Machining stability in high speed drilling—Part 2: Time domain simulation of a bending–torsional model and experimental validations

In this paper, the torsional limits of stability in drilling are first obtained analytically based on Bayly's work [P.V. Bayly, S.A. Metzler, A.J. Schaut, K.A. Young, Theory of torsional chatter in twist drills: model, stability analysis and composition to test, Journal of Manufacturing Science and Engineering, 123 (2001) 552–561]. Subsequently, a time domain simulation model of chatter in drilling is presented. The novel simulation model, developed in this work, combines the effects of both bending and torsion. The major challenge in this model is the tracking of the instantaneous cutting parameters along the lips while vibrating in both modes. This challenge was met here successfully and the simulation results agreed closely with the analytical solutions. Cutting experiments were also conducted to verify the developed chatter models. Two drills, one “short” and one “long” were used in drilling a large number of holes with different pilot-hole diameters. The agreement between the cutting tests and theoretical predictions was not very close for the “short” drill due to inaccuracies in representing the boundary conditions in the mathematical model. On the other hand, the cuttings tests agreed very closely with the analytical and numerical predictions for the “long” drill.     

Investigating chatter vibration in deep drilling, including process damping and the gyroscopic effect

This paper investigates chatter vibration occurring in drills for deep hole machining. A model is developed that considers process damping occurring due to the interference between the drilling flank surface and the workpiece surface. Furthermore, the gyroscopic effect due to the rotation of the tool is included. Borders of stability, which indicate critical radial widths of cut (RWOC) at each spindle speed, are obtained analytically from the eigenvalues of a frequency domain equation. Results at this stage show good agreement with the experimental data. In addition, a numerical method is used to simulate the tool path at different RWOC and spindle speeds. Numerical simulation agreed with analytical results. The hole form produced by the tool tip is investigated at different speeds and RWOC with respect to borders of stability. These investigations show that spindle speed selection is an important manner in industrial practice. That is, even below borders of stability, where chatter does not occur, spindle speed selection affects roundness, concentricity, and surface roughness of the hole.     

A new analytical–experimental method for the identification of stability lobes in high-speed milling

Increased working speeds and accelerations of high-speed machining produce excitation of oscillations and cause dynamic problems. These problems affect the tool life (tool wear and tool failure), produce shoddy end surface, reduce productivity, produces scrap parts and affect the environment. A chatter’s analytical prediction method was combined with experimental multidegree-of-freedom systems modal analysis to achieve the objective of generating a new method to obtain the stability lobes information. This paper describes the development of this new method which obtains the stability information for some vibration modes that can be used to graph the stability lobes for high-speed milling, and these to help in the selection of parameters for chatter free operations. Some tests were carried out to demonstrate the quality of this method and the accomplishment of the proposed goals.     

Linear analysis of chatter vibration and stability for orthogonal cutting in turning

The productivity of high speed milling operations is limited by the onset of self-excited vibrations known as chatter. Unless avoided, chatter vibrations may cause large dynamic loads damaging the machine spindle, cutting tool, or workpiece and leave behind a poor surface finish. The cutting force magnitude is proportional to the thickness of the chip removed from the workpiece. Many researchers focused on the development of analytical and numerical methods for the prediction of chatter. However, the applicability of these methods in industrial conditions is limited, since they require accurate modelling of machining system dynamics and of cutting forces. In this study, chatter prediction was investigated for orthogonal cutting in turning operations. Therefore, the linear analysis of the single degree of freedom (SDOF) model was performed by applying oriented transfer function (OTF) and \tau decomposition form to Nyquist criteria. Machine chatter frequency predictions obtained from both forms were compared with modal analysis and cutting tests.     

Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty׳s law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial–torsional structural coupling in drilling, and the dynamics of slot milling.     

Stability-based spindle speed control during flexible workpiece high-speed milling

High-speed machining (HSM) is a technology used to increase productivity and reduce production costs. The prediction of stable cutting regions represents an important issue for the machining process, which may otherwise give rise to spindle, cutter and part damage. In this paper, the dynamic interaction of a spindle-tool set and a thin-walled workpiece is analysed by a finite element approach for the purpose of stability prediction.The gyroscopic moment of the spindle rotor and the speed-dependent bearing stiffness are taken into account in the spindle-tool set finite element model and induce speed-dependent dynamic behaviour. A dedicated thin-walled workpiece is designed whose dynamic behaviour interacts with the spindle-tool set. During the machining of this flexible workpiece, chatter vibration occurs at some stages of machining, depending on the cutting conditions and also on the tool position along the machined thin wall.By coupling the dynamic behaviour of the machine and the workpiece, respectively, dependent on the spindle speed and the relative position of both the systems, an accurate stability lobes diagram is elaborated.Finally, the proposed approach indicates that spindle speed regulation is a necessary constraint to guarantee optimum stability during machining of thin-walled structures.     

Finite element analysis of machine and workpiece instability in turning

Chatter is a well-known and self-exited vibration. The stock removal rate is highly affected by this phenomenon. In this paper instability analysis of machining process is presented by dynamic model of turning machine. This model, which consists of machine tool's structure, is provided by finite element method and ANSYS software, so that, the flexibility of machine's structure, workpiece and tool have been considered. The model is evaluated and corrected with experimental results by modal testing on TN40A turning machine in which the natural frequencies and the shape of vibration modes are analyzed. Finally, the stability lobes obtained from this model are plotted and compared with experimental results.     

Modelling machine tool dynamics using a distributed parameter tool–holder joint interface

Increasing productivity in machining process demands high material removal rate in stable cutting conditions and depends strongly on dynamic properties of machine tool structure. Combined analytical–experimental procedures based on receptance coupling substructure analysis (RCSA) are employed to determine the stability of machine operating conditions at different tool configurations. The RCSA employs holder–spindle experimental mobility measurements in conjunction with an analytical model for the tool to predict the dynamics of different sets of tool and holder–spindle combinations without the need for repeated mobility measurements. In this paper an alternative approach using the concept of tool on resilient support is adopted to predict the machine tool dynamics in various tool configurations. In the proposed model the tool, represented by an analytical model, is partly resting on a resilient support provided by the holder–spindle assembly. The support dynamic flexibility is measured by performing vibration tests on the holder–spindle assembly. Tool–holder joint interface characteristics are included in the model by considering a distributed elastic interface layer between the holder–spindle and the tool shank part. The distributed interface layer takes into account the change in normal contact pressure along the joint interface and comparing with the lumped joint model used in RCSA it allows more detailed representation of the joint interface flexibility and damping which have crucial roles in machine dynamics. Experiments are conducted to demonstrate the efficiency of proposed model in prediction of milling operation dynamics and it is shown that the model is capable of accurately predicting the dynamic absorber effect of spindle in a tool tuning practice.     

Generalized modeling of drilling vibrations. Part II: Chatter stability in frequency domain

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.     

Analytical prediction of chatter stability in ball end milling with tool inclination

The paper presents an analytical method to predict chatter stability in ball end milling with tool inclination. The chatter stability limits in ball end milling without the tool inclination have been predicted in the previous study by deriving directional milling force coefficients and then solving a simple quadratic equation. However, the tool is generally inclined and not perpendicular to the cut surface in practice. Therefore, a new method is developed to compute the directional milling force coefficients considering the tool inclination. It is confirmed that the chatter stability predicted by the proposed method agrees well with the experiments.     

Uncharted islands of chatter instability in milling

This paper provides conclusive evidence that isolated islands of chatter vibration can exist in milling processes. Investigations show these islands are induced by the tool helix angle and act to separate regions of period-doubling and quasi-periodic behavior. Modeling efforts develop an analytical force model with three piecewise continuous regions of cutting that describe helix angle tools. Theoretical results examine the asymptotic stability trends for several different radial immersions and helix angles. In addition, new results are shown through the implementation of a temporal finite element analysis approach for delay equations written in the form of a state space model. Predictions are validated by a series of experimental tests that confirm the isolated island phenomenon.     

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.     

Rounding and stability in centreless grinding

The paper presents a method for selecting grinding conditions and assists researchers to understand the complex dynamics of centreless grinding. It overcomes the problem of deriving dynamic stability charts for particular geometries and difficulty of interpreting such charts to adjust work speed to overcome lobing problems. Classic dynamic stability charts cannot assess stability levels in proximity to integer lobes, a particular problem for centreless grinding. The paper overcomes these problems employing a simply calculated new dynamic stability parameter A_dyn. The new parameter A_dyn simplifies the optimisation of grinding variables including set-up geometry and work speed in relation to resonant frequency. It is difficult to interpret relative dynamic stability of centreless grinding by classical methods for different set-ups, work speeds and numbers of lobes. A new method is employed in this paper based on the well-established Nyquist stability criterion. The dynamic stability parameter A_dyn is based on the real part of the characteristic equation. It is easily computed and presented on a single chart for particular work speed, resonant frequency and for a wide range of numbers of lobes. The method clearly shows the effect on rounding strength both for stable and unstable conditions. Most authors computing dynamic stability charts have ignored positive down boundaries and negative up boundaries showing a lack of a comprehensive treatment for a situation that conflicts with recommendations for conventional positive up boundaries. The new method simplifies this problem.Small differences in set-up geometry and work speed selection can be easily assessed. The new method can be used as a diagnostic tool for adjusting grinding conditions to overcome roundness problems. The user is not constrained by a historic set-up range since there are practical situations where other set-ups are preferred such as small tangent angles for large and heavy work-pieces, and even negative tangent angle for some types of centreless machine.Previous research is reviewed to provide an understanding of the need for a new approach to stability. Practical implications are explained for selection of grinding conditions. The method is supported by reference to experimental results.     

Stable islands in the stability chart of milling processes due to unequal tooth pitch

The use of unequal tooth pitch is a known means to influence and to prevent chatter vibrations in milling. While the process dynamics of equally pitched end mills can be modeled by non-autonomous differential equations with a single constant delay, the dynamics of unequally pitched end mills lead to differential equations with multiple constant delays. In this paper the process stability of an unequally pitched end mill is investigated experimentally and theoretically. The numerical approximation of the stability limit relies on two fundamental methods: Ackermann's method to control systems with delay and the method of the piecewise constant subsystems. On the basis of these two methods two ways for the theoretical stability analysis are derived. The first way neglects the time dependency of the system by replacing the time varying system matrices by their means. The second way accounts for the time dependency of the system by combining Ackermann's method to control systems with delay with the method of the piecewise constant subsystems, which results in the semi-discretization method. Besides the exemplary investigation of a specific end mill the two methods are compared for a simple one degree of freedom system for different number of teeth, different alternating and linear tooth pitch variations and different helix angles. It is shown, that unlike equally pitched end mills also at high radial immersions the time dependency of the system leads to significant differences between the stability limits of the unequally pitched end mills, predicted by the two methods. Depending on the time variance of the system and the unequal tooth pitch stable islands can arise, which are largely located within the stable peaks of the stability diagram of the system where the time varying system matrices are replaced by their means. The correctness of the results are backed up for several operating points by time domain simulations, taking into account the trochoidal movement of the cutting edges, the time varying character of the system and teeth jumping out of contact.     

Dynamics of boring processes: Part III-time domain modeling

This article presents a mathematical model and a computational algorithm for the time domain solution of boring process dynamics. The model is developed in a modular form; it includes a workpiece geometry and surface topography module, a kinamatics and tool position module, a dynamic chip load module, a dynamic cutting force prediction module and a structural dynamics module. The time domain model takes cutting process parameters, tool and workpiece geometries and modal parameters of the structure as inputs. It predicts instantanous cutting forces and vibrations along the machining time, and machined workpiece topography as outputs. Some of the simulated and experimental results for various cutting conditions are presented and compared for validation purposes.     

Generalized modeling of drilling vibrations. Part I: Time domain model of drilling kinematics, dynamics and hole formation

This two part paper presents a comprehensive exercise in modeling dynamics, kinematics and stability in drilling operations. While Part II focuses on the chatter stability of drilling in frequency domain, Part I presents a three-dimensional (3D) dynamic model of drilling which considers rigid body motion, and torsional–axial and lateral vibrations in drilling, and resulting hole formation. The model is used to investigate: (a) the mechanism of whirling vibrations, which occur due to lateral drill deflections; (b) lateral chatter vibrations; and (c) combined lateral and torsional–axial vibrations. Mechanistic cutting force models are used to accurately predict lateral forces, torque and thrust as functions of feedrate, radial depth of cut, drill geometry and vibrations. Grinding errors reflected on the drill geometry are considered in the model. A 3D workpiece, consisting of a cylindrical hole wall and a hole bottom surface, is fed to the rotating drill while the structural vibrations are excited by the cutting forces. The mechanism of whirling vibrations is explained, and the hole wall formation during whirling vibrations is investigated by imposing commonly observed whirling motion on the drill. The time domain model is used to predict the cutting forces and frequency content as well as the shape of the hole wall, and how it depends on the amplitude and frequency of the whirling vibration. The model is also used to predict regenerative, lateral chatter vibrations. The influence of pilot hole size, spindle speed and torsional–axial chatter on lateral vibrations is observed from experimental cutting forces, frequency spectra and shows good similarity with simulation results. The effect of the drill–hole surface contact during drilling is discussed by observing the discrepancies between the numerical model of the drilling process and experimental measurements.     

Chatter in machining processes: A review

Chatter is a self-excited vibration that can occur during machining operations and become a common limitation to productivity and part quality. For this reason, it has been a topic of industrial and academic interest in the manufacturing sector for many years. A great deal of research has been carried out since the late 1950s to solve the chatter problem. Researchers have studied how to detect, identify, avoid, prevent, reduce, control, or suppress chatter.This paper reviews the state of research on the chatter problem and classifies the existing methods developed to ensure stable cutting into those that use the lobbing effect, out-of-process or in-process, and those that, passively or actively, modify the system behaviour.     

Time domain simulation of torsional–axial vibrations in drilling

A time domain model of the torsional–axial chatter vibrations in drilling is presented. The model considers the exact kinematics of rigid body, and coupled torsional and axial vibrations of the drill. The tool is modeled as a pretwisted beam that exhibits axial and torsional deflections due to torque and thrust loading. A mechanistic cutting force model is used to accurately predict the cutting torque and thrust as a function of feedrate, radial depth of cut, and drill geometry. The drill rotates and feeds axially into the workpiece while the structural vibrations are excited by the cutting torque and thrust. The location of the drill edge is predicted using the kinematics model, and the generated surface is digitized at discrete time intervals. The distribution of chip thickness, which is affected by both rigid body motion and structural vibrations, is evaluated by subtracting the presently generated surface from the previous one. The model considers nonlinearities in cutting coefficients, tool jumping out of cut and overlapping of multiple regeneration waves. Force, torque, power and dimensional form errors left on the surface are predicted using the dynamic chip thickness obtained from the exact kinematics model. The stability of the drilling process is also evaluated using the time domain simulation model, and compared with extensive experiments. This paper provides details of the mathematical model, experimental verification and simulation capabilities. Although the surface finish from unstable cutting can be predicted realistically, the actual drilling stability cannot be determined without including process damping.     

Analytical Modeling of Chatter Stability in Turning and Boring Operations: A Multi-Dimensional Approach

In this study, an analytical model for the stability of turning and boring processes is proposed. The proposed model is a step ahead from the previous studies as it includes the dynamics of the system in a multi-dimensional form, uses the true process geometry and models the insert nose radius in a precise manner. Simulations are conducted in order to compare the results with the traditional oriented transfer function stability model, and to show the effects of the insert nose radius on the stability limit. It is shown that very high errors in stability, which limit predictions can be caused when the true process geometry is not considered in the calculations. The proposed stability model predictions are compared with experimental results and an acceptable agreement is observed.