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.     

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.     

Analytical stability lobes including nonlinear process damping effect on machining chatter

Indentation of the tool edge and flank face into workpiece surface undulations has been recognized in the literature as the main source of process damping. This damping affects the process stability at low cutting speed greatly. Numerical simulations have allowed integrating the nonlinear indentation force into machining chatter models. It is shown in this paper that the indentation force requires very high discretization resolution for accurate numerical simulation. The objective of the current work is to develop the stability lobes analytically taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Plunge turning is utilized in the current work to illustrate the procedure of establishing the lobes analytically. Experimental cutting tests were conducted at three feedrates for sharp and worn tools and the results agreed well with the analytically established lobes.     

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.     

Model-based chatter stability prediction for high-speed spindles

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.     

A study of dynamic stresses in micro-drills under high-speed machining

In this paper, a dynamic model of micro-drill-spindle system is developed using the Timoshenko beam element from the rotor dynamics to study dynamic stresses of micro-drills. The model includes effects of eccentricity of the spindle-clamp-drill system, the axial drilling force, the system rotational inertia, the gyroscopic moment, and bearings of micro-hole drilling machines on bending deformation of micro-drills during machining. After the model is verified using the published work, effects of the clamped length of micro-drills, the bearing stiffness and damping, the spindle speed, the system eccentricity, and the axial drilling force on dynamic stresses of micro-drills are analyzed using the model.     

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.     

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 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.     

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.     

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.     

Dynamics and stability of parallel turning operations

Parallel turning offers increased productivity due to multiple cutting tools in operation. The dynamic interaction between the tools needs to be analyzed as it affects the stability of the process. In this study, dynamics and stability of parallel turning processes are modelled. The results of the developed stability models in frequency and time domains show reasonable agreement. One of the interesting outcomes is that the stability could be increased due to dynamic interaction between the tools creating an absorber effect on each other. The predicted stability limits are compared with experimental results where reasonable agreement is demonstrated.     

Modelling of the stability of variable helix end mills

Chatter in milling is still the main obstacle in achieving high-performance machining operations in industry. In this paper, an analytical model is presented to predict the chatter stability of the variable helix end mills. Owing to the lack of accurate and rapid modelling, variable helix tools are used simply on a trial and error basis, in the hope that they will improve the stability of the process. This work provides a comparative study of the performance of variable helix and variable pitch end mills. Time domain chatter recognition techniques and analytical models are explored and tested against experimental results. For the experimental validation, aluminium test pieces were used to enable a broad range of spindle speeds to be covered. The linearity of the machine tool dynamics is explored through validation of standard stability lobes. A comparison of the predicted and observed performance of variable helix against constant helix, variable pitch end mills are presented.The stability lobes are validated for each of the variable helix, variable pitch and standard tools. The analytical model assumes the variable helix tools to behave as variable pitch tools, calculating the average pitch angle for each flute. This approximation is proven to be accurate for some of the cases. For certain combinations of pitch and helix angle greatly enhanced stability is demonstrated empirically with up to a 20-fold increase in depth of cut for the variable helix over the equivalent variable pitch tool. This enhanced stability is neither predicted by the analytical nor time domain solutions. The time domain chatter recognition criterion is investigated and found to have little influence on the predicted stability plots. It is concluded that the enhanced stability is a result of some mechanism not represented in the well-established time domain model. It is possible that this is a result of the disturbance of regeneration in the manner of an alternating spindle speed or due to a non-linear process damping effect.     

滚珠丝杆进给系统的多自由度柔体建模研究

考虑滚珠丝杠进给系统的机电耦合特性,对系统结构进行分块细化,降低系统的耦合复杂度,提出了丝杠进给系统的分-总式建模方法。将滚珠丝杆系统作多自由度柔体处理,综合考虑系统的弯曲、扭转及沿丝杠轴向的变形,基于动力学理论,采用瞬时变分法,推导出滚珠丝杠进给系统动力学模型,分析得出基于系统结构柔性影响与丝杠轴弯曲剪切综合变形而引起的耦合影响,不同于以往滚珠丝杠进给系统集中质量模型(混合模型)下各向振动之间的耦合影响及振动方程。通过振动实验,借助主分量分析法验证了所建立的动力学模型的正确性,为后续的丝杠进给驱动系统的动力学分析提供研究依据。     

Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process

Chatter is a common vibration problem that limits productivity of machining processes, since its large amplitude vibrations causes poor surface finishing, premature damage and breakage of cutting tools, as well as mechanical system deterioration. This phenomenon is a condition of instability that has been classified as a self-excited vibration problem, which shows a nonlinear behavior characterized by the presence of limit cycles and jump phenomenon. In addition, subcritical Hopf and flip bifurcations are mathematical interpretations for loss of stability. Regeneration theory and linear time delay models are the most widely accepted explanations for the onset of chatter vibrations. On the other hand, models based on nonlinearities from structure and cutting process have been also proposed and studied under nonlinear dynamics and chaos theory. However, on both linear and nonlinear formulations usually the compliance between the workpiece and cutting tool has been ignored. In this work, a multiple degree of freedom model for chatter prediction in turning, based on compliance between the cutting tool and the workpiece, is presented. Hence, a better approach to the physical phenomenon is expected, since the effect of the dynamic characteristics of the cutting tool is also taken into account. In this study, a linear stability analysis of the model in the frequency domain is performed and a method to construct typical stability charts is obtained. The effect of the dynamics of the cutting tool on the stability of the process is analyzed as well.     

Prediction of chatter in high speed milling including gyroscopic effects

Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic effect on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool is presented which uses Timoshenko beam theory to obtain the frequency response of the system when gyroscopic terms are included. Using this response, the stability of a high speed spindle system in the presence of gyroscopic effect is investigated. It is shown that the gyroscopic effects lower the critical depth of cut in high speed milling.     

Predicting the dynamic behaviour of torus milling tools when climb milling using the stability lobes theory

This paper investigates stability and dynamic behaviour of torus tool in climb milling on 5 positioned axes. The stability lobes theory is used to enable stable cutting conditions to be chosen. As the adaptation of such a theory to complex milling configurations is a difficult matter, new methods are presented to identify the dynamic parameters. Tool dynamic characteristics (stiffness and natural pulsation) are determined with an original coupled calculations-tests method. Start and exit angles are computed exactly using an original numerical model. A sensitivity analysis highlights the influence of machining parameters on stability of climb milling. This shows that a third region of “potential instability” must be taken into account in plotting stability lobes, due to the uncertainty of prediction due to modelling and identification of parameters. The results were validated experimentally with an innovative approach, especially through the use of high-speed cameras. Analysis of vibrations and the surface roughness allowed the analytical model to be verified so as to optimise the inclination of the tool on the surface.     

Time domain prediction of milling stability according to cross edge radiuses and flank edge profiles

This article proposes a time domain model for predicting an end milling stability considering process damping caused by a variety of cross edge radiuses and flank profiles. The time domain model of calculating indentation areas, as well as regenerative dynamic uncut chips, is formulated for the prediction of the stabilizing effect induced by interference areas between the edge profiles and undulation left on a workpiece. The interference area generates forces against the vibration motion, which acts as a damping effect. In the model, the present and previous angular position of cross radiuses and flank edge profiles are located to calculate the dynamic uncut chip as well as indentation area based on a time history of the dynamic cutter center position. The phenomenon that chatter is damped according to cross edge radiuses and flank edge profiles is successfully simulated with the proposed dynamic model and validated through the extensive experimental tests.     

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.     

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.