Approach to the selection of the optimal sized of the ear – fork lug

. This paper considers an approach to the selection of a coefficient that takes into account the angle of application of the load to calculate the strength of the ear-plug type eyelets, which are responsible power elements that perceive concentrated forces and affect the efficiency of the connected units and aggregates. The peculiarity of this study is to determine the optimal limits of the ratio range of linear dimensions based on static tests. In order to simplify the visualization task and find the optimal shapes and sizes of the eyelet, various methods for solving this problem were compared. Developed on the basis of MS.Excel, the program for automated calculation of the strength of eyelets of the ear - plug type can be used in the design and calculation of eyelets. The results of calculations in MS.Excel and SimCenter 3D show good accuracy and convergence, including with the results of static tests with an average discrepancy of 2 to 5%. The analysis of the obtained results was carried out and recommendations were developed to expand the range of the coefficient, taking into account the optimal ratio of linear dimensions in accordance with the requirements of strength, technological design, as well as maintainability.


Formulation of the problem
At present, the competitiveness of aviation technology is largely determined by the weight efficiency of its design. The weight efficiency of the structure is laid at the early stages of design, when the optimal shapes and sizes of units and parts of the structure are determined [1]. Strength calculation is a prerequisite for the design and manufacture of critical products. It is important to know how the part will behave in real operating conditions under the influence of all loads and forces [2][3][4].
Eyelets are responsible power elements of parts that perceive concentrated forces. A rigorous calculation of them is difficult due to the need to take into account the stress concentration that occurs near the hole, and at the same time take into account plastic deformations that reduce the concentration. At the same time, the proportion of lugs in the total mass of the entire structure is small, which allows using approximate approaches based on experimental data and giving underestimated values of the limiting forces [4,5].
The lug is an element of the "ear-fork" connection, which can be fixed or movable, i.e. allowing mutual rotation of the connected parts. In the latter case, the assembly is subject to additional requirements to reduce friction and wear, which are satisfied by the installation of plain bearings (bushings) or rolling bearings. These features should also be taken into account when calculating the eyelet and when assigning safe dimensions [6,7]. Figure 1 shows two typical geometry options for symmetrical eyelets, where D is the diameter of the hole, b is the width of the eyelet, y is the distance along the symmetry axis from the edge of the hole to the top of the eyelet, x is the distance from the edge of the hole to the edge of the eyelet in the direction perpendicular to the axis of symmetry. The load on the lug can generally be represented in the form of three forces: axial Px, transverse Pv and lateral P. Lateral loading by the force Pz, normal to the lug plane, is not typical for such connections. In addition, the force Pz can cause significant stresses only at the fixed end. For these reasons, the force Pz is not considered further.
The most rational form of the lug is one shown in the figure: -the value of the angle α is not less than 15 o ; -ratio c = y/x = 1.4; -ratio 2R/d for angle α greater than 0 о (B/d for angle α equal to 0 о ) from 2 to 2.6. The calculation should be made using the correction coefficient for the material K, determined for four materials according to the graphs shown in Figures 2-4 for symmetrical loading of the lugs and the base angle of the lugs profile α = 0 о . It is recommended to select the allowable tension of the material of the lug material based on the following operating conditions of the hinges: -motionless (σadd.collapse = 1.3 σb); -sedentary (σadd.collapse = 0.65 σb); -for mobile (σadd.collapse = 0.2 σb). This article discusses the gap from axial stresses. The breaking load of rupture is found by the formula [6]: where к -is the axial load factor, which takes into account the stress concentration and is determined for various materials according to experimental graphs, depending on the ratio b / D and on the parameter c = y / x destruction = n( − )sectional area of the eye in the center of the hole; δeye thickness; nnumber of eyes; σbreaking stress.

Graphs of correction factors for materials
The graphs below were obtained by approximating the methods of PJSC Ilyushin [8], PJSC Irkut and Boeing. Approximation consisted in the selection of ways to solve and find the rupture load, as well as the selection of materials, according to the characteristics as close as possible to those listed below (30 KhGSA, normalized carbon steel, duralumin alloys and VT -22).

Example of design calculation
Task: Select the geometry of a double lug without eccentricity (i.e. having the following value of the coefficient C=1) from material 30 HGSA for an effective load P0 equal to 1000 kgf with a safety factor η equal to 1.5, provided that the force acts at an angle φ equal to 45⁰ to the axis of symmetry. The lug alignment angle α is taken equal to 0⁰. The ultimate strength σb is taken equal to 34 kgf/mm 2 . In addition, we will take into account two tolerances: 1.5 mm -manufacturing tolerance and 1.0 mm -repair tolerance. To simplify the calculations, a programmed add-in is presented in Excel with the order of the task of the initial data (Figure 6), and the visual result of the solution is also presented ( Figure 6). The next step was the application of the actual load, fixing the model and calculation using the solver. As a result, the result presented in Figure 7 (figure on the right) was obtained.

Conclusion
As a result of the research section, a methodology was obtained, implemented in add-ins for Excel, and verification was carried out using CAE SimCenter 3D.
When validating this article, the CAE environment, SimCenter 3D, was used. For this, an eyelet was modeled taking into account the geometric dimensions obtained using the software package. Next, the median surface was built along pairs of faces, a mesh was applied with an element size of 1 mm (Figure 7 -left). The next step was to check the mesh according to the parameters of the aspect ratio of the element ¼. The material was selected (according to the material selected in the complex -30 HGSA).