Abstract:To the influence of dynamics modeling of machine tool joints and identification method on the coupling relationship between substructure and internal vibration on external response is not adequately considered, the dynamics theory model of joints of machine tool is completely established by adopting the frequency response function matrix. The identification equation is derived based on mechanical equilibrium and displacement compatibility condition, and a new dynamics identification method is proposed.In the process of identification blending in the coupling relationship between substructures and rendering the frequency response function (FRF) difficult to measure as intermediate variable offset, the method avoid equation error using unpredictable response or estimation. On this basis, the identification equation is extended to the whole measurement range, and then the contradiction equation including identification is constructed. The equivalent dynamic stiffness is determined by the least square method and the finite element model of the structure is established. In order to verify the feasibility and correctness of the proposed method, field tests are conducted based on the LMS test platform and acquire good results. Compared with other modeling method such as reducing dimension and ignoring the internal excitation, the results indicate that the proposed method has better prediction.
Key words:joints;dynamics;modeling;dynamic
The dynamic characteristics of a joint affect the machine tool operations notably. In this paper, an improved approach is proposed to identify the dynamic stiffness of the joint and to construct a relevant dynamic model. The theoretical dynamic model assembled of two beams is built using the frequency response functions. The identification formulas are derived based on the mechanical equilibrium condition and the displacement compatibility condition to describe the relationship between the assembled structures and substructures. Then an inconsistent equation containing the identification relationship is developed. The equivalent value of the dynamic stiffness is extracted employing the least square method. In the identification process, a part of frequency response functions, which is difficult to be measured, is considered as an intermediate variable to avoid introducing errors. According to the results, the calculated dynamic responses of the assembly show better agreement with the experimental measured data in comparison with the results derived from a typical method, which validates the feasibility. And the results demonstrate higher accuracy of the proposed method.
Purpose
The purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities.
Design/methodology/approach
The proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities.
Findings
A revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model.
Originality/value
The contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.
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