axial load N in the cross-section, i.e.

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[0071] Three different trends in the change of F(n') were simulated, and the resulting stress cloud maps are as follows: Figure 14(a) is the stress cloud map corresponding to curve a, Figure 14(b) is the stress cloud map corresponding to curve b, and Figure 14(c) is the stress cloud map corresponding to curve c.

[0072] The high-stress region at the base of the male thread typically occurs there, and the magnitude of the stress value is influenced by the combined effect of the axial force F(n') at the male thread and the axial load N(n') at the cross-section (i.e., the force on the entire cross-section (excluding the thread) for n' turns). When a load is applied to the female and male threads and they deform, the axial load N(n') at the cross-section increases from the starting position as the number of turns n' of the screw increases, reaching a maximum value N at n turns. As shown in Figure 13, when the axial force F(n') at the male thread matches curve a, F(n') is small at the starting position and large at the ending position. This is the same as the trend of change of N(n'). As shown in Figure 14(a), Y in the figure represents the area with the largest stress value. As can be seen from the figure, the stress is small at the starting position of the male thread, while the stress is large at the ending position, resulting in a clear stress concentration phenomenon. That is, Y is concentrated at the ending position, and the area of ​​Y increases as it approaches the ending position.

[0073] As shown in Figure 13, when the axial force F(n') in the male thread matches curve b, although F(n') remains constant, the axial load N(n') in the cross-section gradually increases with n'. Therefore, the stress at the base of the male thread is still small at the starting position and large at the ending position, but the stress concentration phenomenon is improved. As shown in Figure 14(b), the area of ​​Y at the ending position becomes smaller. When the axial force F(n') in the male thread matches curve c, F(n') further increases at the starting position and further decreases at the ending position. This further increases the stress at the base of the male thread at the starting position and further decreases the stress at the ending position, making the stress value across the entire base of the male thread more uniform and reducing the stress concentration phenomenon. As shown in Figure 14(c), Y is uniformly distributed from the starting position to the ending position.

[0074] Up to this point, from the analysis in Step 3, if F(n') matches curve c, the stress state is good, and the selected F(n') equation should satisfy curve c. F(n') should satisfy two conditions: namely, it is a decreasing function within the interval 0 ≤ n' ≤ n.

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[0075] Step 4: Determine the pitch adjustment amount ΔP equation of the tapered pitch screw.

[0076] As shown in FIG. 15, the pitch adjustment amount ΔP of the tapered pitch screw is the sum of the screw change amounts Δl within one turn of the screw length, that is, ΔP = ΣΔl. When 1 < n' ≤ n, that is, the following equation holds.

[0077]

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[0078]

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[0079] Once the materials of the female and male screws and the nut outer dimensions are determined, since both E n and A2 are constant values, E w the ratio k3 of A1 to E n and A2 is a constant. For the convenience of calculation, when the modulus of elasticity and the area in the above equation are unified as E w and A1, then

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[0080]

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[0081]

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[0082] Up to this point, Step 4 calculates the pitch adjustment amount ΔP of the gradually changing pitch screw based on the equation for the length adjustment amount l of the gradually changing pitch screw. Since equation F(n') was selected in Step 3, the equation for ΔP only has K as an unknown.

[0083] Furthermore, according to the derivation process of ΔP, the length adjustment amount of the gradually changing pitch screw

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[0084] Step 5: Determine the overall reference coefficient K.

[0085] There are numerous methods for determining the overall reference coefficient K, including test methods and finite element calculation methods, but the finite element calculation method is the preferred method.

[0086] When determining the overall reference coefficient K using the finite element calculation method, first, a trial value of K is taken to establish a finite element model, and the stress distribution of the screw thread under the rated load is calculated. The calculation is repeated until a K value that satisfies the requirements is obtained. If stress is concentrated at the starting position, the K value is decreased and the calculation is repeated, and if stress is concentrated at the ending position, the K value is increased.

[0087] The design method for unequal-pitch screw connection pairs of the present invention is described in detail below in relation to the specific parameters of the screws.

[0088] Specific Embodiment 1:

[0089] 1. Determine the basic thread type, material properties, and rated load for the female and male threads.

[0090] The basic male thread type is a metric thread, with a pitch P=4mm, a large diameter d=42mm, and a small diameter d1=37.67mm. The elastic modulus E=206 Gpa and yield strength σ=930 MPa of the male thread material. The rated load applied to the male thread is N=0.7σA1.

[0091] The basic thread type for female threads is a metric thread, with a pitch P=4mm, a large diameter D=42.33mm, a small diameter D1=38mm, and the number of turns of the female thread n=7 turns.

[0092] 2. Determine the length adjustment amount l for the gradually changing pitch screw.

[0093] Starting from the starting position, the length adjustment amount l of a gradually changing pitch screw with an arbitrary number of n' turns is equal to the total elongation amount l of the male screw. w and the total compression amount of the female thread l n It is the sum of and the following equation holds:

[0094]

number

[0095] 3. Try selecting an equation for the axial force F(n') in the male screw thread.

[0096] Axial force in the male thread selected for testing

Number

Number

[0097] 4. Determine the pitch adjustment amount ΔP equation of the tapered pitch screw.

[0098] In this embodiment, the female thread is a tapered pitch screw, and the pitch adjustment amount ΔP of the tapered pitch screw is as follows.

[0099]

Number

[0100]

Number

[0101] 5. Determine the comprehensive reference coefficient K.

[0102] When K = 2.5, the stress value at the bottom of the male thread is relatively uniform, and the pitch adjustment amount ΔP of the tapered pitch screw is as follows.

[0103]

Number

[0104]

Number

[0105] Table 1 shows the specific adjustment parameters of screws with different comprehensive reference coefficients K. L1 and L2 in Table 1 are the lengths of the female and male screws after length adjustment respectively. A finite element model is constructed using the screw parameters in the table to complete the calculation. According to the numbers (1 - 7) of the male screw threads and the positions indicated by the thickened short vertical lines in Fig. 16, the average stress of each thread of the male screw is extracted, a diagram of the average stress change of each thread is drawn, and the stress concentration coefficient of each thread (stress concentration coefficient = maximum stress / total average stress) is calculated. It can be seen from Fig. 17 that the stress uniformity of the screw with K = 2.5 is good, and from Table 2 that the stress concentration coefficient of the screw with K = 2.5 is the smallest.

[0106]

Table 1

[0107]

Table 2

[0108] Specific Embodiment 2:

[0109] Different from Specific Embodiment 1, the axial force

Number

Number

[0110] In other embodiments of the design method of the non-uniform pitch screw connection pair, the method of determining the comprehensive reference coefficient K may adopt the test method.

[0111] In another embodiment of the design method for unequal pitch screw connection pairs, the upper limit of the length adjustment amount l for the gradually changing pitch screw may vary depending on the yield strength and modulus of elasticity of the screw material.

[0112] In another embodiment of the design method for unequal pitch screw connection pairs, the female screw pitch may be increased by maintaining a constant basic screw pitch and reducing the female screw tooth thickness.

[0113] In another embodiment of the design method for non-equal pitch screw connection pairs, if the variable pitch screw is a male screw, the pitch of the male screw may be reduced by reducing the width of the transition structure or increasing the tooth thickness of the male screw.

[0114] In another embodiment of the design method for non-equal pitch screw connection pairs, the total average elongation of the equivalent force-bearing cylindrical body l over any n' turn count is w1 Using directly the total elongation l of a male screw with any n' turns w It may also represent the total average compressibility l of an equivalent stressed hollow cylinder at any n' turn count. n1 Using directly, the total compression amount l of a female thread of any n' turns n It may also represent this.

[0115] In another embodiment of the design method for non-equal pitch screw connection pairs, the pitch adjustment amount ΔP for gradually changing pitch screws within a screw length of less than one turn may not be considered, and only the calculation process for pitch adjustment amounts ΔP of one turn or more may be studied.

[0116] The above are preferred embodiments of the present invention, and there is no need to limit the present invention. The scope of patent protection of the present invention is in accordance with the claims, and all equivalent structural modifications made using the description and drawings of the present invention should be included within the scope of protection of the present invention.

[0117] (Note) (Note 1) The steps include determining the basic thread type, material properties, and axial load N applied to the male thread for both the female and male threads, The step of determining the length adjustment amount l of a gradually changing pitch screw, wherein l is an expression including F(n'), where F(n') is the axial force acting from the female thread to the male thread at any n' turn position, starting from the starting position of the threading region of the female and male threads.

number

[0118] (Note 2) Adjustment amount for the length of a gradually changing pitch screw

number

[0119] (Note 3) The process for finding the solution for the length adjustment amount l of a gradually changing pitch screw is as follows: (1) Simplifying the male thread in the threaded region of the female and male threads into an equivalent force-bearing cylinder, and based on Hooke's Law and the fact that the elongation of the outer cylindrical surface of the equivalent force-bearing cylinder is less than the average elongation of the equivalent force-bearing cylinder, the total elongation of the male thread of any n' turns, starting from the starting position.

number

number

number

number

number

number

number

[0120] (Note 4) For an equivalent load-bearing cylindrical body with a simplified male thread, f1(n') is the resultant force of the loads on the minute outer cylindrical surface at any n' turn position of the equivalent load-bearing cylindrical body, and the resultant force on all minute outer cylindrical surfaces is equal to the axial load N. An equivalent force-bearing cylinder is subjected to an equivalent force-bearing cylinder, and a small cylinder is cut out at an arbitrary height h=n′P position. The thickness of this small cylinder is dh=Pdn′, and the axial force acting on the lower cross-section of the small cylinder is:

number

number

number

number

[0121] (Note 5) For an equivalent load hollow cylindrical body with a simplified internal thread, f2(n') is the resultant force of the loads on the infinitesimal inner cylindrical surface at any n' turn position of the equivalent load hollow cylindrical body, and the resultant force of all infinitesimal inner cylindrical surfaces is the axial load F N Equivalent to, Cut out a small hollow cylinder at an arbitrary height h = n′P of the equivalent force-bearing hollow cylinder. The thickness of the small hollow cylinder is dh = Pdn′, and the axial force applied to the lower cross-section of the small hollow cylinder is [Number] and the average compression amount of the small hollow cylinder with thickness dh is [Number] and the total average compression amount of the equivalent force-bearing hollow cylinder at an arbitrary number of n′ turns starting from the starting position obtained by integration [Number] can be obtained. Since the compression amount of the inner cylindrical surface of the small hollow cylinder is larger than the average compression amount and the inner cylindrical surface of the equivalent force-bearing hollow cylinder is the internal thread simplification region, the compression amount of the inner cylindrical surface is the compression amount dl of the internal thread n that is, dl n = k2·dl n1 Furthermore, the total compression amount of the internal thread at an arbitrary number of n′ turns starting from the starting position [Number] A design method for a non-uniform pitch screw connection pair described in Appendix 3, characterized in that the above can be obtained.

[0122] (Appendix 6) A design method for a non-uniform pitch screw connection pair described in any one of Appendices 1 to 5, characterized in that the corresponding curve of F(n′) is a decreasing function in the interval 0 ≦ n′ ≦ n.

[0123] (Appendix 7) The pitch adjustment amount ΔP of the tapered pitch screw is the sum of the screw change amounts Δl within one turn of the screw length, that is, ΔP = ΣΔl. When 1 < n′ ≦ n, that is, [Number] , When n′ ≤ 1, the pitch adjustment amount ΔP of the tapered pitch screw is the sum of the screw change amounts Δl within a screw length of less than one turn, that is, [Number] When the materials of the female and male screws and the nut outer dimensions are determined, E n and A2 are both constant values, so E w A1 and E n The ratio k3 of A2 is a constant. When the elastic modulus and area in the above formula are unified as E w and A1, [Number] , For the convenience of subsequent calculations, if the comprehensive reference coefficient K = k1 + k2k3, the pitch adjustment amount ΔP of the tapered pitch screw is [Number] It is characterized by being the design method of the non-uniform pitch screw connection pair described in any one of Appendices 2 to 5.

[0124] (Appendix 8) According to the derivation process of ΔP, the length adjustment amount of the tapered pitch screw [Number] , for the axial load [Number] at the cross-section of any n′ number of turns starting from the starting position, [Number] , Based on the fact that the cross-sectional stress in the equivalent stress-bearing cylindrical body of the axial force applied to the male screw is smaller than the yield strength σ of the male screw material, N = k4σA1 < σA1, where 0 < k4 < 1, therefore, [Number] You can obtain k c =σ / E w And further l <Kk4k c We obtain Pn′, where K is a constant and 0.8 ≤ K ≤ 10, k c =σ / E w =0.001~0.02, k4, k c And K is taken into consideration as a whole to determine the upper limit l of the length adjustment amount l for the gradually changing pitch screw. lim We define = 0.025P·n′, and further l <l lim A method for designing unequal pitch screw connection pairs as described in Appendix 7, characterized by obtaining =0.025P·n′.

[0125] (Note 9) The method for determining the overall reference coefficient K is characterized by including a test method and a finite element calculation method, as described in any one of the appendices 1 to 5, for designing a non-equal pitch screw connection pair.

[0126] (Note 10) The design method for unequal pitch screw connection pairs described in Appendix 9, characterized in that when determining the overall reference coefficient K using the finite element calculation method, first a trial value of K is taken to establish a finite element model, the stress distribution of the screw thread under the rated load is calculated, and until a K value that satisfies the requirements is obtained, the K value is decreased and recalculated when stress is concentrated at the starting position, and the K value is increased when stress is concentrated at the ending position.

Claims

1. The steps include determining the basic thread type, material properties, and axial load N applied to the male thread for both the female and male threads, The step of determining the length adjustment amount l of a gradually changing pitch screw, wherein l is an expression including F(n'), where F(n') is the axial force acting from the female thread to the male thread at any n' turn position, starting from the starting position of the threading region of the female and male threads. [Math 1] n is the total number of turns in the threaded area of ​​the female and male threads, step, The steps involve: tentatively selecting the F(n') equation and obtaining the corresponding curve equation for F(n') when stress uniformity is good; The first step is to determine the equation for the pitch adjustment amount ΔP of a gradually changing pitch screw, and based on the already selected F(n') equation, the ΔP equation has only one unknown, K, where K is the overall reference coefficient, and to determine the value of K. A method for designing non-equal pitch screw connection pairs, characterized by including the following:

2. Adjustment amount for the length of a gradually changing pitch screw [Math 2] (However, P is the pitch of a constant-pitch screw, and k １ tok ２ And all of these are constant values, E ｗ This is the elastic modulus of the male screw material, and A １ This is the stress cross-sectional area of ​​the male screw, E ｎ This is the elastic modulus of the female screw material, and A ２ The design method for an unequal pitch screw connection pair according to claim 1, characterized in that (where is the stress cross-sectional area of ​​the female screw).

3. The process for finding the solution for the length adjustment amount l of a gradually changing pitch screw is as follows: (1) Simplifying the male thread in the threaded region of the female and male threads into an equivalent force-bearing cylinder, and based on Hooke's Law and the fact that the elongation of the outer cylindrical surface of the equivalent force-bearing cylinder is less than the average elongation of the equivalent force-bearing cylinder, the total elongation of the male thread of any n' turns, starting from the starting position. [Math 3] A step to find k, where 0 < k １ <1, [Math 4] N is the axial load simultaneously received by the equivalent bearing cylindrical body at the end position cross section, and the direction of the axial load N is directed from the start position cross section to the end position cross section, step and (ii) Simplifying the female thread in the threaded region of the female and male threads into an equivalent load-bearing hollow cylinder, and based on Hooke's Law and the fact that the amount of compression of the inner cylindrical surface of the equivalent load-bearing hollow cylinder is greater than the average amount of compression of the equivalent load-bearing hollow cylinder, the total amount of compression of the female thread of any n' turns, starting from the starting position. [Math 5] A step to find k, where k ２ >1, [Math 6] , F Ｎ is the axial load received by the equivalent force-bearing hollow cylinder at the end position cross-section, and the direction of the axial load F Ｎ is directed from the end position cross-section to the start position cross-section, step, and Includes, (3) A simplified method for equivalent force-bearing cylinders and equivalent force-bearing hollow cylinders, i.e., from the mechanical relationship F(n') = f １ (n') = f ２ (n'), therefore, [Number 7] 、 [Number 8] Therefore, the length adjustment amount l of the gradually changing pitch screw in n' turns starting from the starting position is equal to the total elongation amount l of the male screw. ｗ and the total compression amount of the female thread l ｎ It is the sum of, that is, [Number 9] The method for designing a non-equal pitch screw connection pair according to claim 2, characterized in that it is the same as described in claim 2.

4. For a cylindrical body with a simplified male screw and equivalent force, f １ (n') is the resultant force of the loads on the infinitesimal outer cylindrical surface at any n' turn position of the equivalent force-bearing cylinder, and the resultant force on all infinitesimal outer cylindrical surfaces is equal to the axial load N. An equivalent force-bearing cylinder is subjected to an equivalent force-bearing cylinder, and a small cylinder is cut out at an arbitrary height h = n'P position. The thickness of the small cylinder is dh = Pdn', and the axial force acting on the lower cross-section of the small cylinder is: [Number 10] And according to Hooke's Law, the average elongation of a small cylindrical body [Math 11] Therefore, the total average elongation of the equivalent force-bearing cylinder at any n' turn number is [Math 12] And, The elongation of the cylindrical surface edge of the equivalent force-bearing cylinder is smaller than the average elongation, and the cylindrical surface of the equivalent force-bearing cylinder is a simplified male thread region, therefore the elongation of the cylindrical surface is equal to the elongation of the male thread dl. ｗ Therefore, that is, dl ｗ = k １ ・dl ｗ１ Furthermore, the total elongation of the male screw with an arbitrary number of n' turns, starting from the starting position. [Number 13] The method for designing a non-equal pitch screw connection pair according to claim 3, characterized in that it is possible to obtain this.

5. For a hollow cylindrical body with an equivalent force bearing and a simplified internal thread, f ２ (n') is the resultant force of the loads on the infinitesimal inner cylindrical surface at any n' turn number position of the equivalent load-bearing hollow cylinder, and the resultant force on all infinitesimal inner cylindrical surfaces is the axial load F Ｎ Equivalent to, Equivalent Force A small hollow cylinder is cut out at an arbitrary height h = n'P of a hollow cylinder, and the thickness of the small hollow cylinder is dh = Pdn'. The axial force acting on the lower cross-section of the small hollow cylinder is: [Number 14] Therefore, the average compression amount of a small hollow cylindrical body with thickness dh is [Number 15] Therefore, the total average compression of the hollow cylinder under equivalent stress at any n' turns, starting from the starting position obtained by integration. [Number 16] We can find out, The compression of the inner cylindrical surface of the minute hollow cylinder is greater than the average compression, and the inner cylindrical surface of the equivalent force-bearing hollow cylinder is in the simplified female thread region, therefore the compression of the inner cylindrical surface is equal to the compression of the female thread dl. ｎ Therefore, that is, dl ｎ = k ２ ・dl ｎ１ Furthermore, the total compression amount of the female thread with an arbitrary number of n' turns, starting from the starting position. [Number 17] The method for designing a non-equal pitch screw connection pair according to claim 3, characterized in that it is possible to obtain this.

6. A method for designing a non-equal pitch screw connection pair according to any one of claims 1 to 5, characterized in that the corresponding curve of F(n') is a decreasing function within the interval 0 ≤ n' ≤ n.

7. The pitch adjustment amount ΔP of a gradually changing pitch screw is the sum of the screw length changes Δl within one rotation, i.e., ΔP = ΣΔl, and when 1 < n' ≤ n, i.e., [Number 18] 、 When n' ≤ 1, the pitch adjustment amount ΔP of a gradually changing pitch screw is the sum of the screw change amounts Δl within a screw length of less than one full turn, i.e., [Number 19] Once the materials for the female and male threads and the outer dimensions of the nut are determined, E ｎ and A ２ Since all of them are constant values, E ｗ A １ and E ｎ A ２ ratio k ３ E is a constant, and the modulus of elasticity and area in the above formula are equal to E. ｗ and A １ If we standardize it to, [Number 20] 、 To facilitate subsequent calculations, the overall reference coefficient K = k １ +k ２ k ３ Therefore, the pitch adjustment amount ΔP for a gradually changing pitch screw is [Math 21] A method for designing a non-equal pitch screw connection pair according to any one of claims 2 to 5, characterized in that it is the same as the present invention.

8. According to the derivation process of ΔP, the length adjustment amount of the gradually changing pitch screw [Number 22] , axial load in a cross-section of any n' turns starting from the starting position [Number 23] Therefore, [Number 24] 、 Based on the fact that the equivalent stress on the cylindrical body of the axial force acting on the male screw is less than the yield strength σ of the male screw material, N = k ４ σA １ <σA １ However, 0 < k ４ <1. Therefore, [Number 25] You can obtain k ｃ = σ / E ｗ And further, l < Kk ４ k ｃ We obtain Pn', where K is a constant and 0.8 ≤ K ≤ 10, k ｃ = σ / E ｗ = 0.001 to 0.02, k ４ , k ｃ And K is taken into consideration as a whole to determine the upper limit l of the length adjustment amount l of the gradually changing pitch screw. ｌｉｍ We define l < l as = 0.025P・n′, and furthermore l < l ｌｉｍ The method for designing a non-equal pitch screw connection pair according to claim 7, characterized in that = 0.025P・n′ is obtained.

9. The method for determining the overall reference coefficient K includes a test method and a finite element calculation method, characterized in that it is a design method for a non-equal pitch screw connection pair according to any one of claims 1 to 5.

10. The design method for unequal pitch screw connection pairs according to claim 9, characterized in that when determining the overall reference coefficient K using the finite element calculation method, first a trial value of K is taken to establish a finite element model, the stress distribution of the screw thread under the rated load is calculated, and until a K value that satisfies the requirements is obtained, the K value is decreased and recalculated when stress is concentrated at the starting position, and the K value is increased when stress is concentrated at the ending position.

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