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    Nomencl
    t10 tn
    n
    Ecs
    A,b    ature
    the cumulative percentage passing 1/10th of the initial mean size (%) the cumulative percentage passing 1/nth of the mean particle size (%) ratio piding to a characteristic size of the mean particle size specific comminution energy (kW h/t) ore impact breakage parameters    Wi
    Pi
    Gbg
    F80
    P80
    X    Bond work index (kW h/t) test sieve size at which the test is performed (106 lm) standard Bond grindability, net weight of ball mill product passing sieve size Pi produced per mill revolution (g/ rev)
    sieve opening which 80% of the feed (lm) sieve opening which 80% of the product (lm) mean particle size (mm)
     
    of disadvantages, including necessity a special apparatus, tiring and particularly the length of time taken to carry out a test. For each drop weight test, 15 samples are tested in five size fractions at three levels of energy input [10–13].
    Narayanan [14] was used a novel procedure for estimation of breakage distribution functions of ores from t-family of curves. In this method, the product size distribution can be represented by a family of curves using marker points on the size distribution defined as the percentage passing (t) at a fraction of the parent particle size. Thus, t2 is the percentage passing an aperture of half the size of the parent particle size, t4 is one quarter and t10 is one-tenth of parent particle size. Narayanan and Whiten [15] have proposed empirical equations for relating the reference curve data t10 with the impact energy.
    The t10 value is related to the specific comminution energy by the Eq. (1):
    t10 ¼ Að1  ebEcsÞ    ð1Þ
    The tn versus t10 relationships can then be used to predict the product size distributions at different grind times [16].
    It is known that there are many difficulties and problems in drop weight and twin pendulum test methods such as being laborious, requiring long test time and requiring a special apparatus. In this study, breakage behaviours of three different limestones in a laboratory impact crusher were investigated. A new size distribution model equation was developed by t-family value evaluation and Bond work index approach, and this model equation was tested.
    2. Materials and method
    2.1. Material
    Three different limestone samples taken from different region of Turkey were used as the experimental materials. The chemical properties of the limestone samples were presented in Table 1.
    2.2. The test of standard Bond grindability
    The Bond grindability tests were conducted less than 3.35 mm of dry feed materials in a standard ball mill (30.5  30.5 cm) following a standard procedural outline described in the literature [17–24]. The work indices were determined at a test sieve size of 106 lm. It has no lifters and all the inside corners are rounded. The Bond ball mill (Fig. 3) is operated at 70 rpm and is equipped with a revolution counter. The grinding charge consists of 285 iron balls weighing 20.125 g. The standard Bond grindability test is a closed-cycle dry grinding and screening process, which is carried out until steady state condition is obtained. This test was described as follow [17–24].
    The material is packed to 700 cc volume using a vibrating table. This is the volumetric weight of the material to be used for grinding tests. For the first grinding cycle, the mill is started with an arbitrarily chosen number of mill revolutions. At the end of each grinding cycle, the entire product is discharged from the mill and is screened on a test sieve size (Pi). Standard choice for Pi is 106 l. The oversize fraction is returned to the mill for the second run together with fresh feed to make up the original weight corresponding to 700 cc. The weight of product per unit of mill revolution, called the ore grindability of the cycle, is then calculated and is used to estimate the number of revolutions required for the second run to be equivalent to a circulating load of 250%. The process is continued until a constant value of the grindability is achieved, which is the equilibrium condition. This equilibrium condition may be reached in 6–12 grinding cycles. After reaching equilibrium, the grindabilities for the last three cycles are averaged. The average value is taken as the standard Bond grindability
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