An equation for the breakage of particles under impact

Using data from the literature, the following simple empirical equation is derived for the cumulative mass fraction of particles broken (m̄) when impacted at a specific impact energy (J/g of impacted mass) of E:m̄i(E)=0 , E≤EminiĀln(E/Ki),Emini≤E≤Emaxi1,E≥EmaxiwhereEmini=KiEmaxi=Kiexp(1/Ā)andKi=C(xi/xo)−m. s equation, i is an integer index of a √2 screen size interval of upper size xi; xo is a standard size of 1 mm; Emini is the minimum specific impact energy required to produce significant breakage of feed material of size i and Emaxi is the specific impact energy that breaks all feed material of size i. Ā, C and m are material-dependent constants. Values of Ā=0.235, m=0.58 and C=0.13 J/g were found for particles of limestone in a thin bed impacted by a falling steel ball. The equation shows that smaller particles require a higher specific impact energy than larger particles to give the same fraction of breakage out of the feed size interval.