Page 15 - June

METALWORKING EQUIPMENT AND TOOLS

Amplitude (dB) Amplitude (dB) Delay (s) Butterworth

Bessel
Gauss
Butterworth
Bandwidth
IVMO
Legendre-Papoulis
Binomial of Newton Chebyshev of the 1st kind Linear phase 0.05
Double proportions
Frequency Hz) Frequency Hz)
Frequency Hz)
a b c

Amplitude (dB) Amplitude (dB)

Gauss
Gauss Gauss
Gauss
Frequency Hz) Frequency Hz)
d i

Fig. 1. LFC of polynomials: a) - with amplitude characteristic without pulsations in the passband; b) - with amplitude ripples
in the passband; b) and c) - with a linear phase part; e) - Gaussian transition filters.

Table 1 shows the relative parameters of the theoretically implemented polynomials. The
Butterworth filter was adopted as the base one - all other polynomials were compared with it.
The bandwidth fp of the position contour is one of the main characteristics of the polynomial,
the value of which affects the accuracy, speed and ability of the drive to suppress the influence
of external influences (cutting forces) [6, 7]. The ± 0.01 dB crossover characteristic indicates at
what frequency LFC of the drive deviates from the zero value by ± 0.01 dB [8]. This characteristic
was added, since the traditional deviation of -3 dB is too large for a machine feed drive, which
says little about the accuracy of its operation at operating frequencies, usually not exceeding
5-10 Hz. Overshoot (σ), rise time (Tн) and settling time (Tу) are characteristics that traditionally
determine the quality of the transient process [6, 7]. The reaction to the disturbance shows the
value maximum deviation from the set state when the force is applied to the drive, tuned to
different polynomials, and the same step load relative to the displacement of the drive, tuned
to the Butterworth filter. The smaller the response, the less external influences exert on the

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