Machine Tool Chatter Research Articles

Dynamic stability of a paralle kinematic machine

Machine tool chatter causes machining instability, surface roughness, and tool wear in metal cutting processes. A stability lobe diagram based on the theory of regenerative vibration is an effective tool to predict and control the chatter. This paper presents the advances in the mechanical design of a parallel kinematic machine tool. The features that make it ideal for machining tasks, and that make unique in its own way, are highlighted. In addition, the description of the progress of this work will be focused on the analysis of the stability limitation for machining systems to derive the stability lobe diagram with modal analysis of the spindle. A vibratory model is developed by adding cutting forces and including analytical equations for the depth of cut and for the cutting speeds, both depending on the frequency of vibration. A step-by-step procedure provides a stability lobe diagram. The results show that it is relatively easy to provide a relationship between depth of cut and spindle speed. In turn, it makes it easy to compare machining processes under different cutting parameters and conditions.

Milling Processes With Active Damping: Modeling and Stability

Abstract Active dampers are on the verge of appearing in commercial machines as devices that assist the avoidance of machine tool chatter. The adjustment of control parameters in these devices is mostly guided by models that do not consider the dynamics within the control loop of active damper. Therefore, these models neglect the dynamics of actuation, measurement, and filtering, which can result in inaccurate stability predictions that hinder the efficient tuning of active dampers. To formulate a more realistic model for milling processes assisted by active damping, this paper derives a novel mathematical model that takes into account the internal dynamics of the actuator, measuring device, and discrete filtering. This study shows that accurate stability prediction requires the incorporation of actuator and filter dynamics into the model, especially at high spindle speeds and large feedback gains.

Chatter in milling with robots with structural nonlinearity

Stiffness and damping nonlinearities are often negligible in machine tool vibrations, but they are shown to be prominent in industrial robots that are used for milling, mainly due to the several nonlinear phenomenon that occur in the robot’s revolute joints. In this paper, a 2DOF nonlinear vibratory model is presented to study regenerative chatter in robotic milling. The presented model includes cubic stiffness and damping terms to account for the robot’s structural nonlinearities. The machining forces are represented by a combination of periodic forces and delayed vibration terms; the former is generated by the feed motion of the tool and the later by chip regeneration. Furthermore, the machining force model is non-smooth due to (a) periodic entrance and exit of the cutting edges to and from the cutting region, and (b) loss-of-contact at high-amplitude oscillations. The dynamics in the presented model is therefore described by a set of nonlinear Delay Differential Equations with periodic coefficients and non-smooth forces. Numerical continuation with smoothing techniques is used to determine the combinations of spindle speed and axial depth of cut at which the forced periodic vibrations go through secondary Hopf or period doubling bifurcations, causing chatter in the milling process. A KUKA robotic arm with milling end-effector is used as a case study. The presented analysis shows that feedrate, which has no effect on chatter in machine tools with linear dynamics, alters the stability of vibrations in milling systems with nonlinear structural dynamics. Nonlinear systems’ stiffness and damping depend on vibration amplitude. Since feedrate directly influences the amplitude of forced vibrations, the nonlinear system’s damping and stiffness and consequently its chatter stability changes by feedrate.

Bi-stability induced by motion limiting constraints on boring bar tuned mass dampers

This paper investigates the effect of displacement constraints on the attenuation performance of tuned mass dampers (TMDs) used in boring and turning applications. A simplified piecewise-smooth mechanical model is investigated through time domain simulations and hybrid periodic orbit continuation, first under harmonic excitation, then under regenerative cutting load. A quasi-frequency response function is derived for impacting TMDs through composition of different families of period-1 orbits, then an acceptability map for turning is formulated based on the appearance of cutting-edge contact-loss and fly-over events. The bi-stable domain boundaries are determined through two parameter continuation of contact-loss grazing events. It is shown that in both cases arising rigid body collisions can significantly hinder TMD damping performance and lead to resonance problems or machine tool chatter.

Online chatter detection in robotic machining based on adaptive variational mode decomposition

Chatter is the main problem that limits the application of industrial robots in the field of machining process. It is critically important to establish an adaptive chatter detection solution for robot machining process and realize the online detection of chatter. However, different from machine tool chatter, the chatter in robotic machining process is more complex to be detected due to the variable stiffness characteristics and weaker stiffness of normal industrial robot, and the existing literature has less research on this problem. This paper presents a comprehensive solution for online chatter detection in robotic machining process. Firstly, in order to detect the chatter in robotic machining process and avoid mode mixing problem in variational mode decomposition (VMD) process, an adaptive variational mode decomposition (AVMD) method based on kurtosis and instantaneous frequency is proposed, which realizes the adaptive selection of the decomposition parameter. Secondly, optimal decomposition parameters are calculated by using genetic algorithm. By optimizing the discrete step length of decomposition parameter, it greatly reduces the optimization time. Last but not least, approximate entropy, energy entropy, and proposed entropy drift coefficient are extracted to distinguish chatter and stable machining state. Simulation and experimental results show that the proposed method can meet the real-time requirements of online detection and detect the occurrence of chatter effectively.

Nonlinear dynamics of delay systems: an overview

Time delays play an important role in many fields such as engineering, physics or biology. Delays occur due to finite velocities of signal propagation or processing delays leading to memory effects and, in general, infinite-dimensional systems. Time delay systems can be described by delay differential equations and often include non-negligible nonlinear effects. This overview article introduces the theme issue 'Nonlinear dynamics of delay systems', which contains new fundamental results in this interdisciplinary field as well as recent developments in applications. Fundamentally, new results were obtained especially for systems with time-varying delay and state-dependent delay and for delay system with noise, which do often appear in real systems in engineering and nature. The applications range from climate modelling over network dynamics and laser systems with feedback to human balancing and machine tool chatter. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Machine Tool Chatter Identification Based on Dynamic Errors of Different Self-Synchronized Chaotic Systems of Various Fractional Orders

Chatter, the vibration between the workpiece and cutting tool, is a common phenomenon during the milling process. Traditionally, the Fourier transform analysis is mainly used to extract the features and determine whether chatter occurs. In this paper, an innovative and practical chatter identification method combining fractional order chaotic system and extension theory is proposed. A lathe spindle with embedded sensors is used in this study. The boundary of chattering state of the lathe spindle is decided by the center of gravity of phase plane of dynamic errors. The boundaries are then fed into extension model and relational function calculation is performed. In this way, chatter identification can be easily achieved based on the position of the chaotic center of gravity. The three chaotic systems, i.e. Lorenz, Chen-Lee, and Sprott, of different fractional orders are used and their results are compared. Compared with the traditional methods, the Fourier transform is time-consuming in terms of mathematical operations and adverse to the establishment of a real-time system. This paper uses the characteristics of the chaotic systems sensitive to input signals in order to more capably detect the boundary state from normal cutting to chattering cutting and more efficiently identify the chatter. The experiment results indicate that the Chen-Lee system (93.5%) exhibits have better chatter diagnosis rate than Lorenz (92.75%) and Sprott (69%) systems. The Chen-Lee system even reaches a diagnosis rate of 100% for orders 0.5 ~ 0.7. Therefore, the method presented in this paper has a very high diagnosis rate and is thus very effective for chatter identification of machine tools.

Frequency domain analysis of regenerative chatter in machine tools with Linear Time Periodic dynamics

Abstract Unstable vibrations (Chatter) during machining operations is caused by the flexibility of various components of the machine tool or the workpiece, which can be stationary and symmetrical or rotating and non-symmetrical. Therefore, the structural dynamics of machining systems are best described by Linear Time Periodic (LTP) systems, but the existing solutions of chatter use Linear Time Invariant (LTI) descriptions of the machine tool dynamics. This paper presents an update to the widely used Multi-Frequency Solution of regenerative chatter by modelling the machine tool dynamics as a LTP system. The stability of the LTP system is then determined by utilizing the concept of Harmonic Transfer Functions (HTF) and Nyquist stability criterion. The presented method provides a unified solution to determine the stability of vibrations in both stationary and rotating coordinate frames, regardless of the stationary or rotating nature of the vibration modes. The accuracy of the presented approach is verified by comparing the predicted stability diagrams with the results of Multi-Frequency Solution, Semi-Discretization Method, and with experimental results.

Machinability Studies on Stainless steel by abrasive water jet -Review

Stainless Steels are alloy steels with high resistance to corrosion and heat, strength, durability, low maintenance, fabrication flexibility and high hardness. Many studies have demonstrated the advantages of using Stainless Steels in the field of automotive and other industrial applications. Stainless steels are generally more challenging to machine due to high alloying content. The major problems with conventional machining of Stainless Steels are high work hardening, poor chip breaking, usage of various tools with different tool geometry, application of huge coolant supply during machining. These problems results in increased production time and cost. While machining Stainless Steels it is important to ensure that there is no machine vibration or tool chatter and conventional tools are prone to edge chipping. Because of these problems other alternate techniques are considered for machining of Stainless Steel. Abrasive Water Jet Machining (AWJM) is an effective method for machining, cutting and drilling of stainless steels. AWJ machining is a non-conventional machining process where material is removed by erosion of high velocity abrasives entrained in water jet. This paper discusses the machining studies on Stainless Steels by Abrasive Water Jet.

On process damping induced by vibration-dependency of cutting direction in milling

The process damping effect is analyzed for regenerative machine tool chatter in milling via a velocity-dependent cutting force model. This model takes into account that the effective cutting direction depends on the vibrations of the machine tool-workpiece system, which modifies the effective rake angle, the chip thickness, and the cutting force. The model was originally introduced for turning operations where it results in a process damping term that improves the stability of metal cutting at low cutting speeds. Now this model is extended to milling. It is shown that the vibration-dependency of the cutting direction induces a time-periodic process damping term that is negative when the radial immersion is low. This decreases the stability at low cutting speeds, thus the low-speed stability improvement phenomenon in low radial immersion milling can be explained by extended process damping models only.

Quantification of uncertainty in machining operations based on probabilistic and robust approaches

Reliable stability predictions of machine tool chatter have high potential in the optimization of machining processes. Industrial applications can benefit from the corresponding stability lobe diagrams, which can guarantee improvement in the performance. However, predictions and experiments often do not match during cutting tests due to uncertain dynamics and operational parameters. In order to provide safe and accurate tools for machining engineers, the importance of reliability of the stability lobe diagrams must be highlighted. There exists several solution to include uncertainty in the model used for stability predictions, such as modal parameter estimations or cutting force characteristics measurements. This paper collects the most well-known techniques that are used for the construction of robust stability lobe diagrams. In order to highlight the potential of such solutions, the results obtained by two different methods are compared to experimental cutting tests.

Prediction of robust stability boundaries for milling operations with extended multi-frequency solution and structured singular values

Reliable prediction of machine tool chatter is an essential problem in efficiency-oriented machine tool centers, since it requires the precise characterization of the dynamics of the machine-tool-workpiece system and the cutting force characteristics. Due to imperfect measurements, noise, uncertain and varying operational conditions, the mathematical models provide a deficient representation of the system. This leads to the need for the adaptation of robust stability analysis methods, which guarantee stability against bounded uncertainties and perturbations. In this paper, a frequency-domain approach is presented to calculate the robust stability boundaries of chatter-free machining parameters for milling operations. The idea is based on the concept of the stability radius and structured singular values, which is combined with the extended multi frequency solution. The proposed method is tested in a real case study.

Robust controller design for turning operations based on measured frequency response functions

One of the most significant limitation of the productivity of machining operations is the regenerative machine tool vibration, also called machine tool chatter, which is a self-excited vibration between the tool and the workpiece induced by the chip formation mechanism. Extension of the chatter-free parameters is possible by active chatter control techniques. The design of the controller requires the identification of the dynamic properties of the system. Uncertainties in the system parameters may result in an inappropriate control performance. Robust control design is therefore a necessary step during the optimization of machining operations. In this paper, a fast and efficient method is presented to determine the region of control gains in the presence of uncertainties in the measured frequency response functions. The method is based on the concept of structured singular values.

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

ABSTRACTIn high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.

Chatter and dynamic cutting force prediction in high-speed ball end milling

ABSTRACTMachine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.

Analysis of rotational speed variations on cutting force coefficients in high-speed ball end milling

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool deflection, tool failure, machine tool chatter and vibration, etc. Thus, an accurate prediction of cutting forces prior to actual machining is very much essential for a good insight into the process to produce good quality machined parts. In ball end milling, the cutting forces are proportional to the chip cross-sectional area and constant of proportionalities are referred as cutting force coefficients and they depend on many factors, like cutter geometry, cutting conditions, tool material and workpiece material properties. However, determining these specific cutting force coefficients in ball end milling process is not at all straightforward; rather it is fairly complex. Machining with higher cutting speed affects the chip formation mechanisms and finally causes a significant change in the cutting force coefficients. In the present study, the effect of rotational speeds has been investigated on the cutting force coefficients. A series of experiments have been performed at higher rotational speed. It has been found that the cutting force coefficients are influenced by rotational speed significantly. The results are also verified using experiments.

Spectral element method for stability analysis of milling processes with discontinuous time-periodicity

This paper presents an application of the spectral element method for the stability analysis of regenerative machine tool chatter models in milling operations. An extension of the spectral element method is introduced in order to handle the discontinuities in the cutting force in an efficient way. The efficiency of the method is demonstrated on some well-known machine tool chatter models taken from the literature. Efficiency is characterized by the computational time, the convergence of the stability boundaries, and the convergence of critical characteristic multipliers. Results show that compared to the most widespread methods in machining literature, the spectral element method provides significant improvements in computational time while maintaining high accuracy levels.

Robust stability analysis of machining operations

Prediction of machine tool chatter requires the characterization of dynamic of the machine-tool-workpiece system by means of frequency response functions (FRFs). Uncertainties of the measured FRFs result in uncertainties of the calculated stability diagrams, therefore robustness of stability prediction against parameter perturbations is of high importance. Although there exist methods to determine robust stability in terms of stability radii, these methods either give a conservative estimate of the real uncertainties or are limited to perturbations of a few modal parameters, only. In this paper, a frequency-domain approach is presented to determine robust stability boundaries using the measured FRFs directly without any modal parameter identification. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is demonstrated in case of a turning operation, where the machine tool structure is characterized by a series of FRF measurements.

Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

Robust Stability of Machining Operations in Case of Uncertain Frequency Response Functions

Prediction of machine tool chatter requires a dynamic characterization of the machine-tool-workpiece system by means of frequency response functions (FRFs). Stability lobe diagrams are sensitive to the uncertainties of the measured FRF, which reduces the reliability of their industrial application. In this paper, a frequency-domain method is presented to determine robust stability boundaries with respect to the uncertainties of the FRF. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is validated on a turning operation characterized by a series of FRF measurements. It is shown that stability analysis using the averaged FRF may considerably overestimate the region of robust stability.