Kinetics of size reduction and associated wear of grinding media

Abstract

Ball milling is an important step in mineral processing to liberate the locked minerals from ore. During milling, the media undergo extensive wear due to abrasion and impact. Corrosion acts synergistically to increase the overall wear of the grinding media. The present work deals with two important aspects of ball milling, namely, the kinetics of size reduction and the associated grinding abrasive wear of the medium (steel balls). Chapter I gives an elaborate introduction on size reduction and grinding media wear. The existing methods of calculating breakage parameters together with the influence of operating variables on such parameters are discussed with reference to dry grinding in batch mills. The associated wear of grinding media reported in the literature is also discussed. The existing population balance model of size reduction assumes first order breakage behaviour in batch mills. Several cases of deviation from this rule have been reported in the literature. To account for such non linear behaviour, three models have been developed and validated in Chapter II. The resulting equations relate the fraction of a particular size interval retained after a grinding time, t:

f=exp ( kt at2 bt3)f = \exp(-kt - at^2 - bt^3)f=exp( kt at2 bt3) f=[1+bsinh (ct)] 1f = [1 + b\sinh(ct)]^{-1}f=[1+bsinh(ct)] 1 f=exp ( k1t)+k1(k2 k1)[exp ( k1t) exp ( k2t)]f = \exp(-k_1 t) + \frac{k_1}{(k_2 - k_1)} \left[\exp(-k_1 t) - \exp(-k_2 t)\right]f=exp( k1 t)+(k2 k1 )k1 [exp( k1 t) exp( k2 t)]

where k,k1,k2,a,b,ck, k_1, k_2, a, b, ck,k1 ,k2 ,a,b,c are constants. The kinetics of size reduction for longer duration grinding of two different size intervals as top size, namely 2 + 1.7 mm and 0.8 + 0.6 mm, has been studied. It is interesting to note that unlike the first order equation, the above equations (1)–(3) are equally applicable to describe the kinetics of size reduction of cumulative fractions as well, thus demonstrating the power and applicability of the proposed equations. Assuming size reduction as a structural relaxation process, the following equation adopted from irreversible thermodynamics has been employed to predict the mean particle size, XtX_tXt , of ore prevailing in the mill at any instant of grinding time t: Xt=X0+(X X0)[1 exp ( (t )n)]X_t = X_0 + (X_\infty - X_0)\left[1 - \exp\left(-\left(\frac{t}{\tau}\right)^n\right)\right]Xt =X0 +(X X0 )[1 exp( ( t )n)] where X0X_0X0 is the starting particle size, X X_\inftyX is the limiting size as t t \to \inftyt , and \tau , nnn are constants. The validity of the equation has been cross checked with data available from the literature. The influence of microstructure and hardness of forged AISI SAE 52100 steel balls (the medium) on grinding wear is presented in Chapter III. Fifteen sets, each consisting of nine balls of 30 mm diameter, were subjected to heat treatment to develop various microstructures such as spheroidite, pearlite, bainite, martensite, and martensite with retained austenite. The study clearly indicates the following:

The hardness of the worn surface alone cannot be used to predict wear behaviour of grinding media. However, when the data are grouped according to types of microstructure, they appear to follow definite trends. Pearlite, spheroidite, bainite, and tempered martensite follow one trend-they wear more when hardness is lower. For microstructures containing martensite, retained austenite, and undissolved carbide, there exists an optimum retained austenite level at which wear is minimum. It is suggested that micro cracks in the heat treated ball samples increase wear, thus offsetting the beneficial effect of retained austenite. The study shows that a judicious selection of microstructure can lead to a marginal improvement in wear resistance for certain matrix structures, with the greatest improvement being about 28%.

The influence of ore particle size on ball wear is presented in Chapter IV. The following conclusions are drawn:

Grinding abrasive wear of the medium in a ball mill is not linear with grinding time. The non linearity appears to be due to a combined effect of coating of ball surfaces with fines and the reduced apparent size of abrasive particles acting through the fine particle barrier. The kinetics of wear with grinding time can be fitted to a power law of the form: w=atbw = a t^bw=atb where w is the weight loss of the medium after grinding time t, and a, b are constants. Using the first derivative of the equation, wear rate has been calculated and correlated with the mean abrasive particle size estimated using Eq. (4). It is demonstrated that grinding wear rate of the medium increases with mean abrasive particle size up to a critical value and then increases at a much lower rate-typical behaviour observed in other abrasive wear processes. The wear exponent b appears to be an indicator of cutting wear mechanisms in dry grinding, as a plot of the inverse of b/Esb/E_sb/Es produces a curve similar to that of wear resistance plots in two body sliding abrasive wear.

The importance of feed amount on the breakage rate and concomitant wear of the medium is presented in Chapter V. Experiments conducted with various feed levels lead to the following conclusions:

Breakage rate of ore particles has a marked influence on wear of the grinding medium. Two domains were observed when particle breakage rate was plotted against feed amount. Similarly, wear rate curves also exhibited two domains-classified as impact dominant and abrasion dominant regions. By treating the overall wear rate curve as the sum of two Lorentzian distribution curves, impact and abrasion components have been resolved within the studied feed interval. The relative importance of impact and abrasion depends on ore amount in the mill. Impact wear dominates at lower feed levels, while abrasion dominates at higher feed levels.