A method of designing a non-uniform thread connection pair

Abstract

The application provides a design method of a non-equal-pitch threaded connection pair, and belongs to the field of non-standard fasteners. The design method of the non-equal-pitch threaded connection pair comprises the following contents: determining the basic thread form, material performance of the inner and outer threads and the axial load N borne by the outer thread; determining the pitch difference ΔP of the inner and outer threads, wherein P is the pitch of the outer thread; trying to select the pitch difference ΔP of the inner and outer threads, adjusting the total axial fit clearance δ of the inner and outer threads when they are used together, δ=P-S w ‑S n , wherein S w is the tooth width of the outer thread at the pitch diameter, S n is the tooth width of the inner thread at the pitch diameter of the outer thread; verifying the stress state of the thread and determining the thread parameters. The application considers the basic thread form, material performance of the inner and outer threads and the axial load N borne by the outer thread, and resets the upper limit value of the pitch difference ΔP of the inner and outer threads, so that the stress uniformity of the thread teeth is better.

Description

Technical Field

[0001] This invention relates to a design method for non-equidistant threaded connection pairs, belonging to the field of non-standard fasteners. Background Technology

[0002] Bolted connections (including bolts and nuts) are a commonly used connection method, widely applied in the machinery and construction fields. Currently, in traditional threaded connections, the pitch of the internal and external threads is equal and constant, P. When the threaded connection is under load, the external thread is subjected to tensile elongation, while the internal thread is subjected to compressive pressure. The elongation of the external thread near the support surface (taking bolts and nuts as an example, the support surface is the end face of the nut used to press the connected parts, that is, the end face at the end position of the internal and external thread engagement area, and the opposite end face is the end face at the beginning position) is greater, while the elongation of the external thread far from the support surface is smaller. This causes the axial load of the threaded connection to be mainly borne by the first three threads near the support surface, resulting in significant stress concentration in the first three threads.

[0003] Currently, two design approaches exist to address the stress concentration problem in the first three threads closest to the support surface: improving the load-bearing uniformity and stress uniformity of each thread. In both of these approaches, at least one thread (internal or external) is a gradually changing pitch thread, which significantly increases the difficulty of thread processing, hindering mass production and resulting in low processing efficiency.

[0004] To address the aforementioned issues, existing technologies also employ a unequal pitch scheme, where the pitches of the internal and external threads are constant, but not equal. For example, Chinese invention patent application CN106438657A discloses an interference fit thread, threaded connector, and thread-correcting tool, in which the pitches of the internal and external threads are unequal, with one thread's pitch being 95% to 99% of the other's. This pitch difference causes axial interference within the engagement length, resulting in contact at both ends and suspension in the middle after assembly. Even without load, significant interaction forces exist between the internal and external threads. When loaded, the thread bearing capacity decreases at the support surface and increases further away from the support surface, inevitably leading to stress concentration in the few threads furthest from the support surface, resulting in uneven stress distribution on the thread teeth. Summary of the Invention

[0005] The purpose of this invention is to provide a design method for non-equidistant threaded connection pairs to solve the problem of uneven stress on the threads of existing threaded connection pairs.

[0006] To achieve the above objectives, the design method for non-equidistant threaded connection pairs in this invention adopts the following technical solution:

[0007] A design method for non-equidistant threaded connections includes the following: determining the basic thread profiles and material properties of the internal and external threads, as well as the axial load borne by the external thread, wherein the axial load borne by the external thread is N; determining the pitch difference ΔP between the internal and external threads. Where P is the external thread pitch, K is a comprehensive reference coefficient and 0.8≤K≤4.5, and k is a load coefficient equal to the ratio of the axial load N borne by the external thread to the product of the yield strength σ of the external thread material and the stress cross-sectional area A1 of the external thread, i.e. k c The material coefficient is equal to the yield strength σ and the elastic modulus E of the external thread material. w The ratio, that is Try selecting the pitch difference ΔP between the internal and external threads, and adjust the total axial clearance δ when the internal and external threads are used together, δ=PS w -S n S w S is the tooth width of the external thread at the pitch diameter. n The tooth width of the internal thread at the pitch diameter of the external thread is used to verify the stress state of the thread and determine the thread parameters.

[0008] The beneficial effects of the above technical solution are as follows: This invention proposes a pioneering design method for non-equidistant threaded connection pairs. This design method considers the basic thread profile and material properties of the internal and external threads, as well as the axial load N borne by the external thread, thus providing a basis for obtaining better stress uniformity; and it determines the pitch difference between the internal and external threads. Compared with existing technologies, this invention reduces the pitch difference between internal and external threads. Then, the pitch difference ΔP between internal and external threads is selected by trial selection, and the total axial clearance δ is adjusted when the internal and external threads are used together to ensure the fit effect of the internal and external threads. Finally, the stress state of the threads is verified and the thread parameters are determined. It has been verified that the design method of this invention can design non-equidistant threaded connection pairs with better stress uniformity.

[0009] Furthermore, if PS w <S n Then it is necessary to reduce the tooth width S of the internal thread. n .

[0010] The beneficial effects of the above technical solution are: it prevents excessive internal thread width from causing interference fit between internal and external threads, thus reducing assembly resistance and improving assemblability.

[0011] Furthermore, if δ < l, where l is the difference in length between the internal and external threads, then the total fit clearance δ needs to be increased.

[0012] The beneficial effects of the above technical solution are: to avoid excessive pitch difference between internal and external threads, which would lead to insufficient clearance and thus interference fit, thereby reducing assembly resistance and improving assemblability.

[0013] Furthermore, when verifying the stress state of the thread, if the stress value at the starting position is greater than the stress value at the ending position, then decrease ΔP; if the stress value at the ending position is greater than the stress value at the starting position, then increase ΔP and readjust the total fit clearance δ.

[0014] The beneficial effect of the above technical solution is that it ensures uniform stress.

[0015] Furthermore, let n be the total number of threads engaged under load on the inner and outer rings. Let the total length of the external thread with n' turns be L1 = n'P, and the length of the internal thread with n' turns be L2 = n'P'. Let P' be the pitch of the internal thread. The pitch difference between the internal and external threads is ΔP = P' - P. Therefore, the length difference between the internal and external threads is l = L2 - L1 = n'(P' - P) = n'ΔP. Thus, the pitch difference between the internal and external threads... The sum of the total elongation of the external thread (n' turns) and the total compression of the internal thread is taken as the length difference l between the internal and external threads. ;make ,but Further conclusions When n'=n, the length difference l between the internal and external threads is: Furthermore, the pitch difference between the internal and external threads .

[0016] The beneficial effect of the above technical solution is that it uses the length difference l between the internal and external threads to calculate the pitch difference ΔP between the internal and external threads, and gives the formula for l and the derivation process of ΔP.

[0017] Furthermore, the process of calculating the length difference l between the internal and external threads includes the following:

[0018] (a) Simplify the external thread in the engagement region of the internal and external threads into an equivalent force-bearing cylinder. According to 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, calculate the total elongation of the external thread with any n' turns starting from the initial position. Where: 0 < k1 < 1; Let be the total average elongation of the equivalent stressed cylinder at any n' turns; n is the total number of turns in the internal and external thread engagement area, and N is also the axial load borne by the equivalent stressed cylinder at the termination section. The direction of the axial load N is from the starting section to the termination section.

[0019] (ii) Simplify the internal thread in the engagement region of the internal and external threads into an equivalent hollow cylinder under stress. According to Hooke's Law and the fact that the compression of the inner cylindrical surface of the equivalent hollow cylinder is greater than the average compression of the equivalent hollow cylinder, calculate the total compression of the internal thread with any n' turns starting from the initial position. Where: k2 > 1; E represents the total average compression of the equivalent hollow cylinder at any n' revolutions. n The elastic modulus of the internal thread material; This is the cross-sectional area of ​​the equivalent stressed hollow cylinder; F N The axial load F is the axial load borne by the equivalent hollow cylinder at the termination section. N The direction is from the end position section to the start position section;

[0020] (iii) The axial load F(n') on the external thread teeth at any n' turns of the internal thread starting from the initial position can be known from the simplified mechanical relationship of the equivalent force-bearing cylinder and the equivalent force-bearing hollow cylinder. Therefore, we have: the total elongation of the external thread l w Total compression of internal threads l n The sum is the difference in length l between the internal and external threads, that is: ;

[0021] (iv) Let E w A1 and E n The ratio of A2 is k3, and let The formula for the length difference l between the internal and external threads is simplified to: .

[0022] The beneficial effects of the above technical solution are: it provides a specific calculation process for the length difference l between the internal and external threads, and simplifies the calculation formula to facilitate subsequent calculations.

[0023] Furthermore, for the equivalent stressed cylinder simplified from the external thread, taking the initial position as the starting point, f1(n') is the resultant force of the loads at any n' turns of the small outer cylindrical surface of the equivalent stressed cylinder. The resultant force of the loads at all small outer cylindrical surfaces is equal to the axial load N. A small cylinder is cut off at any height h=n'P of the equivalent stressed cylinder. The thickness of the small cylinder is dh=Pdn'. The lower section of the small cylinder is subjected to an axial load of... Hooke's Law can be used to derive the average elongation of a tiny cylinder. Therefore, the total average elongation of the equivalent stressed cylinder at any n' turns is Due to the small elongation at the outer cylindrical surface of the tiny cylinder, the average elongation dl w1The outer cylindrical surface of the equivalent stressed cylinder is the simplified region of the external thread; therefore, the elongation of the outer cylindrical surface should be equal to the elongation dl of the external thread. w Then that is This allows us to determine the total elongation of any n' turns of the external thread, starting from the initial position. .

[0024] The beneficial effect of the above technical solution is that it provides the total elongation l of an external thread with any number of n' turns. w The specific derivation process utilizes Hooke's Law and considers the relationship between the elongation of the equivalent stressed cylinder near the axis and the elongation near the cylindrical surface, ensuring more accurate calculation results.

[0025] Furthermore, for the equivalent hollow cylinder simplified to an internal thread, f2(n') is the resultant force of the loads at any n' turns of the infinitesimal inner cylindrical surface of the equivalent hollow cylinder. The resultant force of all loads at the infinitesimal inner cylindrical surface and the axial load F N Equal; A tiny hollow cylinder is cut at an arbitrary height h=n'P of the equivalent stressed hollow cylinder. The thickness of the tiny hollow cylinder is dh=Pdn', and the lower section of the tiny hollow cylinder is subjected to an axial load of... The average compression of a tiny hollow cylinder with thickness dh By integration, the total average compression of the equivalent force-bearing hollow cylinder at any n' revolutions starting from the initial position can be calculated as follows: Because the compression at the cylindrical surface inside the tiny hollow cylinder is greater than the average compression dl n1 The inner cylindrical surface of the equivalent hollow cylinder is the simplified region of the internal thread; therefore, the compression of the inner cylindrical surface is equal to the compression dl of the internal thread. n ,but This leads to the total compression of any n' turns of the internal thread, starting from the initial position. .

[0026] The beneficial effect of the above technical solution is that it provides the total compression amount l of an internal thread with any number of n' turns. n The specific derivation process utilizes Hooke's Law and considers the relationship between the compression of the inner cylindrical surface and the average compression of the equivalent stressed hollow cylinder, ensuring more accurate calculation results.

[0027] Furthermore, according to 0.4 < k < 0.8, Taking into account k, k c And K limits the upper limit of ΔP Further obtained .

[0028] The beneficial effect of the above technical solution is that it provides an upper limit for ΔP, which facilitates the design and manufacturing of threads.

[0029] Furthermore, according to 0.4 < k < 0.8, Taking into account k, k c And K limits the lower bound of ΔP Further obtained .

[0030] The beneficial effect of the above technical solution is that it provides a lower limit for ΔP, which facilitates the design and manufacturing of threads. Attached Figure Description

[0031] Figure 1 This is a tooth profile diagram of the basic external thread of the non-equidistant threaded connection pair in this invention;

[0032] Figure 2 This is a tooth profile diagram of the basic internal thread of the non-equidistant threaded connection pair in this invention;

[0033] Figure 3 This is a schematic diagram showing the starting and ending positions of the non-equidistant threaded connection pair under load in this invention;

[0034] Figure 4 This is a diagram showing the engagement state of the internal and external threads of the non-equidistant threaded connection pair in this invention.

[0035] Figure 5 This is a simplified schematic diagram of the external thread involved in this invention as an equivalent stressed cylinder;

[0036] Figure 6 for Figure 5 Schematic diagram of the average elongation and elongation at the cylindrical surface of a small to medium-sized cylinder;

[0037] Figure 7 This is a simplified schematic diagram of the internal thread involved in this invention as an equivalent stressed hollow cylinder;

[0038] Figure 8 for Figure 7 Schematic diagram of the average compression and compression at the inner cylindrical surface of a small hollow cylinder;

[0039] Figure 9 This is a schematic diagram showing the force on the external thread in the internal and external thread engagement area of ​​the present invention;

[0040] Figure 10 The diagram shows the variation trend of the axial force F(n') acting on the external thread teeth in three common cases.

[0041] Figure 11 for Figure 10 Stress cloud diagrams showing three different trends in F(n');

[0042] Figure 12 This is a schematic diagram illustrating the adjustment of the internal thread pitch involved in this invention;

[0043] Figure 13 This is a schematic diagram illustrating the principle that the internal and external threads involved in this invention do not experience tooth seizing.

[0044] Figure 14 The stress cloud diagrams of the internal and external threads of this application and three comparative threads under load are shown.

[0045] Figure 15 This is a schematic diagram showing the numbering and average value of the external thread teeth;

[0046] Figure 16 The diagram shows the average stress of each thread tooth of the external thread of this application and three comparative threads. Detailed Implementation

[0047] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0048] The design method for non-equidistant threaded connections of this invention first considers the basic thread profile and material properties of the internal and external threads, as well as the axial load N borne by the external thread. Secondly, it provides the range of the pitch difference ΔP between the internal and external threads, i.e. Compared with existing technologies, this method reduces the pitch difference between internal and external threads. Then, by trial selection of the pitch difference ΔP between internal and external threads, the total axial clearance δ when the internal and external threads are used together is adjusted. Finally, the stress state of the thread is verified and the thread parameters are determined. Through the above design steps, stress uniformity can be improved and the stress concentration phenomenon of the thread can be reduced.

[0049] Example 1 of the design method for non-equidistant threaded connection pairs in this invention:

[0050] The design method for non-equidistant threaded connections includes the following: determining the basic thread profiles and material properties of the internal and external threads, and the axial load N borne by the external thread; determining the range of the pitch difference ΔP between the internal and external threads, i.e. Where P is the external thread pitch; try to select the pitch difference ΔP between the internal and external threads, and adjust the total axial clearance δ when the internal and external threads are used together, δ=PS w -S n S w S is the tooth width of the external thread at the pitch diameter. n The tooth width of the internal thread at the pitch diameter of the external thread is used to verify the stress state of the thread and determine the thread parameters.

[0051] The specific design steps are as follows:

[0052] Step 1: Determine the basic thread profile, material properties, and rated load of the internal and external threads.

[0053] The basic thread profile is a standard thread such as metric thread, MJ thread, trapezoidal thread and circular arc thread. Non-standard threads can also be used. The basic thread profile is a thread profile with a width of one standard pitch along the axial direction.

[0054] like Figure 1 As shown, the tooth width at the basic external thread pitch P, major diameter d, minor diameter d1, and external thread pitch diameter d2 is S. w The yield strength of the external thread material is σ, and the elastic modulus is E. w The axial load borne by the external thread is N.

[0055] like Figure 2 As shown, the basic internal thread pitch P', major diameter D, minor diameter D1, and the tooth width of the internal thread at the external thread pitch diameter d2 are S. n The number of internal thread turns is n (i.e., the total number of turns in the engagement area of ​​the internal and external threads), and the elastic modulus E of the internal thread material is... n .

[0056] Step 2: Determine the range of the pitch difference ΔP between the internal and external threads.

[0057] For ease of description, this invention specifies a start position and an end position, as follows: Figure 3 and Figure 4 As shown, taking bolt 1 and nut 2 as an example, within the internal and external thread engagement area, the present invention takes one end face of the internal thread perpendicular to the axis as the starting position section Q, and the other end face of the internal thread as the ending position section Z (traditionally considered as the support surface, that is, the end face of nut 2 used to press the connected parts). The direction from the starting position to the ending position is the same as the direction in which the external thread bears the rated axial load N.

[0058] Since the number of internal thread turns is n, when internal and external threads are used together, the n internal thread turns must mesh with the n external thread turns. Under the condition that no deformation occurs under load, taking the starting position as the starting point, any n' internal thread turns (0 < n' ≤ n) will be longer than the external thread.

[0059] Specifically, the total length of the n'-turn external thread is L1, the length of the n'-turn internal thread is L2, and the length difference between the internal and external threads is: l = L2 - L1; further, the external thread length L1 = n'P, the internal thread length L2 = n'P', and the pitch difference between the internal and external threads ΔP = P' - P, then l = L2 - L1 = n'(P' - P) = n'ΔP, that is... Therefore, to solve for the pitch difference ΔP, it is necessary to find the length difference l between the internal and external threads.

[0060] In traditional equidistant threads, under load and engagement, the external thread elongates under tension, while the internal thread shortens under compression. Furthermore, both the external and internal threads at any point within the engagement area exhibit varying degrees of elongation or compression. This invention addresses this by reducing the total elongation (l) of n external threads. w Total compression of internal threads l n The sum of these two values ​​represents the length difference l between the internal and external threads.

[0061] like Figure 5 As shown, for ease of analysis, the external thread in the engagement region of the internal and external threads is simplified into an equivalent force-bearing cylinder. The two circular cross-sections of the equivalent force-bearing 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 cylinder is... Let be the stress cross-sectional area of ​​the thread. The equivalent stressed cylinder experiences an axial load of N at the termination section Z. The direction of the axial load N is from the starting section Q to the termination section Z. The force between the internal and external threads is simplified as follows: the outer cylindrical surface of the equivalent stressed cylinder bears a surface load. The surface load is opposite in direction to the axial load N, and the resultant force of the surface load is the same as the magnitude of the axial load N. Starting from the initial position, the resultant force of the load at any n' turns of the infinitesimal outer cylindrical surface is f1(n'). The resultant force of the load at all infinitesimal outer cylindrical surfaces is equal to the axial load N, i.e. .

[0062] A small cylinder is cut at an arbitrary height h=n'P of the equivalent stressed cylinder. The thickness of the small cylinder is dh=Pdn'. The lower section of the small cylinder is subjected to an axial load of... Hooke's Law can be used to derive the average elongation of a tiny cylinder. The total average elongation of the equivalent stressed cylinder at any n' turns is .

[0063] Depend on Figure 6 It can be seen that, because the direction of the surface load on the outer cylindrical surface of the micro cylinder is opposite to the direction of the load N1 on the lower section of the micro cylinder, the elongation at the outer cylindrical surface of the micro cylinder is smaller than the average elongation dl. w1 The outer cylindrical surface of the equivalent stressed cylinder is the simplified region of the external thread; therefore, the elongation of the outer cylindrical surface should be equal to the elongation dl of the external thread. w Then that is 0 < k1 < 1. For ease of analysis, we assume k1 is a constant. Then, taking the starting position as the starting point, the total elongation of the external thread for any n' turns... .

[0064] like Figure 7As shown, for ease of analysis, the internal thread in the engagement region of the internal and external threads is simplified as an equivalent stressed hollow cylinder. The two annular sections of the equivalent stressed hollow cylinder are the starting position section Q and the ending position section Z, respectively. The cross-sectional area of ​​the equivalent stressed hollow cylinder is... The axial load borne by the equivalent hollow cylinder at section Z at the termination position is F. N (According to the equilibrium of forces, F) N (Equal to N), the direction is from the termination position to the starting position. The force between the internal and external threads is simplified to the equivalent force. The inner cylindrical surface of the hollow cylinder bears a surface load, and the surface load and the axial force F N The resultant force of the surface loads and the axial force F are in opposite directions. N The magnitudes are the same. Taking the initial section as the starting point, the resultant force of the load at any n'-th revolution position on the tiny inner cylindrical surface is f2(n'). The resultant force of the loads at all tiny inner cylindrical surfaces is equal to the axial load F. N Equal, that is .

[0065] A small hollow cylinder is cut at an arbitrary height h=n'P of the equivalent stressed hollow cylinder. The thickness of the small hollow cylinder is dh=Pdn'. The lower section of the small hollow cylinder is subjected to an axial load of... The average compression of a tiny hollow cylinder with thickness dh By integration, the total average compression of the equivalent hollow cylinder at any n' revolutions starting from the initial section Q can be calculated as follows: .

[0066] Depend on Figure 8 It can be seen that the direction of the surface load on the cylindrical surface inside the tiny hollow cylinder is different from the direction of the load F on the lower section of the tiny hollow cylinder. N The opposite directions of action cause the compression at the cylindrical surface inside the tiny hollow cylinder to be greater than the average compression dl. n1 The inner cylindrical surface of the equivalent hollow cylinder is the simplified region of the internal thread; therefore, the compression of the inner cylindrical surface is equal to the compression dl of the internal thread. n ,but 1 < k2. For ease of analysis, we assume k2 is a constant. Then, taking the starting position as the starting point, the total compression of the internal thread for any n' turns... .

[0067] like Figure 9 As shown, the axial load F(n') acting on the external thread teeth at any n' turns of the internal thread starting from the initial position is known from the simplified mechanical relationship of the equivalent force-bearing cylinder and the equivalent force-bearing hollow cylinder. Therefore, we have: the total elongation of the external thread l w Total compression of internal threads ln The sum is the difference in length l between the internal and external threads, that is: .

[0068] Once the internal and external thread materials, i.e. the nut's external dimensions, are selected, E n Both A2 and E are constants, therefore E w A1 and E n The ratio k3 of A2 is a constant. For ease of calculation, the elastic modulus and area in the formula are unified to E. w And A1, then To further simplify, let K is a comprehensive reference coefficient, which simplifies the formula for the length difference l between internal and external threads to: .

[0069] Furthermore, in In the formula, only F(n') and n' are variables, and the axial load F(n') acting on the external thread teeth follows the variation trend of n' in three common cases, such as... Figure 10 As shown, in curve a, F(n') increases as n' increases; in curve b, F(n') remains constant; and in curve c, F(n') decreases as n' increases. According to mechanical relationships, from the initial position to the final position, the cumulative value of the axial load F(n') on the external thread teeth is the axial load N of the cross section, i.e. .

[0070] Simulation calculations were performed using three different trends for F(n'), and the resulting stress cloud diagrams are shown below. Figure 11 As shown, Figure 11 (a) is the stress contour plot corresponding to curve a. Figure 11 (b) is the stress contour plot corresponding to curve b. Figure 11 (c) is the stress contour plot corresponding to curve c.

[0071] The high-stress region at the root of an external thread typically occurs at the root of the thread. The magnitude of the stress is influenced by the combined effects of the axial load F(n') on the external thread and the axial load N(n') on the cross-section (i.e., the force across the entire cross-section (excluding the thread) in n' turns). When the internal and external threads deform under load, starting from the initial position, the axial load N(n') on the cross-section increases with the number of thread turns n', reaching its maximum value N in n turns. Figure 10 As shown, when the axial force F(n') on the external thread teeth conforms to curve a, F(n') is smaller at the starting position and larger at the ending position. This is consistent with the trend of N(n'). Figure 11 As shown in (a), the stress at the starting position of the external thread is relatively small, while the stress at the ending position is relatively large, resulting in obvious stress concentration.

[0072] like Figure 10 As shown, when the axial force F(n') on the external thread conforms to curve b, F(n') is a constant value. However, since the axial load N(n') on the cross section gradually increases with n', the stress at the root of the external thread still shows a small stress value at the initial position and a large stress value at the end position. The stress concentration phenomenon is somewhat improved, as shown in the figure. Figure 11 As shown in (b), when the axial force F(n') on the external thread conforms to curve c, F(n') further increases at the starting position and further decreases at the ending position, causing the stress at the root of the external thread at the starting position to further increase and the stress at the ending position to further decrease. This results in a more uniform stress value at the root of the entire external thread and less stress concentration. Figure 11 As shown in (c). Furthermore, F(n') conforms well to the stress state of curve c, and the selected F(n') equation should satisfy curve c. F(n') should satisfy two conditions: it is a decreasing function in the interval 0 ≤ n' ≤ n. .

[0073] For ease of calculation, assume the axial force on the external thread is... The expression 0 < n' ≤ n decreases linearly, and Further conclusions When n'=n, the length difference l between the inner and outer threads is: Let k be the load factor. The ratio of the axial force N borne by the external thread to the product of the material's yield strength σ and the stress cross-sectional area A1 of the external thread is... Let k c Let be the material coefficient, which is the ratio of the material's yield strength σ to its elastic modulus E. w The ratio, that is Once the main design parameters and materials of the bolt are determined, k and k c It is a constant. Further, we arrive at... .

[0074] Furthermore, the pitch difference between the internal and external threads , 0.8≤K≤4.5.

[0075] Furthermore, the load factor k typically ranges from 0.4 to 0.8, and the material coefficient of commonly used thread materials is... Taking into account k, k c The pitch difference between the internal and external threads is defined by K. .

[0076] Step 3: Select the pitch difference ΔP between the internal and external threads, and adjust the total axial clearance δ when the internal and external threads are used together.

[0077] Based on the range of values ​​for the comprehensive reference coefficient K, the pitch difference ΔP between the internal and external threads is selected, and the principle is as follows: Figure 12As shown, keeping the basic internal thread teeth unchanged, the width of the internal thread root 21 is increased by ΔP to increase the internal thread pitch. Figure 12 The dashed line represents the area before increasing the tooth base width, and the solid line represents the area after increasing the tooth base width.

[0078] When internal and external threads are used together, the total axial clearance δ = PS w -S n The verification involves the tooth width S of the internal thread at the mean diameter d2 of the external thread. n When considering the size of the gap at the mean diameter d2 of the external thread, if PS w <S n Then it is necessary to reduce the tooth width S of the internal thread. n To prevent excessively wide internal thread teeth from causing an interference fit between the internal and external threads (i.e., not meeting the requirements of the groove C at the mean diameter d2 of the external thread). n The width S is greater than the tooth width S at the mean diameter d2 of the external thread. n (This can lead to a biting phenomenon), thus reducing assembly resistance and improving assemblability. When verifying the length difference l between the internal and external threads and the total axial clearance δ, if δ < l, the total clearance δ needs to be increased to avoid an excessively large pitch difference between the internal and external threads, which would result in an insufficient clearance and thus an interference fit (i.e., insufficient axial clearance causing biting). Therefore, this can reduce assembly resistance and improve assemblability.

[0079] The above principles are as follows Figure 13 As shown in the diagram above, the internal and external threads have equal pitches, with one side of the internal and external threads touching while the other side does not. The axial clearance between the internal and external threads is δ. In the diagram below, the internal and external threads touch on the far left. Since the pitch of the internal thread is greater than that of the external thread, the internal and external threads begin to separate from the touching position. On the far right, the other side of the internal and external threads gradually approaches, at which point the length difference between the internal and external threads is l. When δ = l, the rightmost side of the internal and external threads just touches; when δ < l, the internal and external threads will have an interference fit, making assembly difficult. Therefore, δ ≥ l can prevent insufficient axial clearance from causing tooth seizing.

[0080] Step 4: Verify the stress state of the thread and determine the thread parameters.

[0081] Establish finite element models of internal and external threads, calculate the load distribution of the thread teeth under rated load, and determine the stress state of internal and external threads. If the stress values ​​at the starting and ending positions are approximately equal, the requirements are met. If the stress value at the starting position is larger, decrease ΔP. If the stress at the ending position is larger, increase ΔP. Repeat step 3, establish another finite element model, calculate the load distribution of the thread teeth under rated load, until the pitch difference ΔP of internal and external threads under rated load is obtained, and finally determine the parameters of internal and external threads.

[0082] The design method of the non-equidistant threaded connection pair of the present invention will be described in detail below with reference to specific thread parameters. Specific implementation method one:

[0084] 1. Determine the basic thread profile, material properties, and rated load of the internal and external threads.

[0085] The basic external thread profile is a metric thread, with a pitch P=4mm, major diameter d=42mm, minor diameter d1=37.67mm, pitch diameter d2=39.4mm, and a tooth width at the pitch diameter of the external thread is S. w =2mm. The elastic modulus E of the external thread material. w =206GPa, the yield strength of the external thread material σ=930MPa, and the rated load that the external thread can withstand is .

[0086] The basic internal thread profile is a metric thread, with a pitch P = 4mm, major diameter D = 42mm, minor diameter D1 = 37.67mm, and a tooth width S at the pitch diameter d2 of the external thread. n =2mm, the number of internal thread turns is n=7 turns.

[0087] 2. Determine the range of the pitch difference ΔP between the internal and external threads.

[0088] .

[0089] 3. Select the pitch difference ΔP between the internal and external threads, and adjust the total axial clearance δ when the internal and external threads are used together.

[0090] Taking ΔP = 0.018 mm as an example, the adjusted internal thread parameters are: internal thread pitch P' = 4.018 mm, major diameter D = 42.42 mm, minor diameter D1 = 38.09 mm, and the tooth width of the internal thread at the external thread pitch diameter d2 is S. n =1.76mm.

[0091] Furthermore, l = nΔP = 0.126 mm, δ = PS w -S n =0.24mm.

[0092] Furthermore, PS w =2mm>S n =1.76mm.

[0093] Furthermore, δ=0.24mm>l=0.126mm.

[0094] 4. Verify the stress state of the thread and determine the thread parameters.

[0095] Table 1 shows the pitch difference ΔP between the internal and external threads of different threads. The pitch difference ΔP between the internal and external threads of the comparative thread 1 is 0.01P. Although the pitch difference ΔP between the internal and external threads of the comparative thread 2 is less than 0.01P, it is much smaller than that of the thread in this application. The comparative thread 3 is a normal equidistant thread.

[0096] Table 1. Pitch difference ΔP between internal and external threads

[0097]

[0098] Finite element models of internal and external threads were established based on thread parameters and material properties. It should be noted that the simulation model is an elastic model; in some cases, the calculated average stress far exceeds the yield stress, indicating a significant stress concentration phenomenon. The stress contour plot after calculation is shown below. Figure 14 As shown in the figure, the stress uniformity of the thread in this application is the best compared to the comparative thread.

[0099] according to Figure 15 Using the thread numbering (1-7) and the positions indicated by the bold short vertical lines, extract the average stress of each thread tooth in the external thread, plot the average stress variation diagram for each thread tooth, and calculate the stress concentration factor for each thread tooth (stress concentration factor = maximum stress / total average stress). Figure 16 It can be seen that the thread with ΔP=0.018mm (i.e. the thread of this application) has good load uniformity. As shown in Table 2, the thread with ΔP=0.018mm (i.e. the thread of this application) has the smallest stress concentration factor.

[0100] Table 2 Stress concentration factors of the threads in this application and the comparative threads

[0101]

[0102] In other implementations: the total average elongation l of the equivalent stressed cylinder at any n' turns can also be used directly. w1 Let l represent the total elongation of any n' turns of external thread. w Of course, we can also directly use the total average compression of the equivalent hollow cylinder at any n' revolutions as l. n1 Let l represent the total compression of any n' turns of internal thread. n .

[0103] In other implementations: depending on the specific requirements, the simplified results of the equations for ΔP and l can vary when different simplification methods are used.

[0104] In other implementations, the total axial clearance δ when the internal and external threads are used together can be equal to the length difference l between the internal and external threads.

[0105] In other implementations: the clearance at the pitch diameter of the external thread can be equal to the tooth width S of the internal thread. n That is: PS w =S n .

[0106] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. The scope of patent protection of the present invention shall be determined by the claims. Similarly, any equivalent structural changes made based on the description and drawings of the present invention shall also be included within the scope of protection of the present invention.

Claims

1. A design method for a non-equidistant threaded connection pair, characterized in that, This includes the following: determining the basic thread profile and material properties of the internal and external threads, and the axial load borne by the external thread, where the axial load borne by the external thread is N; determining the pitch difference ΔP between the internal and external threads. Where P is the external thread pitch, K is a comprehensive reference coefficient and 0.8≤K≤4.5, and k is a load coefficient equal to the ratio of the axial load N borne by the external thread to the product of the yield strength σ of the external thread material and the stress cross-sectional area A1 of the external thread, i.e. k c The material coefficient is equal to the yield strength σ and the elastic modulus E of the external thread material. w The ratio, that is Try selecting the pitch difference ΔP between the internal and external threads, and adjust the total axial clearance δ when the internal and external threads are used together, δ=PS w -S n S w S is the tooth width of the external thread at the pitch diameter. n The tooth width of the internal thread at the pitch diameter of the external thread is used to verify the stress state of the thread and determine the thread parameters.

2. The design method for non-equidistant threaded connection pairs according to claim 1, characterized in that, If PS w <S n Then it is necessary to reduce the tooth width S of the internal thread. n .

3. The design method for non-equidistant threaded connection pairs according to claim 1 or 2, characterized in that, If δ < l, where l is the difference in length between the internal and external threads, then the total clearance δ needs to be increased.

4. The design method for non-equidistant threaded connection pairs according to claim 1 or 2, characterized in that, When verifying the stress state of the thread, if the stress value at the starting position is greater than the stress value at the ending position, decrease ΔP; if the stress value at the ending position is greater than the stress value at the starting position, increase ΔP and readjust the total fit clearance δ.

5. The design method for non-equidistant threaded connection pairs according to claim 1 or 2, characterized in that, Let n be the total number of threads engaged under load on the inner and outer rings. The total length of the external thread with n' turns is L1 = n'P, and the length of the internal thread with n' turns is L2 = n'P'. P' is the pitch of the internal thread. The pitch difference between the internal and external threads is ΔP = P' - P. Therefore, the length difference between the internal and external threads is l = L2 - L1 = n'(P' - P) = n'ΔP. Thus, the pitch difference between the internal and external threads... The sum of the total elongation of the external thread (n' turns) and the total compression of the internal thread is taken as the length difference l between the internal and external threads. ; make ,but Further conclusions When n'=n, the length difference l between the internal and external threads is: Furthermore, the pitch difference between the internal and external threads .

6. The design method for non-equidistant threaded connection pairs according to claim 5, characterized in that, The process of calculating the length difference l between the internal and external threads includes the following: (a) Simplify the external thread in the engagement region of the internal and external threads into an equivalent force-bearing cylinder. According to 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, calculate the total elongation of the external thread with any n' turns starting from the initial position. Where: 0 < k1 < 1; Let be the total average elongation of the equivalent stressed cylinder at any n' turns; n is the total number of turns in the internal and external thread engagement area, and N is also the axial load borne by the equivalent stressed cylinder at the termination section. The direction of the axial load N is from the starting section to the termination section. (ii) Simplify the internal thread in the engagement region of the internal and external threads into an equivalent hollow cylinder under stress. According to Hooke's Law and the fact that the compression of the inner cylindrical surface of the equivalent hollow cylinder is greater than the average compression of the equivalent hollow cylinder, calculate the total compression of the internal thread with any n' turns starting from the initial position. Where: k2 > 1; E n The elastic modulus of the internal thread material; Let be the total average compression of the equivalent hollow cylinder at any n' revolutions; This is the cross-sectional area of ​​the equivalent stressed hollow cylinder; F N The axial load F is the axial load borne by the equivalent hollow cylinder at the termination section. N The direction is from the end position section to the start position section; (iii) The axial load F(n') on the external thread teeth at any n' turns of the internal thread starting from the initial position can be known from the simplified mechanical relationship of the equivalent force-bearing cylinder and the equivalent force-bearing hollow cylinder. Therefore, we have: the total elongation of the external thread l w Total compression of internal threads l n The sum is the difference in length l between the internal and external threads, that is: ; (iv) Let E w A1 and E n The ratio of A2 is k3, and let The formula for the length difference l between the internal and external threads is simplified to: .

7. The design method for non-equidistant threaded connection pairs according to claim 6, characterized in that, For the equivalent stressed cylinder simplified from the external thread, taking the initial position as the starting point, f1(n') is the resultant force of the loads at any n' turns of the small outer cylindrical surface of the equivalent stressed cylinder. The resultant force of the loads at all small outer cylindrical surfaces is equal to the axial load N. A small cylinder is cut off at any height h = n'P of the equivalent stressed cylinder. The thickness of the small cylinder is dh = Pdn'. The lower section of the small cylinder is subjected to an axial load of... Hooke's Law can be used to derive the average elongation of a tiny cylinder. Therefore, the total average elongation of the equivalent stressed cylinder at any n' turns is Due to the small elongation at the outer cylindrical surface of the tiny cylinder, the average elongation dl w1 The outer cylindrical surface of the equivalent stressed cylinder is the simplified region of the external thread; therefore, the elongation of the outer cylindrical surface should be equal to the elongation dl of the external thread. w Then that is This allows us to determine the total elongation of any n' turns of the external thread, starting from the initial position. .

8. The design method for non-equidistant threaded connection pairs according to claim 6, characterized in that, For the equivalent hollow cylinder simplified to an internal thread, f2(n') is the resultant force of the loads at any n' turns of the infinitesimal inner cylindrical surface of the equivalent hollow cylinder. The resultant force of all loads at the infinitesimal inner cylindrical surface and the axial load F N Equal; A tiny hollow cylinder is cut at an arbitrary height h=n'P of the equivalent stressed hollow cylinder. The thickness of the tiny hollow cylinder is dh=Pdn', and the lower section of the tiny hollow cylinder is subjected to an axial load of... The average compression of a tiny hollow cylinder with thickness dh By integration, the total average compression of the equivalent force-bearing hollow cylinder at any n' revolutions starting from the initial position can be calculated as follows: Because the compression at the cylindrical surface inside the tiny hollow cylinder is greater than the average compression dl n1 The inner cylindrical surface of the equivalent hollow cylinder is the simplified region of the internal thread; therefore, the compression of the inner cylindrical surface is equal to the compression dl of the internal thread. n ,but This leads to the total compression of any n' turns of the internal thread, starting from the initial position. .

9. The design method for non-equidistant threaded connection pairs according to claim 1, characterized in that, Based on 0.4 < k < 0.8, Taking into account k, k c And K limits the upper limit of ΔP Further obtained .

10. The design method for non-equidistant threaded connection pairs according to claim 1, characterized in that, Based on 0.4 < k < 0.8, Taking into account k, k c And K limits the lower bound of ΔP Further obtained .

Images