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Częstotliwościowa dziedzina rzeczywistych sił oddziaływania górniczych naczyń wodociągowych na zbrojenie szybowe

Płachno M.

Archives of Mining Sciences

2005

Vol. 50, no 1

101-130

Autor zwrócił uwagę, że wymagana przez przepisy górnicze kontrola rzeczywistych sił oddziaływania górniczych naczyń wyciągowych na zbrojenie szybowe (tzw. sił prowadzenia) jest dużym problemem, mimo że w celu takiej kontroli od wielu lat wykonuje się rutynowe pomiary poziomych przyspieszeń naczyń. Istota problemu tkwi w interpretacji wyników pomiarów przyspieszeń, którą rutynowo wykonuje się przy niesprawdzających się w praktyce założeniu, że przy współpracy z prowadnikami, naczynie wyciągowe zachowuje się jak bryła sztywna. Z tego powodu, określanie rzeczywistych sił prowadzenia metodą rutynowej interpretacja poziomych przyspieszeń naczyń jest obarczone dużym błędem, którego poziom może osiągać nawet 300%. Przedstawiono rozwiązanie nowej interpretacji poziomych przyspieszeń naczyń wyciągowych, umożliwiające określanie rzeczywistych sił prowadzenia z błędem na poziomie ok. II %. Istotą nowej interpretacji jest rozpatrywanie przebiegów pomiarowych przyspieszeń naczynia w dziedzinie częstotliwości drgań własnych tego naczynia, po uprzednim zweryfikowaniu przebiegów przyspieszeń ze względu na nieciągłości kontaktu prowadnic naczynia z prowadnikami w szybie. Zaprezentowano niektóre wyniki przemysłowych prób nowej interpretacji, wykonanych w ramach projektu badawczego KBN pt.: "Opracowanie nowych metod projektowania zbrojeń szybowych dla modernizowanych szybów górniczych" (nr rej. 5 TI2A 054 22).

According to the Author, the control ofthe real impacting forces of conveyances and shaft steelworks (i. e the guiding forces) required by mining regulations still presents major difficulties though routine measurements of lateral conveyance accelerations have been rigorously pursued for a number of years. The major concern in raised about the interpretation of results. So far the conveyance interacting with the guides has been treated as a stiff body. Accordingly, lateral accelerations are expressed in terrns of the guiding force of the conveyance by formula (1), where M stands for the mass of a conveyance and [...] is the fraction of the conveyance mass interacting with the guides, taken as 0.2 for the forward direc tion and 0.1 for the lateral direction (Kawulok, 1988). Fig 1 shows the frequency characteristics (power spectral densities) of lateral accelerations of a conventional skip. It appears that the power spectrum of the forward and lateral accelerations extends to several bands, and each band corresponds to a different fraction of conveyance mass impacting on the guides. The conveyance mass fraction [...] is not to be treated as a number, but a function [...](t) of natural frequencies of a conveyance, depending on the direction of the acceleration and the guide type. That is why routine interpretation of lateral accelerations of a conveyance in terms of guiding forces is encumbered with a major error, arnounting to even 300%. In the new approach the real guiding forces are determined more accurately (error 11 %) and the results of acceleration measurements are represented in the frequency domain of natural vibrations of a conveyance. The results are first verified to account for discontinuities in the conveyance/guide contact. The relationship (1) is replaced by (3), where F(t) - guiding force in the function oftime, a(t) - measured accelerations, FFT - time-to-frequency transform operator, [...](f) - frequency-domain characteristics of conveyance guiding inertia, FFT - frequency-to-time transform operator, s(t) - measured discontinuities of the conveyance/guide contact, assuming the value 1 at the instants a(t) when the conveyance slipper plates hit the guides, otherwise it is equal to O; M - total mass of a conveyance during measurements. It is readily apparent that the frequency-based interpretation of lateral accelerations of a conveyance offers certain novel features. First of all, acceleration measurements are supported by simultaneous measurements of the distance between the conveyance and the guide, using the contact-less techniques. Accelerations and distances are measured in the direct vicinity of the slipper plate, that is why the distance pattern can be algebraically transformed into the pattern of discontinuities s(t), further utilised in (3). Apart from the application of FFT and FFT transforms, another novel solution involves the calculation of a frequency-domain characteristics of guiding inertia [...](f), using the specialised algorithm. The study outlines the subsequent stages of formulation of the algorithm (i. e. physical models shown in Fig. 4, 5 and a mathematical model governed by Eq (4) as well as the formulas yielding the guiding inertia (Eq 9-12). Conventional conveyances operated in Polish mines that were subject to research investigations are: a four-deck cage (Fig. 2) and a skip with a movable bottom (Fig. 3). Fig. 7, 8 show examples of frequency-domain interpretation of lateral acceleration of conveyance, measured during the industrial tests. Fig. 7, 8 show the results obtained for a skip with the total mass 25.3 Mg, hauling velocity 15 m/s. On the upper plots in Fig. 7, 8 are measured lateral accelerations, on the lower ones are the corresponding guiding forces, determined by the frequency-based approach. Subsequent stages of the interpretation procedure are shown in Fig. 7, 8, yielding the required force patterns. The fust stage consists in determining the spectral characteristics of the lateral accelerations of a conveyance. Accordingly, those characteristics are represented as power spectral densities of lateral accelerations (Fig. 1). The second stage involves the numerical computation of natural frequency of conveyance vibrations for the predetermined range of guiding stiffness factors. The calculation procedure utilises Eq (4), describing the physical models of conveyances shown in Fig. 4, 5 and hence the statistical parameters of these models were required: the mass of the main conveyance assemblies, their dimensions, inertia moments and stiffness factors for the modelled elastic components. Accordingly, the first part involved the structural analysis of a conveyance design, the second part consisted in numerical computations followed by data verification (part three) by comparing the calculation results with the spectral characteristics of lateral accelerations. In the last section, thus verified results are plotted as guiding stiffness patterns in the frequency domain (see Fig. 9). During the third stage the frequency-domain characteristics of the guiding inertia, governed by Eq (9) and (12), were determined for all conveyance types subjected to research investigation. In order to determine the coefficients [...], the coordinates of the local maximums of the charactristics are first read from the frequency axis in the spectral density characteristics (the upper plots in Fig. 1). These cordinates are then plotted on the frequency axes in the respective diagrams in the upper section of Fig. 9. On the horizontal axes in each of these diagrams are the corresponding stiffness factors [...], for the rolling guiding. Thus obtained results are provided with the diagrams. The procedure to determine the coefficients cx, dx, cy, dy is recapitulated as follows. First, the coordinates corresponding to frequencies [...] setting the lower and upper boundaries of the frequency range of accelerations measured for rolling guiding of the conveyance are found on the frequency axes of the spectral density characteristics in the lower part of Fig. 1. These coordinates are then plotted on the frequency axes on the relevant diagrams in the lower part of Fig. 9. On the horizontal axes of each plot are the corresponding stiffness factors [...] for the rolling guiding. Thus obtained results are given with the plots, together with the straight lines corresponding to Eq (10) and with the coefficients [...] derived from the formula (11). Frequency-domain characteristics of the guiding inertia for the skip are governed by Eq (17), (18). The final stage of the interpretation procedure consists in processing of the lateral acceleration patterns to convert them into the corresponding guiding forces in accordance with the formula (3), yielding the guiding force patterns in the lower plots in Fig. 7. 8. Fig. 10 shows the plots illustrating how the frequency of 1ateral accelerations of a conveyance should affect the value of [...], which expresses the predetermined fraction of the conveyance mass in the guiding force, obtained by the frequency-based approach. In the traditional approach the factor [...] is taken as 0.2 for the forward direction and 0.1 for the lateral direction. It is readily apparent that the results obtained by the frequency-based interpretation and the traditional approach will differ, the error amounting to even 300%. That is why a specialised error estimation algorithm is developed, whereby the guiding displacements obtained by the frequency-based approach are compared with those derived from guiding distance measurements. The resultant algebraic formulae to compute the mean relative error of the frequencybased interpretation are written as Eq (25) and (26). Table 1 compiles the values of error involved in the results shown in Fig. 7, 8. It appears (see table l) that the results shown in Fig. 7, 8 accurately emulate the real guiding forces, with the error below 11 %. In other industrial applications of the frequency-based approach the errors involved in the guiding force calculations were on a very simi1ar level. Hence, it is concluded that the method of controlling conveyance guiding forces using the frequency-based interpretation of lateral accelerations of conveyances should help overcome certain problem experienced in the mining practice.