Nauka i Obrazovanie (Jan 2015)
A Literature Review on Mathematical Models of Drilling Process Dynamics
Abstract
The paper presents an overview of literature describing simulation of drilling process. It considers both the negative impact of vibrations, arising when cutting, on the given technological process (emerging so-called chatter) and the positive effects (chip breakage). The paper also examines different models used in modern works and presents basic equations of dynamics, taking into account the regenerative effect, including transverse, axial and torsional degree of freedom. Besides, it describes methods to calculate the chip thickness desirable in cutting force model. Two existing approaches to study dynamics of drilling process are discussed in detail: analytical stability analysis and time domain investigation. The first method is based on eigenvalue problem solution of delayed differential motion equation discretized in the time domain. As to the second approach, full time domain numerical modeling of drilling process using geometry algorithms is conducted. This work emphasizes the analysis of forces acting on the tool during machining. General cutting force models used in modern works are considered. The paper describes main approaches to process damping phenomenon (interaction between cutting tool flank face and work-piece) modelling. It notes the feature specific only to the drilling – near the tip of the tool the chisel edge occurs to indent to the material instead of cutting. From the authors’ point of view the most complete is the model, where a cutting edge is divided into three zones (indentation zone, secondary cutting edge, and primary cutting edge), each of which uses different equations in the model of forces. Additional advantage of this model is that there is an experimental technique to determine cutting coefficients. The paper ends with a detailed classification of existing models of drilling dynamics.The paper was financially supported by the Ministry of Education and Science of the Russian Federation within the framework of the Project NIR № 9.1073.2014K: design part of the State-guaranteed order in research activities.
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