Method of Reducing the Number of DOF in the Machine Tool-Cutting Process System from the Point of View of Vibrostability Analysis

The model of the mass-damping-spring (MDS) system of a machine tool is multi-degree of freedom model. The model of the cutting process (CP) has to correspond structurally to the MDS system model constituting the machine tool-cutting process (MT-CP) system model. This is often a model of time-variant parameters. Therefore, forecasting the vibrostability, i.e. resistance to the occurrence of self-excited vibrations, in the MT-CP system is a complicated task. To simplify analysis it is justified to reduce the number of degrees of freedom. The method presented simplifies significantly the computational model while the interpretation of the results applies to the whole construction. The reduced model carries information concerning vibration modes that determine vibrostability loss. The paper presents the mathematical fundamentals of the reduction of the machine tool MDS system model, analysis and selection of vibration modes considered in the reduced model and analysis of reduction errors.

[1]  J. C. Bruch,et al.  Piezoelectric patch control using an integral equation approach , 2001 .

[2]  S. Smith,et al.  Efficient simulation programs for chatter in milling , 1993 .

[3]  Harvey Thomas Banks,et al.  The modeling of piezoceramic patch interactions with shells, plates, and beams , 1995 .

[4]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .

[5]  Huang-Nan Huang,et al.  Vibration control of beam–plates with bonded piezoelectric sensors and actuators , 1999 .

[6]  Nagi G. Naganathan,et al.  A finite-element static analysis of smart turbine blades , 1997 .

[7]  Quan Wang,et al.  Optimal placement and size of piezoelectric patches on beams from the controllability perspective , 2000 .

[8]  Sarp Adali,et al.  Analytical solution technique for multiple-patch piezoelectric sensor-actuator vibration control problems , 2000, Smart Structures.

[9]  In Lee,et al.  Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms , 1999 .

[10]  J. C. Bruch,et al.  Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams , 2000 .

[11]  V. Varadan,et al.  Closed loop finite element modeling of active structural damping in the frequency domain , 1997 .

[12]  P. C. Dumir,et al.  Segmented Sensors and Actuators for Thick Plates and Shells Part i: Analysis Using Fsdt , 1999 .

[13]  R. Barboni,et al.  Optimal placement of PZT actuators for the control of beam dynamics , 2000 .

[14]  C. Fuller,et al.  Experiments on active control of structurally radiated sound using multiple piezoceramic actuators , 1990 .

[15]  Osama J. Aldraihem,et al.  Deflection analysis of beams with extension and shear piezoelectric patches using discontinuity functions , 2001 .

[16]  Liviu Librescu,et al.  Oscillation control of cantilevers via smart materials technology and optimal feedback control: actuator location and power consumption issues , 1998 .

[17]  W. H. Huang,et al.  IS A COLLOCATED PIEZOELECTRIC SENSOR/ACTUATOR PAIR FEASIBLE FOR AN INTELLIGENT BEAM? , 1998 .

[18]  Enrico Fantini,et al.  Genetic Algorithm Optimization for the Active Control of a Beam by Means of PZT Actuators , 1998 .

[19]  Vijay K. Varadan,et al.  A review and critique of theories for piezoelectric laminates , 1999 .

[20]  Romesh C. Batra,et al.  Analysis of piezoelectric bimorphs and plates with segmented actuators , 2001 .

[21]  Chien-Chang Lin,et al.  Vibration and sound radiation controls of beams using layered modal sensors and actuators , 1998 .

[22]  R. Sridhar,et al.  A General Formulation of the Milling Process Equation: Contribution to Machine Tool Chatter Research—5 , 1968 .

[23]  Paolo Gaudenzi,et al.  Control of beam vibrations by means of piezoelectric devices: theory and experiments , 2000 .

[24]  Vijay K. Varadan,et al.  Natural frequencies of a smart plate with segmented piezoelectric patches , 2000, Smart Structures.

[25]  I. E. Minis,et al.  A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling , 1993 .