CN-121835313-B - Portal frame dynamics analysis method

CN121835313BCN 121835313 BCN121835313 BCN 121835313BCN-121835313-B

Abstract

The invention is suitable for the field of portal frames and discloses a portal frame dynamics analysis method which comprises the steps of establishing a full-order finite element model of a portal frame, obtaining a quality matrix and a rigidity matrix of the full-order finite element model, dividing the full-order finite element model into a plurality of substructures based on modularized structural characteristics of the portal frame, decomposing the degrees of freedom of each substructure into internal degrees of freedom and boundary degrees of freedom, constructing a fixed boundary main modal matrix and a constraint modal matrix of each substructure, constructing a reduced basis matrix, carrying out modal polycondensation on the quality matrix and the rigidity matrix of the full-order finite element model by utilizing the reduced basis matrix, generating a reduced quality matrix and a reduced rigidity matrix, constructing a reduced dynamics equation, solving the reduced dynamics equation, obtaining reduced modal coordinates, and carrying out inversion reduction by combining the reduced basis matrix and the reduced coordinates to obtain displacement response vectors of the full-order finite element model, wherein key dynamics information of the portal frame is reserved to the maximum extent by reducing the reduced modal efficiency.

Inventors

FENG JIAMING
LIANG HAOQIAN
GONG JING
Yang Guangmeng
ZENG XIANFENG
KUANG ZHANHUA

Assignees

季华实验室

Dates

Publication Date: 20260508
Application Date: 20260312

Claims (10)

1. A gantry dynamics analysis method, comprising: establishing a full-order finite element model of a portal frame, and acquiring a quality matrix and a rigidity matrix of the full-order finite element model; Dividing the full-order finite element model into a plurality of substructures based on the modularized structural characteristics of the portal frame, and decomposing the degrees of freedom of each substructure into an internal degree of freedom and a boundary degree of freedom; Based on the mass matrix, the rigidity matrix and the dividing results of the internal degrees of freedom and the boundary degrees of freedom, a fixed boundary main mode matrix and a constraint mode matrix of each substructure are constructed, and a reduced base matrix is constructed based on the fixed boundary main mode matrix and the constraint mode matrix; performing modal condensation on the quality matrix and the rigidity matrix of the full-order finite element model by using the reduced basis matrix to generate a reduced quality matrix and a reduced rigidity matrix, and constructing a reduced dynamics equation based on the reduced quality matrix and the reduced rigidity matrix; And solving the reduced dynamics equation to obtain reduced modal coordinates, and combining the reduced basis matrix and the reduced modal coordinates for inversion reduction to obtain displacement response vectors of the full-order finite element model.
2. The gantry dynamics analysis method according to claim 1, wherein the gantry-based modularized structural feature divides the full-order finite element model into a plurality of substructures, and when the degrees of freedom of each substructure are decomposed into an internal degree of freedom and a boundary degree of freedom, the boundary degree of freedom is minimized as a target, the cross beam, the left upright, the right upright and the workbench of the gantry are respectively divided into independent substructures based on the gantry-based modularized structural feature, and the core degree of freedom on the connection surface of each substructure is used as the boundary degree of freedom, and the dispersion degree of freedom inside each substructure is used as the internal degree of freedom.
3. The gantry dynamics analysis method according to claim 2, characterized in that the core degrees of freedom include three translational degrees of freedom and three rotational degrees of freedom.
4. The gantry dynamics analysis method according to claim 2, characterized in that the decomposition of the degrees of freedom of each substructure is achieved by blocking the mass matrix and stiffness matrix of each substructure according to the internal degrees of freedom and the boundary degrees of freedom, the blocking being expressed as: in the formula, The quality matrix is represented by a matrix of qualities, Representing a matrix of stiffness values, And For the mass and stiffness sub-matrices corresponding to the internal degrees of freedom, And A mass sub-matrix and a stiffness sub-matrix corresponding to the boundary degree of freedom sub-matrix, 、、 And In order to cross-couple the sub-matrices, The degree of freedom in the interior is indicated, Representing the boundary degrees of freedom.
5. The gantry dynamics analysis method according to claim 4, wherein the constructing a fixed boundary main mode matrix and a constraint mode matrix of each substructure based on the mass matrix, the stiffness matrix, and the division result of the internal degrees of freedom and the boundary degrees of freedom, and constructing a reduced basis matrix based on the fixed boundary main mode matrix and the constraint mode matrix, comprises: After the boundary degrees of freedom of each substructure are fixed, solving a characteristic equation based on a quality submatrix and a rigidity submatrix corresponding to the internal degrees of freedom, obtaining a plurality of internal degree of freedom characteristic vectors, sequencing the plurality of internal degree of freedom characteristic vectors according to the sequence from small to large of the natural frequency, and selecting the first k sequenced internal degree of freedom characteristic vectors to construct a fixed boundary main modal matrix, wherein k is a positive integer; The inertia force of the substructure is set to be zero, a static equilibrium equation is solved based on a block form of the stiffness matrix, a static mapping relation of the internal degree of freedom about the boundary degree of freedom is obtained, and a constraint modal matrix is constructed based on the static mapping relation of the internal degree of freedom about the boundary degree of freedom; and splicing the selected fixed boundary main mode matrix and the constraint mode matrix to form a reduced-order base matrix.
6. The gantry dynamics analysis method according to claim 5, wherein the characteristic equation based on the mass sub-matrix and the stiffness sub-matrix corresponding to the internal degrees of freedom is expressed as: in the formula, The internal free feature vector is represented as such, Representing the generalized eigenvalue.
7. The gantry dynamics analysis method according to claim 6, characterized in that the constrained modal matrix is expressed as: in the formula, Representing a matrix of constrained modalities, Is a cross-coupled sub-matrix.
8. The gantry dynamics analysis method according to claim 7, characterized in that the reduced basis matrix is expressed as: in the formula, Representing the reduced-order basis matrix, An identity matrix representing the dimensions of the boundary degrees of freedom, For a zero matrix of dimension matching, Representing a fixed boundary primary modal matrix.
9. The gantry dynamics analysis method according to claim 8, characterized in that the reduced dynamics equation is expressed as: in the formula, Representing a reduced-order quality matrix of the image, Representing a matrix of reduced order stiffness, In order to reduce the magnitude of the load vector, , For a full-order external load vector, Representing the coordinates of the reduced-order mode, Representing the second derivative of the reduced-order modal coordinate vector with respect to time, Representing the transpose of the reduced base matrix.
10. The gantry dynamics analysis method according to claim 9, characterized in that the displacement response vector of the full-order finite element model is expressed as: in the formula, Representing the displacement response vector of the full-order finite element model.

Description

Portal frame dynamics analysis method Technical Field The invention relates to the field of portal frames, in particular to a portal frame dynamics analysis method. Background The portal frame is a core bearing and moving structure of equipment such as a machine tool, a lifting transportation line, an automatic production line and the like, and the vibration response, the rigidity, the natural frequency and the coupled vibration characteristics of the portal frame directly determine the operation precision, the stability and the service life of equipment, so that the portal frame is a key for avoiding the problems of resonance, insufficient rigidity, structural fatigue and the like. In the research and development and optimization stage, dynamic simulation is an important basis for adjusting structural parameters and improving performance, and has become a core link of high-end portal frame design. In the current engineering, a finite element full-order model is mostly adopted for dynamic analysis, and although the calculation accuracy is high, the portal frame has large span and complex structure, the degree of freedom of the model can reach tens of thousands to hundreds of thousands, and the single simulation consumes several hours to tens of hours. Even if the process automation is realized through software secondary development, the efficiency requirement of developing and quick iteration is still difficult to meet, and the design period is seriously prolonged. The model reduction method can greatly reduce the degree of freedom and improve the calculation efficiency, and is applied and verified in the field of part of complex structures. However, the existing polynomial interpolation-based order reduction method is mainly suitable for beam structures, is not matched with structural features of portal frame modularization and multi-component cooperation, can lose boundary coupling effects among beams, stand columns and working tables, cannot accurately reflect cooperative vibration rules, and is difficult to meet high-end equipment precision requirements. Meanwhile, the method is generally limited to free vibration analysis, the applicability of the method is obviously reduced under strong nonlinear dynamics working conditions such as high-speed movement, variable load, instantaneous impact and the like, and the method is required to be modeled again during parameter adjustment and has poor reusability. With the development of equipment to high speed, heavy load and precision, the nonlinear dynamics analysis of the portal frame is in urgent need of high-efficiency high-precision reduced-order model support. The existing full-order model has low efficiency and the general order reduction method has insufficient precision, so that the contradiction that the design is trapped in the precision and the efficiency are difficult to consider is caused, and the engineering application is restricted. Accordingly, there is a need for improvement and development in the art. Disclosure of Invention The invention aims to provide a gantry dynamics analysis method, which aims to solve the technical problem that the existing gantry uses a full-order model to simulate a long time. In order to achieve the above purpose, the invention provides the following scheme: A portal frame dynamics analysis method comprises the steps of establishing a full-order finite element model of a portal frame, obtaining a quality matrix and a rigidity matrix of the full-order finite element model, dividing the full-order finite element model into a plurality of substructures based on modularized structural features of the portal frame, decomposing the degrees of freedom of each substructure into an internal degree of freedom and a boundary degree of freedom, constructing a fixed boundary main modal matrix and a constraint modal matrix of each substructure based on the quality matrix, the rigidity matrix and dividing results of the internal degree of freedom and the boundary degree of freedom, constructing a reduced basis matrix based on the fixed boundary main modal matrix and the constraint modal matrix, performing modal polycondensation on the quality matrix and the rigidity matrix of the full-order finite element model by utilizing the reduced basis matrix to generate a reduced quality matrix and a reduced rigidity matrix, constructing a reduced dynamics equation based on the reduced quality matrix and the reduced rigidity matrix, solving the reduced dynamics equation, obtaining reduced modal coordinates, and combining the reduced modal coordinates and obtaining displacement response vector of the full-order finite element model. Preferably, the portal frame-based modularized structural feature divides the full-order finite element model into a plurality of substructures, and when the degrees of freedom of each substructures are decomposed into an internal degree of freedom and a boundary degree of freedom, the number of boundary degrees o