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Proceedings of the 26th Chinese Control ConferenceJuly 26-31, 2007, Zhangjiajie, Hunan, China

Signal Analysing of Failure monitoring system for gear chain*

Zheng Lijun1 , Yu Lixin2

1. Zhijiang College , Zhejiang University of Technology ,Hangzhou, Zhejiang 310024, P. R. ChinaE-mail:zhenglijun@sohu.com

2.Hangzhou Youwang Electronics Co. Ltd,Hangzhou,Zhejiang 310052, P. R. ChinaE-mail:yulixin@youwang.com.cn

Abstract: A real-time mechanical fault monitoring system for gear transmission chain was studied and realized, which utiliz-ing the initial phase, the phase difference and the amount of phase modulation of the finite length modulated signal. The signalis demodulated and the phase-modulated signal is retrieved in remote control mode. Furthermore, some key techniques suchas data communicating, data monitoring and anti-jamming methods are designed.Key Words: Gear case,Failure,Monitoring,Long-distance,Signal modulation

1 SIGNAL ANALYSING 1

It’s common that the phase-modulated signal can bewritten as

0( ) ( ) cos[2 ( )]x t A t f t tϕ= π + (1)where 0f , ( )A t and ( )tϕ are the centre frequency,signal envelope, phase modulation function, respectively.The corresponding orthogonal signal is

^x( ) ( )sin[2π ( )]0t A t f t tϕ= + (2)

The analytic signal of x(t) is^

j ( t)px (t) x(t) jx(t) A(t)e ϕ= + = (3)

From (3), the phase modulation function ( )tϕ can be eas-ily written as follows�

02π(t) arg[ ( )e ]j f tpx tϕ −= (4)

There is no value restriction on (t)ϕ in the above equa-tion. The phase detection algorithm is applied to thephase modulation of linear and nonlinear system.Since the modulation frequency 0f is unknown, whatshould be done before estimating the phase modulation

quantity is to estimate the modulation frequency^

0f ,andthen the phase of the discrete signal

( )( 0,1, , 1)px n n n= ⋅⋅ ⋅ − can be gained , according to theminimum phase principle.The instantaneous frequency is obtained by differentiat-ing ( )nθ :

01 1( ) ( )N2π 2π

f n ntθ

θΔ

= ⋅ = ΔΔ

(5)

^0f can be determined by the expectation of 0f (n)

0 0ˆ [ ( )]f E f n= (6)

Therefore the computing formula of phase modulationquantity is

0̂( ) ( ) 2π nn n fN

ϕ θ ⎛ ⎞= − ⎜ ⎟⎝ ⎠

(7)

* This work is supported by Zhejiang Province natural sciences fundproject (Serial number 499010).

Since the demodulation of modulated signal was proc-essed using microcomputer, the resolution ofphase-detecting is dependent on the method of signalquantification.The modulated signal waveform is divided at least into2m-1 equal units within the value range of thepeak-to-peak amplitude, which is assumed to occupyhalf of the dynamic rang of A/D, and the data acquisi-tion unit can process data eight-data simultaneously.The waveform amplitude is quantified uniformly whilethe corresponding angle segmentation is not the case.Consequently, the phase resolution is dependent on theA/D conversion digits.While there is quite a lot of sampling points or thenumber of sampling points N is not equal to 2m .Thesignal x(n) can be divided into q sub-samples ( )ix n

with length j2 . To compute the orthogonal signal( )ˆix n separately, and to form q analytic signals 1( )px n ,

and the analytic signal ( )px n can be constructed by

1( )px n in sequence by the fact that the analytic signal iscontinuous. The adjacent signal groups can be over-lapped.The method of sub-samples makes the computationmuch complexity under the condition that the modula-tied signal ( )x t is narrow-band.By frequency-Shifting of the analytic signal ( )Px t , weget

0( ) ( ) exp( 2π )pg t x t j f t= − (8)Assuming that

0( ) ( ) exp( 2π )G t x t j f t= − (9)

0( )( ) exp( 2π )

πG tG t j f tt

= − (10)

Theng(t) G( ) ( )t jG t= + (11)

The real part of ( )g t is the modulated signal ( )x t ,while the imaginary part is the convolution of the two

signals: 01 exp( j2π )π

f tt

− and ( )x t . ( )G t is input to a

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specific filter and the output is G(t) . The phase transi-tion point of the filter is not lie in the zero-frequency butshifted by 0f on the f axis. The envelope and phase of

( )X t is( ) ( )A t g t= (12)

(t) arg g(t)ϕ = (13)Provided that ( )x t is a narrowband signal, ( )G t isthe signal after being frequency shifted. while the centerfrequency of ( )G t is shifted to nearby the zero fre-quency so as to make a process of disproportionate sam-pling with paired selection, at the same time the sam-pling frequency is chosen properly, and the phenomenonof spectrum overlapping should be avoided as much aspossible. G(t) is obtained by nonzero step transforma-tion. The envelop and phase compression is done bysolving the modulus and phase of the analytic signal.This processing method has an advantage over others inthat the envelope and phase of signal is more compact.Compared with the algorithm of sub-samples, the num-ber of Hilbert transformations is reduced by N-1 times.So the processing speed of this method is more efficient.The sub-sampling frequency subf should satisfy the

Nyquist sampling theorem, after the signal ( )x t hasbeen shifted frequency. Supposing the bandwidth ofmodulated signal is B, and the center frequency is 0f ,and under the condition that the sampling frequencyis 0sf , then the m, maximum multiplying power of com-pression, should be obtained by sampling and choosingto the signal:

0

2sfmB

⎡ ⎤= ⎢ ⎥⎣ ⎦(14)

The sampling-choosing frequency has the relations asfollows:

0 / 2sub sf f m B� � (15)Supposing there is a simple-frequency cosinusoidal sig-nal: 1 0 0( ) cos(2π )X t A f t ϕ= + , and the initial phase is

00

2πarg j f tX epϕ −⎡ ⎤= ⎢ ⎥⎣ ⎦.

When the signal is accompanied by the noise2( ) ~ (0, )m t N σ , the signal expression is:

2 0 0

' '0 0

(t) Acos(2πf t ) (t)A cos[2πf t m (t) ]

x mϕ

ϕ

= + +

= + +(16)

While this method of estimination will be invalid,if thephase of noise ( )'m t greater than or equal to π .Supposing there are two signals: 1 2( ), ( )x t x t ,which hasthe same frequency, and their initial phase estimates are

01ϕ̂ and 02ϕ̂ , respectively. So the estimatied value of thephase separation is 02 01ˆ ˆ ˆϕ ϕ ϕΔ = − .

2 MONITORING SYSTEM DESIGN

This system takes the programmable logic controller

(PLC) as the core, and it is realized by telephone com-munication method. In the system, the hypogynous mi-crocomputer must transmit all kinds of the data col-lected on line to the control center of epigynous micro-computer accurately and reliably. Also, the controlcommands of epigynous microcomputer must be sent toall the hypogynous microcomputer accurately. So thekey technique is data communication.Generally speaking, the monitoring facilities is near thecontrol center. So the data communication can be car-ried directly by the interface RS232 or RS422 .Whilethe distance is far away from each other, data commu-nication can be implemented by MODEM, which iscommon in the public telephone network.The main problem to be considered of the PLC corebased computer communication system is the hardwareconfiguration, the selection and realization of protocol,and compilation communication procedure in the par-ticular system, etc.In computer communication,distance of digital trans-mission of the computer is extended mainly by MO-DEM. Carrier signal is analog signal too, which ismodulated by the data collected from PLC by MODEM,and then it transmits over the communication channel tothe control center. The process of retrieving intelli-gence(data) from a modulated carrier waveform wasmade by epigyny-MODEM, in the end the digital signalof demodulation is sent to the computer. Signal path ofcommunication must be established in order to carry thenormal data communication between the epigyny-PCand hypogyny-PLC.Taking the research into consideration, a remote com-munication procedure was studied, which used in auto-dial of MODEM and by the way of instruction set ofMODEM’s AT written in the ports. Once it is translatedinto the executable program, the calling procedure willbecome flexible and convenient.The schematic diagram of signal procedure is shown inFig. 1.

Initialization of communication port

Carry out communications

If the communication is over?

Close communication port ,finish

Error handling routine

Error handling routine

N

Y

N

Y

N

Y

Fig.1 Flow diagram of signal procedure

As far as communication system the teledata is con-cerned, because the module of communications embed-ded .the functions of real-time monitoring and automaticreclosing to the lines status are provided. In other words,it can provide the real-time monitoring to the lines dur-ing the normal, once there is something wrong with thelines, the rebinding has been carrying on automatically.

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Thereby the reliability and flexibility of the telecommu-nication system is enhanced.In observation system of the SZ-4 series PLC, variousmodule of digital quantities and analog quantities im-plement various kinds functions ,such as real-time datasampling, signal detection to the early warning andalarming output, etc. and then it will be connected withthe sensor, which is on the spot, by all kinds of trans-mission instruments. All kinds of merits are important toa observation system, as a kind of control appliance,PLC does not constitute a observation system, becausethere is a limitation such as disable to perform compli-cated computation, incapable of displaying all kinds ofreal-time graphics, and can’t save a large amount ofhistorical data, and in the same time not displaying Chi-nese-character,and not providing auser-friendly inter-face.while the design of epigynous-PC can compensatefor these deficiencies. Programming, to monitor applica-tion software of the epigynous-PC, selecting the C lan-guage or the corresponding database system in the sametime, and the procedures can process the system histori-cal data too.The PLC of hypogynous-PC introduces ladder dia-gram to program procedures. While the software of PLCcan perform some specific function, such as data acqui-sition, alarming output and so on.The module of data communication completes transfer-ring instructions and data between PLC and the micro-computer, and the program converts the data into allkinds of variables in the format of system requirements .In a given hardware configuration and installation, theAC supply of system has been double isolator, and theinput signal passes through optoelectronic isolator thatraises the ratio of signal-to-noise, and wiring shoule re-moved from the highfield, in the same time the trans-mission of analog signals and digital signals withscreening wire, and taking the steps of earthing and soon reliably to eliminate or weaken the interference ofexternal signal effectively.In software design and programming, the input of mod-ule provides the function of anti-jamming. For example,taking the step of filtering technique of software judgesthe time lag of some important analog quantity parame-ters, and further confirms to give an alarm. while takingvarious steps to improve the system’s performance ofanti-jamming in the design of communication soft ofhypogyny-PC.

3 DESIGN OF FAILURE MONITORING SYSTEM

FOR GEAR CASE

The integrated design programming flow-chart of thesystem see Fig. 2.

Epigynous PC

Monitor Display Print

Hypogynous PC

Sensor1 Sensor2 Control Give an alarm

Signal path

Fig.2 Flow chart of integrated design to system

The hypogyny-PC adopts programmable controllerwhich is a kind of automatic controller. It executivesspecific some of the instructions such as performing thelogic operation, sequential control, and timing andcomputation, and arithmetical operation, etc. Then it cancontrol types of equipments in the input/output mode ofthe analog or digital quantity. While the hypogyny-PChaving serial communication ports, and the PC and theothers tend to constitute a detection control system.thesketch of hypogyny-PC see Fig. 3.

Sensor

Sensor

Epigynous PC

PLC IN OUT

RS232

220V ~

Interface circuit

Sensor Sensor Sensor Sensor

Fig.3 Sketch of hypogynous-PC

In addition to these, The hypogyny-PC provides thesame functionality as communication, network and other.the applied range, in the main, between the relay controlapparatus and the computer of process monitoring. Andthen it also apply to this occasion on which the demandto control function is relatively complexity and there aremore I/O ports too.In control system, the hypogyny-PC mainly achievessomething such as real-time signal sampling control tothe switching value, and signal detection, and alarmingoutput,etc. meantime it connect with the system by sec-ondary meter of kinds of sensors. while the epigynousPC is only an ordinary PC, and can complete graphicdisplay, complicated computation, and data storage ofthe system, and processing and output. it can displaytoothed gearing and fault by the way of dynamic analogand in the form of graphic or form. And then it also candisplay the exceptional fault and warning information,and print kinds of detection reports simultaneously.Acquisition of monitor information is completed by thePLC of hypogyny-PC, and then the PLC is managed bywith the instruments which correspond with interfacespecifications of RS-232C or RS422,and then proceedserial communication.

4 CONCLUSION

Basing on the information of Phase and making diagno-sis of the mechanical failure is a basic way. In using therelative sensor as detecting element, the resolution of thephase detection will improve with the raise of collecting–digit. for detecting element, there’s nothing with thevelocity of its movement ,which provides feasibility andfoundation of theory for further developing the systemof fault monitor . Base on spectrum analysis and diagnosis principle tofault of the gear case chain, it is a polytechnic projectthat is not only appropriate for real-time monitoringsystem of fault diagnosis for the geared head ,but alsoappropriate for other real-time monitoring sys-

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tem .especially it is feasible to proceed fault diagnosisfor parts such as gear or gear case, specially.The fault diagnosis system, which constituted with PC,sensor and others and been in the PLC as core, has theproperties of stable operation, high reliability, andstrong real-time property, and high precision data, andgood capacity of resisting interference and be conven-ient to use. while the PC does not proceed to monitor,the hypogynous PC can continue operating independ-ently that will improve the service efficiency of PC andhave the merit of reference to the congeneic system.The computer. In time of need, the computer send theinstruction to the hypogyny-PC and transfer the infor-mation. General users can easily master a high - levellanguage and make programs in it. while to computer, itmakes programs of computation in high-level language,The communication port of PLC can connect

REFERENCES

[1] Liao Changchu. Philosophy of measurement of phase sepa-

ration by PC-.Electrical Measurement Instrumentation, 1987,(8): 50.

[2] Chu Liaosheng,Cheng Dongyue.The techniques of supple-mentary monitor and diagnostic by computer [M] Xi ’An:Xi’An jiaotong university Press, 1989.

[3] Zhang Xinhua.Investigatation about the system of automaticmonitoring constituted with PC-PLC [J] Telemetry & remotecontrol, 1998, (6): 53-564.

[4] Zhang Xinhua. Remote system of automatic monitoring andData communication [J] Mannufacturing Automation, 2004,(1): 46-495.

[5] Lu Zhikang,Zhang Xinhua.The research of automatic moni-toring system [J] Microcomputer Applications, 2005, (4):18-206.

[6] Lu Zhikang,Zhang Xinhua.The application of PLC in thesystem of humiture [J] Mechanical & Electrical EngineeringMagazine, 2006, (3): 407.

[7] Zhang Xinhua.The data communication of minitoring systemcontrolled by PLC [J] Computer and Network, 2005, (10):388.

[8] Zhang Xinhua.The control of PLC in the system of PLC [J]Machine Tool & Hydraulics, 2006, (3): 48-50.