Abstract
The work index Wi was defined by F. Bond as the specific energy (kWh/ton) required to reduce a particulate material from infinite grain size to 100 microns. The calculation is based on the size-energy relationship e1,2=C.(1/x2n–1/x1n ) , which for n = 0.5, x1 = ∞ and x2 =100, by definition gives e∞, 100 = Wi and consequently C=10Wi. In theory, for a given material the value found for Wi.should be constant regardless of the measured sizes x1 and x2 used to calculate the constant C by measuring the energy e. In practice this is not so due to the fact that n ≠ 0.5 and many correction factors have been proposed to overcome this inadequacy experienced by accepting n= 0.5. The present paper proposes a simple way to calculate the appropriate exponent n using conventional grinding procedures. The same calculation can be used to calculate the true value of Wi and attribute a potential energy state to a material at any size.
Highlights
The size-energy relationship is generally expressed by the following Equation (1), (1)where e1,2 is the specific energy required to grind a particulate material from initial size x1 to final size x2
For all the reasons above, it is not possible to predict whether the energy consumed for grinding is proportional to the new surfaces formed or the new flaws
It appears more reasonable to accept that the net energy is proportional to the new surfaces and the specific net breakage energy is proportional to the specific area that varies according to 1/ d where d is the particle size
Summary
The size-energy relationship is generally expressed by the following Equation (1),. where e1,2 is the specific energy required to grind a particulate material from initial size x1 to final size x2. The value of the constant C in (1) can be calculated using a mill of known power that enables to measure the specific energy as well as screening facilities to measure x1 and x2. The present work attributes a potential energy state, to any particulate material of known Wi, that is a function of its size only. This enables one to find a direct energy—size relationship of a material that does not depend on the initial size of the feed as it is the case of (1). This work presents the results obtained for different minerals and rocks ground under different experimental conditions
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