Chatter Stability Lobes Research Articles

Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency.

Stability Analysis in Milling Based on the Localized Differential Quadrature Method.

Chatter stability analysis is an effective way to optimize the cutting parameters and achieve chatter-free machining. This paper proposes a milling chatter stability analysis method based on the localized differential quadrature method (LDQM), which has the advantages of simple principle, easy application, and high computational efficiency. The milling process, considering the regeneration effect, is modeled using linear periodic delay differential equations (DDE), then the state transition matrix during the adjacent cutting period is constructed based on the LDQM, and finally, the stability of the milling process is obtained based on the Floquet theory. The accuracy and computation efficiency of the proposed method are verified through two benchmark milling models. The simulation results demonstrate that the proposed method in this paper can accurately and quickly obtain the chatter stability lobe diagram (SLD) of the milling process, which will provide guidance for optimizing the process parameters.

Research on the milling stability of thin-walled parts based on the semi-discretization method of improved Runge-Kutta method

Chatter is a very common phenomenon in the milling process. The occurrence of chatter will cause chatter marks on the processed surface, cause the tool to jump, and even bring sharp and harsh noise, making the processed surface unable to meet the accuracy requirements. Thin-walled parts are more prone to chatter due to their lower stiffness. In order to avoid the occurrence of chatter, this paper adopts the method of combining theoretical analysis with milling experiments to conduct in-depth research on the prediction of chatter. Considering the first-order and second-order modal parameters of the tool and thin-walled part as well as the specific processing parameters, based on the milling dynamics model, a semi-discretization method based on the improved Runge-Kutta method (IRKM-SDM) is used to draw the chatter stability lobe diagram. Through simulation and experiments, it is proved that in terms of simulation accuracy and calculation speed, compared with the zero-order analysis (ZOA), multi-frequency solution (MFS), and the traditional semi-discretization method (SDM), the stability lobe diagram obtained by the IRKM-SDM is more advantageous. This study is of great significance for optimizing cutting parameters and suppressing chatter in the actual machining process.

Theoretical and experimental study of the chatter vibration in wet and MQL machining conditions in turning process

Turning is one of the most commonly used cutting processes for manufacturing components in production engineering. The turning process, in some cases, is accompanied by intense relative movements between tool and workpiece, which is called chatter vibrations. Chatter has been identified as a detrimental problem that adversely impacts surface finish, tool life, process productivity, and dimensional accuracy of the machined part. Cooling/Lubrication in the turning process is normally done for some reasons, including friction and force reduction, temperature decrement, and surface finish improvement. Wet cooling is a traditional cooling/lubrication process that has been used in machining since the past. Besides, a variety of new cooling and lubricating approaches have been developed in recent years, such as the minimum quantity lubrication (MQL), cryogenic cooling, nanolubrication, etc., due to ecological issues. Despite the importance of cooling/lubrication in machining, there is a lack of research on chatter stability in the presence of cutting fluid in cutting processes. In this study, the chatter vibration in turning process for two cooling/lubrication conditions of conventional wet and MQL is investigated. An integrated theoretical model is used to predict both the metal cutting force and the chatter stability lobe diagram (SLD) in turning process. This model involves deriving a math equation for predicting metal cutting force for both wet and MQL conditions using experimental training force data and a Genetic Expression Programming (GEP)-based regression model. Also, the traditional single degree of freedom chatter model is used here for predicting the SLDs. The chatter model is discussed and verified with experimental tests. Then, the experimental results of the tool's acceleration signal, work surface texture, surface roughness, chip shape, and tool wear are presented and compared for wet and MQL conditions. The results of this study show that the cooling/lubrication systems such as wet or MQL have a considerable effect on the SLDs. Also, the predicted results of metal cutting force and SLD for both wet and MQL techniques are in good agreement with the experimental data. Therefore, it is recommended that for each lubrication condition including wet, or MQL, the SLD be determined to achieve higher machinability.

Three degrees of freedom chatter stability prediction in the milling process

Chatter in the cutting process has a great influence on workpiece surface quality, machining efficiency, and service life of the machine tool. This work presents three degrees of freedom (DOF) dynamic model applied to tool chatter for thin-walled structures in milling. Combined with dynamic cutting force modelling in the radial, axial and tangential directions, the stability chart was solved by adopting an improved semi-discretization method in time domain. And the stability prediction model considering regenerative effect was validated by cutting tests with specific axial depth of cut and spindle speed. The cutting experimental results performed at different axial depth of cuts were in accordance with predicted stability lobe diagram (SLD). Moreover, the effects of cutting contact angle and radial immersion ratio on SLD were also analyzed. The study results show that the dynamic model could make a good prediction of chatter stability, and the established approach is high efficient in predicting the chatter stability lobe considering the actual situation.

Effect of controllable magnetic field-induced MRF solidification on chatter suppression of thin-walled parts

Aiming at solving the chattering problem of thin-walled parts, magnetorheological fluid (MRF) was used as phase-change clamping material to study the influence of MRF excitation clamping on the modal parameters of thin-walled parts. In this paper, to clamp the cantilever thin-walled parts firmly and stably, a strong and uniform magnetic field was achieved by designing a yoke-type configuration first. Next, to quantify the clamping effect of MRF, its squeeze stress-strain curves were tested and corresponding elastic squeeze parameters in pre-yield stage were applied on the on thin-walled parts. Then, the influence of MRF clamping on the workpiece mode was researched from simulating results and experimental results. After that, to validate the clamping effect of MRF fixture, reasonable cutting parameters on the thin-walled part were chosen according to the milling chatter stability lobes. By comparing surface roughness, surface topography, and chip type, the clamping effect of MRF fixture is validated. The results indicate that MRF flexible fixture can obviously restrain the machining vibration in milling process and contribute to suppress the machining vibration of thin-walled parts.

Investigation of chatter stability of cutting process with a rotating tapered cutter bar considering internal and external damping

The damping of cutting system is an important factor influencing stability in boring and milling process. However, systematical and thorough studies of the influencing mechanism of damping, especially on the chatter stability of rotating cutter bar, are still absent. The damping of a cutting system mainly consists of external damping and internal damping. This study focuses on these damping effects on chatter stability of the cutting system with a rotating tapered cutter bar. The partial differential equation of motion of the cutter bar is derived based on the Hamilton principle combined with the Euler-Bernoulli beam theory. It is assumed that the cutter bar is tapered, and its free ends acts on a two-dimensional regenerative cutting force with time-delay effect. The damping mechanisms of external and internal are described by the viscous damping model and the strain-rate-dependent Kelvin-Voigt model, respectively. The partial differential equation of motion is discretized as an ordinary differential equation using the Galerkin method. The Campbell diagram and the decay rate plots including critical rotating speed and instability threshold of the cutter bar are obtained by free vibration analysis. Also, the chatter stability lobes in the cutting process are plotted and the predicted results of stability in frequency domain are compared with those in time domain. The results indicate that the structural parameters of a cutter bar, including the rotation, the ratio of internal and total damping, damping ratio, and taper and aspect ratios have significant effects on cutter bar dynamics and chatter stability of cutting process. In particular, a new chatter instability is observed for the cutting system in higher rotating speed ranges due to the effects of rotation and internal damping. The onset rotating speed of the new chatter instability equals to the instability threshold of rotor system of cutter bar. Finally, the present model is validated by comparing both stability prediction given by previous study and natural frequencies and decay rates by ANSYS FE code.

Mechanics and dynamics study of helical milling process for nickel-based superalloy

Helical milling is a new high-quality hole-making process which offers many advantages such as better chip transportation and lower cutting forces and cutting temperature than conventional drilling. This paper presents the mechanics and dynamics of helical milling process for nickel-based superalloy. Firstly, according to the kinematics and undeformed chip geometry of helical milling, a cutting force model which considers the variation of the axial depth of cut, the rounded corner effect, and the helix angle of the cutter is established. Next, on the basis of proposed cutting force model, the dynamic cutting forces of helical milling are calculated, and the stability of the operation is simulated with full-discretization method. Finally the cutting force and chatter stability models are validated by verification tests on a nickel-based superalloy GH4169 workpiece. The results show that the simulated cutting forces and chatter stability lobes agree with the measured data well and it is feasible to replace the conventional drilling with helical milling when machining the nickel-based superalloy.

Characteristics of Chatter Stability Lobe in 2-DOF Machining System

A chatter lobe analysis is frequently used to look at the chatter state [1-4]. Even if there is a lot of research on chatter, chatter lobe characteristics are not well defined. In this study, the chatter lobe behavior according to several variables of vibration mode is verified for further clarity. The dynamic variables of the chatter model are defined and their behaviors on chatter lobe boundary are analyzed in detail. In this sense, the chatter model with 2-DOF (2-DOF) was used to analyze chatter stability characteristics [4]. The discussed results are satisfying and these can be used for the prediction of chatter existence in machining processes of 2-DOF systems in several revolution range. These analyses indicate a better agreement for predicting an appropriate stability lobe over a wide detailed range of critical depths of cut in machining operation. The results allow an excellent prediction of chatter according to various static and dynamic variables in machining states. The behavior of chatter dynamic variables in machining were also discussed in detail. All these results can also be applied to other machining processes by establishing a chatter model in a 2-DOF system.

Generation of Tool-Life-Prolonging and Chatter-Free Efficient Toolpath for Five-Axis Milling of Freeform Surfaces

Short tool service life is always a major concern when milling hard materials, such as Ni-based superalloy. In the current research of tool life optimization in multi-axis machining of freeform surfaces, the focus is mostly on choosing suitable cutting parameters and better application of coolant. In this paper, aiming at averaging the tool wear on the entire cutting edge and hence prolonging the tool service life, we report a study on how to generate a multilayer toolpath with a varying tool lead angle for multi-axis milling of an arbitrary freeform surface from an initial raw stock. The generated toolpath is guaranteed to be free of chatter, which is well known for its detrimental effect on the cutting edge. In this study, we first experimentally construct the chatter stability lobe diagram, which reveals the relationship between the lead angle and the cutting depth. With the chatter stability lobe diagram as the major constraint, we then generate the machining toolpath by selecting a proper pair of the best lead angle and cutting depth along the toolpath. While the proposed algorithm currently is restricted to the iso-planar type of toolpath, it can be adapted to other types of milling. The physical cutting experiments performed by us have convincingly confirmed the advantage of the proposed machining strategy as compared to the conventional constant lead angle and constant cutting depth strategy—in our tests the maximum wear on the cutting edge is reduced by as much as 39%.

Trochoidal milling: investigation of dynamic stability and time domain simulation in an alternative path planning strategy

Trochoidal milling is an alternative path planning strategy with the potential of increasing material removal rate per unit of tool wear and therefore productivity cost while reducing cutting energy and improving tool performance. These characteristics in addition to low radial immersion of the tool make trochoidal milling a desirable tool path in machining difficult-to-cut alloys such as nickel-based superalloys. The objective of this work is to study the dynamic stability of trochoidal milling and investigate the interaction of tool path parameters with stability behavior when machining IN718 superalloy. While there exist a few published works on dynamics of circular milling (an approximated tool path for trochoidal milling), this work addresses the dynamics of the actual trochoidal tool path. First, the chip geometry quantification strategy is explained, then the chatter characteristic equation in trochoidal milling is formulated, and chatter stability lobes are generated. It is shown that unlike a conventional end-milling operation where the geometry of chips remains constant during the cut (resulting in a single chatter diagram representing the stability region), trochoidal milling chatter diagrams evolve in time with the change in geometry (plus cutter entering and exiting angles) of each chip. The limit of the critical depth of cut is compared with conventional end milling and shown that the depth of cut can be increased up to ten times while preserving stability. Finally, the displacement response of the cutting tool is simulated in the time domain for stable and unstable cutting regions; numerical simulation and theoretical results are compared.

An improved stability lobe and turning chatter characteristic investigation

A quick chatter identification method using continuous variable speed programing was proposed to solve radial turning chatter. A width-distance lobe (b-d lobe) was presented to improve width-speed lobe (b-n lobe) for turning chatter prediction. The turning dynamic model for chatter prediction considering modal parameters of tool system and workpiece system, tool angles and modal angles was established. And the model verification was carried out by the combination of improved chatter lobe with surface contour, which showed that the improved chatter stability lobe can well corresponds to the machined surface. On this basis, the mechanism of surface formation of turning chatter were analyzed. In addition, the advantages of the improved b-d lobe were discussed compared with the previous b-n lobe no matter in workload, difficulty, skill requirements and time consumption. And, the method was verified useful by an application example of brake disc processing in automotive industry. Another finding is the chatter direction of the radial turning which is expressed by mathematical models of chatter angles.

Dystamill: a framework dedicated to the dynamic simulation of milling operations for stability assessment

Dystamill is an open-source framework, available for free on the Internet, that allows its user to perform milling simulations from a model of the machine tool dynamics, a description of the cutting tool, a representation of the workpiece and a cutting force model. First developed as a program to study the stability of milling operations, the C++ code was ported into a library so that it can now be coupled with a multi-physics engine or used standalone. Restricted to 2D $\frac {1}{2}$ cases, achievable cutting operations include contouring, slotting and face or pocket milling since the tool only moves in a plane perpendicular to its revolution axis. Dystamill permits computing the machining forces applied on the tool and generating the geometry of the machined workpiece. Achieving dynamic simulations in a row for various cutting conditions enables determining the chatter stability lobes needed to choose optimal cutting parameters. The C++ library is composed of 12 modules interacting with each other to model the milling studied case, involving namely a modelling of the tool and the machined surface, a cutting force model and a representation of the system dynamics through a modal model. It is completed with a GUI that generates an input file for Dystamill while the post process of the results can be carried out by Matlab™. Born from a Ph.D. thesis, Dystamill was tested and validated on numerous test cases from the literature and real experiments. This paper is an opportunity to shed light on the functions and algorithms of Dystamill. In the hope that it will be useful for users, this document presents the Dystamill library, namely its modules are described from a technical point of view. An early example is built up and validated through real measurements. Finally, the capabilities of Dystamill are illustrated by comprehensive examples leading to the chatter stability lobes.

An efficient experimental approach to identify tool point FRF by improved receptance coupling technique

Chatter can be predicted and avoided through the chatter stability lobe, which is computed by dynamic response (frequency response function) at the tool point. Modal impact testing is time-consuming and inefficient, which is not suitable for tool point dynamic prediction. On the contrary, receptance coupling method can efficiently identify the tool point dynamic by combining the full (translational and rotational) receptance matrix of spindle-holder assembly with numerical or analytical model of any attached free-free tool. Generally, it is difficult to directly obtain the rotational receptances of spindle-holder assembly. This paper proposes an efficient experimental method which deduces the rotational receptances from translational receptances on a single experimental setup by improved receptance coupling technique. One main advantage of this method is to further reduce required impact tests and increase efficiency of tool point dynamic prediction. Besides, a wider application of the proposed method can be achieved. The presented approach is experimentally verified and compared with the state-of-the-art methods.

Stability of milling with non-uniform pitch and variable helix Tools

We study mechanical vibrations in milling with non-uniform pitch and variable helix tools. The process is modeled by a periodic delay differential equation with distributed delay, which takes into account, for example, the nonlinear cutting force behavior, the effect of runout, and the exact delay distribution due to the unequally spaced flutes. We present a new method for the identification of the chatter stability lobes from the linearized system that is based on the multifrequency solution. We give detailed remarks on the truncation of the resulting infinite dimensional matrices and the efficient numerical implementation of the method. Cutting tests for steel milling with a customary end mill with non-uniform pitch and variable helix angle and a conventional end mill with uniform pitch and constant helix angle are performed. The numerical and experimental results coincide well. They reveal a significant increase of the limiting depth of cut for the variable helix tool compared to the conventional tool. Moreover, we show that in contrast to conventional tools, for non-uniform pitch and variable helix tools, an exact model with time-varying coefficients, nonlinear cutting force behavior, and runout is necessary for an accurate prediction of the stability lobes.

Effect of the cutter path and the workpiece clamping position on the stability of the robotic milling system

The milling robots have many advantages compared with the traditional numerical control machine, but the chatter phenomenon in the robotic milling obstructs its popularization. Therefore, the chatter problem in the planar milling by robot is discussed in the way of cutter path and clamping position to give directions for chatter suppression and quality improvement. Firstly, the dynamic behaviour of the robotic milling system is studied by the models of the chatter stability domain analysis, which include robot stiffness model and dynamic milling force model. The mode coupling effect is considered in chatter stability lobe diagram of robotic milling, which is different with the machine tool. Then, the robotic milling experiments are conducted at six different clamping positions relative to robot by two ways of cutter path. Based on the obtained modal parameters under the different milling conditions, the corresponding chatter stability lobe diagrams are plotted. By the comparative analysis about the experiment results, it is found that the surface quality of workpiece with the feed motion of milling tool along the Y-axis direction of robot world coordinate system is better than the X-axis direction and the chatter is more likely to occur in the down milling than in the up milling. Furthermore, a proper workpiece clamping position can availably prevent the chatter in the robotic milling. These conclusions can be references for designing a suitable machining scheme in the robotic milling to ensure the application of robot in the metal cutting.

Effects of curvature characteristics of sculptured surface on chatter stability for die milling

In this paper, a predictive model of milling stability, which considers the surface curvature and the lead angle of the milling cutter, is proposed for milling of the panel die with sculptured surface. Firstly, influences of the radius of curvature and lead angle of milling cutter on uncut chip thickness are analyzed by exploring the curvature characteristics of sculptured surface. Subsequently, influence of the curvature characteristics of sculptured surface on chatter stability lobes in milling process is investigated by utilizing the full-discretization method. This analysis implies that the milling stability decreases with the increase in the radius of the die surface’s curvature; the milling stability decreases with the increase in lead angle. The experimental results demonstrate that the prediction of chatter stability lobes could match well with the measured results on the change trend, where the maximum relative percent error is less than 11.1 % in stable milling. It is further validated that this method can effectively predict the chatter stability lobes of the domain in ball end milling of sculptured surface of die.

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.

Experimental Analysis of Damping Fixture for Thin-Walled Workpiece Milling

Thin-walled workpieces are widely used in the aerospace manufacturing industry in order to reduce the weight of structure and improve working efficiency. However, vibration is easy to occur in machining of thin-walled structures due to its low stiffness. Machining vibration will result in lower machining accuracy as well as machining efficiency. In order to reduce the machining vibrations of thin-wall workpieces, commonly used method is to select proper machining parameters according to the chatter stability lobes, which is generated according to the machining system parameters. However, this method requires exact system parameters to be determined, which are always changing in the machining process. In this paper, a special designed fixture with damping materials for the thin-walled workpiece is presented based on the machining vibration control theory, and analysis of the effect of vibration suppressing is obtained through the contrast of vibration tests of milling the thin-walled workpiece on the damping clamp. The damping material is used to consume vibration energy and provide support for thin-walled structure. Machining test was carried out for thin-walled structure machining to validate the effectiveness of the proposed method.

Chatter stability prediction for CNC machine tool in operating condition through operational modal analysis

The stability of high-speed machining operations is crucial in machining process and presents a key issue for insuring better surface quality, increasing productivity and protecting both machines and safe workpiece. Stability prediction in milling is based on experimental modal analysis by the estimation of frequency response functions using a tap test. One limitation of accurately estimating the stability using such approach is the change in process and the dynamic characteristics of the machine tool under operation. This paper proposes a signal processing procedure applied to vibrations in machining process in order to obtain spindle’s modal variations in operation. The novelty of the proposed approach consists in removing “virtual modes”, caused by harmonic excitations, from the system response before performing operational modal analysis. Thus, the proposed procedure combines two existing techniques that are the Cepstral Editing Procedure and the Least Square Complex Exponential. The importance of the developed methodology is in adjusting the chatter stability criterion for material removal on a dynamic basis. The main work is given as follows: first of all, the Cepstral Editing Procedure (CEP) algorithm is applied on the acceleration signals for removing deterministic vibrations caused by harmonic excitations. The residue signal is the system response to white noise excitation. The frequency response functions (FRF) are then calculated from these signals at different cutting conditions. The outcome is compared to the result of impact test on the spindle under static condition. Similarities in the form of FRFs obtained in static and operational conditions validate the proposed approach while variations of modal properties under different cutting conditions are successfully captured. Secondly, the Least Square Complex Exponential (LSCE) method in operational modal analysis is invoked to find the natural frequencies and damping ratios of the system at different spindle speeds and cutting depths. Then, the dynamic chatter stability lobes diagrams (SLD) are established which account for spindle’s speed-dependent modal variations. A significant change in the stability border is observed which is interesting in machining fields. It will be shown that some depths of cut that are stable with static stability lobes become unstable with dynamic stability lobes and vice versa.