ISSN 1392-1207. MECHANIKA. 2015 VOLUME 21(1): 8-11

Fault Diagnosis for Supporting Rollers of the Rotary Kiln Using theDynamic Model and Empirical Mode Decomposition

Kai Zheng *, Yun Zhang *, Chen Zhao*, Tianliang Li**School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, ChinaE-mail:zhengkai2001@163.com, whkasco@aliyun.com, zhaochen@whut.edu.cn, tianliangliwhut@sina.com

1. Introduction

Rotary kiln is a typical large slow-speedrunning (2-6 rpm) mechanical equipment. As keyequipment, rotary kiln is widely used in the cementindustry, metallurgical industry and environmentalprotection industry. It is mainly composed bytransmission system, driving system, supporting rollersand heat exchange system [1], as shown in Fig. 1. Theplain bearings in the supporting rollers enable the rotarykiln to run at a low speed with heavy load (12 supportingrollers support 15,000-20,000 kN load)[1-2]. And theoperation state of the rotary kiln was largely determinedby the working condition of supporting rollers [1-3].During long-term operation, supporting rollers vibratedue to the kiln crank [2]. Early fault diagnosis for therotary kiln’s supporting rollers has important engineeringsignificance in that it can help to reduce equipmentmaintenance cost and economic loss resulting fromproduction suspension of the rotary kiln [1-2]. Toachieve the above-mentioned purposes, it is of greatimportance to study the dynamic model and identify thefault features of the supporting rollers.

Until now, a limited research has been done forthe fault diagnosis of the supporting rollers. Eng.Zbignieet al have studies the causes of the kiln crank, andpointed that the kiln crank would affect the supportingbearings and lead to the deflection of the supportingrollers’ shaft [4]. Świtalski, Maciej proposed a methodfor the diagnostic of the rotary kiln’s technical state bythe measurement of the shell’s elastic [5]. Alma ŽigaHertz, et al. studied the distribution of contact pressurebetween the supporting roller and tyre based on Hertzcontact theory and did a simulation research based onfinite element method [6]. Gebhart, Walter et al proposedthe measurement principle and method of the supportingroller’s deflection. They adopted curve fitting method tocalculate the deflection of the roller shaft [3]. X.j. Li, etal. presented that dynamic change of the operating axisof the rotary kiln will lead to complex vibration of theequipment, so as to speed up fatigue failure of thesupporting rollers. They used transfer matrix method toestablish a kinetic model of the rotary kiln’s cylinder [7].Stamboliska, Zhaklina, Eugeniusz Rusiński, et al. studiedthe cause of the vibration of the rotary kiln’s supportingrollers and pointed out that the vibration of the

supporting rollers essentially resulted from the kiln crankof rotary kiln's cylinder. Meanwhile, they made anin-depth study on the fault mode of the supporting rollersand proposed an online signal processing method basedon the FFT method [1-2].

However, few work has been involved thevibration mechanism and the fault extraction of thesupporting rollers. In order to explore the impact of thecrank of the rotary kiln’s cylinder on the supportingrollers as well make fault diagnosis, this paper putforward the dynamic model of the supporting rollers andmade a numerical simulation analysis. Moreover, as thevibration signals of the supporting rollers are normallycharacterized with nonstationary behavior, to analyze thevibration signals with nonstationary properties, wepresented features extraction and fault diagnosis methodof the rotary kiln supporting rollers based on empiricalmode decomposition (EMD), so as to realize thecondition monitoring of the low-speed operation rotarykiln.

The remainder of this paper is organized asfollows. In Section 2, an analysis was made on theimpact of the rotary kiln crank on the supporting rollersand the dynamic model was established. In Section 3,numerical simulation analysis was done. In Section 4, afeatures extraction and fault diagnosis method based onempirical mode decomposition was presented. InSection 5, an analysis was made on the signals from theindustry field experiment based on the numericalsimulation analysis result and the proposed the faultdiagnosis method. Section 6 is a conclusion of this paper.

Fig.1 Rotary kiln in a China cement plant

2. Physical model of the supporting rollers

2.1. The effect to supporting rollers of kiln operation

According to FMECA result, the fault of thesupporting rollers is a main factor which can lead to thebreakdown of the rotary kiln [1-2]. According to [3], thefault of the supporting rollers is mainly caused by thekiln crank generated by the internal thermal process ofthe rotary kiln. During long-term operation, the profile ofthe cylinder will change, which will lead to misalignmentbetween the geometric center and the rotation center,thereby causing the eccentricity of the cylinder section.And the dynamic load caused by the deformation of thecylinder eccentricity gives rise to the vibration of thesupporting roller. The snowball effect in the rotary kiln’scylinder will further intensify the vibration of thesupporting rollers. According to [1], the materials willform a basic ball in the kiln called the snowball effectduring the operation of the rotary kiln. The ball movesslowly around the kiln’s axis. When the weight of thesnowball exceeds the adhesive force on the kiln coatingand the snowball surface, the snowball will come offfrom the kiln coating. Under extreme conditions, such athermal effect may lead to significant load unbalance ofthe supporting rollers.

Fig 2 shows the straightness deviation of therotary kiln we measured in a cement plant in China. Itcan be found that the straightness deviation of rotary kilncylinder was large due to various factors. The supportingrollers in the three stations of the rotary kiln are freefrom the restraint of the tyre. When the snowball effectappears in the rotary kiln’s cylinder, the straightnessdeviation of the axis will increase, leading to heavycyclic loads, which will cause the vibration of supportingrollers in the radial direction. If the vibration amplitudeis too large, the plain bearing may not make up thedisplacement of the roller shaft, so as to cause frictionalheating in them. And the bearing alloy will melt with thehigh temperature, causing significant failure of thesupporting rollers.

Fig.2 The measurement result of straightnessdeviation of the rotary kiln in a cement plant

Fig.3 The vibration of supporting rollers caused bythe Kiln crank effect

To establish the dynamic equation of thesupporting rollers, it is very important to describe thecyclic load resulting from the kiln crank. According to[2,4], the change of the kiln cylinder profile is animportant factor resulting in the dynamic load, and theeccentricity (e) can be used as a main parameter forassessing the section profile. To establish the dynamicmodel of the supporting rollers, a simplified formula wasput forward for the cyclic load calculation. And it can beexpressed as:

12

11 emf (1)

Where 1m is the equivalent unbalance mass atthe corresponding station, 1 is the kiln cylinder’srotational speed and 1e is the eccentricity of the crosssection.

2.2. The equations of the supporting rollers

To establish the dynamic model of thelow-speed rotary kiln’s supporting system underthermal load, we established a simplified model asshown in Fig 4. In Fig 4, supposing that the rotarykiln’s supporting roller is a disc with a mass m , thesupporting shaft is an isotropic shaft without mass,and the left and right rollers at the same position of therotary kiln bear the same load, and that OXY is theinertial coordinate system, Oxy is the rotatingcoordinate system, O is the whirling center (rotationcenter) of the supporting roller, 'O is the centroid, Gis the center of mass of the supporting roller, R isthe radius of the supporting roller, e is theeccentricity of the center section of the supportingroller, we can derive the equation concerning thesupporting roller’s vibration according to Lagrange'sdynamical equations.

Station#1 Station#2 Station#3

Fig.4 The model schematic of supporting rollers

According to the force analysis for thesupporting rollers, the external loads of them can beexpressed by Formula (2):

)sin()cos(

)cos()cos(

1

12

2

)(

)(

tftf

tmetme

QF

nj

nj

(2)

Where f is the cyclic load caused by therotary kiln cylinder, is the rotation speed of thesupporting roller and e is the eccentricity of thesupporting roller’s section. Based on formulas (2) wecan derive the dynamic equation of the supportingroller as expressed by Formula (3):

)(

)(

2

1

2

1

00

00

00

nj

nj

QF

yx

kk

yx

cc

yx

mm

(3)

Where 1k and 2k are the stiffness values ofthe supporting roller in x and y directions,respectively, 1c and 2c are the damping forces of thesupporting roller in x and y directions, respectively;as we suppose the supporting roller is isotropous, it canbe regarded that 21 kk , 21 cc ; m is the equivalentmass of the supporting roller at the related gear, 1m isthe equivalent mass of the materials and cylinder at therelated station.

3. Numerical prediction for the response ofsupporting rollers

3.1. The simulation parameters estimation

It is great important to carry out a carefulestimation of the physical parameter values of thesupporting rollers to perform a numerical simulation.However, it is difficult to take this task as that thespecific parameters of the support rollers depend on theproduction, the length and the tyre number of a rotarykiln. In this research, we take a qualitative analysis to thenumerical simulation of a three tryes rotary kiln with theproduction of 5000-6500 dt / . According to [8], thebasic material of the supporting rollers is ZG42GrMoand the elasticity modulus of it is 51009.2 MPa . Themass density of the rollers is 6-1086.7 3/mmkg and

the radius is 1150mm. Based on the above data, we canobtain the approximate physical parameter values ofsupporting rollers, which are shown in table.1

Table.1 Estimation parameters of the supporting rollersused for numerical simulations

Parameter ValueRollers stiffness of x , y axis

1k , 2k51048.1 mN /

Rollers viscous damping ofx , y axis 1c , 2c

41092.6 mNs /

Equivalent mass of rollers m 41005.4 kgEquivalent imbalance mass of

station#2 1m51097.7 kg

The rotating speed of therollers

10.7 min/r

The rotating speed of the kiln 1 4 min/rMass unbalance angle 0 rad

3.2 Numerical analysis of the supporting rollers

In this section, the dynamic response of thesupporting rollers under the influence of the kiln cylindercrank was studies. The influence of the cyclic load tosupporting rollers caused by thermal effects of the kilncylinder was stimulated.

As it is difficult to achieve analytical solution ofthe complex dynamics equation, the numerical methodswas used to solve the problem. And the fourth-orderRunge-Kutta method [9] is selected to solve the eq.(10)to obtain the dynamics response of the supporting rollers.

The effect on the supporting rollers of the rotarykiln crank was analyzed in this section. According tosection II, during the operation of the kiln, it will changethe dimensional size as the result of the internal thermalprocesses. As the rotation center and the center of mass isnot overlap in the cylinder section, thus producingsection eccentricity. Therefore, the eccentricity of thecross section can be used as a main parameter torepresent the kiln crank. And we compared the vibrationresponse of the supporting roller under whether or notthere is kiln crank. And the simulation result was shownin Fig.5. Furthermore, the relationship between thesection eccentricity of the kiln cylinder and theamplitude of the kiln harmonic and the amplitude of therollers harmonic was analyzed, and the result was shownin Fig.6.

Fig. 5. The vibration response in the y direction ofthe supporting rollers when 31 e and mme 101

Fig.6 Relationship between the section eccentricity of thekiln cylinder and the amplitude of the kiln harmonic andthe amplitude of the rollers harmonic

From the above numerical simulation results, itcan be found that: (1) when there is kiln crank, there willhave a kiln harmonics (RH) in the vibration signal. (2)When the magnitude of the kiln harmonic (KH)increased, it is a sign that the crank of the rotary kiln isbeing enhanced. And it has larger deviations from thenormal operation in terms of eccentricity and deflectionsfrom regular rotation axis in section corresponding tomonitored station. Therefore, the operation condition ofthe rotary kiln can be monitored by collecting thevibration signals of the supporting rollers.

4. Feature extraction using empirical modedecomposition method

As mentioned in section III, the vibrationsignals of the supporting rollers contain multiple faultinformation. According to the numerical analysis for thesupporting rollers, it can be found that the vibrationsignal mainly includes the harmonic component causedby the kiln crank and the harmonic component caused bythe deflection of the roller shaft. In [10], authors pointedout that it also contains the harmonic component of thesurface characteristic, such as the harmonic componentof waviness, the roughness and micro-irregularities. Infact, the vibration signal arenonlinear, non-stationary signal which are not suitableprocessed by the traditional signal processing methodsuch as fast Fourier transform (FFT) or Wavelettransform (WT)[11-12]. In this research, we proposed amethod for feature extraction of supporting rollers basedon empirical mode decomposition.

4.1. Empirical mode decomposition

Empirical mode decomposition was firstproposed as a part of Hilbert–Huang transform (HHT) byNorden E.huang, which is effective method to analysisthe nonlinear, non-stationary signal [13]. As the key partof HHT, the method of EMD to decompose signal isintuitive, direct and adaptive. This decompositionmethod is based on local characteristic of local timedomain of signals. Based on this characteristic, anylinear, stationary or nonlinear, non-stationary signal canbe decomposed into a set of Intrinsic Mode Functions(IMFs) which are amplitude and frequency modulatedsignals. It has been proven to be an effective method inanalyzing nonstationary signals for rotational machinefault detection [14-15]. According to [15], each IMFsatisfies two basic conditions: (1) over the entire dataset,the number of extreme and the number of zero crossingsmust either be equal or differ at most by one; (2) at anytime point, the local mean value of the envelope whichdefined by the average of the maximum and minimumenvelopes is zero.

The specific processes of EMD are described asfollows:

Step 1) For the given signal ( )x t , construct itsupper envelope )(max te and lower envelope )(min teby connecting all local maxima and local minima withcubic spline functions. And:

2)()( minmax

11tetem

(4)

Step 2) Compute the envelopes mean 11m ,and )()( 111 thmtx . And the definition of IMF isproposed mainly to get the physical meaning of the

instantaneous frequency.Step 3) If )(1 th satisfies the definition of

IMF, then we can obtain the first-orderIMF )(11 thIMF . And then go to the next step. Inaddition, the IMF component )()( 11 thtc k is saved.If it is not the IMF, repeat Steps 1)–3). The stopcondition for the iteration is given by:

Tt

ji

ijji

th

ththSD

0 2)1(

2)1(

)(

|)()(|(5)

Where )()1( th ji and )(thij denote the IMFcandidates of the 1j and j iterations, respectively,and usually, SD is set between 0.2 and 0.3.

Step 4) Separate )(1 tc from )(tx , we couldget )()()( 11 tctxtr , )(1 tr is treated as the originaldata and repeat the above processes, the second IMFcomponent )(2 tc of )(tx could be got. Let us repeatthe process as described above for n times, then n-IMFsof signal )(tx could be got.

Step 5) The decomposition process can bestopped when )()( tr n becomes a monotonic function fromwhich no more IMF can be extracted. We can finallyobtain:

nn

i i rtctx )()(

1(6)

Residue )()( tr n is the mean trend of )(tx .The IMFs )(1 tc , )(2 tc , . . ., )(tcn include differentfrequency bands ranging from high to low. Thefrequency components contained in each frequency bandare different and they change with the variation ofsignal )(tx , while )()( tr n represents the centraltendency of signal )(tx .

4.2. Feature extraction and fault diagnosis procedure

Numerical simulation results shown that thekiln harmonic (KH) and the rollers harmonic (RH) willlead to significant change as the kiln cylinder crankhappens or the rollers behavior changes. Therefore, theenergy variation of the kiln harmonic (KH) and therollers harmonic (RH) of the vibration signals can reflectthe running condition of the rotary kiln. When themalfunction occur in a mechanical equipment, the energyof the vibration signal would change strongly in somefrequency bands, but in other frequency bands the energymaybe change weakly [12]. According to [16], the IMFenergy moment not only contains the size of IMFsenergy, but also considers the distribution of IMF’senergy change with the time parameter t . It can be usedto express the energy distribution of the faultcharacteristic frequency component for the vibrationsignals. In this research, the IMF’s energy moment isemployed for fault diagnosis of the supporting rollers.And the procedures are summarized as follows.

Step 1) The signal )(tx is decomposed into

several IMFs based on the EMD method, and theredundant IMFs were removed based on the correlationcoefficient. And the physical meaning of the effectiveIMFs can be found.

Step 2) The HHT marginal spectrum of eachIMF component was calculated based on Hilberttransformation. And the IMF energy moment wascalculated. The operation state of the rotary kiln wasdetermined according to the IMF energy moment.According to [16], the energy of each IMF componentcan be calculated by the formula (7):

N

j ii tkctkE 12|)(|)( (7)

Where t is the period of data samples, N isthe total number of data samples, and k represents thenumber of data samples.

The IMF energy moment can be calculated byformula (8)：

n

i ini EEEEE 121 }.......,{T (8)

Where

ni iE1 is the summary energy of all

the IMF components of the signal, n is the number ofthe effective IMF components. T is the percent of theenergy of IMF components in the whole signal energy.

5. Experiment and discussions

The measurement system comprises anacquisition card, the non-contact eddy current sensors,the hall sensor and the measuring software, as shown inFig.10(a). During the measurement, the non-contact eddycurrent sensor is mounted through fixture to keep thesensor probe in the contact direction of roller and kilntyre( y direction), as shown in Fig.10(b), and probeshould be kept close enough to the surface of the rolleraccording to the eddy current sensor range. The hallsensor is installed in a fixed position of rotary kiln tointeract with magnet mounted on the kiln cylindergenerating pulse signal per lap which is used tosynchronize the collected vibration signal and therotation of the rotary kiln. Then the collected vibrationsignals are sent by NI data acquisition card to the uppercomputer for management and storage by Labview-baseddata acquisition software and SQL database.

We did the experiments in a cement plant inChina, and the measured object was a rotary kiln whichconsist three tyres. The speed of the kiln cylinder was3.5 min/r while the supporting rollers were10.5 min/r .The vibration signals of all the supportingrollers were collected based on the measurement system.The sample frequency of the channel was settled to20HZ.

Fig.7 (a) The installation position(in the ydirection) of the displacement sensors and (b) schematicdiagram of the experimental setup.

The kiln crank leading to the vibration of thesupporting rollers often takes place in the second andthird tyre. Therefore, for verifying the dynamics modelof the supporting rollers, the vibration signal ofsupporting rollers of the second station was used toanalyze, as shown in Fig. 8(b). Also the profile data ofthe cross section near to the second station werecollected. The geometric centre, base circle andeccentricity can be calculated by the computationalalgorithm proposed by literature [4], and the processedresult was shown in Fig 8(a). And physical map of theexperiment was shown in Fig.11.

Based on the computational algorithm, theeccentricity of the cross section near to the second stationis mme 2.6 . It means that there should be RH andKH components in the vibration signals of the supportingrollers according to the numerical simulation result. Weadopted FFT method to process the vibration signals ofthe second hand roller, as shown in Fig 8 (b). From Fig 8(b), we can find two major frequency components(0.05859 HZ and 0.1758 HZ) in the signals, which arebasically the same as the rotation frequencies of therotary kiln’s cylinder and supporting roller, respectively.In particular, great eccentricity appeared in thecylinder’s section and correspondingly, KH componentappeared in the vibration signals of the supporting roller.This was the same as the simulation result and provedthat the model was correct. And the physical map of infield industry experiment was shown in Fig.9.

2 4 6 8 10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

Time (sec)

Am

plitu

de

/mm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.05

0.1

0.15

0.2

X: 0.1758Y: 0.2321

Frequency (Hz)P

SD

X: 0.05859Y: 0.06806

KHRH

Fig.8 (a) The calculation result of the sectioneccentricity near to the second station (b) The vibrationsignal and its spectrum of the second left supportingroller.

Fig.9 Physical map of experiment for verifying thedynamics model of the supporting rollers

We processed the vibration data of allsupporting rollers based on empirical modedecomposition method. Specifically, the vibration signalof the second right supporting roller was analyzed. EMDprocessing results are shown in Fig. 10. After thevibration signals were processed with EMD method, theIMF components ranked from high to low frequency. Inparticular, the specific physical meanings of each IMFcomponent are as follows: IMF6 (frequency: 0.05853HZ)is harmonic component caused by the kiln crank; IMF5(frequency: 0.01758HZ) is the vibration componentcaused by the supporting roller shaft deflection;

a)

b)

a)

b)

according to [19], IMF4 is the ripple deformationcomponent of the supporting roller’s surface; IMF3 is theharmonic component of the supporting roller’s surfaceroughness; IMF2 is the harmonic component ofmicroscopic deformation; and IMF1 is the noisecomponent. The frequency spectrum of IMF6 and IMF5are as shown in Fig 10.

0 5 10 15-1

0

1

signalA

mplitu

de

0 5 10 15-0.1

0

0.1

imf1

0 5 10 15-0.5

0

0.5

imf2

0 5 10 15-0.5

0

0.5

imf3

0 5 10 15-0.5

0

0.5

imf4

0 5 10 15-0.5

0

0.5

imf5

0 5 10 150.02

0.04

0.06

r5

Time/s

RH KH

Fig.10 The EMD decomposition result of the vibrationsignal of the second right supporting roller

In order to decide the operation status of therotary kiln, the IMF energy moment is proposedaccording to the definition mentioned in section V.And the proposed IMF energy moment is

T , whose computation formulas is shownin (9):

EEEEEEEE )(,, 23456 (9)Where, represents the energy coefficient of

the harmonic component caused by kiln crank; represents the energy coefficient of the harmoniccomponent resulting from deflection of the supportingroller’s shaft; and represents the energy coefficient ofharmonic component of the supporting roller’s surfaceroughness and harmonic.

Fig. 11 Calculation results of IMF energycoefficient of the supporting rollers

From the calculation result, we can find that theenergy coefficient of IMF2, IMF3 and IMF4 components( ) representing the contour deformation of the secondleft and right supporting rollers and the third rightsupporting roller are great, and the energy coefficient ofIMF5 ( ) and IMF6 ( ) components representing thekiln crank and deflection of the supporting roller’s arerelative small. And the energy coefficient of IMF5 andIMF6 of the second left supporting roller are great, asshown in Fig 11. It shows that the contour of the secondleft and right supporting rollers and the third rightsupporting roller deformed to some extent due to heavyload on them, but the impact vibration resulting from thekiln’s thermal effect is small. However, the impactvibration of the third left supporting roller is big due tothe heavy kiln crank. If no maintenance measures aretaken, the bearing of the supporting roller’s bearing mayburn out and even melt due to the high temperature.

5. Conclusion

The operation condition of the rotary kiln canbe reflected by monitoring the vibration signals of thesupporting rollers as they are core components of it. Inorder to extract the feature of the vibration signals, thenumerical simulation of the supporting rollers wasanalyzed and a signal processed method based on HHTwas proposed. From the above simulation andexperimental results, the contributions and conclusion ofthis research are made as follows: (1)The numericalsimulation result indicated that when there is kiln crank,there will have a kiln harmonics (RH) in the vibrationsignal. When the kiln crank enhance, the amplitude ofkiln harmonics (RH) will increases while the rollersharmonics (RH) almost has no change.(2)The changes ofthe kiln harmonics and rollers harmonics reflect theenergy variation of vibration signals when the rotary kilnis in different running statuses. Therefore, a faultdiagnosis method based on EMD was proposed. Thesignal was decomposed into a serial of IMF componentsbased on EMD. An analysis was made over energydistribution of fault features under different frequencybands, and the IMF energy moment was calculated todetermine the operating state of the rotary kiln. (3)Thesimulation and experimental results indicated that theproposed method could be used to extract the feature forthe vibration signals of the supporting rollers effectively,which provide a new method for the fault diagnosis ofthe low speed machinery like the rotary kiln.

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Kai Zheng, Yun Zhang, Chen Zhao, Tianliang Li,Lei Liu

FAULT DIAGNOSIS FOR SUPPORTING ROLLERSOF THE ROTARY KILN USING THE DYNAMICMODEL AND EMPIRICAL MODEDECOMPOSITION

S u m m a r y

Rotary kiln is key equipment widely used in the cement,metallurgical and environmental protection industry. Theoperation state of the rotary kiln was largely determinedby the working condition of supporting rollers. Thispaper models the vibration mechanism of the supportingrollers under the rotary kiln crank caused by the internalthermal process. Based on the numerical analysis, amethodology based on empirical mode decomposition(EMD) for the fault diagnosis of the supporting rollerswas proposed. By using EMD, the complicated vibrationsignal of the kiln can be decomposed into a number ofintrinsic mode functions (IMFs). An analysis was madeover the energy moment of IMF components to indicatethe energy variation of the kiln harmonic and the rollerharmonic of the vibration signals. Simulation and in fieldexperiment results proved that the proposed methodprovided a validity of the approach for the conditionmonitoring and fault diagnosis of the low-speedmachinery like the rotary kiln.

Keywords: Supporting rollers, fault diagnosis, numericalanalysis, empirical mode decomposition, vibrationmonitoring