It is common to use fasteners for structural connection in the structure of the aircraft. When analyzing the fatigue strength of the fastener connection, the flexibility coefficient of the fastener is a necessary parameter for calculating the transmitted load. When performing fatigue analysis and damage tolerance analysis, most analyses require the calculation of the load and total load at the end of a row of fasteners (required that the fasteners in this article refer only to rivets or tight-fitting bolts). The ratio. At present, there are two methods for calculating the load transmitted by the first row of fasteners: 1 according to the engineering formula, check the graph; 2 analytical method. Both of the above methods rely on the flexibility factor of the fastener, strip and substrate. Because the structural form of the plate that is in contact with the analysis is usually relatively regular, it is relatively easy to determine the flexibility coefficient of the substrate and the strip (the flexibility coefficient of the plate referred to herein actually refers to the equivalent compliance coefficient of the plate), then The flexibility factor of the fastener is the only important parameter that affects the accuracy of the load calculations transmitted by the end row of fasteners.
According to the review of relevant data, the methods commonly used at home and abroad to calculate the flexibility coefficient of fasteners mainly come from: 1 engineering experience formula, which is not conducive to accurate calculation; 2 the fitting of test data, the method needs to implement a large number of test. In this paper, the flexibility coefficient of the fastener is studied from the perspective of theoretical derivation, in order to obtain a calculation method with certain application value.
1 Factors affecting the calculation of the compliance coefficient of the fasteners The factors affecting the calculation of the compliance coefficient of the fastener are: the geometrical dimensions of the fastener, the stiffness of the fastener material, the geometry of the substrate and the strip, the substrate and the tape. The stiffness of the board material.
In the actual structure, the ratio of the diameter of the fastener to the effective length d/i = 1 ~ 2, can be regarded as a very "thick and short" beam, the shear stress has a great influence on its deformation. In practical applications, the deformation state and stress state near the fastener and its hole edge are extremely complicated, and it is difficult to describe it with a simple mathematical expression. In order to find a way to calculate the load transfer of the fastener, the following assumptions must be made: the deformation of any part of the structure is completely within the linear elastic range; neglecting the influence of friction and assembly stress, the fasteners effectively transmit the load; all the plates are In the plane stress state, it only bears the normal stress and shear stress in the plane.
2 The method of calculating the flexibility coefficient proposed in this paper attempts to calculate the flexibility coefficient of the fastener from the perspective of theoretical derivation. In order to simplify the derivation and calculation process, the following preconditions are proposed: (1) the extrusion stress along the thickness direction Evenly distributed as shown.
Let r = d/2, d be the fastener diameter. The distribution of the compressive stress on the BCB' strip (as shown) can be obtained: due to the symmetry and depending on the needs of the actual application, the component of r in the x-axis direction is not considered.
(2) The axis of the fastener is always parallel to the normal plane of the plate.
Based on the assumptions in the previous section, this paper considers that it is constrained by the simple support at the centroid of the fastener, as shown, but the bending moment is flat at the centroid at the centroid, taking a plane parallel to the x-axis and the y-axis, then BCB 'The projection on this plane is the shaded part in the middle. The distribution law by (2) is as shown.
Since the unit thickness is taken when the above formula is derived, the deformation amount of the thickness of the fastener compliance coefficient should at least include: the induced deformation, and 4' is the lateral displacement.
The following derivation takes the form of a single-shear lap joint as an example.
The calculations for 4bend and 4shear should be based on the Ironwood Xinkeliang Theory1, and the derivation process is as follows.
Take the micro-dds as the research object, the force of action is: Description: The upper z' corresponds to the z-axis coordinate value of the position of the middle projection strip. In order not to cause confusion, replace z with z'. According to the reference, it is known The change trend of the calculation result of the method is very close to the method proposed by the well-known aviation enterprise and the NACA report, and the numerical value is also close to the calculation result of the method proposed by the well-known aviation enterprise, which indicates that the method proposed in this paper has certain value in the fatigue analysis. .
Three methods for calculating the comparison of fastener compliance coefficients (changes in fastener parameters)
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