Comparison of Analytical Milling Stability Analyses with Time Domain Simulation (original) (raw)
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Experimental and simulated milling stability tests
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Self-excited vibrations significantly reduce the milling productivity, deteriorate the quality of machined surface and tool life. One of the ways to avoid these vibrations is to modify the cutting parameters based on the stability analysis results. A method of numerical simulation of self-excited vibrations in the time domain can be used for this purpose. A comparison of numerical simulation results with those from experiments conducted using a milling machine is presented. The results confirm the correctness of applied modeling.
Influence of Milling Cutter Dynamics on Stability Lobe Diagrams
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In milling, both dimensional accuracy and productivity depend on several parameters of milling. As these parameters influence the material removal rate and the stability of process in terms of vibrations and chatter, it is important to examine the role of these parameters on the level of vibration and chatter. Since 1960s, the researchers have studied chatter problems with a view to understand the mechanism, parameters responsible for this phenomena and its behaviour in milling operation. Out of several methods that can be followed for minimizing and avoiding chatter, stability lobe diagram is considered to be the most reliable way of identifying the cutting parameters for chatter free condition. Since the chatter depends on the interaction of milling cutter with work piece during milling of parts on the milling machine, it is essential to examine the influence of dynamic parameters of milling cutter on the stability of cutting process. This paper covers the generation of stability ...
International Journal of Machine Tools and Manufacture, 2014
Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty's law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial-torsional structural coupling in drilling, and the dynamics of slot milling.
STABILITY LOBE AND CHATTER PREDICTION IN HIGH-SPEED BALL-END MILLING
High-speed machining (HSM) played a successful and significant role in the field of metal cutting as it helped in producing very intricately shaped thin walled and pocketed surfaces at low cost and with higher productivity. Machine tool chatter is a self-excited vibration due to interaction of the structural and process dynamics in a machining process. In the present study an analytical expression for the stability lobes have been developed for a single degree of freedom system using zero order approximation at various rotational speed and depth of cut. Modal parameters like natural frequency, damping ratio and machine stiffness constant have been determined directly from the experimental tests without measuring the transfer function. The predicted stability lobes for the chatter prediction are further compared with the experimental result. Experimental and predicted results are in good agreement. It has been observed that at lower depth of cut of (0.6, 1, 1.4 mm) the cutting process is stable. The process becomes unstable with increase in depth of cut.
Analytical models for high performance milling. Part II: Process dynamics and stability
Chatter is one of the most important limitations on the productivity of milling process. In order to avoid the poor surface quality and potential machine damage due to chatter, the material removal rate is usually reduced. The analysis and modeling of chatter is complicated due to the time varying dynamics of milling chatter which can be avoided without sacrificing the productivity by using analytical methods presented in this paper. r
Analytical expressions for chatter analysis in milling operations with one dominant mode
Journal of Sound and Vibration, 2016
In milling, an accurate prediction of chatter is still one of the most complex problems in the field. The presence of these self-excited vibrations can spoil the surface of the part and can also cause a large reduction in tool life. The stability diagrams provide a practical selection of the optimum cutting conditions determined either by time domain or frequency domain based methods. Applying these methods parametric or parameter traced representations of the linear stability limits can be achieved by solving the corresponding eigenvalue problems. In this work, new analytical formulae are proposed related to the parameter domains of both Hopf and period doubling type stability boundaries emerging in the regenerative mechanical model of time periodical milling processes. These formulae are useful to enrich and speed up the currently used numerical methods. Also, the destabilization mechanism of double period chatter is explained, creating an analogy with the chatter related to the Hopf bifurcation, considering one dominant mode and using concepts established by the Pioneers of chatter research.
Analytical prediction of part dynamics for machining stability analysis
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An analytical procedure is developed to predict workpiece dynamics in a complete machining cycle in order to obtain frequency response functions (FRF), which are needed in chatter stability analyses. For this purpose, a structural modification method that is an efficient tool for updating FRFs is used. The mass removed by machining is considered to be a structural modification in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on different geometries. The predictions are compared and verified by FEA. Predicted FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied. Different cutting strategies are compared for increased chatter-free material removal rates considering part dynamics.
Prediction of stability limit for multi-regenerative chatter in high performance milling
International Journal of Dynamics and Control, 2014
Chatter is one of the most important factors that inhibit the improvement of productivity and deteriorate the machined surface quality in milling process. In order to obtain good surface quality, classical machining process usually has to take conservative milling parameters. Based on the authors' previous work, this paper presented a new thirdorder discretization method to compute the stability lobes considering multi-regenerative chatter effect. A mathematical model, which is suitable for the dynamic system with non-uniform pitch cutter or cutter run-out, is first established for multi-regenerative chatter. Then, three examples are performed to test the validity of the proposed method. The first example is for the case that the system takes a non-uniform pitch cutter. In the second example, after the modal parameters, run-out parameters and cutting force parameters are gained from experiments, the stability lobes are predicted using the proposed method and subsequently testified by a series of experiments. The third example is for the case of existing cutter run-out. The final computation and experiment results indicate the effectiveness and validity of the proposed method. It is applicable in high performance machining for achieving a good parameter combination.
Generalized Model for Dynamics and Stability of Multi-Axis Milling with Complex Tool Geometries
Journal of Materials Processing Technology, 2016
Multi-axis milling offers increased accessibility in milling of parts having geometrical constraints or free form surfaces, where variety of cutting tools and edge geometries are utilized to improve stability and productivity of the processes. In order to machine the desired geometries effectively, in conjunction with multi-axis orientations, special tools ranging from taper end mills to process specific form tools are utilized. For such cases, the cutter workpiece engagement boundaries (CWEB) and directional force vector definitions are very complex and cannot be defined analytically. Furthermore, irregular cutting edge geometries, such as variable helix, pitch and serrations introduce multiple time delays between successive cuts where the conventional analytical frequency domain stability solution cannot be used. Prediction of stability diagrams for such variety of tool forms and edge geometries requires both the process and the tool to be defined in a generalized manner. In this paper, a numerical frequency domain milling stability solution method is proposed. The CWEB for complex multi-axis cases are calculated by the general projective geometry 2 approach, where the cutting tool envelope and the cutting edges are represented as organized point clouds. Zeroth-Order approximation (ZOA) frequency domain method is adapted by introducing a speed average time delay term to encompass regular and irregular tool geometries. The stability limits are predicted by iterative solution of the eigenvalue problem using the ZOA frequency domain with the proposed revision. The effect of the process damping is also introduced into the generalized stability solution in order to predict the increase in the stability limits at low cutting speeds. A previously proposed approach is used to calculate the average process damping coefficients, which are introduced as modifiers to the modal parameters. The proposed generalized methodology is applied on several cases and it is shown that stability limits can be predicted within a reasonable accuracy for wide variety of cutting tools and milling operations.
On stability prediction for milling
International Journal of Machine Tools and Manufacture, 2005
Stability of 2-dof milling is investigated. Stability boundaries are predicted by the zeroth order approximation (ZOA) and the semidiscretization (SD) methods. While similar for high radial immersions, predictions of the two methods grow considerably different as radial immersion is decreased. The most prominent difference is an additional type of instability causing periodic chatter which is predicted only by the SD method. Experiments confirm predictions of the SD method, revealing three principal types of tool motion: periodic chatter-free, quasi-periodic chatter and periodic chatter, as well as some special chatter cases. Tool deflections recorded during each of these motion types are studied in detail.