Tumbling Mill Research Articles

Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

The object of this study is the grinding process in a tumbling mill when the mechanism of destruction by abrasion is implemented, which is caused by the mechanism of shear loading. The abrasive effect due to the impulse interaction during the mutual chaotic movement of granular particles in the shear layer of loading, characterized by the granular temperature, is taken into account. The task solved was determining the parameters of the shear interaction, which is caused by the difficulties of modeling and complexity of the hardware analysis of behavior of the internal loading in the mill. A mathematical model was built based on data visualization for the abrasion grinding mechanism. The power of the shear interaction forces was taken as an analog of the grinding performance. The initial shear characteristic was considered to be the average value of the shear velocity gradient in the central averaged normal section of the shear layer. The impact on productivity of the granular temperature and mass fraction of the shear layer and loading turnover was taken into account. The effect of rotation speed on performance was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative particle size of 0.0104. The maximum value of the energy and productivity of grinding by abrasion was established at the relative speed of rotation ψω=0.55–0.6. The results have made it possible to establish a rational speed when grinding by abrasion, ψω=0.5–0.6. This value is smaller in comparison with grinding by crushing ψω=0.55–0.65 and breaking ψω=0.75–0.9. The established effect is explained by the detected activation of the chaotic quasi-thermodynamic movement of particles of the shear layer at slow rotation. The model built makes it possible to predict rational technological parameters of the energy-saving process of fine grinding in a tumbling mill by abrasion

Correction: Liao et al. A Comparison of the Fine-Grinding Performance between Cylpebs and Ceramic Balls in the Wet Tumbling Mill. Minerals 2022, 12, 1007

In the original publication [...]

Building a model of the compression grinding mechanism in a tumbling mill based on data visualization

The object of the study reported here is the grinding process in a tumbling mill where the mechanism of destruction by crushing is implemented, which is caused by the mechanism of compression loading. The compressive interaction in the active zone of the lower end of the granular loading chamber of the rotating drum at the transition of the shear layer to the solid zone was taken into account. The task to determine the parameters of the compressive action was solved, which was caused by the difficulties of modeling and the complexity of the hardware analysis of the behavior of the internal loading of the mill. A mathematical model was built based on data visualization for the compression grinding mechanism. The power of compressive forces was taken as an analog of grinding performance. The initial characteristic of compression was considered to be the mean speed of movement in the central averaged normal cross-section of the shear layer. The influence on the performance of the mass fraction of the shear layer and the reversibility of loading was taken into account. The effect of rotation speed on productivity was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative size of grinding bodies of 0.0104. The maximum value of energy and grinding productivity was established at a relative speed of rotation ψω=0.6–0.65. The maximum value of the share of the shear layer loading was found at ψω=0.4–0.45. The results have made it possible to establish a rational speed during crushing by compression, ψω=0.55–0.65. This value was smaller in comparison with impact crushing, ψω=0.75–0.9. The observed effect is explained by the detected activation for the shear loading layer during slow rotation, in contrast to the fast rotation for the drop zone. The model built makes it possible to predict rational technological parameters of the process of medium and fine grinding in a tumbling mill by compression.

Building a model of the impact grinding mechanism in a tumbling mill based on data visualization

A mathematical model was built based on data visualization for the impact grinding mechanism in a tumbling mill, which is mainly implemented during coarse grinding. The determination of impulse interaction parameters is problematic due to the difficulty of modeling and the complexity of hardware analysis of the behavior of intramill loading. Conceptually, it was envisaged to identify the relative dynamic parameters of the impact action as components of the model, which are criteria for the similarity of the loading movement and the grinding process. Impact power was taken as an analog of grinding performance. The initial characteristic of the impact was considered to be the averaged vertical component of the speed of loading movement in the flight zone at the boundary of contact with the shear layer. The formalization of the model revealed the effect on the performance of the mass fraction of the flight zone and the reversibility of loading. The method of numerical modeling was applied, based on experimental visualization of the behavior of granular loading in the cross section of a rotating chamber. The influence of the rotation speed on the performance at a chamber filling degree of 0.45 and a relative particle size of a milling load of 0.0104 was estimated by experimental simulation. The maximum productivity value was found at the relative speed of rotation ψω=1–1.05. A rational condition for impact grinding at ψω=0.75–0.9 has been established. The test proved the effectiveness of using visualization to evaluate dynamic loading interaction analogs. Verification of modeling results was implemented by comparison with the data of the technical standard. The use of similarity criteria unifies approaches to modeling different mechanisms of destruction. The model built makes it possible to predict the rational parameters of the grinding processes by impact, crushing, and abrasion

Impact and Abrasion Power Modeling of a Tumbling Mill for Control Design

In this research, the model of the net power draw of a tumbling mill is proposed, which is described considering the contribution of the impact power and the abrasion power separately. Nowadays, in phenomenological models used in mill control design, the net power draw in the grinding of the mineral is not described by a dynamic representation (but by experimental formulation); therefore, the validity of the model thus obtained is restricted to a given operating condition. The proposed model describes the dynamics of the impact power and the abrasion power through variables and parameters that depend on the operating conditions, therefore this model is obtained for a whole range of operation, also it is represented in the state space, which will facilitate the control design task of the milling process. Finally, simulation tests were carried out for a tumbling mill using the proposed approach.

Can ceramic balls and steel balls be combined in an industrial tumbling mill?

Recent research contends that ceramic balls significantly reduce energy consumption in industrial tumbling mills. In this work, the binary media method is proposed to enhance ceramic ball grinding performance. Specifically, when feed ore hardness is high and the ceramic ball grinding effect on coarse minerals degrades, a certain proportion of steel balls mixed with ceramic balls needs to be added. The results demonstrated that mixing ceramic and steel balls can improve the grinding of coarse particles, offering grinding results that are nearly equal to those of grinding with only steel balls. Furthermore, the binary media method has considerable energy-saving benefits. According to statistical findings, binary media has less media wear than steel balls when grinding, and its energy consumption is just 49% of that of steel balls at the same throughput. • Proposing the Binary Media Method for perfecting ceramic ball grinding. • Conducting industrial tests to verify the feasibility of the Binary Media Method. • Comparing the grinding effect of steel balls, ceramic balls, and binary media.

A Comparison of the Fine-Grinding Performance between Cylpebs and Ceramic Balls in the Wet Tumbling Mill

This study investigated the effect of grinding media on the fine-grinding performance in the wet tumbling mill. Comparative experiments between cylpebs and ceramic balls were conducted in a laboratory wet ball mill under various conditions, such as different total masses, total surface areas, and total numbers. The results indicated that ceramic balls produce a slightly smaller instantaneous breakage rate than cylpebs due to their small bulk density at the same charge volume. However, a larger instantaneous breakage rate can be obtained by ceramic balls with the same total mass due to the larger surface area. According to experiments related to the total surface area and total number of ceramic balls, it was found that the fine grinding of ceramic balls also needs to meet a certain break force, which is mainly determined by the diameter of the ceramic balls. Moreover, two models were developed to use ceramic balls instead of cylpebs as fine-grinding media in the wet tumbling mill based on the ball size and the ratio of the total mass of cylpebs. Cylpebs can be replaced by ceramic balls with 1.16–1.75 times the diameter of cylpebs, taking up only 76%–83% of the total weight of cylpebs. When the charge volume of cylpebs is between 20% and 35% in the wet ball mill, cylpebs can be replaced by ceramic balls of the same single mass, with the total weight of the ceramic balls being only 74%–77% of that of the cylpebs.

The first attempt of applying ceramic balls in industrial tumbling mill: A case study

In mineral processing, ceramic balls have first been applied in secondary mill of the two-stage grinding circuit, showing great positive effect on the grinding process. This study evaluated the impact of replacing steel cylpebs with ceramic balls on the grinding effect, circulating load, classification effect, and the change of the particle size distribution and the distribution of valuable mineral (tungsten) in grinding products. The results obtained indicated that the particle size distribution of grinding products has been obviously improved, creating a reduction not only in the overall particle size, but also in the phenomenon of overgrinding (10 μm). Reflected in the final product, the distribution of tungsten in the range of −74 + 10 μm increased, while the distribution of that in the range of −10 μm decreased. This is largely to the larger specific surface area created by ceramic balls in comparison with the steel cylpebs. Additionally, it is observed that circulating load was reduced by one-third, and the classification effect has been improved in secondary grinding circuit. According to the verification of grinding circuit model, the results revealed that the decrease of circulating load and the increase of classification effect is direct related to the improvement of grinding effect, and also presented that the secondary mill now has more reserved space for grinding based on the difference of relative capacity of the two media. Furthermore, it is worth mentioning that the application of ceramic balls in tumbling mill is exceedingly economic, given that the power consumption of the tumbling mill has been reduced by 38.5%, and the wear consumption of the grinding media by 60%.

The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number

The influence of the filling degree of the drum chamber on the bifurcation value of the Froude number in the case of self-excitation of self-oscillations of a two-fraction granular charge with a minimum swing is considered. Such a pulsating mode of the charge movement is used in the self-oscillating grinding process in a tumbling mill. The coarse fraction that simulated the milling bodies consisted of spherical particles of an incoherent granular material with a relative size in the chamber ψb=0.00733. The fine fraction, simulating the material to be ground, was cement with a relative particle size ψm≈0.092∙10-3. The value of the adopted analogue of the kinematic viscosity of the two-fraction granular loading approached the value of 10-3 m2/s. The main variable factor in experimental studies was the filling degree of the drum chamber with loading at rest κb=0.25, 0.35, and 0.45. An additional factor was the degree of filling the gaps between the spherical particles of the coarse fraction with particles of the fine fraction κb=0, 0.25, 0.5, and 1. The method of visual analysis through the transparent end wall of the chamber of transient processes of the loading behavior with a smooth change and fixation of the velocity was applied. The bifurcation minimum value of the rotation speed was recorded, at which the steady-state circulation mode of the load movement turns into a transient pulsation one with a minimum swing. A decrease in the bifurcation values of the Froude number Frb on the cylindrical surface of the chamber with an increase in κb has been established. An increase in the intensity of the decrease in Frb with an increase in κm was revealed. The recorded effect is due to an increase in the connected properties of a two-fraction loading during self-excitation of self-excited oscillations with an increase in κb and κm. The numerical values of the boundaries of the range of bifurcation values of the Froude number for a tumbling mill Frb=0.0484–1.17 have been determined. The obtained Frb range corresponds to the Reynolds value in the range Re=40–197. The maximum Frb value is obtained with coarse grinding. An increase in the likelihood of self-excitation of self-oscillations of the intra-chamber loading with a decrease in the fineness of grinding was revealed

A consolidated summary on the evolution of a dynamic tumbling mill model

A mechanistic model for tumbling mills was developed based on breakage characteristics and tumbling mill operational features. The concept was presented at the IMPC (International Mineral Processing Congress) 2014, followed by progress in a sub-process of the model presented at the IMPC 2016. Additionally, a number of papers on the sub-models and breakage function have been published. This paper provides a consolidated summary of the outcomes and status of the model. The overall model structure is presented along with the sub-models such as appearance functions, breakage rate functions, energy distribution, transport, and dual component grinding interaction model. The strengths and capabilities of the model structure as achieved to date are presented.The approach developed can be used as a platform for building multicomponent models. The modelling work can be done quicker by using an existing structure such as the one presented in this paper. It is recommended that researchers assess compatibility prior to embarking on model development work if the intention is to use this model structure.

Establishing the effect of a simultaneous reduction in the filling load inside a chamber and in the content of the crushed material on the energy intensity of self-oscillatory grinding in a tumbling mill

The effect of a simultaneous change in the degree of filling a chamber with load κbr and in the content of the crushed material κmbgr on the efficiency of the self-oscillatory grinding process has been estimated.
 Using a method of numerical modeling based on the results of experimental visualization of the flow has helped establish an emergent dynamic effect of the sharp increase in the self-oscillatory action of two-faction loading at a joint reduction in κbr and κmbgr. A significant decrease in the passive quasi-solid loading motion zone has been detected, as well as an increase in the active pulsation zone and a growth of dilatancy. The manifestation of the effect is enhanced by the simultaneous interaction of increasing the scope of self-oscillations and weakening the coherent properties of particles in a loose large fraction under the influence of the particles of fine fraction. A significant decrease in the values of the inertial loading parameters has been established: maximum dilatancy υmax, the relative scale of self-oscillations ψRυ, the maximum share of the active part of κfammax, and the generalized complex degree of dynamic activation Ka. A 2.65-time growth of υmax was detected, ψRυ increased by 5 times, κfammax ‒ by 4.36 times, Ka ‒ by 18.4 times, at a joint decrease in κbr from 0.45 to 0.25, in κmbgr ‒ from 1 to 0.
 The synergistic technological effect of a sharp decrease in the specific energy intensity Еo/Еs has been established, as well as an increase in the relative performance Co/Cs in the self-oscillatory grinding, due to a significant increase in the dynamic action of loading, which is exacerbated by the joint interaction of reduced κbr and κmbgr.
 The process of the self-oscillatory grinding of cement clinker has been investigated. A 62 % reduction in Еo/Еs and a 125 % increase in Co/Cs were detected at a joint decrease in κbr from 0.45 to 0.25, in κmbgr ‒ from 1 to 0.125.
 The established effects make it possible to substantiate the parameters for the energy-efficient self-oscillatory process of grinding in tumbling mills with a conventional structure

ESTABLISHING THE ROTATION SPEED VARIATION RANGE LIMITS FOR AUTO-EXCITATION OF SELF-OSCILLATING GRINDING IN A TUMBLING MILL

The influence of the structure of a two-fraction polygranular feed of the chamber on the value of the drum rotation speed at auto-excitation of self-excited oscillations with a maximum swing is considered. Such a pulsating mode of movement of the charge is used in the self-oscillating process of grinding in a tumbling mill. The coarse fraction simulated the grinding bodies was steel bullets with a relative size ψdb=0.026. The fine fraction, simulated the particles of the crushed material, was a cement clinker with a relative particle size ψdm=0.00013. Variable factors of experimental studies were: the degree of filling the chamber in the state of rest κbr=0.25; 0.29; 0.33 and the degree of filling the gaps between the particles of the coarse fraction with particles of the fine fraction κmbgr=0.0625; 0.375; 0.6875; 1. The method of visual analysis of transient processes of self-oscillating modes of feed behavior in the cross section of the rotating drum chamber is applied. Measurements of the speed limits of the drum rotation were carried out with auto-excitation of self-oscillations of the filling. The magnitude of the self-oscillation swing was estimated by the increase in the difference between the maximum and minimum values of the filling dilatancy for one period of pulsations. An increase in the upper limit of the speed range ψω2 with a decrease in κbr and κmbgr was established. The growth rate of ψω2 increases at low values of κbr and κmbgr. Some increase in the lower limit of the ψω1 range with a decrease in κbr and κmbgr was revealed. An increase in the range of speeds of rotation was recorded at the maximum range of self-oscillations ψω1–ψω2 with a decrease in the connected interaction of the intra-mill filling. This coherent interaction is due to an increase in κbr and κmbgr. The value of the ψω1–ψω2 range varies from 1.01–1.03 at κbr=0.33 and κmbg=1 to 1.22–1.66 at κbr=0.25 and κmbgr=0.0625. The range gets its maximum value with fine and superfine grinding

Ball-impact energy analysis of wet tumbling mill using a modified discrete element method considering the velocity dependence of friction coefficient

A modified three-dimensional quasi-wet discrete element method (DEM), which is constructed by adding the drag force and buoyancy and the velocity dependence of the friction coefficient of a ball to a conventional dry DEM model, is proposed for analyzing the impact energy of balls in wet ball-milling processes. A comparison of the calculated ball motion in water as the liquid medium with the experimental results demonstrated the validity of the proposed model. The friction coefficient decreased with the increase in the vessel rotational speed and was expressed as a function of the rotational speed and loading amount of the balls. The velocity dependence of the friction coefficient was similar to the variation in the friction coefficient with the sliding velocity, as derived from the lubrication theory. A numerical analysis of the impact energy distribution in the vessel showed that relatively high-impact energies of the balls were intensively generated near the vessel wall, indicating that the wet ball-milling processes were controlled by the impact energy between the ball and the wall. Our model can contribute to reducing the calculation load for simulating the ball motion in wet ball-milling processes compared with the coupling models such as DEM-CFD.

Establishing the effect of decreased power intensity of self-oscillatory grinding in a tumbling mill when the crushed material content in the intra-chamber fill is reduced

The influence of the content of crushed material in the intra-chamber grinding fill on the efficiency of the self-oscillatory grinding process in the tumbling mill was assessed. A dynamic effect of a significant decrease in self-oscillatory action of the two-fraction fill of the rotary chamber with an increase in the content of fine fraction was revealed by the method of visual analysis of motion patterns. A decrease in values of the following inertial fill parameters was established: maximum dilatancy υ max , the relative amplitude of self-oscillations ψ Rυ and a maximum share of the active part κ fam max with an increase in the degree of filling the gaps between particles of the coarse fraction κ mbgr . A decrease in the generalized complex degree of dynamic activation K a was also established. The effect is due to the strengthening of the cohesive properties of the incoherent coarse fraction under the influence of the fine fraction. There was a decrease in by 29 % for υ max, by 7 % for ψ Rυ , 2.9 times for κ fam max and 4.2 times for K a with an increase in κ mbgr from 0 to 1 at the degree of filling the chamber with the fill κ br =0.45. Technological effect of a significant decrease in specific energy intensity and an increase in productivity of the innovative self-oscillatory grinding process in comparison with characteristics of the conventional steady-state process at a decrease in the content of crushed material in the fill was established. A process of milling cement clinker with grinding bodies at relative size of 0.026 and κ br =0.45 was considered. A decrease in specific energy intensity by 27 % at κ mbgr =1, by 38 % at κ mbgr =0.5625 and by 44 % at κ mbgr =0 was found. An increase in relative productivity by 7 % at κ mbgr =1, by 26 % at κ mbgr =0.5625 and by 39 % at κ mbgr =0.125 was established. The established effects will make it possible to forecast rational parameters of the self-oscillatory grinding process in a tumbling mill at the variation of the content of the crushed material in the fill

THE DRUM ROTATION VELOCITY VALUE WHEN AUTO-OSCILLATION SELF-EXCITATION WITH MAXIMUM SWING OF A POLYGRANULAR INTRACHAMBER FILL

The influences of the structure of two-fractional polygranular intrachamber fill on the drum rotation velocity value when auto-oscillation self-excitation with maximum swing is considered. The pulsating mode of flow of such intrachamber fill is used in the self-oscillating grinding process in a tumbling mill. Spherical particles of non-coherent granular material of 2.2 mm size were used as a large fraction modeling the grinding bodies. Cement was used as the small fraction modeling the particles of the crushed material. The factors of experimental studies were accepted: the gaps between particles of large fraction degree of filling at rest dispersed particles of small fraction 0, 25, 50 and 100%, the relative size of particles of large fraction in the drum chamber 0.519, 0.733, 1.04, 1.47, 2.08, 2.93, 4.15 and 5.87% (drum chamber radius 212, 150, 106, 75, 53, 37.5, 26.5 and 18.75 mm), the chamber degree of filling at rest 25, 35 and 45%. The method of visual analysis of transient processes of self-oscillating fill flow modes in the cross section of a rotating chamber was applied. Measurements of the drum rotation velocity during fill self-excited self-oscillations were performed. The magnitude of the self-oscillation swing was estimated by the increase in the difference of the maximum and minimum values of the fill dilatation over one period of pulsating. The magnitude of the relative drum rotation velocity at the maximum range of fill self-oscillation swing varied within 0.777-1.4. The effect of a decrease in the relative drum rotation velocity value, when the maximum polygranular intrachamber fill self-oscillations swing, with enhanced fill coherent properties has been registered. A decrease in the relative rotational velocity was established with a decrease in the relative particle size of large fill fraction and an increase in the content of small fill fraction and an increase in the chamber degree of filling. A sharp intensification of the decrease in the relative rotation velocity at a value of the relative size of large particles of less than 0.015 is revealed.

Determining a lower boundary of elasticity modulus used in the discrete element method (DEM) in simulation of tumbling mills

Discrete Element Method (DEM) simulations of industrial tumbling mills could involve millions of particles. Even with the considerable increase in the computational power, the simulations still require a large amount of time. Reducing the computational load by selecting a small value for the particle elasticity modulus to increase the time step has become a common approach. As the elasticity modulus decreases, the overlap required to provide the rebound force increases. The appropriate value of overlap is application-dependent and requires a detailed study to ascertain that the accuracy of the results do not adversely affected. In this study, a relationship incorporating particle density and mill diameter was proposed between the elasticity modulus and the interparticle overlap for tumbling mills. The effect of interparticle overlap on the accuracy of the simulated charge shape (i.e. toe and shoulder positions) by DEM was then investigated. A model tumbling mill (100 cm by 21 cm) with a transparent end wall was used to measure the actual charge trajectory by photography. A comparison of the DEM simulations with the model mill charge shape showed that when the overlap was assumed to be lower than the particle radius, the error was negligible. When the interparticle overlap became equal to the particle radius, the lower boundary of elasticity modulus and the maximum simulation speed was achieved. The speed was 102 times of the speed of simulation when an overlap equal to 0.01 of the particle radius was chosen.

INFLUENCE OF SMALL FRACTION OF POLYGRANULAR FILL OF ROTATING DRUM ON SELF-OSCILLATION SWING

The influence of the structure of two-fractional polygranular fill of a rotating drum on the self-oscillation swing is considered. The pulsating mode of flow of such intrachamber fill is used in the self-oscillating grinding process in a tumbling mill. Spherical particles of non-coherent granular material of 2.2 mm size were used as a large fraction modeling the grinding bodies. Cement was used as the small fraction modeling the particles of the crushed material. The factors of experimental studies were accepted: the gaps between particles of large fraction degree of filling at rest dispersed particles of small fraction 0, 25, 50 and 100%, the relative size of particles of large fraction in the drum chamber 0.519, 0.733, 1.04, 1.47, 2.08, 2.93, 4.15 and 5.87% (drum chamber radius 212, 150, 106, 75, 53, 37.5, 26.5 and 18.75 mm), the chamber degree of filling at rest 25, 35 and 45%. The method of visual analysis of fill motion patterns in the cross section of a rotating chamber and measurement of dilatation was applied.Video of the fill pulsating flow was taken. The magnitude of the self-oscillation swing was estimated by the increase in the difference of the maximum and minimum values of the fill dilatation over one period of pulsating. The maximum range of self-oscillation swing reached the value of 1.36. The change of the self-oscillation swing from zero at the beginning of self-excitation of pulsations to the maximum value with the greatest increase of dilatation was revealed. The effect of a decrease in the maximum range of self-oscillation swing with enhanced fill coherent properties has been registered. The attenuation of the spray of particles of large fraction in the chamber due to the coherent effect of the small fraction was established. An increase in the self-oscillation swing of single-grain fill was found with a decrease in the relative particle size and the chamber degree of filling. A decrease in the self-oscillation swing of two-fractional fill was found with an increase in the content of small fraction, a decrease in the relative size of particles of a large fraction, and an increase in the chamber degree of filling.

Establishing the effect of a decrease in power intensity of self-oscillating grinding in a tumbling mill with a reduction in an intrachamber fill

Effect of the degree of chamber filling with the charge on efficiency of the self-oscillating grinding process in a tumbling mill has been assessed.By using the approximate analytical and experimental method, dynamic effect of increasing the self-oscillating impact action of grinding fill on the crushed material was compared with the conventional steady-state motion mode. A significant increase in average sums of vertical components of the self-oscillating collision momenta and the average sums of power of such components with a decrease in the chamber filling degree was found. Manifestation of this effect is due to the increase in the self-oscillations swing with decreasing filling. An increase in the maximum momentum values was found to be approximately 2.4 times at the degree of filling κ=0.45, 3.1 times at κ=0.35 and 5.8 times at κ=0.25. An increase by 5.7 times in maximum values of momentum power was found at κ=0.45, by 9.6 times at κ=0.35 and by 45.5 times at κ=0.25.Technological effect of significant decrease in the specific power intensity and productivity growth of the innovative self-oscillating grinding process as compared to the characteristics of the conventional steady-state process with a reduction in the chamber filling degree have been experimentally established.The process of grinding cement clinker with a complete filling of gaps between spherical grinding bodies with a relative size of 0.026 with particles of the crushed material was considered. It was found that during excitation of self-oscillations, power intensity of grinding decreased and productivity increased. A decrease in relative specific power intensity was observed: 27 % at κ=0.45, 42% at κ=0.35 and 55 % at κ=0.25. A 7 % increase in relative productivity was found at κ=0.45, 30 % at κ=0.35, and 46 % at κ=0.25.The effects established in operation have allowed us to predict rational parameters of the self-oscillating grinding process carried out in a tumbling mill with variation in the chamber filling degree

Geometric features of tumbling mill flows: A positron emission particle tracking investigation

Positron emission particle tracking (PEPT) allows for the in situ tracking of particles (rocks, balls, slurry) in experimental tumbling mills. For sufficiently long tracking times, the trajectory fields can be cast into time averages per unit volume of kinematic and dynamical information which constitute the key ingredients for fundamental modelling of tumbling mills. Central to this objective is the accurate delineation of geometric features making up the tumbling mill in the azimuthal plane. To this end, algorithms for extracting bulk features of the media (free surface, equilibrium surface, centre of circulation, toe and shoulder positions) are presented. These algorithms are then employed to compare results from dry, batch experiments spanning a wide range of mill speeds, lifter heights and lifter angles.

Revealing the effect of decreased energy intensity of grinding in a tumbling mill during self-excitation of auto-oscillations of the intrachamber fill

We have investigated a possibility to perform comparative evaluation of the effectiveness of grinding process in a tumbling mill under conventional steady and self-excited auto-oscillatory flow modes of the intrachamber fill. A mathematical model for the parameters of impact influence of the milling fill on the ground material has been constructed. We applied an analytical-experimental method to visually analyze flow patterns in the cross-section of a rotating chamber. Numerically, by using approximate procedures, we have established a dynamic effect of increasing mean sums of vertical components in impact pulses and mean sums of power of such components at self-excitation of auto-oscillations. The technological effect has been experimentally established of a significant decrease in energy intensity and a certain increase in productivity of the identified self-oscillatory grinding process, compared with the characteristics of conventional steady-state process. This involved a sieve analysis of the ground product, as well as measuring the fill flow turnover and the power of a drum rotation drive. The example considered was the process of grinding cement clinker at a degree of filling the chamber with a fill of 0.45, at a relative size of ball grinding elements of 0.026, while the gaps between grinding bodies were completely filled with the ground material. It was established that at auto-oscillation self-excitation the grinding energy intensity reduces by 27.2 %, while performance increases by 6.7 %. The effects established in this work make it possible to predict the rational parameters for aself-oscillatory process of grinding in a tumbling mill