Experimental investigation of process damping nonlinearity in machining chatter

Neglecting the damping generated at the tool/workpiece interface, known as process damping, leads to inaccurate prediction of limit of stability at low cutting speed. Linear and nonlinear models have been reported in the literature that account for process damping. Although linear models are easier to implement in predicting stability limits, yet they could lead to misinterpretation of the actual status of the cut. Nonlinear damping models, on the other hand, are difficult to implement for stability estimation analytically, yet they allow predicting “finite amplitude stability” from time domain simulations. This phenomenon of “finite amplitude stability” has been demonstrated in the literature using numerical simulations. The objective of this paper is to investigate that phenomenon experimentally. The presentation in this work is focused on un-interrupted cutting, in particular plunge turning, to avoid unduly complications associated with transient vibration. The experiments confirm that because of the nonlinearity of the process damping, the transition from fully stable to fully unstable cutting occurs gradually over a range of width of cut.     

Identification and modeling of process damping in turning and milling using a new approach

Process damping can be a significant source of increased stability in machining particularly at low cutting speeds. However, it is usually ignored in chatter analysis as there is no model available to estimate process damping coefficients. In this study, a practical identification and modeling method is presented where process damping coefficients are obtained from chatter tests. The method is generalized by determining the indentation force coefficient responsible for the process damping through energy analysis. This coefficient is then used for process damping and the stability limit prediction in different cases, and predictions are verified by time domain simulations and experimental results.     

Prediction of chatter stability for multiple-delay milling system under different cutting force models

This paper systematically studies the stability lobe prediction methods for the milling process with multiple delays, which are often induced by cutter runout. Emphasis is put on how to effectively incorporate the instantaneous cutting force model into the prediction procedure of stability lobes. Two original methods are proposed based on the vibration time history of the cutter motion, which is numerically obtained by time domain simulation. A comparison study is made with the existing method taken from the literature and experimental verifications are also carried out to validate both methods.In this study, two different instantaneous cutting force models together with the constant cutting force model are considered in the calculation of the cutting force coefficients during the simulation. The effects of different cutting force models on stability lobes, their consistencies and limitations are highlighted. At the same time, cutting force coefficients calibrated from three tests with different feeds per tooth are also considered in order to show the influences of cutting force coefficient's accuracy. It is found that both types of cutting force models and the calibration accuracy of the cutting force coefficients have great influences on the reliability of the stability lobes.     

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.     

Modeling the mechanics and dynamics of arbitrary edge drills

This paper presents a new approach for modelling the cutting forces and chatter stability limits in drills with arbitrary lip geometry. The oblique cutting geometry at each point on the drill lip is modelled using parametric curve equations. The cutting force and process damping coefficients at different parts of the drill lip are identified empirically; the cutting force coefficients are identified from non-symmetric drilling tests, and the process damping coefficients are identified from chatter-free orthogonal turning tests. The presented approach provides a practical method for modelling the cutting forces and vibration stability without needing the detailed geometry of drill lips. The accuracy of presented model in predicting lateral and torsional-axial chatter stability limits is verified by conducting drilling tests using drills with various edge geometries.     

Identification of dynamic cutting force coefficients and chatter stability with process damping

This paper presents a cutting force model which has three dynamic cutting force coefficients related to regenerative chip thickness, velocity and acceleration terms, respectively. The dynamic cutting force coefficients are identified from controlled orthogonal cutting tests with a fast tool servo oscillated at the desired frequency to vary the phase between inner and outer modulations. It is shown that the process damping coefficient increases as the tool is worn, which increases the chatter stability limit in cutting. The chatter stability of the dynamic cutting process is solved using Nyquist law, and compared favourably against experimental results at low cutting speeds.     

Flank face texture design to suppress chatter vibration in cutting

Process damping is useful in improving chatter stability in a low cutting speed range. This paper presents a texture design on tool flank faces that can effectively generate process damping. A convex structure on the flank face dampens chatter vibration even at general cutting speeds. An orthogonal cutting simulation utilizing a finite element analysis was conducted to estimate process damping force coefficients that are the functions of cutting and vibration conditions and tool geometry. Sufficient damping effect was predicted using the proposed texture via a chatter stability analysis in frequency domain. Face turning experiments verified the significant chatter suppression effect.     

A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling

The accuracy of cutting force coefficients plays an important role in predicting reliable cutting force, stability lobes as well as surface location error in ball-end milling. In order to avoid chatter risk of the traditional calibration test with an entire-ball-immersed cutting depth, a cylindrical surface milling method is proposed to calibrate the cutting force coefficients with the characteristics of low cutting depth and varying lead angle. A dual-cubic-polynomial function is also presented to describe the non-uniform cutting force coefficients of the ball part cutting edge and the nonlinear chip size effect on cutting force. The variation of the maximum chip thickness versus the lead angle is established with the consideration of cutter runout. According to the dependence of chip thickness on lead angle, a runout identification method is introduced by seeking the critical lead angle at which one of the cutter flutes is just thoroughly out of cut. Then, a lumped equivalent method is adopted for the low cutting depth condition so that the dual-cubic-polynomial model can be calibrated for the chip size effect and the cutting force coefficients respectively. The accuracy of the proposed calibration method has been validated experimentally with a series of milling tests. The stability examinations indicate that the proposed method has an evident chatter-free advantage, compared with that of varying cutting depth method.     

Effects of micro-milling conditions on the cutting forces and process stability

Determining stable cutting conditions for corresponding cutting tools with specific geometries is essential for achieving precision micro-milling with high surface quality. Therefore, this paper investigates the influence of the tool rake angle, tool wear and workpiece preheating on the cutting forces and process stability. An advanced micro-milling cutting force model considering the tool wear is proposed. The micro-milling cutting forces are predicted and compared with experimentally obtained results for two cutting conditions and four edge radii measured at different stages of the tool wear. It is found that the cutting forces increase by increasing the edge radius. It is also observed that the cutting forces are higher at a rake angle of 0° compared with a rake angle of 8°. The increase of the cutting forces is mainly associated with the change of the friction conditions between the tool and workpiece contact. Stability lobes are obtained for different edge radii, rake angles of 0° and 8°, initial workpiece temperature and different measured static run-outs. The predicted stability lobes are compared with the micro-milling force signals transformed into the frequency domain. It is observed that the predicted stability limits result in good correlation with the experimentally obtained chatter free conditions. Also, the stability limits are higher at smaller edge radii, higher preheating workpiece temperature and positive rake angles.     

Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect

Simulation of multi-axis ball-end milling of dies, molds and aerospace parts with free-form surfaces is highly desirable in order to optimize the machining processes in virtual environment ahead of costly trials. This paper presents a mechanics model that predicts the cutting forces in feed (x), normal (y) and axial (z) directions by modeling the chip thickness distribution, and cutting and indentation mechanics. The shearing forces are based on commonly known cutting mechanics models. The indentation of the cutting edge into the work material is modeled analytically by considering elasto-plastic deformation of the work material pressed by a rigid cutting tool edge with a positive or negative rake angle. The distribution of chip thickness and geometry of indentation zone are evaluated by considering five-axis motion of the tool along the toolpath. The proposed model has been experimentally validated in plunge indentation, as well as in three and five-axis ball-end milling of free-form surfaces. The prediction of axial (z) cutting forces is shown to be improved significantly when the proposed indentation model is integrated into the mechanics of ball-end milling.     

A comprehensive chatter prediction model for face turning operation including tool wear effect

This paper presents a three-dimensional mechanistic frequency domain chatter model for face turning processes, that can account for the effects of tool wear including process damping. New formulations are presented to model the variation in process damping forces along nonlinear tool geometries such as the nose radius. The underlying dynamic force model simulates the variation in the chip cross-sectional area by accounting for the displacements in the axial and radial directions. The model can be used to determine stability boundaries under various cutting conditions and different states of flank wear. Experimental results for different amounts of wear are provided as a validation for the model.     

Improvement effects of vibration on cutting force in rotary ultrasonic machining of BK7 glass

Rotary ultrasonic machining (RUM) exhibits a high potential for a significant reduction in the cutting force, which directly associates with tool wear, machining accuracy, machining temperature, and surface integrity. However, the improvement mechanisms of the ultrasonic vibration on the cutting force are still not fully recognized, restricting the currently optimization methods for further reducing the cutting force occurred during the RUM process. In this research, by incorporating the kinematics principles of the abrasive, the evolution features of the material strain rate in the loading phase were first discussed with respect to the indentation mechanics theory. Taking these features into account, the RUM scratching tests were carried out on the polished specimen surfaces under various process parameters to capture the integrated damage patterns evoked in the high strain rate stage. Following, the comparative indentation tests were respectively conducted on the RUM scratches and the gentle polished surfaces. The indentation-induced damage structures and the load–displacement curves were characterized and assessed to investigate the improvement mechanisms of the superimposed ultrasonic on the cutting force in formal RUM process. It was found that superimposing an ultrasonic vibration led to the incipient cracks nucleated in the abrasive loading phase, and their propagations would increase the material removal rate (MMR) obtained in formal RUM process. Furthermore, the incipient cracks provided a shielding effect to the indentation force, which was a dominant factor in diminishing the cutting force of the diamond tool. The nucleation of the incipient cracks resulted in more energy dissipation after the abrasives penetrating into the hard substrate of the material, which would lead to a higher residual stress on final RUM surface. In addition, a failure pattern (plastic deformation or brittle fracture) evolution model involved in abrasive loading phase was developed with respect to the strain rate effects of the material.     

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.     

Effects of cutting conditions on dynamic cutting factor and process damping in milling

This paper investigates how cutting conditions affect dynamic cutting factor and system process damping in a dynamic milling process. By considering variation of edge plowing force, a frequency domain method is presented to identify the dynamic cutting factor through measured vibration in a milling process, and cutting conditions most suitable for the identification experiments are also discussed. A series of experiments are carried out to investigate the effects of cutting conditions on the dynamic cutting factor. This factor is shown to be significantly affected by the cutting speed, but relatively independent of the feed per tooth and the radial depth of cut. An average process damping model is further constructed and shown to be effective in representing the time-varying damping function. The average process damping is shown to increase rapidly at lower cutting speed, but remain constant as the cutting speed beyond a critical value.     

Machining prediction of spindle–self-vibratory drilling head

The drilling of deep holes with small diameters remains an unsatisfactory technology, since its productivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropriate conditions of use. A dynamic high-speed spindle/drilling head/tool system model is elaborated on the basis of rotor dynamics predictions. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. Investigations are focused on the drill's torsional–axial coupling role on instability predictions. A generic accurate drilling force model is developed by taking into account the drill geometry, cutting parameters and effect of torsion on the thrust force. The model-based tool tip FRF is coupled to the proposed drilling force model into an analytical stability approach. The stability lobes are compared to experimentally determined stability boundaries for validation purposes.     

Chatter Stability of Plunge Milling

Plunge milling operations are used to remove excess material in boring cylinders, roughing pockets, dies and mold cavities. This paper presents a frequency domain, chatter stability prediction theory for plunge milling. The regenerative chip thickness is modeled as a function of lateral, axial and torsional vibrations. The stability of the plunge milling is formulated as a fourth order eigenvalue problem by relating the regenerative chip thickness, cutting forces and torque, and the structural modes of the cutter. The stability lobes are predicted analytically from the eigenvalue solution. The stability lobes are experimentally proven by conducting over one hundred plunge milling tests.     

Robust chatter stability in micro-milling operations

Micro-milling utilizes miniature end mills to fabricate complex shapes at high rotational speeds. One of the challenges in micro-machining is regenerative chatter, which results in severe tool wear and reduced part quality. The high rotational speeds of micro-milling cause changes in dynamics; and, the elasto-plastic nature of micro-machining operations results in changes to the cutting coefficients. Variations in dynamics and cutting coefficients affect the stability lobes. The tool tip dynamics can be indirectly obtained through mathematical coupling of substructures using the receptance coupling method. The effect of process damping is also considered. The robust chatter stability theorem, which is based on the edge theorem, is employed to provide the robust stability within the minimum and maximum boundaries of changing parameters.     

Force control grinding of gamma titanium aluminide

This paper addresses the grinding of ordered intermetallic compounds and their brittleness at ambient temperature. The depth of plastic deformation is supposed as the measure of surface integrity. The current paper expands the work of a previously reported indentation model that correlated the depth of plastic deformation and the normal component of the grinding force. This paper studies the indentation model using force control grinding of gamma titanium aluminide (TiAl-γ). Reciprocating surface grinding is carried out for a range of normal force 15–90 N, a cutting depth of 20–40 μm and removal rate of 1–9 mm³/sec using diamond, cubic boron nitride (CBN) and aluminum oxide (Al₂O₃) abrasives. The measured depths of plastic deformation are in the range of 150–300 μm. The deviations from the indentation model are explained by changes in the ductility during the grinding process. Furthermore, a force-based model for specific energy is developed and evaluated. The measured specific energies are in the range of 40 J/mm³ (diamond) to 400 J/mm³ (CBN).     

Novel ancillary device for minimising machining vibrations in thin wall assemblies

Milling thin wall structures is challenging due to their low stiffness and hence consequential vibration problems. Most of the research in this area was focussed on minimising chatter vibrations—either through generation of stability lobes or by employing targeted damping solutions such as piezoelectric damping; such solutions are suitable only for damping resonant vibrations. However, most of the thin wall structures also get poor surface finish due to forced vibrations either at tooth cutting frequency or tool natural frequencies. In this work, relying on the importance of improving mass and stiffness for greater vibration reduction in milling circular thin-wall components, an innovative articulated device pre-tensioned by torsion springs is proposed. The concept is novel in the sense that it is compact and light-weight and can be used on any shape of thin wall structure. Employing such a device does not alter the nature of dynamic characteristic of the structure thus ensuring better control of achieved dimension of structure. Significant (8 times) vibration reduction was observed using proposed device.     

A new method for the identification of stability lobes in machining

This paper introduces a new method for identifying the stability lobes in milling. The method depends on ramping the spindle speed while monitoring the behaviour of a chatter indicator. Based on the pattern of this indicator, the stability lobes are located accurately. The lobes are identified on-line without stopping the machine. It is not necessary to calculate the frequency spectrum of any vibration signal. The method was tested successfully in immersion down-milling and was shown to be applicable to slotting. Experimental results showed that the frequency characteristics of the stability lobes identified using the developed method are the same as those of the lobes established using constant speed cutting.