Research On Nonlinear Dynamic Characteristics Identification Of NC Table

NC (numerical control) table is one of the main components of NC machine. Factors such as backlash, friction and elastic deformation among each part have become the bottleneck for feed system to enhance positioning precision, tracing precision and dynamic behaviors. There are many researches on dynamic behavior of NC table, but only few focused on its nonlinear dynamic characteristics.Using 'experimental probe-theoretical analysis-experimental verification' approach and 'synthesis-analysis-synthesis' procedure, this research starts from testing the dynamic signals of NC table. By means of a series of analysis on the colleted time series, a judgment is made that its dynamic behavior is nonlinear. The mathematic model of its dynamic system is established. The model structure discrimination, bifurcation and chaotic analysis of the nonlinear dynamic characteristics of its stiffness and friction are made. Massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained. The applicability of the model is tested via experiments. The effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A serise of corresponding improving measures are proposed. The main contributions of this dissertation are shown as follows.Firstly, the judgment that the dynamic behaviors of NC table have chaotic characteristics is made. So the nonlinear properties of the system are clearly exhibited. The systematic mathematic model of NC table is established. It clearly shows the relationship of every components of NC table.Secondly, stiffness of every component of NC table is analyzed separately. The mechanical models of four types of supporting ball screw are suggested. The varying regulation of axial stiffness, torsion stiffness and bending deflections of ball screw supported by each support types are analyzed. Stiffness of bearings, ball nut and sockets are briefly analyzed also. The nonlinear dynamic characteristics of stiffness are emphatically studied and the following conclusions are presented. Stiffness values vary with displacement and moving direction of NC table and show soft spring property or hard spring property. The responses of nonlinear springs obey soft or hard property Duffing equation. These conclusions above are of general applicability to the dynamic behavior reseaches on a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.Thirdly, the friction properties and friction models are introduced briefly. Nonlinear frictional dynamic characteristics of NC table are emphatically studied and the following conclusions are presented. The varying regulation of frictional force obeys Streibeck curve according the velocity and moving direction of NC table. The responses of nonlinear frictional forces in four different frictional regions on the Streibeck curve obey different regulations separately. These are as follows. In the full lubrication region, it's action effects are equivalent to increasing the systematic damping. In the boundary lubrication and half liquid lubrication regions, the negative slope of the Streibeck curve occurs and their action effects are equivalent to decreasing the systematic damping. When the negative systematic damping occurs, their responses obey Van Der Pol equation. In the static friction region, it's action effects are equivalent to increasing the systematic damping suddenly and the systematic responses are suppressed significantly. These conclusions above are of general applicability to the reseaches on nonlinear frictional dynamic behaviors of a kind of friction pairs such as machine tool guidway pair and a kind of metal machining processes.Meantime, the conclusion that the coupling effect of nonlinear stiffness and friction,when the negative systematic damping occurs, obeys Van Der Pol-Duffing coupling equation, the concrete type of Lienard equation, is presented. This conclusion is of general applicability to the dynamic behavior reseaches on nonlinear stiffness and friction coupling of a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.By means of analytic solutions, numerical simulation, bifurcation and chaotic analysis, massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained.A ZJK7532 NC drilling and milling machine made by Huazhong NC Company serves as a test object. The experiments are made to demonstrate the applicability of above theoretic analysis from different aspects. According to the regulations obtained via theoretic analysis and experiments, the effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A series of corresponding improving measures are proposed.A series of related softwares are written using MATLAB. The softwares such as correlation dimension analysis software etc are of general applicability to analyzing and processing chaotic time senses. The softwares such as systematic bifurcation diagram drawing software etc are of general applicability to bifurcation and chaotic analysis on nonlinear systems with determinate mathematic model.