Page 14 - June

METALWORKING EQUIPMENT AND TOOLS

The theoretical feasibility consists in of the integral of the weighted modulus of
the requirement that the calculated values error (IWMO), tuned to double proportions and
of the parameters of the synthesized drive Newton's binomial (Figure 1, a). It has a close-
correspond to the physical meaning of the to-unity frequency response without ripple
problem. In other words, the values of the in the passband and a rather uneven group
moments of inertia, stiffness, damping delay (Figure 1, d). The stop band is smooth,
coefficient, motor parameters and controller monotonically decreasing, with a low rate of
settings must have non-zero positive values signal suppression;
corresponding to the ranges of possible ● Chebyshev, Legendre, Legendre-Papoulis
changes in the parameters of real-life drives. filters can be used when the rate of damping
To set up the drive for operation in accordance of oscillations outside the passband is more
with the selected polynomial, it is necessary important than the type of frequency and
to adhere to certain relationships between transient characteristics (Figure 1, b). They
the moments of inertia and the rigidity of are characterized by the presence of ripple in
structural elements. In a real drive, with the amplitude characteristic in the passband,
a certain mass of the unit, it is not always but provide a steeper roll-off in the frequency
possible to select components to ensure response in the stopband compared to filters
these ratios (practical feasibility). with a flat frequency response. Tuning the drive
The reference polynomials from [1] can be in machine tools to none of these polynomials in
conditionally divided into several groups [4, most cases is not possible due to the complexity
5]: of the implementation of mechanical (requires
With a flat amplitude characteristic in high rigidity and a small moment of inertia of
the passband, which include: the screw) and electrical (large required gains
● Butterworth filter based on the minimum make the drive unstable) drive parameters.

Filters with a linear phase characteristic include Bessel, Gaussian filters and filters with a
linear phase of 0.05° and 0.5° (Figure 1, c). If filters with a flat frequency response provide the
required type of amplitude characteristic, then these filters are designed to obtain a constant
group delay in the passband, which corresponds to a linear phase change (Figure 1, d). Gaussian
crossover filters -6 and -12 dB combine the positive characteristics of various filters. These
filters are a transition from the Gaussian filter to the Chebyshev filter. They have a smooth
amplitude characteristic, a linear phase and a steep slope in the stop band (Figure 1, e).

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