Breakage function determination for HPGR

2019 ◽  
Author(s):  
Hernán Francisco Anticoi Sudzuki
Keyword(s):  
Breakage Function

A matrix analysis of processes involving particle assemblies

1956 ◽  
Vol 249 (960) ◽  
pp. 99-123 ◽  
Keyword(s):  
Particle Size ◽  
Matrix Analysis ◽  
Mathematical Form ◽  
Size Distributions ◽  
Ball Mills ◽  
Particle Assembly ◽  
Coal Particles ◽  
Breakage Function ◽  
Grinding Machine ◽  
Particle Assemblies

The processes analyzed in this paper are the size reduction and size classification of particle assemblies. Particle size distributions are described by vectors, and alterations to size distributions during breakage processes are described by matrices multiplying the vectors. The matrix approximation gives an adequate representation of the processes studied, and the manipulation of the matrices is easy and flexible. The breakage of a particle assembly is thought of as two processes. In the first, the machine breaking the particles is said to select for breakage a proportion of the particles, and the remaining particles are unbroken. To discover a function or matrix which describes the process of selection is to understand how the machine operates. In the second process, the particles selected are broken in a regular way; the proportions of particles of each size formed by the breakage are described by a breakage function or a breakage matrix. The analysis of breakage is in this way given convenient mathematical form. These matrices depend on the characteristics of the machine and on the nature of the particle assembly. After breaking the particles, crushing and grinding machines frequently pass the product assemblies to a classifier from which the larger particles are returned, mixed with fresh material, to the grinding zone. The analysis is extended to the description of such circuits. The experimental work reported concerns the breaking of coal particles in a new grinding machine, ball mills, shatter tests and a beater mill. The selection functions derived throw light on the operation of these machines. Coal breakage has been studied since it is an important field of application, and because coal is typical in breakage of homogeneous rocks. For each of the machines examined and for each particle size, a single breakage function has sufficed to describe the product of breakage: [1 —exp ( —z)]/[ 1 —exp ( — 1)] is the proportion of the product smaller than a fraction z of the original particle size.

On the breakage function for constructing the fragment replacement modes

Particuology ◽  
2019 ◽  
Vol 44 ◽  
pp. 207-217 ◽  
Author(s):  
Wei Zhou ◽  
Kun Xu ◽  
Gang Ma ◽  
Xiaolin Chang
Keyword(s):  
Breakage Function

Extending the Normalised Kumaraswamy Breakage Function for roller milling of wheat flour stocks to Second Break

2013 ◽  
Vol 237 ◽  
pp. 107-116 ◽  
Author(s):  
Fernán Mateos-Salvador ◽  
Jhuma Sadhukhan ◽  
Grant M. Campbell
Keyword(s):  
Wheat Flour ◽  
Breakage Function ◽  
Roller Milling

scholarly journals Investigation of Error Distribution in the Back-Calculation of Breakage Function Model Parameters via Nonlinear Programming

Minerals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 425
Author(s):  
Jihoe Kwon ◽  
Heechan Cho
Keyword(s):  
Flat Surface ◽  
Error Function ◽  
Model Parameters ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
Initial Values ◽  
Wide Range ◽  
Minimum Number ◽  
Breakage Function ◽  
Back Calculation

Despite its effectiveness in determining breakage function parameters (BFPs) for quantifying breakage characteristics in mineral grinding processes, the back-calculation method has limitations owing to the uncertainty regarding the distribution of the error function. In this work, using Korean uranium and molybdenum ores, we show that the limitation can be overcome by searching over a wide range of initial values based on the conjugate gradient method. We also visualized the distribution of the sum of squares of the error in the two-dimensional parameter space. The results showed that the error function was strictly convex, and the main problem in the back-calculation of the breakage functions was the flat surface of the objective function rather than the occurrence of local minima. Based on our results, we inferred that the flat surface problem could be significantly mitigated by searching over a wide range of initial values. Back-calculation using a wide range of initial values yields BFPs similar to those obtained from single-sized-feed breakage tests (SSFBTs) up to four-dimensional parameter spaces. Therefore, by searching over a wide range of initial values, the feasibility of the back-calculation approach can be significantly improved with a minimum number of SSFBTs.

The normalised Kumaraswamy breakage function: A simple model for wheat roller milling

2011 ◽  
Vol 208 (1) ◽  
pp. 144-157 ◽  
Author(s):  
Fernán Mateos-Salvador ◽  
Jhuma Sadhukhan ◽  
Grant M. Campbell
Keyword(s):  
Simple Model ◽  
Breakage Function ◽  
Roller Milling

The breakage function; What is it really?

1990 ◽  
Vol 3 (5) ◽  
pp. 405-414 ◽  
Author(s):  
E.G. Kelly ◽  
D.J. Spottiswood
Keyword(s):  
Breakage Function

scholarly journals Calibration and Validation of a Cone Crusher Model with Industrial Data

Minerals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1256
Author(s):  
Robson A. Duarte ◽  
André S. Yamashita ◽  
Moisés T. da Silva ◽  
Luciano P. Cota ◽  
Thiago A. M. Euzébio
Keyword(s):  
Least Squares Method ◽  
Operator Training ◽  
Industrial Data ◽  
Calibration And Validation ◽  
Calibration Problem ◽  
Breakage Function ◽  
Cone Crusher ◽  
Equipment Sizing ◽  
Strong Candidate ◽  
Validation Tests

This paper reports the calibration and validation of a cone crusher model using industrial data. Usually, there are three calibration parameters in the condensed breakage function; by contrast, in this work, every entry of the lower triangular breakage function matrix is considered a calibration parameter. The calibration problem is cast as an optimization problem based on the least squares method. The results show that the calibrated model is able to fit the validation datasets closely, as seen from the low values of the objective function. Another significant advantage of the proposed approach is that the model can be calibrated on data that are usually available from industrial operation; no additional laboratory tests are required. Calibration and validation tests on datasets collected from two different mines show that the calibrated model is a strong candidate for use in various dynamic simulation applications, such as control system design, equipment sizing, operator training, and optimization of crushing circuits.

Sign in / Sign up

Export Citation Format

Share Document