Influence of Torsional Motion on the Axial Vibrations of a Drilling Tool (original) (raw)
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International Journal of Machine Tools and Manufacture, 2007
A time domain model of the drilling process and hole formation mechanism is presented in Part I, and the general solution of drilling chatter stability in frequency domain is presented in this paper. The drill's flexibility in torsional, axial and lateral directions are considered in determining the regenerative chip thickness. Stability is modelled as a fourth order eigenvalue problem with a regenerative delay term. The critical radial depth of cut and spindle speed are analytically determined from the eigenvalues of the characteristics equation of the dynamic drilling process in frequency domain. The method is compared against the extensive numerical solutions in time domain which were presented in Part I, cutting experiments and previously published partial stability laws. The time domain model presented in Part I of the paper considers tool geometry dependent mechanics, all vibration directions and the true kinematics of drilling, while allowing for nonlinearities such as tool jumping out of cut and nonlinear cutting force models. It is shown that accurate prediction of drilling stability requires modeling of drill/hole surface contact stiffness and damping which is still a research challenge.
Generalized modeling of drilling vibrations. Part II: Chatter stability in frequency domain
International Journal of Machine Tools and Manufacture, 2007
A time domain model of the drilling process and hole formation mechanism is presented in Part I, and the general solution of drilling chatter stability in frequency domain is presented in this paper. The drill's flexibility in torsional, axial and lateral directions are considered in determining the regenerative chip thickness. Stability is modelled as a fourth order eigenvalue problem with a regenerative delay term. The critical radial depth of cut and spindle speed are analytically determined from the eigenvalues of the characteristics equation of the dynamic drilling process in frequency domain. The method is compared against the extensive numerical solutions in time domain which were presented in Part I, cutting experiments and previously published partial stability laws. The time domain model presented in Part I of the paper considers tool geometry dependent mechanics, all vibration directions and the true kinematics of drilling, while allowing for nonlinearities such as tool jumping out of cut and nonlinear cutting force models. It is shown that accurate prediction of drilling stability requires modeling of drill/hole surface contact stiffness and damping which is still a research challenge.
Analysis of drilling vibrations: A time-delay system approach
2012
The main purpose of this study is the description of the qualitative dynamical response of a rotary drilling system with a drag bit, using a model that takes into consideration the axial and the torsional vibration modes of the bit. The studied model, based on the interface bit-rock, contains a couple of wave equations with boundary conditions consisting of the angular speed and the axial speed at the top additionally to the angular and axial acceleration at the bit whose contain a realistic frictional torque. Our analysis is based on the center manifold Theorem and Normal forms theory whose allow us to simplify the model.
Self-Excited Vibration Drilling Models and Experiments
CIRP Annals - Manufacturing Technology, 2002
A nonlinear dynamical model of vibration drilling is presented. It takes in consideration cutting interruption through surface generation equations. The linear stability analysis yields stability charts and the nature of Hopf bifurcation is discussed at critical values of cutting parameters. Dimensionless equations have been employed in order to obtain graphical charts that completely describe the dynamics of a pair of vibrationdrilling headworkpiece material. The analysis of "finite amplitude instability" phenomenon is carried out in time domain by computer simulations. A dynamic cutting fixture was used to run vibration drilling experiments. Based upon simulations and general vibration cutting model described here, the dispersion of the results from experimental work was explained. Important conclusions are drawn concerning forthcoming experiments in vibration drilling.
Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling
Journal of Manufacturing Science and Engineering, 2002
Large-amplitude vibrations in drilling often occur at frequencies near multiples of the rotation frequency, even when these are much lower than the system’s first natural frequency. These vibrations are responsible for out-of-round, “lobed” holes. A simplified model of the mechanics of this phenomenon is presented in this paper. The model includes cutting and “rubbing” forces on the drill, but inertia and damping of the tool are neglected at low speeds. This quasi-static model remains dynamic because of the regenerative nature of cutting; the force on each cutting element depends on both the tool’s current position and its position at the time of the previous tooth passage. Characteristic solutions, including unstable retrograde “whirling” modes, are found in terms of eigenvalues and eigenvectors of a discrete state-transition matrix. These unstable modes correspond closely to behavior observed in drilling tests.
Modeling of chatter vibrations in gun drilling process
Vibroengineering PROCEDIA, 2021
The dynamics of the gun drilling process is analyzed in this paper. The tool shank is modeled as long straight beam vibrating in transverse direction under action of cutting forces. Axial force component is expressed as proportional to cutting thickness, which is determined as nonlinear function of beam transverse deflection with time delay. Nonlinear equations of motion of the drilling shank are derived. The stability diagram of the system dynamics was determined. The bifurcation analysis of nonlinear differential delay equations by means of multiple scale method was performed. The obtained results were verified by numerical integration of nonlinear equations. The influence of cutting conditions on system stability and chatter amplitude was observed.
Mathematical Approach for Drilling
International Journal of Automotive and Mechanical Engineering, 2011
The present paper is on the study of whirling dynamics of the tool workpiece system in a deep hole machining process. An innovative analytical model is proposed in order to carry out simulation studies on the whirling vibrations of the tool workpiece system in a deep hole boring process. At the interaction point of the boring bar-workpiece system there will be an additional displacement in addition to the torque transmitted. This displacement is of a dynamic origin and could be simulated as a wedge introduced between the cutting head-workpiece assemblies. An assumed mode method with the Lagrangian equations was used to derive the mathematical model of the system.
Effects of Drill Vibrations on Cutting Forces and Torque
CIRP Annals-Manufacturing …, 1994
Drill bit vibrations can have an adverse affect on drilling performance resulting in lobed holes, burr formation and tool breakage. An analytical model for predicting torque, thrust and radial forces in drilling has been developed. The model includes the effects of the drill bit transverse deflections which lead to variations from the mean values in the cutting forces. Simulations for a drill, exhibiting increasing elliptical translational motion due to drill vibrations, indicate a significant increase in the ranges of the torque and thrust while maintaining essentially constant mean values. The same qualitative trends are also observed experimentally. The model, when drill vibrations are negligible, reduces to previous models for predicting the mean torque and thrust in drilling. The mean drilling torque and thrust values predicted are in good agreement with experimental data and with previously published models.
Qualitative properties of a model of coupled drilling oscillations
2018 22nd International Conference on System Theory, Control and Computing (ICSTCC), 2018
The model of the axial and torsional vibrations for a drillstring with distributed parameters is obtained using the variational approach within the Hamiltonian Mechanics. Further there is considered the model of the axial vibrations which is a linear system with control and perturbation input signals. To the aforementioned equations of the model a system of equations with deviated argument is associated by integration along the characteristics. The system with deviated argument is of neutral type and allows construction of the basic theory but has its difference operator marginally (critically, not strongly) stable. This aspect is discussed finally and suggests the use of the methodology of the singular perturbations.
Journal of Vibroengineering, 2015
Chip segmentation is one of the major factors of process quality assurance while deep hole drilling. The reliable chip segmentation can be obtained if a special self-vibratory drilling head is applied. The required self-excited vibrations are maintained due to the regenerative cutting mechanism and the embedded special elastic element which provides sufficient axial flexibility. The algorithm of adaptive control with vibration velocity feedback is proposed for a self-excited vibrations maintenance. The feedback gain is adjusted by cutting continuity index in order to provide the required cutting conditions. The mathematical model of vibratory drilling process dynamics with control is presented in the paper. The results of a multi-variant simulation are also presented and analyzed.