Abstract
This paper presents a mathematical perspective, to complement the intuitive or practice-oriented perspective, to classifying machining operations as parallel-process (simultaneous) or single-process in nature. Illustrative scenarios are provided to demonstrate how these two perspectives may lead in different situations to the same or different conclusions regarding process parallelism. A model representation of a general parallel-process machining system is presented, based on which the general parallel-process stability eigenvalue problem is formulated. For a special simplified case of the general system, analytical methods are employed to derive a fully analytical stability solution. Thorough study of this solution through eigenvector analysis sheds light on some fundamental phenomena of parallel-process machining stability, such as dependence of the stability solution on phasing of the initial conditions (disturbances). This establishes the importance, when employing numerical time-domain simulation for such analyses, of specifying initial conditions for the multiple processes to be arbitrarily phased so that correct results are achieved across all spindle speeds.
Full Tensor Eigenvector Analysis on Air-Borne Magnetic Gradiometer Data for the Detection of Dipole-Like Magnetic Sources
