Active–Passive Hybrid Effects of Nonlinear Damping on Chatter Suppression of a Piezoelectric Composite Bar in Boring Operation

An active and passive control method is presented to suppress chatter vibrations of the spinning and cylindrical composite boring bar by combining the cutting process damping derived from indentation effect with piezoelectric damping stemmed from Macro Fiber Composite (MFC). The kinetic, potential and electrical energies of the composite boring bar based on the continuous distributed function are established by taking the constitutive relations of piezoelectric materials and the derivative feedback algorithm into account. Introducing the viscoelastic, the hysteretic, the process damping forces, the electrical field as well as cutting forces subjected to the boring process system and forming the virtual work of the non-conservative forces, a final nonlinear equation of motion is derived by utilizing extended Hamilton’s principle and Galerkin procedure. Afterward, the dynamic responses of composite boring bar are derived by using the method of multiple time scales. The proposed approach is validated by comparing the present results with those related papers. A combined model considering process damping effect and feedback gain is also confirmed. The influences of machining, internal and external damping and control parameters on vibration response and process stability of the novel composite boring bar are investigated and discussed. The nonlinear model proposed in this paper can assist in achieving optimal design for composite boring bar and improve the machinability of boring process.