Investigation On Elastodynamics And Chatter Stability Of A Newly Patented3-DOF PKM Module

The dynamic characteristics and chatter stability of a newly patented3-DOFPKM module named A3Head, which is designed for high-speed machining of largestructural components in aerospace industry, are investigated to provide usefulinformation for its application in aerospace and aeronautic fields. With this purpose,the present research explores the issues of kinematic analysis, post process systemdeveloping, mathematical modeling and prediction of multi-axis cutting force,elastodynamic modeling and dynamic analysis, regenerative chatter modeling andchatter stability prediction, followed by experimental tests of a A3-Head-basedfive-axis CNC prototype. The main content of this dissertation are listed asfollowings:Firstly, an inverse kinematic model for the A3-Head-based five-axis CNCprototype is established with vector-loop method, based on which the mappingbetween the pose of end effector and the kinetic joints are formulated and theworkspace of the end effector is predicted. On the basis of kinematic analysis, astrategy for post process system development is proposed and a customizedprocessing package is programmed with C Language. The developed package canoutput NC codes without manual intervention and can pre-alarm the over stroke of theCNC unit.Secondly, a mathematic model for cutting force prediction under complexoperating conditions is proposed by considering the effects of transient cuttingthickness of cutter, infinitesimal cutting thickness of5-axis milling cutter and radialcontact zone of tool and workpiece. The correctness of this model is validated by theexperimental tests and thus it can be used for further optimization of processparameters.Thirdly, an elastodynamic model of A3Head is presented by using thesubstructure synthesis and modal reduction techniques. With the proposed dynamicmodel, the distributions of natural frequencies, modal shapes and frequency responsefunctions (FRFs) of the end effector are simulated to show an axial-symmetry of thePKM’s configurations. The simulation results indicate that the spherical and revolutejoints are the bottle-necks of the system and their vibration amplitudes are muchhigher than other components. Besides, the FRFs of the end effector are stronglydependent with the module’s configuration in that the dynamic compliance decreasesdramatically with the increment of rotation angle. The following modal testexperiment confirms the validity of the theoretical results, manifesting that theproposed dynamic model can predict the system dynamic performance throughout theworkspace and lay a solid foundation for further chatter stability analysis. Fourthly, the distributions of chatter stability with respect to A3Headconfigurations are predicted. By using the zero-order approximation (ZOA) methodand modified full-discretization method (FDM), the mapping between the naturalmodes of A3Head and its chatter stability lobi are obtained. Then the FRFs at the tooltip point are predicted with the receptance coupling substructure analysis (RCSA)technique and the chatter stability of the whole system is determined. The resultsshow that the extreme cutting depth is strongly configuration-dependent in that itincreases with the increment of rotation angle. The A3Head is easy to occurregenerative chatter under lower speed milling, therefore it is strongly recommendedthat this module is applied in high-speed milling situation. A following experiment isconducted to identify the cutting forces coefficients and validate the regenerativecutting stability.The main contributions of this research may be concluded as followings:(1) A methodology of five-axis cutting force prediction is proposed based on thesecondary development of CNC virtual machining system. With the proposedmethodology, the multi-axis cutting forces of any position under complex operatingconditions can be predicted in a quick manner.(2) A methodology of elastodynamic modeling for A3Head is proposed by usingthe substructure synthesis and modal reduction techniques. With the proposedmethodology, the dynamic performance of the system throughout the workspace canbe predicted with high computation efficiency.(3) A methodology of chatter stability analysis is proposed by using the ZOAand modified FDM. With the proposed methodology, the process parameters can bepredetermined without causing regenerative chatter.The outcomes of this dissertation is of great importance in both theoretical andpractical fields in that it provides guidelines for designers and users of PKMequipments applied in high-speed machining industries.