A modeling method for closing self-locking nuts for aircraft engines
By summarizing and mathematical expression of the geometric features of the closed self-locking nut, a gradient elliptical region and thread model was established, which solved the problem of lack of precise modeling in the existing technology, and improved its connection stability and reliability in aero engines. Prevent loosening.
Patent Information
- Application Number
- CN202211115452.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-14
- Publication Date
- 2024-12-27
- Estimated Expiration
- 2042-09-14
AI Technical Summary
The prior art lacks research on the failure process of the self-locking nut and the decay mechanism of anti-loosening performance, and lacks accurate modeling methods, which affects its connection stability and reliability in aircraft engines.
By summarizing and mathematically expressing the geometric features of the closing self-locking nut, a gradient elliptical region and thread model is established, and a finite element simulation technology is used to combine the perfect circle region and the gradient region to generate an accurate geometric model to improve connection stability.
A reliable theoretical model is provided, which improves the connection stability of the closing self-locking nut, prevents loosening, and ensures its reliability and durability in aircraft engines.
Smart Images
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Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of finite element simulation, and in particular relates to a modeling method of a closed-end self-locking nut for an aero-engine. Background Art
[0002] Self-locking nuts have become the most widely used connections and fasteners in aerospace structures because of their reliable vibration resistance, anti-loosening and reusable functions. The stability and durability of their self-locking performance determine the reliability of product connections. The closed-end self-locking nut uses a non-circular closed end to expand after the nut is tightened. The rebound force of the closed end is used to press the screwed threads against each other, generating a locking torque, which plays a role in preventing the connection from loosening. Although domestic and foreign scholars have conducted long-term and in-depth research and exploration in the field of thread loosening prevention, and have conducted a lot of analysis, calculation and experimental research on the influence of various external environmental factors and structural factors on the loosening process of threaded connections, most of the research on closed-end self-locking nuts is based on the life of self-locking nuts on the basis of experiments. There is little research on its failure process and the mechanism of anti-loosening performance degradation, and there is a lack of methods for accurately modeling closed-end self-locking nuts. Summary of the invention
[0003] Based on the above technical problems, the present invention proposes a modeling method for a closed-end self-locking nut for an aircraft engine. By modeling the closed-end self-locking nut, a reliable theoretical model is provided for the finite element simulation of the self-locking nut, thereby improving the stability of the nut connection and preventing loosening.
[0004] The present invention adopts the following technical solution:
[0005] A modeling method for a closed-end self-locking nut for an aero-engine comprises the following steps:
[0006] Step 1: Summarize the geometric features of the closed-end self-locking nut;
[0007] Step 2: Use mathematical formula to express the thread position of the gradual elliptical area of the closed self-locking nut;
[0008] Step 3: Establish a geometric model of the gradual elliptical area of the closed self-locking nut in the finite element method;
[0009] Step 4: Create a gradual elliptical spiral line of the closed self-locking nut in the finite element;
[0010] Step 5: Establish a geometric model of the gradual elliptical thread of the closed self-locking nut in the finite element method;
[0011] Step 6: Establish the perfect circle area and thread geometry model of the closed self-locking nut in the finite element method;
[0012] Step 7: Combine the perfect circle area and the gradient area of the closed-end self-locking nut in the finite element method to obtain the modeling of the closed-end self-locking nut.
[0013] Furthermore, the step 1 is specifically as follows: according to the geometric characteristics of the closed self-locking nut, a perfect circle area and a gradient elliptical area are summarized, the radius of the perfect circle area is r, and the height is h1; the gradient elliptical area gradually transitions from a perfect circle to an ellipse, the height is h0, the semi-major axis of the ellipse at the top is a0, the semi-minor axis is b0, and the wall thickness is e.
[0014] Further, the step 2 is specifically as follows: obtaining the expression of the ellipse at any cross section, that is, the size of the semi-minor axis and the semi-major axis of the ellipse at any height, and at any height h, the distance a from the hypotenuse of the trapezoid to the center line is expressed as:
[0015] a=r+l (1)
[0016] Where l is obtained according to the triangle proportional parallel formula, l is a parameter in the calculation process, which represents the difference between the major diameter of the ellipse and the initial nut radius.
[0017]
[0018] Substituting formula (2) into formula (1) to obtain the expression of the semi-major axis a of the ellipse at any height h is:
[0019]
[0020] Similarly, when any height h is obtained, the expression of the length b of the semi-minor axis is:
[0021]
[0022] Furthermore, the step 3 is specifically as follows: according to the geometric characteristics of the closed self-locking nut, the bottom circle and ellipse of the gradient zone are established on the reference plane using finite elements, and then the gradient body is obtained by stretching the gradient body from the bottom circle to the top elliptical gradient body through a sweeping function; a gradient body with a consistent wall thickness and shape is established on the outside of the gradient body to obtain a hollow cylindrical gradient body.
[0023] Furthermore, the gradient body is obtained by stretching the gradient body from the bottom circle to the top elliptical gradient body through the sweep function, specifically: two sections and required guide lines are selected in the sweep function to gradually change from the bottom circle along the guide line direction to the top elliptical shape.
[0024] Furthermore, the step 4 is specifically as follows: generating a spiral line of a gradual elliptical thread, and representing the gradual elliptical spiral line with three-dimensional coordinates:
[0025]
[0026] Where a and b are the semi-major and semi-minor axes of the ellipse, respectively. is the rotation angle, and ω is the angular velocity of rotation, t is the parameter, v is the rising speed, here t is 0-8, ω=π,
[0027] According to the elliptical helix expressions (3) and (4), they are substituted into the coordinate formula (6), the finite element expression module is called, and the gradual helix expression is edited according to the actual geometric dimensions of the closed self-locking nut. The regular curve is inserted and the gradual elliptical helix is generated after confirmation.
[0028] Furthermore, the step 5 is specifically as follows: selecting the thread form, the starting point of the thread is on the bottom circle section, selecting the xz plane where the point is located to make the thread section, and calling the sweep function to generate a gradual elliptical thread along the gradual compass spiral line.
[0029] Furthermore, the step 6 is specifically as follows: stretching the annular surface of the bottom circle to form a perfect circular area, selecting a curve module, calling a spiral function, generating a perfect circular spiral line of the perfect circular area, and generating a perfect circular area thread through a thread section.
[0030] Furthermore, the step 7 is specifically as follows: merging the perfect circular thread and the gradient elliptical thread, the perfect circular body and the gradient body respectively, and then performing Boolean operations to complete the finite element establishment of the closed-end self-locking nut.
[0031] The advantages and beneficial effects of the present invention are:
[0032] The present invention proposes a modeling method for a closed-end self-locking nut for an aero-engine. The method can accurately simulate the geometric shape of the closed-end self-locking nut, provide an accurate modeling method for closed-end self-locking nuts of different sizes, provide a reliable theoretical model for finite element simulation of the self-locking nut, improve the stability of the nut connection, and prevent loosening. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 It is the geometric model of the closed-end self-locking nut;
[0034] Figure 2 Schematic diagram of the closed-end self-locking nut structure, where (a) is a side view and (b) is a top view;
[0035] Figure 3 This is a geometric diagram of the gradient zone of the closed self-locking nut;
[0036] Figure 4 It is a schematic diagram of the basic framework of the gradual elliptical area of the closed self-locking nut;
[0037] Figure 5 This is a schematic diagram after the Boolean operation of the elliptical gradient area is executed;
[0038] Figure 6 Editing process for gradient ellipse spiral expression;
[0039] Figure 7 It is a schematic diagram of a gradient elliptical spiral;
[0040] Figure 8 It is a schematic diagram of the cross section of a gradual elliptical thread;
[0041] Fig. 9 It is a schematic diagram of a gradual elliptical thread;
[0042] Fig.10 It is a schematic diagram of a perfect circle area and an ellipse area;
[0043] Fig.11 It is a schematic diagram of the thread in the perfect circle area;
[0044] Fig.12 Schematic diagram of a closed-end self-locking nut with thread features. DETAILED DESCRIPTION
[0045] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.
[0046] The present invention is a modeling method for a closed-end self-locking nut for an aero-engine, comprising the following steps:
[0047] Step 1: Summarize the geometric features of the closed-end self-locking nut
[0048] According to the geometric characteristics of the closed-end self-locking nut, a perfect circle area and a gradual elliptical area are summarized. The radius of the perfect circle area is r, and the height is h1. The gradual elliptical area gradually transitions from a perfect circle to an ellipse, with a height of h0, the semi-major axis of the ellipse at the top is a0, the semi-minor axis is b0, and the wall thickness is e.
[0049] Step 2: Use mathematical formula to express the thread position of the gradual elliptical area of the closed self-locking nut
[0050] The expression of the ellipse when obtaining any cross section is the size of the semi-minor axis and semi-major axis of the ellipse at any height. At any height h, the distance a from the hypotenuse to the center line of the trapezoid is expressed as:
[0051] a=r+l (1)
[0052] Where l is obtained according to the triangle proportional parallel formula, l is a parameter in the calculation process, which represents the difference between the major diameter of the ellipse and the initial nut radius.
[0053]
[0054] Substituting formula (2) into formula (1) to obtain the expression of the semi-major axis a of the ellipse at any height h is:
[0055]
[0056] Similarly, when any height h is obtained, the expression of the length b of the semi-minor axis is:
[0057]
[0058] Step 3: Establish the geometric model of the gradual elliptical area of the closed self-locking nut in the finite element method
[0059] The step 3 is specifically as follows: according to the geometric characteristics of the closed self-locking nut: the radius of the perfect circle is r, the height is h1; the height of the gradual ellipse is h0, the semi-major axis of the ellipse at the top is a0, the semi-minor axis is b0, the wall thickness is e, and the pitch is p. The bottom circle and ellipse of the gradual change area are established on the reference plane using finite elements, and then two sections and the required guide lines are selected in the sweep function, so that the circle on the ground gradually changes to the ellipse at the top along the guide line direction, and the stretching of the gradual change from the bottom circle to the top ellipse is realized.
[0060] Step 4: Create a gradient elliptical spiral line of the self-locking nut in the finite element
[0061] Generate a spiral line of a gradual elliptical thread and express the gradual elliptical spiral line with three-dimensional coordinates:
[0062]
[0063] Where a and b are the semi-major and semi-minor axes of the ellipse, respectively. is the rotation angle, and ω is the angular velocity of rotation, t is the parameter, v is the rising speed, p is the pitch of the thread, t is 0-8, ω=π.
[0064] According to the previously derived elliptical helix expressions (3) and (4), they are substituted into the coordinate formula (6), the finite element expression module is called, and the gradient helix expression is edited according to the actual geometric dimensions of the closed self-locking nut. The regular curve is inserted and the gradient elliptical helix is generated after confirmation.
[0065] Step 5: Establish the geometric model of the gradual elliptical thread of the self-locking nut in the finite element method
[0066] Select the thread form, the starting point of the thread is on the bottom circle section, select the xz plane where the point is located to make the thread section, and call the sweep function to generate a gradual elliptical thread along the gradual elliptical spiral line.
[0067] Step 6: Establish the perfect circle area and thread geometry model of the closed self-locking nut in the finite element method
[0068] The annular surface of the bottom circle is stretched to form a perfect circular area, the curve module is selected, the spiral function is called to generate a perfect circular spiral line of the perfect circular area, and the perfect circular area thread is generated through the thread section.
[0069] Step 7: Combine the perfect circle area and gradient area of the closed self-locking nut in the finite element to obtain the modeling of the closed self-locking nut
[0070] The perfect circular thread and the gradient elliptical thread, the perfect circular body and the gradient body are merged respectively, and then Boolean operations are performed to complete the finite element establishment of the closed-end self-locking nut.
[0071] Example 1
[0072] Step 1: Summarize the geometric features of the closed-end self-locking nut
[0073] In this embodiment, since only the inner thread shape of the nut is considered, the twelve-angle wrench structure and the boss on the outer side of the nut are ignored. The geometric model of the closed self-locking nut is as follows: Figure 1 The simplified model and geometric dimensions are shown in Figure 2 shown.
[0074] According to the geometric characteristics of the closed-end self-locking nut, a perfect circle area and a gradual elliptical area are summarized. The radius of the perfect circle area is r, and the height is h1. The gradual elliptical area gradually transitions from a perfect circle to an ellipse, with a height of h0, the semi-major axis of the ellipse at the top is a0, the semi-minor axis is b0, and the wall thickness is e.
[0075] Step 2: Use mathematical formula to express the thread position of the gradual elliptical area of the closed self-locking nut
[0076] In this embodiment, in order to obtain the expression of the elliptical helix of the gradual thread, it is necessary to obtain the expression of the ellipse at any cross section, that is, the size of the semi-minor axis and semi-major axis of the ellipse at any height. The side view of the gradual change zone in the x-axis and y-axis directions can be regarded as a trapezoid of two sizes, and its geometric schematic diagram is as follows: Figure 3 As shown, Figure 3 -(a) and Figure 3 -(b) The distance from the hypotenuse to the center line of the trapezoid corresponds to the semi-minor axis and semi-major axis of the ellipse at any height of the trapezoid.
[0077] Viewed from the side along the semi-major axis Figure 3 -(a) as an example, at any height h, the distance a from the hypotenuse to the center line of the trapezoid can be expressed as:
[0078] a=r+l (1)
[0079] Where l can be obtained according to the triangle equal proportion parallel formula,
[0080]
[0081] Substituting formula (2) into formula (1) can obtain the expression of the semi-major axis a of the ellipse at any height h:
[0082]
[0083] Similarly, when any height h is obtained, the expression of the length b of the semi-minor axis is:
[0084]
[0085] Step 3: Establish the geometric model of the gradual elliptical area of the closed self-locking nut in the finite element method
[0086] In this embodiment, the specific geometric characteristic dimensions of the closed self-locking nut are first determined: the radius of the perfect circle area is r = 2.5 mm, and the height is h1 = 6 mm; the height of the gradient elliptical area is h0 = 4 mm, the semi-major axis of the ellipse at the top is a0 = 2.785 mm, the semi-minor axis is b0 = 2 mm, the wall thickness is e = 1 mm, and the pitch p = 1 mm.
[0087] Using the finite element software NX 12.0, firstly, the bottom circle of the gradient area is established on the reference plane, with a radius of 2.5 mm for the radius of the perfect circle area, and an ellipse is established at a height of 4 mm, with a semi-major axis of 2.785 mm and a semi-minor axis of 2 mm. Figure 4 The solid line inside shows this. (According to the processing technology of the closed-end self-locking nut, the circumference of the top ellipse is equal to the circumference of the bottom circle.) Then, in the Sweep function, select two sections and the required guide lines to gradually change the bottom circle into the top ellipse along the guide line direction, thus achieving the stretching of the gradient from the bottom circle to the top ellipse.
[0088] In order to realize the hollowness of the nut, it is necessary to create a gradient body with the same shape outside the above gradient body so as to perform Boolean operation to transform it into a cylindrical body with a wall thickness of 1mm. Figure 4 As shown by the solid line on the outside, the radius of the bottom circle is 3.5mm, the semi-major axis of the top ellipse is 3.785mm, and the semi-minor axis is 3mm, ensuring that the wall thickness of the self-locking nut is 1mm. Select the subtraction function in the Boolean operation function, select the entity with a large external radius as the target body, and select the entity with a small internal radius as the tool body. After executing the Boolean operation, a hollow cylindrical gradient body is realized, as shown in Figure 5 shown.
[0089] Step 4: Create a gradient elliptical spiral line of the self-locking nut in the finite element
[0090] In this embodiment, the helical line of the gradual elliptical thread is first generated, since the parametric equation of the ellipse is:
[0091]
[0092] Where a and b are the semi-major and semi-minor axes of the ellipse, respectively. is the rotation angle, and ω is the angular velocity of rotation and t is the parameter.
[0093] The gradient elliptical spiral is now expressed in three-dimensional coordinates:
[0094]
[0095] in, v is the rising speed, p is the pitch of the thread, t is 0-8, ω=π.
[0096] According to the previously derived elliptical helix expressions (3) and (4), they are introduced into the coordinate formula (6), and the expression module of the finite element software is called. According to the formula editing specification of the finite element software NX 12.0, the gradual helix expression is edited according to the actual geometric dimensions of the closed self-locking nut. The specific editing method is as follows: Figure 6 Then select Insert Regular Curve under the menu, and select Based on Equation for all three coordinate regularity types. After confirming, a gradient elliptical spiral is generated, as shown in Figure 7 Note: The helix height is 8mm here, and after the thread is generated, it is sheared with the top elliptical surface reference plane to ensure the continuity of the thread at the end face of the nut.
[0097] Step 5: Establish the geometric model of the gradual elliptical thread of the self-locking nut in the finite element method
[0098] In this embodiment, the selected thread is a standard thread with a tooth angle of α=60°. The starting point of the thread is on the bottom circle section, and the xz plane where the point is located is selected to make the thread section, such as Figure 8 As shown in , this point can ensure the continuity of the thread when transitioning to the perfect circle. Call the sweep function to generate a gradual elliptical thread along the gradual elliptical spiral line, such as Fig. 9 shown.
[0099] Step 6: Establish the perfect circle area and thread geometry model of the closed self-locking nut in the finite element method
[0100] In this embodiment, the annular surface of the bottom circle is stretched to a length of 6 mm to form a perfect circular area with a wall thickness of 1 mm. Fig.10 Select the curve module, call the spiral function, generate a perfect circular spiral line in the perfect circular area, and pass Figure 8 The thread section in generates a perfect circle thread, such as Fig.11 shown.
[0101] Step 7: Combine the perfect circle area and gradient area of the closed self-locking nut in the finite element to obtain the modeling of the closed self-locking nut
[0102] In this embodiment, the perfect circular thread and the gradual elliptical thread, the perfect circular body and the gradual body are first merged, and then the Boolean operation is performed to subtract to complete the finite element establishment of the closed self-locking nut. The closed self-locking nut with thread features is as follows: Fig.12 shown.
[0103] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.
Claims
1. A modeling method for a closed-end self-locking nut for an aircraft engine, characterized in that: The steps include: Step 1: Summarize the geometric features of the closed-end self-locking nut; Step 2: Use mathematical formula to express the thread position of the gradual elliptical area of the closed self-locking nut; Step 3: Establish a geometric model of the gradual elliptical area of the closed self-locking nut in the finite element method; Step 4: Create a gradual elliptical spiral line of the closed self-locking nut in the finite element; Step 5: Establish a geometric model of the gradual elliptical thread of the closed self-locking nut in the finite element method; Step 6: Establish the perfect circle area and thread geometry model of the closed self-locking nut in the finite element method; Step 7: Combine the perfect circle area and the gradient area of the closed-end self-locking nut in the finite element to obtain the modeling of the closed-end self-locking nut; The step 1 specifically comprises: summarizing a perfect circle area and a gradual ellipse area according to the geometric characteristics of the closed-end self-locking nut, wherein the radius of the perfect circle area is r and the height is h1; the gradual ellipse area gradually transitions from a perfect circle to an ellipse, the height is h0, the semi-major axis of the ellipse at the top is a0, the semi-minor axis is b0, and the wall thickness is e; The step 2 is specifically as follows: obtaining the expression of the ellipse at any cross section, that is, the size of the semi-minor axis and the semi-major axis of the ellipse at any height, and at any height h, the distance a from the hypotenuse to the center line of the trapezoid is expressed as: a＝r + l (1) Where l is obtained according to the triangle proportional parallel formula: l is a parameter in the calculation process, which represents the difference between the major diameter of the ellipse and the initial nut radius Substituting formula (2) into formula (1) to obtain the expression of the semi-major axis a of the ellipse for any height h is: Similarly, when any height h is obtained, the expression of the length b of the semi-minor axis is: The step 4 is specifically as follows: generating a spiral line of a gradual elliptical thread, and representing the gradual elliptical spiral line with three-dimensional coordinates: Where a and b are the semi-major and semi-minor axes of the ellipse, respectively. is the rotation angle, and ω is the angular velocity of rotation, t is the parameter, v is the rising speed, p is the pitch of the thread, t is 0-8, ω=π; According to the elliptical helix expressions (3) and (4), they are substituted into the coordinate formula (6), the finite element expression module is called, and the gradual helix expression is edited according to the actual geometric dimensions of the closed self-locking nut. The regular curve is inserted and the gradual elliptical helix is generated after confirmation.
2. The modeling method of a closed-end self-locking nut for an aircraft engine according to claim 1, characterized in that: The step 3 is specifically as follows: according to the geometric features of the closed-end self-locking nut, a bottom circle and an ellipse of the gradient zone are established on a reference plane using finite elements, and then a gradient body is obtained by stretching the gradient body from the bottom circle to the top ellipse through a sweeping function; a gradient body with a consistent wall thickness and shape is established on the outside of the gradient body to obtain a hollow cylindrical gradient body.
3. The modeling method of a closed-end self-locking nut for an aircraft engine according to claim 2, characterized in that: The gradient body is obtained by stretching the gradient body from the bottom circle to the top elliptical gradient body through the sweep function, specifically: two sections and required guide lines are selected in the sweep function to gradually change from the bottom circle to the top elliptical shape along the guide line direction.
4. The modeling method of a closed-end self-locking nut for an aircraft engine according to claim 1, characterized in that: The step 5 is specifically as follows: select the thread form, the starting point of the thread is on the bottom circle section, select the xz plane where the point is located to make the thread section, and call the sweep function to generate a gradual elliptical thread along the gradual elliptical spiral line.
5. The modeling method of a closed-end self-locking nut for an aircraft engine according to claim 1, characterized in that: The step 6 is specifically as follows: stretching the annular surface of the bottom circle to form a perfect circular area, selecting a curve module, calling the spiral function, generating a perfect circular spiral line of the perfect circular area, and generating a perfect circular area thread through a thread section.
6. The modeling method of a closed-end self-locking nut for an aircraft engine according to claim 1, characterized in that: The step 7 is specifically as follows: merging the perfect circular thread and the gradient elliptical thread, the perfect circular body and the gradient body respectively, and then performing Boolean operations to complete the finite element establishment of the closed-end self-locking nut.