Qualitative and Experimental Analysis of Ball Mill Shell Vibration Production Mechanism

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Communications in Control Science and Engineering (CCSE) Volume 3, 2015

Qualitative and Experimental Analysis of Ball Mill Shell Vibration Production Mechanism Jian Tang*1,2,a, ZhuoLiu2,b, Zhiwei Wu2,b, Xiaojie Zhou2,c Research Institute of Computing Technology, Beifang Jiaotong University, Beijing, China

1

State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China

2

powernature@126.com; bzhuoliu_mail@neu.edu.cn; czwwu_mail@neu.edu.cn; dxj_zhou@neu.edu.cn

*a

Abstract Ball mill is a type of rotating heavy mechanical device in grinding process with characteristics of continuous running and closing working. Its load parameters have direct relation with production quality and grinding process safety. Strong shell vibration and acoustic signals are normally used to measure ball mill load. However, multi-component and non-stationary characteristics of these signals are very difficult to be explained under different grinding conditions. In this paper, an integrated analysis method is given out. It is based on the qualitative production mechanism analysis of the shell vibration production and ensemble empirical mode decomposion results to a laboratory-scale ball mill vibration signals with certain domain expert experiences. Results show that the quanlitative analysis conclusion is consistent with the experimental decomposition results.

This research makes a foundation for accurately quatitative and mathematical simulation of the shell vibration production mechanism. Further, it is valuable to construct soft sensing mode with clear interpretation and high prediction accuracy.

Keywords Vibration Production Mechanism; Quanlitative Analysis; Ensemble Empirical Mode Decomposion; Ball Mill

Introduction Ball mill is a type of widely used heavy rotating mechanical devices. Accurate measure load parameters within ball mill on time is important for ensuring safety, product quality and quantity of mineral grinding process. Numerous approaches have been used to address this issue. These methods include: direct measuring approach using Sensomag instrument [1], mathematical calculation approach based on first principal model; load status identification approach based on expert experiences; indirect data-driven soft measuring approaches based on mill shell vibration and acoustic signals [2,3], or based on mill shaft vibration signal and other measured process variables [4]. Recently, the indirect data-driven soft measuring method based on mill shell vibration has been a new focus. However, detailed production mechanism of the mill shell vibration and reasonable interpretation of these soft sensor models are far more understand.

In practice, millions of balls inside the ball mill arrange hierarchically. Impact forces and periods of different layers’ balls to mill shell are different, which cause strong mechanical vibration. Shell vibration is the main source of the acoustical signal. Thus, shell vibration and acoustic signals have characteristics of non-stationarity and multicomponent. The shell vibration signals under different grinding conditions have different characteristics. Discrete element method has been widely used in dry ball mill (only ball and material in the mill), which has also been used to analyse shell vibration of the dry mill. However, most of the mathematical simulation models aren’t suitable for wet ball mill (ball, material and water load in the mill) [5]. Empirical mode decomposition (EMD) can adaptively decompose the original signal into some intrinsic mode functions (IMFs) from high frequency to low frequency orderly. Newly proposed ensemble EMD (EEMD) can overcome the mode-mixing problem of EMD. Thus, the shell vibration signal can be decomposed into sub-signals adaptively.

Motivated by the above problems, the qualitative production mechanism analysis of the mill shell vibration and EEMD decomposition results of a laboratory-scale ball mill vibration signal is given out. After integrated with certain domain experts’ experience, some reasonable conclusions are obtained.

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Qualitative Analysis of the Shell Vibration Production Mechanism Comminution of the mineral load mainly relies on cyclical movement of the ball load. Motion track of the ball can be divided into ascending and falling phases. In the ascending phase, the ball ascends from the dropping point Bshell to leaving point A with a circular track following rotation of the mill shell. In the falling phase, the ball falls from the leaving point A to dropping point Bshell with a parabolic trajectory. The motion of the ball can be divided into four parts: falling, impact, grinding and sliding. Therefore, the mill shell is impacted by a variety of forces. In grinding process of the wet ball mill, motion of the ball is also affected by buoyancy and viscous effection of the mineral pulp. Thus, impact and strip grinding forces are affected, whose energy at Bshell can be calculated:

EV 

1 ' 1 4 3 Lbs V 2  (Lbs   [( Rbs   )3  Rbs ]  m )  [ bwet ( , mb , mw , bmw )  V n ]2 2 2 3

(1)

EV 

1 ' 1 4 3 Lbs V 2  ( Lbs   [( Rbs   )3  Rbs ]  m )  [ bwet ( , mb , mw , bmw ) V t ]2 2 2 3

(2)

n

n

nwet

twet

where,  is the coating thickness of the ball;  bwet is an unknown nonlinear function;  is the viscosity of the mineral pulp; L bs and Rbs are the ball’s mass and radius. Based on momentum theorem, impact force of the outmost (first) layer ball at Bshell can be denoted as Fb . Therefore, impact force to Bshell can be represented as: 1stlayer Fbmw  bmwf ( ,  , mw , Top , mb , bmw )  Fb

(3)

where,  bmwf is an unknown nonlinearity function; Top is the temperature of mineral pulp. Normally, mill shell and its inside liners can be looked as a uniform shell. Only considering the radial deformation, its radial acceleration ( xVt )1stlayer can be represented as: 1stlayer ( xVt )1stlayer  a [M wet ( Bshell ), Cwet ( Bshell ), K wet ( Bshell ), Fbmw ]

a

where,

is

an

unknown

Cwet ( Bshell )  CB ( Lm, Lb , Lw ) and Kwet ( Bshell )   KB ( Lm, Lb , Lw )

nonlinear represent

(4)

function; the

mass,

M wet ( Bshell )

damping

and

,

stiffness

characteristics of the ball mill shell mechanical vibration system, respectively. During one ball mill rotating period, impact forces of the outmost layer (the first layer) load to Bshell point can be represented as: istlayer (Fbmw )period  [( Fbmw )1stlayer ,...,( Fbmw )1stlayer ,...,( Fbmw )1stlayer ,...,( Fbmw )1stlayer ,...,( Fbmw )1stlayer ,...,( Fbmw )1stlayer ,...] i1 in g1 gm s1 s1

(5)

where, ( Fbmw )1stlayer , ( Fbmw )1stlayer and ( Fbmw )1stlayer are the impact forces at different grinding phases, such that in s1 gm impact, grinding and sliding phases. These forces have different impact amplitudes and frequencies. Thus, the st

1 layer shell vibration sub-singals caused by ( Fbmw )period is denoted as: t 1stlayer (xVt )1stlayer ,...,( xVt )1stlayer ,...,( xVt )1stlayer ,...,( xVt )1stlayer ,...,( xVt )1stlayer ,...,( xVt )1stlayer ,...,] period  [( xV )i1 in g1 gm s1 sl

(6)

In practice, there are a large number of balls inside the mill. These balls are layered. Balls in different layers are thrown down at the same time with different impact forces. The hardness, particle distribution and other properties of the material load also affect the impact force. In some grinding conditions, the impact forces are difficult to descript. These impact forces with different amplitudes and frequencies overlay each other. Moreover, mass un-balance and installment bias of the ball mill, and other reasons can also stir up the shell vibration. These sub-signals are coupled and layered together. Thus, the shell vibration signal can be represented as: t 2ndlayer t 3rdlayer t millself xVt  (xVt )1stlayer  (xVt )install  (xVt )others ... period  (x V ) period  (x V ) period ,..., (x V )

JV

  x tj jV 1

V

(7)

t 2ndlayer where, x tj and J V are the jV th component and the number of multi-component; (xVt )1stlayer , (xVt )3rdlayer period , period , (xV ) period V

(xVt )millself

, (xVt )install and (xVt )others are the components caused by the first layer balls, the second layer balls, the third

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Communications in Control Science and Engineering (CCSE) Volume 3, 2015

layer balls, mass un-balance, installment bias and other reasons.

Ensemble Empirical Mode Decomposion of the Experimental Shell Vibration Signal The experiments were performed on a laboratory scale ball mill. The copper ore was crushed to about less than 6 mm before used. The diameters of the steel balls are 30, 20 and 15 mm respectively. The vibration signal was picked up by accelerometer located on the middle of the mill shell with a sampling frequency of 51,200 Hz. Experiments under three different grinding conditions are carried out, which include: (1) Mill was operated with ball-only load (zero mill); (2) Mill was operated with ball and mineral load (dry mill); and (3) Mill was operated with ball, water and mineral load (wet mill).

Zero load

The mill load under different grinding conditions are: zero mill with only small ball load 40Kg, dry mill with mineral load 30Kg and ball load 40Kg, and wet mill with mineral load 30Kg, water load 5Kg and ball load 40kg.

Shell vibration data of the mill rotating four periods are decomposed into 17 IMFs using EEMD with noise amplitude 0.1 and ensemble number 10. In order to compare with the above four grinding conditions, zero load (without any load in the mill) experiments are also carried out in this studies. The results are shown in Figs. 1 and 2.

1th IMF 2 0 -2

0

2th IMF

1

2

2 0 -2

0

5

Zero mill

0

1

2

20 0 -20

0

5

0

1

2

1

Dry mill Wet mill

1

2

2 0 -2

0

1

2

10 0 -10

0

2

0

1

2

1

0

2

1 0 -1

0

1

2

5 0 -5

0

1

2

1

0

2

0.5 0 -0.5

0

1

2

5 0 -5

0

1

2

1

0

2

0.2 0 -0.2

0

1

2

2 0 -2

0

1

2

1

0

2

0.5 0 -0.5

0

1

2

1 0 -1

0

1

2

1

0

2

0.5 0 -0.5

0

1

2

1 0 -1

0

0

1

2

1

2 5

x 10 8th IMF 0.1 0 -0.1

0

5

1

2 5

x 10 8th IMF 0.1 0 -0.1

0

1

5

x 10

2 5

x 10 7th IMF 0.5 0 -0.5

1 x 10 8th IMF

5

5

x 10

2

x 10 7th IMF

5

0

1

5

x 10 6th IMF 0.5 0 -0.5

8th IMF 0.1 0 -0.1

x 10 7th IMF

5

5

x 10

2

x 10 6th IMF

5

0

1

5

x 10 5th IMF 0.5 0 -0.5

7th IMF 0.2 0 -0.2

x 10 6th IMF

5

5

x 10

2

x 10 5th IMF

5

0

1

5

x 10 4th IMF 1 0 -1

6th IMF 0.5 0 -0.5

x 10 5th IMF

5

5

x 10

2

x 10 4th IMF

5

0

1

5

x 10 3th IMF 2 0 -2

5th IMF 0.5 0 -0.5

x 10 4th IMF

5

5

x 10

2

x 10 3th IMF

5

5

1

5

x 10 2th IMF 5 0 -5

4th IMF 0.5 0 -0.5

x 10 3th IMF

5

5

0

0

x 10 2th IMF

x 10 1th IMF 5 0 -5

2

x 10 2th IMF

x 10 1th IMF 2 0 -2

1

5

x 10 1th IMF 50 0 -50

3th IMF 0.5 0 -0.5

2 5

x 10

x 10

Zero load

FIG. 1 EEMD DECOMPOSITION RESULTS UNDER DIFFERENT GRINDING CONDTIONS (IMF1-IMF8) 9th IMF 0.5 0 -0.5

0

10th IMF

1

2

1 0 -1

0

Zero mill

5

0

1

2

0.5 0 -0.5

0

5

Dry mill

0

1

2

Wet mill

1

2 5

x 10

1

2

1 0 -1

0

1

2

0.5 0 -0.5

0

1

2 5

x 10

2

0

1

2

0

1

2

1 0 -1

0

1

2

0.1 0 -0.1

0.05 0 -0.05

0

1

2

0

2

5 0 -5

0

1

2 5

x 10

0

1

2

2 0 -2

0

1

2

0.05 0 -0.05

1

1

2

5 0 -5

1 0 -1

x 10 -3 14th IMF x 10

0

1

2

2 0 -2

5

x 10 14th IMF x 10

2

5 0 -5

0

1

1

2

x 10 -3 15th IMF x 10

0

0

1

2

x 10 -3 15th IMF x 10

0

1

2

2

5 0 -5

0

1

2 5

x 10

2 5

0.5 0 -0.5

0

1

2 5

x 10 16th IMF 0.1 0 -0.1

0

5

x 10 15th IMF x 10

1 x 10 16th IMF

1

2 5

x 10 16th IMF

-3

5

x 10

0

16th IMF 0.1 0 -0.1

5

-3

5

x 10

0

-3 15th IMF x 10

5

5

5

0

2 5

x 10 13th IMF 0.01 0 -0.01

1

5 0 -5

x 10 14th IMF

5

5

x 10 12th IMF x 10

2

x 10 -3 13th IMF x 10

-3

5

x 10

1

1

5

5

5

0

0

14th IMF 0.01 0 -0.01

x 10 13th IMF

x 10 12th IMF

x 10 11th IMF 0.02 0 -0.02

2

-3 13th IMF x 10

5

5

0.05 0 -0.05

1

5 0 -5

x 10 12th IMF

x 10 11th IMF

5

0

1

5

x 10 10th IMF 1 0 -1

12th IMF 0.1 0 -0.1

x 10 11th IMF

5

5

0

0

x 10 10th IMF

x 10 9th IMF 0.1 0 -0.1

2

x 10 10th IMF

x 10 9th IMF 0.5 0 -0.5

1

5

x 10 9th IMF 0.5 0 -0.5

11th IMF 0.1 0 -0.1

0.05 0 -0.05

0

1

2 5

x 10

FIG. 2 EEMD DECOMPOSITION RESULTS UNDER DIFFERENT GRINDING CONDTIONS (IMF10-IMF16)

Figs. 1 and 2 show that: (1) All IMF1s under four grinding conditions have the biggest amplitude among all IMFs; (2) All IMFs sort from high frequency to low frequency orderly; (3) There are many differences among IMFs under different grinding conditions, especially between the dry mill and the wet mill.

Integration Analysis Results In order to show the changes of the frequency range clearly, curves of the fast Fourier transformation (FFT) for the former 8 IMFs are plotted out in Fig. 3.

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4

-5 x1th 10 IMF

2 0

1

-4 x2th 10 IMF

0.5 0 500010000 1th IMF

0.01

0 5

0

Wet mill

4

2

0 1

0 5000 -4 x2th 10 IMF

0.5 0 500010000 -4 x1th 10 IMF

1 0

-5 x3th 10 IMF

1

0 1

0 2 0

2

0 1 0.5

0 20004000 -5 x3th 10 IMF

0 5

0 4

5000

0

-5 x5th 10 IMF

5

0

0 2 0

4

4

5

0

0 500 -4 x6th 10 IMF

4

2 0 10002000 -6 x4th 10 IMF

0 10002000 -5 x4th 10 IMF

1 0 20004000

-5 x6th 10 IMF

0 2 0 4 0

1

1

0

0 500 -4 x6th 10 IMF

5

0 1 0

4

0 500 -4 x8th 10 IMF

0 2

0 500 -5 x8th 10 IMF

1 0

0 500 -4 x6th 10 IMF

5

0 500 -5 x7th 10 IMF

0.5 0 500 1000

0

2 0 500 -5 x7th 10 IMF

0.5 0 500 1000 -5 x5th 10 IMF

-5 x8th 10 IMF

0.5 0 500 -4 x7th 10 IMF

2 0

0 500 1000 -5 x5th 10 IMF

2 0 10002000

-5 x7th 10 IMF

2 0

0 500 1000 -4 x5th 10 IMF

1 0 20004000 -5 x3th 10 IMF

2 0

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1 0 10002000 -3 x4th 10 IMF

1 0 5000 -4 x2th 10 IMF

1 0 500010000

0

-5 x4th 10 IMF

0.5 0 20004000 -3 x3th 10 IMF

0.5 0 500010000 -5 x1th 10 IMF

2 0

2 1

0 5000 -3 x2th 10 IMF

0.005

Dry mill

Zero mill

Zero load

Communications in Control Science and Engineering (CCSE) Volume 3, 2015

0 4

0 500 -5 x8th 10 IMF

2 0

0

500

0

500

0

0

500

FIG. 3 CURVES OF THE FAST FOURIER TRANSFORMATION (FFT) FOR THE FORMER 8 IMFS

Combination qualitative analysis and Figs. 1-3 with some prior knowledges, some interesting results can be obtained: (1) There are some install un-biases or using damages for this ball mill. In practice, this mill has been used for long time; (2) The high frequency vibration is mainly caused by the mill shell itself; (3) Some IMFs can be physical interpretation clearly. For example, IMFs of the four period sine waves must be a sub-signal caused by the mill shell self rotating; (4) IMFs with the same physical meanings may be denoted as different decomposition number under different grinding conditions. Thus, more researches should be done.

Conclusions A new shell vibration signal of the wet ball mill analysis method is proposed in this paper. Qualitative analysis of the vibration signal’s multi-component characteristic is described with the basis of ball mill grinding process and vibration production mechanism firstly. Then, shell vibration signal of a laboratory-scale ball mill is decomposed into a set of sub-signals with different time scales. Finally, a simple analysis result is obtained with some prior knowledges. All the results show that it is an interesting issue to make further research on quantitative analysis and mathematical simulation of the shell vibration production mechanism.

ACKNOWLEDGMENT

The research was sponsored by the post doctoral National Natural Science Foundation of China (2013M532118, 2015T81082), National Natural Science Foundation of China (61573364, 61273177), State Key Laboratory of Synthetical Automation for Process Industries, China National 863 Projects (2015AA043802).

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