The optimum force-pulse duration in rock breaking

Abstract

In impulsive rock breaking, the question of the best shape of the active force pulse on the bit is very ~mpor-rant. It is involved in the design of powerful impulse planes.The problem of the optimum relation between the duration of the active force pulse and the natural period of the bit-rock system was discussed by Dokukin [1]. The optimum ratio is considered to be that corresponding to the maximum dynamicity coefficient 15. The dynamicity coefficient is defined as the ratio of the static force to the amplitude of a force pulse of finite duration with an equivalent action [2]. Optimization of the dynamicity coefficient involves trying to get the maximum breaking effect per unit force pulse amplitude. The system bit-rock is regarded as a linear one-mass vibrating system with rigidity (quasielasticity) k and damping H.The frequency properties of such a system depend on two constants: the natural frequency u) 0 = 2rr f0 = 4 k/M and the reduced damping factor g = H/2M w0, where M is the mass of the bit. According to determinations made in tests of impulse planes on a coal--cement block [1], g = 0.6-0.7.If the active force pulse is a half-period of a sine wave, with duration At, the dynamicity coefficient of the bit-rock system depends on the ratio of the duration of the active force pulse to the natural period of the system (see Fig. 1). Let us consider the curve for g = 0.6 in more detail. For small values of the argument, for 0 _< 2At/T 0 = 2f0At _< 0.7 the curve 8 =/3 (2At/T 0) coincides with a straight line making an angle of 45" to theaxis. In this case the dynamicity coefficient is equal to the ratio of twice the force pulse duration to the natural period, B = 2At/To = 2:oAt.The static force equivalent to the pulse is To the right of the value At = 0.35T 0 or 2At/T 0 = 0.7, the curve for the dynamicity coefficient begins to flatten out, and the static force equivalent to the pulse p becomes less than 4f0 p. In this range the active energy for fracture of the rock is not fully utilized, although the coefficient of dynamicity continues to increase with the pulse duration up to 2At/T 0 = 2. Finally, for pulse durations greater than T 0, the impulsive action becomes equivalent to a static value which is equal to the force pulse amplitude.The right-hand boundary of the region of complete utilization of the energy on fracture, AEop t = 0.35T 0' is the optimum duration, because it permits fracture with a dynamicity coefficient 15 which is maximal forthe region in which a fall in static force equivalent to the pulse is still not observed. The optimum duration depends on the natural frequency of the bit-rock system, which is in turn governed by the strength properties of the rock, the A. A. Skochinskii Institute of Mining, Moscow.