Design method for non-equidistant threaded connection pair

Abstract

The present invention relates to the field of non-standard fasteners, and provides a design method for a non-equidistant threaded connection pair. The design method for a non-equidistant threaded connection pair comprises the following content: determining the basic thread profiles of inner and outer threads, material performance, an axial load N borne by the outer thread; calculating a length adjustment amount (l) of a variable pitch thread, (l) being a formula containing F(n'), i.e., equation l, and trying to select an F(n') equation to obtain an F(n') curve equation corresponding to the case of better stress uniformity; and determining a pitch adjustment amount ΔP equation of the variable pitch thread, on the basis of the selected F(n') equation, there being only one unknown number K in the ΔP equation, K being a comprehensive reference coefficient, and the value of K being determined. According to the present invention, the basic thread profiles of the inner and outer threads, the material performance, the axial load N borne by the outer thread are considered, and upon analytical verification, the non-equidistant thread connection pair having better stress uniformity can be designed by using the design method of the present invention.

Description

A design method for non-equidistant thread connection pairs Technical Field

[0001] The invention relates to a design method for a non-equidistant thread connection pair, and belongs to the field of non-standard fasteners. Background Art

[0002] Bolted connection structure (including bolts and nuts) is a relatively common connection method, widely used in the fields of machinery and construction. At present, the pitch of the internal and external threads of the traditional threaded connection pair is equal and is a constant value P. When the threaded connection pair is subjected to load, the external thread is subjected to tension and elongation, and the internal thread is subjected to pressure and compression. 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 tighten the connected parts, that is, the support surface is the end face at the end position of the screwing area of ​​the internal and external threads, and the other end face is the end face at the starting position) becomes larger, and the elongation of the external thread away from the support surface is small. This causes the axial load of the threaded connection pair to be mainly borne by the first three threads close to the support surface, causing significant stress concentration in the first three circles of threads.

[0003] Existing technical solutions employ a method where the pitch of the internal thread is greater than the pitch of the external thread (i.e., the internal thread is a gradual-pitch thread). This allows the threads farther from the support surface to contact first when the internal and external threads engage, and subsequent threads to contact one another sequentially. This increases the bearing capacity of the threads farther from the support surface and reduces the bearing capacity of the threads closer to the support surface, thereby reducing stress concentration at the bottom of the first three threads near the support surface. For example, Chinese invention patent application publication number CN101796312A discloses a threaded connection with a variable gap. While this solution improves stress uniformity across each thread turn to a certain extent, simulations based on the trend of the pitch difference ΔP between the internal and external threads gradually decreasing from the start to the end of the engagement region reveal that stress uniformity is not perfect, leaving significant room for improvement.

[0004] After research and analysis, the above scheme does not take into account the load conditions and the performance of the internal and external thread materials, nor does it clearly provide the specific calculation formula for the length adjustment amount and pitch adjustment amount of the gradual pitch thread, and it is impossible to obtain a threaded connection pair with better stress uniformity. Based on these problems, this application proposes a new design method for non-equidistant threaded connection pairs.

[0005] Summary of the Invention

[0006] The object of the present invention is to provide a design method for a non-equidistant threaded connection pair, so as to solve the problem that the stress uniformity of the existing threaded connection pair needs to be improved.

[0007] To achieve the above objectives, the design method of the non-equidistant thread connection pair in the present invention adopts the following technical solutions:

[0008] A design method for a non-equidistant thread connection pair includes the following steps: determining the basic thread profiles of the internal and external threads, material properties, and the axial load N borne by the external thread; calculating the length adjustment l of the progressive pitch thread, where l is a formula containing F(n'), where F(n') is the axial force exerted by the internal thread on the external thread at any n' number of turns, starting from the starting position of the internal and external thread engagement area. n is the total number of turns of the internal and external thread engagement areas; try to select the F(n') equation to obtain the curve equation of F(n') corresponding to the case of better stress uniformity; determine the equation for the pitch adjustment ΔP of the gradual pitch thread. According to the selected F(n') equation, there is only one unknown number K in the ΔP equation, and K is the comprehensive reference coefficient. Just determine the K value.

[0009] The beneficial effect of the above technical solution is that: the present invention proposes a pioneering design method for non-equidistant threaded connection pairs, which takes into account the basic thread profiles, material properties and axial load N of the internal and external threads, and has the basis for obtaining better stress uniformity; by calculating the length adjustment amount l of the gradual pitch thread, the length difference between the internal and external threads can be known, and l is a formula containing F(n'), which is related to the axial load N, and by trying to select the F(n') equation, the curve equation of F(n') corresponding to the case of better stress uniformity is obtained; finally, the pitch adjustment amount ΔP equation of the gradual pitch thread is determined. There is only one unknown number K in the ΔP equation, that is, the comprehensive reference coefficient. It is sufficient to determine this coefficient. After analysis and verification, the design method of the present invention can be used to design non-equidistant threaded connection pairs with better stress uniformity.

[0010] Furthermore, the length adjustment of the gradual pitch thread Where P is the pitch of the constant pitch thread, k1 and k2 are both constant values, E w is the elastic modulus of the external thread material, A1 is the stress cross-sectional area of ​​the external thread, E n is the elastic modulus of the internal thread material, and A2 is the stress cross-sectional area of ​​the internal thread.

[0011] The beneficial effect of the above technical solution is that: a specific calculation formula for the length adjustment amount l of the gradual pitch thread is given, and a connection with F(n') is established, so that there is a certain relationship between the length adjustment amount l and the axial load N borne by the external thread, which facilitates the design of the gradual pitch thread.

[0012] Furthermore, the process of calculating the length adjustment amount l of the gradual pitch thread includes the following:

[0013] (1) Simplify the external thread in the screwing area of ​​the internal and external threads into an equivalent load-bearing cylinder. According to Hooke's law and the fact that the elongation of the outer cylindrical surface of the equivalent load-bearing cylinder is less than the average elongation of the equivalent load-bearing cylinder, calculate the total elongation of the external thread with any number of n turns starting from the starting position. Among them: 0<k1<1, N is also the axial load borne by the equivalent loaded cylinder at the end position section. The direction of the axial load N is from the starting position section to the end position section.

[0014] (2) Simplify the internal thread in the screwing area of ​​the internal and external threads into an equivalent force-bearing hollow cylinder. According to Hooke's law and the fact that the compression of the inner cylindrical surface of the equivalent force-bearing hollow cylinder is greater than the average compression of the equivalent force-bearing hollow cylinder, calculate the total compression of the internal thread with any number of n' turns starting from the starting position. Where: k2>1, F N is the axial load borne by the equivalent hollow cylinder at the end section, the axial load F N The direction is from the end position section to the start position section;

[0015] (3) From the simplified method of equivalent loaded cylinder and equivalent loaded hollow cylinder, i.e. the mechanical relationship, we know that F(n′)=f1(n′)=f2(n′), so we have: Therefore, the length adjustment amount l of the n'th turn of the gradual pitch thread with the starting position as the starting point is the total elongation l of the external thread w Total compression with internal thread l n The sum is:

[0016] The beneficial effect of the above technical solution is that it provides a specific calculation process for the length adjustment amount l of the gradual pitch thread and establishes a theoretical research basis.

[0017] Furthermore, for the equivalent load-bearing cylinder simplified by the external thread, f1(n') is the resultant force of the load on the small external cylindrical surface at any n' number of turns of the equivalent load-bearing cylinder, and the resultant force of all small external cylindrical surfaces is equal to the axial load N; a small cylinder is cut at any height h = n'P of the equivalent load-bearing cylinder, the thickness of the small cylinder is dh = Pdn', and the axial force on the lower section of the small cylinder is The average elongation of a small cylinder can be obtained from Hooke's law Therefore, the total average elongation of the equivalent loaded cylinder at any n' number of turns is Since the elongation of the edge of the cylindrical surface of the equivalent force-bearing cylinder is less than the average elongation, the cylindrical surface of the equivalent force-bearing cylinder is the simplified area of ​​the external thread, so the elongation of the cylindrical surface should be the elongation dl of the external thread.w , then dl w =k1·dl w1 , and then the total elongation of the external thread with any n' turns starting from the starting position is obtained

[0018] The beneficial effect of the above technical solution is that it gives the total elongation l of any n' number of turns of external thread w The specific derivation process utilizes Hooke's law and takes into account the relationship between the elongation of the equivalent loaded cylinder near the axis and the elongation near the cylindrical surface to ensure more accurate calculation results.

[0019] Furthermore, for the equivalent hollow cylinder simplified by the internal thread, f2(n') is the resultant force of the load on the small inner cylindrical surface at any n' number of turns of the equivalent hollow cylinder. The resultant force of all small inner cylindrical surfaces and the axial load F N Equal; a small hollow cylinder is cut at any height h = n'P of the equivalent force hollow cylinder. The thickness of the small hollow cylinder is dh = Pdn', and the axial force on the lower section of the small hollow cylinder is Average compression of a tiny hollow cylinder with a thickness of dh By integration, the total average compression of the equivalent loaded hollow cylinder at any n' number of turns starting from the starting position can be calculated as follows: Since the compression of the inner cylindrical surface of the tiny hollow cylinder is greater than the average compression, the inner cylindrical surface of the equivalent force-bearing hollow cylinder is the simplified area of ​​the internal thread, so the compression of the inner cylindrical surface is the compression of the internal thread dl n , then dl n =k2·dl n1 , and then the total compression of the internal thread with any n' turns starting from the starting position is obtained

[0020] The beneficial effect of the above technical solution is that it gives the total compression amount l of any n' number of turns of internal thread n The specific derivation process utilizes Hooke's law and takes into account the relationship between the compression of the inner cylindrical surface of the equivalent loaded hollow cylinder and the average compression to ensure more accurate calculation results.

[0021] Furthermore, the curve corresponding to F(n') is a decreasing function in the interval 0≤n'≤n.

[0022] The beneficial effect of the above technical solution is that the stress uniformity is better when the condition is met.

[0023] Furthermore, the pitch adjustment amount ΔP of the gradual pitch thread is the sum of the thread variation Δl within one thread turn, that is, ΔP = ∑Δl. When 1 < n' ≤ n, that is:

[0024] When n'≤1, the pitch adjustment ΔP of the gradual pitch thread is the sum of the thread changes Δl within less than one turn of the thread length, that is:

[0025] After the internal and external thread materials and nut dimensions are selected, E n and A2 are both constant, so E w A1 and E n The ratio k3 of A2 is a constant, which unifies the elastic modulus and area in the above formula into E w and A1, then In order to facilitate subsequent calculations, let the comprehensive reference coefficient K = k1 + k2k3, then the pitch adjustment amount ΔP of the gradual pitch thread is:

[0026] The beneficial effects of the above technical solution are: providing a specific derivation process of ΔP and simplifying the equation to facilitate the implementation of the design method, while taking into account the cases of more than one circle and less than one circle, the design result is more comprehensive and accurate.

[0027] Furthermore, according to the derivation process of ΔP, it can be known that the length adjustment amount of the gradual pitch thread is Since the axial load at any n' number of circles starting from the starting position Therefore According to the cross-sectional stress of the axial force borne by the external thread on the equivalent load-bearing cylinder is less than the yield strength σ of the external thread material, that is, N = k4σA1 < σA1, where 0 < k4 < 1, it can be obtained make Then we can conclude that l<Kk4k c Pn′, where K is a constant and 0.8≤K≤10, Comprehensive consideration of k4, k c and K define the upper limit of the length adjustment l of the gradual pitch thread lim =0.025P·n′, further we get l<l lim =0.025P·n′.

[0028] The beneficial effect of the above technical solution is that it simplifies the formula for the length adjustment amount l of the gradual pitch thread, provides an upper limit value of l, and facilitates the implementation of the design method.

[0029] Furthermore, methods for determining the comprehensive reference coefficient K include experimental method and finite element calculation method.

[0030] The beneficial effect of the above technical solution is that it facilitates the determination of the comprehensive reference coefficient K.

[0031] Furthermore, when the finite element calculation method is used to determine the comprehensive reference coefficient K, a finite element model is first established by trying out the K value, and the stress distribution of the thread under the rated load is calculated. If the stress is concentrated at the starting position, the K value is reduced and recalculated. If the stress is concentrated at the ending position, the K value is increased until a K value that meets the requirements is obtained.

[0032] The beneficial effect of the above technical solution is that it facilitates the determination of the comprehensive reference coefficient K. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] FIG1 is a schematic diagram of a basic external thread profile involved in the present invention;

[0034] FIG2 is a schematic diagram of a basic internal thread profile according to the present invention;

[0035] FIG3 is a schematic diagram of the internal thread profile after adjusting the pitch in the present invention;

[0036] FIG4 is a schematic diagram of the basic thread profile before and after deformation according to the present invention;

[0037] FIG5 is a schematic diagram of the pitch adjustment amount ΔP of the gradual pitch thread involved in the present invention;

[0038] FIG6 is a schematic diagram of the starting position and the ending position of the non-equidistant threaded connection pair during loading in the present invention;

[0039] FIG7 shows the length relationship between the internal and external threads of the non-equidistant threaded connection pair when not loaded in the present invention;

[0040] FIG8 is a schematic diagram of the external thread involved in the present invention simplified into an equivalent force-bearing cylinder;

[0041] FIG9 is a schematic diagram of the average elongation of the tiny cylinder and the elongation at the cylindrical surface in FIG8 ;

[0042] FIG10 is a schematic diagram of the internal thread involved in the present invention simplified into an equivalent force-bearing hollow cylinder;

[0043] FIG11 is a schematic diagram showing the average compression amount and the compression amount at the inner cylindrical surface of the tiny hollow cylinder in FIG10;

[0044] FIG12 is a schematic diagram of the force applied to the external thread in the screwing area between the internal and external threads of the present invention;

[0045] FIG13 shows three common cases of the changing trend of the axial force F(n') acting on the external thread;

[0046] Figure 14(a) is the stress cloud corresponding to curve a in Figure 13;

[0047] Figure 14(b) is the stress cloud corresponding to curve b in Figure 13;

[0048] Figure 14(c) is the stress cloud corresponding to curve c in Figure 13;

[0049] FIG15 is a schematic diagram of a curve showing a change in thread variation Δl;

[0050] FIG16 is a schematic diagram of the numbering and average value positions of the external thread teeth in the first embodiment;

[0051] FIG17 is a schematic diagram of the average stress of each thread tooth of the external thread in FIG16. DETAILED DESCRIPTION

[0052] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in various different configurations.

[0053] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely intended to represent selected embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0054] It should be noted that relational terms such as "first" and "second" that may appear are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, terms such as "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article or device. In the absence of further limitations, an element defined by a sentence such as "including a..." does not exclude the presence of other identical elements in the process, method, article or device that includes the element.

[0055] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0056] Example 1 of the design method of the non-equidistant threaded connection pair in the present invention:

[0057] The design method for non-equidistant thread connection pairs includes the following: determining the basic thread profiles of the internal and external threads, the material properties, and the axial load N borne by the external thread; calculating the length adjustment l of the gradual pitch thread, where l is a formula containing F(n'), where F(n') is the axial force acting on the external thread teeth at any n' number of turns, starting from the starting position of the internal and external thread screwing area. n is the total number of turns of the internal and external thread engagement areas; try to select the F(n') equation to obtain the curve equation of F(n') corresponding to the case of better stress uniformity; determine the equation for the pitch adjustment ΔP of the gradual pitch thread. According to the selected F(n') equation, there is only one unknown number K in the ΔP equation, and K is the comprehensive reference coefficient. Just determine the K value.

[0058] The design method of the present invention takes into account the basic thread profiles, material properties and axial load N of the internal and external threads, and has the basis for obtaining better stress uniformity. In the process of calculating the length adjustment amount l of the gradual pitch thread, the relationship between the axial load N is established through F(n'), and by trial selecting the F(n') equation, the curve equation of F(n') corresponding to the case of better stress uniformity is obtained. Finally, the pitch adjustment amount ΔP equation of the gradual pitch thread is determined. There is only one unknown number K in the ΔP equation, that is, the comprehensive reference coefficient. It is sufficient to determine this coefficient. The design method of the present invention can be used to design non-equidistant thread connection pairs with better stress uniformity.

[0059] Example 2 of the design method of the non-equidistant threaded connection pair in the present invention:

[0060] The design method for non-equidistant thread connection pairs includes the following: determining the basic thread profiles of the internal and external threads, the material properties, and the axial load N borne by the external thread; calculating the length adjustment l of the gradual pitch thread, where l is a formula containing F(n'), where F(n') is the axial force acting on the external thread teeth at any n' number of turns, starting from the starting position of the internal and external thread screwing area. n is the total number of turns of the internal and external thread engagement areas; try to select the F(n') equation to obtain the curve equation of F(n') corresponding to the case of better stress uniformity; determine the equation for the pitch adjustment ΔP of the gradual pitch thread. According to the selected F(n') equation, there is only one unknown number K in the ΔP equation, and K is the comprehensive reference coefficient. Just determine the K value.

[0061] The specific design steps are as follows:

[0062] Step 1: Determine the basic thread profile, material properties and rated load of internal and external threads

[0063] The basic thread profile is a standard thread such as metric thread, MJ thread, trapezoidal thread and arc thread. Non-standard threads can also be used. The basic thread profile is a thread profile along the axial direction with a width of one standard pitch.

[0064] A specific basic external thread profile is shown in FIG1 . The external thread profile is the basic external thread profile, the external thread pitch P1 is equal to the basic external thread pitch P (i.e., the spacing between AA'), the major diameter d, the intermediate diameter d2, the minor diameter d1, the yield strength of the external thread material is σ, and the elastic modulus of the external thread material is E w , the axial load borne by the external thread is N.

[0065] A specific basic internal thread profile is shown in Figure 2. The basic internal thread profile has a pitch P (i.e., the spacing between BB'), a major diameter D, a medium diameter D2, a minor diameter D1, and the number of internal thread turns is n. The elastic modulus of the internal thread material is E n .

[0066] At this point, step 1 determines all parameters except the pitch of the internal and external threads.

[0067] Step 2: Calculate the length adjustment l of the gradual pitch thread

[0068] When designing a non-equidistant thread connection, the pitch of one of the internal and external threads is maintained constant while the other is adjusted. For ease of description, this design method maintains the pitch of the external thread constant while adjusting the internal thread. This means the external thread is a constant-pitch thread, while the internal thread is a variable-pitch thread. In this invention, the external thread is composed of multiple basic external threads, and the pitch of the external thread is the same as the pitch of the basic external threads, i.e., P1 = P.

[0069] In the present invention, the internal thread is obtained by adjusting the pitch based on the basic thread profile. During the adjustment, the basic thread profile is kept unchanged, and a transition structure is added at the bottom of the internal thread. As shown in Figure 3, the internal thread profile after pitch adjustment on the through-axis plane is composed of multiple basic internal thread profiles and transition structures G spliced ​​end to end, and the longitudinal section of the transition structure G is a straight line segment. The pitch P2 of the internal thread is the distance between any set of corresponding points MM' on the internal thread profile of two adjacent basic internal thread profiles and the external thread screwing area. The pitch P2 of the internal thread is a non-fixed value, and the pitch of the internal thread is greater than or equal to the pitch of the basic thread profile of the external thread, that is, P2≥P. The pitch adjustment amount ΔP of the gradual pitch thread is P2-P. Since the pitch of the external thread P1 is P, the pitch adjustment amount ΔP of the gradual pitch thread is the difference between the pitch of the internal and external threads, and is also the width of the transition structure G.

[0070] When traditional equidistant threads are loaded and engaged, the external thread will be stretched and lengthened, while the internal thread will be compressed and shortened. The sum of the two is the total change of the internal and external threads, and the external and internal threads at any position in the screwing area will have different degrees of elongation or compression (for example, the dotted line in Figure 4 is before the deformation of the basic thread profile, and the solid line is after the deformation). Therefore, as shown in Figure 5, the pitch adjustment amount of the gradual pitch thread is based on the basic thread profile, and the sum of the total elongation of the external thread and the total compression of the internal thread within one circle of thread ∑Δl is calculated. When adjusting the gradual pitch thread, keep the basic thread profile unchanged, and add a transition structure G at the bottom of the internal thread. The width of the transition structure G is the gradual pitch thread adjustment amount ΔP, then ΔP = ∑Δl.

[0071] For the convenience of description, the present invention sets a starting position and an ending position, as shown in Figures 6 and 7. Taking the bolt 1 and the nut 2 as an example, in the screwing area of ​​the internal and external threads, the present invention uses 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 the 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.

[0072] The number of turns of an internal thread is n. When the internal and external threads are used together, n turns of internal thread must be used in conjunction with n turns of external thread. When no load deformation occurs, starting from the starting position, the length of the internal thread for any n' turns (0 < n' ≤ n) is greater than the length of the external thread. As shown in Figure 7, for a non-uniform pitch threaded connection, starting from the starting position, the length of the external thread for any n' turns is L1 = n'P1 = n'P, and the length of the internal thread for any n' turns is L2 = n'P1 + l = n'P + l. Therefore: L2 - L1 = l, where l is the difference in length between the internal and external threads for any n' turns starting from the starting position, i.e., the length adjustment amount for the progressive pitch thread.

[0073] As shown in Figure 8, for the convenience of analysis, the external thread in the screwing area of ​​the internal and external threads is simplified into an equivalent force-bearing cylinder. The two circular sections of the equivalent force-bearing cylinder are the starting position section Q and the ending position section Z. The cross-sectional area A1 of the equivalent force-bearing cylinder is the stress cross-sectional area of ​​the external thread. The axial load N borne by the equivalent force-bearing cylinder at the ending position section Z is in the direction of the axial load N from the starting position section Q to the ending position section Z. The acting force between the internal and external threads is simplified to the outer cylindrical surface of the equivalent force-bearing cylinder bearing a surface load. The surface load is in the opposite 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. Taking the starting position as the starting point, the resultant force of the load on the small external cylindrical surface at any n' number of turns is f1(n'), and the resultant force of the load on all small external cylindrical surfaces is equal to the axial load N, that is,

[0074] A small cylinder is cut off at any height h=n'P of the equivalent force-bearing cylinder. The thickness of the small cylinder is dh=Pdn'. The axial force on the lower section of the small cylinder is The average elongation of a small cylinder can be obtained from Hooke's law The total average elongation of the equivalent loaded cylinder at any n' number of turns is

[0075] As shown in Figure 9, 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 cross-section of the micro-cylinder, which makes the elongation on the outer cylindrical surface of the micro-cylinder smaller than the average elongation dl. w1 , the outer cylindrical surface of the equivalent load-bearing cylinder is the simplified area of ​​the external thread, so the elongation of the outer cylindrical surface should be the elongation dl of the external thread w , then dl w =k1·dl w1 , 0<k1<1, for the convenience of analysis, assuming k1 is a constant value, then taking the starting position as the starting point, the total elongation of the external thread with any n' turns is

[0076] As shown in Figure 10, for the convenience of analysis, the internal thread in the screwing area of ​​the internal and external threads is simplified into an equivalent force-bearing hollow cylinder. The two annular sections of the equivalent force-bearing hollow cylinder are the starting position section Q and the ending position section Z. The cross-sectional area of ​​the equivalent force-bearing hollow cylinder is A2. The axial load borne by the equivalent force-bearing hollow cylinder at the ending position section Z is F. N (According to the balance of forces, F N The direction is from the end position to the starting position, and the force between the internal and external threads is simplified to the inner cylindrical surface of the equivalent hollow cylinder under the surface load. The surface load and the axial force F N The direction is opposite, the resultant force of the surface load and the axial force F N The same size is taken from the starting section. The resultant force of the load on the small inner cylindrical surface at any n' turn position is f2(n'). The resultant force of the load on all small inner cylindrical surfaces is equal to the axial load F N Equal, that is

[0077] A small hollow cylinder is cut off at any height h=n'P of the equivalent force-bearing hollow cylinder. The thickness of the small hollow cylinder is dh=Pdn'. The axial force on the lower section of the small hollow cylinder is Average compression of a tiny hollow cylinder with a thickness of dh By integration, we can find the total average compression of the equivalent hollow cylinder at any n' turns starting from the starting section Q:

[0078] As shown in Figure 11, due to the surface load direction of the cylindrical surface inside the tiny hollow cylinder and the load F on the lower section of the tiny hollow cylinder, N The direction of action is opposite, making the compression on the cylindrical surface of the tiny hollow cylinder greater than the average compression dl n1 The inner cylindrical surface of the equivalent hollow cylinder is the simplified area of ​​the internal thread, so the compression of the inner cylindrical surface is the compression of the internal thread dl n , then dl n =k2·dl n1 , 1<k2, for the convenience of analysis, assuming k2 is a constant value, then starting from the starting position, the total compression of the internal thread with any n' turns is

[0079] As shown in Figure 12, starting from the starting position, the axial force of the internal thread acting on the external thread at any n' turns is F(n'). From the simplified mechanical relationship of the equivalent force-bearing cylinder and the equivalent force-bearing hollow cylinder, we can know that F(n') = f1(n') = f2(n'). Therefore, we have:

[0080] Furthermore, taking the starting position as the starting point, the length adjustment amount l of n' turns of gradual pitch thread is the total extension amount l of the external thread. w Total compression with internal thread l n The sum of , then:

[0081] At this point, step 2 solves the external thread stretching amount and the internal thread compression amount, and then sums them up to obtain the length adjustment amount l of the gradual pitch thread.

[0082] Step 3: Try to select the equation for the axial force F(n') on the external thread

[0083] In the formula for the length adjustment l of the gradual pitch thread obtained in step 2, only F(n') and n' are variables, and there are three common situations in which the axial force F(n') acting on the external thread follows the change trend of n'. As shown in Figure 13, F(n') in curve a increases as n' increases, F(n') in curve b is a constant and remains unchanged, and F(n') in curve c decreases as n' increases. According to the mechanical relationship, the cumulative value of the axial force F(n') on the external thread from the starting position to the end position is the cross-sectional axial load N, that is,

[0084] Simulation calculations were performed with three different trends of F(n'), and the calculated 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.

[0085] High stress areas typically occur at the root of external threads. The magnitude of this stress is influenced by the combined effects of the axial force F(n') on the external threads and the cross-sectional axial load N(n'), which is the force applied to the entire cross-section (excluding the threads) over n' turns. When the internal and external threads are deformed under load, the cross-sectional axial load N(n') increases with the number of thread turns n', starting from the starting position, and reaches its maximum value N at n turns. As shown in Figure 13, when the axial force F(n') on the external threads conforms to curve a, F(n') is smaller at the starting position and larger at the ending position. This trend mirrors the variation in N(n'), as shown in Figure 14(a). Y in the figure represents the location with the highest stress. The figure shows that the stress at the starting position of the external thread is smaller, while the stress at the ending position is larger, indicating a significant stress concentration phenomenon. Specifically, Y is concentrated at the ending position, and the area of ​​Y increases as it approaches the ending position.

[0086] As shown in Figure 13, when the axial force F(n') on the external thread teeth conforms to curve b, F(n') is a constant and unchanged value. However, since the cross-sectional axial load N(n') gradually increases with n', the stress at the root of the external thread teeth still shows a small stress value at the starting position and a large stress value at the end position. However, the stress concentration phenomenon is improved. As shown in Figure 14(b), the area of ​​Y at the end position becomes smaller. When the axial force F(n') on the external thread teeth conforms to curve c, F(n') further increases at the starting position and further decreases at the end position, causing the stress at the root of the external thread teeth at the starting position to further increase and the stress at the end position to further decrease. The stress value of the entire external thread root is more uniform, and the stress concentration phenomenon is smaller. As shown in Figure 14(c), Y is evenly distributed from the starting position to the end position.

[0087] At this point, step 3 analyzes that F(n') conforms to the stress state of curve c better, and the selected F(n') equation should satisfy curve c. F(n') should meet two conditions: it is a decreasing function in the interval 0≤n'≤n,

[0088] Step 4: Determine the pitch adjustment ΔP equation for the gradual pitch thread

[0089] As shown in FIG15 , the pitch adjustment amount ΔP of the gradual pitch thread is the sum of the thread variation Δl within one thread turn, that is, ΔP = ∑Δl. When 1 < n' ≤ n, that is:

[0090] When n'≤1, the pitch adjustment ΔP of the gradual pitch thread is the sum of the thread changes Δl within less than one turn of the thread length, that is:

[0091] After the internal and external thread materials and nut dimensions are selected, E n and A2 are both constant, so E w A1 and E n The ratio k3 of A2 is a constant. In order to facilitate calculation, the elastic modulus and area in the above formula are unified into E w and A1, then To facilitate subsequent calculations, let k1+k2k3=comprehensive reference coefficient K, then the pitch adjustment ΔP of the gradual pitch thread is:

[0092] At this point, step 4 solves the pitch adjustment ΔP of the gradual pitch thread based on the length adjustment l equation of the gradual pitch thread. Since the F(n') equation has been selected in step 3, there is only one unknown number K in the equation of ΔP.

[0093] In addition, according to the derivation process of ΔP, it can be known that the length adjustment amount of the gradual pitch thread is Since the axial load at any n' number of circles starting from the starting position Therefore According to the cross-sectional stress of the axial force borne by the external thread on the equivalent load-bearing cylinder is less than the yield strength σ of the external thread material, that is, N = k4σA1 < σA1, where 0 < k4 < 1, it can be obtained make Then we can conclude that l<Kk4k c Pn′, where K is a constant and 0.8≤K≤10, Comprehensive consideration of k4, k c and K define the upper limit of the length adjustment l of the gradual pitch thread lim =0.025P·n′, further we get l<l lim =0.025P·n′.

[0094] Step 5: Determine the comprehensive reference coefficient K

[0095] There are many methods to determine the comprehensive reference coefficient K, such as experimental method and finite element calculation method, and the preferred method is finite element calculation method.

[0096] When using the finite element calculation method to determine the comprehensive reference coefficient K, first establish a finite element model by trying out the K value, and calculate the stress distribution of the thread under the rated load. If the stress is concentrated at the starting position, reduce the K value and recalculate. If the stress is concentrated at the ending position, increase the K value until a K value that meets the requirements is obtained.

[0097] The design method of the non-equidistant thread connection pair of the present invention is described in detail below in conjunction with specific thread parameters.

[0098] Specific implementation method one:

[0099] 1. Determine the basic thread profile, material properties and rated load of internal and external threads

[0100] The basic external thread profile is metric, with a pitch of P = 4 mm, a major diameter d = 42 mm, and a minor diameter d1 = 37.67 mm. The elastic modulus of the external thread material is E = 206 GPa, and the yield strength σ = 930 MPa. The rated load for the external thread is N = 0.7σA1.

[0101] The basic external thread profile of the internal thread is a metric thread, the basic internal thread profile pitch P = 4mm, the major diameter D = 42.33mm, the minor diameter D1 = 38mm, and the number of internal thread turns is n = 7 turns.

[0102] 2. Calculate the length adjustment l of the gradual pitch thread

[0103] Taking the starting position as the starting point, the length adjustment amount l of the gradual pitch thread with any number n turns is the total extension amount l of the external thread w Total compression with internal thread l n The sum of , then:

[0104] 3. Try to select the equation of axial force F(n') on external thread

[0105] Select the axial force on the external thread 0<n'≤7 is linearly decreasing (according to the previous analysis, F(n') is a decreasing function. In fact, F(n') is not necessarily a linear decreasing function. This embodiment is just an example. There are many similar equations). The sum of the loads of each circle of thread teeth on the starting position to the end position is equal to the axial load N, that is,

[0106] 4. Determine the pitch adjustment ΔP equation for gradual pitch threads

[0107] In this embodiment, the internal thread is a gradual pitch thread, and the pitch adjustment amount ΔP of the gradual pitch thread is:

[0108] 5. Determine the comprehensive reference coefficient K

[0109] When K=2.5, the stress value at the root of the external thread is relatively uniform, and the pitch adjustment ΔP of the gradual pitch thread is:

[0110] Table 1 shows the specific adjustment parameters for threads with different comprehensive reference coefficients, K. In Table 1, L1 and L2 are the lengths of the internal and external threads after adjustment, respectively. A finite element model was established using the thread parameters in the table, and calculations were completed. The average stress of each thread was extracted based on the numbering of the external threads (1-7) and the positions indicated by the bold short vertical lines in Figure 16. A graph of the average stress variation for each thread was plotted, and the stress concentration factor (stress concentration factor = maximum stress / total average stress) for each thread was calculated. Figure 17 shows that the thread with K = 2.5 exhibits better stress uniformity, and Table 2 shows that the thread with K = 2.5 has the lowest stress concentration factor.

[0111] Table 1 Specific adjustment parameters of threads with different comprehensive reference coefficients K

[0112] Table 2 Stress concentration factors of each thread tooth of external thread

[0113] Specific implementation method two:

[0114] Different from the first embodiment, the axial force on the external thread 0<n'≤7 decreases linearly, and the sum of the loads of each circle of thread teeth from the starting position to the end position is equal to the axial load N, that is, The other processes are the same as those in the first embodiment and will not be elaborated here.

[0115] In other implementations of the design method for non-equidistant threaded connection pairs: the method for determining the comprehensive reference coefficient K may also adopt an experimental method.

[0116] In other implementations of the method for designing a non-equidistant thread connection pair: the upper limit of the length adjustment amount l of the gradual pitch thread may be different depending on the yield strength and elastic modulus of the thread material.

[0117] In other implementations of the design method for a non-equidistant thread connection pair: the internal thread pitch can also be enlarged by reducing the internal thread tooth thickness while keeping the basic thread pitch unchanged.

[0118] In other implementations of the design method of a non-equidistant thread connection pair: if the gradual pitch thread is an external thread, the external thread pitch can be reduced by reducing the width of the transition structure or increasing the external thread tooth thickness.

[0119] In other embodiments of the design method of non-equidistant threaded connection pairs, the total average elongation l of the equivalent force-bearing cylinder at any n' number of turns can also be directly used. w1 To represent the total elongation l of any n' number of turns of external thread wOf course, we can also directly use the total average compression of the equivalent hollow cylinder at any n' number of circles as l n1 To represent the total compression of any n' number of internal threads l n .

[0120] In other embodiments of the design method of a non-equidistant thread connection pair: the pitch adjustment amount ΔP of the gradual pitch thread within a thread turn length is no longer considered, and only the calculation process of the pitch adjustment amount ΔP of more than one turn is studied.

[0121] The above description is only 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 based on the claims. Any equivalent structural changes made using the description and drawings of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A design method for a non-equidistant threaded connection pair, characterized in that: The following contents are included: determine the basic thread profiles of internal and external threads, material properties and the axial load N borne by the external thread; calculate the length adjustment amount l of the gradual pitch thread, l is a formula containing F(n'), where F(n') is the axial force of the internal thread acting on the external thread teeth at any n' number of turns, starting from the starting position of the internal and external thread screwing area. n is the total number of turns of the internal and external thread engagement areas; try to select the F(n') equation to obtain the curve equation of F(n') corresponding to the case of better stress uniformity; determine the pitch adjustment ΔP equation of the gradual pitch thread. According to the selected F(n') equation, there is only one unknown number K in the ΔP equation. K is the comprehensive reference coefficient. Just determine the K value.

2. The design method of a non-equidistant threaded connection pair according to claim 1, characterized in that: Length adjustment of progressive pitch thread Where P is the pitch of the constant pitch thread, k1 and k2 are both constant values, E w is the elastic modulus of the external thread material, A1 is the stress cross-sectional area of ​​the external thread, E n is the elastic modulus of the internal thread material, and A2 is the stress cross-sectional area of ​​the internal thread.

3. The design method of a non-equidistant threaded connection pair according to claim 2, characterized in that: The process of solving the length adjustment l of the gradual pitch thread includes the following: (I) Simplify the external thread in the screwing area 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 external 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 number of n' turns starting from the starting position. Among them: 0<k1<1, N is also the axial load borne by the equivalent force-bearing cylinder at the end position section. The direction of the axial load N points from the starting position section to the end position section. (ii) Simplify the internal thread in the screwing area of ​​the internal and external threads into an equivalent force-bearing hollow cylinder. According to Hooke's law and the fact that the compression of the inner cylindrical surface of the equivalent force-bearing hollow cylinder is greater than the average compression of the equivalent force-bearing hollow cylinder, calculate the total compression of the internal thread with any n' turns starting from the starting position. Where: k2>1, F N is the axial load borne by the equivalent hollow cylinder at the end section, and the axial load F N The direction is from the end position section to the start position section; (III) From the simplified method of equivalent force-bearing cylinder and equivalent force-bearing hollow cylinder, that is, the mechanical relationship, we can know F(n′)=f1(n′)=f2(n′), so we have: Therefore, the length adjustment amount l of the n'th turn of the gradual pitch thread with the starting position as the starting point is the total elongation l of the external thread w Total compression with internal thread l n The sum is:

4. The design method of a non-equidistant threaded connection pair according to claim 3, characterized in that: For the equivalent force-bearing cylinder simplified by the external thread, f1(n') is the resultant force of the load on the small external cylindrical surface at any n' number of turns of the equivalent force-bearing cylinder. The resultant force of all small external cylindrical surfaces is equal to the axial load N. A small cylinder is cut at any height h = n'P of the equivalent force-bearing cylinder. The thickness of the small cylinder is dh = Pdn'. The lower section of the small cylinder is subjected to an axial force of From Hooke's law, we can get the average elongation of a tiny cylinder: Therefore, the total average elongation of the equivalent loaded cylinder at any n' number of turns is Since the elongation of the edge of the cylindrical surface of the equivalent force-bearing cylinder is less than the average elongation, the cylindrical surface of the equivalent force-bearing cylinder is the simplified area of ​​the external thread, so the elongation of the cylindrical surface should be the elongation dl of the external thread. w , then dl w =k1·dl w1 , and then the total elongation of the external thread with any n' turns starting from the starting position is obtained 5. The design method of a non-equidistant threaded connection pair according to claim 3, characterized in that: For the equivalent hollow cylinder simplified by the internal thread, f2(n') is the resultant force of the load on the small inner cylindrical surface at any n' number of turns of the equivalent hollow cylinder. The resultant force of all small inner cylindrical surfaces and the axial load F N equal; a small hollow cylinder is cut at any 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 on the lower section of the small hollow cylinder is Average compression of a tiny hollow cylinder with a thickness of dh By integration, the total average compression of the equivalent hollow cylinder under load at any n' number of turns starting from the starting position can be calculated as: Since the compression of the inner cylindrical surface of the tiny hollow cylinder is greater than the average compression, the inner cylindrical surface of the equivalent force-bearing hollow cylinder is the simplified area of ​​the internal thread, so the compression of the inner cylindrical surface is the compression of the internal thread dl n , then dl n =k2·dl n1 , and then the total compression of the internal thread with any n' turns starting from the starting position is obtained 6. The design method of a non-equidistant threaded connection pair according to any one of claims 1 to 5, characterized in that: The corresponding curve of F(n') is a decreasing function in the interval 0≤n'≤n.

7. The design method of a non-equidistant threaded connection pair according to any one of claims 2 to 5, characterized in that: The pitch adjustment amount ΔP of the gradual pitch thread is the sum of the thread change amount Δl within one circle of thread length, that is, ΔP = ∑Δl. When 1 < n' ≤ n, that is: When n'≤1, the pitch adjustment ΔP of the gradual pitch thread is the sum of the thread change Δl within less than one turn of thread length, that is: After the internal and external thread materials and nut dimensions are selected, E n and A2 are both constants, so E w A1 and E n The ratio k3 of A2 is a constant, which unifies the elastic modulus and area in the above formula into E w and A1, then In order to facilitate subsequent calculations, let the comprehensive reference coefficient K = k1 + k2k3, then the pitch adjustment amount ΔP of the gradual pitch thread is:

8. The design method of a non-equidistant threaded connection pair according to claim 7, characterized in that: According to the derivation process of ΔP, it can be known that the length adjustment amount of the gradual pitch thread Due to the axial load at the section with any n' number of turns starting from the starting position Therefore According to the cross-sectional stress of the axial force on the equivalent force-bearing cylinder borne by the external thread is less than the yield strength σ of the external thread material, that is, N = k4σA1 <σA1, where 0 < k4 < 1, it can be obtained make Then we can get l <Kk4k c Pn′, where K is a constant and 0.8≤K≤10, Comprehensive consideration of k4, k c and K define the upper limit l of the length adjustment amount l of the gradual pitch thread lim =0.025P·n′, and further we can get l <l lim =0.025P·n′.

9. The design method of a non-equidistant threaded connection pair according to any one of claims 1 to 5, characterized in that: Methods for determining the comprehensive reference coefficient K include experimental method and finite element calculation method.

10. The design method of a non-equidistant threaded connection pair according to claim 9, characterized in that: When the comprehensive reference coefficient K is determined by the finite element calculation method, the finite element model is first established by trying the K value, and the stress distribution of the thread under the rated load is calculated. If the stress is concentrated at the starting position, the K value is reduced and recalculated. If the stress is concentrated at the ending position, the K value is increased until a K value that meets the requirements is obtained.

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