Stability and nonlinear dynamic behavior of drilling shaft system in copper stave deep hole drilling

Abstract

The stability and nonlinear dynamic behavior of drilling shaft system in copper stave deep hole drilling were analyzed. The effects of the fluctuation of the cutting force, the mass eccentricity and the hydrodynamic forces of cutting fluid could be taken into consideration in the model of drilling shaft system. Based on the isoparametric finite element method, the variational form of Reynolds equation in hydrodynamic fluid was used to calculate nonlinear hydrodynamic forces and their Jacobian matrices simultaneously. In the stability analysis, a new shooting method for rapidly determining the periodic orbit of the nonlinear drilling shaft system and its period was presented by rebuilding the traditional shooting method and changing the time scale. Through the combination of theories with experiment, the correctness and effectiveness of the above methods are verified by using the Floquet theory. The results show that the mass eccentricity can inhibit the whirling motion of drilling shaft to some extent.

A Nonlinear Dynamic Finite Element Analysis of Drilling Shaft including Multispan Auxiliary Supports in Deep-Hole Machining

“…In addition, it can be seen from Figures 7-9 that with an increase in rotational speed, whirling magnitude value at nodal point increases obviously, whereby resulting in an increase in roundness errors of the holes to be machined. As a result, this law has been proved in the correlative experiment [7,10]. "D" region is the complete unstable machining region for the drilling shaft.…”

“…To ensure the scheme accuracy, the drilling shaft system in this paper is modeled on the basis of [7], where the nonlinear vibration behaviors of drilling shaft was investigated when considering the imbalance forces of drilling shaft, cutting forces fluctuation, and nonlinear cutting fluid forces, and the numerical results was confirmed by the experiments. So, the deep-hole drilling shaft system model with the multiauxiliary supports is established as shown in Figure 1.…”

“…{Q} ∈ is the external force vector (including the imbalance forces and cutting forces fluctuation in drilling shaft rotation). Their concrete forms are detailed in Appendix A; {f} ∈ is the nonlinear cutting fluid force vector, whose calculation method is detailed in [7]. x is the displacement vector of drilling shaft system containing some node points, which can be described as…”

“…In the model, the drilling shaft mass eccentricities and cutting forces impact are taken into full account. The variational constraint principle is introduced to make the fluid forces necessary for nonlinear analysis, and Jacobian's metric calculation can be completed at the same time, and also, the correlative experiments are used to test the feasibility of the method, but the shear deformation and rotary inertia impact of the drilling shaft cannot be considered [7]. Generally speaking, the above-mentioned researches have simplified the drilling shaft into beams or axis models with the extreme few freedom degrees, and there exist gaps with the actual conditions.…”

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

“…Drilling shaft system as a rotating machine is a typical nonlinear dynamic system, and hence nonlinear hydrodynamic forces of cutting fluid do not have analytical formulation in fact. Kong et al [10] established the concentration mass dynamic model of drilling shaft system with the multi-degrees but without considering the effects of inertia and shear, and proposed a method to calculate the nonlinear hydrodynamic forces of cutting fluids and their Jacobian matrices of compatible accuracy simultaneously, and in addition, it was found that the mass eccentricity can inhibit the whirling motion of drilling shaft reported from the experimental results. Hussien et al [11] studied dynamic drilling shaft modeling with one-span and developed a mathematical approach to study the whirling motion of a continuous boring bar-workpiece system by transforming the problem into nonhomogeneous equations with homogenous boundary conditions.…”