Laboratory studies on ball wear in the grinding of a hematite-magnetite ore

Marked-ball grinding tests were carried out under different grinding conditions and environments. Three types of balls were used, namely, cast hyper steel, high chrome cast iron and EN-31 (forged), which cover a wide range of chemical composition, microstructure and media hardness. The effect of pulp density on ball wear and grinding efficiency was also studied. Relative pulp viscosities at different percent solids for the ore slurry were also determined. As the Kudremukh ore contained about 0.2% pyrite, the effect of addition of pyrite on ball wear was studied separately. Results of marked-ball grinding tests indicated that ball wear increased with time and showed a sharp increase for wet grinding over dry grinding. Ball wear under wet grinding conditions was also influenced by the gaseous atmosphere in the mill. At 70% solids, the best results in terms of reduced ball wear coupled with satisfactory grinding efficiency were obtained. The influence of oxygen on the corrosive wear of grinding balls was increasingly felt only if sulphide minerals such as pyrite were also present in the ore. The various ball materials could be arranged in the following order with respect to their overall wear resistance: high chrome cast iron > EN-31 (forged) > cast hyper steel.Possible ball wear mechanisms involved in the grinding of Kudremukh ore are discussed.

Ball wear and its control in the grinding of a lead-zinc sulphide ore

Marked ball grinding tests were carried out in the laboratory with a lead-zinc sulphide ore under different experimental conditions using high carbon low alloy steel (cast and forged) and high chrome cast iron balls. Relative ball wear as a function of grinding period and milling conditions was evaluated for the different types of ball materials. The role of corrosion and abrasion-erosion in the wear of grinding media is brought out. Methods to minimise ball wear through control of mill atmosphere and addition of reagents are discussed.

Effect of microstructure and hardness on the grinding abrasive wear resistance of a ball bearing steel

Grinding media wear appears to be non-linear with the time of grinding in a laboratory-scale ball mill. The kinetics of wear can be expressed as a power law of the type w=atb, where the numerical constant a represents wear of a particular microstructure at time t = 1 min and b is the wear exponent which is independent of the particle size prevailing inside a ball mill at any instant of time of grinding. The wear exponent appears to be an indicator of the cutting wear mechanism in dry grinding: a plot of the inverse of the normalised wear exponent (Image ) versusHs (where Hs is the worn surface hardness of the media) yields a curve similar to that of a wear resistance plot obtained in the case of two-body sliding abrasive wear. This method of evaluating the cutting wear resistance of media is demonstrated by employing 15 different microstructures of AISI-SAE 52100 steel balls in dry grinding of quartz in a laboratory-scale ball mill.

Grinding abrasive wear and associated particle size effect

The type of abrasion that the grinding medium experiences inside a ball mill is classified as high stress or grinding abrasion, because the stress levels at the surface of the medium exceed the yield stress of the metal when hard abrasives are crushed. During dry grinding of ores the medium undergoes not only abrasion but also erosion and impact. As all three mechanisms of wear occur simultaneously, it is difficult to follow the individual components of wear. However, it is possible to show that the overall kinetics of wear follows a simple power law of the type w = at(b), where w is the weight loss of the grinding medium for a specified grinding time t and a and b are constants. Experimental data, obtained from dry grinding of quartz for a wide range of times using AISI 52100 steel balls having various microstructures in a laboratory scale batch mill, are fitted to the proposed equation and the wear rate w is calculated from the first derivative of the equation. The mean particle sizes of the quartz charge DBAR corresponding to 50 and 80% retained size are determined by mechanical sieving of the ground product after a grinding time t and thus the relationship between wear rate and particle size of the abrasive is established. It is found that w increases rapidly with DBAR up to some critical size and then increases at a much lower rate.

Ball wear mechanisms and control in the grinding of sulfide and phosphate ores

Marked ball grinding tests were carried out in the laboratory using high carbon low alloy steel (cast and forged) and high chrome cast iron balls. Relative ball wear as a function of grinding period and milling conditions was evaluated for the different type of ball materials in the grinding of lead-zinc sulphide and phosphate ores. Results indicated that ball wear increased with time and showed a sharp increase for wet grinding over dry grinding. Ball wear under wet grinding conditions was also influenced by the gaseous atmosphere in the mill. The influence of oxygen on the corrosive wear of grinding balls was increasingly felt in case of sulphide ore grinding. The grinding ball materials could be arranged in the following order with respect to their overall wear resistance:

Laboratory studies on ball wear in the grinding of a chalcopyrite ore

Wear of high carbon low alloy (HCLA) cast steel balls during the grinding of a chalcopyrite ore was evaluated under different experimental conditions. The role of oxygen in enhancing ball wear during wet finding is brought out. The influence of pH on ball wear was also examined from the view point of acid production during grinding and reactivity of sulphides. Contributions from corrosion and abrasion towards ball wear are quantified in terms of ball wear rates as a function of time, particle size and gaseous atmosphere in the mill.

Roughness generated in surface grinding of metals

When a metal is surface ground the roughness generated is the summation of a function of the wheel roughness and the roughness due to wheel attrition and damage to the workpiece. We identify this function here as a maximum em,elope profile, which is fractal within certain cut off wavelengths determined by the dressing conditions of the wheel. Estimating the global displacement of the binder-grit-workpiece system from the maximum envelope power spectra, we determine the plastic indentation of the workpiece at characteristic length scales using simple contact-mechanical calculation. The estimated roughness corresponds well with that recorded experimentally for hard steel, copper; titanium and aluminium.

Studies on grinding media wear and its effect on flotation of ferrugenous phosphate ore

Marked ball grinding rests were carried out in the laboratory with a low grade phosphate ore under different experimental conditions. Two types of balls were used, namely high carbon low alloy (HCLA) cast steel and high chrome cast iron. Results of marked ball grinding tests indicated that ball wear increased with time and showed a sharp increase for wet grinding over dry grinding. Ball wear under wet grinding conditions was also influenced by the gaseous atmosphere in the mill. The grinding ball materials could be arranged in the following order with respect to their overall wear resistance: High chrome cast iron > HCLA cast steel balls Methods to minimize ball wear through control of mill atmosphere and addition of flotation reagents are discussed. Effect of grinding media and additions of flotation reagents during grinding on phosphate ore flotation are also discussed. (C) 1999 Elsevier Science Ltd. All rights reserved.

Structure constants of beta deformed super Yang-Mills

We study the structure constants of the N = 1 beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS(5) x S-5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

Optimal control of grinding mill circuit using model predictive static programming: A new nonlinear MPC paradigm

The recently developed reference-command tracking version of model predictive static programming (MPSP) is successfully applied to a single-stage closed grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of model predictive control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, which can be viewed as a `new paradigm' under the nonlinear MPC philosophy, is compared to the performance of a standard nonlinear MPC technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and nonlinear MPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices and using a closed form expression to update the control. To alleviate the burden on the optimization procedure in standard MPC, the control horizon is normally restricted. However, in the MPSP technique the control horizon is extended to the prediction horizon with a minor increase in the computational time. Furthermore, the MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for online applications of the nonlinear MPC philosophy to real-world industrial process plants. (C) 2014 Elsevier Ltd. All rights reserved.

Yang-Mills theory in six-dimensional superspace

The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.

In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions.

N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed.

Virtual Sensors for On-line Wheel Wear and Part Roughness Measurement in the Grinding Process

Grinding is an advanced machining process for the manufacturing of valuable complex and accurate parts for high added value sectors such as aerospace, wind generation, etc. Due to the extremely severe conditions inside grinding machines, critical process variables such as part surface finish or grinding wheel wear cannot be easily and cheaply measured on-line. In this paper a virtual sensor for on-line monitoring of those variables is presented. The sensor is based on the modelling ability of Artificial Neural Networks (ANNs) for stochastic and non-linear processes such as grinding; the selected architecture is the Layer-Recurrent neural network. The sensor makes use of the relation between the variables to be measured and power consumption in the wheel spindle, which can be easily measured. A sensor calibration methodology is presented, and the levels of error that can be expected are discussed. Validation of the new sensor is carried out by comparing the sensor's results with actual measurements carried out in an industrial grinding machine. Results show excellent estimation performance for both wheel wear and surface roughness. In the case of wheel wear, the absolute error is within the range of microns (average value 32 mu m). In the case of surface finish, the absolute error is well below R-a 1 mu m (average value 0.32 mu m). The present approach can be easily generalized to other grinding operations.