The cutting length necessary to determine the form and parameters of the correlation function for the loads on the cutting tool

Conclusions

o li]1.|To determine the type and parameters of the correlation functions of the loads on the cutting tool, it is necessary to determine the latter by averaging not only timewise, but also over a set of realizations including the actual cutting conditions. li]2.|For a required accuracy of determination of the parameters of the correlation function, the total cutting path length depends on the variation of the parameters of the cut medium. li]3.|In determining the type of the load correlation function, it is necessary to average for a total length of the cutting path of at least 2.5 m if the coefficient of variation of the cutting resistance of the coal isv=0.2. li]4.|In determination of the parameters of the correlation function of the load withv \t-A =0.2, the total length of the cutting path must be at least 4.5 m.

The error of determination of the parameters of the correlation function will then be less than 10%:

$$\left( {\frac{{\sigma K_x \left( \tau \right)}}{{\bar D_x }} = 0.1} \right).$$

li]5.|In processing of a realization by double averaging, the choice of origin has practically no effect on the form and parameters of the correlation function.

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Literature Cited

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Additional information

A. A. Skochinskii Institute of Mining, Moscow, Dongiprouglemash. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 49–52, May–June, 1972.

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Pozin, E.Z., Deinichenko, V.A. & Tuyakhov, L.S. The cutting length necessary to determine the form and parameters of the correlation function for the loads on the cutting tool. Soviet Mining Science 8, 283–285 (1972). https://doi.org/10.1007/BF02505712

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Keywords

  • Correlation Function
  • Single Realization
  • Cutting Length
  • Cement Block
  • Normalize Correlation Function