Abstract
Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. The composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. The nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. The effects of the moment of inertia, gyroscopic effect, and internal and external damping are also considered, but shear deformation is neglected. Equation of motion is derived based on Hamiltonʼs extended principle and discretized by the Galerkin method. The analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. The response of the cutting system is studied for primary and superharmonic resonances. The effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. The results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. The equivalent nonlinearity of the cutting system shows hard spring characteristics. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves.
Highlights
In boring or milling machining applications, the chatter problem during the cutting process is increasingly more significant because, for these operations, a flexible cutter bar is used
Τ denotes delay time (τ 2π/NΩ), N denotes the number of cutting teeth, (Ktc, Kte) and (Krc, Kre) are the cutting force coefficients along tangential and radial directions, respectively, a denotes the axial cutting depth, cf denotes the feed per tooth per revolution and corresponds to the static part of the chip thickness, and vj(t − τ) − vj(t) denotes the dynamic chip thickness produced due to vibrations of the cutter bar at the present (vj(t)) and previous (vj(t − τ)) tooth periods
The classical viscous damping model is employed in our work to describe the external and internal damping. ce is proportional to the speed in the inertial coordinate system and ci is proportional to the speed in the rotating coordinate system [23, 31, 32]
Summary
College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China. Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. E composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. E nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. E analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. E effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. E results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
