Numerical investigating nonlinear dynamic responses to rotating deep-hole drilling shaft with multi-span intermediate supports

• By introducing a modified transformation, the linear degrees of freedom of the drilling shaft model with free-interface are reduced significantly.
• A modified Newton shooting method is used to integrate the periodic trajectories of the reduced system.
• The periodic trajectories of the drilling shaft are used as numerical example to demonstrate and validate the proposed method.
• The numerical schemes are applied to deep hole drilling machine with two intermediate supports, whereby some interesting phenomena are revealed.

An approach is presented to study the nonlinear dynamic responses to rotating drill shaft with multi-span supports. Based on the finite element method, the drilling shaft is modeled as lots of 2-node Timoshenko shaft element model with free-interface that can take the effect of inertia and shear into consideration. In these cases, the governing equations of drilling shaft system consist of the coupled linear and nonlinear components. According to the feature of such systems, a modified transformation is introduced, by means of which the linear degrees of freedom of the drilling shaft system are reduced significantly whereas nonlinear degrees of freedom of the system are retained in the physical space. A modified Newton shooting method is used to obtain the periodic trajectories of the dynamic system. The advantage of this method has reduced much of the computational cost in the past, and the hydrodynamic forces of cutting fluid, cutting forces and unbalance forces can easily be added to the system equations. Further, the numerical schemes of this study are applied to a large-scale deep-hole drill machine with two intermediate supports. The periodic dynamic behaviors of the drilling shaft system and the region of unstable rotation are investigated numerically, whereby revealing some interesting phenomena.