Model Of Regenerative Chatter Research Articles

Finite-amplitude stability in regenerative chatter: The effect of process damping nonlinearity and intermittent cutting in turning

The damping forces generated at the tool and workpiece interface, known as process damping, greatly influence the dynamics of regenerative chatter in machining. In addition to the increased stability against chatter at low cutting speeds, which is the well-known effect of process damping, post-chatter dynamics are also affected significantly by process damping nonlinearity, which is the less-studied effect of this phenomenon. Once the process vibrations become unstable after chatter occurrence, the process becomes intermittent in the sense that the tool loses contact with the workpiece and they are no longer in continuous engagement due to large-amplitude chatter vibrations. When vibration amplitudes are relatively large, process damping nonlinearity is shown to create stable limit cycles around which vibrations stabilize at a finite-amplitude. The relationship between the amplitude of the resulting limit cycles and the applied machining parameters is only known approximately from simplified models. Besides, the bifurcation of the resulting limit cycles by machining parameters such as cutting depth and spindle speed has not been studied. In this work, we use numerical continuation to develop the bifurcation diagrams of an SDOF model of regenerative chatter that includes process damping nonlinearity and non-smooth dynamics due to the disengagement of the tool and workpiece in post-chatter large-amplitude oscillations. The developed bifurcation diagrams accurately determine the relationship between the applied machining parameters and the amplitude of the resulting limit cycles. They also show that the stable limit cycles lose their stability by a subcritical non-smooth fold bifurcation when the amplitude is large enough to cause tool-workpiece disengagement. We also show that the static forces in the process, which are normally neglected in existing studies, become dynamic due to the intermittent tool-workpiece disengagement and alter the nature of limit cycle bifurcations. The findings of this study are validated numerically and by comparison to experimental results.

A regenerative chatter observer analysis for micro-milling

The regenerative chatter in micro-milling that is employed to produce small products with complex 3D geometries and high precision is gradually getting attention from researchers in the field of manufacturing, mechatronics and control for its severe damage to the cutting tool and micro-milling stability. To facilitate developing observer-based control strategy for suppressing the regenerative chatter, the integrating an adopted observer proposed for nonlinear systems with time delay and a practical regenerative chatter model for micro-milling is presented in this paper. And the observer analysis is shown. Simulation results are given to validate the integration scheme.

An approach for optimization of turning parameters considering uncertainty parameters

Regenerative chatter in turning can cause serious tool wear or breakage, along with poor surface finish on the machined workpiece. Consequently, it is critical to avoid the occurrence of chatter in turning process. In this paper, dynamic model of regenerative chatter in turning process is established to predict the limited cutting width and derive the stability lobe diagram. This study addresses the influences of uncertain factors on the turning process, and a reliability based optimization model is established to obtain optimal turning parameters. In the optimization model, the maximum material removal rate is taken as the objective function and the reliability of turning stability, surface precision, and cutting power is defined as the constraint function. The sequential optimization and reliability assessment (SORA) is utilized to solve the optimization model. Finally, a discussion of the practical application of this method is presented.

Reliability of chatter stability in CNC turning process by Monte Carlo simulation method

In turning process, regenerative chatter stability is regarded as an outcome favor in achieving reliable cutting performance. Since nowadays there is great demand in producing very high quality parts, researchers devoted great efforts in developing theoretical and analytical means for understanding, analyzing and solving the stability of a given machining process. In general, the stability of turning process could be influenced by random variables such as machine stiffness, damping and cutting force. Therefore, in this paper, a new method for predicting the reliability of regenerative chatter stability in turning process is proposed. This involves application of Monte Carlo simulation (MCS) tool to study the statistical distribution of regenerative chatter stability during turning process. The employed dynamic model of the regenerative chatter was defined, and the relationship between cutting depth and spindle speed was obtained by Laplace transformation. The sampling distribution information of kinetic parameters of the cutting system was evaluated for the regenerative chatter model. Thus, the limit cutting width of the samples was obtained. The statistical characteristics probability showed that the actual cutting width is less than the limit cutting width. Therefore, the regenerative chatter stability prediction by Monte Carlo simulation was regarded as a criterion.

Breakthrough of regenerative chatter modeling in milling by including unexpected effects arising from tooling system deflection

Self-excited anomalous vibrations called chatter affected milling operations since the beginning of the industrial era. Chatter is responsible for bad surface quality of the machined part and it may severely damage machining system elements. Although the significant advances of recent years, state of the art dynamic models are not yet able to completely explain chatter onset even when some conventional cutting tools are applied for conventional milling operations. In this work, a more general model of regenerative chatter is presented. The model takes into account some additional degrees of freedom and cutting forces which are neglected in the classical approach. By so doing, a more accurate representation of milling dynamics is obtained, especially when considering large diameter cutters. An improved mathematical formulation of regenerative cutting forces is provided with respect to a very recent publication where the new model has been first outlined. This approach allows −45 % of computation time. Moreover, here a new, independent, and stronger experimental validation is provided, where the new model successfully predicts an increase of about +(50 ÷ 100) % of the stability boundaries with respect to the classical prediction, thus showing the potential breakthrough of the new approach.

An accurate regenerative chatter model in the ball-end milling process that considers high feed rate and shallow axial immersion conditions

ABSTRACTThis paper proposes an accurate model of a ball-end milling process that considers high feed rate and shallow axial immersion conditions with multiple varying time delays (VTDs) to determine the stability of the system. The criteria that the time delay must satisfy are derived. The effect of the feed motion on the entry and exit cutting angles is discussed herein for the first time to the authors’ knowledge in the ball-end milling process. The system dynamics are described by a set of delay differential equations (DDEs) with periodic coefficients and multiple VTDs. In this paper, an improved semi-discretization method (ISDM) is also proposed to determine the stability of the VTD system, which greatly extends the computational efficiency. Then, a discrete dynamical map is deduced to establish the state transition matrix over one time period to predict the stability via the Floquet theory. The improvement of the proposed ISDM is validated by comparing the results with those in other studies.

Probabilistic analysis of chatter stability in turning

In practical engineering, randomness of the parameters (mass, stiffness, and cutting coefficients) significantly impacts the stability of turning processes. In this study, the method involving the probabilistic analysis of the regenerative chatter stability in turning is comprehensively investigated. Considering the influences of random factors, the probability characteristic of the regenerative chatter stability in turning is studied using the Monte Carlo simulation (MCS) method and advanced first order second moment (FOSM) method. Dynamic model of regenerative chatter in turning is obtained, and the relationship between the limiting width of cut for stable machining and the rotation speed of the spindle is acquired based on the Laplace transform. The MCS and advanced FOSM methods for predicting the reliability of the stability in turning are proposed by identifying whether the actual cutting width is less than the limiting width of cut. Finally, practical applications and a detailed analysis to evaluate the accuracy of the proposed methods are discussed.

Stability analysis for the crankshaft grinding machine subjected to a variable-position worktable

This paper serves to evaluate the dynamic performance and the cutting stability of the crankshaft grinding machine. The governing equations for the 7 degrees of freedom (DOF) lumped-mass model are formulated by the Lagrange energy method. The absolute value of the maximum negative real part of the overall dynamic compliance (MNRPODC) and the limiting chip width are the main performance indicators used to explore the structure's dynamic characteristics and the cutting stability of the grinding machine in various worktable positions. The effect on system performance of the distance between the mass center of the workpiece and the worktable module in the z direction is also analyzed. Based on the stability theory for regenerative chatter model, a computer program has been developed that utilizes the three-dimensional stability lobe diagrams of the multi-DOF system to automatically identify the stable and chatter zones. Time domain simulation of the cutting conditions is used to verify the stability lobe diagrams. Finally, an optimization analysis utilizing the particle swarm optimization method is carried out to obtain the optimal design variables. The results, in terms of |MNRPODC| or the limiting critical chip width, show improvements by a factor of 6.5 and are superior to that of the prototype machine.

Dynamics and stability analysis of the simplified model for the surface grinder in various worktable positions

This study proposes a procedure to evaluate the dynamic performance and the cutting stability of a surface grinder. The governing equations for the 3 degrees of freedom (DOF) lumped-mass model are formulated by the Lagrange energy method. The absolute value of the maximum negative real part of the overall dynamic compliance and the limiting critical chip are the main performance indicators used to assess the machine tool structure’s dynamic characteristics and the cutting stability in various worktable positions. The major factors influencing the system performance is obtained by sensitivity analysis. A computer program which is based on the stability theory of the regenerative chatter model for producing a three-dimensional stability lobe diagram of the multi-DOF system has been developed. The developed program can identify the stable or chatter region defined by the lobe curves. A randomly selected point in the stable or chatter region can also be verified by time domain analysis. The procedure proposed in this study can be applied to analyse dynamic performance for other machine tools.

Study of tool dynamics with a discrete model of workpiece in orthogonal turning

This paper proposes a realistic analytical stability model of regenerative chatter in orthogonal turning operation. Tool geometry is initially developed as a solid model and analysed at different tool overhang conditions. In each case, stiffness, fundamental bending mode and corresponding damping ratios of the tool are evaluated. With this data, cutting tool can be represented with a lumped parameter single-degree of freedom vibration oscillator. Workpiece dynamics on the other hand is considered independently using a discrete finite element beam model. At some contact node of the workpiece, tool mass imposes a regenerative cutting force and second order dynamic delay differential equations are formulated in terms of tool and modal parameters. Stability criterion is formulated from characteristic equation. The effects of tool-overhang and work cross-section on the stability from the proposed model are reported. Results are illustrated with a commonly used HSS cutting tool with tailstock-supported workpiece. Experimental analysis is carried out to show the effect of tool-overhang on cutting dynamics.

Determination of the Anti-Chatter Weak Component on a Machine Tool

The processing stability of machine tool system is studied in this work. In terms of the mass distribution and the need of sufficient energy to keep chatter, it is most possible that the chatter will occur on the final executive component of a machine tool. Based on it, the machine system may be simplified as a regenerative chatter model with double elastic bodies. This new model can adapt to improvement of component structure well. When there is a big difference between the receptances of two elastic bodies, the one with bigger receptance should become the active body of chatter, namely it is the weak one of the system. When the receptances of two elastic bodies are close, then the structure of two bodies should be optimized.

Dynamic analysis of a turning tool with a discrete model of the workpiece

The present paper proposes an analytical stability model of regenerative chatter in orthogonal turning operations. Tool geometry is initially developed as a solid model and analysed at different tool overhang conditions. In each case, stiffness, fundamental bending mode, and corresponding damping ratios of the tool are evaluated. With these data, the cutting tool can be represented with a lumped-parameter, single-degree-of-freedom vibration oscillator. Workpiece dynamics, on the other hand, is considered independently using a discrete finite element beam model. At some contact node of the workpiece, tool mass imposes a regenerative cutting force and second-order dynamic delay differential equations are formulated in terms of tool and modal parameters. The stability criterion is formulated from a characteristic equation. The effects of tool overhang and workpiece cross-section on stability using the proposed model are reported. Experimental analysis is carried out to show the effect of tool overhang on cutting dynamics.

Multiple-scales approximation of a coherence resonance route to chatter

This article considers the effect of random variation in the material parameters of a model of machine tool vibrations - specifically, it examines a model of regenerative chatter

Stability analysis of the rolling process and regenerative chatter on 2030 tandem mills

Chatter in the rolling stack of high-velocity tandem mills and temper mills is a widespread problem and affects the quality of the finished product and the productivity of the rolling mill. One factor that clearly plays an important role in causing mill vibration is the inherent gap between the roll chocks and mill housings. In order to control chatter in cold rolling operations, a much deeper understanding of the basic mechanics of the problem is required. Therefore, this paper proposes a rolled piece vibration model for comprehending instability of the strip due to the variation of the friction coefficient in the roll bite. Subsequently, owing to the time delay effect of the chatter marks between the immediate stands, a regenerative chatter model is developed and stability analysis of the regenerative chatter model due to negative damping is presented. Finally, for a more detailed understanding of the regenerative chatter phenomena, a simulator is developed and industrial investigations are carried out in practice. It follows from the numerical simulations and industrial investigations that regenerative chatter is a more serious vibration phenomenon than simple chatter.

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.