Abstract
The article dwells upon the assessment of the strain state of metal-cutting machines with the help of the numerical method of finite elements in the form of displacements. A metal-cutting machine is considered as a system consisting of a set of structural elements taking a set position in space in relation to each other, and a part of them may execute relative motions (displacements). The paper suggests a modification of the finite element method on the basis of combining a set of finite elements into a group with the use of the response function. The author provides an analytical calculation method to resolve the problem of assessing the strain state of the machine mechanism elements in linear and non-linear settings. The developed algorithm allows analyzing geometrical, physical and contact non-linearity of metal working. The research provides a practical implementation of the developed method by the examples of assessing the strain state of a rod element modeling the roughness of the contact surface of the machine mechanism elements under temperature and tensile loads.
Highlights
IntroductionAt design of metal-cutting machines a relevant task is to make a geometrical image of the structure with a subsequent analysis of its strain state under the action of a system of perturbing factors
At design of metal-cutting machines a relevant task is to make a geometrical image of the structure with a subsequent analysis of its strain state under the action of a system of perturbing factors.A metal-cutting machine can be considered as a system consisting of a set of structural elements taking a set position in space in relation to each other, and a part of them may execute relative displacements
Internal and external perturbing factors changing the state of structural elements induce the violation of initial connections and relations leading to strains or deviations in the geometrical images of mechanism elements
Summary
At design of metal-cutting machines a relevant task is to make a geometrical image of the structure with a subsequent analysis of its strain state under the action of a system of perturbing factors. To achieve the set objective, the following research tasks are stated in the paper: develop a concept for solving elastic problems on the basis of the response function method; identify key relations of the finite element method in the form of displacements; develop an algorithm for calculating the matrix for response function coefficients. Within the framework of the “glass box” concept the transfer of the output signal after obtaining the roots of the solving system and their assessment through a feedback chain allows correcting the input signal {δ} and building all the cycle again until a satisfactory solution is found {δ}0 Under this approach main FEM ratios in the form of displacements will be written as follows [4,5,6]: the finite element in the system of coordinates xyz is defined by nodal points {i, j, k, ... The design order corresponds to the model order, i.e. the degrees of the approximating polynomial
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