某型货车驱动桥三维设计翻译原文

Proceedings of the IEEE International Conference on Mechatronics noise vibration analysing wavelet transform I INTRODUCTION As various automobiles come into daily life the noise caused by automobile is in majority of the city s noise Contacting noise long it not only affects health of those people but also causes traffic accidents indirectly Thus the noise is one of the significant targets in weighing the quality of automobile Besides the engine and exhaust system the main retarder is another primary noisemaker in automobile To reduce the noise of main retarder is an important aspect to realize low noise automobile The main retarder is often manufactured separately 1 It is assembled firstly as retarder assembly according to the technical demands And then it is put into the drive shaft housing The retarder assembly consists of three main segments driving cone gear assembly differential assembly and retarder housing Fig 1 shows the retarder assembly of a camion and it s fixed into the drive shaft shell A comprehensive test has been taken when the assembly of main retarder finishes for ensuring the pair of screwy bevel gears keeping relative location correctly It s a key means to guarantee the quality of those productions and prevent the rejects entering into the next working procedure The noise of main retarder is an important aspect in the comprehensive evaluating for it reflects the meshing conditions of the pair screwy bevel gears The conventional method for noise testing in the old ones is that the operators listen to the sound from the pair of screwy bevel gears when they are meshing and make decisions according to their own experiences Obviously the efficiency and accuracy are low via using this old method There is another improved method which detects the noise signal of the main retarder directly and analyses it using noise pressure analysing method It advances the old one in a certain extent However the request conditions for realising the measuring and analysing of noise are high Even a silencer room is needed some times As Fig 1 denoting the test is usually taken in the workshop where the environment noise are loud The improved method is obvious not suitable for such an industrial circumstance Fig 1 The retarder assembly and drive shaft shell According to the research on the vibration and noise of the main retarder the vibration and noise signal are in close relationship When the frequency of vibration varies from 20 to 20000Hz the vibration source is the noise source either This vibration transmits in form of wave in solid and radiates noise in the meanwhile The vibration of drive shaft housing reflects the meshing impact of the pair of screwy bevel gears ultimately That is to say the vibration signal of drive shaft shell contains abundant dynamic information of the meshing screwy gears Thus this article brings up that analysing the vibration signal instead of measuring noise signal directly II INFORMATION ABOUT WAVELET As all know there are many ways and means in the field of signal processing and the conventional Fourier Transform FT is more often used FT represents a signal by a family of complex exponents with infinite time duration Therefore FT is useful in identifying harmonic signals However it is weak in analysing transitory signals The reason is that shape of wave of the signal in time domain doesn t contain the information in frequency domain and the Fourier spectrum is a statistical characteristic of the signal which isn t provided with function of localization There is another developing method called Short Time Fourier Transform STFT The 782 Authorized licensed use limited to Northeastern University Downloaded on May 27 2009 at 02 45 from IEEE Xplore Restrictions apply essential idea of STFT is that it divides signal into many interval of time at first then implements FT in each divided time zone for obtaining the frequency information included in this interval Obviously it contains the information both in time and frequency However for the invariable of the time intervals it is difficult to detect the signals which have short time duration and high frequency It is really only suit to analysis of signals where all of the patterns appear at approximately the same size Wavelet Transform WT is a time frequency localization analysis method whose shape of window changes but the magnitude keeps invariable For its ability of alterable extension of window essentially WT can take a long time to obtain information about low frequency more exactly and take a shorter time to get information about high frequency On the other hand the most important characteristic of WT is that it can perform multiresolution analysis of the signals Thus it is useful in detecting the signal which carries instantaneous abnormal components Generally wavelet is a family of functions satisfying the condition expressed as follow 12 x t WTatx tx tdt a a a 1 Where indicates the inner product the asterisk represents the complex conjugate the factor 12 a is used to ensure energy conservation t a denotes the daughter wavelets that are derived from the mother wavelet t by continuously varying both the scale factora and the translation or time shift factor and the mother wavelet t should satisfy the condition shown as follow 0 R t dx 2 WhereR denotes the set of real numbers III SCHEME OF THE ANALYZING SYSTEM A Frame of the system There is a vibration signal analysing and supervising system in low cost which uses the sound card of computer instead of a data acquisition card and analyses signal using Matlab program 2 It uses common personal computer and analysing software which is programmed by themselves It predigests the analysing system in a certain extent For the comprehensive testing takes place in product line the environment should be wicked and the influencing factors are uncertainty On the other hand the analysing system will be embedded into the comprehensive testing system and the effects which come from the other parts of the whole system are inevitable The data acquisition system aforementioned can not solve those problems well Thus an approximate but different system is adopted in this article The vibration signal of the drive shaft shell should be firstly obtained via an accelerometer then the transformed signal should be processed via a signal modulated module at last the inspected signal is inputted to a personal computer via a data acquisition card Fig 2 shows the frame of the system Fig 2 The frame of the analysing system Nowadays the accelerometer of piezoelectric material is commonly used for its small size light weight and favourable sensitiveness The main function of transducer is that changing the physical signal into electric signal It s a sense organ of force When under the effects of stress press and acceleration charges are generated on the surface of the electric medium Thus it tests the acceleration on the vibrating drive shaft shell to get the needed electric signal This output signal is proportion to the acceleration The general range of the vibration signal is from 10 to 1000Hz However an impulse signal may up to 10KHz while the fault occurs This should be taken into consideration as well as the measurement when choosing the accelerometer In this provided system a piezoelectric transducer is adopted As the data acquisition system using in more widely fields the involved type of signal and source becoming more and more and the demanded precision getting higher ordinary acquisition modules are difficult to satisfy those conditions at one time To accommodate the different measuring situations various series of signal modulated module with singularity function have been manufactured which can be assembled neatly and expediently according to the actual instance Thus the appropriative signal modulated modules are adopted in modern data acquisition system The main functions of them are magnifying linearizing or filtering the signals collected by transducer In the provided system it must get through a signal modulated module before processed for the charge signal outputted from the accelerometer is very faint Data acquisition is the most important approach in signal processing In order to conveniently cooperate with the personal computer the adoptive data acquisition card is USB UNIVERSAL SERIER BUS card USB card not only connects the computer and external fixtures simply but also takes us into a bran new PC age Firstly a normal port takes place of all the other different serial ports and parallel ports Secondly it possesses of the function with plug and play Finally the transmission rate of it is up to 100 kHz with 12 bit resolution that it can well achieve high speed data acquisition which the industrial platform needs 783 Authorized licensed use limited to Northeastern University Downloaded on May 27 2009 at 02 45 from IEEE Xplore Restrictions apply This system works at testing situations that to simulate the different conditions which are caused by tuning around of the automobile or the roughness of the road Considering the automobile running as usual turning or braking there are four simulated testing phases in this provided system And the parameters which are concerned in those four phases are listed as in Table I Table I The parameters in 4 phases Testing phase Loading situation Rotating orientation Rotating speed I No load Right 940 r min II Load the right side gear till it stops Right 940 r min III Load the left side gear till it stops Right 940 r min IV Keep load both of the side gears Left 540 r min The vibration signal of the drive shaft housing should be measured in those four phases respectively Then it will be analysed via the arithmetic motioned latter And the cue information should be displayed on the screen of the personal computer according to the analysing results when they are caused by anomalous signals B Select of the wavelet for analysis In a number of publications WT is widely recognized as an effective tool for vibration based machine fault diagnosis for it can detect both stationary and transitory signals In actual application especially in realizing of computer it needs to disperse the continuous wavelets and its transform The discrete wavelet transform DWT is built up mainly based on binary wavelet transform It disperses the scaleaas exponential progression That is to say order scale factora 0 0 a 1 0 a 2 0 a 0 j a j 1 2 N When the scale magnifies 0 j atimes which means the frequency reduce the same times so the sampling interval magnifies 0 j a times accordingly A more natural notion is disperse the time shift as 0 j a times According to Nyquist sampling theorem it won t lose information of the original signal by doing this Dispersing the signal as exponential progression is an effective dispersing method For the exponential indexjvaries in a small degree it will induce the scale varying a lot In this provided system makea 2 which is suitable for analysing and the calculating of the computer For the series of wavelets are derived from mother wavelets and choosing the different wavelet basis would obtain different results the wavelet basis is important for analysing There are several properties for the choosing of a wavelet basis that one could want to be fulfilled 1 orthogonality 2 compact support rational coefficients 4 symmetry 5 smoothness 6 interpolation The problem concerned in the provided system is vibration of the drive shaft shell The configuration of drive shaft housing is complex For there are many vibration excited sources the signal is made up of periodic components which generated by the meshing of the screwy bevel gears and the instantaneous components that generated by the other excited source Considering those factors aforementioned the Daubechies wavelet is chosen in analysing The series of Daubechies wavelets are marked as dbN in MATLAB Where N is the serial number and N 2 3 10 There is no specific expression for it The effective compact support length of the wavelet function t and scale function is 2N 1 and the vanishing length is N C Analysing process with a simulated signal Before practical measurement the adopted analysing system should be tested The frame of the system is testified to be reasonable by many other data processing systems The only different is that this vibration analysis is a part of the comprehensive evaluating for the main retarder The analysing system should be embedded into the whole evaluating system Thus the chosen wavelet analysis should be tested A simulated signal is taken into the provided system as shown in Fig 3 It consists of periodic signal which is used to simulate the signal generated by the meshing of screwy bevel gears random noise signal and impulse signal which are used to simulate the signals generated by the fault of the gears or other interferential complications Fig 3 The simulated original signal A common phenomenon has been observed when decomposing a given signal within a selected time frame if a daughter wavelet which is generated by a particular scale has the largest value of the wavelet coefficient it often implies that the shape of that daughter wavelet can match the shape of the inspected signal better than other daughter wavelets generated by other scales 6 According to the principle mentioned above and the shape of the simulated signal the db10 is chosen for the simulated analysing system The scale function and the wavelet function of db10 are showed as in Fig 4 Fig 4 The scale function and wavelet function of db10 784 Authorized licensed use limited to Northeastern University Downloaded on May 27 2009 at 02 45 from IEEE Xplore Restrictions apply The time frequency characteristics of the chosen wavelet basis db10 are listed as follow the effective compact support length N is 20 the support zone is 0 20 the vanishing moment is 10 At the point of multiresolution DWT is equivalent to a band pass filter and a low pass filter The original signal is decomposed into two sub signals each time and it equivalent to the signals in frequency zone 0 2 j are decomposed into two components that in the frequency zones 0 1 2 j and 1 2 j 2 j which named as approximation and detail signal respectively The decomposed components should be decomposed in frequency zone 0 1 2 j approximately as the previous step does And the Nth level of the wavelet analysing result can be obtained via N time s decomposition therefore the results can match the analysing demands of the system well Fig 5 denotes the tree of the decomposing Fig 5 The wavelet decomposing tree Where S indicates the original signal cA is the wavelet coefficient of the low pass filter and cD is the wavelet coefficient of the band pass filter The simulated signal is decomposed by performing the chosen wavelet basis And the results are shown as in Fig 6 Obviously when the decomposition achieves 5 th level both the approximation and detail component represents the raw simulated signal well Because the range of normal vibration signal is usually smaller than the impulse signal the former is the details compared with the later in the collected signals The approximation component shown as in a contains the anomalous information which is used to simulate the fault situations usually generated in high frequency zones and the detail component shown as in b denotes the periodic information which is used to simulate the meshing of the screwy bevel gears When testing in an actual application it can be performed with a threshold while the wavelet coefficient over a certain value as in Fig 6 a The practical threshold can be obtained from the statistical datum of the approximate coefficients Thus the conclusions can be drawn with the remained signal For example if the fault appears at the driving screwy bevel gear the periodic information would be accord with the rotating information of the driving bevel gear And the same conclusions also can be drawn according to the fault information from driven screwy bevel gear or factors affected by the other parts of the drive shaft a b Fig 6 The decompositions of the simulated signal a The wavelet coefficients of the low pass filter b The wavelet coefficients of the band pass filter IV CONCLUSION The proposed vibration analysing is complementary to the comprehensive evaluating analysis with the main retarder of the automobile drive shaft In old method the operator makes the estimations only according to their experiences Both the efficiency and dependability are low Besides for the environment noise is inevitable in practical the method that analysing the noise pressure of the drive shaft shell directly is also testified to be reasonless The given analysis system uses the vibration analysing with the drive shaft shell instead of measuring the noise signal directly And the theory of WT and the tool of MATLAB are also used in this system A simulated signal is taken into the system According to the results of 5 th decomposition the characteristic information can be abstracted commendably In actual application it can