Analytical estimation of cyclic fracture of rocks during drilling

Abstract

The driving of various types of mine workings for commercial mineral production involves the process of rock breaking. Roller-bit drills are the instruments most used to break rocks [1][2][3].In the operation of a roller bit, breakage occurs after single or repeated cyclic action of the teeth on the rock. An urgent problem [4][5][6][7] is the influence of the cyclic loading parameters, especially the amplitude and frequency of the dynamic load components, on the process of rock breaking at the face.In this article we shall suggest a method for quantitative estimation of the influence of the cyclic loading parameters on the process of rock breaking by roller bits at the face of a vertical working, with allowance for the time dependence of the strength and the mining-geological and technical fractors. The problem can be formulated as follows. Suppose we have a vertical mine working with internal diameter D and depth L, filled to its mouth with unfiltered wash liquid, the parameters of which are given in [8,9]. We also know the mechanical properties and stress-strain state of the face rocks lying at depth L [10,11]. We are to determine the number of cycles N before the rock breaks owing to the action of the roller teeth under given axial load and rotation speed.If the angular velocity of the roller about its axis is w = 2nn/60 x D/d, then the frequency of reciprocatory motion of the body of the bit for synchronous roiling of the rollers from tooth to tooth over the face will be wz. The period of longitudinal vibration of the body of the bit will be 2n/wz, which corresponds to the time of rolling of the rollers from one tooth to the next, and represents the duration of contact during a single event of interaction of a tooth with the rock The number of cycles to breakage, N, and the duration of contact of a tooth of the roller with the rock, t c, are linked with the time to complete breakage as follows: d 2,-:During drilling, as the angular speed of the bit increases, so do the number of blows inflicted on the face rock by the roller teeth in unit time, the speed of impact, and the dynamic component of the load. This increases the efficiency of rock breaking and the mechanical rate of advance.After a large number of cycles of loading by the roller teeth, as damage to the rocks increases, so does the probability of breakage of the rocks at the face of the working increase. Fatigue breakage is a result of the time dependence of the strength, and in this context the duration of action of the load is important [13][14][15].The rule of summation of damage for the long-term strength for time-dependent stress is as follows [16]. If we divide up the variable stress into a series of values acting during successive small time intervals, we can neglect stress changes and regard the stress as constant in each interval. Then if the duration of the action of load on the the rock is dt, owing to the irreversibility of the deloading process, the relative decrease in life is dt/t(o), where V. I. Lenin Dagestan State University, Makhac...