Multi-dimensional chatter stability for enhanced productivity in different parallel turning strategies
Introduction
Chatter may results in jeopardizing enhanced productivity in parallel turning operations [1]. However, parallel machining can be employed as a chatter suppression technique in machining of flexible workpieces [2] and machining with flexible tools [3], [4], [5]. In parallel turning of a flexible workpiece, not only the tools' dynamics and their dynamic interaction but also the dynamics of the workpiece are crucial factors in stability analysis of the process. Consequently, ensuring a chatter-free cutting condition requires an appropriate selection of process parameters and process geometry which is achievable by having a precise and comprehensive insight into the modeling of the process geometry and dynamics.
Even though, the number of publications on the one-dimensional chatter stability analysis is considerably high and go back to almost half a century ago [6], [7], there are few authors who investigated a general model for stability analysis of turning operations. Rao [8] developed an analysis in which the nose radii and cross-coupling effects between radial and axial displacement, in addition to sensitivity of the cutting force coefficients to smaller chip thicknesses has been taken into account. Later, Ozlu and Budak [9] presented an analytical multi-dimensional model to predict the stability limits in turning and boring processes. Their model considers all major parameters of the process geometry such as oblique angle, approach angle and nose radius, and more importantly the dynamic effects of tool and workpiece in different directions. Nonetheless, until recently, dynamics and stability of parallel turning operation has not been investigated extensively. Ozturk and Budak [1] proposed both frequency and time domain models for the stability of an orthogonal multi-delay parallel turning operation. In their model, the tools were coupled through the shared surface while each of the tools was cutting different depth of cuts. Results demonstrate that stability limit could increase according to the dynamic interaction between the tools creating an absorber effect. Brecher [10] investigated the parallel turning operation in which cutters removed the same depth of cut from the workpiece considering various dynamic coupling of the tools through the machine structure. Frequency and time domain approaches supported that the radial angle between the tools has remarkable effects on shifting the stable depth of cut for the dynamically coupled tools [10]. Ozturk [3] for the first time emphasized the prominent influence of natural frequency ratio of the tools in chatter stability of parallel turning operations. They demonstrated that by adding or removing mass, and changing the tool holder's length, the system can be tuned for enhanced productivity. The results denoted that dynamically identical tools give the worst stability limit. Similarly, Reith [4], [5], theoretically and experimentally scrutinized the effect of tuning natural frequency of the tools and dynamic vibration absorbing potential on the stability of parallel turning operation. They have confirmed that using detuned cutters in parallel turning the MRR can be increased by shifting the stability boundaries upwards. Recently, Reith [11] utilized non-proportional damping to model the multi-cutter system which includes the dynamic coupling between the cutters via the fixture. Their results showed that presence of non-proportional damping further improves the stable boundaries of a detuned cutter system. Although several works have been reported mainly focusing on 1D dynamic modeling of chatter stability for parallel turning operations and tuning the process to suppress chatter, multi-dimensional chatter stability considering true geometry of cutting tool and workpiece dynamics for different parallel turning strategies has not been investigated so far. Azvar [12] investigated the chatter stability of parallel turning operation where tools mounted on different turrets and cut a shared surface with identical depth of cut. While flexibility of the workpiece and the cutters are considered the true geometry of inserts was not modeled. Even though [12] provided a preliminary multi-dimensional model for chatter stability of parallel turning, it only includes a specific configuration without accounting for nose radii effects restricting optimal stable process and geometry parameters to the side edge cutting angle and depth of cut of the tools which were assumed to be identical.
The primary objective of this study is to develop a general multi-dimensional stability model for different parallel turning strategies. Two main strategies where tools can cut the workpiece's surface, i.e. cutting a shared surface, or cutting different surfaces are presented. For the first time in modeling of parallel turning, main parameters of process geometry, i.e. side edge cutting angle and nose radii of the tools, are completely included in the analysis. Moreover, tool and workpiece dynamic compliance effects are accounted for in the model to improve the stability limit predictions. Frequency and time domain stability models are developed for parallel turning strategies where effects of process parameters on the chatter behavior are thoroughly investigated. Simulation predictions are compared and verified with the experimental results. Finally, for each parallel turning strategy, best process parameters for a stability-guaranteed and productivity-enhanced operation is identified.
Section snippets
Different strategies in parallel turning
Configurability is another advantage of parallel turning operations. Although increased process and geometry parameters in addition to dynamic interactions among the components may hamper controlling the chatter, adjusting proper cutting conditions in each configuration can be advantageous for attenuating the chatter vibrations. Different configurations of parallel turning operation used in this study is illustrated in Fig. 1.
Dynamic modeling and process stability
Formulation is developed for parallel turning in which cutters cut a shared surface. The formulation of the case where tools cut different surfaces is provided briefly in Appendix A.
Simulation and experimental results
In order to discuss the chatter stability solutions of parallel turning obtained from frequency and time domain simulations, two different configurations with flexible tools and workpiece combinations (four cases in total) are investigated and verified experimentally on a Mori Seiki NT CNC machine. Modal parameter were derived from fitted curves to tap testing results [15]. In experiments, sound spectrum was measured and image of surface was taken in order to detect chatter. The force
Conclusion
In this paper, a multi-dimensional chatter stability model for parallel turning operation is presented and solved for various cutting strategies considering the tools and workpiece dynamic compliance effect in frequency and time domain. The model predictions were verified by the experiments. Parallel turning potential to enhanced cutting performance can be achieved by selecting the proper parameters for the process and cutter geometry based on the developed stability maps. By setting depth of
Acknowledgment
The author acknowledges fruitful discussions with Dr. Emre Ozlu and Dr. Daniel Bachrathy on the using of the MDBM [18] and the formulation of the problem.
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