Issue 27

G. Kuidong et alii, Frattura ed Integrità Strutturale, 27 (2014) 43-52; DOI: 10.3221/IGF-ESIS.27.06 45 According to the relevant references, the work done by conical pick mainly translate into rock fracture energy, damage energy, plastic strain energy and so on [12-13]. The fracture energy E F can be express as: F T E kW  (5) where k is an ideal coefficient which only has relation with pick’s shape and cutting angle, and it can be obtained through rock cutting test. In Verification of the Model paragraph, acquisition process of k value will be presented. On the basis of Griffith fracture mechanics theory [14], the fracture energy E F for generating new fracture surface when the main rock fragment formed can be expressed as: 2 2 2 s I F s 2 tan 2 tan 2 cos cos G d K d E G A E        (6) where G s represents surface free energy per unit area of rock material; K I stands for fracture toughness of rock material in the type of model I cracking, it can be approximately calculated by σ t /6.88 [15]; σ t is rock tensile strength. Combining Eqs. 3-6, the maximum penetration depth of conical pick before main rock fragment formed can be expressed by:   1 2 2 2 3 max 2 3 1 tan tan cos I K d h k E                (7) Submitted Eq.7 to Eq.1, then the peak cutting force of conical pick P c can be expressed as: 1 2 4 2 I 3 3 3 2 3 tan tan 2( ) ( ) cos (1 ) c K P d k E        (8) C ALCULATION OF ROCK FRACTURE SURFACE AREA he similarity of geometry shape of brittle material (glass, ceramic, rock, coal and so on) fragment under indenters or cutting tools has been verified through experiments, and there are linear relationship between width, length of fragments and cutting depth [16-18]. According to Eq.8, it is visible that the area calculation of new facture surface generated by conical pick is the basis for predicting the peak cutting force of conical pick, which means to establish the calculative method for horizontal and vertical fracture angle of rock fragment. C ALCULATION OF HORIZONTAL FRACTURE ANGLE orizontal fracture angle of rock fragment is directly related to the optimal intercept of conical picks. The optimal intercept of conical picks in rock cutting process is 3.46 times the cutting depth according to Evans calculate method [1]. Optimal intercepts of 22 different rock types have been obtained through rock cutting experiments by Bilgin [5], and their values are very close to 3.23 times the cutting depth. In view of 7% difference between Evans calculated result and Bilgin experimental result, Evans calculate method is considered reliable and correct. So, in this paper, horizontal fracture angle of rock fragment in the mathematical model for predicting the peak cutting force will adopts Evans calculate model, which means that horizontal fracture angle is equal to 60 degree. C ALCULATION OF VERTICAL FRACTURE ANGLE he influence of cutting angle on the rock fragment is ignored in Evans theory, but the geometric shape of rock cutting fragment has play an important role in perfect prediction of peak cutting force. Base on Evans theory, some assumptions are put forward in present paper: rock broken is caused by tensile failure, and it accords with the maximum tension theory; the generated total force by tensile stress in fracture surface is through the center of arc AC; the crushing zone caused by conical pick head is shown in Fig.2, and AG is an arc with the center O. T H T