# Prediction Methods and Experimental Techniques for Chatter Avoidance in Turning Systems: A Review
## 2 Vibration Prediction in Turning Processes
They applied this methodology when turning difficult-to-cut materials such as nickel-based superalloys leading to 100 times faster computational times. [PERSON] and [PERSON] [61] presented an original representation of chatter problems considering modal parameters of tool and workpiece, tool angles, and modal angles. They developed the stability model based on the directions of motion velocity, motion displacement and related them with the generation of chatter marks. [PERSON] and [PERSON] [62] applied the receptance coupling method for the estimation of the dynamical properties in a turning system with a compliant part. They obtained the cutting parameters with the aid of a program integrated in the CNC (Computer Numerical Control) system. In this way, the need of measurement equipment can be saved. Recently, parallel turning has attracted the attention of researchers. In this turning operation two cutting inserts are engaged during cutting. Depending on how these tools are arranged, they can cut the same surface or not, leading to different configurations. For parallel turning centers, the tools are  
Figure 3: (a) Chatter originated from a dominant mode in the tangential direction [33]; (b) multi-mode analysis of chatter in a cylindrical turning operation [55]. often fixed in independent turrets. [PERSON] and [PERSON] [63] published the first results regarding this technique. Their work showed that stability limits could be increased due to the dynamic coupling between the tools with respect to common turning systems. Later, these authors used a time- and frequency-domain model to study the influence of one tool on the other [64]. They depicted a view of the stability boundaries in terms of the frequency ratio between both tools. In close relation with the group from [PERSON], [PERSON] et al. followed the investigation of the parallel turning technique in [65]. Here, they studied and validated the effects of changing the overhang of one of the tools over stability analysis. Afterwards, they analyzed the behavior of 2- and 3-DOF models using an artifact with two opposite tools [66]. They demonstrated the presence of non-proportional damping is responsible for an increase in chip width limit that allows a more robust prediction when using a 3-DOF model. Finally, [PERSON] and [PERSON] [67] presented a multi-directional chatter stability model for different turning configurations (Figure 4) using frequency- and time-domain approaches. Using a model capable of including workpiece dynamics and tool geometry, results showed maximum stability is achieved when the total radial dynamic forces acting on the workpiece are minimized. In this way, inserts having smaller cutting coefficients, nose radius and side edge angle should be considered to reduce radial forces. [PERSON] et al. [68] also investigated the stability of turning systems when different tools are simultaneously engaged in cutting. They presented a slightly different approach for the mathematical modeling, using a surface formation equation. The amount of literature regarding chatter gives a clear idea of the magnitude of the problem. In fact, after analyzing the numerous models and methods proposed in the past, the authors identified some key aspects: (1) the stability lobes are extremely important charts for improving productivity if these conditions are met: high spindle speeds; light materials; rough conditions and systems having low natural frequencies; (2) in any case, stability lobes are often related to local problems and need to be considered case by case. A more systematic application is desirable; (3) unless process damping emerged as a hot topic over the last decade, the developed models are to remain in the scientific domain rather than being used in practice due to their inherent complexity; (4) chatter is expected to continue to be present during the next years as new materials with better properties and lower machinability grades emerge and thinner workpieces are to be designed and produced.