On some methods of determining proper frequencies torsional oscillations in metal-working machines

Abstract

Forced torsional vibrations that occur in machine tool drives are one of the pressing problems of modern machine tool industry. The reasons for these fluctuations may be imbalances of rotating masses, structural imperfections of bearing units, operating or technological process features (for metal-cutting machines – eccentric clamping of the workpiece, processing of non-round workpieces, etc.). In this work, using the example of a real metal-cutting machine, the task of dynamic analysis of the drive of the main movement of the machine with determination of the natural frequencies of torsional vibrations is realized. The real object is replaced by a dynamic model (DM). When constructing the DM, the inertial and rigidity characteristics are determined from the conditions: – the kinetic energy of the object is equivalent to the kinetic energy of the DM (from this condition the axial moments of inertia of the concentrated masses of the row model are obtained); – the potential energy of elastic deformations of the object is equivalent to the potential energy of deformation of the DM (from this condition the rigidity coefficients of the DM are obtained). The natural frequencies of the row DM were determined in three ways: 1) by solving the frequency equation (exact method) in combination with the method of reducing the number of masses of A.P. Cherevkov; 2) partial systems method (fundamental frequency only); 3) method of residuals (Tolle). The following conclusions were made: 1) the main (smaller) frequency can be found by any of the methods considered (since the results of the three methods coincided); 2) when simplifying the DM using the method of partial systems, the criterion for the possibility of further simplifications over the specified frequency range should be taken into account; the transition from a three-mass DM to a two-mass one if the criterion in this calculation was not met led to an error in determining the value of the fundamental frequency of about 10%; 3) dynamic calculations of machines using DM and methods for determining natural frequencies make it possible, based on known frequencies of disturbing forces, to identify possible near-resonant operating modes and avoid them in advance by making changes to the design of the machine at the design stage