Page 20 - June

METALWORKING EQUIPMENT AND TOOLS

The area of rational application of the Gaussian filter is in the range of masses from 100 to
1500 kg and displacement up to 2000 mm, Bessel - 10 ... 1000 kg, up to 2000 mm, Butterworth
and IVMO filters have practically the same range of application with a mass of up to 500 kg and
displacement up to 4000 mm ... In this case, the bandwidth of these polynomials varies widely
from 54 to 142 Hz. Polynomials with linear phase of 0.05 ° and 0.5 °, Gaussian transitions of
-12 and -6 dB have the narrowest range possible. applications (names are in descending order).
For a polynomial with a linear phase of 0.05 °, the best application with a node mass of up to
300 kg and a displacement of 1500 mm, 0.5 ° - up to 200 kg and up to 1000 mm, Gaussian -12
and -6 dB - with a mass of up to 100 kg and displacement up to 1250 mm. These polynomials
have one of the widest bandwidths from 126 to 230 Hz, but their practical implementation is
the most problematic, since even for small masses of the unit being moved, a very high axial
rigidity of the drive mechanism is required. For example, when tuning to a Gaussian polynomial
of -6 dB with a mass of a movable unit of 50 kg and a travel length of 500 mm, the minimum
possible diameter of the working part of the screw is 50 mm.
As a result of the research, quantitative relationships have been determined between the
main quality indicators of the polynomials used to approximate an ideal low-pass filter, and the
design parameters, including a control system, a feed drive with a ball screw, the mechanical part
of which is represented by a two-mass model that takes into account the inertial characteristics
of the movable unit, rotating elements and the axial rigidity of the mechanism. It was found
that in the parametric synthesis of a two-mass drive, limitations arise due to the fact that the
coefficients of the characteristic polynomial depend on the parameters specified at the design
stage, and the required form of the transfer function cannot be obtained only by changing
the drive adjustments. This circumstance significantly limits the possibilities of adapting the
machine, in the design of which the rolling screw-nut transmission is used, to the solution of
specific technological problems during operation.

V.V.Bushuev, Ph.D.,
V.V. Molodtsov, D.Sc., Associate Professor.
V. A. Novikov.
FGBOU VO MSTU STANKIN.

References:
1. Bushuev V.V., Molodtsov V.V., Novikov V.A. Method of reference polynomials for parametric synthesis of feed drives for metal-working machine tools
with CNC // STIN. 2017. No. 12.
2. Evstafieva S.V., Molodtsov V.V. Modeling of the servo drive of the feed of modern CNC machines. Moscow, Mechatronics, automation, control. No. 9,
2010, pp. 37 - 44.
3. Bushuev V.V., Evstafieva S.V., Molodtsov V.V. Modeling of control contours of the feed servo drive // STIN. - 2016. - No. 3. pp. 7 - 14.
4. Williams, A. B. Electronic Filter Design Handbook, Fourth Edition / A. B. Williams, F. J. Taylor // (McGraw-Hill Handbooks), 2010.
5. Zverev, A. I., Handbook of Filter Synthesis, John Wiley, 1967. 576 p.
6. Phillips Ch., Harbor R. Feedback control systems // Moscow, Laboratory of Basic Knowledge, 2001. - 616 p.
7. Brzhozovsky B.M., Martynov V.V., Bochkarev P. Yu., Skhirtladze A.G. Management of machine tools and machine complexes // Stary Oskol: TNT,
2014. - 352 p.
8. Bushuev V.V. Improving the accuracy of CNC machines for contouring by improving the dynamic characteristics of electromechanical feed drives:
dissertation to-that tech. Sciences 05.02.07 / Bushuev Viktor Valerievich. Moscow, 2017. 183 p.
9. Mikhailov O.P. Dynamics of electromechanical drive of metal-cutting machines // Moscow, Mashinostroenie, 1989. 224 p.
10. Molodtsov V.V. Methods for the design of highly efficient metalworking machines as mechatronic systems: dissertation of Dr. Tech. Sciences
05.02.07 / Molodtsov Vladimir Vladimirovich. Moscow, 2016. 390 p.

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