CN107103126B - Method for quickly predicting interference quantity of riveting structure - Google Patents
Method for quickly predicting interference quantity of riveting structure Download PDFInfo
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Abstract
The invention relates to a method for quickly predicting interference quantity of a riveting structure, and belongs to the technical field of riveting processing. The method comprises the following steps: obtaining a riveted rivet indication configuration according to the thickness of a riveted plate and the initial configuration of the rivet; step two, mapping the triangular meshes on the revolution surface of the initial configuration of the rivet to the revolution surface of the indication configuration of the rivet; step three, taking the triangular mesh of the rivet indication configuration revolution surface as an initial solution of the rivet configuration revolution surface, and solving the final configuration of the rivet by a finite element method; and step four, obtaining the diameter of any height on the riveted rivet rod according to the final configuration of the rivet, wherein the difference value between the diameter and the rivet aperture is the required interference amount of the riveting structure. The method can quickly predict the interference amount of the riveting structure before riveting without actual riveting operation, and can assist designers to adjust process parameters and the like.
Description
Technical Field
The invention relates to a method for quickly predicting interference quantity of a riveting structure, and belongs to the technical field of riveting processing.
Background
For the assembly manufacturing process of modern aircraft, mechanical connection is still the main connection technology, in particular riveting, which is the most important connection form in the assembly of parts such as aircraft skin, wall panels and the like. Interference riveting is a connection technique that can strengthen the connection site, which can improve the structural fatigue performance while ensuring good sealability. The pressure stress generated by the interference of the riveting part can effectively inhibit the generation of fatigue cracks and delay the fatigue failure. And the interference stress generated in the riveting process is directly related to the interference amount. Therefore, the research on the interference amount of the riveted structure has important significance on the performance analysis of the riveted structure.
The existing riveting interference amount analysis mainly comprises interference amount detection after riveting, and is mainly divided into destructive detection and non-destructive detection. Destructive testing is a method of cutting (longitudinally or transversely) a riveted member by wire cutting or the like and then testing. The nondestructive detection is a method for fitting the upset contour by detecting the upset parameters after riveting and obtaining the interference amount by calculation. In engineering, the interference amount is usually detected after experiments to determine process parameters. However, repeated riveting experiments are required, the cost is high, the period is long, and the experimental result can only be used for rivet connection of specific material sizes.
Disclosure of Invention
The invention aims to solve the technical problems that: the method overcomes the defects of the technology and can quickly predict the interference amount of the riveting structure before riveting without actual riveting operation.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a method for quickly predicting interference quantity of a riveted structure comprises the following steps:
step one, according to the thickness t of a riveting plate before riveting0The aperture D of the rivet hole, the initial configuration of the rivet, the preset height h of the upset head after riveting, and the preset drum-shaped maximum diameter D of the upset head after rivetingmaxAccording to the profile curve equation of the upset head revolution surface and the principle of unchanged volume of the rivet before and after riveting, the minimum diameter d of the upset head is calculatedminSo as to obtain the indicating configuration of the riveted rivet;
the center of the upset head is taken as the origin of coordinates, the central axis of the rivet is taken as the y axis, and the profile curve equation of the upset head revolution surface is as follows:
the diameter of the rivet rod in the rivet hole after riveting is equal to the aperture D of the rivet hole;
dividing triangular meshes for the revolution surface of the initial configuration of the rivet, and mapping mesh nodes on the contour of the revolution surface of the initial configuration of the rivet to a contour curve of the revolution surface of the indication configuration of the rivet based on an overrun mapping method to obtain contour nodes of the revolution surface of the indication configuration of the rivet;
thirdly, mapping the internal grid nodes of the revolution surface of the initial rivet configuration to the revolution surface of the rivet indication configuration based on a grid parameterization algorithm to obtain the internal nodes of the revolution surface of the rivet indication configuration;
step four, connecting the outline nodes and the internal nodes of the rivet indication configuration revolution surface according to the topological relation before mapping to form a triangular mesh of the rivet indication configuration revolution surface as an initial solution of the rivet configuration revolution surface, and solving the final configuration of the rivet by a finite element method, wherein the process is as follows:
1) according to the initial solution of the rivet configuration revolution surface, the material parameters of the rivet and the preset pressure, obtaining the plastic strain and stress of each grid node of the rivet configuration, and further calculating to obtain the internal force acting on each grid node;
2) obtaining the external force of each grid node on the contact surface of the rivet configuration and the riveting plate according to the internal force of the grid node on the contact surface of the rivet configuration and the riveting plate and the friction coefficient between the rivet configuration and the riveting plate;
3) establishing a finite element balance equation according to the sum of the internal force and the external force of all the grid nodes formed by the rivet as zero;
4) solving a finite element balance equation by a Newton-Laplacian iteration method according to a preset convergence criterion to correct the grid nodes on the rivet configuration to obtain the final configuration of the rivet;
step five, obtaining rivets according to the step fourThe final configuration of the nail yields the diameter d of any height on the riveted shank1And diameter d1The difference value with the rivet aperture D is the required interference amount of the riveting structure.
The riveting structure is a typical axisymmetric volume forming structure and is characterized in that: the geometry, constraints, physical properties and applied external loads are all symmetrical about a fixed axis, i.e. the axis of symmetry. All the displacement, stress, strain and the like generated by the action of the load are also symmetrical to the axis, and all the planes passing through the axis are symmetrical planes. The displacement, stress and strain of the revolving body can be completely expressed by the displacement, stress and strain on the symmetrical plane. The space problem of axisymmetric volumetric shaping can be handled by simplifying the problem of a plane of revolution (i.e., a plane of symmetry).
In the second step of the invention, the triangular mesh of the revolution surface of the initial configuration of the rivet is mapped to the revolution surface of the indicating configuration of the rivet, so that a plurality of existing methods can be adopted when the triangular mesh of the revolution surface of the indicating configuration of the rivet is obtained, and the following methods are preferably adopted in the invention: firstly, mapping grid nodes on the revolution surface profile of the initial configuration of the rivet to a revolution surface profile curve of the indication configuration of the rivet based on an overrun mapping method to obtain profile nodes of the revolution surface of the indication configuration of the rivet; and then mapping the internal grid nodes of the revolution surface of the initial configuration of the rivet to the revolution surface of the indication configuration of the rivet based on a grid parameterization algorithm to obtain the internal nodes of the revolution surface of the indication configuration of the rivet, and connecting the contour nodes and the internal nodes of the revolution surface of the indication configuration of the rivet according to the connection sequence before mapping to form a triangular grid of the revolution surface of the indication configuration of the rivet.
The method comprises the following steps of mapping a mesh on the surface of the initial configuration of the rivet to an outline curved surface of the heading foreshadowing configuration based on an overrun mapping method, and obtaining an outline mesh. The overrun mapping method is also called an infinite interpolation method, and is a method for converting an irregular area on a physical plane into a regular area on a calculation plane through a certain algebraic relational expression. The method is also the prior art for mapping the internal grid of the initial rivet configuration into the heading prediction configuration based on a grid parameterization algorithm to obtain the internal grid, and the grid parameterization is a method for obtaining the parameterized grid according to the corner relation expressed by the triangles of the grid and by the principle of similar triangles in mathematics, namely the ratio of the adjacent side lengths of the triangles and the included angle are equal. The method is intuitive in geometric principle performance, and the solving process only needs to solve the established linear equation set, so that the calculation is simple and quick. The overrun mapping method and the grid parameterization algorithm can refer to relevant documents and are not described in detail.
It should be noted that the overrun mapping method can map the nodes on the initial grid structure to the predictive configuration one by one through the calculated mapping function, but the phenomenon of internal grid unevenness of the predictive configuration is easily generated, so that only the contour nodes of the predictive configuration are mapped, and the internal grid nodes are solved by adopting a grid parameterization method. That is, although both the overrun mapping method and the mesh parameterization algorithm are prior art, the combination of the two and the mapping between planar meshes is not disclosed in the prior art.
In addition, the convergence criterion in step four is more commonly used in three types, namely, a displacement criterion, an imbalance (residual force) criterion and an energy criterion, and the convergence criterion in the present invention is preferably: when the norm of the residual force vector of all the grid nodes with rivet configurations calculated by a certain iteration step is smaller than the corresponding value calculated by the previous iteration step, judging whether the sum of the displacement differences of all the grid nodes with rivet configurations in two adjacent iteration steps is smaller than a preset value, if so, finishing the iteration, otherwise, continuing to perform the next iteration; when the norm of the residual force vectors of all rivet-shaped grid nodes calculated in a certain iteration step is greater than or equal to the corresponding value calculated in the previous iteration step, the iteration is failed; wherein the residual force vector of a rivet-configured mesh node is the difference between the internal and external forces acting on the rivet-configured mesh node.
The invention has the beneficial effects that: according to the invention, the predicted configuration of the upset head after riveting is estimated, the interference amount of the riveting structure is quickly predicted by using a quick finite element method, the method can be completed in one step, the efficiency is higher, and the actual riveting operation is not required, so that the manpower and material resources are saved, the cost is low, the calculation is simple, the requirement on software operators is lower, the existing commercial finite element software can be fully utilized, and the operators do not need to have deep finite element knowledge, so that the engineering application is easy. The method can be completed from the initial configuration (rivet) to the final configuration (rivet after riveting) only by one step, and the intermediate deformation process is omitted, so that the calculation speed is high, the use is convenient and quick, the method can conveniently assist designers to adjust process parameters, and the mass production cost and time can be saved.
Drawings
The invention will be further explained with reference to the drawings.
FIG. 1 is a schematic illustration of an initial configuration of a rivet in an embodiment of the present invention.
FIG. 2 is a schematic representation of the final configuration of a rivet in an embodiment of the present invention
Detailed Description
Examples
In order to more vividly and intuitively represent the initial solution prediction method of the section and verify the effectiveness of the method, in the embodiment, the diameter of a rivet is 3.97mm, the length of a rivet rod is 9.5mm, the diameter of a rivet hole on a riveting plate is 4.1mm, the thickness of a plate is 2mm, the friction coefficient mu between the rivet and the riveting plate is 0.2, and the height h of an upset head is controlled to be 2.28 mm. The material parameters for the rivets and rivet plates are shown in tables 1 and 2.
TABLE 1 rivet Material-2117-T4 aluminum alloy
TABLE 2 riveting plate material-2024-T3 aluminum alloy
The analysis model takes a half section of the rivet diameter and divides a triangular mesh, and the total number of the nodes is 231, and 400 triangular units are arranged.
The method for quickly predicting the interference amount of the riveting structure comprises the following steps:
step one, according to the thickness of a riveting plate before rivetingDegree t0The aperture D of the rivet hole, the initial configuration of the rivet, the preset height h of the upset head after riveting, and the preset drum-shaped maximum diameter D of the upset head after rivetingmaxAccording to the profile curve equation of the upset head revolution surface and the principle of unchanged volume of the rivet before and after riveting, the minimum diameter d of the upset head is calculatedminSo as to obtain the indicating configuration of the riveted rivet; the center of the upset head is taken as the origin of coordinates, the central axis of the rivet is taken as the y axis, and the profile curve equation of the upset head revolution surface is as follows:
maximum diameter d of upset drummaxPreset to 3mm, the diameter of the shank of the rivet in the predicted configuration of the rivet corresponds to the diameter of the rivet hole when calculating the volume of the predicted configuration of the rivet after riveting. According to the volume invariance principle, the minimum diameter d of the upset head can be obtainedminAnd finally obtaining the indicating configuration of the riveted rivet according to the profile curve equation of the upset head revolution surface.
Dividing triangular meshes for the revolution surface of the initial configuration of the rivet, and mapping mesh nodes on the contour of the revolution surface of the initial configuration of the rivet to a contour curve of the revolution surface of the indication configuration of the rivet based on an overrun mapping method to obtain contour nodes of the revolution surface of the indication configuration of the rivet; mapping the internal grid nodes of the revolution surface of the initial configuration of the rivet to the revolution surface of the indication configuration of the rivet based on a grid parameterization algorithm to obtain the internal nodes of the revolution surface of the indication configuration of the rivet; and connecting the contour nodes and the internal nodes of the rivet predicted configuration revolution surface according to the topological relation before mapping to form a triangular mesh of the rivet predicted configuration revolution surface.
The triangular mesh after mapping obtained in the step two is pure geometric mapping, the action of mechanical deformation is not considered, and the obtained final configuration precision is poor, so that the final configuration is required to be corrected by the finite element method in the step three to obtain more accurate final configuration.
Step three, taking a triangular mesh of the rivet indication configuration revolution surface as an initial solution of the rivet configuration revolution surface, and solving the final configuration of the rivet by a finite element method, wherein the process is as follows:
1) according to the initial solution of the rivet configuration revolution surface, the material parameters of the rivet and the preset pressure, obtaining the plastic strain and stress of each grid node of the rivet configuration, and further calculating to obtain the internal force acting on each grid node;
calculating the plastic strain and stress of each grid node and the internal force acting on each grid node are the prior art and are not described again;
2) and obtaining the external force of each grid node on the contact surface of the rivet configuration and the riveting plate according to the internal force of the grid node on the contact surface of the rivet configuration and the riveting plate and the friction coefficient between the rivet configuration and the riveting plate.
During the forming process, friction occurs due to relative movement and flow of the metal material between the exterior surface of the rivet formation and the rivet plate. Decomposing an external force F acting on the grid nodes of each riveting plate into a normal force F in a direction perpendicular to the surface of the riveting platenAnd a tangential force F directed tangentially to the surface of the riveted platetI.e. by
F＝Fn+Ft
The friction at the nodes of the grid is, according to coulomb's law of friction:
f＝μFn。
3) establishing a finite element balance equation for zero according to the sum of the internal force and the external force of all the grid nodes formed by the rivet by using the virtual work principle;
4) and solving a finite element balance equation by a Newton-Laplacian iteration method according to a preset convergence criterion to correct the grid nodes on the rivet configuration to obtain the final configuration of the rivet.
The convergence criteria are three criteria, namely, a displacement criterion, an imbalance (residual force) criterion and an energy criterion, which are commonly used, and the convergence criterion in this embodiment is preferably: when the norm of the residual force vector of all the grid nodes with rivet configurations calculated by a certain iteration step is smaller than the corresponding value calculated by the previous iteration step, judging whether the sum of the displacement differences of all the grid nodes with rivet configurations in two adjacent iteration steps is smaller than a preset value, if so, finishing the iteration, otherwise, continuing to perform the next iteration; when the norm of the residual force vectors of all rivet-shaped grid nodes calculated in a certain iteration step is greater than or equal to the corresponding value calculated in the previous iteration step, the iteration is failed; wherein the residual force vector of a rivet-configured mesh node is the difference between the internal and external forces acting on the rivet-configured mesh node.
When the iteration fails, the final rivet configuration is considered unsatisfactory and process parameters need to be adjusted.
Step four, according to the final configuration of the rivet obtained in step three, the diameter d of any height on the rivet stem after riveting can be easily obtained1And diameter d1The difference value with the rivet aperture D is the required interference amount of the riveting structure.
The present invention is not limited to the specific technical solutions described in the above embodiments, and other embodiments may be made in the present invention in addition to the above embodiments. All technical solutions formed by equivalent substitutions fall within the scope of the claims of the present invention.
Claims (3)
1. A method for quickly predicting interference quantity of a riveted structure comprises the following steps:
step one, according to the thickness t of a riveting plate before riveting0The aperture D of the rivet hole, the initial configuration of the rivet, the preset height h of the upset head after riveting, and the preset drum-shaped maximum diameter D of the upset head after rivetingmaxAccording to the profile curve equation of the upset head revolution surface and the principle of unchanged volume of the rivet before and after riveting, the minimum diameter d of the upset head is calculatedminSo as to obtain the indicating configuration of the riveted rivet;
the center of the upset head is taken as the origin of coordinates, the central axis of the rivet is taken as the y axis, and the profile curve equation of the upset head revolution surface is as follows:
the diameter of the rivet rod in the rivet hole after riveting is equal to the aperture D of the rivet hole;
dividing a triangular mesh on the revolution surface of the initial configuration of the rivet, and mapping the triangular mesh to the revolution surface of the predictive configuration of the rivet to obtain the triangular mesh of the revolution surface of the predictive configuration of the rivet;
step three, taking the triangular mesh of the rivet indication configuration revolution surface as an initial solution of the rivet configuration revolution surface, and solving the final configuration of the rivet by a finite element method, wherein the process is as follows:
1) according to the initial solution of the rivet configuration revolution surface, the material parameters of the rivet and the preset pressure, obtaining the plastic strain and stress of each grid node of the rivet configuration, and further calculating to obtain the internal force acting on each grid node;
2) obtaining the external force of each grid node on the contact surface of the rivet configuration and the riveting plate according to the internal force of the grid node on the contact surface of the rivet configuration and the riveting plate and the friction coefficient between the rivet configuration and the riveting plate;
3) establishing a finite element balance equation according to the sum of the internal force and the external force of all the grid nodes formed by the rivet as zero;
4) solving a finite element balance equation by a Newton-Laplacian iteration method according to a preset convergence criterion to correct the grid nodes on the rivet configuration to obtain the final configuration of the rivet;
step four, obtaining the diameter d of any height on the riveted rivet rod according to the final configuration of the rivet obtained in the step three1And diameter d1The difference value with the rivet aperture D is the required interference amount of the riveting structure.
2. The method for rapidly predicting the interference amount of the riveted structure according to claim 1, wherein the convergence criterion in the third step is as follows: when the norm of the residual force vector of all the grid nodes with rivet configurations calculated by a certain iteration step is smaller than the corresponding value calculated by the previous iteration step, judging whether the sum of the displacement differences of all the grid nodes with rivet configurations in two adjacent iteration steps is smaller than a preset value, if so, finishing the iteration, otherwise, continuing to perform the next iteration; when the norm of the residual force vectors of all rivet-shaped grid nodes calculated in a certain iteration step is greater than or equal to the corresponding value calculated in the previous iteration step, the iteration is failed; wherein the residual force vector of a rivet-configured mesh node is the difference between the internal and external forces acting on the rivet-configured mesh node.
3. The rivet structure interference amount rapid prediction method according to claim 1 or 2, characterized in that: firstly, mapping grid nodes on the revolution surface profile of the initial configuration of the rivet to a revolution surface profile curve of the indication configuration of the rivet based on an overrun mapping method to obtain profile nodes of the revolution surface of the indication configuration of the rivet; and then mapping the internal grid nodes of the revolution surface of the initial configuration of the rivet to the revolution surface of the indication configuration of the rivet based on a grid parameterization algorithm to obtain the internal nodes of the revolution surface of the indication configuration of the rivet, and connecting the contour nodes and the internal nodes of the revolution surface of the indication configuration of the rivet according to the topological relation before mapping to form a triangular grid of the revolution surface of the indication configuration of the rivet.
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